Lattice site occupation of non-soluble elements implanted in metals

Nuclear Instruments and Methods in Physics Research B19/20 (1987) 123-131 North-Holland, Amsterdam

123

Section 11. Ion implantation in metals LATrlCE

SITE OCCUPATION OF NON-SOLUBLE ELEMENTS IMPLANTED IN METALS

A. T U R O S * , A. A Z Z A M * * , M.K. K L O S K A , and O. M E Y E R Kernforschungszentrum Karlsruhe, lnstitut f~r Nukleare FestklJrperphvsik, P.O.B. 3640, D-7500 Karlsruhe, FRG

Recent studies of the lattice location of different atomic species implanted in metals are reviewed. It has been found that the most important factor influencing the substitutionality of implanted atoms is the heat of solution A H s°j. Since the vacancy-impurity binding energy increases with increasing A H s°t for non-soluble systems which have a rather high positive heat of solution, the formation of vacancy-impurity complexes is a decisive mechanism of the impurity displacement from the substitutional lattice site. The vacancy-impurity interaction leads to some new effects such as: a) the dependence of the substitutional fraction on the substrate temperature during implantation and on the annealing temperature, b) the anomalous change of the substitutional fraction as a function of the impurity concentration and c) the improvement of the substitutionality due to postirradiation.

1. Introduction

The properties of solids depend crucially on impurity additions. Whether a given impurity is substitutional, interstitial or at all soluble in a host is a question of fundamental interest. The prediction of the lattice position of the implanted atoms is one of the most formidable problems in ion implantation metallurgy. Many attempts have been made so far to answer this question [1]. As a first step one considers the alloying rules for the formation of binary equilibrium phases. Since a clear understanding of the nature of interatomic forces between impurities and host atoms has not yet been elucidated, almost all of the alloying rules are empirical. The Hume-Rothery [2] rules and Darken-Gurry plots [3] have been quite successful for decades. A better accuracy has been attained by Chelikovsky [4] and Alonzo and Simozar [5] who applied the Miedema parameters [6] to the study of solid solubility. Recently, Singh and Zunger [7] derived nonempirically, from a pseudopotential description of free atoms the orbital radii coordinates which provide a systematization of the solubility data equal or better than the empirical ones. Nevertheless, there are always some exceptions which do not fit to any of the schemes. Ion implantation is a nonequilibrium process leading often to metastable situations. Both substitutional and interstitial solid solutions at compositions not allowed *Permanent address: Institute for Nuclear Studies, Warsaw, Poland. **Permanent address: Nuclear Physics Department, Nuclear Research Center, Atomic Energy Establishment, Cairo, Egypt. 0168-583X/87/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

by equilibrium phase diagrams can be formed. 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 solubility [1]. Such systems have a large positive heat of solution. Some atoms are 100% substitutional after being implanted at 5 K where no long range migration should occur [8]. Therefore, the final state can only be reached via an athermally activated process. The implanted ion comes to rest in a series of binary collisions with host atoms at the end of the trajectory. It may undergo a replacement collision [9] and thus reach a substitutional lattice site. In high density cascade regions, where a collective motion of all atoms prevails, the lattice site occupation mechanism could be the result of an ultrafast quenching process from a liquid like region [10]. Replacement collisions can not explain the fact that many atoms implanted in Be prefer to occupy substitutional lattice sites [11]. Thus an important question concerning the origin of the driving force producing atomic displacement from substitutional lattice sites is to be answered. Apparently the schemes based on equilibrium systems fail to explain the behavior of the low temperature implants. So far we have considered the impurity-host atom interactions neglecting the presence of lattice defects created by the ion implantation itself. It is well known that an attractive interaction between point defects and impurities leads to the formation of defect-impurity associations so-called complexes [23]. Impurity atoms on substitutional sites which are smaller than the host atoms contract the lattice. Thus self-interstitial atoms (SIA) which expand the II. METALS

