MOBILITY PARAMETERS FOR THE VACANCIES AND THE SELF-INTERSTITIALS IN CONCENTRATED α-AgZn ALLOYS

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MOBILITY PARAMETERS FOR THE VACANCIES AND THE SELF-INTERSTITIALS IN

CONCENTRATED α-AgZn ALLOYS

D. Beretz, J. Hillairet, M. Halbwachs

To cite this version:

D. Beretz, J. Hillairet, M. Halbwachs. MOBILITY PARAMETERS FOR THE VACANCIES AND

THE SELF-INTERSTITIALS IN CONCENTRATED α-AgZn ALLOYS. Journal de Physique Collo-

ques, 1981, 42 (C5), pp.C5-747-C5-752. �10.1051/jphyscol:19815115�. �jpa-00220984�

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JOURNAL DE PHYSIQUE

CoZZoque C5, suppl6rnent au nO1O, Tome 4 2 , octobre 1981 page C5-747

MOBILITY PARAMETERS FOR THE VACANCIES AND THE SELF-INTERSTITIALS I N CONCENTRATED

a-AgZn

ALLOYS

D. Beretz, J. Hillairet and M. ~albwachs*

C'Eiltre d ) E t d s s 8ueZ6aire.s de Grenohle, D6partemeizt de Hecherche I;%inbentaZe Section de F?zgsique du S o l i d e , 85 ,Y - 38041 Grenoble Ce:edex, France

*

~ c o l e mationale SupBrieure de CGrwmqw I n d u s t r i e l Z e , 47, rue Albert Thomas, 87200 Limoges, France

Abstract.- In-flux relaxation measurements were carried out to monitor the radiation enhanced Zener ordering rate in a Ag- 9 at. % Zn alloy. From considera- tation of both the quasistationary and the stationary rates it is inferred that the vacancies are the faster diffusers, with activation energy close to

0.60 eV. 'lore generally, the migration properties of the point defects in the

whole range of the concentrated a-solid solutions ofthe AqZn systeinare presented and discussed.

1. Introduction.- Zener relaxation methods are a convenient tool for the study of the point defect populations associated with irradiation and the derivation of the mobility parameters for threlemental radiation defects, in appropriate concentrated alloys (1-6). In this respect the AgZn system is of particular interest. Among other pertinent data, the self-interstitials were found to be less mobile than the vacancies in a series of concentrated a-AgZn solid solutions, with respective concentrations 1 8 , 2 4 and 30 at. % Zn (2,3,7). The present paper describes further research intended at determining the interstitial and vacancy mobilities in the case of lower zinc concentrations. Attention is focussed primarily to a Ag-9 at. % Zn alloy in which the relative mobility of the two defect species considered is controversial (8). New experimental findings are presented together with a reanalysis of previous data. They lead to the conclusion that the self-interstitials are still migrating less rapidly than the vacancies at this lower zinc composition.

2. Experimental and phenomenological approaches.- Alloying was by melting in a quartz tube under vacuum 6N Cominco Ag and 6N5 Zn prepared by the Laboratoire d.Elec- tronique et de Traitement de 1'Information du Centre Nuclsaires de Grenoble. To avoid the complications arising from grain boundary relaxation a single crystal was elaborated. The specimens were strips 250 Ilm x 2 mm x 10 mm cut along a < ] l o > direc- tion. They were given a five day anneal at a temperature within fifty degrees of melting to produce a very low dislocation density. The final impurity content was about 30 at.ppm.

The experimental approach to the determination of the defect parameters was based on the realization of strain relaxation measurements. These were conducted directly under irradiation to monitor the enhanced Zener relaxation rate associated with the radiation produced defects. For this purpose an inverted torsion pendulum with negligible inertia was adapted to work in-line with a Van de Graaff accelera-

tor. Details about the experimental arrangements and irradiation conditions were

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19815115

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C5-748 JOURNAL DE PHYSIQUE

given elsewhere (6). Analysis of the data was made with use of the formalism develo- ped by Nowick and Berry (9) and Berry and Orehotsky (10) in which the ordering kinetics for the Zener relaxation is considered to be first order but with a lognormal distribution of the characteristic relaxation times, T.

