Lattice site occupation of non-soluble elements implanted in metals

Materials Science Reports 2 (1987) 371-468 North-Holland, Amsterdam

LATTICE SITE OCCUPATION IMPLANTED IN METALS

373

OF NON-SOLUBLE

ELEMENTS

0. MEYER and A. TUROS ’ Insrimt fir Nukleare FesrkBrperphysik, Kernforschungszentrum P. 0. Box 3640, D-7500 Karlsruhe, FRG

Karlsruhe,

Received 27 April 1987; in final form 23 October 1987

A question of fundamental interest in ion implantation metallurgy concerns the lattice site which the implanted ions will occupy at the end of their trajectories. This review describes the results of a systematic study on the basic mechanisms which determine the lattice site occupation of impurities implanted in metals. Current models on the prediction of the substitutionality are reviewed and the mechanisms of impurity-point-defect interactions on the lattice site occupation are outlined. Recent experimental results are reviewed which demonstrate that implanted ions will preferentially occupy substitutional lattice sites within the relaxation phase of the collision cascade. Their displacements from the substitutional sites are due to the interaction with point defects which leads to the formation of defect-impurity complexes. These processes occur during the cooling phase of the cascade and at temperatures at which point defects are mobile. The probability of the complex formation increases as a function of the heat of solution and the size-mismatch energy.

’ Permanent address: Institute for Nuclear Studies, Warsaw, Poland.

0920-2307/87/$34.30 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

374

0. Meyer

and A. Twos

1. Introduction The properties of solids are very often determined by impurity additions. In most cases the property changes depend on whether or not the impurities are located on substitutional lattice sites in a given host. When compared to other doping methods, ion implantation has the unique advantage that it allows almost all elements to be incorporated in the near surface region of materials without any metallurgical constraints. Moreover, the concentration and the depth location of implanted atoms can be easily controlled, the doping can be carried out under extremely clean conditions at practically any target temperature. Due to these capabilities ion implantation is an established technique for the doping of semiconductors and has been expanded rapidly for the improvement of metal surfaces in the last decade. Numerous systematic studies have proven that mechanical, chemical, electrical and optical properties can be optimized for special applications [1,2]. The experimental results on the lattice site occupation of ions implanted into metals mainly at 293 K have been summarized by Poate and Cullis [3]. The general aspects of ion implantation metallurgy have been recently reviewed by Picraux [4]. Ion implantation is a non-equilibrium process leading often to metastable situations [5]. Substitutional as well as interstitial solid solutions of compositions not allowed by equilibrium phase diagrams can be formed. Thus, solubility is not a necessary condition for substitutionality. Many of the implanted species are highly substitutional in a given host although they are immiscible in the melt or exhibit limited solid solubilities. Because of the great variety of basic processes which are involved, the prediction of the lattice positions of implanted atoms is one of the most formidable problems in ion implantation metallurgy. These processes may be of collisional nature, due to cascade effects or may be caused by thermodynamical or mechanical driving forces. There is, however, another factor that should be taken into account. This is the radiation damage which is created by ion implantation itself. Recent research has shown that the knowledge of the production and annealing of defects and their interactions with impurities is of great importance in almost all ion implantation studies [6,7]. It will be demonstrated in this paper that interactions of point defects with impurity atoms play a decisive role with respect to the lattice site occupation of implanted atoms in metals. It seems, therefore, to be expedient to begin with the presentation of experimental techniques which are currently used to study the point-defect behaviour in metals. Table 1 presents a survey of the various methods for studying point defects, their mutual interactions as well as their interactions with impurity atoms. Further details of these techniques can be found in the review papers cited in table 1. In this review we focus on the use of ion channeling. The application of the channeling technique for lattice location studies has a long tradition and is well documented in the literature [22,23]. This technique makes it possible to determine directly the lattice site location of the implanted atoms. It is not restricted to a few radioactive probe elements, as the hyperfine interactions (HFIs) are, but allows one to investigate the behaviour of a large number of atomic species. In addition, the depth distributions of the implants and the defect structures can also be measured. It has been proven that the channeling method is extremely powerful when the experimental set-up is equipped with a cryogenic goniometer and coupled to both a Van de Graaff accelerator and an implanter in such a way that ion implantation and analysis can be performed in situ in the temperature range from 5 to 293 K. Most of the experiments reported in sections 5, 6 and 7 were performed using such a set-up at the Kernforschungszentrum

Lattice

Table 1 Comparison

of methods

for defect

Method

Diffuse

resistivity

X-ray

ion microscopy

Positron troscopy

annihilation

quantity

spec-

elements

implanted

in metals

375

Limitations

Refs.

Cannot distinguish between different types of defects. Absolute concentrations cannot be determined

[8-lo]

Point-defect structures (mainly interstitials)

Requires single crystals. Interpretation of data is model dependent

[ll-141

Single tials

Requires metals with melting temperature

[15-17)

Concentration pairs

scattering

of non-soluble

studies Probed

Electrical

Field

site occupation

vacancy

of

Frenkel

and intersti-

Single vacancy vacancy clusters

and

small

high

Sensitive only to vacancies. Does not yield defect geom-

[l&191

etry Limited to a few radioactive probe atoms. Quantitative interpretation of data is difficult

[20,211

location of impurity and displaced host

Requires Analysis complex

[22-241

clusters

Only defects with sions above 1 nm visualized

Hyperfine interactions (perturbed angular correlations and Miissbauer spectroscopy)

Small defect-impurity plexes

Ion channeling

Lattice atoms atoms Defect

Transmission croscopy

electron

mi-

com-

single crystals. is difficult for structures dimencan be

[25261

Karlsruhe. Aligned and random backscattering spectra of 2 MeV He ions were measured before and after implantation to study the lattice disorder as well as the substitutionality of the implanted impurities. Fig. 1 shows as an example typical energy spectra of an Al single crystal before and after implantation with Pb ions. The peak concentration of the implanted impurity atoms in the host was determined from the relative height of the impurity yield to that of the host yield, taking into account the backscattering cross-section ratio [27]. The minimum yield of the impurity (xi&) is defined as the ratio of the impurity peak area in the aligned to that in the random spectrum. The minimum yield of the host lattice atoms (xh,i,) was determined from the ratio of the number of counts in an energy window corresponding in depth to the range of the implanted species in the aligned spectrum to that in the random one. The substitutional fraction (f,) is defined as

f, = (1- xiLn)/(l - Xh,in).

0.1)

As discussed in ref. [22], this formula is only a first-order estimate of the substitutional component and is rigorously valid only if the non-substitutional atoms occupy random lattice sites. In order to determine if a fraction of the implanted ions occupied perfect substitutional lattice sites, angular-dependent yield curves were taken. The angular yield curves are characterized by the minimum yield value (xtii,) as defined above and the critical angle ($,,z) which is half the angle at half height between the normalized minimum and random yield. Comparison between the angular yield curves for the impurities and the host atoms provides

0. Meyer

376

and A. Twos Channel

4uuu -

a, E &y

1

400 200 Oepthin ml Al-Energy Window

3000

Number 400

300

200

100

6

500

400 Oepth

200 (nm)

b

- A,

-. Pb

f.ii a ;

2000

Pb-Energy Window -

.-IF = 2

-

1000

200

400

600

800 Energy

of

1000 Backscattered

1200

1400 Particles

Fig. 1. Backscattering energy spectra of 2 MeV 4He ions incident in random crystal implanted with Pb ions (b). Also shown is a (110) aligned energy crystal (c).

1600

1800

2000

IkeV)

(a) and (110) directions of an Al single spectrum for an unimplanted Al single

information about the exact position of the implanted impurity. Examples of different angular yield curves are given in fig. 2. The impurity scattering yield is proportional to the He-ion flux at the lattice position where the impurity is located. The He-ion flux within a channel which is bordered by the atomic rows depends on the position within the channel as well as on the angle of incidence. For incidence parallel to the atomic rows, the flux distribution shows a maximum in the middle of the channel and, therefore, a maximum in the impurity scattering yield is obtained if the impurity is located in the centre of the channel (fig. 2d). With increasing angular incidence the flux distribution is smeared and the scattering yield decreases. Close to the surface up to a depth of about 200 nm the flux distribution exhibits depth oscillations [22,23]. Angular yield curves for impurities at various lattice locations within the channel can be evaluated using analytical calculations based on the continuum model [28,29] and Monte Carlo calculations based on the binary-collision model [30]. For the analyses of the angular yield curves of ions implanted into the near surface region (< 100 run), the Monte Carlo calculations seem to be more appropriate as they take the flux oscillations into account. It has been shown that the “substitutional fraction” as determined by applying eq. (1.1) does not deviate by more than 20% from the real f, values when f, is about 0.5 [31]. This paper is organized as follows: in section 2 we discuss the different semi-empirical and theoretical approaches to the solid solubility problem,) section 3 describes the basic processes occurring during ion bombardment and section 4 reviews the current understanding of defect-impurity interactions. A survey of experimental results is given in the next sections. The influence of the implantation and annealing temperature on the substitutionality of the non-soluble implanted

Lattice

site occupation

of non-soluble

elemenrs

implanted

in merats

377

X

b

0‘k!!l

0 a. SUBSTITUTIONAL

JI CHANNEL

CROSS SECTION

0 h SMALL

DISRACEYENT

c IARGE

DISPLACXMENT

a

JI

d CENTER OF CHANNEL I INTERSTITIAL 1

Fig. 2. Typical

angular

dependence

Q

e RANUOM

I SU~STITLITIC$AL INTERSTITIAL

PLUS

9 SUBSTITUTIONAL PLUS SMALL DISPLACEMENT

of the yield of 2 MeV He ions backscattered from the positions a, b, c and d in an axial channel.

impurities

which

are located

at

atoms is discussed in section 5, in section 6 the role of post-bombardment on the substitutional fraction is elucidated whereas section 7 describes the lattice occupation by elements which are known to form inter-metallic phases and to have a rather low solid solubility.

2. Solid solubility

in equilibrium

2.1. Phenomenological

and ion implanted

alloys

models

The prediction of the solid solubility in alloys is one of the most important and not yet solved problems in metallurgy and solid state physics. No element can be prepared in the state of total purity. Very often its properties depend strongly not only on the amount of the impurity but also on whether it is soluble or not in the host matrix.

0. Meyer

378

and A. Twos

Generally, the equilibrium phases are formed at compositions where the Gibbs free energy = H - TS + PV has a minimum. For solid intermetallic solutions ideal mixing without any change in enthalpy and with a maximum increase of entropy never occurs. The enthalpy change (AH) due to immersing a solute atom in the host matrix is non-zero because of lattice strains induced by the atomic size mismatch and the valence difference. On the other hand, the entropy change is smaller than that of ideal solutions due to short-range ordering and clustering effects. However, if AH is not too large and positive the entropy term prevails and the reduction of the free energy will promote the formation of a solid solution. If the change in enthalpy is large and negative an ordered phase will be formed instead of a solid solution. The requirement of a small enthalpy change implies small differences in the sizes of solute and solvent atoms in order to minimize the elastic strain energy. Also the electrochemical nature of the atoms should not be very different; otherwise the charge-transfer processes cause large and negative enthalpy changes. Based on these thermodynamical considerations Hume-Rothery et al. [32] proposed three rules to be obeyed if the equilibrium solid solutions are expected to be formed: (i) the atomic sizes of the solvent and the solute should not differ by more than 15%, (ii) the electrochemical nature of the solvent and the solute should be similar, (iii) the crystal structure of the two elements should be the same. One notes that only the first constraint is a quantitative one which makes the application of the Hume-Rothery rules rather difficult. In fact, the Hume-Rothery rules are usually reduced to the simple size criterion. They provide a necessary but not a sufficient condition for extensive solid solubility, i.e. in excess of 5 at%. Detailed analysis performed by Waber et al. [33] showed that if the atomic sizes of two elements differ by more than 15% extensive solid solution will not be formed with a probability of 95%. On the other hand, among elements of nearly equal size only about 50% of binary systems exhibit high mutual solubility. The Hume-Rothery rules are in such a case of little use. A more successful attempt was made by Darken and Gurry [34] who were able to quantify the second of the Hume-Rothery rules by introducing the concept of electronegativity [35]. The graphical scheme of Darken and Gurry consists of a two-dimensional plot where the two coordinates are electronegativity and atomic size. Each element is represented by a point on this map. The soluble elements are expected to lie within an elliptical region which is centred at the coordinates of the solvent atom and the axes of which have a length of 30% of the solvent’s atomic radius and a length of 0.8 on the electronegativity scale. According to Waber et al. [33] the Darken-Gurry scheme has an overall predictive value of about 80%. In this context the search for more precise coordinates, closely related to the thermodynamical properties of alloys, has been undertaken in the last decade. More successful are the schemes based on the semi-empirical theory of heats of alloy formation developed by Miedema and co-workers [36,37]. Miedema et al. introduced two fundamental parameters: the electron density at the boundary of the Wigner-Seitz cell (nws) and the electronic work functions ($I*) of the binary alloy. A difference in electron density between the solute and the solvent (An ws) implies the need to provide an energy to smooth the discontinuity in electron density at the boundary of the Wigner-Seitz cell. This gives rise to a positive contribution to the heat of formation. On the other hand, adifference in work function (A+* ) results in a charge transfer across the boundary between dissimilar cells thus providing a negative contribution to the heat of formation. Accordingly the heat of formation (AH,,,) of a fictitious 50-508 intermetallic alloy formed by the two partners is given by G

AH,,, = -P(Ac#a*)2

+ Q(Anl,/;)‘-

R,

(2.1)

Lotrice

sire occupation

of non-soluble

elemenrs

implanted

in metals

379

where P and Q are universal constants. The third constant R is different from zero only if one of the components is a polyvalent metal with p electrons. Miedema analyzed over 500 intermetallic alloy systems. He was able to determine the parameters $* and n,s for more than 50 metallic elements by examining the signs of AH,,, according to the following rule: if ordered phases exist at low temperature then AH, is negative, if no ordered phases exist and the solubility is not extensive then AH, is assumed to have a positive sign. To study the solid solubilities Chelikowsky [38] used the Miedema parameters +* and n’w/i as coordinates. Fig. 3 shows the Chelikowsky plot for solubilities in three different hosts: Hg, Cd, and Zn. One notes that most soluble impurities tend to cluster in elliptical domains. The main uncertainty of the method is due to the fact that there is no prescription how to draw such ellipses. Actually they are drawn to include in them as many soluble elements as possible. Nevertheless, this diagramatic procedure provides a separation of soluble from insoluble elements with a considerably higher confidence level than the Darken-Gurry scheme. Despite of the success of the two-parameter schemes, it has been pointed out [38,40] that two parameters are insufficient, in general, to explain solid solubility in alloys. Alonso and Simozar [40] have proposed an empirical method based on three parameters: nws, cp and the atomic Wigner-Seitz radius R,. In order to conserve the pictorial simplicity of the two-parameter schemes, An ws and A$J are combined into a new parameter AH,,,, as given by the semi-empirical theory of Miedema and de Chstel [37]. Using then AH,,, and AR, as final parameters, the authors [40] made two-dimensional plots for the case of transition metal hosts and they found that the separation between soluble and insoluble elements in a given host is more successful than in the case of the two-parameter schemesmentioned above.

Pd

1.5

1.0 Electron

Density

2.0

n!,$ (ad

Fig. 3. Chelikowsky solubility maps for alloys of Hg, Cd and Zn. The three ellipses enclose the regions of elements which are soluble in Hg(l), Cd(2) and Zn(3) [39].

0. Meyer

380

2.2. Quantum-mechanical

and A. Twos

approach

The study of the solubility trends in solids using parameters derived from first-principles quantum-mechanical calculations is a formidable problem because of the very small energy differences involved: the structure-determining energy of most ordered solids is lo3 to lo4 times smaller compared to the total cohesive energy. One is then faced with the situation that the complex weak interactions which stabilize the crystal structure are masked by uncertainties in the calculation of the strong interactions due to the total interaction potential. Only recently has a pseudopotential orbital-radii approach by Zunger [41] and Singh and Zunger [39] been successfully applied for systematizing the trends in solid solubilities in divalent solvents and elemental semiconductors. The derivation of the first-principles, i.e. entirely non-empirical, pseudopotential is described in detail elsewhere [42,43]. Inherent in constructing such pseudopotentials are the requirements that they, when used in calculations, accurately reproduce the atomic valence orbital energies and the valence wavefunctions. The orbital radii {r,, r,,, rd} represent the effective core size of an atom as sampled by valence electrons of angular momentum s, p, and d, respectively, and are determined as the crossing points of d-dependent screened atomic pseudopotentials. In order to use the two-dimensional diagramatic representation, the orbital radii coordinates R, and R, were introduced. They are related to the orbital radii by [41]

(2.2) and RO=I(r;+r;)

- (r,“+r;)l,

(2.3)

where superscripts A and B denote the different atoms of an AB binary alloy. Fig. 4 shows the solubility maps for the Mg host using orbital radii, Miedema and Darken-Gurry coordinates. The degree of success of the orbital radii method is about the same as when using the Miedema scheme. Considering the fact that its parameters are calculated exclusively from the free-atom properties, the agreement is remarkably good. 2.3. Solid solubility

in ion implanted systems

Ion implantation is a non-equilibrium process which leads to the formation of alloys of unique metallurgical properties. The experiments on ion implantation in metals [44-461 showed that surface alloys can be formed which were far outside the limits given by the equilibrium phase diagrams or predicted by solubility rules discussed in the previous section. These alloys are metastable, i.e. they relax back to their equilibrium configuration upon annealing. Any comprehensive theory of alloying must be able to explain the behaviour of these alloys. Early attempts to systematize the ion implantation data were based on equilibrium schemes. Sood [47] noticed that for many metal hosts most of the dilute metastable alloys lie well outside the Hume-Rothery limits. He has formulated an empirical criterion to obtain a separation between substitutional and non-substitutional implanted impurities. These rules state that a metastable substitutional solution will be formed if the implanted species have [47]: (i) atomic radius which is at most 15% smaller or 40% larger, and (ii) electronegativity which is 0.7 smaller or 0.7 larger than that of the host atom.

Lattice

site occupation

ojnon-soluble

SOLUEILITY

l

elements

implanted

in merals

381

IN My

Solubility?O.Ol%

2.0

0.0 0.25 6 l

L

0.5 0.75 RJa.b.1

Miedema Coordinates Solubility?O.Ol%

”

1.0 I Yd

Au

’

Co

0.6 1.0 1.4 1.8 2.2 2.6 3.0 Goldschmidt Radius !A) Fig.

4. Solubility

maps

for

alloys

of

Mg

using

coordinates Darken-Gurry

of Zunger [34].

[41],

Miedema

and

de Chltel

[37]

and

0. Meyer

382

A. Turos

and

.

T-300K

SUBST.

o NON - SUBST.

3 Se

f, so5 fs < 0.5

I .

.

B,”

I

0.5 Fig. 5. Darken-Gurry

map for implanted

I

Kr

2.0 1.0 1.5 ATOMIC RADIUS ( A,

vanadium-based performed

diluted alloys. at 300 K.

cso

“,”

I

2.5

The implantations

and measurements

were

Fig. 5 presents a Darken-Gurry plot for different species implanted in V. It may be noted that most of the substitutional alloys lie outside the Hume-Rothery zone (full line circle) of solubility. Such a strong violation of the equilibrium solubility criteria is expected for metastable system. On the other hand, the agreement with the prediction of the extended solubility boundaries (dashed line rectangle) is in general good. Unfortunately, there are other metallic systems which do not obey so nicely the extended solubility rules. Fig. 6 shows a Darken-Gurry plot for the Al host. It is remarkable that after RT implantation only a few implants are substitutional, the majority of them is occupying irregular lattice positions. Note the case of Cd: although its electronegativity and atomic radius are very close to those of Al, it is completely non-substitutional in that matrix (f, = 0.0). The usefulness of Darken-Gurry plots for ion implanted systems is limited. Not only because a number of exceptions are found but also because this method cannot predict or explain the appearance of the near substitutional component of the implants. One of the best studied ion implanted metallic hosts is that of Be. Kaufmann et al. [48,49] have implanted 25 metallic elements into Be at concentrations of about 0.1 at% and produced a wide range of new and unique metastable alloy systems. The impurity atoms were found to occupy the substitutional sites or one of the regular octahedral or tetrahedral interstitial sites. The results were analyzed using Miedema’s set of coordinates as shown in fig. 7. To facilitate a more quantitative discussion of the results, the site energies on Miedema coordinates were expanded using a Landau-Ginzburg expansion. This altered coordinates made it possible to construct three domains: an ellipse which sets a boundary for the substitutional region and a hyperbolic contour which separates the octahedral and tetrahedral regions. The attempts of predicting the shape of the domains starting from more basic physical laws failed [38]. Nevertheless, it is remarkable how the Miedema model developed for equilibrium alloys can be used to describe the implantation data. Alonso and Lopez [50] have analyzed several ion implanted systems using, in addition to the Miedema parameter AHf, the atomic radius as an independent parameter. Their method provides slightly better separation between substitutional and non-substitutional elements than the Chelikowsky method.

Lattice

sire occupation

of non-soluble

elements

implanted

in metals

383

7

Q’

Kr 0

3.CI-

r----------

2.t )x c > c % : z +” w z 1.0 L---------

0.c I--

it

I

0.1 Fig. 6. Darken-Gurry

map for implanted performed

0.2 Atomic Radius (nml aluminium-based diluted alloys. at 300 K (0: non-substitutional

r

The implantations elements).

(

and measurements

were

Singh and Zunger [39] have also analyzed the data of Kaufmann et al. using orbital radii coordinates. The success rate of this method is similar to that based on the Miedema theory. Although all these methods are relatively successful in predicting solid solubilities in ion implanted systems there are persisting doubts whether they are applicable at all for systems produced by ion implantation. Since the limits of the solubility domains are set purely empirically by the methods discussed above the question arises if the agreement with experimental data has a fundamental meaning. Certainly, the separation between substitutional, tetrahedral and octahedral sites as given by the Chelikowsky scheme or by the orbital radii variables provide useful guidelines. However, they do not answer the very important question why a given kind of atoms occupies a particular interstitial site. Moreover, it has been found that in agreement with these schemes some large atoms implanted in Be like Cs, Ge, I or Xe reside at the very small octahedral hole sites [48]. This is a very surprising result because if the touching spheres model were valid this interstitial site would not be occupied at all. The success rate of the discussed method ranges from 70% to 85%. There is little or no overlap between prediction errors made for a given host by different schemes. This suggests that exceptions are more artefacts than that they are due to some yet unknown physical

0. Meyer

384

. SUBSTITUTIONAL A TETRAHEDRAL n OCTAHEDRAL

7.0I-

and A. Twos

AND/OR

SOLUBLE ON /

OPEN SYMBOLS SOLID SYMBOLS

PREDICTED OBSERVED

6.0 OCTAHEORAL

I-

I-

TETRAHEORAL

Na

I

1

/ I

0.5 map for elements

‘SUBSTITUTIONAL

Ba

.Cs

Fig. 7. Chelikowsky

““LS;”

I

I

1.0 1.5 2.0 ELECTRON DENSITY n:/: (a.u.)

implanted

in Be (solid symbols). Open some other elements [38].

symbols

15 show the predicted

positions

of

phenomena. Finally, none of the schemes can distinguish between regular and near substitutional lattice locations which often occur in ion implanted alloys. The further study should go, therefore, in the other direction: instead of trying to adapt the methods developed for equilibrium systems one has to elucidate the fundamental processes of ion implantation and their influence on the lattice site occupation of implanted atoms.

