Defect trapping of gas atoms in metals

Nuclear Instruments and Methods 182/183 (1981) 413-437 North-llolland Publishing Company

413

Section I V. Defects DEFECT TRAPPING OF GAS ATOMS IN METALS *

S.T. PICRAUX Sandia National Laboratories **, Albuquerque, NM 87185, U.S.A.

Ion implantation provides a way to controllably introduce both defects and gas atoms into metals. This paper reviews implantation studies of the trapping of hydrogen and helium by simple defects in metals. In particular, the increasingly strong evidence for the role of vacancies as trap centers is exanfined. Interpreted trap structures and binding energies are summarized. Related effects for lighter particles of elementary charge (muons) and heavier inert gases (Xe) are discussed.

1. Introduction

The behavior of hydrogen and helium in metals is important to fission and fusion reactors, and a wide variety of other energy-related technologies [1,2]. There is increasing awareness that defect trapping of gas atoms commonly occurs in metals. A knowledge of the trap structures and energies bears on the understanding o f gas atom transport, accumulation and bubble nucleation in materials. This, in turn, is important for quantitative descriptions of embrittlement processes. A fundamental understanding of hydrogen and helitlm trapping by defects in metals requires a knowledge of the basic atomistic processes. Experimental progress in this area has been almost totally dependent on the use of ion implantation to controllably introduce both the gas atoms and the lattice defects. Particularly important is the interaction with vacancies, and there is now strong evidence for the structure and binding energies of hydrogen-vacancy (I-I-V) and helium vacancy (HeV) centers in a variety of simple cubic metals. This evidence is based primarily on channeling location studies, thermal release measurements, theoretical calculations, and independent knowledge of the temperature at which vacancies and interstitials become mobile in metals. In this paper we review our current understanding of hydrogen and helium trap structures and binding energies in metals due to vacancies. No attempt is made to survey the full range of literature on gas implantation. In the case of helium multiple trapping * This work supported by the U.S. Department of Energy, DOE, under contract DE-AC04-76-DP00789. ** A U.S. Department of Energy Facility. 0029-554x/81/0000-0000/$02.50 © North-Holland

and its relevance to bubble nucleation is discussed. We conclude by contrasting results for H and He with vacancy interactions for heavier inert gases and light hydrogen-like particles in metals.

2. Hydrogen-defect interactions 2.1. Hydrogen site structures

Hydrogen site occupancies are relevant to the solubility and migration of hydrogen, and in cases of defect trapping help characterize the structure of the trap center. Such microscopic information is essential for a fundamental description of hydrogen-defect interactions and can be directly correlated with theoretical studies. The ion channeling technique for the lattice location of foreign atoms in a host crystal [3] has been the primary means for determining site information. Ion-induced nuclear reactions provide good sensitivity to detect all hydrogen isotopes and ion backscattering allows the host crystal to be simultaneously monitored over the same depth region where the hydrogen has been implanted. Lattice location measurements along a given crystal direction provide the projected position of the impurity for a welldefined site, and measurements along several crystallographic directions isolate the position in three dimensions. For channeling location the close encounter yield of backscattered or nuclear reaction particles is measured as a function of incident beam angle, ~, about channeling directions. The technique is based on the principle that the flux density of the channeled particles is high in the center of the channel and low near IV. DEFECTS

414

S.T. Picraux / Defect trapping

era1 there is a large qualitative distinction between different sites. Tlms for an impurity atom in a single site the channeling effect technique provides for a definitive determination of that site.

the atom rows. For axial channeling the flux, F, at position r in the channel is determined by the area, A, allowed to a particle of transverse energy, E±, riding within the continuum potential contours, U, of the atom rows. Then the number of particles e~tering the channel near ro is proportional to dA(ro) and their transverse energy Ej. = Eta 2 + U(ro), so the total flux

F(r, ~) =

f dA(ro) A(Ez)'

2.1.1. Untrapped site Hydrogen implantation and location studies typically are done for concentrations ~0.1 at.%. High concentrations ('>1 at.%) tend to perturb the channeled particle flux distribution and therefore complicate interpretation. Interstitial site location requires the flux distribution be established, which implies the hydrogen must be located at depths of several hundred angstroms or more. Thus the hydrogen is usually introduced by implantation energies in excess of ! keV where some defects are produced during implantation. In cases of metals with high hydrogen solubility, diffusion allows the introduction of hydrogen without defects. Itowever, some defects are introduced by the analysis beam. Thus to probe the site of an untrapped hydrogen in a metal lattice, either the temperature must be sufficiently low that the hydrogen have negligible mobility or the hydrogen concentration must be well in excess of the defect concentration. An example for the hydrogen location in a bcc lattice is that for D implanted into W at 90 K. Here the

(1)

o

where U(r)<,E±. This flux density must be convoluted with the vibrating impurity atom positions, of which there are typically several equivalent projected positions for a given interstitial site. In fig. 1 the calculated variation in angular distribution for an impurity in the center of the channel is shown as a function of (a) rms vibrational amplitude, 0, transverse to the channeling direction and (b) lateral displacement, 6, from the center of the chan. nel to a nearest neighbor row [4]. Interstitials in the center of the channel give a large "flux peak". As the impurity position moves closer to the lattice rows the angular distribution becomes broader and then deeper, approaching that of the host crystal. For a near-substitutional impurity narrowing of the angular dip relative to the host angular scan allows determination of displacements as small as 0 . 1 - 0 . 2 3,. In gen-

MULTI-ROW

CONTINUUM CALCULATION Cr < 1 0 0 > : 0 . 7 M e V He

a) V I B R A T I O N F

" "

i

~---

1-

d=o

--

b) D I S P L A C E M E N T -r

:- ......

fi

r .....

[---~

.

.

.

.

T-

Q=o

4

'

T

.---

/I

',

~

-~

0.2~

~.

INTERSTITIAL ~F~

0.4

1 44,~,

] I 0.4

=

j ' "k °6 "

0 ~,

~

C

oo

"

r

I ~

-l.0

1.0

-0.5

!

0.0

0.5

1.0 -1.0 -0.5 NORMALIZED ANGLE (W/'~I)

0.0

0.5

1.0

......

Fig. 1. Calculated axial channeling angular s~ans for an interstitial impurity as a function of (a) impurity rms vibrational amplitude about the center of the channel and (b) lateral displacement from the channel center.

S.T. Picraux / Defect trapphlg

EXPERIMENT

W(D)

,°i4 i

<100> AXIS

I-"

(100) PLANE

I

I

OCTAHEDRAL SITE

ii

t:

~'t

V

I

0.5

00

TETRAHEDRAL SITE

415

i ~ L -0.5 0.0 0.5 TILT ANGLE (Degrees)

V

Fig. 2. Calculated and measured channefing angular scans for implanted D in Windicating tetrahedral interstitial occupancy. Projections on right for T and O site show atom sows by circles, planes by lines and projection of interstitial sites by triangles; the expected channeling behavior is shown schematically. After ref. 4.

D is found to occupy the tetrahedral (T) interstitial site as implanted at 90 K where the D has negligible mobility and 'also after trapping for room temperature implantation or annealing [4,5]. The channeling results for two major directions, the (100) axis and the (i00) plane are shown in fig. 2. This result is consistent with T site occupancy observed by ion channeling [6,7] and by neutron scattering [8] for hydrogen introduced by diffusion in the bcc metals Nb and Ta. However, due to the very low solubility of hydrogen in W such site identification studies are only possible by the combination of ion implantation and channeling techniques discussed here. In contrast to the bcc lattice, the fcc metal lattices are generally thought to local~e untrapped hydrogen in the octahedral (O) interstitial site. Channeling measurements for deuterium implanted in Pd at 25 K have indicated near-octahedral occupancy [9], with perhaps some fraction of the implanted D trapped in other sites. Again this is consistent with channeling studies in Pd where the hydrogen was introduced by diffusion [10] and "also with neutron scattering studies at high concentrations [8].

For the hcp metal lattice, results have been reported for D implantation [11] at 5 0 K in Mg (fig. 3). The sharp features in the (0001) plane are characteristic of a high symmetry site (see, for example, the angular distribution in fig. 1 for displacements 0.6-0.8 A), and the large dip along the (0001) axis indicates the majority of the D (~95%) are in or very close to the high symmetry tetrahedral interstitial site. The deuterium angular distribution for the (0001) axis is observed to be slightly narrower than that for the Mg lattice, whereas the dip would be identical to that for the Mg lattice if 100% of the deuterium occupied exactly tetrahedral interstitial sites and had the same vibrational amplitude as that for the Mg. Possible reasons for the narrowing include somewhat increased vibrational amplitudes for the light interstitial D. Neutrons scattering results in other metals typically give for hydrogen Prms ~ 0.2 which is larger than the host lattice atoms [8,12]. Also if there is some small displacement of the D or some small fraction of the D is within a capture radius of a defect as implanted this component could give rise to an increased yield. IV. DEFECTS

416

S.T. Picraux /Defect trapping

Mg(D)

OCTAHEDRAL SITE

EXPERIMENT

TETRAHEDRAL SITE

<0001> AXIS .

