THE THERMAL STRESS COMPONENT IN NaCI SINGLE CRYSTALS

HAL Id: jpa-00215442

https://hal.archives-ouvertes.fr/jpa-00215442

Submitted on 1 Jan 1973

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

THE THERMAL STRESS COMPONENT IN NaCI SINGLE CRYSTALS

F. Appel, U. Messerschmidt

To cite this version:

F. Appel, U. Messerschmidt. THE THERMAL STRESS COMPONENT IN NaCI SINGLE CRYS- TALS. Journal de Physique Colloques, 1973, 34 (C9), pp.C9-389-C9-392. �10.1051/jphyscol:1973966�.

�jpa-00215442�

JOURNAL DE PHYSIQUE Co/ioque C9, .supp/it?iet~l uu

1 1 - 12, To~?ze 34, Novembre-Dkcernbre 1973, page C9-389

THE THERMAL STRESS COMPONENT IN NaCI SINGLE CRYSTALS (*)

F. APPEL and U. MESSERSCHMIDT Akademie der Wissenschaften der D D R ,

Institut fiir Festkorperphysik und Elektronenmikroskopie, DDR-401 Halle/SaaIe

RbumC. - Le volume d'activation fictif et l'energie libre d'activation de La deformation de monocristaux de chlorure de sodium ont ete mesures en fonction de la contrainte effective au-des- sous de la tempCrature arnbiante. Les donnees obtenues lors de deformations faibles ont ete expli- quees par I'interaction de Fleischer entre les dislocations glissantes et le champ de tension tetrago- nal de complexes impurete-lacune. Nos hypotheses ont ete verifiks par comparaison des energies d'activation mesurees lors d'experiences de changement de vitesse et de temperature, et de donnees dCduites du potentiel de Fleischer. Les parametres du potentiel de Fleischer ont ete dMuits de I'influence de la tension effective sur le volume d'activation. La tension effective a ete determink par relaxation de la tension. La variation des parametres d'activation lors de deformation croissante a ete discutee en relation avec un modele special Jog-drugging.

Abstract. - The fictive activation volun~e and the activation free energy of deformation of sodium chloride single crystals were measured below RT as a function of the effective stress. The values at small strains were interpreted by the Fleischer type interaction between the moving dislocations and the tetragonal stress field of impurity-vacancy associates. The consistency of the assumptions made was checked by comparing the activation energies measured by strain rate and temperature cycling with values deduced from the Fleischer potential. The parameters of the Fleischer potential were determined by the dependence of the strain rate sensitivity on the effective stress, measured by stress relaxation. The change of the activation parameters with increasing strain is discussed in terms or a special jog-dragging model.

The present paper is concerned wit11 a n exper~rnental determination of the activation parameters of the ther- mal stress part of sodium chloride single crkstals of different impuritycontent. At measurements bq macro- scopical deformation tests usuall! difficulties arise, since (i) in many cases several thermal stress components superimpose and

(ii) further processes contribute t o the yield stress besides the long range elastic interactions between dislocations and the short range interactions under investigation. This may be. e. g., the induced Snoek effect, which can also depend on temperature and strain rate. As an attempt t o overcome the difficulties:

the measurements were carried out on C a + + doped NaCl crystals at a lower temperature. Thus. i t is hoped that :it the beginning of deforn~:ltiolt the influence of impurities exceeds the other short range interactions arid that the Snoek effect vanishes by the temperature being lowered. The consistency of the assumptions made was checked by comparing some parameters gained by different ways of evaluation.

The change of the a c t i ~ a t i o n parameters during strain is attributed to a second thermal process. It is inter- preted a s the nonconser\,ativc molion of jogs.