3. Basic processes during ion bombardment

3. I. Energy-loss processes An energetic ion penetrating a solid looses its energy in a series of collisions with the target atoms. The foundation to the understanding of these problems has been laid by Lindhard and co-workers. In the well known “Notes on Atomic Collisions” [51]. they described the slowing down of the incident ions in terms of two uncorrelated processes: - interaction with atomic electrons which is inelastic in nature and leads to excitation and/or ionization of the electronic system, and - elastic collisions between the impinging ion and target nuclei. Although both kinds of interaction are in principle interrelated, it turned out that the

Lattice

sire occupation

of non-soluble

elemems

E

implanted

in metals

385

4/Z

Fig. 8. Nuclear (S,) and electronic (S,) stopping power as a function of energy.

assumption that they are uncorrelated is valid to a very good approximation. stopping power, S, i.e. the energy loss per unit path length is given by s=s,+s,,

Thus, the total

(3.1)

where S, and S, are the nuclear and electronic stopping power, respectively. The energy dependences of S, and S, are plotted in fig. 8. The coordinates are scaled in units of reduced energy (E) and range (p) derived by Lindhard et al. [51] from the Thomas-Fermi interaction potential. They represent the dimensionless energy e=E

aM2 Z,Z2e2( Ml + M,) ’

(3.2)

and range 4aa 2A4, p = RNA4,

(3.3) wl+M,)2’

where M, and M, are the masses of the projectile and the target atom, Z, and Z, are the corresponding atomic numbers, E is the energy of the projectile, R is the range of the projectile, a is the Thomas-Fermi radius, and N is the atomic density of the target. The advantage of such an energy scaling is that it allows one to express S, in terms of a semi-universal curve for all combinations of Z, and Z,. Moreover, it permits the separation of ion bombardment studies into two different regimes: ion implantation and nuclear microanalysis. As can be seen in fig. 8, S,, exhibits a maximum at about ~‘1~ = 0.6. The ion implantation regime extends up to e1’2 G 4. This consists of relatively slowly moving heavy ions (Z, > 4). Unlike S, the electronic stopping S, does not exhibit the property of a Thomas-Fermi scaling

0. Meyer

386

and A. Twos

and cannot be represented by a single universal curve. However, in the energy range corresponding to the ion implantation regime, S, varies linearly with the velocity of the projectile, thus giving a straight line in fig. 8. The slope k is a slowly varying function of M,, M, and Z,, Z,. As long as Z, < Z,, the k-value falls within the narrow interval 0.14 f 0.03. For Z, > Z, the typical k-values are ranging from 0.1 to 0.3. Thus, both S, and S, contribute significantly to the slowing down. Electronic stopping never becomes negligible compared to S,, not even at extremely low values of z. As a consequence the theoretical treatment is rather complex and the choice of the interaction potential becomes crucial [52,53]. The nuclear microanalysis regime covers the high-energy region e’12 > 4, where electronic stopping dominates and S,, has decreased to a very small fraction of S, (SJS, = 10e3). This region is widely used for nuclear analysis methods like Rutherford backscattering and nuclear reaction analysis and is beyond the scope of the present review. Once the stopping power is known the total path length can be evaluated. It is composed of many small increments in different directions caused by large angle deflections at depths where nuclear scattering occurred. The total average path length projected on the original direction of the incident ion is defined as the projected range R,. The sequence of nuclear collisions is a stochastic process: the energy loss and thus the path length of individual projectiles varies and their distribution is usually described by a Gaussian. Thus the concentration distribution of implanted ions is given by

N(x) =NP exp[ -0.5(x

- R,)‘/ARi],

(3.4)

where NP = NJ(2n) ‘I2 AR is the peak concentration, N, is the number of implanted ions per m2, R, and AR, are the aterage projected range and the standard deviation of the projected range, respectively. Values of the projected ranges and their standard deviations are tabulated in refs. [54,55].

3.2. Atomic displacements in the binaty-collision

approximation

The stopping power (energy loss) concept provides a convenient parameterization of the fate of an average incident particle. However, it contains no information about the transformations in the medium being traversed by the particle. In this respect the effects of particle-target atom interactions are twofold: the electronic system of the target atom can be excited or ionized and a sudden transfer of kinetic energy can occur due to elastic scattering. In the case of metals the first process has no influence on the stopping medium. Any electronic excitation in metals will be dissipated among the conduction electrons in a time on the order of lo-l5 s. This time is much shorter than the mininum lifetime of any electronic excited state (about lo-l2 s) that is energetic enough to produce an atomic displacement by direct energy transfer. The second process is of great importance: an energetic particle can transmit a large amount of its kinetic energy to a lattice atom. The transferred energy, T, reaches its maximum for head-on collisions which is given by 4WM2 T max= (Ml+M2)2Ey

where Mr and Mz are the masses of the incident kinetic energy of the impinging particle.

(3.5) and target atoms, respectively,

and E is the

Luttice

site occupation

of non-soluble

elements

implanted

in metals

387

The transferred energy decreaseswith decreasing scattering angle (glancing collisions) and becomes more efficient if M, approaches M2. A lattice atom can be displaced from its position if it receives a certain minimum amount of energy which is called the threshold displacement energy Ed which depends on the metal or alloy, the crystal structure and the direction of displacement [56]. A value of 25 eV is generally accepted as a good estimate of Ed, independent of the material and the displacement mechanisms. The typical energies for the thermal formation of a vacancy (1 eV) and a self-interstitial atom (SIA) (5 eV) are significantly smaller than Ed. The collisional formation of Frenkel pairs requires more energy than the thermal formation of vacancies and interstitials due to the highly irreversible nature of the collisional processes. The reason for this is closely related to the stability of the Frenkel pairs in a bulk lattice. Vacancies and SIAs are attracted due to an elastic interaction which is effective within a few lattice spacings. Computer simulations by Gibson et al. [57] have shown that a surprisingly large separation of the pair is needed to produce a stable configuration, particularly in a close-packed direction. An interstitial atom which comes to rest inside the instability region of approximately 100 atomic volumes around the vacancy recombines athermally with the vacancy. This process is called spontaneous recombination. For low-energy events the transport of a SIA at distances exceeding more than a few lattice spacings occurs by focused collision sequences. The focusing of isolated, uniformly spaced straight line of hard spheres has been predicted by Silsbee [58] and confirmed by computer simulations [57-601. It should be pointed out that such chains focus at kinetic energies below approximately 40 eV and defocus at higher energies. The focused collision sequence can propagate only along closely packed rows of the lattice producing replacements of subsequent atoms in the row until finally a SIA is produced. Consequently, lessenergy is needed to provide large separations between vacancies and SIAs, i.e. stable Frenkel pairs if the recoiled atom can initiate a seriesof replacement collisions along one of the main crystallographic directions. Fig. 9 shows the trajectories calculated by Gibson et al. [57] for a Cu single crystal when one of the lattice atoms is set in motion with 40 eV kinetic energy. Its initial velocity lies in a (100) plane. Large open circles show the initial positions of the atoms in the (100) plane, small dots are initial positions of atoms in the planes immediately above and below. Atoms for which no

Fig. 9. Atomic trajectories produced by a 40 eV scattering event in Cu. The PKA (A) is directed 22.5” above the y axis, a vacancy is left at A, an interstitial is formed at C. The AB sequence does not lead to a stable defect production [57]. The dotted line indicates the instability zone: inside this volume a Frenkel pair is unstable.

0. Meyer

388

and A. Twos

trajectory is shown suffered negligible displacements, the others relax back to their initial positions after dissipation of their kinetic energy. Two focusing chains AB and AC are seen. The atoms in the AB chain return to their original sites. A chain of replacements also occurs in the AC direction. An interstitial is formed at the site C and a vacancy is left at the site A. The dotted line separates the stable from unstable sites around the vacancy A. Since the site C lies outside of the instability region a stable Frenkel pair is created as a result of four replacements. As mentioned above, collision chains propagating with very low energy loss along a regular arrangement of lattice atoms have an important influence on the disorder production. In effect they produce many more replacements than displacements. An atom which has been displaced by the incident ion or “primary knock-on atom” (PKA) may have an energy ranging from eV to keV. PKAs with energies below E,, cannot displace further atoms and will loose their energy in various inelastic interactions which produce localized heating of the lattice. More energetic PIUs penetrate through the lattice knocking other atoms from their sites and leaving a damaged region behind. Each of the secondary knock-on atoms may in turn displace further atoms. From the theoretical point of view this is a complex many-body problem which is very difficult to solve without making drastic approximations. One of the most frequently used models is the linear cascade model. The model neglects the interaction between recoil atoms and collective excitations. The cascade development is considered as a chain of independent two-body collisions between knock-on atoms and stationary atoms. The knock-ons have been assumed to move freely between collisions. Kinchin and Pease [61], in their simplest version of a linear cascade, assumed that atoms behave as hard spheres of the same masses. The energy of the incident particles is transferred to PIUS which in turn share it in equal portions between the subsequent collision partners. Thus, the collision cascade consists of a chain of scattering events in which the number of displaced atoms is doubled in each step while the kinetic energy of a displaced atom is reduced to half of that of the knock-on atom of the previous generation. The sequence of collisions is interrupted after n steps when the energy E/n becomes smaller than 2E,. According to Kinchin and Pease there are four distinct regions depending on the energy of a PKA. The number of displaced atoms Nd amounts to: (i) Nd = 0 for E < Ed, the transferred energy is below the displacement threshold. (ii) Nd = 1 for Ed Q E < 2E,, an atom receiving an energy greater than Ed will be displaced while the impinging atom with an energy less than Ed will fall into the vacancy just created. In fact only one lattice atom is displaced. (iii) Nd = E/2E, for 2E, < E < E,, the displacement cascade propagates until the energy of the subsequent generation of knock-on atoms falls into the region (ii). (iv) Nd = E,/E for E > E,, at energies above E, the recoils loose their energy only by electronic excitation which gives no atomic displacements. A rough estimate for E, is E, = M, keV. The Kin&in--Pease model is highly simplified. In particular, the sharp limits at Ed, 2 Ed and E, do not exist. Moreover, the atomic collisions are not hard-sphere collisions and the electronic energy losses are not negligible, even at low energies. The number of Frenkel pairs generated in a cascade is given accurately by the modified Kin&in-Pease formula [62] N,, =

K( E

-

Q)/2E,

(3.6)

for E - Q > 2E,, where Q is the total energy lost in the cascade by electron excitation, and the displacement efficiency. Robinson and Torrens [63] have found that K = 0.8, independent energy and target.

K

is of

L.urrice

Fig. 10. Computer

simulation

sire occuparion

o/non-soluble

elements

200

40 I1 )

of collision

cascades produced

0

600

100

implanted

in metals

389

600

by 100 keV Ar ions incident -I

on a Cu target

[65].

200 (A)

Fig. 11. Computer

simulation

of collision

cascades

produced

by 100 keV Au ions incident

on an Au target

[65].

0. Meyer

390

and A. Twos

In order to study in detail the spatial distributions of displacement cascades computer simulation codes are necessary. There exist several codes based on the binary-collision approximation which are well documented elsewhere [63,64]. The results of such a calculation for 100 keV Ar ions impinging on Cu targets are shown in fig. 10 [65]. A displacement cascade has a root-like structure due to atomic displacements produced not only by PKAs but also by higher-order knock-ons. For projectiles with high velocity the mean free path between successive collisions is large, so the distance between the primary recoils is also large. Each PKA can be considered to initiate an independent subcascade. Since the probability of interaction increases as the recoils slow down the displaced atoms become more closely spaced at the end of the subcascade. With increasing recoil energy the number of subcascades increases while each subcascade contains approximately the same defect density. A different type of cascade develops in the case of low-velocity, heavy ions for which the mean free path is rather small. Fig. 11 shows the structure of a cascade produced by bombardment of a Au target with 100 keV Au ions. Because of the high density of scattering events the subcascades overlap and are hardly distinguishable. The collision cascade consists of a region with a large density of displaced atoms. 3.3. Dense collision

cascade effects

A question that frequently arises in connection with computer simulation studies is to what ,extent the linear cascade approximation is realistic. Sigmund [66] defined the linear and non-linear collisions cascade in terms of the spatial density of atoms displaced by the projectile. For a non-linear cascade the spatial density is large enough so that nuclear collisions between recoil atoms cannot be neglected. One notes that such collisions do not occur in a linear cascade regime. A typical illustration of a non-linear cascade is shown in fig. 11 for the case of low-velocity, heavy ions incident on a heavy target. It has been verified [67] that during the initial development of a high-energy cascade the scattering events can be considered as a sequenceof two-body collisions. When in the course of the time development of a cascade the recoil energies fall below a few hundred eV, the approximation of binary collisions begins to break down, as many-body collisions become important. Thus every cascade becomes finally a non-linear one, the only exception possibly being those initiated by very light ions. After the displacement cascade has terminated, many of the atoms are occupying unstable configurations while the entire cascade region contains substantial kinetic energy. The following relaxation process is very complex: recombination of Frenkel pairs, interactions between very close defects leading to their clustering and defect diffusion due to the residual lattice agitation are taking place. Clearly all these effects cannot be studied in the frame of the binary-collision model. A microscopic understanding of many-body scattering effects and the development of the relaxation phase has been obtained from molecular-dynamic computer simulation which follows the entire evolution of a cascade. This method was pioneered by Vineyard and co-workers [57] and has been rapidly expanded in the last decade. The procedure is to consider a crystallite containing a large number of atoms (up to 60000) which interact with realistic forces. The simulation event starts with one atom given an arbitrary kinetic energy and direction of motion and all other atoms at their lattice sites at rest. The classical equation of motion for the set of atoms was integrated while following the transfer of energy to neighbouring atoms, the dissipation of the kinetic energy and the relaxation of the atoms of the crystallite to a new, damaged configuration. Practical limitations of this method have been imposed by

Lattice

site occupation

of non-soluble

elements

implanted

in metals

391

the computational speed and the very large computer memory required. Up to now only low-energy events (PKA energy below 10 keV) have been simulated. Fig. 12 shows the time development of an energetic cascade initiated by a 2.5 keV PKA in W simulated by Guinan and Kinney using molecular dynamics [67]. Three phases can be delineated in fig. 12: (I) Displacement phase, lasting approximately lo-l3 s. During this phase the number of displaced atoms increases rapidly as the PKA energy is distributed successively among new generations of recoil atoms until their energy falls below a few eV so that atoms can no longer leave their lattice sites. (II) Relaxation phase, lasting about 5 X lo-l3 s. After termination of phase I the cascade region is highly excited and the lattice greatly disordered due to large concentrations of defects. The spontaneous recombination of close pairs becomes important while the surviving defects begin to reach their equilibrium configurations and to develop strain fields. It should be pointed out that the recombination of a close pair can occur as soon as a SIA has stopped, thus phase II starts before phase I ends. (III) Cooling phase, lasting (l-10) X lo-l2 s. This is the final relaxation phase of the cascade induced by the large strain fields and residual agitation of the lattice. The number of displaced atoms decreases further as a result of additional recombination promoted by their diffusive motion. This phase of the cascade is often referred to as a thermal spike. At the end of this phase the cascade region reaches thermal equilibrium with its surroundings. The displacement phase of the cascade is reasonably well approximated by the binary-collision model. Sigmund [68] has shown that the energy distribution of secondary recoils falls off approximately as l/E2 and, thus, phase I is characterized by a small number of high-energy recoils and many of low energy. When the energies have dropped below a few hundred eV the molecular dynamics must be employed. Molecular dynamics calculations indicate that most of the displacements occur via replacement collisions at low recoil energies, leaving the vacancy at the beginning of the chain and transporting the excess atom to the end of the chain. These are so-called open chains. The fact that the interstitials are transported over a finite distance before coming to rest results, at the end of phase I, in a different spatial distribution for interstitials and vacancies. A pronounced depleted zone is observed at the centre of the cascade, surrounded by a halo of interstitials. The displacement phase is terminated when the instantaneous number of Frenkel pairs reaches a maximum and then begins to decrease as a result of a thermal recombination of defects. At the end of phase II the number of Frenkel pairs agrees well with the prediction of the Kin&in-Pease model. Note that the directionally averaged threshold energy used to evaluate the data shown in fig. 12 is a factor of 2.5 larger than the minimum threshold energy of 65 eV in W. A large fraction of the defects remaining at the end of the relaxation phase recombines due to a substantial defect migration which occurs during the cooling phase. The reduction factor can be as large as three. One of the most important findings of molecular dynamics simulations in the existence of the closed replacement chains [69]. These chains consist of several straight segments along different close-packed atom rows, connected end to end. They form a closed replacement loop in which case no vacancy-interstitial pair is left behind. Closed chains are remnants of transient Frenkel pairs that recombined during the cooling phase of the cascade. As a consequence many more atoms change their lattice sites at the end of the event than at the end of the collisional phase. This result points out the crucial role of the cooling phase of the cascade in determining the final arrangement of defects. Moreover, since no closed chains exist at the end of the collisional phase, their formation is obviously due to many-body interactions. The importance of the cooling phase of the cascade has been appreciated long before the molecular dynamics simulation. Already in 1956 Seitz and Koehler [70] suggested that colli-

392

28

0. Meyer

and A. Turos

I

I

~14

+-II

OO

--I

-111

--

L--------------I I 0.5 1.0 Time ( plcoseconds

Fig. 12. Time development

of two collision

I

cascades

produced

I 1.5 1

by PKAs

with energies

of 0.6 keV and 2.5 keV.

sional cascades can be considered as local “hot spots” in the lattice. An important contribution to the development of the thermal-spike theory has been made by Sigmund [66]. He defined a spike as a limited volume, in which the majority of atoms is temporarily in motion. Under the assumption of local equilibrium he was able to estimate analytically the “temperature” and lifetime of a spike. Although this theory deals with order-of-magnitude estimates only, it was possible to predict the dependences on ion and target masses and energy. If the deposited energy per atom is greater than the cohesive energy, i.e. about 1 eV/atom, the spike region can be considered to be a portion of molten or superheated material embedded in a matrix of a given temperature. The cooling down of a spike due to heat transport to the lattice is equivalent to rapid quenching. The calculated quench times are of the order of 10-i’ s which agrees well with the duration of the cascade cooling phase as estimated by the molecular dynamics calculation. 3.4. Defect structures produced by collision cascades

At the end of the relaxation phase the dynamic segregation of defects within the cascade results in the formation of a vacancy-rich centre surrounded by a shell enriched in interstitials. Field ion microscope studies by Pramanik and Seidman [71] have shown that the core of the cascade contains a large number of vacancies, many of which at nearest-neighbour sites. Fig. 13 shows a typical observation of the depleted zone in W after 20 keV self-ion irradiation at 30 K. The number of vacancies produced by each ion is about 200 and the vacancy concentration amounts to about 20%. This is an extremely large value which provides an ample driving force for the rearrangement of vacancies into lower-energy configurations. It is apparent that during the cooling phase of the cascade vacancy clusters can nucleate and grow. The precise morphology of these clusters, i.e. whether they form three-dimensional voids, dislocation loops or stacking fault tetrahedra, was extensively studied using transmission electron microscopy [72,73]. It has been found that in many cases the vacancy-rich centres of

Lntrice

Fig. 13. Structure

of vacancy

sire occupalion

clusters

of non-soluble

in W produced

elemenls

by different

implanted

in metals

ions as observed

by field

393

ion microscopy

[71].

the cascades collapse to form planar vacancy defects, usually faulted dislocation loops. A striking feature of this process is the effect of ion mass on the cascade collapse: the number of collapsed cascades increases with increasing ion mass at constant incident energy. The sensitivity to the ion mass cannot be attributed to the differences in the total number of defects, since the same number of Frenkel pairs has been produced. It is the increase of vacancy supersaturation which is thought to be largely responsible for the increase in the number of collapsing cascades. The major parameter that changes with increasing ion mass at constant energy is the cascade size. For heavier ions the cascade becomes more compact resulting in an increase of the energy density and the vacancy concentration. Cascade collapse is opposed by the activation barrier for the formation of a critical size faulted-loop nucleus. The barrier height depends on a variety of parameters such as the stacking fault energy and surface energy. As the cascades become more dense, the increased vacancy supersaturation results in a larger driving force for a collapse, thus making loop formation more probable. The critical value of the vacancy concentration is approximately between 0.5 and 1%. The vacancy concentration can be locally increased when two or more displacement cascades overlap spatially [74]. Thus for medium mass ions the dislocation loops are formed not from the direct collapse of the individual cascades but due to interaction of depleted zones of subsequent cascades. On average, l-10% of the produced vacancies collapse to form dislocation loops visible by TEM. Turning to the collapse process itself a basic question arises whether the loop formation is due to a process of nucleation and growth involving diffusion or to a diffusionless transformation driven by the instability of the depleted zone. The molecular dynamics simulation of Kapinos and Platonov [75] suggests that the loop can be formed by vacancy migration provided the activation energy for vacancy migration during the cooling phase of the cascade is much lower than the bulk value. This can result from the

394

0. Meyer

1

and A. Twos

10 Dose

Fig. 14. Calculated defect concentrations in Al (1 = interstitials, I, = di-interstitials, I, = interstitial

100

(1014at/cm2) as a function of the clusters, V = vacancies,

dose of incident V, = divacancies,

85 keV Al V, = vacancy

ions [78). clusters.)

increase of internal pressure due to the reaction of the elastic matrix to the thermal expansion of the heated volume and the lowering of the local melting temperature due to the high vacancy supersaturation. Migration of small vacancy clusters (di- and tri-vacancies) which occurs with lower activation energy than that of monovacancies can also play an important role. The vacancy migration in the cooling phase is not thermally activated, i.e. it is independent of the bulk lattice temperature. The fate of interstitials has also been studied by TEM and HFI techniques [76]. SIAs which have survived the recombination in the cascade can also form their own clusters, mostly dislocation loops. The tendency to cluster is much stronger for interstitials than for vacancies. This can also be concluded from the observation that the nature of damage clusters is sensitive to the density of deposited energy [77]. Vacancy loops are formed preferentially at high density of deposited energy and interstitial loops at low density. Fig. 14 shows the defect concentrations as a function of the irradiation dose calculated by Verbiest and Pattyn [78] for Al bombarded with 85 keV Al ions at 4.2 K, i.e. below stage I. At very low doses single vacancies, SIAs and di-interstitials dominate. At dosesaround 1014 at/cm* the cascadescverlap and the created interstitials can only be found in clusters. With increasing dose the number of interstitial clusters decreasesas the large clusters begin to grow at the expense of the smaller ones. In contrast, most vacancies survive as single vacancies although vacancy clusters are also formed. The typical fate of the SIAs after irradiation at temperatures at which they are mobile (300 K) is the following: about 85% of SIAs annihilate in the cascade, 10% are captured at vacancy clusters, 4% form their own clusters and about 1% are trapped at other sinks (grain boundaries, external surfaces, etc.) [79].

3.5. Influence of collisional processeson the lattice location of implanted atoms So far virtually nothing has been said about the fate of the incident ion. Similarly to the energized host atoms the projectile loosesits energy by producing primary knock-ons along the track until the energy falls below the displacement threshold. In section 2 we have discussedthe thermodynamical factors which may influence the final lattice site occupation of implanted atoms. There are, however, other processes of collisional origin which may also play a role. Firstly, a replacement collision between the incident ion and

Lmtice

sire occuparion

of non-soluble

elements

implamed

in merols

395

.8

.6 $

Au-AAl

--

.L

.2

0

2

L

6

8

10

E/E, Fig.

15. Kinematics

of replacement

collisions for different replacement collisions

ions in Al. are possible

The hatched 1821.

area

shows

the region

where

a host atom can occur, when the ion displaces a host atom and the energy left is insufficient to escapethe just produced vacancy. In such a case the host atom becomes an interstitial while the incident ion occupies the substitutional lattice site. The conditions for replacement collisions to occur have been discussed in detail in refs. [80-821. On the one hand, the energy transferred to the host atom must be greater than Ed. On the other, if the remaining energy of the scattered atom is smaller than the capture energy then there exists a certain probability that the incident ion will recombine with the resultant vacancy. The capture energy is usually assumed to be equal to E,. A target atom can be displaced if E > E,/y, where y = T,,,,/E is given by eq. (3.5). The scattered ion can escapeif E > E,/(l - y). Fig. 15 shows the region (hatched area) in the y-E plane where these conditions are fulfilled. Consider Au ions incident on Al( y = 0.42) and Fe( y = 0.69) targets. As shown in fig. 15, the replacement cannot occur in the first case, whereas in the second case it is possible for Au energies between 40 and 120 eV. The probability for replacement collisions has been calculated by Brice [82] for all ion-target combinations and lies between 0.0 and 0.8. Fig. 16 shows the comparison between calculated probability of replacement and measured substitutional fraction for diluted solid solutions produced by ion implantation into vanadium and aluminium at 4 K [83,84] (see also table 7). It is clear that the replacement process alone is not sufficient to explain the substitutionality of implanted ions. The theory is based on binary-collision arguments and does not consider the many-body effects in the cooling phase of the cascade. The estimated lattice temperature attained during the spike is of the order of 1000 K [73]. Due to the short lifetime of the thermal spike (about lo-l2 s), the cooling rate amounts to lOi K s-l. The local “hot spot” is thus rapidly cooled in a manner similar to that in conventional rapid quenching techniques (pulsed laser melting, splat cooling, vapour quenching, etc.). Since these techniques allow the production of the metastable phase outside the range of stability for equilibrium phases quite similar to those produced by ion implantation, the thermal-spike model may be appropriate for explanation of the lattice site occupation of implanted ions [5].

0. Meyer

396

and A. Twos

Lb

-0.8 -0.6

T 0.0 0 Fig. 16. Probability

of replacement

20 collisions

40 in V (dashed

z

60 line and points)

80 and Al (solid

100 line and squares)

[83,84].