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A. Turos et al. / Lattice sites of non-soluble elements in metals

lattice may be trapped by small solute atoms to form mixed dumbbells. In contrast to small impurities, large solute atoms expand the lattice. In this case the elastic stress will be released by trapping one or more vacancies. It should be emphasized that this is the case of nonsoluble atoms having positive heat of solution. Numerous techniques have been applied to label specific small defect clusters [12]. The channeling technique [13] for example is a convenient technique to study the trapping of vacancies and SIAs by substitutional solute atoms in metals [14]. Since the impurity atoms are displaced from their substitutional sites and are shifted to interstitial sites of low or high symmetry depending on the different complex configurations they can be easily detected using this technique. The main purpose of this paper is to review the experimental data and to provide evidence that defect-impurity, in particular vacancy-impurity interaction is the governing process which determines the lattice site occupancy of atomic species implanted at low concentrations. First, we shall consider some general features of vacancy-impurity interactions in metals in order to provide a basic framework for the subsequent treatment of some implantation phenomena such as the temperature dependence of the substitutional fraction, its anomalous change as a function of the impurity concentration and the improvement of the substitutionality due to postirradiation. 2. Vacancy-impurity interactions in metals Temperature is the key parameter in the interaction between point defects and impurity atoms. The annealhag behavior of irradiated metals is governed by distinct recovery stages which appear at temperatures where different defects become mobile. The five principal stages of the so-called one-interstitial model according to Schilling [15] are summarized in table 1. Two of the recovery stages namely stage I and III are of special interest for the study of defect-impurity

interactions. Mobile defects diffusing toward sinks (external surfaces, extended defects, etc.) can be captured by impurity atoms forming more or less stable defect-impurity complexes. The probability of such an encounter depends on the long range part of their mutual interaction potential and is usually expressed in terms of a trapping radius R t. Whenever a point defect enters into a sphere with the radius R t around an impurity atom the attractive potential causes trapping. For this to occur, it is necessary that the defect coming from the infinity has gained an amount of potential energy, A~ D at least equal to the thermal energy. Hence, the trapping radius is given by ~D(OO) -- ~s(Rt) = k T [16] where ~s is the interaction potential at the saddle point. An encounter of a SIA with an impurity atom will lead to the formation of a stable association if an arrangement can be found where the strain energy can be reduced. Dederichs et al. [17] have shown that this is the case for small impurity atoms which are incorporated into mixed dumbbell configurations. The criterion for atomic misfit is the difference between the partial atomic volume ~B of the impurity atom and the atomic volume of the solvent 12A [18]. The size factor, ~st, is defined as fist = (~B - ~ ' ~ A ) / ~ ~ A . Undersized atoms which form mixed dumbbells have f2sr < 0. Accordingly the oversized solutes (f2sf > 0) cannot be incorporated into the dumbbell and thus only a weak interaction with SIA has been observed [14]. It should be pointed out that undersized atoms which have a negative heat of solution form either extended solid solutions or intermetallic compounds. On the other hand, the oversized atoms are usually characterized by the positive heat of solution and are non-soluble in a given host. The lattice expansion produced by the incorporation of an oversized impurity atom into the substitutional lattice site can be largely released by capturing of one or more vacancies. Doyama [19] has indicated that the binding energy of such a complex is proportional to the heat of solu-

Table 1 Recovery model for metals Recovery stage

Temperature a) (K) A1 V 5-40

Description Fe

IA-I D

15-37

60-120

Ix II III IV V

40-45

50

140

190-250

200

200

775

600

700

Recombination of close interstitial-vacancy pairs Free migration of interstitial atoms Growth of interstitial clusters followed eventually by dislocation loop formation Free migration of vacancies Growth of vacancy clusters Dissociation of defect dusters, annealing of residual damage

a)The temperature data are taken for AI, V and Fe from refs. [47,48].