In the Arrlienius cquation of the strain rate the Gibbs free cncrg! of activation A G is composed of the free energ. A F charactcrihtic of the obstacle and

the itrork done by the effective stress 7* during the activation event

AG = A F - o r * . (1) c is the so-called fictive activation volume. In a constant strain rate test, the following quantities can be measured, thus determining the process of activation at the existing effective stress :

(i) the activation volume by the strain rate sensi- tibity

(ii) the Gibbs free energy by the temperature sen- sitivity in connection with the strain rate sensitivity.

according t o a formula by Schoeck [ I ] Q, + ^{sc(T,p) (itp/dT)}

AG = ---

1 - (Tip) (?p]i?T) with Q, ⁼ - L~T(~^T/'CT);, and

(iii) the effective stress s * by stress relaxation, with the stress

( = 2

being determined a t which the relaxation rate becomes unmeasurable.

Here. r = G/? is the total shear stress, u = 2

the ihear strain rate.

the ihear modulus and k and T hat-e their usual meaning. The analysii pre- supposes that ~ i ) the pinning point distance does not depend on stress and that liii entropy terms onl!

(*) Thc major part of' thiz paper i z contained in 1'. Appel's

thesis fol- the doctol.ate ; l i ~ d \ + i l l bc pLlblishcd in detail in PI?..<. arise due to the temperature depenLence of the ahear

Sf

sol. niodului.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1973966

C9-390 F. APPEL A N D U. MESSERSCHMIDT

As already mentioned, the parameters measured on doped crystals at the beginning of deformation are assumed to be characteristic of only one single and dominating process : the interaction between dislocations and the tetragonal stress field of impurity- vacancy associates.

The experimental results were interpreted alter- natively in two ways :

(i) The quantities outlined were measured and the activation energies were calculated as a function of the effective stress.

(ii) A theoretical force-distance relation of the presumed obstacles was supposed and the parameters of this relation were determined by the dependence of the activation volume on the effective stress only.

As a test of the consistency of the experimental pro- cedure and the assumptions made, the activation energies were derived from the interaction potential and were compared with the values gained in the more direct way ( i ) .

A representative description of the interaction between dislocations and the tetragonal stress field of the impurity-vacancy associates in alkali halides ought to be given by the Fleischer interaction poten- tial [2], [3]. From Fleischer's approximation of his original force-distance relation the dependence of the activation volume and of the Gibbs free energy on the effective stress is expressed as

and

with b being tlie absolute value of the Burgers vector, I the obstacle spacing and

the stress contribution at zero temperature. According to eq. (3), both characteristic parameters,

and 1, can be gained by simply plotting the activation volume v versus the reciprocal square root of the effective stress.

It is therefore necessary to measure and to vary tlie effective stress without changing the structure and concentration of tlie obstacles. Thus, changing tlie effective stress by strain, which is often used, is not appropriate, since tlie internal structure does not remain constant. I n tlie present paper all data neces- sary for the evaluation of tlie parameters of impurities were selected from the beginning of deformation and the effective stress was altered by variations of the basic strain rate and the temperature. The expe- rimental quantities listed above were measured on crystals of different Ca content in tlie ranges of 1.7, ..., 136 ppni total divalent impurity concentra- tion, 3.3 x 10-"1s < < 2.1 x 1 0 - ~ / s and 212 K d T d 31 3 K by a self-designed compression machine with a Peltier element cascade cooling stage in vacuum.

As an example of the experimental results, figure I shows the dependence of the strain rate sensitivity on the basic strain rate and on the strain for a crystal

FIG. 1.

Dependence of stress increments at strain rate cycling on strain and strain rate for NaCl crystals containing 34 ppni divalent impurities. Deformation temperature T

222.5 K.

containing about 34 ppm divalent impurities. The increase of the stress increments with rising strain rate (and therefore rising effective stress) is well consistent with the proposed Fleischer interaction.

The corresponding temperature sensitivity and the relaxed and total stresses are plotted in figures 2 and 3.

oc, 1 I

2 3

5 6

E

[%I -

FIG. 2. - Dependence of stress increments at temperature cycling on strain and strain rate. Parameters as in figure 1.