The ultimate fate of the ion is apparently affected by many-body interactions with “hot” lattice atoms after its energy has fallen below the displacement threshold. In the local region near the end of its track the ion can make a few jumps, moving several lattice spacings, before the spike decays. During the sampling of its neighbourhood, the ion will find a site corresponding to the local minimum of potential energy in which it can be trapped. The most abundant potential minima are vacancies. It is believed that the recombination of implanted atoms with vacancies during the cooling phase of the cascade is the most probable mechanism of the formation of the supersaturated solid solutions (see section 6.3). It is worth pointing out that this statement may be valid only for low dose implantation. With increasing concentration of implanted atoms the chance for an implant of coming to rest near a previously implanted atom also increases. In this case, the lowest potential minimum could be associated with another impurity atom and not with a vacancy.

4. Interactions of impurity atoms with lattice defects

4.1. Structure and recovery of point defects An important property of point defects is the static displacement field due to the forces exerted by the defect on its neighbours. In the case of a vacancy, the nearest neighbours move towards the vacant site, whereas the second neighbours move away from the vacancy. The relaxation energy, 0.1 eV, is small compared to the vacancy formation energy E,’ being of the order of 1 eV. In contrast, the relaxations are extremely important for interstitials. The formation energy El which amounts approximately to 5 eV would be nearly an order of magnitude larger if no relaxation would occur. The concentration of different defects at a given temperature can be obtained from thermodynamic considerations [85] and is given by C = Co exp( -E’/kT),

(4-I)

where C, = exp(S’/k) is the entropy factor, S’ being the formation entropy. One finds that at a temperature of 1000 K the concentrations of vacancies and interstitials are lo-’ and 10-26,

Louice

site occupation

of non-soluble

elements

implanted

in metals

391

bee

Fig. 17. Configuration

of SIAs in fee and bee metals.

respectively. This demonstrates that the concentration of SIAs being in thermal equilibrium with the lattice can generally be neglected. The large difference between the formation energies for vacancies and interstitials also indicates that these defects, unlike Frenkel pairs, are not produced at the same time. Vacancies are generated at grain boundaries or external surfaces by local rearrangements of the outermost atomic layer. Some of them can diffuse into the bulk of a crystal. The stable configuration of a defect is determined by the minimization of the appropriate thermodynamic energy function. It is usually the configuration for which the lowest lattice strain is attained. For self-interstitials in metals it is a dumbbell, i.e. two atoms that share a common lattice site. As shown in fig. 17 the dumbbell axis points along a (100) axis in fee crystals and along a (110) axis in the bee lattice. These dumbbell configurations have been predicted theoretically [86] and confirmed in various experiments [87]. When the concentration of point defects is high enough, multiple defect association can occur. It has been shown [88] that the binding energy per vacancy increases with the number of clustering vacancies. Thus, large, compact vacancy agglomerates will be favoured. Interstitials also form clusters with binding energies depending on the number of trapped defects: the binding energy of a di-interstitial is usually less than 1 eV [89] whereas the dissociation of a tri-interstitial into a mono- and di-interstitial requires about 1.5 eV [86]. Interstitial loops which form by agglomeration of many interstitials are very stable and dissociate only at very high temperature. The binding energy per interstitial in the loop can be as large as 3 eV [86]. The preceding section described the ion bombardment process up to the stage where the kinetic energy delivered by the incident ion has been dissipated and the collision cascade region is in thermal equilibrium with the surrounding lattice. Upon annealing, thermal vibrations of atoms lead to the migration of defects through the lattice. A defect can change its site provided it can overcome a potential barrier. A measure of the height of this barrier is the migration energy, EM. The jump rate is given by Y=v,, exp(-EM//CT),

(4.2)

where ~a is the attempt frequency. Due to the strong relaxation, the rearrangement in the centre of the interstitial requires only little energy. The migration energy is therefore quite small, typically about 0.1 eV. The migration energy of vacancies is substantially larger and amounts to about 1 eV. It is evident that due to their much lower migration energy the SIAs are significantly more mobile than vacancies. The defects can migrate through the lattice until they undergo one of the following reactions:

0. Meyer

398

and A. Twos

-

annihilation of vacancies and interstitials by recombination, aggregation into more complex defects such as larger defect clusters or dislocation loops, annihilation at fixed sinks such as dislocations, grain boundaries or free surfaces, trapping at impurities. The study of these reactions has been the object of extensive experimental and theoretical work [90,91]. To a considerable extent, the annealing experiments of irradiated metals have been performed by observing the changes of electrical resistivity. These measurements have the advantage of high sensitivity and accuracy and are easy to perform. Unfortunately, electrical resistivity is unspecific for different kinds of defects as well as rather unsensitive to their agglomeration. Thus only an approximate number of vacancies and interstitials can be estimated irrespective of their detailed arrangement. Nevertheless, through a large number of systematic electrical resistivity measurements it was possible to develop a model of recovery providing a common language for radiation damage research. The model distinguishes five characteristic recovery stages in an isochronal annealing curve as shown in fig. 18. For pure metals these stages are assigned to different defect reactions. of Stage I is usually divided into substages I,, I, and I,, which are due to recombination close Frenkel pairs and substages I, and I, occurring at temperatures at which isolated interstitials become mobile. At stage I, an interstitial needs to make a few jumps only before it arrives at the instability zone of its own vacancy and recombines spontaneously (correlated recombination. In stage I, a long-range migration of SIAs occurs. During the migration a SIA can recombine with an alien vacancy (uncorrelated recombination) or cluster with other interstitials. At the end of stage I, interstitials survive only in the form of small agglomerates. Stage II is due to the migration and dissociation of small interstitial clusters (e.g. di-interstitials) and the release of interstitials from shallow traps leading to the growth of large interstitial clusters, mainly dislocation loops. STAGE

T(K) Fig. 18. IsochronaI

recovery

curve of

electronirradiatedCuand assigned recoverystages.

Lattice Table 2 Recovery Recovery stage

model

site occupation

of non-soluble

implanted

in merals

399

for metals

Temperature Al 15-37 40-45

‘A-1,

1,

‘) (K)

Description

V

Fe

5-40 50

60-120 140

II

III

elements

Recombination Free migration

of close interstitial-vacancy of interstitial atoms

Growth of interstitial clusters dislocation loop formation 190-250

200

200

IV

Free migration Growth

V

775

600

700

‘) The temperature

data for Al, V and Fe are taken

from

eventually

by

of vacancies

of the vacancy

Dissociation

followed

pairs

of defect

clusters clusters,

annealing

of residual

damage

refs. [96,97].

The nature of the migration processes occurring during stage III is a matter of dispute since at least 20 years. Two principal recovery models have been developed which assume a different type of freely migrating defect in this stage: in the one-interstitial model it is a vacancy [92] whereas in the conversion-two-interstitial model it is a different kind of interstitial [93]. Although the controversy still persists, the majority of recent experimental results are in favour of the first model. Especially the study of the production and annealing of isolated Frenkel pairs in copper using low-energy (29 eV) In recoils from neutrino emission during the decay of “‘Sn to i”In in Cu has provided clear evidence that 60% correlated recombination occurs in stage I, while the remaining 40% of monovacancies detrap and vanish in stage III [94,95]. Consequently, the following discussion and interpretation of the experimental results presented in the next sections will be based on the one-interstitial model which assumes that vacancies become mobile in stage III. Migrating vacancies annihilate at interstitial clusters or form vacancy agglomerates so that at the end of stage III vacancies exist only in the form of small clusters. At increasing annealing temperature, the vacancy clusters grow in size and vacancy dislocation loops are formed (stage IV). The remainder of radiation damage recovers finally in stage V. The vacancy clusters dissociate thermally and the released vacancies annihilate at interstitial loops or at external sinks (grain boundaries, surfaces). The properties of the recovery stages are summarized in table 2 where the temperatures at which the particular stages occur for Al, V and Fe are also listed. The model behaviour of the recovery curve as shown in fig. 18 has been observed only after irradiation with fast electrons or very light ions (H or He ions). In this case the majority of the displacements occur with energies just above the displacement threshold and the damage created will be essentially in the form of randomly distributed vacancy-interstitial pairs. One notes that for a low density of defects the clustering probability is very low and the principal recovery mechanism is due to the annihilation of freely migrating SIAs and vacancies at external sinks in stages I and III, respectively. In contrast to electron or light-ion irradiation, fast-neutron or heavy-ion irradiation produces high-energy recoils which initiate large displacement cascades. The suppression of stage I recovery increases with increasing defect density in the collision cascades [98]. There seems to be an enhanced probability of SIAs to cluster in cascades with high defect densities and for the elimination of many close pairs in the thermal spike. It has also been observed that cascade

0. Meyer

400

and A. Twos

effects influence the recovery in stage III. For high-dose heavy-ion bombardment, when the cascades have overlapped several times, stage III recovery is much more pronounced than in the case of light-ion irradiation. This observation clearly confirms that the tendency for defect clustering is greatest for dense cascades. In contrast to what would be expected, the irradiation temperature does not change the presented scheme. After irradiation at temperatures corresponding to stage II the defect structure is essentially the same as after irradiation at stage I and subsequent warming to stage II. After annealing above stage III roughly l/3 of the damage observed by electrical resistivity measurements at low temperatures is retained. Since all point defects are mobile at this temperature the defects can survive in the form of clusters only. The TEM investigations have shown that all the clusters are of vacancy type. Thus, the interstitial clusters break up and SIAs annihilate predominantly at external sinks [98]. Some influence of the irradiation temperature above stage III has been observed for collision cascades of medium density. The out-diffusion of vacancies can lower the defect density in depleted zones below a critical value so that collapse into dislocation loops becomes impossible [99]. 4.2. Vacancy-impurity

interactions

4.2.1. Binding energies of structures

of vacancy-impurity

complexes

There are two approaches to elucidate the problem of impurity-point-defect interaction based on the theory of elasticity and on electronic structure calculations. An impurity atom at a regular lattice site produce a different potential compared to that of a host atom and thus can attract or repel point defects. An attractive interaction leads to a preferential association or defect-impurity complex formation usually termed defect trapping. Fig. 19 shows schematically the potential distribution in the presence of an impurity atom. The probability of a defect-impurity encounter depends on the long-range part of their mutual interaction potential and is usually expressed in terms of the trapping radius R,. Whenever a ALTEWNE

ATOW

RAN3

oo~~o$--yyo

0

I

I

0

R,

Fig. 19. Schematic representation of the defect-impurity

l

R interaction potential.

Lattice

sire occupation

of non-soluble

elements

implanted

in metals

401

point defect enters into a sphere of radius R, around an impurity atom (trapping volume) the attractive potential causes its drift towards the impurity which leads inevitably to trapping. For this to occur, it is necessary that the defect coming from infinity has gained a potential energy at least equal to the thermal energy. Hence, the trapping radius is given by [99]

d4

- +s(Rt) 2 kT,

(4.3)

where $+( R,) is the interaction potential at the saddle point at the distance R, from the impurity atom. The defect trapping is strongly temperature dependent. According to eq. (4.3) the trapping volume decreases with increasing temperature and is zero, i.e. no trapping occurs, when the thermal energy exceeds the dissociation energy E,. On the other hand, at temperatures where defects are immobile practically no trapping occurs. The morphology of defect-impurity complexes is subject to changes when defect-antidefect reactions can occur. The simplest reaction of this type is SIA-vacancy recombination. By changing the temperature so that the antidefects become mobile, one observes a reduction of the number of trapped defects in the previously formed complexes. In such a way the SIA-impurity complexes formed in stages I or II would disappear after warming up to stage III where the vacancies become mobile. It should be pointed out, however, that this process can only take place if the energy released by the recombination exceeds the binding energy of the defect. Otherwise the complexes are stable against defect-antidefect reactions. Ion implantation produces very specific conditions for defect-impurity interactions. In general, an implanted atom interacts with the damage produced by its own collision cascade termed correlated damage. Fig. 20 shows the range distribution of 300 keV ‘9’Au ions implanted into Fe and of the radiation damage simultaneously produced by the implantation, both calculated by the computer code TRIM [loo]. One notes that the distributions largely overlap. Only ions with the largest ranges are stopped in a region of little or no damage. The behaviour

300keV

Au-Fe

80 40 60 DEPTH (nml Fig. 20. Range distribution of 300 keV Au ions implanted in Fe and the corresponding damage distribution.

0

20

402

0. Meyer

and A. Twos

of this small fraction of implanted ions can be easily taken into account using a depth sensitive analysis technique like ion channeling. As will be shown in section 5, defect trapping by impurity atoms may already take place during the cooling phase of the cascade. Therefore, the dynamics of the collision cascade and the structure of correlated damage are strongly dependent on the type of implanted species and bombarding conditions. Irradiation of alloys previously produced by ion implantation or classical equilibrium techniques (melting, diffusion, etc.) produces uncorrelated damage. Because defects so formed are randomly distributed with respect to the impurity atoms, they can be trapped only after thermal activation. The main virtue of introducing uncorrelated damage is that the initial type of damage structures is completely independent of the type of solute. Interactions between vacancies and impurity atoms are of great importance for the understanding of diffusion mechanisms and basic properties of defects. They are also important for technological applications, especially for nuclear reactor materials. In spite of these facts and the large amount of experimental data accumulated during the last decade the theory of vacancy-impurity interactions is still not well developed. There are two approaches used to elucidate the problem: the theory of elasticity and electronic structure calculations. It should be pointed out that, although both methods are based on different phenomenological representations, they are interrelated and show two aspects of the same phenomenon. In the elastic model the binding energy originates from the stress field produced by the size misfit of the impurity atom. If a vacancy arrives at the nearest-neighbour position to an impurity, the lattice can relax. The amount of released energy which is proportional to the initial distortion is the vacancy-impurity binding energy. The criterion for atomic misfit is the difference between the partial atomic volume, aa, of impurity atoms and the atomic volume of the solvent, 52, [loll. The size factor, Sz,,, is defined as (4.4) Undersized atoms have 52,, < 0. The size-mismatch energy can be estimated elastic continuum theory [102]. According to Eshelby, AHsize is given by

using Eshelby’s

where p is the shear modulus of the host, V, and Vu are the molar volumes of the impurity and the host, respectively, and y = 1 + 4a/3K, where K, is the bulk modulus of the solute. Rough estimates indicate that one-twelfth of the elastic strain is released by single-vacancy trapping [103]. There are, however, other factors which influence the vacancy-impurity binding energy. Doyama [104] has noticed that the binding energy between a monovacancy and a substitutional impurity atom is proportional to the heat of solution, AH,,,. Fig. 21 shows this dependence for Al. In fact, if the energy required to replace a host atom by an impurity atom, i.e. the heat of solution, is non-zero, the lattice and electronic system in the vicinity of the impurity will be distorted. The distortion increases with the magnitude of AH,,,. Miedema [105] discussed in detail the factors which may influence the binding energy. Firstly, the size effect plays an important role. Oversized impurity atoms (L?,, > 0) being nearest neighbours to a vacancy produce a reduction of the vacancy-hole size and an increase of the electron density in the centre of the hole. Both factors reduce the vacancy formation enthalpy in the vicinity of an impurity which makes the occupation of a nearest-neighbour position by a vacancy energetically favourable. Moreover, the diminishing of the hole size reduces the

Lattice

site occupation

of non-soluble

ZnMgAg

0

20

elements

implanted

Cu Si

LO

Cd

bU

in metals

In

403

Sn

LIU

1 kl / mol 1 AHSOL Fig. 21. Binding energy of vacancy-impurity complexes versus the heat of solution for different impurities in Al [104].

original lattice strain. Secondly, the change of electron density due to the presence of a vacancy will influence the positive term of the heat of solution (cf. eq. (2.1)). As a neighbour to the vacancy, the solute atom looses that fraction of the positive term which corresponds to the missing host atom. Unfortunately, at present, it is not clear how to deal with the negative term due to electronegativity differences. From this discussion one can conclude that an attractive interaction between vacancies and impurity atoms is the stronger the larger the heat of solution, provided the size-mismatch energy term is included. Theoretical models and calculations of vacancy-impurity binding energies have been reported for at least three decades [106]. However, only recent developments based on the pseudo-potential approach represent an important progress toward a more realistic theory [107,108]. Especially worth mentioning is the work of Ho and Benedek [109] who were able to include relaxation effects in their calculations. The obtained binding energies are not inconsistent with the experimental data. Although the theory is being developed quite rapidly, the quantitative results should still not be taken too seriously. Anyhow, both theory and experiment indicate that the binding energy of a vacancy-impurity pair is quite low (0.1 to 0.3 ev). It is expected that the simplest complex, a single vacancy attached to a substitutional impurity atom at the nearest-neighbour position is aligned along (110) for fee metals and (111) for bee metals. However, if the supply of mobile vacancies is large enough, multiple vacancy trapping occurs. Fig. 22 shows the structure of the simplest vacancy-impurity

0. Meyer

404

and A. Twos

tY1 Dl

,770, x n (717)

(i70)

d!!cl c-1 Fig. 22. Configurations

of vacancy-impurity

complexes in bee metals and the corresponding the backscattering yield.

angular

dependences

of

complexes for bee lattices. Also shown are the channeling angular scans characteristic of each complex. A solute atom which is associated with one vacancy may relax only a small distance, less than than 0.01 nm, from the lattice site [85]. Such small displacements are difficult to detect by ion channeling. In this respect channeling of conversion electrons seems to be more sensitive to small displacements than ion channeling [llO]. However, when several vacancies are trapped the solute atom may be displaced into an interstitial site of high symmetry which is easily seen by ion channeling as shown in fig. 22. Consider the complex XV, which was

Lotrice

sire occupation

of non-soluble

elements

implanted

in metals

405

originally formed by trapping of three vacancies. As a result of the interaction the solute atom can be spontaneously ejected into a tetrahedral interstitial site creating a fourth vacancy. Because of its higher symmetry the resultant strain release makes this type of complex energetically favourable as compared to the unrelaxed configuration [ill]. In a similar manner trapping of five vacancies may result in the creation of a sixth vacancy by ejection of the solute atom into the octahedral site (XV,). There are indications that even larger complexes can be formed with appreciable binding energies. The calculations of Drentje and Ekster [112] have shown that Xe atoms in the Fe host can form a cigar-shaped cluster consisting of 22 vacancies associated with two Xe atoms located on the symmetry line of the complex. The binding energy per vacancy is almost as large as in the case .of XeV,. The increase of the number of trapped vacancies may lead to the transformation of the complex into a dislocation loop. The critical number of vacancies which is necessary to initiate the collapse of a three-dimensional cluster into a two-dimensional loop is at present not known. The population of different types of complexes depends on the irradiation conditions and the lattice temperature. With increasing irradiation fluence it is expected that the average number of vacancies in a complex would increase. Also the mobility of complexes should be taken into account. In general, the complexes which can migrate without dissociation as distinct entities, e.g. XV, in the fee lattice, can vanish at lower annealing temperatures than immobile complexes although their binding energy is not appreciably smaller. 4.2.2. Experimental evidence The experimental evidence of vacancy-impurity complex formation is based mostly on methods which are inherently microscopic, i.e. which give direct information about the structure of the complexes. The most important methods are based on hyperfine interactions and ion channeling. These methods are sensitive to trapping of defects at impurity atoms and thus have the potential to determine defect configurations. However, in most cases it is not possible to identify unambiguously the trapped defect species directly from the experimental parameters. Since the theoretical models are not able to reproduce these values with sufficient accuracy one has to employ the data of other defect studies to determine whether vacancies or SIAs are trapped and to obtain systematics of the different types of defect clusters. For example, one can introduce only one type of defects, e.g. vacancies by quenching, or use a selective measurement method like positron annihilation which is only sensitive to vacancies. Further, according to the recovery stages scheme, thermal activation can be used to restrict the mobility of defects, and finally the defect-antidefect reactions can be used. (a) Uncorrelated damage. In order to study the interaction of impurity atoms with uncorrelated damage, one should dope the samples with the selected atomic species such that they are essentially damage-free. This can be achieved if the doping process itself does not produce damage, e.g. diffusion or doping during crystal growth, or if the damage produced during doping is completely removed by appropriate annealing. Subsequently, the samples are irradiated by a given projectile to a preselected dose. In this case, the defects are randomly distributed and can be trapped only if they become mobile after thermal activation. The fee metals have been extensively studied using hyperfine interactions combined with ion channeling [113-1151. The most important results are summarized below. The different vacancy-impurity complexes that were identified by these methods in fee metals are shown in fig. 23. These configurations were all identified by perturbed angular correlation spectroscopy (PAC). Since by ion channeling one can detect only complexes containing displaced impurity

0. Meyer

406

n-vacancy

xv2

XV,(a)

and A. Twos

o-impurity

XV,(b)

xv, (cl

XV&cl

FL

Fig. 23. Vacancy-impurity complexes identified in fee metals by means of HFI [115]. From left to right: the first three figures show configurations in the unrelaxed state, the fourth and fifth figures show relaxed configurations.

atoms, the relaxed versions XV, and XV, were observed. In the case of faulted loops (FL) the impurity atom is thought to be located inside the stacking fault region. The formation and annihilation of vacancy-impurity complexes in fee metals can be at best presented following the comprehensive study of the CuIn system by Swanson et al. [116]. The authors used PAC and ion channeling techniques to investigate the vacancy trapping at impurities in a Cu-0.1 at% In single crystal. Both techniques showed that before irradiation In atoms occupy substitutional positions. The defects were introduced by bombardment with 350 keV or 1.5 MeV 4He ions at temperatures below stage III and subsequent annealing at temperatures where vacancies become mobile (250-280 K, cf. table 2). Before annealing no changes in the lattice positions of In atoms were observed so that a strong interaction of solute atoms with migrating SIAs could be ruled out. Trapping of the freely migrating vacancies resulted in the formation of InV,, InV,(a) and InV, complexes. InV, and InV,(a) were not observed by channeling because of very small relaxations of solute atoms from regular lattice sites. On the other hand, they were easily detected by PAC because of the large electric field gradient (EFG) due to strong perturbation of the impurity surroundings. The tetrahedral configuration XV, is not observable by PAC becauseof cubic symmetry of the complex which produces no EFG with respect to the In atom. This configuration can be unambiguously determined by channeling because In atoms in this configuration are occupying positions at the centre of the (100) channels. Thus, only the complementary use of these two techniques permits the study of vacancy-solute complexes in Cu. Besides these three types of complexes, the channeling analysis has indicated the presence of one more component which was labelled “random” component. The detailed morphology of this complex is not known though it is possible that it is partially composed of InV, complexes having (100) symmetry with In atoms displaced by about 0.08 nm. Upon thermal annealing the complexes evolve as shown in fig. 24. It is seen that all components appeared in approximately the same temperature interval. Within a temperature range of 50 K the smallest complexes InV, and InV, are formed and their population has reached a maximum. With increasing temperature the number of InV, complexes remains fairly constant whereas the number of InV, and InV, ones decreases.Since the disappearance of these complexes is not accompanied by an increase of InV,, it cannot be due to the complex transformation but it is apparently due to detrapping of vacancies.. The InV, complexes anneal out at temperature above 500 K (stage V). Once the smallest complexes InV, and InV, have dissolved by releasing vacancies, two other complexes form: f, which is attributed to In atoms trapped in a faulted (111) vacancy loops, and an unidentified cluster called f,. Fig. 25 shows the results of a further experiment which elucidates the behaviour of the complexes with varying supply of free vacancies. The CuIn sampleswere irradiated at 35 K to

Lattice

site occupation

of non-soluble

elements

implanted

in merab

407

5

0

100

200

300

600

500

T, (KI Fig. 24. Annealing behaviour of In-vacancy complexes after He-ion irradiation of In doped Cu at 80 K [116]

various fluences of 0.35 MeV He ions and then annealed at 280 K. Since the number of created vacancies increaseswith the irradiation fluence, the relative population of different complexes should change depending on the trapping mechanism. It is expected that with increasing irradiation fluence the average number of vacancies trapped at each In atom would increase. As can be seenin fig. 25, the number of InV, increases fastest at the beginning of the irradiation and slows down when the trapping of the second and next vacancies becomes likely, thus giving rise to the formation of multivacancy complexes. One notes the S-shape of the InV, curve which signifies a second-order formation kinetics expected for subsequent trapping of two monovacancies. Somewhat surprising is the large growth rate of InV,. This could be due to the direct trapping of mobile trivacancies. However, it is also possible that the fraction identified by channeling as InV, contains other multivacancy clusters of such configurations that the interstitial In position remains unchanged.

TI=

35K

T,.70K

-

\

1

2

0

1

2

Dose 110'SHe*cm-2 1 Fig. 25. Evolution of In-vacancy complexes observed by PAC (f, and f,) and by channeling (fT and fa) during a post-irradiation experiment [116].