125

A. Turos et al. / Lattice sites of non-soluble elements in metals

tion. In fact, the higher is the energy required to replace a host atom by an impurity atom, i.e., heat of solution, the greater is the distortion in the vicinity of an impurity. The lattice strain can be partially released when a vacancy is trapped at a neighbour site of an impurity. The amount of released energy is therefore equal to the binding energy [20]. Miedema et al. [6] have calculated the heats of alloy formation using a macroscopic, semiempirical model which is quite successful for liquid alloys and for solid compounds containing a transition metal. However, it is not clear how to deal with the size mismatch contribution. Miedema et al. [6] have estimated the size mismatch energy from the Eshelby elastic continuum theory [21], but it is doubtful whether such a macroscopic theory can be applied to the atomic scale. Moreover, as pointed out by Chelikowsky [4], the energy involved in local lattice relaxation around the impurity may be partially inherent in A H~oI as determined by Miedema. In conclusion it can be stated that although not completely quantitative Miedema's model provides useful guidelines for vacancy-impurity interaction. The interaction potential consists of two parts. The long range interaction which determines the trapping radius is dominated by the strain field produced by the size mismatch. The short range interaction due to electronic interactions appears first when the vacancy occupies a neighbour position to the impurity atom. It is an important factor determining the binding energy of vacancy-impurity complex [20]. The trapping of vacancies by the impurity atom produces its relaxation towards the centre of a complex. The relaxation of a substitutional impurity atom towards the single vacancy is estimated to be 0.01 - 0.02 am [22]. Such small relaxations can be determined from the narrowing in the angular yield curves measured by the channeling and backscattering technique [13]. When multiple vacancy trapping occurs, an appreciable displacement of the impurity atom will be displayed into quite specific interstitial positions in the host lattice [14,23]. The multivacancy-impurity complexes have been observed in many fcc and bcc metals [8,24,25].

3. Temperature dependence of the substitutional fraction Lattice site location studies in ion implanted metals have been extensively performed in the last decade. The previous results have been summarized and discussed in ref. [1]. From this summary it can be seen that after being implanted at 293 K heavy elements from groups IIIa to VIIa of the periodic system usually reveal high substitutionality in the hosts like Cu, Ni, Fe and V whereas those of groups Ia, IIa, IIIb and some rare

•

1.0-

f~

VBi

CI = 0.1- 0.2 or%

/', _~ cd oFeBo oVl~

\

\

o____~ \ 0.5.

0.0

°------A\\\~

"~

,

Tx(K}

soo

Fig. 1. Temperature dependence of the substitutional fraction (fs) for different ion implanted systems [8,29,30]. earth elements are almost nonsubstitutional. The comparison with the modified Darken-Gurry plots [26,27] shows that the substitutionality of implanted species can be predicted with a success of about 90%. Several elements which do not obey the modified rules are: Ce, La, Se and I in V, Cd in A1 or Ba in Fe. Detailed studies on the substitutional fraction (f~) performed by in situ implantation and channeling analysis at different temperatures ranging from 5 to 293 K revealed that this parameter is crucial for the lattice site occupancy of non-soluble implants [8,28-30]. Some of the results are shown in fig. 1. The following characteristics should be pointed out: (i) there are systems like _VBi where fs of the impurity is equal 1.0 independent of the lattice temperature. (H) f~ for other systems like VBa, FeBa or AICd is 1.0 or less and is independent of the--]attice t ~ p e r a t u r e for temperatures below 77 K. For these systems a pronounced decrease of f~ is noted after implantation at 293 K. These results can be understood by noting the correlations between the recovery stages as listed in table 1 and the temperatures at which the change of the substitutionality has been observed. Since stage I sets in below 77 K and stage III lies between 200 K and 300 K it can be concluded that for the investigated systems mobile SIAs do not play any role in the lattice site occupancy. The interaction of impurity atoms with vacancies which are mobile at 293 K would lead to the decrease of f~ via vacancy capturing and subsequent displacement of the impurity. A relatively simple experiment has been performed to prove that hypothesis [31]. A (110) Fe single crystal was implanted at 77 K with 1 × 10 t5 Au cm -2. Fig. 2 shows the angular scans for the asimplanted sample and after postirradiation with 2 × 1016 4He cm -2 (200 keV) also at 77 K and subsequent warming up to 293 K. The angular scan for the asimplanted sample reveals a 100~ substitutionality of the impurity. The postirradiation at 77 K with fight ions II. METALS

126

A. Turos et aL / Lattice sites of non-soluble elements in metals

o - Fe

• - Au 1[

AS IMPLANTED at 77K 1.0-

{

&77K o -293K

I

k

SeAsTeAu Sn Bi Pb --o-o--o--o~< ~ : ~

C[ = 0.1 - 0.2 at %

08.