In general Zener methods are well suited to irradiation studies since (i) the relaxation rates can be determined directly during exposure to a fast particle flux, i.e. at the irradiation temperature and in a continuous manner. Thus the atomic mobility can be obtained at every instant of the irradiation, (ii) the measuring sensi- tivity is the same at any time in the irradiation schedule by the mere fact that it is possible to reestablish the same initial, fully relaxed, state before triggering the successive measurement cycles. This coverage of the whole time range from the initial transients on the application of flux until the time when a steady state is reached is a unique property of the methods based on analysis of the directional order. A serious limitation to the resistivity measurements which are most frequen- tly employed to monitor the short range ordering rate resides precisely in the non- possibility of this procedure, (iii) measurements can be performed at temperatures when both created defect species are mobile which enables, as indicated below, the direct determination of their respective jump frequencies. In short, these are very favorable conditions for the study of the detailed dynamic behaviour of the defect populations which are generated during permanent irradiation.

It is recalled that the relaxation rates under flux, T - 1

are related to the irr'

vacancy and self-interstitial concentrations, cV and ci, and jump rates, uV and u i'

-

¹

= av CV VV + a. C. u.

'irr 1 1 1

The a's are efficiency factors of the order of unity (3). Interpretation of the radiation enhancement of the relaxation rate is based on consideration of the general balance equations which describe the time evolution of the point defect concentrations during irradiation (12). From combining the numerical solution of these equations and expression (1). it is readily shown that the curve for the variation of the relaxation rate with irradiation time under a constant flux goes through a quasistationary maximum before it evoluates towards a stationary level. This scheme essen- tially applies to the case when defect elimination is predominantly by mutual recom- bination. Then the quasistationary and stationary rates are written (I) :

Here the subscripts f and s denote the faster and the slower migrating defect species respectively, independent of the type they are, vacancies or self-interstitials.

0

is the flux rate, and the B's are constants in a given material, since they depend only on the intrinsic parameters, displacement cross-section and spontaneous recom- bination radius. Thus from a temperature dependence study: the migration energies

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for both the faster and the slower moving defects can be inferred. Typical experimental profiles are shown in Fig. I for the two extreme compositions studied, 9 and 30 at. % Zn.

Fig. I . Relaxation rate versus time of irradiation for the two compositions Ag-30 at.

% Zn and Ag-9 at. % Zn. The corresponding stationary rates are indicated by the ar- rows.

Fig, 2. Arrhenius plot for the anelastic ordering rate in Ag-9 at. % Zn. The left curve refers to zero Flux. The two other curves indicate the ordering rates for the quasistationary and the stationary conditions under a constant electron flux of 2.1 x 1 0 1 1 e- cm-2 s-1

.

^(E⁼2.5 MeV).

3 . The Ag- 9 at. % Zn case. Fig. 2 is an Arrhenius plot of the ordering rates mea-

sured in the three conditions, thermodynamical equilibrium vacancy concentrations, quasistationary and stationary defect concentrations under a constant electron flux.

The associated activation energies refer to self-diffusion and one half the migration energy for the faster and the slower migrating radiation defect species, respectively. Thus, from the quasistationary evolution,a migration energy of 0.58 eV is inferred for the faster diffusers. On the other hand high voltage electron microscopy observations conducted in quasistationary conditions also yielded a neighbour value of 0.60 eV for the same alloy composition ( 1 3 ) . However these values are at

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C5-750 JOURNAL DE PHYSIQUE

variance with previous data by Bystrov et a1 (14). The resistivity measurements they performed to monitor the radiation enhancement of short range ordering yieIded values for the mean quasistationary ordering rate very close to the ones observed in the present anelasticity study, for a given flux (cf. fig. 3). But from a temperature dependence analysis, Bystrov et a1 deduced a value of 0 . 8 2 eV. As was shown by Balanzat (15) the observed difference in the activation energies determined by thetwo methods, anelastic and resistometric, arises from the inadequacy of the procedure used to analyze the S F 0 kinetics. Instead consideration of the Nowick and Ber-v formalism ( 1 1 ) leads to a migration energyof 0.66 e V which is in satisfactory agree- meent with the presently determined values. Consequently the activation energy for

the faster migrating defect is consistently found co be close to the one forvacancymj-.

gration, 0 . 6 4 eV, which was derived by Schdle (8) from quench studies in the same material. This finding strongly suggests that the vacancies are more mobile than the self-interstitials For the alloy composition considered.