., 1

=

i

,j

i

-1

0

1

& 1 . o / . ~

© --

- & - -

-

-,&.

o--

-

-

.41,--

- -

l:¢-o

(0001)

--•

- -

_~_

_

i

-

-

-.dk--

-

-

- A - -

_ _.&__

PLANE A

i 0.0

L -1

.....

22-

L _..~

0

1

TILT ANGLE (Degrees)

Fig. 3. Angular scans for D in Mg indicating O-site occupancy. From ref. 1 l.

In all three of the simple cubic lattices it is easy to distinguist/between the major high symmetry interstitial sites for occupancy of a single site. This is because channeling along the major crystal directions shows large qualitative differences between these different sites. 2.1.2. Trapped sites Several observations confirm the trapping of hydrogen in a wide variety of metals. Firstly, implantation or annealing to temperatures sufficiently high that the implanted hydrogen is known from diffusivity measurements to be mobile and yet remains in the near-surface implanted layer implies trapping or precipitation must have occured. This is illustrated schematically in fig. 4 and has been observed, for example, for D-implanted Fe [13]. In the c~ phase of Fe hydrogen is known to be mobile well below 100 K, whereas no loss of hydrogen is observed until anneal temperatures ~ 260 K. Thus the D may occupy a trap site at temperatures above ~100 K. Secondly, even more direct evidence for trapping has been obtained in certain cases by observing a

change in the hydrogen site. When all measurements are made at the same temperature and a change in site is observed after annealing to temperatures where the hydrogen becomes mobile, it may be inferred that the hydrogen has moved to a trap and now occupies this new trap site. Furthermore, randomly oriented hydride precipitates or gas bubbles of hydrogen would

H MOBILE

H RELEASED I I

13 100%

I

(X Z ill

H TRAPPED

o

-!\ I I

-r

I 0

"-

v

TEMPERATURE

Fig. 4. Schematic of hydrogen release behavior from the near surface region after low temperature implantation and trappmg.

S.T. Picraux / Defect trapping TETRAHEDRAL SITE

CdD) <100> AXIS f

not give peaks or dips in the channeling angular scans for hydrogen. This is illustrated for the bcc lattice Cr in fig. 5 where results for implantation at 90 K are consistent with a majority of the D (;~2/3) lying in or near the tetrahedral site whereas after annealing to 300 K the D is observed to occupy a near-octahedral (O') position [4]. Contrasting behavior has been observed for the fcc lattice Pd, as illustrated in fig. 6, where upon annealing a majority of the implanted D moves from the untrapped O site to a trapped T site [9]. The most significant change in the angular distributions is observed between 80 and 90 K. Using a value for the diffusivity from the literature [14] together with an estimated annealing time of 15 min we obtain a diffusion length l ~--30 A, which is quite consistent with the expected mean distance between D and implant-produced defects. Further evidence for trapping is given by annealing to temperatures where the hydrogen is released from the sample. Under these conditions depth profile measurements have shown a uniform reduction in the approximate Gaussian implanted hydrogen profile without a significant broadening [9]. This is indica-

i ~

1.0

1/3

0,5

>-

OCTAHEDRAL SITE

0.0

1.0

0.5

0.0

~;

-4

-2 0 2 TILT ANGLE (Degrees)

V

4

417

Fig. 5. Angular scans for D in Cr showing change in site from majority in T-site to near O-site occupancy upon annealing due to trapping.

Pd(D) <100> AXIS u

OU

PO

z

n

OCTAHEDRAL SITE

T

u

1,o

I IMPLANTED \

_~

T A~(NEAL

"_~

TETRAHEDRAL SITE

Pd" 3

2

1

0

-1

3

2

1

0

~

-1

TILT ANGLE (Degrees)

Fig. 6. Angu "lar scans for D in Pd showing change from near O-site to near T-site upon trapping. From ref. 9. IV. DEFECTS

418

S.T. Picraux /Defect trapping

Table 1 Hydrogen position as a function of anneal temperature and temperature of detrapping release. Implantation and site measurement m-e at lowest temperature indicated. From refs. 4,9. H Y D R O G E N SITE VS TEMPERATURE

CRYSTAL

ITI

i0'i

Cr

Mo (bcc) Pd

(fcc)

Pt

(fcc)

"i *~400 (K)

90

(bcc)

I,' C)

LT' ,~?, *

:0'1 ,

90

io] L i -ll 25 90 i0!

J" ',', 25 70

RELEASE TEMPERATURE (°K)

'1 ~-450

-~400

~450

ITI I i 180 ~Tj i

A

180

;I

310

310

tive of a trap energy appreciately greater than the migration energy so that at the release temperature the hydrogen is either trapped or rapidly migrating such that diffusional broadening is not observed. A summary of the movement of hydrogen upon trapping in several metals is given in table 1, Mlere the interpretation is only given in terms of the majority of the hydrogen being near the T or O site. In the case of Cr and Mo the transition temperatures are not well known at present, but the hydrogen in the O site is known, to have distortions along high symmetry directions, e.g. the (100) for Cr, and therefore is labeled O'. Although only limited data are available at present, it is interesting to note that the transition goes from the T site to the O site for the bcc lattice and vice versa for the fcc lattices. 2.1.3. Detailed trap structure

We now give several examples of detailed trap site occupancy for hydrogen. In the bcc lattices high symmetry distortions have been observed from the major interstitial site for the trapped hydrogen location. Detailed results for the case of D-implanted Fe at l l 0 K after annealing to 2 0 0 K [13] are shown in fig. 7, with new results included for the (110) and (112) planes. The D angular distributions are similar to that expected for the O site for the axial, but not the planar data. In particular, the (100) planar dip is not identical to the Fe lattice, but is significantly higher and somewhat narrower. This cannot be explained simply by increasing D vibrational amplitude, since the comparative narrowing and increase of

the dip would be observed in the 1/3 dip component along the (I00) axis. There is one site, however, in which 100% of the D could reside and be consistent with the observed angular distributions, the O' site. This is along the (100) row displaced from the O site a distance 8 = 0.4 A in the dkection of the nearest neighbor Fe lattice site (see fig. 8). Calculations for this case for the (100} axis and (100) plane are shown in fig. 7 and the qualitative results expected for the other directions are indicated. One of the limitations of the channeling technique is that site determination involves an iterative procedure of assuming a particular site and then calculating the angular distribution until agreement between measurement and calculation is obtained. Thus while the technique is very direct, it is sometimes difficult to assess the certainty of the interpretation when low symmetry or multiple sites could be involved. Several points aid in this however. For example, in the particular case of D in Fe the very sharp flux peak for the (100) axis is characteristic of a high symmetry site and thus suggests a single site may be involved. The good agreement between calculations and observation give further confidence in this interpretation, especially since other positions not "along the (100) axis would not give agreement with the (100) axial a n ~ lar distribution. The displacement distance 6 along the (100)axis is well-established by the (100)planar data (see fig. 7). Even the alternative two-site interpretation of 1/3 substitutional and 2/3 1" site is inconsistent with the data of fig. 7 since the (112) planer direction has only a flux peak, consistent with the O' site but inconsistent with any combination of substitutional and T sites, both of which give dips. An almost identical O' site was earlier found for D trapped in Cr [4], where the displacement in both cases is approximately one-third of the way towards the nearest neighbor lattice site along a (100) direction. The reason t'or this well-defined distortion will be discussed later. Another related distortion for trapped D in a bcc lattice is shown in fig. 9 for Mo [4]. Here the position is less well specified, but the well-defined narrowing of the envelope of the dip along the (100} direction from that which would be expected for a perfect 0 site suggests 0.2 A displacement normal to the direction of the O' site displacement. In this case only the magnitude and not the direction of the component withha the shaded plane (fig. 9) has been determined, and small distortions along the O' direction may also be present. However, again the large, sharp flux peak

S. T. Picraux / Defect trapping

Fe(D)

DISTORTED O-SITE

EXPERIMENT

D~

la

O-SITE

CALC(6: 0.4A)

q

;i

LU 0.8 B >-


=_.

AXIS

T-SITE

+++

o

~,

419

'.~

~ "

o.6t!

o1: 0.4

...... Fe

0~. OI

I

,

-4

-2

0

1

I

~

,

2

4

t

1.0

-f." •

(loo)

V

4/J-. o

PLANE c,c

:oa/J

J

J. Ca-.

--C,---~-
V

- - ( ~ 3 -

V

'-

~= o~ I

t-

I

I

)

I

t

I

-.;. •

,.3

-C • • C

@

A C.

-?~-.,a~>

--C,--~T-

--.~3

(>

(110) PLANE

Fe/" .2/I

l -1

_.J L

~ 0 L

P '

' -

&A

•

1.0

(ll2) PLANE

Fe" .

2

t -1

1)

m 1

TILT ANGLE (degrees)

Fig. 7. Angular scans for D in Ire showing disorted O-site (O'-site) occupancy after annealing to 200 K. The (100) and (100) data from ref. 13.