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N

t

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t

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I

POSTIRRADIATED WITH ~'He-IONS AT 77K

J


La

04

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C] UJ

Lx

0.5 -

1.0

,_

I

I

0

I

200

~,,

OI

Z.00

I

I

600

AHsol (kJ/mol}

WARMED UP TO 293K,o° ~

Fig. 3. Variation of the substitutional fraction of different elements implanted in V as a function of the heat of solution for different implantation temperatures [42].

d

0.5

(b) 0.0

!

-200

%0-0`0 I

-1.0

i

I 0

t

I

I

1.0

~u (deg)

Fig. 2. Angular scans through the (110) axial direction of Fe single crystals implanted with 1 × 10t5 Au cm -2 at 77 K (a) and after postirradiation with 2 X 10164 He cm- 2 200 keV and subsequent warming up to 293 K (b) [31].

like 4He produces mainly point defects which are immobile (see table 1) and do not affect the angular scan curve. Warming up to the temperature at which vacancies became mobile, a decrease of fs has been observed. The correlation between fs and the corresponding heat of solution (AHsol) as estimated from Miedema's model [6] for vanadium is shown in fig. 3 [42]. The elements having a negative heat of solution in V are 100% substitutional at 293 K. Other elements with a small positive heat of solution (for example Bi) are 100% substitutional independent of the lattice temperature. Elements like Ce, La, Ba and Cs, which have a rather high heat of solution (between 120 and 690 kJ/mol) reveal a temperature dependent substitutional fraction. It can also be seen from the fig. 3 that Ce, La, Ba and Cs have only a small or no substitutional component when implanted at 293 K. At temperatures below 100 K, where vacancies are not mobile the elements Ce, La, Xe, Ba and Cs still have

non-substitutional components, which cannot be attributed to the trapping of mobile vacancies in the delayed regime beyond the cascade. These components can also not be attributed to impurity precipitate formation, as the average distance between the impurities is about 30 A 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 range between 0.03 and 0.3 at.% which would otherwise be expected for precipitate formation. Thus, the only explanation for these non-substitutional components is that the impurity atoms have a certain probability to come to rest, during the slowing-down process, in a vacancy rich re#on or to trap further vacancies within the cooling phase of the collision cascade. A similar behaviour of fs as a function of A HsoI and of the implantation temperature has been observed for other metallic hosts, both bcc (Fe) and fcc (A1) [29,30]. In general, it is concluded that the empirical methods which are based on thermodynamic equilibrium are not successful in predicting the substitutionality of atomic species implanted in a host metal. The basic mechanism for lattice site occupation in metals is the spontaneous recombination of the impurity atoms with lattice vacancies in the cascade and subsequent vacancy trapping either within the cascade or in the delayed regime.

4. Postirradiation

enhanced

lattice site occupation

Cadmium and aluminium are almost completely immiscible even in the liquid state [32]. After implantation

127

A. Turos et aL / Lattice sites of non-soluble elements in metals

[

8.0 "1015Cd+in AI O10>at 77K £1.2at %Cd

8.0.1015 Cd~'cm2 in AI (110)ai 293K i analyzed at 293K 20 MeV He+

o

AI

analyzed at 77K ,20 MeV He+ { x° cdAI}

x Cd

:

1.0-

\

S _w >-

Cl LLI

N05 d < c~ O Z

\

/

\

p

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!

(a) - 1.0 '

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(b) '

0 io

'

1.0 '

TILT ANGLE (deg)

- 1.0

"~~ '

ol 0

'

1.0 '

TILT ANGLE (deg)

Fig. 4. Angular scans through the (110) axial direction of A1 single crystals implanted with 8 × 1015 Cd cm -2 at 293 K (a), and implanted with the same dose at 77 K (b) [30].