0. Meyer

408

and A. Twos

1.0 0.8 0.6 0.4 0.2 0 i

-1

I 1

0

ANGLE FROM ~100~ DIRECTION (degrees) Fig. 26. Angular

dependence

of the normalized

backscattering

yield

from

Al and In atoms

through

a (100)

axis [117].

The second part of this experiment consists in the study of the complex decay due to absorption of freely migrating SIAs. During the irradiation with He ions the samples were cooled down to 70 K at which temperature only SIAs are mobile and can interact with the previously formed complexes. The decay rates of InV, and InV, are considerably smaller than that of InV,. Swanson et al. [117] have analyzed in detail the shrinking of the vacancy clusters by SIA absorption. The best fit to the experimental data has been obtained assuming that the cross section of free interstitial annihilation at vacancy-impurity complexes increases as the square of the number of vacancies. The shrinking of large clusters can produce a temporary increase in the population of smaller ones. The vacancy trapping in Al, which is another extensively studied fee metal, behaves differently. Fig. 26 shows the angular yield curves through the (110) and (100) axes for an Al single crystal doped with 0.02 at% In. The sample was irradiated with 1 MeV 4He ions to the indicated fluences at 35 K, annealed at 220 K and measured again at 35 K. The strong peak in the middle of the scan indicates that In atoms are displaced into specific lattice sites due to vacancy trapping. In this case it is the InV, complex which grows rapidly with increasing supply of free vacancies. The detailed analysis of the experimental data leads to the following model for the growth of In-vacancy complexes as illustrated in fig. 27. A complex composed of two vacancies trapped at a substitutional atom transforms spontaneously into the energetically favourable InV,(c) complex by strain-induced In relaxation. Capture of the next vacancy produces the InV, configuration while five vacancies trapped at an In atom give rise to a relaxed InV, complex. The second part of the experiment, labelled “70 K irradiation” in fig. 27, shows the annihilation of In-vacancy complexes by migrating SIAs. The decay of InV, into InV, is clearly visible. The PAC measurements have additionally indicated the existence of InV. configurations.

Lattice

site occuparion

of non-soluble

elements

implanted

in merals

409

70K IRRADIATION

Ci

01230

2

IRRADIATION Fig. 27. Population

of different

In-vacancy

4

6

8

10 12

FLUENCE(1015cm-2) complexes

during

irradiation

experiments

[117].

Based on investigations in other fee metals [118] the vacancy trapping exhibits several common features. The clustering begins with the formation of XV2 and XV, complexes. Depending on the magnitude of impurity relaxations in some metals, XV, can transform spontaneously into XV,. With increasing vacancy supply the larger complexes grow by multiple-vacancy trapping. The tetrahedrally relaxed trivacancy complex XV, exists in all fee metals. This complex seems to be an intermediate stage of a dislocation loop or a tetrahedral stacking fault. So far we have considered only the trapping of defects created by irradiation with light ions producing mainly Frenkel pairs. One might expect that heavy-ion irradiation will lead to the formation of other defect-impurity complexes. However, a comparative study by Deicher et al. [119] on the defect properties in Au after quenching and irradiation with different projectiles has shown that the types of clusters remain unchanged; merely their populations depend on the defect density produced by the collision cascades (see fig. 28). As compared to fee metals, the situation in bee metals is more complicated. In spite of the vast amount of experimental data, the interpretation of the recovery stages is far less conclusive. This is mainly due to the fact that bee metals easily dissolve gaseous impurities which can shift the recovery stages to other temperature regions. In addition, high melting temperatures make quenching experiments difficult to perform. A frequently studied bee metal is o-iron. Muon spin rotation experiments performed by the Constance group [19,120] have shown that vacancies migrate in Fe at 200 K and form vacancy-impurity pairs. The binding energies of these complexes are listed in table 3. Depending on B,, the complexes dissolve at temperatures between 210 and 250 K. According to PAC measurements for Nb, Ta, MO and W the InV, complexes are also formed [121]. It is not certain whether a third type of complex, namely XV,, is formed in all metals: it has been observed in MO and W, but not in Nb and Ta. In contrast to the fee metals, no collapse of large clusters into planar loops has been observed (see section 3.4). The channeling experiments of Howe and Swanson [122] and Turos and Meyer [123] on the Au doped Fe did not furnish any conclusive information about the structure of Au-vacancy

410

0. Meyer

ANNEALING Fig. 28. Influence

of temperature

and A. Twos

TEMPERATURE

and mass of bombarding particles defects in Au [119].

I Kl

on the relative

population

of different

types

of

complexes although their formation and dissolution was clearly observed. This is apparently due to the fact that successive trapping of vacancies leads to the simultaneous formation of several types of clusters which cannot be distinguished, neither by channeling nor by HFI methods. It is concluded that more complementary experiments on bee metals are needed to elucidate the detailed mechanisms of vacancy accretion. (b) Correlated damage. In ion implantation

experiments energetic ions are injected into metal targets producing defects which are spatially correlated with the position of the implanted ion. For low-temperature implantation defect-impurity complexes may form during the cooling phase of the cascade. Other types of complexes can be formed after thermal activation, e.g. at high-temperature implantation and annealing, when the defects are trapped from the immediate neighbourhood of the ion at the end of its trajectory. Fig. 29 shows the radial vacancy distribution around the implanted ion calculated by Post et al. [124] using the binary-collision computer code MARLOWE [63]. The lattice temperature was below recovery stage III and the spontaneous recombination distance was 3.7 lattice units. Here again the information about fee metals is more abundant, mostly due to the extensive studies performed by means of the HFI techniques. Pleiter and Hohenemser [118] reviewed the PAC data for seven fee metals (Ag, Al, Au, Cu, Ni, Pd, Pt) implanted with “‘In ions. In all these metals with Ni being the only exception, InV, complexes have been observed already after implantation at temperatures below recovery stage III. Upon thermal annealing above stage III the simple complexes transform into extended ones, including dislocation loops. Due to the large concentration of vacancies in the vicinity of the ion, different types of large complexes were formed at the same time. Recent MSssbauer and channeling studies of Besold et al. [125] have identified InV, as the dominant complex formed at about 350 K in Ni, Al, Cu and Co. Concerning bee metals Table 3 Binding energies

of XV, complexes

in a-iron

Impurity

& W

co

Ni

Si

CU

Au

0.12

0.21

0.21

0.11

0.24

Lattice

site occupation

of non-soluble

elemenrs

c-1

7

i

I

implanted

411

in metals

-

@=O”

--

@=20”

6

5 Ln w ls

I I I

4 C-

I I

J

I

i

2 > IL

3

2

2

I

0

1 I I. --l I

0

I

1

10 IMPLANT-

Fig. 29. Radial distribution

‘I

VACANCY

I

I

I

20 SEPARATION

L-s I

.

I

30 ( LU 1

of vacancies for In implanted into W at various angles 0 with respect to the surface normal [124].

much insight can be gained from the study of Ag and In implanted into tungsten performed by van der Kolk et al. [126]. Annealing behaviour of the defect-impurity complexes observed in these PAC measurements is shown in fig. 30. The recovery stage III for W is located at about

Ag W

400 800 1200 T,(K) Fig. 30. Annealing behaviour of impurity-vacancy

InW

ASSIGNED CONFIGURATION

400 800 1200 complexes in Ag and In implanted W at 293 K [126].

0. Meyer

412

and A. Twos

600 K. From fig. 30 it is clear that about 90% of the implanted atoms occupy substitutional lattice sites whereas each of the remaining atoms has trapped one vacancy thus forming an InV, complex. Only when vacancies become mobile does the substitutional fraction decrease due to the formation of In-vacancy complexes, mainly InV,. The type of complexes which appears at temperatures above 800 K has not yet been determined. 4.3. Self-interstitial

atom-impurity

interactions

4.3.1. Binding energies and structures

of SIA-impurity

complexes

The stable configuration of the SIA in metals is a dumbbell. A large amount of strain energy is associated with this arrangement. This is due to the fact that an additional atom has been squeezed into the lattice thus making the configuration highly compressed. The stable SIA-impurity complex will be formed if an arrangement can be found where this strain energy can at least partially be released. One can expect that this would be the case for solute atoms which are smaller than the host atoms (a,, < 0). Comprehensive theoretical studies carried out by Dederichs et al. [86] have shown that such a complex has the form of a mixed dumbbell. The interatomic potentials used were those of Born-Mayer and Morse. The interaction potential was obtained by shifting the atomic potential by r,, towards smaller interatomic distances (r,, < 0). For oversized solutes (Sz,, > 0) the potential was shifted in the opposite direction. The binding energies for the mixed dumbbells were then calculated as a function of the ratio ‘,-JR,,, where R, is the equilibrium nearest-neighbour distance. The binding energy of the mixed dumbbell depends on the magnitude of r,,/R,. It is positive for undersized solutes (-0.06 i ro/R, d 0) and varies linearly with r,,/R,-, within the range -0.05 < r,,/R, < 0.03. The binding energy as a function of r,,/R, is shown in fig. 31. For an oversized impurity we have r,/R, > 0 and the mixed dumbbell configuration is not stable. Nevertheless, large solute atoms can trap SIAs. Because each of these defects compresses the lattice, the binding energy is small and the stable arrangement is a nearly substitutional impurity atom and an adjacent SIA dumbbell, which retains its identity. This trapping configuration is a weak one and is shown in fig. 32. The use of AE [eVl

t

Fig. 31. Binding

energy

of mixed

dumbbells

as a function

of rO/10

[86].

Lattice

of non-soluble

sire occupation

o-Al,

l -Mn

elements

implanted

in metals

413

"-Ag

WEAK TRAPPING

UNTRAPPED

STRONG TRAPPING Fig. 32. Trapping

of SIAs at solute atoms

in Al [127].

shifted potentials oversimplifies the real situation. However, recent calculations of Lam et al. [128,129] using the molecular dynamics method with interatomic potentials derived from first principles confirmed the general features of the simple model. Multiple trapping, i.e. binding of more than one SIA at one solute atom, can also occur. Such complexes consist of either parallel or mutually perpendicular dumbbells which surround an oversized impurity atom occupying a nearly substitutional site. The binding energy per SIA is of the order of 1 eV. Also mixed dumbbells can trap several SIAs though with smaller binding energy. Ion channeling is an especially suitable technique to study interstitial trapping. The atomic displacements of impurity atoms in mixed dumbbells are on the order of 0.1 run making their lattice location determination relatively simple. Fig. 33 shows the projections of a (100) mixed dumbbell in the fee lattice into different channels and their corresponding channeling dips. 4.3.2. Experimental

evidence

The SIAs in metals migrate by a replacement mechanism as shown in fig. 32. Under conditions where SIAs are mobile but vacancies are not, migrating SIAs which encounter an undersized substitutional solute atom will be trapped forming a mixed dumbbell. Such experiments are relatively easy to perform for suitably doped samples when uncorrelated damage is produced by irradiation. One can expect that the study of SIA trapping due to correlated damage will provide valuable information about the nature of collisional processes (size of collision cascades, length of replacement chains, etc.). Some results of such detailed experiments have been described in refs. [94,95]. The channeling results have unambiguously shown that undersized solute atoms are displaced from the lattice site when they trap SIAs [130-1321. In Al, which is the most extensively studied host, and other fee metals the solute atoms are displaced along the (100) directions by about 2/3 of the distance to the octahedral position. The magnitudes of solute atom displacements in mixed dumbbells agree qualitatively with theoretical estimates of Dederichs et al. [86] and are shown in table 4 (after Swanson [24]). As can be seen from table 4, large solute atoms do not form mixed dumbbells though they do trap SIAs.

0. Meyer

414

and A. Twos



A

Fig. 33. Configuration

Table 4 Trapping

of mixed

configurations

Impurity Cr Mn Fe cu Zn

in fee metals

and the corresponding ing yield.

angular

dependence

of the backscatter-

of SIA in Al Trapping configuration

Qsr -

Ag Ga Ge Sn Mg ‘) md and st stand

dumbbells

for mixed

0.57 0.47 0.38 0.38 0.06 0.001 0.05 0.13 0.24 0.41 dumbbell

a)

0.146 0.143

100 md 100 md md 100 md 100 md 100 md 100 md 100 md St st and shallow

trapping,

Impurity displacement

0.148 t-j.139 0.110

respectively.

(run)

Lattice

site occupation

of non-soluble

elements

implanted

0.6

in metals

415

7

x

0.4

0.2

0 -0.6

0

0.6

ANGLE FROM
All these trapping processes have been observed after irradiation with electrons or light ions at temperatures corresponding to stage I. An interesting question concerning the stability of mixed dumbbells is whether this configuration can be altered by trapping additional SIAs. Fig. 34 shows the angular yield curves for 1 MeV 4He ions scattered from Al and Ag atoms for an Al-O.05 at% Ag alloy [127]. The disappearance of the Ag peak with increasing irradiation fluence at 70 K indicates the change of Ag atom positions. It is worth pointing out that the peaking in the angular yield is very sensitive to the solute displacement. The peak disappears when the displacement is changed by about 0.02 nm. Similar experiments performed for Al-O.16 at% Mn crystal did not reveal any change in the Mn atoms positions. This result reflects the much greater stability of Mn-Al mixed dumbbell than of the Ag-Al one. Since Mn atoms are much smaller than Al atoms, the binding energy of a Mn-Al dumbbell is expected to be quite large. The channeling results clearly indicate that largely oversized solute atoms, such as Sn in Al [130], are not significantly displaced from lattice sites when multiple trapping occurs. Electrical resistivity data show [133] that such solutes trap SIAs in stage I and release them when the temperature is raised to stage II. Thus the binding energy is very small (shallow trapping). The mixed dumbbells are generally much more stable. Fig. 35 shows the effect of isochronal annealing on the displacement of Mn atoms. An Al-O.09 at% Mn alloy was irradiated at 30 K and subsequently annealed for 600 s. The solute displacement appears when the migrating SIAs (stage I) are trapped by Mn atoms. The mixed dumbbells are then stable up to stage III (- 200 K). It is not known whether mixed dumbbells anneal out due to defect-antidefect reactions

416

0. Meyer

and A. Twos

a ' 0

0.8

z

?i 0.6 sl E 0.4 E -N s 0.2 5 0

40 80 120 160 200 240 ANNEALING TEMPERATURE (KI

Fig. 35. Displaced fraction of the Mn atoms due to mixed dumbbell temperature [24].

280

formation as a function of the annealing

with mobile vacancies or dissolve by releasing SIAs from the solute atom. In conclusion, it can be stated that mixed dumbbells containing small solute atoms in Al and Cu hosts persist up to recovery stage III whereas large solutes loose their trapping capability already in stage II.

5. Lattice site occupation of elements with positive heats of solution

In this section we will deal with impurity atoms which have positive values of the heat of solution and, therefore, are non-soluble in Al, Fe and V. In fact, the systems under consideration have been chosen because they have increasing, positive values of AH,,, according to Miedema (eq. (2.1)). These systems also have large values of AH,, as determined by eq. (4.5) and are able to trap vacancies and form impurity-vacancy complexes (see section 4.2). Here we focus on the substitutional component although more information on the configurations of the impurity-point-defect complexes can be obtained by a careful analysis of the channeling results, especially of the angular scans. 5.1. Aluminium-based

ion implanted systems

The study of Al-based ion implanted systems is of great interest as the solid solubility rules fail to describe the results for systems produced by ion implantation at 293 K (see section 2.3). Therefore, such elements as Ga, Cd, Hg, Sb, Kr, In, Xe Pb, Rb and Cs (in order of increasing AH,, values) were implanted in Al single crystals at temperatures of TI = 5 K, 77 K and 293 K, using energies between 200 and 300 keV and doses with corresponding peak concentrations between 0.05 and 10 at% [84]. During implantation, the Al crystal was rotated in order to avoid channeling. Some experiments were performed for channeled implants, however no change of the substitutional component was noted as compared with the results for non-channeled implants. Samples implanted at 5 and 77 K were warmed up stepwise up to 293 K in order to study the influence of point defects in the temperature regions where self-interstitial atoms and

Lattice

sire occupation

-2

of non-soluble

-i

36. Anguler

yield

curves

for 2 MeV

He ions

implanted

TO AXlS

backscattered 293 K [136].

from

417

in metals

i

cl

TILT RELATIVE Fig.

elements

i (DEG)

an Al single

crystal

implanted

with

Ga

at

vacancies become mobile (see table 2). All the systems given above, except -AlGa and AlSb, reveal monotectic equilibrium phase diagrams. AlGa: Although Ga is soluble in Al [134,135], it was shown that it occupies a near-substitutioa position in Al after implantation at 293 K [136]. This can be seen from the angular yield curves in fig. 36, where the critical angle ( #1,2) for Ga is smaller and the minimum yield (xti,,) is larger than the values measured for the host. From the difference in I/~,~ it is estimated that Ga is displaced from the substitutional lattice site by 0.015 nm. This is presumably so because Ga has relaxed towards a vacancy at a neighbouring lattice site. After annealing with electron pulses of 150 ns length and a total energy density of 2.5 J/cm*, which leads to an ultrarapid melting and quenching process, complete annealing with a substitutional fraction f, = 1.0 was reached [137,138]. The fact that at fast quenching from the melt a higher substitutional fraction of Ga can be obtained than for systems implanted at 293 K indicates that either ion implantation is not a fast enough quenching process or that a different mechanism affects the substitutionality. After implantation of Ga in Al at 77 K the f, value of 1.0 was determined. As shown in fig. 37, the angular yield curves for Al and Ga match perfectly. From these results one could draw the conclusion that the lattice site occupation mechanism during ion implantation is the result of an ultrafast quenching process of liquid-like thermal-spike regions [140]. This conclusion, however, would not be in accord with the results on the lattice site occupation obtained from the post-irradiation experiments which will be discussed in section 6. Warming up of the AlGa system implanted at 77 K to 293 K leads to a slight decrease off, from 1.0 to 0.93. The angular yield curve of Ga, however, did not change. This result is quite different from the slightly displaced Ga position obtained for the sample as implanted at 293 K. AlGa differs from the systems given below because f, does not change strongly during warmup. Therefore, it is concluded that Ga has a relatively small trapping volume and binding energy for vacancies. AlCd: Cadmium and aluminium are almost completely immiscible in the solid and in the liqa states [134], although this system lies within the limits of the Hume-Rothery rules as is

0. Meyer

418

1.0~10'6Ga'/cm2,

and A. Twos

2OOkeV

in

Al~1.35at.%

Ga

:;

IO-

-u .-Jii >

z OS.N ii E b z 0.0

I

I

I 0.0

10 Tilt

Angle

I

I

t 1 qJ

1.0

(degl

Fig. 37. Angular yield curves of 2 MeV He ions backscattered from an Al single crystal implanted with Ga ions at 77 K [139].

displayed in the Darken-Gun-y plot (see fig. 6). The maximum solubility of Cd in Al is 0.1 at% at 649OC [135]. Previous studies of ion implanted surface alloys of aluminium indicated that Cd is non-substitutional after implantation into Al at 293 K [141] (see fig. 38a). Short laser pulses used for ultrarapid melting and solidification of Cd implanted Al single crystal surfaces did not yield a substitutional component of Cd, indicating that solid solutions cannot be

X

80.10"

Cd?cm*

analyzed

in Al

at 293K,2.0MeV

He+

3.0 .lO"

at 293K, 0 Al <'lo>

Cmolyzed

x Cd 1.0

0.5

(a) I

- 1.0

I

I 0.0

I

L

, 1.0

Cd+/cm'

Iv

in AL

at 77K

I

- 1.0

I

at 77K

.2.0

MeV

I

0.0

E 1.2 at % C

He+

I

o AlcllO> x Cd

I

.l.O

qJ

Tilt Angle (degl

Fig. 38. Angular yield curves of 2 MeV He ions backscattered from an Al single crystal implanted with Cd ions at 293 K (a) and at 77 K (b) [142].

L.arrice site occupation

8.0~10'5

x

I

of non-soluble

Cd'/cm2,200keV

I

I Relative

in

to

implanted

in metals

419

AI11.2at.%Cd

I 0.0

-10 Tilt

elements

I

I 10

4J

cllO>Axisideg)

Fig. 39. Angular yield curves of 2 MeV He ions backscattered from a Cd implanted Al single crystal. The angular curves for Cd are measured at 77, 220 and 293 K. Solid curves are from Monte Carlo calculations [145].

yield

produced by ultrafast quenching from the melt if the components are immiscible [143]. This statement has to be proved by performing pulsed electron or laser quenching experiments at quenching temperatures well below recovery stage III. It was shown previously that defect configurations depend on the quenching temperature [144]. Implantation of Cd into Al at 5 K yielded an f, value of 1.0. When implanted at 77 K, an f, value of 0.94 was obtained for impurity concentrations ranging from 0.2 to 10.2 at% Cd [142,145]. In fig. 38 the angular yield curves for Al and Cd are shown which match nearly perfectly after implantation at 77 K, indicating that 95% of the Cd atoms are at substitutional sites without any relaxation. No effect of annealing on f, could be noted in the temperature region of recovery stage I (- 40 K). The Cd atoms are displaced from their substitutional sites not until about 220 K (see fig. 39) at which temperature vacancies become mobile. At 293 K the displacement increases and the Cd atoms are shifted to interstitial sites of lower symmetry. For this case the angular yield curves closely resemble that of a random distribution of Cd atoms. In order to test these statements, Monte Carlo simulations [84] have been performed the results of which are presented as solid lines in fig. 39. The parameters used for the calculations are as follows: - for the angular scans at 220 K, 80% of the Cd atoms are displaced in the (110) direction with an average one-dimensional displacement amplitude (U,) of 0.016 nm, and 20% of the Cd atoms are at random sites; - for angular scans at 293 K, 80% of the Cd atoms are displaced in the (110) direction with U, = 0.068 nm, and 20% of the Cd atoms are at random sites. There exists a certain fine structure in both calculated and experimental yield curves which strongly depends on the tilt plane. These details are still under study and there is some hope to obtain more information on the specific location of the impurity atoms by analyzing these features.

420

0. Meyer

and A. Twos

,,,.I,,,,,xi

4 O~10'6Cd'/cm2, 8OkeV

-1.0 Tilt Fig. 40. Angular The signals from

in Al^=ll.lat%Cd

0.0 Angle (deg)

yield curves of 2 MeV He ions backscattered Al(O) and Cd(a) are shown for the implanted

1.0 w

from an Al single crystal implanted with 11.7 at% Cd. surface region and from Al(X) for the bulk region [84].

It is generally known that the increase of the implantation dose can lead to the formation of supersaturated solid solutions, to the formation of coherent and non-coherent precipitation, to plastic deformation and to amorphization of the implanted region [146]. Increasing the Cd dose to 10 at% (peak concentration) at 77 K, the f, value stayed constant at 0.94. Upon warming up to 293 K, f, decreased to 0.48 which means that about 50% of the Cd atoms are displaced from the substitutional lattice sites. If only Cd-single-vacancy complexes were formed and no vacancies were lost at other sinks, the saturation concentration of vacancies at 77 K would amount to 5%. This value is in rather good agreement with data from the literature [147]. After increasing the implanted Cd concentration to about 12 at% at 77 K, a plastic deformation of the implanted region was observed. In this case the minima of the angular yield curves for Al in the implanted and in non-implanted regions do no longer coincide. Such effects have been studied in detail for high-dose V-based and Nb-based ion implanted systems [148,149]. The results for the AlCd system are shown in fig. 40. It is seen that the minima of the angular yield curves for the implanted region (up to 100 MI) and the bulk (200 to 300 nm) are tilted by about 0.55 O. In order to force Cd precipitation, two experiments have been performed. In the first experiment a sample produced by high-dose Cd implantation (12 at%) at 77 K was post-irradiated at 77 K with Hg, ions to a fluence corresponding to 1.2 dpa. Hg, ions are used as there is a certain probability that subcascades produced by each Hg ion overlap in time and form regions of high energy densities (see section 3.3). No effect was observed although the deposited energy density amounted to 0.48 eV/at, close to the calculated value of 0.49 eV/at at which the cascade region is expected to become liquid-like [66,150]. Assuming a cascade radius of 1.53 nm [150], a diffusion constant of 5.7 X 10” nm2/s [151] and a cascade lifetime of lo-” s [66], the average diffusion distance of the Cd atoms would be 13 run. This value is much larger than the mean distance, 0.53 nm, between the Cd atoms, calculated from the Cd concentration. As the f, value is not affected by the Hg, bombardment, obviously Cd does not precipitate incoherently; small coherent precipitates may form, however. Coherent precipitates of 10 nm or larger would

Lotrice

‘5ooo

RANDOM 1

site occupation

of non-soluble

1.6.1016 Cd+/cm', and annealed

elements

2OOkeV at 670K

implanted

in metals

in Al at 293K for

421

; 1.9 at.%

Cd

30min. Cd

I

r

x3

0 100 Fig. 41. Random

-IIF

200 and (IlO)-aligned

backscattering

300 Channel Number spectra of an Al single 670 K for 30 min [84].

crystal

c

400 implanted

with

Cd and annealed

at

give rise to an increase of the critical angle for the Cd atoms, similar to the case of coherent Pt precipitates in MgO [152]. From the results of these post-irradiation experiments it can be concluded that neither large coherent nor incoherent precipitates do form. Further results are presented in section 6. In a second approach to force Cd precipitation, annealing experiments above 293 K were performed. After annealing the sample containing 1.9 at% Cd at 520 K for 30 min, no change in f, and the Cd profile was observed. After annealing at 670 K for 30 min, about 10% of the Cd had moved to the surface and formed an incoherent surface precipitate while the f, value of 0.2 for the Cd atoms in the bulk had not changed as demonstrated by the random and the (llO)-aligned spectra in fig. 41. From these results it was concluded that the Cd-vacancy complexes are rather stable, they diffuse as an entity to the surface and form there an incoherent precipitate. Such a behaviour has been observed and studied in more detail for the AlIn system [153] and for the -FeAu system [154]. AlHg: After implantation of Hg into Al at 77 K the f, value is 0.79, independent of the Hg concentration between 0.05 and 0.1 at%. After the sample had warmed up to 293 K, the aligned yield was slightly larger than the random yield (f, = -0.12) indicating that some Hg-vacancy complexes (probably HgV,) had formed. The results are similar to those obtained for the implanted -AlSb system which will be discussed next. AlSb: Aluminium and antimony form an intermetallic phase (AlSb), while the solubility of Sbs Al is 0.25 at% at 933 K [134,135]. Using laser beam melting the solubility at 293 K was enhanced from 0.03 to 0.9 at% [155]. Implantation of about 1 at% Sb into Al at 293 K resulted in a substitutional component of 10% [156]. The non-substitutional component was assigned to

422

0. Meyer

O.O’ Fig. 42.