(fwhm --~ 0.2 °) strongly indicates a single high symmetry site for the trapped D. In the case of the fcc lattice studies the trapped site for D has been found to be the tetrahedral interstitial position. For example, for D trapped in A1 in

fig. 10 the angular distributions clearly distinguish the T

site from O site occupancy and suggest only high-

symmetry T site occupancy [15]. In table 2 channeling results for hydrogen lattice location in metals are summarized. IV. DEFECTS

S.T. tS"craux / Defect trapping

420

~ Fe

energy levels of the hydrogen in a solutionized site and in the trap site. Although estimates of the binding energy can be made simply from a knowledge of the temperature at which hydrogen is released from traps (see table 2) and the migration energy, this only gives an upper bound on the binding energy since at the typical concentrations (~0.1 at.% of hydrogen and traps) the hydrogen is detrapped and retrapped many times before being released from the implanted region [13]. This can be treated by the set of coupled diffusion equations with the appropriate trapping terms [13],

/VACANCY

D - SITE

~oop

T/,o,o,

f. x OCTAHEDRAL SITE -I- TETRAHEDRAL S ITE

Fig. 8. Position of D in Fe corresponding to the distorted O-site in the bcc lattice. F r o m ref. 13.

a2C ~ C s ( x , t) = D ~x ~- - ~ Si(x, t) 0

(3)

Ci(x, t) = si(x, t),

at

2.2. Trap energies

(2)

where

Quantitative analysis of the binding energy of hydrogen to traps can be carried out if the hydrogen diffusivity and the depth distributions of the hydrogen and the traps are known. Here we specify the binding energy as the energy difference between the

Si(x, t) = 4nRTDN[CsAi(x ) - C,G - Ciz e x p ( - e u / k T ) ] ,

(4)

and Cs, Ci are the hydrogen concentrations in solu-

Mo ( D ) < I 0 0 ) I

'

I

i

700 key 3He I

i

. •& INTERSTITIAL SITES bcc LATTICE

'

I

• D-SIGNAL o Mo-S I GNAL

].8 ~,6-8

l

(2.6) O (2.4) O-II

1.6

CALCULATED

1.4

, ,,, o;,,,E<,,;!

1.2

~" 1.o "0.8 0.6 o • • X

LATTICE ATOMS OCTAHEDRAL SITE TETRAHEDRAL SITE DISTORTED O-SITES ([ and ll)

0.4 0.2

O.O

-4

-2

0

2

ANGLE (degrees)

Fig. 9. Angular s~an for D in Mo showing distortion from O-site location. F r o m ref. 4.

4

;

00

f,lOO,

,,

(loo)

tl

0c

!1-1~3)i~~

i1 ......

(110)

< 1 1 0 ~

-1

_1

{l v

(11o)

ttijiv

0

1

2

(100)

a!.uminium -+-+- deuterium

6 J

0

TETRAHEDRAL

OCTAHEDRAL

Fig. 10. Angular scans for D in A1 showing T-site occupancy for trapped D. From ref. 15.

Table 2 Summary of interpreted untrapped and trapped hydrogen site locations by ion channeling technique. Metal

TI a) (K)

(bcc) V Cr Fe Nb Mo Ta W

(diff) 90 110 300 and diff 90 diff 90

Equilibrium site b)

T -T T ~T T T

Trapped site e)

~T O' (site I) O' (site I) O" (site II) T

Release temperature (K)

-400 260 ~450 -

Inferred trap

-

Vacancy Vacancy Vacancy clusters Vacancy or V-clusters

Ref.

16 4, 5 13 6 4

-

7

-

4 , 5

(fcc) A1 Cu Pd Ag Pt Au

35 25 25 25 25 <100

O O O O -

T O near-T O T -

300 300 180 320 310 350

Vacancy Vacancy Vacancy Vacancy Vacancy Vacancy

15 17 9,10 9 9 18

(hcp) Mg

40

T

near-T

230

Vacancy and divancy

11

a) TI = implant temperature, diff = diffusion loading of hydrogen. b) Some uneertainity must remain for equilibrium site assignment since it is difficult to eliminate all defects in ion beam experiments. c) Site I is along (100> direction towards nn lattice site - 0 . 4 A from O-site. Site II has 0.2 A displacement transverse to the O'-site direction. IV. DEFECTS

S.T. Picraux /Defect trapping

422 1.0

D__I,~___O_.@

0 0

O

©o

z~ -

0.6

~

'

(~ ~

0.8 -

-

o"-~

1 1D.'sNF1016Dicta2 2 K/bllNUTE

THEORETICAL.........~\ FIT ~

.

O

0.4 t_

0.2

I

O. 0

,

I~

I

L

,

ZOO

300

400

500

Tgt',~,PER,\l L~R[ ~KI Fig. 11. Release of implanted D from the implanted region in Fe upon ramp heating. Theoretical calculation corresponds to two trap energies of 0.48 and 0.8 eV. From ref. 13.

tion and in traps of type i, Ai the trap density, R T the effective trap radius, N the atomic concentration, z the number of solution sites per host atom, E B the trapping enthalpy relative to an untrapped site (binding energy) and D the hydrogen diffusivity. A detailed analysis using eqs. (2)---(4) has been carried out for ramp heating measurements of D release in Fe [13] (see fig. 11). Two trap energies were assumed and adjusted for best agreement with the experimental results. It is seen in fig. 11 that the first stage at 260 K is as sharp as expected theoretically for a single well-defined trap energy, consistent with the single high synunetry O' site observed (figs. 7 and 8). The resulting trap energy for the 260 K stage is 0.48 eV. This is appreciably greater than the activation energy for migration of ~4).045 eV [ 14]. Relatively few detailed studies of trap energies have been made where simple lattice defect interactions are expected to apply. Recently ramp heating release of D in Ni has been studied [19] and gives only slightly higher temperature for the onset of release than expected for diffusional release in the absence of traps. There have also been studies of the

gas release as measured by quadrupole mass analyzers as a function of ramp heating. Detailed measurements have been reported for the case of Mo [20] and for stainless steel [21]. The 316 stainless steel data were analyzed in terms of diffusion in a field of traps similar to the treatment of eqs. (2)-(4). The results contrast to those for Fe since the migration energy is much larger (-~-0.6 eV) relative to the trap energy

(4.3 eV). Hydrogen release for ion-implanted materials has often shown broad release stages, characteristic of a distribution of trap energies. This broadening, together with significant enhancement in the hydrogen trap energies, has especially been observed for materials predamaged or alloyed by implanting heavier ions [19,22,23]. These interesting effects likely involve more complex clusters of defects, as well as hnpurity-hydrogen chemical interactions. Therefore, we restrict the present review to relatively low fluence (<~1016/cm 2) low energy ( 1 - 3 0 keV) implant studies in pure metal lattices and discuss the atomic interpretation of this simplest possible case.

S.T. Picraux /Defect trappbzg

duced is given by

2.3. EvMence ]'or the hydrogen-vacancy center

Where E d is the threshold energy for displacement and/3 is an efficiency factor taken to be ~0.6 here for low energy hydrogen [24]. In fig. 12 we give the resulting vacancy production per II or D atom for several materials, Si, Cr, Mo and W, assuming in each case E d ~ 35 eV. ["or typical implantation energies ~5--10 vacancies per hydrogen are created. Taking an approximate factor of 2 - 5 for spontaneous recombination based on the experience of various workers in radiation effects, we obtain ~1--5 vacancies per implanted hydrogen and little dependence on the target atomic number. Thus implantation at typic',d hydrogen ion energies is expected to produce sufficient vacancies as possible trap centers, but not so many displacements that large numbers of more complex defects are likely to be available to trap the hydrogen.

2.3• 1. Vacancy production

One may estimate the number of vacancies produced by the incident hydrogen ions during implantation from theoretical calculations [24] of the fraction kr) of the ion energy E which is deposited into atomic processes. From the modified Kinchin-Pease relationship the number of vacancy--interstitial pairs pro-

A 2000 -

I

l

(5)

r~D = ~kol:'/2Ed ,

Many of the recent hydrogen trapping results have been interpreted in terms of the trapping of hydrogen at single vacancies [9,11,13], and indeed it may be possible that the entire class of simple trapped structures that are summarized in table 2 are due to the H-V center. In what follows we review the evidence that the observed hydrogen sites are associated with vacancy traps and offer new results to further support that interpretation•

I

423

I

'

I

I

I

I

t

O

v

4\

.%

~J

. % •

Z

•. \ ".

~ . . . ~ 1 5 keY D O.

h-

o

,%

,,v H/" 0

I

""'

t

......

I

I

I

Z W

30 keV D

o "" a

I

Oo °

12

. . . . . .