of Cd ions into A1 single crystals at 293 K the Cd atoms occupy nonregular lattice sites in agreement with the phase diagram [30]. This is clearly demonstrated by the angular scan shown in fig. 4a. However, if the implantation and analysis are performed at 5 K f~ is as large as 1.0 [30]. Similar results have been obtained after implantation and in situ analysis at 77 K (see fig. 4b), above stage I, indicating that mobile SlAs do not influence the lattice site occupation. From the perfect matching of the angular yield curves for A1 and Cd it can be concluded that the Cd atoms are located on substitutional lattice sites without any relaxations. After warming up the low temperature implants to 293 K, f~ decreases to 0.15. This is due either to the formation of vacancy-Cd clusters or Cd-precipitate formation. The method of investigation of the nature of defect clusters is based on the use of defect-antidefect reactions. When vacancy-impurity complexes are already formed the irradiation at temperatures below stage III may annihilate the trapped vacancies through absorption of mobile SIAs. Light ion irradiation is an effective means of producing separated point defects [33]. On the other hand, it is expected that irradiation with heavy mass ions would, by recoil dissolution, dissolve precipitates if they exist. The following experiments have been performed to answer the questions raised above [30,34]. Postirradiation at 77 K of an A1Cd system as produced by Cd implantation at 293 K (f~ = 0.15) with 300 keV Ne ions leads to a steep increase of fs. This effect is demonstrated in fig. 5 where the Cd peaks from random and (110) aligned spectra are shown for the asimplanted case and after irradiation with various fluences of Ne ions. The decrease of the Cd-peak area

with increasing Ne ion fluence is due to the transfer of Cd atoms to substitutional lattice sites. Postirradiation experiments have been performed at 77 K as well as at 5 K using 1H- and 4He-ions [30]. The results show that the annealing of possible Cd-vacancy clusters by long range migration and adsorption of SIAs is not the dominant process for the observed enhanced lattice site occupation. In fig. 6 the increase of f~ due to He and Xe postirradiation is shown. Two important features of these results should be pointed out. Firstly, by increasing the postirradiation fluence complete recovery of Cd can be 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 dissolution of Cd precipitates. It has been found that the increase of f, does not depend on the Cd concentration indicating that in the used concentration range no precipitate formation occurs [30]. The fact of complete recovery even at high Cd concentration is a further hint that Cd precipitation does not occur after implantation at 293 K or during annealing to 293 K as it is known that precipitates will not dissolve completely by recoil dissolution [35]. Therefore, the displacement of the Cd atoms after implantation at 293 K is obviously due to the formation of vacancy-impurity complexes. Since, as discussed above, these complexes do not anneal out by absorbing migrating SIAs the question arises as to which process could contribute to the large cross section for the Cd recovery. The infuence of sub-threshold collisions is ruled out by the TRIM2 calculations [36] and analytical calculations of the recoil spectra [37]. The II. METALS

A. Turos et a L / Lattice sites of non-soluble elements in metals

128

2000,

//

/ 0

J

,

"

2so

200

~//

36o';o

. . . .

"~"

d.o

,'0

CHANNEL NUMBER Fig. 5. Aligned (I) and random (zl) energy spectra for 2 MeV 4He+ ions backscattered from an A1 single crysta] implanted at 293 K with 8 × 1015 Cd cm -2. After implantation the sample was cooled down to 77 K and subjected to postirradiation with 300 keV Ne-ions. The aligned spectra marked (B) and (*) correspond to the postirradiation fluences of 4 x 1014 Ne cm -2 (0.14 dpa) and 2 × 1016 Ne cm -2 (7.0 dpa), respectively.

ratio of the energy density deposited in nuclear collision to that deposited in subthreshold collisions and in phonon production is about 5 for He and about 220 for Xe irradiation. Due to this fact one would expect a far steeper slope for He irradiation in contrast to the observed result. Further, it is noted that the initial slope is independent of the average cascade density as the mean transferred energy is about 0.15 keV for 200 keV He and 2.5 keV for 600 keV Xe irradiation. In the fluence region where tingle cascades do not yet overlap the fraction of Cd atoms which move to substitutional

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$

[] 600 keY Xe* ]

Postirradioted

h-

A 200 keV He+

ot 77K

0.8-

%

u_

Z

06-

A []

n Z~

n Z~

_(2 I--

2 ok[]

tn ,-I-i

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lattice sites is about a factor of 8 larger than the calculated number of displacements per atom. Molecular dynamic calculations [38,39] have shown that 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. Using the instantaneous number of Frenkel pairs the displacement cross section would be of similar magnitude as the cross section for the recovery process. The only process which is proportional to the number of displaced atoms and independent on the cascade density and the damage production efficiency is the spontaneous recombination of neighboured Frenkel pairs. The Cd-vacancy cluster can be considered as a neighboured Frenkel pair especially because the A1Cd system fulfills the H u m e - R o t h e r y conditions and--Cd fits nicely in a substitutional lattice site. The recovery mechanism can then be described as an unstable pair recombination process within the cascade and would be a measure of it [34]. The same recovery phenomena have also been observed for other systems like FeAu and AlIn and A1Pb [30].