4. Survey of the self-interstitial and vacancy mobilities in a-AgZn solid solutions The existing data about the migration parameters of the point defects fot the va- rious zinc compositions studied at the moment are given in table I. The migration energies for both defect species, referred to hereafter as being of the more mobile and the less mobile type, were derived from direct analysis of the temperature dependence of the quasistationary and stationary relaxation rates, respectively. An eva- luation of the migration energy of the more mobile defect was made too by using equ. 2 and considering that B I is not dependent on the solute concentration. Then in an Arrhenius plot all 7-I (T) variations should be linear with same ordinate at the origin. This is illustrated in fig. 3, in which both anelasticity and resistivity data (present work and ref. 14 respectively, are shown. The inferred activation energies are compared in table 1 to the vacancy migration energies measured by anelastic ( 2 , 1 0 ) or resistanetric (8) methods, after quenching.

It comes out of the results that, for every composition, the more mobile

radiation defects and the vacancies are characterized by the same mobility parameters, within experimental error. It is concluded that the vacancies are more mobile than

the self-interstitials, in the alloys considered. This was confirmed by further anelasticity (17) and microscopy (18) observations.

A striking feature of the self-interstitial mobility parameters is that not only the activation energy is high but the preexponential term in the Boltzmann expression, V i = Uo exp(-Ei/kT), is unexpectedly large, in particular for the more Y concentrated alloys. The physical reason why the self. interstitials are slowed down has already been evoked (3). The fundamental effect is the trapping of the self- interstitial at undersized solute atoms, which has been shown to result, in a number of dilute alloys, in the formation of mixed dumbbells, which are not mobile until stage 111 (19). It is speculated that, in the concentrated AgZn alloys, in which the zinc atoms are markedly undersized with respect to silver several neighbour

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T a b l e I. M i g r a t i o n p a r a m e t e r s , f o r t h e e l e m e n t a l i r r a d i a t i o n p o i n t d e f e c t s i n con- c e n t r a t e d a -AgZn s o l i d s o l u t i o n s : (+) measured i n t h e q u a s i s t a t i o n a r y r e g i m e ,

( 0 ) d e r i v e d from f i g . 3 , assurcing ;r_ = 2 . 3 x 1014 s d l , ( x ) measured i n t h e s t a t i o n a r y regime.

i

%Zn

30

24

18

I@, - - 8 I I I -

_- -

-

AOJpmE4znkL

-

^-

P i g . 3 . A r r h e n i u s p I o t f o r t h e q u a s i - lo2 I

s t a t i o n a r y r a t e s : 2 2,s 3 5.5 4

a g o h : a n a l a s t i c i t y d a t a ( t h i s work) I,+(K-~~IO~)

: r e s i s t i v i t y r e s u l t s i a Ag- 9 F i g . 4 . Jump r a t e s f o r t h e v a c a n c i e s a t . Z Zn ( 1 4 , 1 5 ) . and the s e l f - - i n t e r s t i t i a l s , a s d e r i v e d A11 d a t a were s t a n d a r d i z e d t o a f l u x from t h e q u a s i s t a t i o n a r y and s t a t i o - of 4 x 1011 e-.cm-2 s l , a s s w i n g a n a r y r e l a x a t i o n r a t e s , i n c o n c e n t r a -

s q u a r e r o o t dependence. t e d a-AgZn s o l i d s o l u t i o n s .

0.64"

0.66 (15) f a s t e r d e f e c t s ( q u a s i s t a t i o n a r y c o n d i t i o n )

V a c a n c i e s (quench)

~ 7 "

^{( e v )}

0 . 5 4 (10) 0.52 ( 2 )

0.56 (10)

( s - l )

0

-

2 x 10 14'

-

1 x I 0 14'

-

14'

0.64 ( 8 )

G'

^{( e ~ )}

0.55' 0 . 5 2 "

0.56' 0.58'

0.54' 0 . 5 8

0.58+

s l o w e r d e f e c t s ( s t a t i o n a r y c o n d i t i o n ) vo ( 2 )

8 x 10 18

3 x 10 I 6

1 x 10 14

>, 10 14

E ' ( e v )

0 . 94X

0 . 8 2 ~

0 . 6ox

>, 0.8'

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C5-752 JOURNAL DE PHYSIQUE

atoms can share the strain energy associated with the interstitial to better accomo- date the complex elastic interactions between the alloying elements. Accordingly the interstitial configuration is more smeared out than in a monoatomic crystal and interstitial motion is less favored than in the case of the split interstitial in pure metals.

References

.-

[ I ] M . Halbwachs, J. Phys F : Metal Physics, 8 , 1053, 1978.

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.

Yetal Physics, in press, 1981.

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