FIG. 3.

Dependence of stress cr and rcla\cd srrcsb

on

strain and strain rate.

THE THERMAL STRESS COMPONENT I N NaCl SINGLE CRYSTALS

Activation parameters of deformation of sodium chloride single crystals at 222.5 K.

Total diualent impurity concentration 34 ppm

Stain rate [l/s] 3.26 x 1.34 x 5.21 x lo-' 2.09 x

- - - - -

( a ~ j a In

[p/mm2] 9.0 10.4 13.0 16.2

AG [eV], according to eq. (2) 0.28 0.26 0.26 0.25

z* = a,/2 [p/mm2] 27 36 43.5 57

AG [eV], according to Fig. 4 and eq. (4) 0.33 0.29 0.27 0.23

d / b 2.8 1.9 1.9 1.5

By means of the first way of analysis (including the temperature sensitivity but without supposing a special interaction potential and without using the effective stress) the first 3 lines of table I have been evaluated for the dislocation-impurity interaction.

The plot of v versus JCs*, characteristic of the interpretation by the Fleischer potential, is shown in figure 4 using the same material as above. It should

FIG. 4.

Dependence of activation volume on the reciprocal square root of the elfective stress.

be noted that the data obtained bq variations of the basic strain rate and those gained bj sariation of the temperature coinc~de up to a temperature of about 250 K. This hints at the fact that up to this temperature the obstacle structure does not seem to be influenced hq changes of the experimental parameter5 Zho\e 250 K de~iatrons ariie. whrch

\till be di,cusscd ~lsc-~\herc The Intsr,ietiun prirri- meters gained b? t h ~ s of an.iIj\l\ dre , u m m d r ~ ~ e d In the second p,irt of tcibIt: 1 4 comp,ir]>an rlf rhs differentlq e\alucited

tluei of 30 polnls to

barn>- factor) consistcrlck ^of t 1 ~ e~.pernmen~~il prticedlure and the suppointlons ~n'ide

The activation distance d has been estimated by eq. (3) considering that v = Ibd. The established values correspond to the expected diameter of the Caf '-vacancy associates. The average obstacle dis- tance I gained by figure 4 can be compared with the distance I, between the Cai '-vacancy dipoles arranged in a square array. I, is calculated from the impurity concentration c according to I, = a/tl(4/3) r . The experimental value of the lnaterial above is 1/1, = 1.9.

The computer s~mulation of dispersed obstacle har- dening by Foreman and Makin [4] shows the spacing ratio to be expected in thls order of magnitude.

The parameters presented here are characteri\tic of all other impuritj concentrations investigated, except the l o ~ e s t one. In this case the assumption of the impuritl pinning pcjlnts predominating the other short range obstacles

not fulfilled any longer.

As shown in a prekious paper [5] and also ~n figure 1 , e. g., the actitation lolume decreases with increasing strain. This decrease is accompanied by an increase of the effecti\e stress and the activation free energy.

Tjpical values of the above material are

? ( I 'c) i a = 7.2

1013 ~ r n - ~ . C:T*IZLI = 755 p mrn2 - -

in comparison to c r l a = 3500 p'mm2 and A F r~sing from 0.37 eV at 0.5 ",, strain to U,42 eV at 5 % strain. Since the stare of ~mpurities is not expected to change during straining, the reduction of the activat~on kolume ought to be due to a decrease of the obstacle spaclng and accrrrdinglj to the occurrence of new obstacles.