•

>"l-

. . - o--

a

15 keV D

OS

M.J

"

O

8 o ev. o. (,q

4

A

15 keY H

Z

0

=

t 20

=

I 40

J

I 60

n

I 80

TARGET ATOMIC NUMBER - Z T

Fig. 12. Projected ranges and vacancy p r o d u c t i o n per hydrogen for various targets• IV•DEFECTS

S.T. Picraux / Defect trapping

424

2. 3.2. Alternative traps We consider five possible alternative traps for the hydrogen. First, impurities are not a reasonable candidata for the trap center in these studies since their concentrations (typically ,~0.01 at.%)are appreciably lower than the hydrogen concentration ('-43.1 at.%). The second "alternative, host interstitial atoms, is unlikely since trapping is observed to proceed equally efficiently below and above temperatures where both the interstitial and the hydrogen atoms are mobile. Also the detrapping temperatures seem rather high compared to what would be intuitively expected for isolated interstitial-- interstitial binding energies. A third possible trap to consider is extended defects such as dislocations. However, the high symmetry of the observed hydrogen lattice site seems inconsistent with that anticipated at a dislocation. While sharp channeling features might be observed for one particular orientation relative to the channeled beam, the well-resolved features would appear to be inconsistent with the associated distortions for the various possible equivalent orientations of dislocations or other extended defects. As a fourth possibility, we may consider hydrog e n - h y d r o g e n interactions as the major source of the binding energy. While it is not possible to completely exclude the possibility of 2 or more hydrogen atoms in the trap center, theoretical analysis of solubility measurements [25] and theoretical calculations [26] suggest that H - H interactions in metals without large cavities are, at best, weak and may be either positive or negative in sign. Thus it still would seem necessary that some defect centers, such as vacancies, be present to trap the hydrogen.

The fifth possibility, small vacancy or interstitial clusters, is the most difficult to exclude. Since trapping is observed at temperatures where vacancies are immobile and the direct production of clusters by isolated hydrogen cascades is not expected to be large, the trapping due to vacancy clusters should not be important at low fluences. Little is known about interstitial clusters and their interactions with hydrogen. Certainly production of clusters would be much higher for predamaged or very high fluence H implants and these have previously been suggested [22] as trap centers under such conditions (see also Mg in table 2). The major argument against these clusters for the simple trap sites discussed here, aside from their low density, is the high symmetry of the trap sites and for Fe the well-defined trap energy. These facts seem inconsistent with the multiple possibilities for site position and binding energy that might be anticipated for clusters. Instead, these facts point to a high symmetry point defect, such as isolated vacancies.

2. 3.3. Correlations with Stage 3 vacancy migration Annihilation of a hydrogen-vacancy center in a given metal could proceed in one of three ways: (1) detrapping could occur at a temperature where the vacancy is immobile, thus implying a binding energy lower than the mi~ation energy for the vacancy; (2) the center could become mobile and migrate to sinks to be annihilated ; (3) the hydrogen could stabilize the vacancy until at breakup both the vacancy and hydrogen would be mobile. In table 3 the observed temperature for detrapping is seen to occur at temperatures comparable to the vacancy migration temperature for

Table 3 Anneal and implant temperature at which hydrogen is released compared to appro.,dmate temperature at which vacancies and interstitials became mobile. II trapping references in table 2. Metal

Temperature (K) Detrap by anneal

Trap during implant

Stage III (vacancies)

Stage ID (interstitials)

~cc) Fe Mo

260 ~450

~450

~410 ~450

105 40

(~c) A1 Cu Pd Ag Pt

300 300 180 320 310

180 250 220 275

~200 ~260 ~500 ~240 ~300

35 35 30 20

S.T. Picraux /Defect trapping

a number of the metals studied by ion channeling. Also shown is the implant temperature above which trapping rapidly decreases. This temperature should be near the lower of (1) the temperature of the trap center migration or (2) the temperature ofdetrapping. Present results are seen to be consistent in all cases with these criteria for vacancy trapping and inconsistent with interstitial trapping. 2.3.4. Theoretical correlations with binding energy and trap sites We first consider a simple order of magnitude argument in order to establish an upper bound on the binding energy for a hydrogen-vacancy center [27]. First, hydrogen is known to be bound to surfaces relative to bulk solution sites through chemisorption. For a cavity of many vacancies in a metal the internal boundary might be considered to approximate a surface. As the cavity decreases in size the binding may be reduced, but due to the short interaction distances between hydrogen and other atoms, even a single vacancy may attain an appreciable fraction of the binding energy. Thus as an approximate upper bound on the binding energy of a hydrogen to a vacancy, we determine in table 4 the lowering of energy, ET, for a hydrogen atom chemisorbed on a surface relative to a solutionized site in the bulk. The ET values given in table 4 for a number of metals based on experimental chemisorption and heat of solution energies indicate binding energies up to ~1 eV. For example, the value of 0.8 eV for Fe is only slightly larger than the =43.5 eV binding energy observed for the trapped D site (fig. 5) which corresponds to the 260 K stage in fig. 11. Also, we note that the theoretical fit to the higher stage in fig. 11 gave 0.8 eV and appears to correspond to a distribution of trap energies about this value; although the closeness of agreement with table 4 is likely fortuitous, it is possible that this stage corresponds to trapping by small vacancy clusters. Recently, calculations of the equilibrium trap site and energy for hydrogen in a vacancy have been carried out for fcc nickel [28]. In addition, these calculations were extended to a Ni bcc structure of lattice constant appropriate to c~-phase Fe [29]. These extended cluster calculations include a quantum mechanical treatment of the inner (200 atoms) region about the hydrogen and two body potentials in the outer (600 atom) region. Results for fcc Ni are shown in fig. 13 where the hydrogen is seen to have a minimum energy configuration in site displaced 0.9 A

425

Table 4 Estimated lowering of hydrogen energy by moving from solutionized bulk site to surface site. Eo = 2.3 eV was used for the binding energy per atom of a D 2 molecule. The chemisorption energies are referenced to the free H atom and the heat of solution data to the H2 molecule.

vAcoo,LI BOL. SURFACE

E

H IN SOLUTION

H CHEMISORPTION

E o = BINDING OF H 2 MOLECULE E c = CHEMISORPTION BINDING ENERGY E H = HEAT OF SOLUTION E T ,= LOWERING OF H ENERGY FROM BULK TO SURFACE =

Ec-Eo

4- EH

Ec

EH

ET

(eV) (i) 2.68 2,84

(eV) (i) 29 .54

(eV)

Cu

2.41

.57

.7

Ni Pd

2.71 2.69

.17 .-10

.6 .3

METAL

(bcc) o~ - Fe

Mo

.8 1.1

(tcc)

(i) S.W. Wang and W.tl. Weinberg, Surf. Sci. 77 (1978) 14; The nature of the chemical bond (eds. T.N. Rhodin and G. Ertl; North-Holland Publ. Co. NY. 1979) p. 324. (ii) R.B. McLellan and e.G. llerkins, Mat. Sci. Eng. 18 (1975) 5.

from the vacancy in the direction of the octahedral interstitial site, i.e., approximately half-way between the vacant atoms site and the neighboring O site. Such a site has not been reported experimentally for fcc metals (table 2) although experimental data for Ni are not yet available. For the theoreticaUy simulated Fe case using a bcc Ni lattice, the hydrogen was "also found to displaced from the vacant atom site toward the adjacent O site, with a displacement dis'tance 0.96 A (~2/3's the way to the O site) and a binding energy ~0.3 eV [29]. Tiffs is in close agreement with the experimental result for trapped D in Fe which gave a displacement distance of (1.04 -+ 0.1) A from the lattice site towards the O site (see fig. 8) and binding energy 0.48 eV [13]. IV. DEFFCTS

S.T. Picmux / Defect trapping

426

(llO)

PLANE CONTAINING

HYDROGEN IN VACANCY

EooQ

Iz,~ I

i

Y

/

l

/

I

I

I

I

t

I

I

I

I

/,'/'i~ ;

Z__ O.

0

I

t

I

,l ~

I

/

I

/

I

I

I

I

~

I

I

I

L

host metal atoms defect atoms vacancy

Fig. 13. Calcu 'lated electronic charge density and equilibrium site for hydrogen in a vacancy in fee Ni. From ref. 28.