0.2~E rr

z° 0o

B '~-~

' ~'"i6-, ~ ' ' ~ ' " . ~ o

~ ' ' ~ ....

FLUENCE (dpo)

Fig. 6. Increase of the substitutionaJ fraction of Cd implanted in A1 at 293 K and postirradiated at 77 K with different fluences of 200 keV 4 He-ions (zx) and 600 keV Xe-ions (t-l).

5. Concentration dependence of the substitutional fraction Another new effect has been observed for some systems of limited solid solubility which are characterized by a positive heat of solution less than about 100

129

A. Turos et al. / Lattice sites of non-soluble elements in metals

kJ/mol. The substitutionality of some elements implanted at 293 K improved with increasing implantation dose. This is opposite to what can be expected for such systems. In fact, f~ should be 1 at low implant concentrations, and should decrease eventually at higher 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 [31]. - - A l t h o u g h Au in Fe does not satisfy well the H u m e - R o t h e r y rules, a limited solubility of Au in Fe has been reported [40]. In agreement with this expectation the implantation of Au into Fe at 77 K and the in situ analysis yield a fs value of 1.0 independent of the implanted Au concentration in the range between 0.1 and 2 at.%. The experimental results after implantation of Au into Fe at 293 K however reveal the opposite trend. As presented in fig. 7, 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 does not change even at the highest implanted concentration of 7 at.% although the solubility limit was exceeded by a factor of more than 70 [411. The similar effect has been observed for the VCe system [42]. In this system, however, because of a much lower solubility the initial value of f~ is about 0.15 and increases as a function of the implantation fluence up to 0.7 for 3.5 at.% (fig. 7). With a further increase of the Ce concentration fs decreases, apparently due to Ce precipitation. The angular dependences of the normalized yields are shown in fig. 8. These angular scans provide a more detailed information on the lattice location of the implanted species than the f~ values alone. For small Au

10..

Iv----

08

./

o6/ f~ 0./~ ~

, Fe Au

/

02

o V_Ce

o

OC

0

,

l

1

,

l

2 CI (or %)

i

3

Fig. 7. Variation of the substitutional fraction (fs) with the implanted concentration (cl) for the FeAu (O) and the VCe (O) systems [31,42].

::, 1.0

) o,

"%%.

,9f

#

%

05

£

(o)

U.I >-

I

o O.C

I

..-q < 1.0 :E

I

%

n-" O Z

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./'"

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",2

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• - 6 . 1 0 1 5 A u / c m 2 ot 293K o - Fe &~.~

[.U N

I

-1.6

I

-08

I

0 02 (deg)

I

I

0,8

1.6

Fig. 8. Angular scans through the (110) axial direction of a Fe single crystal implanted with different doses of Au [31].

doses (fig. 8a) the angular scans for the impurity are not only shallower but also narrower with respect to the scan for the host lattice. Increasing the implantation dose the impurity scan becomes broader and deeper and finally matches perfectly that of the host as shown in fig. 8b. 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 . 0 1 rim) displaced from the regular lattice sites and the second one consists of Au atoms randomly distributed on 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 of f~ further postirradiation 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 of fs with the Xe dose was approximately the same as that shown in fig. 8. For doses exceeding 6 x 1015 Xe + cm -2, fs reached saturation at 1.0. A similar postirradiation experiment performed at 293 K using 4He-ions did not II. METALS

130

A. Turos et al. / Lattice sites of non-soluble elements in metals

result in a noticeable change of the Au substitutional fraction [31]. From these results it is 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 large clusters [43]. Since the binding energy of a vacancy in a dislocation loop ( - 1.2 eV) [44] is substantially higher than the estimated binding energy of an Au atom-vacancy pair of 0.24 eV [45], the capture of vacancies by extended defects is energetically favourable and represents a stronger vacancy sink than an impurity atom. The vacancy-impurity complexes formed during ion implantation at 293 K decompose due to the overlap of cascades produced by the successively impinging Au ions. The released vacancies will preferentially migrate towards the extended defects and, provided the competing sink density is large enough, the decomposed complexes will not be restored. If 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 means of prebombardment of 5 × 1015 Xe cm -2. After implantation of 0.2 at.% Au into the prebombarded region a f~ value of about 1 was observed. This result confirms 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 effect is thermally activated and was not observed after implantation at temperatures below stage III where the vacancies are immobile.