Angular yield curves of

2 MeV The angular

Tilt

and A. Twos

Angle

(deg)

He ions backscattered from an Al single crystal implanted with Sb ions at 77 K. yield curves of Sb are measured at 77 and 293 K [84].

dislocations and larger Sb-vacancy complexes. The formation of Sb precipitates was not observed and Sb remained submicroscopically dispersed until about 520 K. Implantation of 0.45 at% Sb into Al at 77 K yielded an f, value of 0.73. From the angular yield curves for Sb and Al through the (110) crystal direction shown in fig. 42 it is seen that the critical angles for Sb and Al are the same. After warming up to 293 K the angular yield curve for Sb exhibited a broad peak (f, = - 0.08). Implantation of 0.54 at% Sb at 293 K resulted in f, = 0.12. From the width of the angular scans being the same for Sb and Al it was concluded that 73% of the Sb atoms implanted at 77 K are at substitutional sites. The peak structure of the angular yield curve for Sb after warming up to 293 K indicates the formation of either SbV, complexes (Sb at octahedral sites) or SbV, complexes (Sb at tetrahedral sites). During implantation at 293 K a large variety of different Sb-vacancy complexes seem to form which cannot be distinguished by channeling. AlIn: The equilibrium phase diagram of AlIn is quite similar to that of AlCd. The maximum sol&My of In in Al is 0.04 at% at 909 K [134,135]. Implantation of 0.55 and 1.1 at% In into Al at 77 K yielded an f, value of 0.83. Warming up to 293 K leads to an increase of the non-substitutional fraction of In atoms. Angular yield curves for In at 200,220 , 230 and 293 K are shown in fig. 43. Obviously, there is spme structure in the angular yield curves indicating that some In atoms occupy regular interstitial sites of low symmetry. This is due to the formation of several In-vacancy configurations in this temperature region. A narrowing of the yield curves as has been observed for AlCd, however, did not occur. Implantation of 0.4 at% In into Al at 293 K resulted in an f, value of 0.07. Here again, the corresponding angular yield revealed some fine structure. The lattice site occupation of “‘In in Al has been extensively studied using the PAC technique [118,125,157,158]. About 0.35 at% of In containing a small fraction of ‘i’In was implanted into Al at 80 K. From the PAC results it is concluded that 76 f 1% of the In atoms are at substitutional sites, 8 f 2% formed InV, complexes, 4 + 2% formed InV, complexes and

Lattice

site occupahon

X

6.0~10%/cm2 T,=77K

of non-soluble

290keV

elements

implanted

in metals

423

in Al90.55at.%ln

m l.O.-aJ > 73 .-z 2 0.5&J z

o.o+ -1.0

1.0

0.0 Tilt

Angle

v

(deg)

Fig. 43. Angular yield curves of 2 MeV He ions backscattered from an Al single crystal implanted with In ions at 77 K. The In signals are measured after annealing to 200 K (A), 220 K (A), 230 K (0) and 293 K (m) [84].

12% of the In atoms were located in larger In-vacancy complexes of unknown structure. In comparing these data with the channeling results the agreement is rather good as 8% InV, complexes are included in the substitutional component of 83% as determined by the channeling technique. After the sample had warmed up to 293 K, the PAC measurement yielded 14 &- 3% In at substitutional sites, 16 + 2% In in small In clusters and finally 70% In atoms located in extended defects of unknown structure. Cold implants that had been warmed up to 293 K did not show a substitutional component in the channeling experiment (fig. 43) contrary to samples that had been implanted at 293 K. The general picture of impurity-vacancy complex formation at low-temperature implantation during the lifetime of the cascade and during annealing at temperatures above recovery stage III is corroborated by these PAC results. AlKr, AlXe: after implantation of Kr the substitutional fraction was 0.49 and 0.47 at 5 and 77x, res&tively, for concentrations up to 0.2 at%. For Xe a substitutional fraction of 0.33 was measured at 77 K. Noble gas atom-vacancy complexes usually have low migration energies and tend to form bubbles. The concentration of 0.2 at% used in this study is below concentration values for which bubble formation has been observed [159]. As angular yield curves have not been measured, it is not possible to state that Kr and Xe atoms are located at substitutional sites. The estimated values of AH,,, and AHsize for noble gas elements in Al, Fe and V should be considered with caution. Since the bulk moduli (B) are known, the AHsize values may be correct. Rather low values of 0.8 for the electronegativities were assumed here to estimate AH,, [160]. The n,, values were estimated from the B versus nws relation [161]. AlPb: Al and Pb form a monotectic system. The solubility of Pb in solid Al is not higher thG0.025 at% Pb at the monotectic temperature [135]. The separation of immiscible melts of AlPb has been studied under reduced gravity and no alloying has been observed [162]. After ~plantation of Pb into Al at 5, 77 and 293 K the substitutional fractions were 0.76, 0.59 and

424

0. Meyer

1

5.5~10'5Pb'/cm2,3COkeV

0 -0

5 s

lo%

x Jj

and A. Twos

in Al;l.O3at.%Pb

0

LPAoooooooooooo

0000000 &%P+

lAAA c\

A

0

_

A 1

z

A

$

,^AA

AAA) A~AAA

2

OS-

7 B

&I

0 Al

A Pb q

1

IIK

98

1 293K

Pb

0.0

I I 0.0 1.0 Tilt Angle (deg) Fig. 44. Angular yield curves of 2 MeV He ions backscattered from an Al single crystal implanted The angular yield curves of Pb are shown after implantation at 77 K and after annealing I

-1.0

with Pb ions at 77 K. at 293 K [139].

0.0, respectively. At 5 and 77 K the substitutional fraction was independent of the concentration in the range between 0.06 and 1.03 at%. As can be seen from the angular yield curves presented in fig. 44 the critical angles for Pb ( #1,2 = 0.65 ’ ) and Al (#,,, = 0.67 ’ ) agree rather well, indicating that a fraction of the Pb atoms is located at substitutional sites. AlRb, AlCs: The solubility of Rb and Cs in solid Al is negligible. Both species were im$anted%to Al at 293 K with a peak concentration of about 1 at%. For Rb an f, value of -0.07 and for Cs a value of 0.12 were measured [55]. The f, value of Rb implanted at 77 and 293 K is close to 0.0. The angular yield curve of Rb implanted at 77 K revealed some fine structure indicating that some Rb atoms occupy interstitial lattice sites. This fine structure disappeared after the sample had been warmed up to 293 K. The substitutional fractions of Cs implanted at 5, 77 and 293 K are 0.0, 0.0 and 0.13, respectively. The angular yield curve for the 293 K implant is rather narrow, indicating that only a near-substitutional fraction does exist. Warming up the 5 K implant to 293 K leads to a peaked angular yield curve with f, = -0.17. This result indicates that one type of a Cs-vacancy complex with the Cs atom located near the octahedral site is preferentially formed during annealing above stage III [84]. 5.2 Iron-based ion implanted systems

Many experiments have been performed to determine the lattice site location of ions implanted into Fe at 293 K. Both the backscattering/channeling and the hyperfine interaction techniques have been used for this purpose. A first review on such studies in Fe and a comparison of the results obtained with these techniques was presented by de Waard and Feldman [163]. A compilation of all known results up to 1979 was given by Thorn6 et al. [164]. These authors related the substitutional fraction to the normalized difference between the atomic radii of the impurities and the Fe host and observed that f, decreases linearly with

httice

site occupation

of non-soluble

elements

implanred

in metals

425

increasing normalized radius difference. They studied mainly the lattice location in Fe at temperatures between 293 and 800 K and interpreted their results in terms of vacancy migration towards the impurity and migration of the so formed impurity-vacancy complexes. A detailed study on vacancy-assisted impurity migration at temperatures from 293 K up to 950 K has been performed for the implanted FeAu systems [154]. Lattice location studies below 293 K were not performed because it was generally believed that f, is temperature independent up to at least 293 K [45,165,166]. In this context it is worthwhile to note that an increase of substitutional fractions had been observed using Mijssbauer spectroscopy for Xe and Te implanted into Fe at 90 K [167]. These impurities belong to the group of elements with a positive heat of solution in Fe, which is treated in this section. In a systematic study [168] the systems FeAu, FeSb, FeHg, FeBi, FePb and FeCs had been chosen because they have increasing, positive values of the hearof solution. Thesystem FeCs has a AH,,, value of 518 kJ/mol which is the largest value of all iron-based alloys. As in Fzhe recovery stage I, for free migration of SIAs is at 140 K and that for vacancies is at 200 K (see table 2), it is not possible to study the interaction between impurities and SIAs on the one hand and between impurities and vacancies on the other hand separately by just implanting at 77 K and 293 K. From the results described here for the Al- and V-based ion implanted systems it is inferred, however, that the impurity-SIA interaction does not influence the lattice location of oversized impurities. A further support for this statement is due to PAC results obtained for the FeIn system, which has a positive AH,,, value similar to that of FeHg. After implantation of In &o poly- and mono-crystalline Fe at 80 K, 55% of the In atoms were at substitutional sites. The substitutional fraction decreased to 40% at 210 K due to vacancy trapping, and subsequently increased to 0.55 by detrapping at 293 K [169]. Mossbauer spectroscopy of ‘19Sn implanted into Fe at temperatures between 100 and 500 K essentially supported the PAC results and it was proposed that a certain fraction of the Sn impurities is located in large vacancy clusters which are formed within the lifetime of the collision cascade [170]. FeAu: Although Au in Fe does not satisfy the Hume-Rothery rules very well, a limited solubility has been reported [171]. Therefore, one could expect the substitutional fraction to be close to 1.0 at low Au concentrations, and to decrease eventually at high concentrations when precipitation occurs. In agreement with this expectation, in situ analyses after the implantation of Au into Fe at 77 K yield a substitutional fraction of 1.0 independent of the implanted Au concentration in the range of 0.1 to 2 at% [172]. The experimental results after implantation of Au into Fe at 293 K, however, show the opposite trend: the substitutional fraction increased monotonically from 0.6 at 0.1 at% Au up to 1.0 for Au concentrations above 1.0 at%. Even at the highest implanted concentration of 7 at% this value of f’ did not change, although the solubility limit was exceeded by a factor of more than 70 [154]. The value f, = 0.85 was also reported previously for low-dose Au implants produced at 293 K [164]. The mechanism which causes this unusual concentration dependence of f, for 293 K implants will be discussed in more detail in section 6. Warmin g up a 77 K implant to 293 K did not lead to a change of f, for the FeAu system. However, prolonged irradiation with He ions at 77 K, e.g. during the measure&&t of an angular yield curve, may lead to a decrease of f, after warming up to 293 K. Such post-irradiation effects are also described in section 6. FeSb: The solubility of Sb in Fe has not yet been determined accurately [134,135]. After im$krtation of about 0.15 at% Sb into Fe at 293 K, the critical angles for Sb and Fe were the same indicating that about 90% of the Sb atoms are at substitutional sites [163]. After implanting Sb into Fe at 77 K, the angular yield curves of Sb and Fe matched nearly perfectly resulting in an f, value of 1.0 [168].

0. Meyer

426

and A. Twos

FeHg: According to ref. [134], Hg is insoluble in solid Fe. The substitutional fractions observed after implantation at 293 K and 77 K are rather close to the values obtained for -FeSb: 0.9 and 1.0, respectively [168]. FeBi: Neither liquid nor solid solubility values could be found for Bi in Fe [134]. First lattice location studies on 293 K implants of Bi in Fe yielded an f, value of about 0.80 [173]. The substitutional component decreased for annealing temperatures above 670 K. Detailed angular scan studies [174] for Bi implanted into Fe at 293 K yielded a complex behaviour, indicating three possible lattice positions: 40% of the Bi atoms were at substitutional sites, 30% were slightly displaced from their substitutional sites, probably due to vacancies trapped at nearestneighbour lattice sites, and 30% were randomly distributed. The random fraction was observed only by the angular yield curve through the (110) direction. From this result it was concluded that the random component is associated with dislocation loops and single vacancies. Slightly different results have been obtained after implanting 0.25 at% Bi at 300 keV into Fe at 293 K. Under these implantation conditions no substitutional component was observed [31]. As can be seen in fig. 45, the angular yield curves for Bi through the (100) axial direction (fig. 45a) and through the (111) axial direction (fig. 45b) are narrower than those for the Fe atoms. The solid lines were obtained from Monte Carlo calculations in which the one-dimensional thermal vibration amplitude (V,) and the random fractions of Fe and Bi were treated as parameters to be fitted to the experimental results. For the Fe lattice, a value U, = 0.0061 nm was used, corresponding to a Debye temperature of 430 K. The Bi atoms were assumed to have the same thermal vibration amplitude. The curve for Fe in fig. 45a was calculated assuming that 12% of the Fe atoms are at random positions; that for Bi was calculated assuming that 39% of the Bi atoms are at random positions and 61% of the Bi atoms are at near-substitutional sites with a displacement of 0.012 nm in the (111) direction, probably due to the presence of a

(al

(b1

I O.ZSat%

T, =T,., :293K

I

I

-2

-1

Bi TI =T,., : 293K

I

I

I

0 '1 2 W (deg) Fig. 45. Angular yield curves of 2 MeV He ions backscattered from a Fe single crystal implanted with Bi ions at 293 K. (a) Angular yield curves of Fe and Bi through the (100) axial direction. (b) Angular yield curves of Fe and Bi through the (111) axial direction. The solid lines are from Monte Carlo calculations [31].

Latrice

sire occuparion

of non-soluble

elements

(al

implanred

in metals

421

(bl

0.20at%

Bi

TI =77K TM = 77K

TM = 293K

xxx

-2

,fs :0.92, -1

l @

0 ‘Y (deq)

, f =0.7 , 1 2

Fig. 46. Angular yield curves of 2 MeV He ions backscattered from a Fe single crystal implanted with Bi ions at 77 K. (a) Angular yield curves for the as-implanted system at 77 K. (b) Angular yield curves after annealing to 293 K. The solid lines are from Monte Carlo calculations [31].

vacancy on the nearest-neighbour lattice site. The curves for the (111) axial direction shown in fig. 45b were calculated assuming that 8% of the Fe atoms are at random positions, 37% of the Bi atoms are at random positions and 63% of the Bi atoms are at near-substitutional sites again with a displacement of 0.012 nm in the (111) direction. The deviation of these results from those reported in ref. [174] may be attributed to the fact that a delicate balance exists between formation and dissolution of vacancy-impurity complexes on the one hand and the production of different competing vacancy sinks in Fe on the other. Such processes will strongly depend on the dose rate, the dose and the substrate temperature during implantation (see section 6). From this it is obvious that slightly different implantation conditions will change the substitutional component at 293 K to a great extent. A high substitutional lattice component of 0.92 has been obtained by implanting Bi in Fe at 77 K. This is demonstrated in fig. 46a, from which it is seen that the critical angles for Bi and Fe are very similar. Annealing of the 77 K implant to 293 K leads to the displacement of an additional 23% of the Bi atoms from their substitutional sites. As can be seen in fig. 46b, the critical angles for Bi and Fe are still of similar size in contrast to the results obtained for 293 K implants. From these results it was concluded that during annealing at 293 K Bi atoms move to sites of low symmetry due to Bi-multiple-vacancy complex formation indicating that multiple-vacancy clusters become mobile and are trapped by the substitutional Bi atoms. In this case the deviations between the Monte Carlo simulations assuming random positions and the experimental results for Bi in fig. 46b are a direct hint that the Bi atoms are located at sites of low symmetry [31]. FePb: The solubility of Pb in Fe at the monotectic temperature (1808 K) is 0.17 at % [134]. Firxlattice site location studies of -FePb systems produced by implanting Pb into Fe at 293 K

428

0. Meyer

I

and A. Twos

o-

0 - Fe

Fe

TI =77K POSTIRRADIATED AT 77K WARMED UP TO 293 K

y 1 ;“b

(b) I I O-IL

I 0.7

I 0

I 0.7

I 1.L

0’

’ -14

I -07

yield curves

of 2 MeV

I 07

I 1.L

q.~(degl

9 (degl Fig. 47. Angular

I 0

He ions backscattered from a Fe single (a) and at 77 K(b) [168].

crystal

implanted

with Pb ions at 293 K

to a maximum peak concentration of 0.25 at% yielded an f, value of about 0.84 [163]. As expected from similar AH,,, values this is in close agreement with the value of 0.82 obtained after implanting Bi into Fe at 293 K to a peak concentration of 0.15 at% [168]. As the critical angle for Pb is very close to that of Fe (see fig. 47a), it is concluded that 82% of the Pb atoms are at substitutional sites without relaxation, while 18% of Pb atoms are located at positions of low symmetry. After implanting Pb into Fe at 77 K, a substitutional fraction of 0.94 was obtained (fig. 47b) which decreased while the sample was warmed up to 293 K. The amount of decrease depended strongly on the number of vacancies produced by the He beam used during the analysis at 77 K. As discussed before, these results can be explained in terms of impurity-vacancy interactions within the lifetime of the collision cascade and afterwards during annealing procedures.

FeBa, FeCs: Ba and Fe as well as Cs and Fe systems form monotectic systems. The solid sol?bilityf Ba and Cs in Fe is negligibly small [134]. For 0.15 at% Ba unplanted into Fe at 293 K, no substitutional fraction could be determined. The angular yield curve revealed some fine structure which indicated that Ba is located at lattice sites of low symmetry. After implanting Ba into Fe at 77 K, 60% of the Ba atoms were located at substitutional lattice sites. A decrease of f, was noted during warming up to 293 K [168]. The lattice site location of ‘*‘Cs implanted into Fe at 293 K to a dose of about 1 x 1014 at/cm* was investigated by means of Miissbauer spectroscopy. Four components with different values of the magnetic hyperfine field were observed in the spectrum and assigned to four different local environments of the probe atom, the component with the highest field (30%) corresponding to a substitutional Cs atom [175]. The channeling measurements for the FeCs system yielded substitutional components of 0.4 and 0.15 for Cs implanted into Fe at 77K with peak concentrations of 0.15 and 0.3 at%, respectively. The angular scan curves in fig. 48 show that the critical angle for Cs is similar to that of Fe, indicating that 40% of the Cs atoms are located at substitutional sites without relaxation [168].

Lattice

site occupation

of non-soluble

elements

implanted

O.O7at.%Cs T,=T,=77K

E

. xx

txx

F Cl

xx

l . XXX/X* Xx x . . xx

0.5

l .

a x cx cx

curves

of 2 MeV

..

l . . .

..

*Fe<1007 -1

yield

.

..

i? i?

Fig. 48. Angular

429

.x

1.0 0

in metals

..

x cs

0 TILT ANGLE Idegl

He ions backscattered 5 K [168].

from

1 a Fe single

crystal

implanted

with

Cs ions

at

Channeling analysis of the FeCs system produced at 293 K did not reveal any substitutional component, in disagreement Gth the Mossbatter spectroscopy results. It should be noted, however, that smaller Cs concentrations have been used in the Mijssbauer experiment. 5.3. Vanadium-basedion implanted systems

In a systematic study of the behaviour of implanted ions in vanadium it became obvious that highly non-soluble elements like Ce, La, Ba and Cs were substitutional to an extent which depends strongly on the substrate temperature during implantation [176]. In contrast elements which were highly or slightly soluble exhibited f, values of 1.0, independent of the substrate temperature. _VBi, VPb: Bi and Pb have a rather low solid solubility in V at 293 K [134,135]. Pt atoms occupy substitutional lattice sites in V after implantation at 293 K with peak concentrations between 0.1 and 0.6 at%. This is shown in fig. 49 by comparing the random and (Ill)-aligned backscattering spectra for a V single crystal implanted with 300 keV Pb ions. The large reduction of the scattering yield from the Pb atoms in the aligned spectrum relative to that of the random one shows that all Pb atoms occupy substitutional lattice sites [83]. Bi atoms were observed to occupy substitutional lattice sites if implanted into V single crystals at 293 K up to a concentration of about 4 at% [177,178]. After implantation of Bi in V at 5 K the f, value was also 1.0 [176]. This result shows that replacement collisions do not play an important role as a basic process for the lattice site occupation as has been discussed in section 3.5. VCe, VLa: Ce and La are not soluble in V [134,135]. La atoms occupy non-substitutional la&e sites if implanted into V at 293 K, even at the fairly low concentration of about 0.07 at%. However, about 60% of the La atoms occupy substitutional lattice sites if implanted at 5 K or 77 K [176]. The substitutional fraction decreases to 0.37 when the peak concentration is

0. Meyer

430

and A. Twos

ENERGY WINDOW 9000 -

2

5 s

5 w >

---*\

l\

‘----I

l1.\

0.52 at % Pb In V 2MeV

1

-2

He+

I

l----* ’

1

-.-

RANDOM

\

-o-

< 111, ALIGNED

ii

TI = TM = 293K

Fig. 49. Random and (Ill)-aligned

f+”

li

CHANNEL NUMBER backscattering spectra from a V crystal implanted with 0.52 at% Pb at 293 K 1831.

increased to about 2.3 at% La, probably due to La precipitate formation. Warming up a sample implanted at 5 K to 293 K leads to a reduction of f, from 0.58 to 0.46 which occurs in the temperature region above 200 K due to vacancy trapping. The implanted YCe system has been studied in great detail [179]. The substitutional fraction of 0.1 at% Ce atoms implanted in V depends on the substrate temperature during implantation and is 0.73, 0.73 and 0.15 at 5, 77 and 300 K, respectively. Increasing the implanted Ce concentration at 293 K to 3.3 at% leads to an anomalous increase of f, from 0.15 to 0.66. The origin of this behaviour will be discussed in more detail in section 6.4. Warming up the sample implanted at 5 K to 293 K results in a decrease of f, from 0.73 to 0.65 in the temperature region above 200 K. me: Xe implanted into V at 293 K and at 5 K reveals a large near-substitutional fraction. This is demonstrated by the angular yield curves for V and Xe as shown in figs. 50a and 50b. The ratio of the critical angle for the Xe atoms to that for the V host atoms is smaller than 1.0, even after implantation at 5 K. After warming up the 5 K implant to 293 K (fig. 50~) the ratio of the critical angles decreases and is similar to that obtained after direct implantation at 293 K P31. VBa, VCs: Ba and Cs are in soluble in V in the solid as well as in the liquid phase [134]. The substitutional fraction of 0.1 to 0.2 at% Ba implanted into V at 5,, 77 and 293 K amounts to 0.43 f 0.02, 0.46 f 0.05 and 0.0, respectively. At 5 K the f, value decreases to 0.09 when the Ba concentration is increased to 0.6 at%. It was noted that the same value of f, is obtained for the (111) and the (110) crystal directions. Warming up a sample implanted at 77 K to 293 K resulted in a reduction of f, from 0.46 to 0.35 (see fig. 55b). This decrease can be enhanced by post-irradiation with He ions as will be discussed in section 6.1.