S. T. Picraux /Defect trapping

A second quite different set of theoretical calculations also supports the interpretation of the hydrogen-vacancy trap center. Self-consistent jellium calculations supplemented by a first order calculation of the energy contribution of the pseudopotential lattice were carried out for hydrogen in a vacancy in AI and Mg [30]. Tile result of these calculations was that untrapped (solutionized) hydrogen occupied the T site in both A1 and Mg. In A1 the hydrogen trapped at a vacancy occupied an off-center position with nearly equal binding ~1 eV for a position near the T site and one near the O site (see fig. 14). Both the untrapped T site for Mg [11] and the trapped T site for A1 [15] are consistent with experimental observation and further support the previous interpretation [15] of the vacancy being the hydrogen trap center in these studies. While the O versus T site lbr A1 could not be distinguished theoretically, a substitutional site was again clearly excluded. Also, in the case of Mg for hydrogen trapping in a vacancy the preferred site could not be uniquely established, but substitutional occupancy could be excluded, again constant with experiment [ 11 ]. Although theoretical calculations of hydrogenvacancy centers in metals are difficult and may be

1~

H in AI voc.

i

subject to some revision, the qualitative trends presently predicted strongly support the experimental observations of hydrogen trapping discussed here and further help to establish the identification of the H-V center. 2.3.5. Interstitial replacement hTteractions We propose the existance of tile interstitial replacement mechanism for self interstitials in the vicinity of the H-V center. This would be expected to be possible provided the vacancy formation energy Ely is greater than the hydrogen binding energy to the vacancy, and observation of this effect would provide further evidence for the identification of the hydrogen-vacancy center. This suggestion is motivated by recent channeling studies of mixed dumbbells in metals which monitor the mixed dumbbell production as a function of irradiation above and below the temperature at which interstitials migrate [31]. Also, we have previously observed radiation sensitivity for the D site in W [32], Me and Cr upon continued bombardment by the 3lie analyzing beam. In each case the measurement temperature, ~90 K, was above Stage IE where free migration of interstitials produced by the 3tie could occur, and one possible interpretation of this sensitivity is that interstitial lattice atoms migrate to the hydrogen-vacancy center and replace the D. Subsequent D migration to other traps or clustering could account for the observed reduction in flux peak and associated change in the D site distribution. We have tested this interstitial replacement mechanism for the case of trapped D in Fe

Fel + HV ~ Fesub. + HI ,

-'P

I- - - - .,~'.d._

.z'..

/----"d

0

~,00~

i

/i

/,'

I

I

I I Tetrahedrol

I

2

3

/.

I

i site I

5

d ( a u.)

Fig. 14. Calculated energy tbr hydrogen as a function of distance from vacancy along various directions in AI. From ref. 30.

427

(6)

Where 1 and Sub. denote interstitial and substitutional atoms, respectively. Since for Fe E f = ! .53 eV [33] and E ° v ~ 0.5 eV [13], we anticipate the reaction to proceed with a net gain of ~1 eV per replacement. Irradiation by 750 keV 3tie to produce Fe interstitials was carried out above and below the temperature at which free interstitial migration occurs (Tlv:"~ 120 K [34]). Prior to 3He irradiation the Fe sample was implanted at 100 K with 1016D/cm 2 and annealed to 200 K to populate fully the H-V center. The flux peak was observed (fig. 15) to drop rapidly when the interstitials could migrate (T = 190 K) and not to change appreciably when the interstitials were not mobile (T = 100 K). This is consistent with the D being replaced by Fe interstitials and the D migrating to be rctrapped in part by other vacancies, and in part IV. DEFECTS

S.T. t~'craux/ Defect trapping

428

t 1.4

i

i

i

Fe (D)

Both hydride phase precipitates and gas bubbles have been observed in metals after high fluence hydrogen implantation. For example, ordered arrays of hydrogen gas bubbles have been observed in Cu [35] and hydride phases have been observed to form and grow in Ti [36].

l

~

o

12 I--

i-1

-

3. He-vacancy interactions

-_L ~

T=lCJOK

--

T IE = 12OK

1.o

I

5

10 1

1

15

3He FLUENCE (10 15/cm2)

Fig. 15. Measured change in flux peak height with 750 keV 31te irradiation along random direction above and below the temperature of free interstitial migrations (Stage IE). by more complex traps (formed by the irradiating beam) which results in a lower flux peak. The He irradiation fluence [(0--5) × 101S/cm :] over which this effect is observed is consistent with the interstitial production cross sections found in previous studies of mixed dumbbells [31]. Thus the results in fig. 15 are consistent with our proposed interstitial replacement mechanism and the existance of the H-V center. While no single one of the above experimental or theoretical results irrefutably proves the identification of the hydrogen-vacancy center for the hydrogen trap sites discussed in this paper, the net weight of all the evidence strongly supports this hypothesis. In contrast, no alternative trap center seems consistent with the available evidence. Therefore we conclude that the trap sites discussed above are largely due to the trapping of single hydrogen atoms at a vacancy.

In this section we contrast helium-vacancy interactions in metals with the hydrogen results of the previous section. In general He is quite insoluble in metals, is mobile at room temperature and is strongly trapped in vacancies [37]. This is indicated schematically in fig. 16 where EF, EM, E D and E B are the formation, migration, dissociation, and binding energy respectively. For Mo, for example, EF~--4.9 eV, EM ~ 0.2 eV, and ED ~ 3.1 eV; in contrast the migration energy for a vacancy is only 1.45 eV, so that the presence of a He atom stabilizes the vacancy [38,39].

3.1. He trapping and trap energies Detailed evidence for He interactions with simple defects in several metals has been obtained by extensive thermal desorption spectroscopy measurements in several systems. The emitted He is detected as a function of temperature upon ramp heating. In these studies heavy inert gas atoms are implanted to low fluences at a few keV to create vacancies at temperatures where the vacancies are immobile. Then He is injected at energies too low to create displacements so that the He is trapped only by existing defects. An advantage of this approach is that the defect and He introduction are independently controlled. SURFACE VACUUM

2.4. Bubble and hydride phase formation One important consequence of the above hydrogen-vacancy trapping and the appreciable binding energies involved is that hydrogen migration in the presence of traps will be retarded. This may have consequences for such steps which can lead to hydrogen embrittlement of alloys as permeation, transport and accumulation. A second important consequence is that these trap centers may provide sites for the heterogeneous nucleation of hydride precipitates or hydrogen gas bubbles.

HE ATOM

VACANCY

"'~(~ [ / t

•

•

,/ •

•

/ C

"~ •

~

~ •

(~.~" •

ALTERNATE PLANES

•

/

l:ig. 16. Sche~tic diagram of energies of formation (EF), migration (EM), dissociation from vacancy (ED), and binding to vacancy (EB) for He. After ref. 38.

429

S.T. l~'craux / Defect trapping

e~

He ions/cm 2

/

1.8 X 1013 ..... 1.08 X 1013 --'~ 4"4X1012 .... 1.36 X 1012 ........ 4.4 X 1011

II I I I I I.I llll

Z

o_ i.a. rig C) t/) r~

w -r

L• /

PREDAMAGED

,NO PREDAMAGED

[1 400

I

I

p

I I 12013

1

~

i J 2000

HLI

i

T (K)

Fig. 17. He desorption rate vs. temperature in W after 2.4 × 1013 He/cm 2 implant at 250 eV with and without damage produced by 2.4 × 1011 Kr/cm 2 at 5 keV. From ref. 40.

In fig. 17 the He desorption spectra from W are shown after He injection to 2.4 × 10~S/cm " at 250 eV for undamaged crystal and for a crystal with prior 5 keV Kr damage b o m b a r d m e n t to 2.4 × 101l/cm 2 [40]. The lack o f retention without predamage is consistent with a high lie mobility at room temperature and the trapping to high temperatures indicates strong defect trapping. In an elegant series of experiments involving systematic variation o f the parameters it was demonstrated that such spectra (see fig. 18) could be interpreted in terms of the following helium-vacancy interactions [40]

(7) (8)

He4V -+ He3V + He (E p e a k ) , He3V ~ He2V + He (F p e a k ) ,

(9) 00)

He2V ~ HeV + He (G p e a k ) , HeV ~ V + He (H peak) ,

where HenV stands for n He atoms trapped at one vacancy. Several additional more complex centers involving multiple vacancies were also present, but will not be discussed here. By restricting the implantations to low fluences the release stages could be described by single step dissociation processes [38, 40], for example for eq. (10), --dN/dt = No exp(-ED/kT(t))

,

(11)

where N is a number of HeV centers, T ( t ) the tern-

/ ! ijJ l

/

//il//il l 'J!t i', !1

/a UI

/~-,j

1 3 4

I 8

' I

I I I i

i/, !,iil

i

.. ',.ILL:

*.11~|

f

~

fft

E

FG I 12

H'H I I 16

J 20

24

TEMPERATURE (100 °K) l:ig. 18. He desorption for various injected He fluences after predamage with Kr. From ref. 40.

perature during release at time t, o is a pre-exponential factor o f the order o f the vibrational frequency of the metal lattice and E D the dissociation energy for the center. Comparisons are given in table 5 o f experimental results and theoretical atomistic cluster calculation results for the dissociation energies in both W and Mo. The observed tie binding energies o f 3 - 4 eV are IV. DEFECTS

430

S. T. lh'craux /Defect trapp&g

Table 5 Comparison of experimental and theoretical He-vacancy dissociation energies for W and Mo. Reaction

W:

HeV ~ He + V

He2V --* tte + tleV Hc3V --*lle + Ite2V He4V ~ He + He3V Mo: HeV~ He +V lle2V --* He + lteV He3V ~ He + He2V He4,5,6 ,V ~ He + He3,4,s,V

Experiment a)

Theory

Tp (K)

ED (eV)

ED b) (eV)

ED c) (eV)

1560 1220 1120 950

4.05 3.14 2.88 2.14

4.39 2.89 2.52 2.50

5.07 3.43 3.02 2.94

1180 960 900

3.05 2.5 2.3

4.19 --

4.2 2.82 2.50

800

2.05

-

2.37

a) W results from rcf. 40, Mo from ref. 41. b) From refs. 39,42. c) From ref. 41.