6. Conclusions The backscattering and channeling technique has proven to be very useful in studying lattice site occupation of implanted nonsoluble elements. When combined with the cryostat goniometer [46] to perform in situ implantation and analysis at temperatures ranging from 5 up to 293 K this method was able to elucidate several important questions in ion implantation metallurgy. The most important was the search for factors determining the substitutionality of implanted species. Although many models based on the properties of equilibrium systems have been applied to implanted systems with different degree of success the main question remained still open whether these models are applicable

at all to the highly metastable system often produced by ion implantation. We have shown that the lattice site occupation of non-soluble atoms is govemed by at least three processes: spontaneous recombination of the impurities with vacancies within the relaxation phase of the collision cascade and trapping of additional vacancies within cooling phase of the cascade and at temperatures above stage III. Since the trapping radius for vacancies is related to the heat of solution a decrease of the substitutiouality is observed with increasing AH~ol. 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 for a rough estimation of the substitutionality limits. The temperature dependence of the substitutional fraction is therefore due to the formation of vacancy-impurity complexes. The overlap of dense collision cascades as produced by subsequently incoming ions may cause a 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 a complex is smaller than the binding energy of competing trapping centers for vacancies an increase of the concentration of these centers will be followed by an increase of the substitutional impurity component. The decomposition of vacancy-impurity complexes due to postirradiation does also occur even at temperatures below stage I. In this case the energy supplied by the collision cascade induces spontaneous recombination of the impurity with the neighbouring vacancy. It is shown that this effect provides means to study the dynamics of collision cascades [34]. Although up to now most of the experiments have dealt with non-soluble impurities forming vacancy-type complexes, one may expect that the study of impurities having negative heat of solution will be of great interest. This type of impurities are usually undersized and tend to form interstitial-impurity complexes at low temperatures. We hope that this will be one of those areas where important contributions to the physics of implantation metallurgy can be made in the future.

References

[1] J.M. Poate and A.G. Cullis, in: Treatise on Materials Science and Technology, vol. 18, ed., J.K. Hirvonen (Academic Press, London, 1980) p. 85.

A. Turos et al. / Lattice sites of non-soluble elements in metals

[2] W. Hume-Rothery, R.E. Smallman and C.W. Haworth, Structure of Metals and Alloys (Institute of Metals, London, 1969). [3] L.S. Darken and R.W. Gurry, Physical Chemistry of Metals (McGraw Hill, New York, 1953). [4] J.R. Chelikowsky, Phys. Rev. B19 (1979) 686. [5] J.A. Alonzo and S. Simozar, Phys. Rev. B22 (1980) 5583. [6] A.R. Miedema, P.F. de Ch~tel and F.R. de Boer, Physica 100B (1980) 1. [7] V.A. Singh and A. Zunger, Phys. Rev. B25 (1982) 907. [8] A. Azzam and O. Meyer, Phys. Rev. B33 (1986) 3499. [9] D.K. Brice, Inst. Phys. Conf. Ser. no. 28 (Institute of Physics, Bristol, 1976) p. 334. [10] J.M. Poate, J.A. Borders, A.G. Cullis, and J.K. Hirvonen, Appl. Phys. Lett. 30 (1977) 365. [11] E.N. Kaufmann, R. Vianden, J.R. Chelikowky, and J.C. Phillips, Phys. Rev. Lett 39 (1977) 167. [12] Proc. Int. Conf. Point Defects and Defect Interactions in Metals, eds., J.I. Takamura, M. Doyama and M. Kiritani (North-Holland, Amsterdam, 1981). [13] L.C. Feldman, J.W. Mayer and S.T. Picraux, Materials Analysis by Ion Channeling (Academic Press, New York, 1982). [14] M.L. Swanson and L.M. Howe, Nucl. Instr. and Meth. 218 (1983) 613. [15] W. Schilling, Hyperfine Interactions 4 (1978) 636. [16] K. Schroeder and K. Dettmann, Z. Physik B22 (1975) 343. [17] P.H. Dederichs, C. Lehmann, H.R. Schober, A. Scholz, and R. Zeller, J. Nucl. Mater. 69/70 (1978) 176. [18] H.W. King, J. Mater. Sci. 1 (1966) 79. [19] M. Doyama, J. Nucl. Mater. 69/70 (1978) 350. [20] A.R. Miedema, Metallkunde 70 (1979) 345. [21] D.J. Eshelby, Solid State Physics 3, eds., F. Seitz and D. Turbull (Academic Press, New York, 1956). [22] H. Hofs~iss, G. Lindner, E. Recknagel and T. Wichert, Nucl. Instr. and Meth. B2 (1984) 13. [23] A. Turos, Phys. Star. Sol. 94A (1986) 809. [24] M.L. Swanson, L.M. Howe, A.F. Quenneville, Th. Wichert, and M. Deicher, J. Phys. F14 (1984) 1603. [25] M. Vos, D.O. Boerma and F. Pleiter, Nucl. Instr. and Meth. B15 (1986) 333.