Luttice

site occupation

of non-soluble

elements

implanted

in metals

431

0.34 at. % Xe in V TI qTM =300K lo-

05-

1 0.5 at% Xe In V

0:

I

T, Z-L.. = SK lo-

OS-

‘. \

/

‘1.,;‘4) v (11 Xe qJ,,2=0.700 4J,,*=1.0 Xm,n=0.31 X,,,," = 0.60 I I 0.5 at. % Xe in V 0

07

lo-

0.5 -

0 Xe qJ,,*=0.440 X,,,," = 078 OL

-2

-1

l

I 0

V(l>

q&=0.76 xmln=0.4E I I 1

2

TILT ANGLE ldeg) Fig. 50. Angular

yield curves

of 2 MeV He ions backscattered (a), at 5 K(b) and after warming

from a V single crystal implanted up from 5 K to 300 K (c) [83].

with Xe ions at 300 K

The substitutional fractions of Cs atoms implanted into V to concentrations between 0.02 and 0.2 at% are 0.65 + 0.08, 0.5 &- 0.08, and 0.14 f 0.08 at 5, 77 and 293 K, respectively. As the critical angle ratio is 1.0, the Cs atoms occupy substitutional lattice sites. Upon annealing to 400 K, f, decreasesto 0.0 for all samples implanted at temperatures below 100 K. This was observed for both the (111) and (110) crystal directions. Increasing the Cs concentration to 0.85 at% leads to a decreaseof f, from 0.5 to 0.3 for 5 K as well as for 77 K implants. Plastic deformation of the implanted region is observed upon implantation of 3 at% Cs into V at 77 K [149].

0. Meyer

432

and A. Twos

CI = 0.1- 0.2 at.%

YBi IO- AaCd -o&&l fs _ q VBa l

A

0

0.5 -

0.0

Fig. 51. The substitutional implantation

0

1

5

lo

So

T,(K)

100

c.,

fraction (/,) of various implanted systems as a function of the substrate temperature (T,). The dashed lines indicate the decrease off, during warming up to 293 K [180].

during

5.4. Summary and conclusions

The substitutional fractions of non-soluble elements implanted into Al, Fe and V single crystals depend strongly on the substrate temperature during implantation. This is demonstrated for various systems in fig. 51. A strong decrease is noted for 293 K implants while f, remains nearly constant for implantation temperatures below 100 K. It has been shown that the non-substitutional components depend on the heats of solution and the size-mismatch energies. The experimental values of f, for the as-implanted Al, Fe and V hosts are summarized in tables 5, 6 and 7, respectively. Further included in the tables are the A Hso, and AHSiZe values as determined from eqs. (2.1) and (4.5) for diluted alloys. In figs. 52, 53 and 54 the substitutional fractions for the as-implanted samples have been plotted versus the total energy, AH, which is the sum of AH,,, and A Hsize.This procedure is justified by recalling that the impurity-vacancy binding energy is proportional to AH,,, and the trapping radius is proportional to AHSiZe (see section 4.4). The main trend in figs. 52, 53 and 54 is the decrease of the substitutional component with increasing total energy. This decrease is attributed to the interaction of the Table 5 Summary

of the substitutional

fractions

(f,)

Implanted element

AHso, @J/m00

A%, (kJ/mol)

Ga Sb Cd Hg In we We) Pb Rb cs

3.7 11 14 17 30 36 44 49 134 151

4.3 48 9.4 13 34 28 68 68 316 339

for various

elements

as-implanted

into AI at 5, 77 and 293 K

f, SK 1.00

0.49 0.76 0.03

77 K 1.00 0.73 0.94 0.79 0.83 0.47 0.33 0.57 0.02 0.00

293 K 0.87 0.11 0.14 0.07

- 0.02 0.13

Concentration (at%) 0.75-1.35 0.45-0.51 0.20-11.7 0.05-0.10 0.10-1.10 < 0.20 < 0.20 0.06-1.03 0.10-1.50 0.03-0.20

L&rice Table 6 Summaty

of the substitutional

site occupation

fractions

(j,)

of non-soluble

for various

elements

elements

implanted

as-implanted

in metals

into Fe at 77 and 293 K

Implanted element

A &I (kJ/mol)

Wizc W/mob

fs 77 K

293 K

Au Sn Sb

37 56 57 105 146 159 242 259 518

37 188 186 70 254 241 610 116 531

1.0

0.65 (1) 0.85 0.9 0.9 0.7 0.83 0.0 0.45 0.0

Hg Bi Pb Ba VW cs

1.0 1.0 0.92 0.96 0.6 0.65 0.45 (0.1)

433

Concentration (at%) 0.1 (7) 0.1 0.1 0.1 0.1 0.1 0.1 0.1 (0.3)

implanted impurities with vacancies which causes a displacement of the impurities from their substitutional sites. The reduction of f, is strongest during warming up to 293 K or during implantation at 293 K, i.e. above stage III. At temperatures below 100 K, where vacancies are immobile, the elements with large AH values still have non-substitutional components which cannot be attributed to the trapping of freely migrating vacancies. On the other hand, these non-substitutional fractions also cannot be attributed to impurity precipitate formation as the average distance between the impurities is about 3 nm and diffusion is negligible at low temperatures. Further, the fraction of non-substitutional atoms does not depend on the concentration of the impurities in the concentration range between 0.02 and 0.03 at%, contrary to what would be expected in the case of precipitate formation. Thus the only explanation for the non-substitutional fractions is that the impurities trap vacancies already during the cooling phase of the collision cascade with a probability, which increases with increasing AH. This is due to elastic distortions, caused by the size mismatch, in the neighbourhood of the impurity at the substitutional lattice site. From molecular dynamics calculations of the development of the collision cascade with time it is known that during the cooling phase of the cascade (- lo-‘i s) point defects are able to make Table 7 Summary

of the substitutional

fractions

(j,)

for various

elements

as-implanted

Implanted element

Wo, W/moU

AHsize (kJ/mol)

fs

Se As Te Au I Sn Bi Pb Ce La

-200 - 161 -115 -86 -41 -4 57 80 126 190 335 384 680

0.55 21 193 12 178 122 177 164 158 234 92 483 438

-

WeI Ba cs

5K

into V at 5, 77 and 293 K

77 K

293 K

1.0

-

0.73 0.58 0.57 0.45 0.65

0.73 0.56 0.45 0.4

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.1-0.4 0.08 (0.48) 0.0 0.0

434

0. Meyer

and A. Twos

1.0 f*

Host

\

Lattice:

Al

0.8

i% c 0.4 .o+ 3

c

A .-) -=-A

0.0

-0.2 r 0 Fig. 52. Substitutional

100 fraction

AH,,,

150

(kJ/mol)

200

of various ions implanted into Al single crystal at 5, 77 and 293 K and after to 293 K (+) as a function of the total energy AH [84].

annealing

about 100 jumps (see section 3.3). As the impurity-vacancy binding energy is proportional to the heat of solution a decrease is observed with increasing AH,,, as well as with increasing AH,,. As discussed above the trapping of vacancies by impurities in the cascade was observed

fs

A o

293K 77K

AH = Ah S,ZE+ AH

SOL

3a

Fig. 53. Substitutional

fractions

of different

ions implanted into Fe single crystals of the total energy AH [168].

at various

temperatures

as a function

Lnttice

site occupation

of non-soluble

elements

implanted

in metals

435

AH = AHSIZE+ AHSoL 00

~, 0 Fig. 54. Substitutional

fractions

200 of different

400

700

AH[ kJ Imoll

ions implanted into V single crystals of the total energy AH [146].

at various

temperatures

as a function

by PAC measurements for the system -AlIn produced at 80 K [157], and for -FeIn produced at 100 K [170]. From the results on the lattice site occupation of Al-, Fe- and V-based ion implanted systems the following conclusion can be drawn: (i) The empirical models which are based on the thermodynamic equilibrium fail in predicting the substitutionality of soluble and non-soluble elements implanted into Al at 293 K and of non-soluble elements implanted into Al, Fe, and V at temperatures below 100 K. The apparent success of the empirical methods to predict the substitutionality of atomic species implanted in host metals like Fe, V and Cu is due to the fact that the impurity-point-defect interaction depends on the heat of solution and on the size-mismatch energy. Due to these dependencies the alloying models based on the h&edema parameters have an apparent success to separate substitutional from non-substitutional systems although the real mechanism which causes the non-substitutional component is the displacement of oversized impurities from their substitutional sites by the interaction with vacancies. (ii) Replacement collisions are also not an important process for the lattice site occupation of the implanted impurities. As is clearly demonstrated by the results shown in fig. 16, the f, values obtained for implants performed at 5 K do not correlate with the calculated replacement collision probability. (iii) The basic mechanism for the lattice site occupation of impurities in metals is the spontaneous recombination of the impurity atoms with the lattice vacancies during the relaxation phase of the collision cascade which leads to the occupation of the substitutional site. This process is similar to recombination of close Frenkel pairs (see also section 6.3).

6. Stability of vacancy-impurity complexes during post-irradiation

In section 5 we have shown that non-soluble oversized impurities are able to trap vacancies either in the cooling phase of the collision cascade or by annealing the samples above stage III

436

0. Meyer

and A. Twos

where vacancies and small vacancy clusters become mobile. The formation of vacancy-impurity complexes does depend on many parameters such as the trapping radius of the impurities, the concentration of mobile vacancies and the concentration of other vacancy traps. Some experiments have been performed to study the formation probability of vacancy-impurity complexes which will be described in section 6.1. Defect-antidefect reactions have been used to annihilate vacancy-impurity complexes (see section 4.2.2). For example, it should be possible that these complexes annihilate by absorbing mobile SIAs which are produced during postirradiation at temperature above stage I. The results of such experiments will be discussed in section 6.2. In the course of these experiments it was noted that vacancy-impurity complexes can dissociate during post-irradiation even at temperatures below stage I. This mechanism has been studied in more detail and the results provide some information on the various processes which occur during the lifetime of the collision cascade (section 6.3). The equilibrium between complex formation and complex dissociation in the cascade may be disturbed by the formation of an increasing density of competing trapping centers during post-irradiation. Such a process may lead to an anomalous increase of the substitutional fraction as will be discussed in section 6.4. 6.1. Vacancy-impurity

complex formation

In section 5 it was shown that metastable Al-based alloys produced by ion implantation at ,temperatures below 100 K usually exhibit a high substitutional component which decreases strongly during annealing at 293 K due to the formation of vacancy-impurity complexes (see e.g. figs. 39 and 43). The decrease of f, was minor for Ga indicating that this soluble element has a small trapping radius. For the Al&d,, system it was estimated that the lower concentration limit of free vacancies amounts to at least 5 at% (see section 5.1). Such an effect was not observed for V- and Fe-based alloys in which case a decrease of f, during warming up of low-temperature implants was only noted if extended irradiation with the analyzing He beam had taken place at low temperatures. As a possible explanation it is suggested that in V and Fe the vacancies have a low nucleation barrier and form vacancy clusters. These clusters can trap additional vacancies with large binding energies while this is not the case for vacancies in Al. The impurity-vacancy complex formation probability in V and Fe can be enhanced by post-irradiation with He ions at 77 K in order to produce randomly distributed point defects and subsequent annealing at 293 K. The interstitials are mobile and can migrate to sinks while some vacancies which have survived the recombination and clustering become mobile during warming up. In order to study the formation probability of the complexes, 77 K implants of VCe (0.13 at% Ce) and of VBa (0.11 at% Ba) were produced with f, values of 0.73 and 0.46, respectively. After the samples had been warmed up to 293 K, f, decreased from 0.73 to 0.62 (15%) in the case of J&e and from 0.46 to 0.35 (24%) in the case of VBa. Post-irradiation with 200 keV He ions to a dose of 1 X 1016/cm2 did not change the f, values of the YCe and the VBa samples. Warming up to 293 K led to a decrease of I, from 0.65 to 0.2 (69%) for the VCe sample and to a decrease from 0.35 to 0.09 (74%) for the VBa one. The results of this procedure are demonstrated for the VBa system in fig. 55. Fig. 55a shows the angular yield curves for Ba and V after implantation of Ba at 77 K. The critical angle for Ba is slightly smaller than that for V which indicates that the Ba atoms are somewhat (- 0.01 nm) displaced from their substitutional lattice sites. Warming up to 293 K (fig. 55b) results in a decrease of f,, while post-irradiation with He ions at 77 K and subsequent annealing at 293 K leads to an even stronger decrease of f, (fig. 55~). Similar results were observed for the ~CS system. In addition,

Lotrice

site occupation

of non-soluble

X,,=

elements

0.5 -

I

I

i

\

8 N x

Ba

JI,,,

=

d

MY3 0.71 I

\

I l

i

4-/

(J,,, = 0.67O 0.83

0.8L0

111)

I

= LNzT

ANNEALED UP

/ ? \

/

‘\

(

=

I

!

Ba

v

Xmn = 0.17

I

TI=TH

x,,,:

437

I

(Jr2

0

x,,,= I

x

in metals

0 61 I

z s

implanted

Ye,

/

l

TO

RT

V

lJJ,,2= 0.85O Xmm- 0.17

Fig. 55. Angular yield curves of 2 MeV He ions backscattered from V single crystals implanted with Ba ions at 77 K (a) for the as-implanted sample; (b) after implantation at 77 K, annealed at 293 K and measured at 77 K; (c) implantation at 77 K, post-irradiated with 200 keV He ions to a fluence of 1 x 1016/cm2 at 77 K, annealed to 293 K and measured at 77 K [181].

77 K implants of _VCswith f, values of 0.6 + 0.05 were post-irradiated at 77 K with 600 keV Bi ions to fluences up to 1.0 x 10’4/cm2 without any noticeable change of f, [181]. Several conclusions can be drawn from these results: (a) The non-substitutional component observed for several non-soluble elements implanted into V at temperatures below 100 K is rather stable, indicating that the vacancy-impurity

0. Meyer

438

and A. Twos

o - Fe

l

AS IMPLANTED

- Au

at 77K

1.0

0.5 9 Y s 0.0 b! 2 g4 1.0

I I

I

I I

POSTIRRADIATED

I I

I I

WITH ‘He- IONS AT 77K

0.5

0.0

Fig. 56. Angular

I

-1.0

I

I

0 q Ideg)

I

I

I

1.0

yield curves for 2 MeV He ions backscattered from Fe single crystals implanted with Au ions at 77 K (a) and after post-irradiation with He ions and subsequent warming up to 293 K [172].

complex formation and dissociation within the cascades does not depend on the cascade density during implantation or during post-irradiation with light and heavy ions at 77 K. (b) When the implanted YCe and VBa samples are post-irradiated with He ions at 77 K, a certain amount of vacancies survive the recombination and clustering processes. These vacancies become mobile upon warming up and can be trapped by the impurity atoms. The trapping efficiency of Ba and Cs is slightly higher than that of Ce. This enhanced trapping radius for Ba and Cs is more clearly demonstrated during implantation at 293 K where the f, values for Ba and Cs are 0.0 and independent of the impurity concentration while that for Ce is small (0.15) for low Ce concentrations and increases with increasing Ce concentration (see section 6.4). Similar post-irradiation experiments were performed on Fe-based alloys produced by implantation at 77 K [168]. All samples were implanted at 77 K t9 the peak concentration of 0.15 at% and post-irradiated at 77 K with 200 keV He ions to a fluence of 2 x 1015/cm2. As an example, the angular yield curves of Au and Fe are shown after implantation of Au at 77 K, and after post-irradiation with He ions at 77 K and annealing at 293 K (fig. 56). The f, values obtained after implantation at 77 K and after post-irradiation at 77 K followed by annealing at 293 K for various systems are summarized in fig. 57. Cold implants have large f, values which

Lattice

site occupation

Au SbHg

fs

1.0 -

of non-soluble

BiPb

elements

Ba

implanted

in merals

439

CS

l ----l.. A-AA,

d

200

400

600

aH[kJ/moll Fig. 57. Substitutional fractions of different ions implanted into Fe single crystals at 77 K (0). then post-irradiated 200 keV He ions to a fluence of 2 X 10t5/cm2, at 77 K and annealed at 293 K (A) [168).

with

are 1.0 for systems with AH values below 200 kJ/mol. The f, values decrease to a value of 0.35 with increasing AH. Post-irradiation with He ions at 77 K followed by annealing to 293 K leads to a decrease of the f, values by an amount which increases with increasing value of AH. This fact indicates that the trapping radii of these insoluble elements also increase with increasing AH. It is conjectured that such a change of the non-substitutional component for low-temperature implants has the same origin: the increase of the trapping radius with increasing AH leads to an enhanced trapping probability within the cooling phase of the cascade. It was noted that annealing at 293 K without post-irradiation leads only to a slight decrease of f,, indicating that either only a few vacancies survive the recombination processes in the dense collision cascade or that a high concentration of competing traps does exist. Further, it was noted that f, did not change after post-irradiation at 77 K, similar to the results obtained for V-based implants discussed above. 6.2. Defect-antidefect

reactions

The rather large non-substitutional components observed after implanting insoluble elements into V, Fe and Al at 293 K could consist of impurity precipitates, formed by radiation-enhanced diffusion, or of vacancy-impurity clusters. Post-irradiation with light and heavy ions should provide some information on that question. Light ion irradiation would be an effective means to produce well separated point defects and the SIAs which are mobile at 77 K would annihilate the complexes. This mechanism was used to enhance the f, values of AlIn and Al!% samples, where the impurities had been displaced in advance from their substitutional sitesdue to vacancy trapping at 200 K, by post-irradiation with 1 MeV He ions at 70 K [117,182]. In contrast, irradiation with heavy ions would, by recoil dissolution, provide an effective means to dissolve precipitates if they existed. Dissociation of vacancy-impurity complexes within the displacement spike is also a possible mechanism to be considered. In order to test these assumptions, 293 K implants of YCe were cooled to 77 K and subsequently post-irradiated with 200 keV He ions [179]. The results of these post-irradiation experiments are summarized in table 8. With increasing He-ion fluence f, increased and

0. Meyer

440

and A. Twos

Table 8 Influence of post-irradiation with implantation at room temperature

He ions

at 77 K on the substitutional

Ce (at%)

Fluence

(He/cm*)

0.08

0 2 X10’S 5 X10’S 1.8~10’~ 0 2 x10’6 0 2 x1016

0.17 0.3

fraction

of YCe

systems

produced

by Ce

I,( + 0.05) 0.38 0.64 0.71 0.75 0.36 0.56 0.46 0.58

reached a maximum saturation value of 0.75 for low-dose (0.08 at’%) implants. This value is in agreement with the f, values obtained after implantation at 77 K. Angular yield curves before and after post-irradiation are shown in fig. 58. It should be noted that f, as well as the critical angle of the Ce atoms increase after post-irradiation. In contrast, post-irradiation of a 77 K implant with 2 x lO”j He/cm2 at 293 K resulted in a decrease of f. from 0.67 to 0.38 apparently due to trapping of mobile vacancies. Detailed post-irradiation studies have been performed on the AlCd system [142]. This system has the advantage that there is a large difference between thef, value of 0.1 for the 293 K implant and that of 0.96 for the 77 K implant. The latter result and the fact that an f, value of 1.0 is observed after implantation at 5 K show that the substitutional site is preferentially occupied in the cascade. Post-irradiation of an AlCd system produced by Cd implantation at 293 K with Kr ions at 77 K leads to a steep increase of f, as is demonstrated in fig. 59. The Cd peaks from the (llO)-aligned spectra are shown for the as-implanted case and after post-irradiation with various fluences of Kr ions. The decrease of the Cd peak area with increasing Kr-ion fluence is due to Cd atoms being transferred to substitutional lattice sites. A similar recovery effect had been observed using H and He ions for the post-irradiation experiments. Angular yield curves shown in fig. 60 demonstrate this result. After implantation of 1.75 at% Cd into Al at 293 K an f, value of 0.15 and critical angles for Al of 0.52” and for Cd of 0.39” were obtained. Post-irradiation with 1 X 10” He/cm2 (200 keV) at 77 K leads to an increase of the substitutional fraction to 0.81. The critical angle for Cd (0.56”) is only slightly smaller than that for Al (0.63O). This corresponds to an average static displacement amplitude of the Cd atoms of 0.005 nm, which is most probably due to a single vacancy trapped on the nearestneighbour site. After warming up to 293 K the system returned to its original state (see fig. 60). In order to compare the post-irradiation results obtained by H and noble gas ions of various masses and energies the fluence r$ is scaled in dpa using eq. (3.6): dpa = 0.8+F,,/2E,N, where N is the atomic density of the target, E, the threshold energy (18 eV for Al [183]) and in nuclear collisions. In order to calculate F,, the TRIM2 computer program was used [loo]. The increase of f, due to He and Xe post-irradiation is shown in fig. 61. Two important features which are characteristic also of other post-irradiation experiments [84] should be pointed out. Firstly, by increasing the post-irradiation fluence complete recovery of Cd can be F,, the linear energy density deposited

Loftice

site occupation

x

elements

implanted

in metals

441

Ce

+,,2=0.60

o5

of non-soluble

. v
Xm,n=0.61

I

\

i

J,,,, = 0.86O

t

X,," = 0 l!

i

.ED He+/cm2

tlll

>

088O 0 15

I

t

I -2

I

-1

4 1

I 2

C

J, Pdegl Fig. 58. Angular sample implanted

yield curves of 2 MeV He ions backscattered from a V single crystal implanted with Ce ions (a) for a at 293 K and measured at 77 K; (b) for a sample implanted at 293 K, post-irradiated with 1 x lOI He/cm2 and measured in situ at 77 K [179].

obtained (f, = 0.94) and secondly the influence of He and Xe irradiation on f, is the same if the fluence is scaled in dpa. In order to interpret the above observations one should first examine the possibility of the radiation-induced dissolution of Cd precipitates. It has been found that the increase of f, does not depend on Cd concentration up to 10 at% indicating that in the used concentration range no precipitate formation occurs [145]. The fact of complete

0. Meyer

and A. Turos

1.0-l@ Cd'/cm', 17OkeV implanted at 293K

l

2.0 MeV

0 Aligned

He'ot

77K Cd

Aligned

I x Aligned a Aligned

I

Random

postirrodioted at 77K with: r2.0~10" Kr+/cm*, 300keV 5.0.10'2 Kr+/cm*, 300keV L.0.1013

Kr*/cm*, I I

f

I

I

2LO

280

320 Channel

360

LOO

680

51 0

Number

Fig. 59. Random and (llO)-aligned backscattering spectra from an AI single crystal implanted with Cd and post-irradiated with Kr. Implantation (at 293 K), post-irradiation and analysis (at 77 K) were performed in situ [142].

recovery even at high Cd concentration is a further hint that Cd precipitates do not form after implantation at 293 K or during annealing to 293 K as it is known that precipitates do not dissolve completely by recoil dissolution [184]. Therefore, the displacement of the Cd atoms after implantation at 293 K is obviously due to the formation of vacancy-impurity complexes. It should be noted that the initial slope in fig. 61 is independent of the average cascade density

x

8.0.10" Cd'/cm', T, = 293K

200keV

in AL f 1.75at.%Cd

I

0.01

I -1.0 Tilt

0.0 Angle

1.0

w

(deg)

Fig. 60. Angular yield curves of 2 MeV He ions backscattered from an AI single crystal implanted with Cd at 293 K. Angular scan curves for Cd are shown after implantation at 293 K (x), after post-irradiation with 200 keV He ions to a fhmce of 1 X lO”/cm*, at 77 K (0) and after annealing to 293 K (A) [84].