factors involving nucleation o f lte bubbles will be discussed later. Theoretical calculations for lle in vacancies are in rather good agreement with experiment (table 5) and thus have been extended to a wide variety of metals (see table 6). In contrast, detailed interpretation of the thermal desorption data is difficult and little has been reported for other metals. However, from the theoretical results of table 6, the trends o f low migration energy and high binding energy to vacancies appear to hold for simple cubic metals. The fcc metals seem to have a somewhat higher migration energy and lower binding energy than the bcc metals. Also, the formation energies are all quite large, consistent with negligible solubility of He in most metals. It is for this reason that He implantation has been such an important tool to investigate He-defect interactions in metals; it is very difficult to introduce lte in metals except by implantation or tritium decay. 3.2. Trap structures

quite large compared to that for hydrogen trapping at a vacancy (~<1 eV). Also the binding energies for additional lie added to the vacancy are still appreciable ( > 2 eV) for up to ~ 6 lte in a vacancy for Mo. This contrast to the case for hydrogen where, althougll experimental evidence is minimal, theoretical considerations have suggested that the trapping of many hydrogen atoms at an H-V center may be weak unless additional vacancies are added. This may in part explain the apparently stronger proclivity for bubble formation for helium than for hydrogen in metals for which hydride formation does not occur. Additional

Table 6 Theoretically predicted formation and migration energies of interstitial He and dissociation energy of He in vacancy. From ref. 39 except in parentheses ref. 38. Metal

EF (eV)

EM (eV)

ED (eV)

(fcc) Ni Cu

4.52 2.03

0.43 0.45

0.5 2.15

¢occ) V Fe Mo Ta W

4.61 5.36 4.91 (4.97) 4.23 5.47 (5.91)

0.13 0.17 0.23 (0.3) ~0.0 0.24 (0.29)

3.20 3.98 4.19 (4.2) 3.44 4.39 (5.07)

Information on the structure of ttenV centers in metals is due almost entirely to theoretical cluster calculations. In contrast to H where appreciable interactions with host atom electrons can lower its energy, a single He in a vacancy is predicted to be centrally located at the substitutional site. This is consistent with the He closed shell configuration, since its energy is lowered most be staying in the region o f minimum electron density. The structure for multiple He trapped at a vacancy is less obvious and predicted structures for one to six He at a Cu vacancy [43] are shown in fig. 19. Similar structures are predicted for W and Mo and an example of two configurations of comparable stability for three [te atoms in a W vacancy [44] is given in fig. 20. Channeling angular distribution measurements for the case of He implanted in W to higher fluences (101S/cm 2) than the thermal desorption studies ( 1 0 x l - 1 0 a 3 / c m 2) are shown in fig. 21 for the (100) axis [45]. Because of the multiplicity o f sites involved, a unique interpretation of the Ile location was not possible from the channeling measurements. However they do indicate that the majority o f the He (>~90%) are not in the substitutional HeV center, and within limits o f the statistical resolution o f these measurements the very narrow dip with multiple peaks is consistent with the calculated structures (similar to those for Cu in fig. 19) for HenV centers. The data are consistent, for example, with a combination of

S. 7". Picraux I Defect trapphTg

431

~'i(Hel<100> !.if ~ ,[,,

CALCULATED He POSITIONS AT Cu VACANCY

'

T

'

, a.

T

L 0 ~ ~..___ :Tr} +

~ 0oo)

_-

1.0

/

o.+p.7~~:':

i °+

"

/ ,,- .ioo /

"

+0F

-io.+

/

0+r j • 0

i

"

[

olo>

jl.2

0.5

1. O

!0+ i. 5

D . ' ~ G L E ('.)c'q t e e 5

2.0

..5

3.0

I

Fig. 21. Angular scan for SlIe implanted into W to ~1 X 10151cm2 at 60 keV. From ref. 45. I I

I

O

i

Fig. 19. Calculated minimum energy configurations for 1-6 lie trapped at a vacancy in Cu. From ref. 43.

H%V and He3V centers predominating the distribution. Furthermore, they are inconsistent with randomly distributed He as in a macroscopic gas bubble. No other channeling location studies have been reported, to the author's knowledge, for He implanted in metals.

CALCULATED He 3 V CONFIGURATIONS IN W

-V •

-V-

lie

©w FI VACANCY Fig. 20. Two equilibrium configurations calculated for three lle atoms trapped at a vacancy (He3V center) in W. From ref. 44.

3.3. Trap mutation and bubble nucleation tlelium-vacancy centers are believed to form the nuclei for bubble formation in metals, which at high fluences grow and lead to surface deformations such as blistering or flaking. Recently, experimental studies have been extended to follow larger numbers of He atoms trapped at vacancy centers, going up to as many as 100 trapped He atoms. This corresponds to a bubble the size o f ~5 A, and thus such studies provide a link between the microscopic HenV centers and the bubble reghne where one can begin to monitor their evolution by transmission electron microscopy. Two notable effects have been discovered in this transition region. The first effect has been referred to as trap mutation [46]. This process can be viewed as follows: at early phases the growth of the bubble nuclei proceeds by He filling o f a vacancy, ttowever with each IIe added the local Frenkel pair formation energy is lowered, such that after sufficient number o f tie are added to the vacancy it becomes energetically favorable for a substitutional host lattice atom to be ejected as an interstitial. Such a process would be expected to provide a strong driving force for the formation o f lle gas bubbles. Exidence for this process has been obtained for Mo by interpretation o f thermal desorption spectra in conjunction with clusIV. DEFECTS

S. T. Picraux / Defect trapping

432

ter calculations [46]. The reaction

He CLUSTER IN Ni

n

IN,.

i

I

i

/

I

He + HenV + MOSub. -* He,2+IV2 + Moi

is inferred to occur at n ~- 5 where MOsub. and Moj refer to substitutional and interstitial Mo atoms respectively. Thus not only He, but also vacancies are added to the center, providing for its eventual growth into a gas bubble. A similar effect has also been inferred for W at n ~ 6 He atoms in eq. (12) [47]. Recently atomistic cluster calculations of a different but related situation have found additional support for substitutional atom ejection upon increased clustering of He atoms [48]. For fcc Ni no vacancy was initially present, and a positive binding of several tenths of an eV was found for two or more He atoms located along (100) directions about the body centered Ni atom (see inset in fig. 22). On the addition of 4 - 5 He atoms the structure became unstable and spontaneous ejection of a Ni atom from the body centered site is predicted to occur along a (100) direction that does not contain an He atom. This result is shown in fig. 22 where the relative energy for the Ni

1.6 A

.8-

3

- 1.6

-

i

I 0.2

0

i 0.4

Ni DISPLACEMENT ALONG tloo] (lattice units)

Fig. 22. Calculated energy for Ni atom with n He atoms trapped to it along <100) directions as function of distance along indicated (100) direction in fcc Ni. From ref. 48.

2OOO

A v

I

I

i

(12)

l

I l llll[

I

I I llll

I

I

l lOO

I

1600

W

I-Q: IJJ Q.

W p-

1200

Z

_o I.-p,,

o( / )

x

V

+

He V Ne

LIJ

8OO

Ar

oJ 40G

I 1

I

I

I 111111

I 10

f_3

Kr

©

Xe 1 f Ill,

N U M B E R He TRAPPED

Fig. 23. He desorption temperature vs. number of trapped tte for the indicated inert gas or vacancy nucleating centers in W. From ref. 49.

S.T. Picraux /Defect trapping atom is plotted as a function of distance along this (100) direction and according to the number n of He atoms in the cluster. This suggests that in some metals it may be possible to form bubble nuclei spontaneously without radiation production of vacancies. The second important effect which has recently been observed in this transition region involves thermal disorption measurements of the strength of He binding as a function of the number of He added to the cluster. Results have been obtained in W for 1 - 1 0 0 He atoms in the cluster, both for the trap nucleus consisting of an isolated vacancy and of a single inert gas atom of He through Xe [49]. These results (fig. 23) indicate that in the region of 1 - 1 0 He atoms in a cluster, the binding energy 9f each additional He for a vacancy nucleus drops with the number of trapped He, is relatively flat for a Ne trap and increases for heavier inert gases. For the first He the trap energy ranges from 3.1 eV for HeV center to 1.2 eV for the first He trapped to a Xe center; after 10 Fie atoms, the binding ranges from ~--'2.2 eV for the Xe center to~2.5 eV for the Ne center. For greater than I0 He the nature of the nucleating species no longer appreciably influences the binding energy. In fig. 23 the range of cluster sizes over which trapping occurs at a given desorption temperature (binding energy) is indicated by the line and dots. The binding energy monotonically increases with increasing number of He atoms out to 100 trapped He. The capture radius is essentially constant at - 2 . 8 A for <10 He and thereafter increases for increasing number of He atoms trapped at the bubble nucleus. These results clearly demonstrate how energetically favorable it is for bubble nucleation and growth to result from He-vacancy trap centers in a metal.

