LATTICE DEPECTS AND GRAIN BOUNDARY TRANSPORT IN THE ALKALI HALIDES

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LATTICE DEPECTS AND GRAIN BOUNDARY

TRANSPORT IN THE ALKALI HALIDES

L. Harris

To cite this version:

L. Harris. LATTICE DEPECTS AND GRAIN BOUNDARY TRANSPORT IN THE

LATTICE DEFECTS AND GRAIN BOUNDARY TRANSPORT

IN THE ALKALI HALIDES

L. B. H A R R I S

School of Physics, University of N e w South Wales, P . 0 . Box 1, Kensington, N . S. W . 2033. Australia

Résumé. — Une étude minutieuse de la diffusion de 2 2Na le long des joints de grain dans des

cristaux doubles de NaCl, a montré qu'il est possible de réconcilier les rapports contradictoires précédents concernant l'accroissement de la diffusion des cations le long des joints de grain, et d'établir un. modèle compatible avec le comportement de la diffusion des deux ions : anions et cations. Des observations à Pultramicroscope et de la diffusion de la lumière suggèrent que le transport le long des joints de grain a lieu d'une manière sélective près des précipités à cause de la réaction de la modification des phases.

Abstract. — A careful investigation of 2 2Na diffusion along grain boundaries in NaCl bicrystals has

shown that it is possible to reconcile previous contradictory reports concerning the enhanced sion of cations, and to establish a consistent pattern of behaviour for both anion and cation diffu-sion. Ultramicroscopic and light-scattering observations suggest that boundary transport takes place selectively near precipitates as a result of the phase change reaction.

1. Introduction. — T h e interpretation of transport in ionic crystals in terms of lattice defects has been conditioned in recent years by concern with the p r o -perties a n d problems of the well-characterised single crystal [ 1 , 2 ] . A consequence is that relatively slight attention h a s been given t o the influence of crystal substructure on transport behaviour, in spite of the existence of experiments which demonstrate that this influence can be significant [3, 4]. Overall, however, the evidence from these experiments is fragmentary and n o t always consistent. Thus, though it has long been acknowledged t h a t dislocations a n d grain boundaries increase axion diffusion in the alkali halides [5], it is only recently that observations have been made that can point t o a particular mecha-nism [6], while in the case of cation transport it is not even certain that dislocations a n d grain b o u n -daries exert any influence. The present work is an attempt to sort out some of the differences of opinion held concerning the influence of substructure o n cation transport in the alkali halides [7].

A complete review of experimental results on cation transport and substructure is n o t particularly valuable at this stage, since it is n o t easy to make a valid comparison of the differing types of experiments carried out on assorted materials in which various mobile impurity ions, as well as host cations, have been investigated. If, however, we confine o u r atten-tion to host caatten-tion transport in one material, selecting sodium transport in sodium chloride as the most suitable system, a n d use the grain b o u n d a r y as the

most obvious form of substructure, then comparison becomes much easier. T h e contradictions also become more apparent. T w o attempts to detect enhanced grain b o u n d a r y diffusion in N a C l down t o 573 K , one by autoradiography of hot-pressed compacts [8], one by tracer diffusion a n d sectioning of bicrystals [9], have been reported as unsuccessful. In other experi-ments, by contrast, preferential grain b o u n d a r y diffusion h a s been clearly demonstrated by t h e a u t o -radiography of bicrystals [10], a n d considerable enhancement of grain b o u n d a r y conduction h a s been found in hot-pressed compacts [11]. It has also been shown t h a t N a+ ions injected into grain b o u n

-daries in N a C l enhance the conduction [12]. These are the types of contradiction that need t o be reconciled. 2. Experimental methods. — 2 . 1 CRYSTAL G R O W T H Crystal growth and specimen preparation techniques were similar to those described previously [7]. Prior t o melting, the salt in the growth system was preheated under vacuum at 773 K for 6 h, the system being periodically flushed with dry nitrogen, in order t o remove water a n d volatile impurities. Previous work [13] h a d indicated that b o u n d a r y transport in nominally pure bicrystals pulled from the melt was determined primarily by residual impurities that h a d segregated t o the b o u n d a r y a n d formed precipitate. F o r this reason, it eventually became s t a n d a r d practice t o carry out a full analysis b y emission and a b s o r p t i o n spectroscopy of the impurity content of each specimen used. This was necessary in order to account for

C7-366 L. B. HARRIS tions in behaviour between specimens from different

ingots and, occasionally, between specimens from the same ingot. All bicrystals contained 100 tilt boundaries.