Lotrice

site occupation

of non-soluble

elements

implanted

in metals

1.0

fSN

0 600 keV Xd 200 keV He+

A

443

1

Postirradiation at IIK

0.8-

: $

0.6-

q

0.4-

A

:

0 El

0.2-

A

8"

dpa - Fluence Fig. 61. Increase of the substitutional fraction of Cd implanted into Al at 293 K by post-irradiation different fluences of 200 keV He ions and 600 keV Xe ions (841.

at 77 K with

as the mean transferred energy is about 0.15 keV for 200 keV He and 2.5 keV for 600 keV Xe irradiation. Post-irradiation experiments had also been performed on the AlSb, AlIn and AlPb systems produced by ion implantation at 293 K with f, values of 0.11, O.O%nd r0.02, respectively (see table 6). After post-irradiation of AlSb with Kr ions, f, was found to increase from 0.11 to 0.7, a value close to that obtained by direct implantation of Sb into Al at 77 K. This result indicates again that the non-substitutional fraction which is formed in the cascade cannot be altered. This component is thus governed by processes within the cascade. Therefore a normalized substitutional fraction fSN(9) defined by fsdd

= [f&4

-fdG

= 293 K)]/[f,(T,

= 77 K) -.##‘I

= 293 K)]

(6-l)

had been used to present the results [84]. In fig. 62 the increase of fsN with increasing Kr fluence is shown. In the low-fluence region the slope is similar to that observed for the AlCd system, while at high fluences enhanced annealing is seen. It should be noted that for %Sb AH,,, is smaller and AHsize is larger than that for AlCd (see table 5). It was argued [84] thatthe enhanced AH,, value should not affect the recovery process while the reduced AH,,, value would lead to an enhanced recovery at higher fluences. Post-irradiation of the AlIn system with 100 keV H ions at 77 K caused an increase of f, from 0.2 to 0.61. This rest&can be compared with that of an almost similar PAC experiment, where the AlIn sample was post-irradiated with 5 x 1016 He/cm*, 120 keV at 80 K [158]. According G this experiment 50% of the In atoms were on perfect substitutional lattice sites after post-irradiation, 6% on near-substitutional sites and 44% were located at extended defects while no indication was found for In-In interactions excluding In cluster or precipitate formation. It can be stated that the agreement of the channeling and PAC results is rather good. The implanted AlPb system was post-irradiated at 77 K with He and Kr ions [84]. As for the other systems discussed before, f, could be enhanced up to the value which is reached by direct

444

0. Meyer

and A. Twos

1.0 -

l-l

u

0

A Sb f 94 o,8 _ Tp =llK q q

0.6 -

0

0.01 IO"

*

q

5

10'2

2

5

1013

2

5

1014

2

5

,015

Fluence (300keV Kr'/cm') Fig. 62. Increase of the substitutional fraction of Sb implanted into Al at 293 K by post-irradiating fluences of fi ions at 77 K [84].

with different

implantation at 77 K. The increase of the normalized substitutional fraction, fsN, with increasing Kr fluence is shown in fig. 63 where the data are compared with those obtained for Kr irradiation of the AlCd system. The agreement is rather good besides at very high fluences. Compared to AICd, the AlPb system has larger AH,, and AH,,, values (see table 5). It was assumed that the relativeFlarge AH,,, value is responsible for the reduced recovery rate of the AlPb system at high fluences. -There is some experimental evidence that non-linear effects may occur in high-density cascades (see section 3.3). High-density non-linear cascades can be produced by implanting or 1.0 q AlCd

f SN 0,8-

q

a -AlPb

0 A

A

A

z

0.6-

B x

0.4-

Cl

0.2-

ogA

A cl

dpa

- Kr'-hence

Fig. 63. Increase of the substitutional fraction of Pb implanted into Al at 293 K by post-irradiating with different fluences of Kr ions at 77 K. The results obtained after post-irradiation of the &d system are shown for comparison [84].

Luitice

site occupation

of non-soluble

elements

implanted

in metals

445

irradiating with heavy diatomic molecular ions exhibiting a certain probability that the subcascades of both atoms overlap in space and time. A high-density cascade in the thermalspike regime could lead to precipitates formation in the cascade or could influence the recovery effect in a characteristic way. Therefore the AlCd system produced by implanting 5 x lOI Cd/cm’, 80 keV, at 293 K was post-irradiatedwith 150 keV Hg ions and 300 keV Hg, ions. Although the increase of fsN with the Hg- and Hg,-ion fluence revealed the same slope, the absolute values were smaller for the Hg, irradiations. From these results it can be concluded that non-linear effects, which would affect the slope do not occur. Summarizing the post-irradiation results it was shown that the substitutional component of impurities in Al can be increased by an amount which corresponds to the difference of the f, values after implantation at 77 K and 293 K. During implantation at 293 K or annealing to 293 K nearly all of the impurities will trap vacancies. The effectivity of the recovery process by post-irradiation is independent of the mass and energy of the ions used in the post-irradiation experiments. This independency reflects the independence of the recovery process of the mean transferred energy and of the cascade efficiency in the defect production process. This efficiency factor was determined by the change of the specific resistivity of irradiated Al foils and is 0.92 for H irradiation, 0.6 for Ar irradiation and reached the saturation value of about 0.4 for higher mean transferred energies [98]. It is therefore concluded that the annealing of the complexes by mobile SIAs is not the main process of the recovery mechanism. As a further test of this assumption post-irradiation experiments have been performed at 5 K in order to exclude the influence of freely migrating point defects. The results of these experiments are discussed in section 6.3. 6.3. Dissociation of Cd-vacancy complexes within the displacement spike Post-irradiation experiments were performed in order to test if the decrease of the number of vacancy-impurity complexes is due to annihilation of the trapped vacancies by absorbing mobile SIAs or to a recovery process which occurs within the lifetime of the collision cascade. The experimental results showed that the Cd-vacancy complexes are dissociated by post-irradiation even at 5 K using H as well as Kr ions [142,145]. The recovery of the substitutional Cd component by Kr post-irradiation is demonstrated in fig. 64 where the random spectrum from an Al single crystal implanted with 1.0 at% Cd is shown together with three (llO)-aligned spectra. The decrease of the Cd peak area of the aligned spectra with increasing Kr-ion fluence clearly demonstrates the increase of the substitutional component of Cd in Al. The increase of f, at 5 and 77 K as a function of the ion fluences is shown in figs. 65a and 65b for H and Kr, respectively. It is obvious that the results do not depend on the substrate temperature, indicating that the annihilation of trapped vacancies by long-range migrating SIAs is not necessary for the improvement of f,. The substitutional fraction is proportional to In + ($I = fluence). This relationship is obeyed up to nearly complete recovery (see fig. 65b). The complete recovery indicates that the probability for vacancy trapping is small within the lifetime of the cascade. The 100% substitutionality obtained after implantation at 5 K showed that stable Cd-vacancy complexes do not form in Al and that the substitutional lattice site is the site of lowest energy. Previously it was noted that f, versus + is independent of the Cd concentration in the range from 0.1 to 1.4 at% [142]. This range has been extended up to 10 at% Cd revealing the same result [145]. The fact of complete recovery even at high Cd concentration was a further hint that Cd precipitation did not occur after implantation at 293 K or during annealing to 293 K. It is known that precipitates do not dissolve completely by recoil dissolution [184] and that the

446

0. Meyer

and A. Twos

240 Energy

WIndOW :

Cd

r

-ii z 2 800 -0 P .a, > m 400 .c iii 2= s u-l 0 200

4 160

80

300 420 Channel Number

0 480

450

Fig. 64. Random and (IlO)-aligned backscattering spectra from an Al single crystal implanted with 200 keV Cd ions and post-irradiated with 300 keV Kr ions. Implantation at 293 K, post-irradiation and analysis at 5 K were performed in situ [145].

1.0 0.8- TN= a 5K I 0 77K 0.6-

n 0

fs

n 0.4-

4

B

0.2- 2

(al 0.0 1 10’6

2

ld7 2 @ 5 Fluence (100 keV H+/cm 2 1 5

1.0

A

0.8fs

A$

0.6-

0

0.4-

Q

*O

8 4 AB

0.2- 0

0.0 8 ’ 1o12

(b). “1’1’1 ’ ’ -‘zs’*’ ’ r lQ”“’ ’ ’ 1o13 lolL 1o150 Fluence ( 300 keV Kr+/cm’ 1

Fig. 65. Increase of the substitutional fraction of Cd, implanted into Al single crystals at 293 K and post-irradiated with He ions (a) and Kr ions (b) at 5 K (A) and 77 K (0) [145].

Lnttice

site occupation

of non-soluble

0.6 1

elements

implanred

in metals

447

A

I

.2 Fluence Fig. 66. The post-irradiation

(dpa 1

normalized substitutional fraction of Cd implanted into Al at 293 K versus in dpa. The post-irradiations and analysis were performed at 5 K. A straight slope of the data points [145].

the ion fluence used for line is fitted to the initial

precipitate size will influence the recovery process. The fact that the increase of f, with + does not depend on the Cd-vacancy complex concentration again indicates that the recovery process is not due to the absorption of SIAs within the lifetime of the cascade which, if we assume a constant capture radius, would cause such a dependence. The results for H- and Kr-ion irradiation at 5 K are compared in fig. 66 using the dpa scale evaluated as discussed above. The initial slope shows that in the low-fluence region where single cascades do not yet overlap the fraction of Cd atoms which move to substitutional lattice sites, was by about a factor of 8 larger than the number of displacements per atom. As the ratio of the recovered Cd-vacancy complexes to the initial number of complexes was independent of the Cd concentration, the cross section for the recovery process could be determined. Therefore, it was concluded that within a single event the recovery cross section is 8 times larger than the displacement cross section. Further, it was noted that the initial slope was independent of the average cascade density since the mean transferred energy is 0.12 keV for 100 keV H and 2.0 keV for 300 keV Kr irradiation. The question arises which processes could contribute to the large cross section for the Cd recovery. The influence of subthreshold collisions was ruled out by the TRIM2 calculations and analytical calculations of the recoil spectra [98]. The ratio of the energy density deposited in nuclear collision to that deposited in subthreshold collisions and in photon production is about 2.2 for H and about 130 for Kr irradiation. As a result of this fact one would expect a far steeper slope for H irradiation in contrast to the observed result. According to molecular dynamics calculations the maximum number of displaced atoms in the collision phase is usually a factor of 4 to 10 larger than the modified Kinchin-Pease value which is reached at the end of the relaxation phase (see section 3.2). The relaxation phase is characterized by an extensive thermal rearrangement and an annihilation of defects. By use of the instantaneous number of Frenkel pairs, the displacement cross section should be similar in size to the cross section for the recovery process. The recovery process could then be described as an unstable-pair-recombination process and would be a measure of it.

448

0. Mqver

and A. Twos

The influence of the reduced damage efficiency within the cooling phase could be excluded as the recovery process was independent of the cascade density. Molecular dynamics calculations and the thermal-spike model show the influence of enhanced recombination for dense cascades only. As a result of the fact that spontaneous recombination is faster than defect diffusion, it is not possible to see any influence of the cascade efficiency factor. Replacement collisions also do not contribute to the enhancement of the substitutional fraction (see section 3.5). In summary, the only component which is proportional to the number of displaced atoms and independent of the cascade density and the damage production efficiency is the spontaneous recombination of unstable neighbouring Frenkel pairs. The Cd-vacancy complex dissociates within the collision phase of the displacement spike and the Cd atom comes to rest at a substitutional lattice site within the relaxation phase. The substitutionality of Cd is supported by the fact that the AlCd system fulfils the Hume-Rothery conditions (see fig. 6), and thus Cd fits nicely in a subst&ional lattice site. The results showed that the instantaneous number of displaced Al atoms within the collision phase is 8 times larger than that determined with use of the modified Kin&in-Pease formula. This value supports the results of molecular dynamics calculations. As after post-irradiation the Cd atoms are located at substitutional sites (f, = 1.0) it can be concluded that the process of lattice site occupation within the relaxation phase of the cascade is the most important mechanism which determines the lattice location of ions implanted in metals. We have shown that the lattice site occupation of non-soluble atoms is governed by at least three processes: spontaneous recombination of the impurities with vacancies within the relaxation phase of the collision cascade, trapping of additional vacancies within the cooling phase of the cascade and finally trapping of migrating vacancies at temperatures above stage III. 6.4. Anomalous concentration

dependence of the substitutional

fraction

Another interesting effect had been observed for some systems of limited solubility that are characterized by a positive heat of solution of less than about 100 kJ/mol. The substitutionality of some elements implanted at 293 K improved with increasing implantation dose. This is the opposite to what could be expected for such systems. In fact, f, should be 1 at low implant concentrations, and decrease eventually at high concentrations when precipitation does occur. The anomalous change of f, as a function of the implantation dose has been studied in detail for the FeAu system [172]. Although Au in Fe does not satisfy well the Hume-Rothery rules, a limited solubility of Au in Fe has been reported [171]. In agreement with this expectation the implantation of Au into Fe at 77 K and the in situ analysis yielded an f, value of 1.0 independent of the implanted Au concentration in the range between 0.1 and 2 at%. The experimental results of implantation of Au into Fe at 293 K revealed, however, the opposite trend. As presented in fig. 67, f, is 0.6 at 0.1 at% Au and increases monotonically up to 1.0 for Au concentrations above 1.0 at%. This value did not change even at the highest implanted concentration of 7 at% although the solubility limit was exceeded by a factor of more than 70. A similar effect has been observed for the YCe system [179]. In this system, however, because of the much lower solubility the initial value of f, was about 0.15 and increased as a function of the implantation fluence up to 0.7 for 3.5 at% (fig. 67)..With a further increase of the Ce concentration f, decreases, apparently due to Ce precipitation. The angular dependence of the normalized yields is shown in fig. 68. These angular scans provide more detailed information on the lattice location of the implanted species than the f, values alone. For small Au doses (fig. 68a) the angular scans for the impurity are not only shallower but also narrower with respect to the scan for the host lattice. Increasing the

Lotrice

001

site occupation

I

0

I

1

of non-soluble

I

elemenls

/

implanted

I

2

in metals

I

449

I

3

CI (at %I Fig. 67. Variation

of the substitutional

fraction

with the implanted impurity YCe (0) systems [172,179].

concentration

for the -FeAu

(0) and the

implantation dose the impurity scan becomes broader and deeper and finally matches perfectly that of the host as shown in fig. 68b. The detailed analysis of the shape of the angular scans has shown that there are two fractions of Au atoms: the first one is composed of Au atoms which are slightly (- 0.01 nm) displaced from the regular lattice sites and the second one consists of Au atoms randomly distributed at lattice sites of low symmetry. The displacement of impurity atoms implanted at low concentrations can be easily understood in terms of vacancy-impurity complex formation, as discussed in the previous sections. To elucidate the question concerning the mechanisms of the dose dependence on f, further post-irradiation experiments were performed. A sample implanted at 293 K with Au ions to the maximum concentration of 0.2 at% (f, = 0.75) was bombarded with 600 keV Xe ions. The variation off, with the Xe dose was approximately the same as that shown in fig. 67. For doses exceeding 6 X 10 l5 Xc/cm’, f reached a value of 1.0. A similar post-irradiation experiment performed at 293 K using ‘He ions did not result in a noticeable change of the Au substitutional fraction [172]. From these results it was concluded that the vacancy-Au complexes dissociate at 293 K in high density collision cascades. During the dynamic development of the collision cascade, vacancy-rich regions surrounded by an envelope of interstitials are formed. During the relaxation phase local vacancy supersaturation is a strong driving force for transformation of the cascade region into dislocation loops or larger clusters (see section 3.4). Since the binding energy of a vacancy in a dislocation loop (- 1.2 eV) [164] is substantially higher than the estimated binding energy of an Au atom-vacancy pair of 0.24 eV [19], the capture of vacancies by extended defects is energetically favourable and these defects represent a stronger vacancy sink than an impurity atom. The vacancy-impurity complexes formed during ion implantation at 293 K dissociate in the cascades produced by the successively impinging Au ions. The released vacancies will prefer-

0. Meyer

450

and A. Twos

.-3-10’5Au/cm2 o- Fe

1-

"73K 1 “’ ,L‘; .,g&

lb) 0.0

Fig. 68. Angular

yield curves

of 2 MeV

I -l.G

I -0.8

I 0 9 (degl

I 0.8

I 1.6

He ions backscattered from a Fe single crystal Au at 293 K [172].

implanted

with different

doses of

entially migrate towards the extended defects and, provided that the competing sink density is large enough, the dissociated complexes will not be restored. For the case that such competing trapping centers are formed prior to the impurity implantation, the subsequent introduction of an impurity, even at a very low concentration, will reveal a much higher substitutionality. Such an experiment has been performed by prebombardment with 5 X lOi Xc/cm’. After implantation of 0.2 at% Au into the prebombarded region an f, value of about 1 was observed. This result confirmed the assumption made above that trapping centers which compete successfully with impurity atoms in trapping of vacancies are produced by high density collision cascades in Fe and V. This anomalous increase of f, needs freely migrating vacancies and was not observed after implantation at temperatures below stage III where the vacancies are immobile. In summary, the overlap of the dense collision cascades as. produced by subsequently incoming ions may cause the dissociation of formerly formed complexes. In principle, this makes it possible for an impurity atom to occupy again a regular lattice site. Here the delicate balance between the vacancy retrapping and escaping probabilities determines the lattice position of an impurity. We have shown that if the binding energy of an impurity for vacancies

Loftice

site occupation

of non-soluble

elements

implanred

in merals

is smaller than that of the competing trapping centers, an increase of the concentration centres produces an increase of the substitutional impurity fraction.

451

of these

7. Lattice site occupation of elements with negative heats of solution The stable form of a SIA is the (100) dumbbell in fee metals and the (110) dumbbell in bee metals (see section 4.1). From channeling experiments there is ample evidence that the defects trap mainly at solute atoms with smaller radii than that of the host atom, in configurations that are related to the stable SIA (see section 4.3). Thus, dilute alloys of Al containing Cr, Mn, Cu. Zn and Ag form (110) mixed dumbbells during He-ion irradiation at 70 K, at which temperature SIAs migrate freely (see table 2). Warming up to temperatures above recovery stage III causes annealing of these dumbbells by mobile vacancies. It should be noted, however, that Mijssbauer experiments on irradiated 57Co doped Al single crystals revealed a displacement of the impurity which is consistent with a (111) rather than a (100) symmetry [185]. The impurities are displaced from the octahedral position by about 0.06 nm. Trapping may also occur during the irradiation of Al alloys containing large solute atoms. Channeling results for Sn in Al indicate that the solute atoms are not displaced from their substitutional lattice position [186]. Electrical resistivity data, however, indicate that these solutes do trap SIAs in stage I and release them in stage II [187]. It is of interest to compare trapping configurations obtained by post-irradiation of dilute Al-based alloys (uncorrelated damage) with those produced by direct implantation of the impurity atoms at low temperatures (correlated damage). In this context it is interesting to note that post-irradiation of Al-O.005 at% Co alloys with neutrons [188] leads to multiple interstitial trapping by Co atoms, probably due to a higher concentration of di-interstitials produced in more dense cascades [189]. As the mean energies transferred in nuclear collisions in the case of high-energy neutrons and of heavy ions in the 100 keV range are rather similar, the same complex trapping configurations are expected for the implanted impurities. All the systems to be considered in this section have in common that they possess a negative heat of solution. Thus, their equilibrium phase diagrams are characterized by the occurrence of many intermetallic compounds. Due to the low free energy values of these compounds the solubility limit is nevertheless strongly restricted and even decreases with increasing size-mismatch energy, in contrast to systems with a positive heat of solution. Thus it is possible to select systems with different negative AH,,, values and rather small AH,i, values, and systems with different A Hsize values and similar average values of AH,,, , in order to study the influence of these parameters on f, separately. 7.1. Aluminium-based

ion implanted systems

AlAg, AlMo: These systems possess rather moderate values of AH,,, and AHsize (see table 9).Thannxhg measurements on single crystals of Al-O.1 at% Ag irradiated with 1 MeV Kr ions at 70 K revealed the formation of (100) mixed dumbbells displaced by 0.13 nm from the substitutional site along the (100) direction. These displacements produced a large increase of xti for Ag along the (110) direction (see fig. 34). In addition, the angular yield curves for Ag show a pronounced peak at zero tilt angle for low irradiation fluences. High-dose He irradiations as well as Kr irradiations did not lead to such a peak structure but only to a large increase of xmin for the Ag atoms, indicating multiple interstitial trapping [190].

0. Meyer

452 Table 9 Summary

of the substitutional

Implanted element 4% Au MO Pd Mn CU Cr Hf

fractions

(/,)

for various

A H,I W/mol)

A Hs,, W/mob

0.1 0.2 0.6 1.3 6.7 11 11 16

-22 -92 -20 -186 -70 -32 -36 -170

Ni co Ce Te

16 17 77 100

-81 -68 -44 -79

La Ca Sr Ba

118 142 233 318

-160 -111 - 103 -107

and A. Twos

elements

as implanted

into Al at 5, 77 and 293 K

f, 77 K

5K

293 K

0.93 0.68 0.71 0.96 0.82 1.0

0.73 0.94 1.0

0.60 0.65 0.45 0.47

0.51 0.3 - 0.04 0.0

0.44

0.15

0.0

0.1 0.0

0.0 - 0.05 0.05 -0.17

0.93 0.87 -

1.0

0.56

0.96 0.68 1.0 0.7

Implantation of 0.07 at% Ag into Al single crystals at 77 K and in situ channeling analysis lead to quite different results [191]. From the angular yield curve in fig. 69a it was concluded that after implantation at 77 K, 95% of the implanted Ag atoms are located at substitutional lattice sites. A slight narrowing of the bottom part of the angular yield curve indicates that about 20% of the Ag atoms are slightly displaced. In order to obtain more information on the quite different trapping probabilities in post-irradiated dilute alloys and as-implanted samples,

T,=293K T,=77K

0.07 at.% Ag T,=77K T,=77K

-i

0

1:o

-1.0

0

1.0

TILT ANGLE (deg) Fig. 69. Angular

yield curves of 2 MeV He ions backscattered from an Al single crystal implanted (a) for the as-implanted sample, (b) after warming up to 293 K [192].

with Ag ions at 77 K

Lattice

site occupation

of non-soluble

elements

implanted

in metals

453

the latter samples were post-irradiated with Kr and He ions with energies and to fluences similar to those used for dilute alloys. No trapping could be provoked in the as-implanted samples although higher fluences were applied than in the case of dilute alloys. In order to explain the high stability against post-irradiation, it was assumed that a large density of competing, non-saturable traps for SIAs exists in the as-implanted samples which prevents SIA trapping by the substitutional Ag atoms. In order to test this assumption, the as-implanted samples were annealed at 500 K, cooled down to 77 K and post-irradiated with 1 MeV He ions. Now the minimum yield of Ag increased from 0.05 to about 0.35 with increasing He-ion fluence, as expected. From this result it was concluded that competing trapping centres formed during implantation at 77 K reduce the concentration of freely migrating SIAs and, thus, diminish the probability of Ag-SIA complex formation. Warming up of the as-implanted AlAg system from 77 to 293 K, i.e. above stage III, did not alter the substitutional fraction, indi&ng that vacancies do not play a large role (see fig. 69b). However, a small part (20%) of the angular yield curve is still narrow. This rather high thermal stability indicates that the corresponding defect complex is not one of the simple shallow trapping configurations mentioned in section 4.3. Implantation of 2.68 at% Ag into Al at 293 K resulted in an f, value of 0.78 [141]. MO implanted into Al at 293 K exhibited the large I, value of 0.98 + 0.05 [141]. The maximum substitutional concentration was 3.85 at% what can be compared with the solid solubility limit of 0.006 at% at 56O’C [134,135]. AlMn, AlAu, AlPd: These systems are characterized by relatively large negative values of AH:, andxther&nall values of AH,,, (see table 9). The solid solubility is 0.04 at% at 500 K [134]. Implantation of Mn into Al at 293 K with concentrations from 0.1 to 5 at% resulted in substitutional fractions of 0.96 f 0.05 independent of the impurity concentration. Increasing the concentration above 5 at% leads to amorphization [193]. For all the as-implanted systems studied up to now, the f, value obtained at 293 K was smaller than or equal to the f, value

0.1 at. % Au in Al TI =TM= 293K

12000

5 9 z

A”

,3

+

I

-I160

160

2io

CHANNEL Fig.