As alread! puin;ted o u t 161. [TI. the increase in the dislocation densnu! dc~ording to the etch pit studies of Heise [8] ns too Pow as to explain bhc effect b) a cutting mechanism s f dislocations arP secondark slip rqstemr. O n the srher hand. jog, are created in the major para of intersections. Since the jog\ remain on ahe dnc~eteations for some time bcrore b a n g annihnlated b? mutual collisions. the akerage spacnng bcrneen t h e jog5 %ill be lev5 r h d n th.;: a:crdge dn-tdn-i. Thcrueen ehe ic~re-1 dln>lr,-

catinn, C~,su-i-qurntl:~. n O the rsiajllor~t:~ ~ r ~ l jog? cdnnc~r miq.L: c ,n-tr;dnn:~I~. !hz dccrsare of t h s acUlrv.anrijn

u~l1um.c-

ns

m

r , jog-drdgging

Z rn dsI ~t 1 ;-drl;p,r.g h r - l ~ , n

+ * , h . ~ ~ h

I, S e a If11

d-:. .rl I t ron-nder~ ~ h u ~ n t i ~ i ~ t n ~ c :

C9-391 F. APPEL A N D U. h;IESSERSCHMIDT of impurity pinning points

the modes of jog motlon

and is based on the follo\~ing arguments. The inter- section jogs have to move nonconservativelj. They produce vacancies and interstitials, with the latter diffusing into the crystal and representing a super- saturation. The excess interstitials tend to anneal out, nucleating pairs of jogs on moving and unmoving dislocations. The pairs can glide along the moving dislocations which leads t o collisions with the inter- section jogs moving nonconservatively, as shoun in figure 5. The quantitative description of the kinetics

FIG. 5. - Motion of a dislocation which contains single climbing jogs and glissile jog pairs.

taking into account only mono jogs yields a system of differential equations. one of the jog density and the other of the interstitial supersaturation. The asymptotic solution suggests a linear increase of the jog density with strain. as has been proved esperi-

mentally by the course of the strain rate sensitivity (Fig. 1). While the jog-dragging is well suited to interprete the strong rise of the obstacle density, it fails to explain the experimentally observed change of the activation free energy. The increase by only a few tenths of eV is in contradiction t o the expected value of the energy of self-diffusion of the defects produced. Therefore, further work is necessary to clarify the variation of the activation parameters during straining.

In summarizing the foliowing points should be noted :

I ) The activation parameters at the beginning of deformation can well be interpreted by the interaction betneen dislocations and the tetragonal stress field of C3+ *-vacancy associates.

2) The acticatiori free energ! AF is in the order of magnitude of about 0.4 eV. almost independent of the Ca-- concentration and the effective stress.

3 ) The actit ation distance \aries between I and 3 b in the in\estigated range of effecti\e stress, the average obstacle spacing is greater than the corresponding distance in a square arrn! b j a factor between l.4 and 3.7.

4) The decrease of the activation iolume during strainins is consistent with jog-dragging. \\~hile the chanse of the activation energy disagrees with this interpretation.

The authors wish to thank Prof. H. BetRge for continuously supporting the \\ark and criticall!

reading the manuscript.

References

[I] SCROECK. G . , P/ZYS. Sfat. Sol. 8 (1965) 499. (51 APPEL. F. and MESSERSCH~IIDT, U.. PIJ~s. Siaf. SO/.

121 FLEECHR~, R. L., J. Appl. Phys. 33 (1961) 3501. ⁴ (1971) 87.

[6] MESERSCHMIDT. U., PIips. Sfat. Sol. 4 1 (1970) 549 ; Phjs.

[3] FLEISCHER, R. L., Act0 Met. 10 (1962) 535. Star. Sol. (b) 48 (1971) 781.

[4] FOREMAN, A. J . E. and M a w , M. J., Phil.

1-8 (1966) APPEL. F., Thesis, Halle, 1972.

911. 181 HESSE. J., Phyr. Stat. Sol. 9 (1965) 209.

DISCUSSION

P. HAASEN. -The formal application of thermal Furthermore stress contributions T, and rsn,k or activation analysis t o deformed and alloyed crystals .me&~,,, are not additive coming both from statis- often leads t o difficulties. G. Schoeck has proposed tical obstacle distributions.

a consistency check for this method using the T depen-

dence of the creep rate as a third test.