131

[26] D.K. Sood and G. Dearnaley, Radiat. Eft. 139 (1978) 157. [27] D.D. Sood, Phys. Lett. A68 (1978) 469. [28] A. Azzam and O. Meyer, Nucl. Instr. and Meth. B7/8 (1985) 113. [29] O. Meyer and A. Turos, these Proceedings (IBMM '86) Nucl. Instr. and Meth. B19/20 (1987) 136. [30] M.K. Kloska and O. Meyer, Nucl. Instr. and Meth. B14 (1986) 268; M. K. Kloska and O. Meyer, these Proceedings (IBMM '86) Nucl. Instr. and Meth. B19/20 (1987) 140. [31] A. Turos and O. Meyer, Phys. Rev. B33 (1986) 8829. [32] W.G. Moffat, The Handbook of Binary Phase Diagrams (General Electric, New York, 1978). [33] L.E. Rehn, P.R. Okamoto and R.S. Averback, Phys. Rev. B30 (1984) 3074. [34] M.K. Kloska and O. Meyer, to be published, Phys. Rev. Lett. (1986). [35] K.C. Russel, Prog. Mater. Sci. 18 (1984) 265. [36] J.P. Biersack and L.G. Haggmark, Nucl. Instr. and Meth. 174 (1980) 257. [37] R.S. Averback, R. Benedek, and K.L. Merkle, Phys. Rev. B18 (1978) 4156. [38] M.W. Guinan and J.H. Kinney, J. Nucl. Mater. 103/104 (1981) 1319. [39] W.E. King and R. Benedek, J. Nucl. Mater. 117 (1983) 26. [40] E. Raub and P. Walter, Z. Metallk. 41 (1950) 234. [41] A. Turos and O. Meyer, Phys. Rev. B31 (1985) 5694. [42] A. Azzam and O. Meyer, Phys. Rev. B33 (1986) 5. [43] M.L. Jenkins, C.A. English and B.L. Eyre, Philos. Mag. A38 (1978) 97. [44] L. Thom~, H. Bemas and C. Cohen, Phys. Rev. B20 (1979) 1789. [45] A. Weidinger, Hyperfine Interactions 17-19 (1984) 153. [46] R. Kaufmann, J. Geerk, and F. Ratzel, Nucl. Instr. and Meth. 205 (1983) 293. [47] G. Burger, K. Isebeck, J. V/51kl, W. Schilling, and H. Wenzl, Z. Angew. Phys. 22 (1967) 452. [48] C.E. Klabunde, J.K. Redmann, A.L. Southern, and R.R. Coltman Jr., Phys. Stat. Sol. 21A (1974) 303; S. Tanigawa, I. Shinta, and I. Iriyama, in ref. [12], p. 294; H. Schulz, ibid. p. 183 and refs. therein.

II. METALS