70. Random

and

(IlO)-aligned

spectra

NtkER

of 2 MeV He ions crystal [192].

backscattered

from

an Au implanted

Al single

454

0. Meyer

and A. Twos

0.10at O/OAu in Al I.(

0.:

0.C I.( 9 e 9 2

.Al(110, Xm,n= 0.10 $,,2= 0.60°

0.E

P 5 OS 1.0

T,=T,,,=5K

0.5 qJ,,2= 0.68O 0.0

q,,2= 0.68O

I I I I -1.0 -0.5 0 0.5 TILT ANGLE (deg)

, 1.0

Fig. 71. Angular yield curves of 2 MeV He ions backscattered from Al single crystals implanted with Au ions at temperatures of (a) 293 K, (b) 77 K and (c) 5 K [192].

obtained by low-temperature implantation. Therefore, it may be safely assumed that implantation of Mn into Al at 77 K also would have resulted in an f, value of about 0.96. It is known that by post-irradiation of diluted AlMn alloys at 70 K (100) mixed dumbbells are formed [194]. This is not the case for ion imTlanted systems which, therefore, behave differently from irradiated dilute alloy ones. Implantation of 1 at% Au into Al at 293 K resulted in an f, value of 0.0 [141]. Reducing the concentration of implanted Au to 0.1 at% led to an f, value of 0.68 f 0.03 (see fig. 70). The same f, value was observed after implantation at 77 K. More information can be obtained from the angular yield curves given in fig. 71. It is seen that for all implantation temperatures the critical angle for Au is similar to that for Al, indicating that a substitutional component

Louice

site occupation

of non-soluble

elements

implanted

in metals

455

without relaxations does exist. The flat bottom of the angular yield curve for Au after implantation at 77 K clearly suggests the displacement of about 10 to 20% of the Au atoms into the (110) channel by a large amount. This may be attributed to the formation of mixed dumbbells at 77 K due either to trapping of freely migrating SIAs or to trapping of SIAs during the cooling phase of the cascade. In order to test this assumption, implantation and channeling analyses were performed at 5 K, the results of which are shown in fig. 71~. About 93 f 0.3% of the Au atoms are at substitutional sites indicating that the dumbbell formation during ion implantation at 77 K is due to the trapping of freely migrating SIAs. Warming up the 5 K implant to 77 K leads to a decrease of f, from 0.93 to 0.81, again indicating the trapping of freely migrating SIAs by the Au impurities. Angular yield curves through the (100) crystal direction revealed an f, value of 0.93, showing that the displaced Au atoms are located close to the octahedral lattice site [192]. The preliminary results for the system AlPd [192] closely follow those observed for the AlAu system. After implantation of Pd into Alxt 293 K the f, value was 0.50 f 0.05. Pd implantation at 5 K produced much higher f, values of 0.83 + 0.05. Warming up from 5 K to 77 K again resulted in a decrease of f, from 0.83 to 0.71 due to the trapping of mobile SIAs. Further annealing to 293 K did not lead to a change of f, indicating the minor influence of mobile vacancies on f,. Comparing the results for Al-based ion implanted systems, it is concluded that the interaction with SIAs is favoured by systems with large negative values of AH,,, ( < -90 kJ/mol) and small values of AHsi, (C 5 kJ/mol). AlSe, AlBr: Solid solubility values are not available for these systems. Implantation studies havebeenperformed in order to test the applicability of the Miedema rules to the interaction of semi- and non-metallic impurities with point defects. Values for A+* and An,, in eq. (2.1) have been estimated from the general correlations between A$ and the electronegativity and between An,, and the bulk modulus [161]. Both systems have large negative values of AH,,, and small values of AHsti, similar to the metallic impurities Ag, Au and Pd which were treated above. After implantation of Se ions into Al at 293 K to a peak concentration of 1 at% an f, value of 0.11 was observed [141]. Implantation of Se or Br ions at 293 K to a concentration of 0.2 at% did not result in a measurable substitutional fraction. Angular yield curves for Se as well as for Br exhibit a pronounced structure indicating that both impurities occupy interstitial lattice sites of low symmetry. The angular scan curve for Se through the (110) direction in the (100) plane is presented in fig. 72b. Implantation of Se at 5 K yielded a near-substitutional fraction with an average displacement from the substitutional lattice site of about 0.03 nm. This substitutional fraction decreased after the sample had been warmed up to 77 K (see fig. 72~). Warming up to 293 K led to a complete disappearance of the near-substitutional fraction and to the formation of Se-vacancy complexes, yielding a similar fine structure in the angular scan curves as that observed for the 293 K implant. This indicates that besides Se-SIA complexes also Se-vacancy complexes are formed. After implantation of Br ions into Al at 293 K, the angular scan curves of Br showed a fine structure similar to that observed for Se. AlCu, AlCr, AlNi, AlCo: The f, values for systems with small and medium negative AH,,, an&mall~H~~~valu~are close to 1.0. Thus it is expedient to choose systems with medium negative A HsO, values and increasing AH,, values in order to study the influence of the latter parameter on f, (see table 9). Implantation of 1 at% Cu into Al at 293 K yielded an f, value of 0.71. The measured solid solubility for the implanted system was 1.57 at% [141], to be compared with a solid solubility

456

0. Meyer

r

kA

0 ri!l

h 'A ‘A

F

z2 0.50

x E

0.2lat%Se T,=T,=293K

O.l7at.%Se T,=SK

T,=SK

l.o-

,T,=77K I I I 0-o- O!3

. pd

I q1

+:,+

A&q

d

'4, .r

,I

I

o \

TILT PLANE:{lOO}

i . .-2'

I

g400'

ASe

ASe

+,-'

/’ /

+\+ \ +, lb)

I (0

Oh ~AlcllO>‘~

A 'd,

-,./

‘i

.I

(a) 0 \

z

and A. Twos

i i++A1<110>

+\ +--+‘yr

$,=0.53f

..

-1

0 TILT

+I -1 ANGLE (deg)

0

+I

Fig. 72. Angular yield curves of 2 MeV He ions backscattered from Al single crystals implanted temperatures of 5 K (a) and 293 (b). The results of annealing from 5 K to 77 K are also shown

with Se ions (c) [191].

at

value between 0.04 and 0.08 at% at 200 a C obtained from the equilibrium phase diagram [134]. For a peak concentration of 0.3 at% Cu the f, value was 0.68 f 0.05 [192] (see fig. 73b). This shows that I, is independent of the impurity concentration in contrast to the results obtained for other implanted systems, for example Al&t. From the difference in the critical angles for Al and Cu in fig. 73b it is concluded that the Cu atoms occupy near-substitutional lattice sites being displaced by about 0.02 nm. Implantation of 0.2 at% Cu at 77 K resulted in a substitutional component of 0.83 f 0.02 without relaxations. This can be deduced from the critical angles having nearly similar values

I

O.Zat%Cu

0.3at.%Cu

TILT ANGLE (deg) Fig. 73. Angular

yield

curves

of 2 MeV

He ions backscattered (a) and 293 K(b)

from Al single [191,195].

crystals

implanted

with

Cu ions at 77 K

Lattice

sire occupation

of non-soluble

elements

implanted

in metals

457

for Al and Cu (fig. 73a). Similar to the angular yield curve for Au in fig. 71b, the bottom of the dip for Cu is rather flat, suggesting the formation of (100) mixed dumbbells. This statement needs to be verified in future experiments. Irradiation of Al-O.13 at% Cu alloys with He ions at 70 K produced a large increase of the Cu minimum yield of up to about 0.5 and an additional peak structure with a maximum of up to 0.8 due to the formation of mixed dumbbells [132]. As in the case of implanted AlAg and AlMn systems, the formation of mixed dumbbells is strongly suppressed in the ion hplanted &stems and the implanted impurity atoms preferentially occupy substitutional lattice positions. The Al-Cr (100) mixed dumbbells were created by trapping SIAs during irradiation with 1 MeV He ions at 50 K [196]. Implantation of 0.3 at% Cr into Al at 293 K yielded an f, value of 0.94 * 0.05 [197]. The solubility of Ni in Al is less than 0.03 at% at 640 K [134]. Various Ni doses corresponding with peak concentrations of about 0.001, 0.06 and 0.6 at% were implanted into Al single crystals at 293 K [198]. For a peak concentration of 0.06 at%, 49% of the Ni atoms were located at random sites and 51% were located at near-substitutional sites displaced by 0.024 nm from the body-centred position into the (110) direction. In view of the low solubility of Ni in Al, the random component was considered to consist of Ni precipitates, although such precipitate could not be identified by TEM using a sample implanted with 0.6 at% Ni. The occupation of the near-substitutional site is apparently due to the relaxation of Ni atoms towards single vacancies trapped at nearest-neighbour lattice sites. Such a model could, in principle, also explain the near-substitutional site observed for Cu in Al as indicated in fig. 73b by the difference of the critical angles of Al and Cu. The solubility of Co in Al is less than 0.01 at% at 657OC [134]. Many studies have been performed on strongly diluted AlCo systems by means of Mijssbauer spectroscopy using the radioactive isotope 57Co. In electron [189] and neutron [188] irradiated dilute AlCo systems dumbbell formation was observed. The interaction of defects with Co implanted into Al at 4.2 K was studied in detail by means of Mossbauer spectroscopy [78] and is considered to be a test case for our systematic studies on implanted systems with negative heat of solution. After implantation of 80 keV 57Co ions at 4.2 K to a dose of 2 x 1014/cm2, the substitutional fraction was 55%, the fraction of Co-interstitial complexes was 35%, while the fraction of Co-vacancy complexes was 10%. Upon annealing to 293 K the f, value increased slightly to 0.60; after annealing to 330 K the f, value had increased to 0.92. In the temperature region from 170 to 200 K the fraction of Co-vacancy complexes increased to about 30%, while the fraction of Co-interstitial complexes decreased to 10%. At annealing temperatures above 290 K these fractions decrease to 8% (Co-vacancy) and to 0.0 (Co-SIA). A further interesting experimental detail was observed after post-irradiation of a well annealed sample (TA = 330 K) with Al ions at 4.2 K. With increasing Al-ion fluence the substitutional fraction of Co decreased from 0.92 to a minimum value of 0.48 at 1 X 1014 Al/cm2 and increased to 0.6 at 1.3 X 1015 Al/cm2. The fraction of the Co-SIA complexes had a maximum value of about 45% after irradiating with 1 x lOI Al/cm’, while the relative number of Co-vacancy complexes increased to a saturation value of about 10% at 6 X lOi Al/cm2 [78]. A mathematical model was developed which could explain these experimental results (see fig. 14). The analysis of samples implanted with Co at 5, 77 and 293 K provided the following results [197]. An f, value of 0.56 f 0.02 was measured after implantation of 0.7 at% Co at 5 K. Warming up to 77 K and 293 K yielded a change of f, to 0.63 and 0.30, respectively. The low-temperature results are in good agreement with those obtained from the Mossbauer experiment described above.

0. Meyer

458

and A. Twos

0.27at.%Co T,=T,=293K

O.l6at.%Co T,=T,=77K

L

hAkllO>-\

-1 Fig. 74. Angular

yield

curves

for 2 MeV

0

I, +l -1 TILT ANGLE (deg)

He ions backscattered from Al single (a) and at 293 K (b) [195].

0 crystals

+I implanted

with

Co ions at 77 K

Implantation and in situ analysis at 77 K yielded an f, value of 0.69 &-0.04. The angular yield curves revealed the same critical angles for Al and Co, as shown in fig. 74a. From this it can be concluded that 69% of the Co atoms are located at substitutional lattice sites without any relaxations. Annealing at 293 K did not produce a large change of the substitutional fraction. Implantation at 293 K, however, led to f, values of 0.2 and 0.4 for Co concentrations of 0.12 and 0.25 at%, respectively (see fig. 74b), indicating that the Co atoms interact strongly with freely migrating point defects. As such a behaviour was not observed after implantation at 77 K, at which temperature only the SIAs are mobile, it is concluded that the strong decreaseof f, after implantation at 293 K is caused by the formation of Co-vacancy complexes. In summary, the Mossbauer and the channeling experiments yielded the same substitutional fraction of 0.56 for Co implanted into Al at 5 K. In addition, the Mossbauer experiments confirmed that the non-substitutional fraction consisted of Co-interstitial and Co-vacancy complexes which form during the cooling phase of the cascade. The relative contributions of these three components vary with increasing defect density. The high formation probability of Co-point-defect complexes after implantation was attributed to the large size-mismatch energy. Therefore, systems with increasing AHsize values have been selected for further studies. AlCe, AlTe, AlLa, AlSr, AlBa: These systems are presented in the order of increasing size--n-&m&h energy (f&m 7fio 318 kJ/mol). In preliminary studies mainly implantations at 293 K were performed which in all cases yielded small or zero substitutional fractions. As examples the results for the implanted AlCe and AlBa systems will be presented in more detail [197]. The solid solubility of Ce in Al is%s than m4 at% [134]. After implantation of 0.02 at% Ce into Al at 293 K a small f, value of about 0.1 was observed. Implanting the same amount of Ce in Al at 77 K an apparent f, value of 0.43 f 0.03 was obtained. This is demonstrated by the angular yield curves shown in fig. 75. The angular yield curves reveal some structure which indicates that the non-substitutional component does not occupy random lattice sites but sites of low and high symmetry. The shallow peak and the dip near zero tilt angle in the (110) and in the (100) direction, respectively, indicate that a small amount of Ce atoms (about 10%) is located at near octahedral lattice sites. Further there is another structure which becomes far more pronounced after annealing to 293 K (see fig. 75). This annealing procedure above

Lattice

sire occupation

of non-soluble

elements

O.O7at% Ce TI= T,. 77K PLANE: CLOSE

TILT

implanted

TO hOO\

in metals

459

-

1.c)-

0.' 5-

\

0 Ld F

0 Al W,,2

B N G s P

q

4

0.16 at% 0

T,=77K oCe T,=293K W,,, : 0.60'

Y

0.64'

I 00

dl Ce

q\

0 00 oo"oo

I TI= T,=77K OH0 CJ 00 ~ooooo 00

1.t1

0. 5

0 Al VI,,, =0.580

l CeT,=77K W,,,:

0.56'

I . Fig. 75. Angular

yield

-1

0 TILT

+l

ANGLE (degl

curves of 2 MeV He ions backscattered from (llO)(a) and (lOO)-aligned implanted with Ce ions at 77 K and after annealing to 293 K [197].

(b) Al single crystals

recovery stage III leads to a strong decrease of the substitutional Ce component. In comparing with Monte Carlo simulations the structures seen in the angular yield curves for Ce at 293 K can be attributed to 100% of Ce located within the faces of Al tetrahedra. The results can be explained by assuming that hexavacancy-Ce and trivacancy-Ce complexes form during implantation at 77 K while only the concentration of trivacancy-Ce complexes increases during annealing above recovery stage III. The real substitutional fraction is about 10% larger than the apparent one given above. Implantation of Ba into Al at 5, 77 and 293 K did not reveal any substitutional fraction. In all cases the angular yield curves of Ba reveal distinct structures which are well formed even after implantation at 293 K (see fig. 76). The peak structure near zero tilt angle for the (110) direction is due to a Ba component on distorted octahedral sites. This component does not provide intensity at zero tilt angle in the (100) direction. The broad peak structure near zero tilt angles for the (100) direction and the rather large intensity at large tilt angles can fully be attributed to Ba within the faces of Al tetrahedra. Such a component on sites of low symmetry will contribute to the yield of Ba in the (110) direction at all tilt angles. Thus the angular yield curves for Ba can be simulated (solid lines) assuming that 80% of the atoms are located in

0. Meyer

460

and A. Turos

0.23at%Ba T,=T,=293K TILT PLANE:

O.lZat%Ba T,=T,=293K TILT PLANE: (100)

(100)

& 1.0 0

000

0000

Id F 0 z

qo 0

0

0

0

0 0 0

0

0

0no

0

i

$

0.5

0

0

z” 0

0 0

o x._/AL

Fig. 76. Angular

.Ba

I

I

-1

0

. Ba

o Al

I ' & +I -1 TILT ANGLE (deg)

I

0

yield curves of 2 MeV He ions backscattered from (llO)(a) and (lOO)-aligned implanted with Ba ions at 293 K. Solid lines are from Monte Carlo calculations

trivacancy-Ba and 20% in hexavacancy-Ba substitutional lattice sites.

complexes,

c

+l (b) Al single [197].

and with no Ba component

crystals

on

7.2. Summary and conclusions

The experimental f, values for as-implanted Al-based systems with negative values of AH,,, are collected in table 9. For a more convenient discussion of the data the values of f, obtained after implantation of metallic impurities in Al are shown in fig. 77 as a function of the size-mismatch energy calculated from eq. (4.5) using a Poisson ratio of 0.34. All the results discussed in section 5.1 for systems with positive AH,,, values have been included in fig. 77. Although our systematic study about the lattice site occupation of implanted ions which form dilute alloys with negative heat of solution is far from complete, several conclusions can already been drawn. Three distinct regions are seen in fig. 77. Large f, values are obtained for systems with AH,, values up to about 10 kJ/mol, irrespective of AH,,,. The influence of large negative AH,,, values, e.g. for AlAu and AlPd, is seen in the temperature region above stage I,, where the self-interstitial atoms are moae. Large f, values for these systems besides AlHf can only be obtained after implantation at 5 K. The formation of mixed dumbbells asobserved by irradiating dilute solid solutions of Al-O.1 at% Ag at 77 K was not found to occur in similar irradiation experiments on the as-implanted systems [191]. In the transition region with AH,,, values between about 10 and 100 kJ/mol the substitutional fraction decreases to zero. For the system AlCo, Mijssbauer experiments at 5 K [78] gave an f, value of 0.56 f 0.03 in good agreement withour value and showed that the non-substitu-

Lnttice

site occupation

Pd $34 1.0 I ' Au 0

of non-soluble

Cd Hg Ni Ga Mn (Cu lHJ??o I -III

implanted

0

Ce In Sb Pb;Te !Ja

Sr !RbBss

1

A A

A A

0 0 0

I.2 TG

A

O0

OIIK .5K

461

in metals

O A

s -1, ‘Z g ( .{ o.s1 z _ z ,$ _

elements

AHSOL

0


0.1

Fig. 77. Substitutional

0

fraction of various metallic species implanted into Al as a function of the size-mismatch energy [197].

tional component consists of Co-SlA as well as of Co-vacancy complexes indicating that interactions with both kinds of points defects do occur in the cooling phase of the collision cascade. These interactions lead to displacements of the impurities from their substitutional sites and are responsible for the decrease of f, especially for the 3d transition elements Fe, Ni and Co, which is an interesting point for further studies. None of the systems with A Hsiz, values above 80 kJ/mol reveal large substitutional fractions after implantation at 293 K. The f, values for the systems AlCe, AlTe and AlLa at 77 K decrease to 0.0 after warming up from 77 to 293 K above recovery stage III (se7e.g. fig. 75). This indicates that the interaction of impurities with vacancies becomes of increasing importance for systems with increasing AH,, values. For systems with AH,, values above 100 kJ/mol, f, is close to zero independent of the substrate temperature during implantation. The non-substitutional components are not due to precipitate formation but to the formation of various impurity-vacancy complexes, where the impurities are located at sites of high and low symmetry as shown in some detail for AlBa. This indicates that the probability of impuritypoint-defect complex formation is about1 in the cooling phase of the collision cascade. It is interesting to note that such high complex formation probabilities were observed neither for Vnor Fe-based ion implanted systems (see figs. 53 and 54). The correlation of f, with AH,, reveals a similar dependence for the Al-based systems with positive values of AH,i,. Thus the dependence shown in fig. 77 offers a universal description for the various substitutional fractions obtained for all Al-based ion implanted systems. In a recent study [199] a set of theoretical vacancy-solute binding energies for Cu-based and Ag-based alloys have been correlated with the difference between solute and host valences, with the slope of the solidus curves and with the changes of the lattice parameter with impurity concentration. The correlation between binding-energy and lattice-constant change was found to be by far the best

462

0. Meyer

and A. Twos

one. This indicates that for dilute equilibrium alloys the vacancy-impurity binding proportional to the size-mismatch energy which supports our findings for implanted

energy is systems.

8. Conclusions The backscattering/channeling technique has proven to be very useful in studying lattice site occupation of implanted non-soluble elements. When combined with the cryostat goniometer [200] which enables in situ implantation and analysis at temperatures ranging from 5 to 293 K, this method made it possible to elucidate several important questions in ion implantation metallurgy. The most important one concerns the factors that determine the substitutionality of implanted species. Although many models based on the properties of equilibrium systems have been applied to implanted systems with different degrees of success, it remained open whether these models are applicable at all to the highly metastable systems often produced by ion implantation. In view of general concepts of impurity-point-defect interactions, the implanted systems were divided in those with positive and those with negative heats of solution. We have shown that the lattice site occupation of non-soluble atoms having positive values of AH,,, is governed by at least three processes: spontaneous recombination of impurities and vacancies during the relaxation phase of the collision cascade, trapping of vacancies during the cooling phase of the cascade, and finally trapping of mobile vacancies at temperatures above stage III. Since the impurity-vacancy interaction depends on the heat of solution and the size-mismatch energy, a decrease of the substitutional fraction is observed with increasing AH,,, and AHsize. It should be pointed out that the apparent success of the Hume-Rothery rules or the Miedema model is due to the fact that they depend in some way on the heat of solution. Thus, in spite of the fact that these methods are unable to indicate the real mechanisms of lattice site occupancy and atomic displacements, they may be applied to obtain a rough estimate of the substitutionality limits. The dependence of the substitutional fraction on the annealing as well as on the substrate temperature during implantation is therefore due to the formation of vacancy-impurity complexes. The overlap of dense collision cascades produced by subsequently incoming ions may cause a dissociation of previously formed complexes. In principle, this makes it possible for an impurity atom to occupy again a regular lattice site. Here the delicate balance between the vacancy retrappmg and escaping probabilities determines the lattice position of an impurity. We have shown that, if the binding energy of a vacancy-impurity complex is smaller than the vacancy binding energy of competing trapping centres, an increase of the concentration of the latter centres results in an increase of the substitutional impurity component. Due to the presence of competing trapping centres implanted systems behave differently from similar dilute solid solutions in post-irradiation experiments. The decomposition of vacancy-impurity complexes due to post-irradiation does occur even at temperatures below stage I. In this case the energy supplied by the collision cascade induces dissociation of the complexes and spontaneous recombination of the vacancy and a neighbouring SIA. The cross section for these dissociation and spontaneous recombination processes was found to be 8 times larger than the displacement cross section as predicted by the modified Kinchin and Pease formula. This large value, however, supports the results of molecular dynamics calculations. As after post-irradiation of AlCd at 5 K all impurity atoms were at substitutional sites it was concluded that spontane&s recombination during the relaxation phase of the cascade is the most important mechanism that determines the lattice location of

Lotlice

sire occuparion

of non-soluble

elements

implanted

in metals

463

ions implanted into metals. Although up to now most of the experiments dealt with non-soluble impurities that form vacancy-type complexes, one may expect that the study of impurities having negative heats of solution will be of great interest. This type of impurities is usually undersized and tends to form interstitial-impurity complexes at low temperatures. In contrast to the case of systems with positive A HsO, values which increase with increasing AHshe, such a correlation does not exist for systems with negative A Hso, values. Thus, the influence of A Hso, and A Hsize on f, could be studied separately. Here we have concentrated on Al-based implanted systems, because the experimental results can be compared with numerous results on impurity-point-defect interactions obtained by irradiating diluted Al alloys [24]. Metallic impurities with negative AH,,, values ( - 200 kJ/mol < A Hso, < - 20 kJ/mol) and AH,, values, if implanted into Al at 5 K, give rise to f, values close to 1.0, indicating a rather small probability for SIAs trapping during the cooling phase of the cascade. This is in agreement with the results for V-based implanted systems with negative AHsol, in which case the substitutional fraction was 1.0 even after implantation at 293 K (see table 7). The substitutional fraction of elements implanted into Al decreases strongly with increasing values of AH,, for all substrate temperatures. Annealing experiments above recovery stage III indicate that impurity-vacancy complex formation contributes strongly to the non-substitutional components. The size-mismatch energy seems to play an important role in ion implantation, not only for the lattice site occupation but also for ion-induced amorphization [201] and plastic deformation [148,149]. The latter processes were shown to be caused by strain-induced mechanisms. Further experiments are in progress to elucidate the important role of the size-mismatch energy in the physics of implantation metallurgy. The semi-empirical theories of Miedema et al. [36] and Eshelby [102] obviously provide excellent guidelines to design systematic ion implantation and channeling experiments and to interpret the obtained results. Microscopic theories as mentioned by Benedek [199] may provide further insight if applied to ion implanted systems.

Acknowledgements

The authors would like to thank their colleagues A. Azzam, R. Gerber, I. Khubeis, M.K. Kloska, G. Linker, F. Pleiter, A. Seidel and G.C. Xiong for valuable discussions and for providing some of their results prior to publication. References [l] [2]

[3] [4] [5] [6] [7]

J.K. Hirvonen, ed., Treatise on Materials Science and Technology, Vol. 18. Ion Implantation (Academic Press, New York, 1980). The development of the current research can be followed from the Proceedings of the Conference Series Ion Beam Modification of Materials, Radiation Effects 48 (1980); Nucl. Instr. Methods 182/183 (1981); 209/210 (1983); B7/8 (1985); B19/20 (1987). J.M. Poate and A.G. CuIIis, in: Treatise on Materials Science and Technology, Vol. 18. Ion Implantation, ed. J.K. Hirvonen (Academic Press, New York, 1980) p. 85. ST. Picraux, Arm. Rev. Mater. Sci. 14 (1986) 809. J.A. Borders, Ann. Rev. Mater. Sci. 9 (1979) 313. A. Turos, Phys. Stat. Sol. 94a (1986) 809. A. Turos, A. Azzam, M.K. KIoska and 0. Meyer, Nucl. Instr. Methods B19/20 (1987) 123.

464

0. Meyer

and A. Twos

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