433

4. Related studies

4.1. Hydrogen-like particles Several properties of light particles with positive elementary charge are listed in table 7. The trapping by vacancies in metals of both positrons and positive muons has been reported. Positrons are so light that their wave-functions are delocalized except when trapped and vacancy trapping by positrons is an established technique for the study of vacancy type defects in metals [50]. It has been used, for example, to establish the vacancy formation energy in a wide variety of metals [51]. The muon, ~ l / 9 t h the mass of a hydrogen atom, is sufficiently heavy that it should provide a good test for theories of the localization and trapping of light positive particles in solids [52]. Energetic muons are implanted and studied by spin depolarLzation due to the interaction of the magnetic moment of the muon with the nuclear or electronic magnetic moments within the crystal. However, due to its short lifetime, there is never more than ~1 implanted muon in the solid at any given time. Muon localization in a purely untrapped state is well-established only for the case of Cu [53]. As shown in fig. 24, at high externally applied magnetic fields the quadrupole interaction terms are sufficiently quenched that the spin depolarization rate, as given by the damping parameter, is sensitive to crystal orientation. Theoretical calculations show good agreement with experiment for the octrahedral interstitial site provided a 5% lattice relaxation is allowed [53], and are inconsistent with either tetrahedral of substitutional occupation of the muon [54]. A comparison of reported equilibrium sites from muons [55] with that for hydrogen are shown in table 8. For the bcc metals, V, Nb and Ta, the trapping of muons to impurities is prevalent, even for the

Table 7 Properties of light particles with positive elementary charge. After ref. 52. Particle

Rest mass

Spin

Lifetime

Atom

Positron (e+) Positive Muon 6u÷) Proton (p) Deuteron (d) Triton (t)

5.45 × 10.4 mp= me 0.113mp mp 1.998 mp 2.993 mp

1]2 1/2 1/2 1 1/2

stable,(annihilates with e- in 10-1 °-10-7 s) 2.2 × 10-6 s stable stable 3.9 × 108 s (12.33 y)

Positronium(e÷ + e-) Muonium 6u++ e-) Itydrogen (p + e-) Deuterium (d + e-) Tritium (t + e-) IV. DEFECTS

S.T. Picraux / Defect trapping

434

LATTICE SITE MUON LOCATION IN Cu i

0 i

Cu

03

~-

0oo)

(1122

.01o) CAke. (O-SITE)

n

K

"

0.2


SUB.

?

t~ U.I

................

T

_<_lp2 _<11_12

0.i

RIGID LATTICE 5% LATTICE EXP.

'~ , , ~ ~ """""

RELAXATION

o

:

~

20K

•

•

•

80K

:iii) i(llO~ --J_-=

" (111)

L

I

0.01

0.1 Bext.(T)

Fig. 24. Measured and calculated dampling constants for muon spin depolarization in Cu, from ref. 53, and calculated high-field levels, from ref. 54, for O, T and substitutional sites.

highest purity cyrstals studied [56]. Although the trap energy is probably low (50.1 eV), it could possibly have some influence on the muon location. The trapping of muons by vacancies appears weU-established only in the case of A1. Here dkect comparisons between muon and positron trapping in quenched AI suggests that muons are trapped mainly at monovacancies and divacancies, whereas positrons are strongly trapped at small vacancy clusters [57].

4.2. Heavy inert gases Because of their larger size the heavier inert gases Ne, Ar, Kr, and Xe are less mobile but interact even Table 8 Comparison between positive muon and hydrogen lattice locations. Metal

/z÷ site a,b)

H site c)

Cu V Nb Ta

O T+O T T

O T T T

octahedral site, T = tetrahedral site. b) M. Camani, F.N. Gygax, W. Ruegg, A. Schenck, H. Schilling, and J. Keller, Z. Phys. Claem. c) References in table 2. a) O =

more strongly with vacancies in metals than does He. This qualitative view appears to be borne out by atomistic cluster calculations and by experimental studies using hyperfine techniques. In particular, the M6ssbauer effect has been used to study Xe in metals by means of gamma emission from the daughter isotope 13aCs. A key result for Xe in Fe has shown that the implanted Xe traps vacancies [58]. The spectra were deconvoluted into four individual contributions involving XeVn where n varied from 1 to 4 with XeV1 corresponding to a substitutional Xe atom in the Fe lattice. While establishing the uniqueness of the deconvoluted components is difficult, it was clear from these studies that multiple vacancy associated with the Xe was occuring. This contrasts to Hevacancy interactions where the major center seen is increasing numbers of He in a vacancy ranging from 1 to 4, versus these studies where only one Xe is inw)lved with 1 - 4 vacancies associated with that Xe. More recently, detailed studies have been carried out for the case of Xe implanted in Mo [59] (fig. 25). Again, the spectra are interpreted in terms of 4 components corresponding to XeV n where the numbers 1 - 4 in fig. 25 correspond to n. Two convincing factors help to establish the identification in this particular case. First, from the calculated structures for Fe [69] (fig. 26) the symmetries involved can be used to argue that quadrupole interaction terms of opposite

435

S. 7". Picraux /Defect trapping ---

,

,

-

,

-'v

r

-~-.-~-._.S.-T~__?_-_~_=~-_--Z::rI~,,~'.~.'r-~..~....-o,.~>, 1)

1.03 •

- -,.,: "~'-'~

[~

> I--

. 0.98

R1--imp~&n,ation ,

, . . .-. ~ - - ' . . . .~. ~' . . .:. . . .:. ' ' '&

04

i

,,

//

... I

'

1.0: +

_J

\\J ,

- - - - ~ - .. .:,,'., . . . . . . "~-..-7.~,,

3) XeV 3

4) XeV 4

,.~e""

.,/

;

"~,M,2.,/

= Xe ATOM

tO0

or.

0.9g

2) XeV2

......... "-'-~'~

~i il

019~ "

0.97

2-

XeV l

•v ~

~

."

annea!ing

[~

= VACANCY

•

= bcc LATTICE ATOM

Fig. 26. Schematic representation of XeVn centers in the bcc lattice, from ref. 59, based on calculations by ref. 58 for an Fe lattice.

J 0.gE

V

1.00

~

,i' ~.4-

,?.'.

0.g9

-

1

V E t OSITY

z

(n':z'/sec)

Fig. 25. M6ssbauer spectra for 133Xe implanted into Mo to ~5 X 1013/cm2 for various anneal temperatures with deconvoluted XeVn contributions for n = 1-4 labelcd. From ref. 59.

tional vacancies are added. This is consistent with the expected lowering of electron density around the Xe atom with additional trapped vacancies. A second convincing point can be seen from fig. 25 where at Stage 3 corresponding to the 425 K anneal spectrum a shift from predominantly XeV~ centers to multiple vacancies Xe centers is observed. This is consistent with vacancies created during the implantation becoming mobile and being captured by the oversized Xe atom. Thus vacancy interactions with the heavier inert gases also appears to be quite strong, and again this is an area where little progress can be made without the aid o f implantation, due to the negligibly small solubility for these species in metals.

5. Conclusions sign should be expected for XeV2 and XeVa centers only. Then from these, together with the peaks for n = 1 and n = 4, as seen from the as-implanted and 1275 K anneal spectra in fig. 25, the necessary isomer shifts required to describe the spectra for the four components are well-established. The isomer shifts show the expected trend of the largest shift (most negative velocity in fig. 25) corresponding to the higher electron density for the HeV1 center and steady progression of decreasing isomer shift as addi-

Well-defined trap sites and binding energies have been obtained for hydrogen trapping to defects in a variety of metals. There is now strong evidence to support the identification of the traps as the hydrogen-vacancy center in metals. The H-V center has not been identified by any other technique, and such structural and energetics information are key elements in building a theoretical understanding of the electronic structure of such a center. Thus if this IV. DEFECTS

436

S.T. Picraux / Defect trapping

hypothesis stands a test of time, implantation will have made a major contribution to the understanding of hydrogen-defect interactions in metals. At present only limited detailed data on the H-V center is available, but several general trends appear to hold: (1) the H-V center often appears to involve high symmetry trap sites for the hydrogen; (2) the hydrogen does not occupy the center of the vacancy but is often displaced towards particular interstitial sites; (3) the binding energies appear to be appreciable ( ~ 0 . 1 - 1 eV) and thus these vacancies will have substantial influence on hydrogen transport. Helium binding to vacancies in metals is even stronger ( ~ 2 - 4 eV) and multiple He trapping at vacancies occurs with only moderate reduction of the binding energies. For the heavier, larger-sized inert gases such as Xe, multiple vacancy collection at single gas atoms appears to be a much more important process. In all these cases ion implantation has played a primary role in establishing the current level of understanding of the interaction of these gases with vacancies. Valuable discussions with W. Gauster, S. Myers, J. Norskov, H. Pattyn, and W. Wilson, and the suggestion for the channeling analysis along the (112) plane by It.D. Carstanjen are gratefully acknowledged.

References [1] J.P. Hirth and H.II. Johnson, Corrosion 32 (1976) 3. [2] F.L. Vook et al., Rev. Mod. Phys. 47 Suppl. no. 3 (1975) S1. [3] S.T. Picraux, New uses of ion accelerators (ed. J.F. Zieglet; Plenum Press. NY, 1975) p. 229. [4] S.T. Picraux, Ion beam surface layer analysis, vol. 2 (eds. O. Meyer, G. Linker, and F. Kappelcr; Plenum Press, N.Y. 1976) p. 527. [5] S.T. Picraux and F.L. Vook, Phys. Rev. Lett. 33 (1974) 1216. [6] H.D. Carstanjen and R. Sizmann, Phys. Lett. 40A (1972) 93; N.A. Sakun, P.P. Matyask, N.P. Dikii and P.A. Svetashov, Soc. Phys. Tech. Phys. 20 (1975) 432. [7] M. Antonini and ll.D. Carstanjen, Phys. Stat. Sol. 34a (1976) K153; J. Takahashi, S. Yamaguchi, M. Koiwa, Y. Fujino, O. Yoshinari, and M. Hirabayashi, Rad. Eft. 36 (1978) 135. [8] K. Skold, Topics in applied physics, vol. 28 Hydrogen in metals I, (eds. B. Alefeld and J. Volkl; Springer-Verlag, Berlin, 1978) p. 267. [9] J.P. Bugeat and E. Ligeon, Phys. Lett. 71A (1979) 93. [10] H.D. Carstanjen, J. Dunstl, G. Lobl and R. Sizmann, Phys. Stat. Sol. 45a (1978) 529.

[]1] A.C. Chami, J.P. Bugeat and E. Ligeon, Rad. Eft. 37 (1978) 73. [12] J. Bergsma and J.A. Geodkoop, Physica 26 (1960) 744. [13] S.M. Myers, S.T. Picraux, and R.F. Stoltz, J. Appl. Phys. 50 (1979) 5710. [14] J. Volkl and G. Alefeld, Topics in applied physics, vol. 28 Hydrogen in metals I (eds. G. Alefeld and J. Volkl; Springer-Verlag, Berlin, 1978) p. 321. [15] J.P. Bugeat, A.C. Clutmi, and E. Ligeon, Phys. Lett. 58A (1976) 127. [16] K. Ozawa, S. Yamaguchi, Y. Fujino, O. Yoshinari, M. Koiwa and J. Hirabayski, Nucl. Instr. and Meth. 149 (1978) 405. [17] H. Fischer, R. Sizmann and F. Bell, Z. Physik 224 (1969) 135. [18] J.P. Bugeat and E. Ligeon, Proc. 2nd Int. Congress on ilydrogen in metals, Paris (1977). [19] F. Besenbacher, J. BCttiger, T. Laurson and M. Moiler, J. Nucl. Mat. 93-94 (1980) 617. [20] G.M. McCracken and S.K. Erents, Applications of ion beams to metals (eds. S.T. Picraux, E.P. EerNisse and F.L. Vook Plenum, NY, 1974) p. 585. [21] K.L. Wilson and M.I. Baskes, J. Nucl. Mat. 76 and 77 (1978) 291. [22] J. B~bttiger, S.T. Picraux, N. Rud, and T. Lausen, J. Appl. Phys. 48 (1977) 920. [23] S.M. Myers, S.T. Picraux and R.E. Stoltz, Appl. Phys. Lett. 37 (1980) 168. [24] I).K. Brice, Fundamental aspects of radiation damage in metals (eds. M.T. Robinson and F.W. Young; USERDA CONF-751006, 1976) p. 35; D.K. Brice, Ion implantation range and energy deposition distributions (Plenum Press, NY, 1975). [25] R.B. McLcllan, Scripta Met. 9 (1975) 681. [26] J.K. Norskov, Phys. Rcv. B20 (1979) 446. [27] Such arguments have been discussed informally by C.F. Melius and J.K. Norskov who have been carrying out theoretical calculations of hydrogen chemisorption and vacancy trapping, as well as others, e.g., A.E. Gorodetsky, A.P. Zakharov, V.M. Sharapov and V.K. Alimov, J. Nucl. Mat. 93-94 (1980) 588. [28] M.I. Baskes and C.F. Melius, Z. Phys. Chemie 116 (1979) 519. [29] W.D. Wilsonand C.F. Melius, private communication. [30] D.S. "Larsen and J.K. Norskov, J. Phys. |7 9 (1979) 1975. [31] M.L. Swanson and L.M. ttowe, Pad. Eft. 41 (1979) 129. [32] S.T. Picraux and F.L. Vook, Ion implantation in semiconductors (ed. S. Namba; Plenum Press, NY, 1975) p. 355. [33] H.E. Schaefer, K. Maier, M. Weller, D. Herlach, A. Seeger and J. Diehl, Scripta Met. 11 (1977) 803. [34] J.S. Koehlcr, Fundamental aspects of radiation damage in metals, vol. 1 (USERDA, CONF-75100G-PI, 1976) p. 397. [35] P.B. Johnson and D.J. Mazey, J. Nucl. Mat. 93-94 (1980) 721. [36] A.E. Pontau, K.L. Wilson, F. Greulich and L.G. ttaggmark, J. Nucl. Mat. 91 (1980) 16. [37] D.J. Reed, Rad. Eft. 31 (1977) 129.

S. T. Picraux / Defect trapping [38] A. van Veen and L.M. Caspers, Proc. Consultants Symp. on Inert gases in metals, Harwell, U.K. (1979). [39] W.D. Wilson and R.A. Johson, Interatomic potentials and simulation of lattice defects (eds. P.C, Gehlen, J.R. Beeler and R.I. Jaffee; Plenum Press, NY, 1972) p. 375. [40] E.V. Kornelsen, Rad. Eft. 13 (1972) 227. [4l] L.M. Caspers, A. van Veen, A.A. van Gorkum, A. van den Beukel and C.M. van Baal, Phys. Stat. Sol. 37a (1976) 371. [42] W.D. Wilson and C.L. Bisson, Rad. Eft. 22 (1974) 63; M.I. Baskes and W.D. Wilson, J. Nucl. Mat. 63 (1976) 126. [43] W.D. Wilson, M.I. Baskes and C.L. Bisson, Phys. Rev. B13 (1976) 2470. [44] L.M. Caspers, H. van Dam and A van Veen, Delft Progr. Rep. Series A, Chemistry and physics, vol. 1 (1974) p.39. [45] S.T. Picraux and F.L. Vook, Applications of ion beams to metals (eds. S.T. Picraux, E.P. Ecrnisse and F.L. Vook; Plenum Press, NY, 1974) p. 407. [46] L.M. Caspers, R.H.J. Fastenau, A. van Veen and W.F.W.M. van Heugten, Phys. Stat. Sol. 46a (1978) 541. [47] A. van Veen, L.M. Caspers, E.V. Kornelsen, R. Fastenau, A. van Gorkum and A. Warnaar, Phys. Stat. Sol. 40a (1977) 235. [48] C.L. Bisson and W.D. Wilson, Proc. Dayton Conf. (1980).

437

[49] E.V. Kornelsen and A.A. van Gorkum, Phys. Stat. Sol. (in press). [50] W.B. Gauster, J. Vac. Sci. Technol. 15 (1978) 688. [51] B.T.A. McKee, W. Triftshauser and A.T. Stewart, Phys. Rev. Lett. 28 (1972) 358. [52] A. Seeger, Hydrogen in metals I, vol. 28 (eds. G. Alefeld and J. Volkl; Spfinger-Verlag, Berlin, 1978) p. 349. [53] M. Camani, F.N. Gygax, W. Ruegg, A. Schenck and H. Schilling, Phys. Rev. Lett. 39 (1977) 836. [54] W.B. Gauser, A.T. Fiory, K.G. Lynn, W.J. Kossler, P.M. Parkin, C.E. Stronaeh and W.F. Lankford, J. Nucl. Mat. 69 and 70 (1978) 147. [55] M. Camani, F.N. Gygax, W. Ruegg, A. Schenck, H. Schilling and J. Keller, Z. Physik. Chemie 116 (1979) 157. [56] H. Orth, K.P. Doring, M. Gladisch, D. Herlach, W. Maysenholder, M. Metz, G. zu Putliz, A. Seeger, J. Vetter, W. Wohl, M. Wigand and E. Yagi, Z. Physik, Chemie 116 (1979) 241. [57] J.A. Brown, R.H. Heffner, M. Leon, M.E. Schillaci, D.W. Cooke and W.B. Gauster, Phys. Rev. Lett. 43 (1979) 1513. [58] S.R. Reintsema, S.A. Drentje, P. Schurer and H. de Waard, Pad. Eft. 24 (1975) 145. [59] S.R. Reintsema, E. Verbrest, J. Odeurs and It. Pattyn, J. Phys. F" 9 (1979) 1511. [60] S.A. Drentje and J. Ekster, J. Appl. Phys. 45 (1974) 3242.

IV. DEFECTS