2.2 TRACER DIFFUSION.

-

TWO improvements were

made to the tracer techniques described previously [7]. In place of the earlier method of drying a drop of NaCl solution on the specimen surface, tracer was deposited by use of a vacuum evaporator built spe- cifically to handle radioactive alkali halides. A drop of saturated aqueous solution containing "NaCl was evaporated to dryness in a small nickel crucible, after which the dried salt was baked under vacuum up to a temperature of 730 K. Removal of moisture caused the pressure to fall to about torr, after 4 to 6 hours baking. A specimen was then exposed to the mouth of the crucible, and a layer of salt containing "NaC1 was deposited from the vapour phase by slow evaporation at 950 K. Some 8 speci- mens were coated in sequence from one charge of the crucible, the average coating thickness of 15 pm being obtained after some 30 min evaporation. This layer acts as a constant concentration source of tracer. Detection of grain boundary diffusion by sectioning requires identification of a tail on the tracer penetration profile, and therefore needs carefuI measurement of low activities at relatively large penetrations [7]. Improved counting techniques were obtained in the present work by use of a scintillation counter with its window centred on the 1.27 MeV gamma emission of "Na, and a statistical treatment of the ratio of specimen to background counts that gave a more reliable determination of low count rates.

2.3 LIGHT-SCATTERING AND ULTRAMICROSCOPY. -

A He-Ne laser was used to illuminate a prismatic block of crystal in the configurations shown in figure 1. In configuration (a) successive observations were made on a sequence of planes parallel to the grain

YE

TUBE

BEAM

C - -

FIG. 1.

-

(a) Ultramicroscopic observation of scattered light S by eye or camera through eyepiece E. Laser and objective traversed in synchronisation, as shown by arrows (1) and (2).

(b) Light-scattering intensity measurements by photornul- tiplier tube across grain boundary in specimen traversed in

direction of arrow (3).

boundary, in order to build up a profile of the density of ultramicroscopic specks, measured as a function of position normal to the grain boundary plane by a micrometer scale attached to objective 0. In this case the small depth of field of the optical microscope is an advantage, since the ultramicroscopic specks in focus are those which lie within a narrow wafer of crystal that approximates to a plane.

In configuration (b) the specimen is driven vertically by an electric motor so that a light-scattering intensity profile across the grain boundary can be automatically plotted out on a chart recorder. Here the finite width of the field of view seen by the photomultiplier within the specimen produces a broadening of the profile, for which it is necessary to make a correction.

3. Theory.

-

The equation used to obtain the product of grain boundary diffusion coefficient D' and grain boundary width 6 from a sectioning expe- riment on a bicrystal at temperature T, using a constant surface concentration of tracer, is

where

Here c is tracer concentration at penetration depth y after time t of diffusion, and the first term on the right-hand side of (1) is obtained from the slope of the tail on the penetration plot. The quantity D in (1) and (2), representing bulk diffusion coefficient, is obtained from a separate experiment at the same temperature T on a piece of single crystal, preferably from the same bicrystal ingot, using the solution of Fick's second law that corresponds to constant surface concentration c, :

c = c, erfc

[(4

.

The third term on the right-hand side of (I), in which y = y / ( ~ t ) l / ~ , can be used in conjuction with the accurate Whipple solution of the grain boundary diffusion problem [14]. In this case the boundary is assumed to be a homogeneous slab embedded within the bicrystal. The two unknowns in (I), the product D' 6 and the quantity

B,

can be obtained by a method previously described [7]. The quantity is of consi- derable interest since its magnitude depends on the ratio of grain boundary to bulk diffusion.

preannealed. Figure 2 shows typical penetration plots in which the curve up to a penetration of about 40 pm is mostly due to bulk diffusion given by equation (3). The tail at deeper penetration, whose slope determines the first term on the right-hand side of (I), represents grain boundary diffusion. The tail for "OAg tracer shows some scatter, since this is an early experiment that used an older type counter, but there is no doubt that the silver impurity ion moves more readily along the boundary than the host cation. The tails for the "Na experiments occur at lower count rate, but are well defined. Note that the ordinate in figure 2 represents the count rate actually measured, these values being comparable with those used to determine 36Cl boundary diffusion [15].

FIG. 3. -Penetration plots of tracer diffusion in as-grown NaCl single crystals, t = 48 h. IloAg, 623 K ; 0 22Na, 623 K ;

a

22Na, 696 K. The curves fit equ. (3) up to the points

indicated by arrows.

FIG. 2. - Penetration plots of tracer diffusion in NaCl bicrystals. IlOAg, t = 48 h, 623 K ; 0 22Na, t = 48 h, 623 K ;

a

22Na, t = 48 h, 696 K ; X 2*Na, t = 32 h, 773 K (after Riggs and Wuttig [9]). Experiments at 623 K on as-grown bicrystals ;

that at 696 K on specimen preannealed at 900 K for

75 h.

In order to show that the tails in figure 2 genuinely represent grain boundary diffusion, it merely seems necessary to make a comparison with penetration plots obtained on single crystals under identical experimental conditions. However, there is the problem that, though single crystals are free from grain boun- daries, they nevertheless contain a substructure whose effect on diffusion can be clearly seen at short diffusion times [7]. Thus, the curves of figure 3 show an additional penetration superimposed on the erfc

plot that is clearly less regular than the grain boundary tails of figure 2. Such substructure diffusion varies considerably between specimens when these are used in the as-grown condition, and it is evident that some form of preannealing treatment is necessary in order to standardise behaviour. Note that substructure diffusion at 696 K as shown for the as-grown single crystal in figure 3 is more prominent than the grain boundary diffusion shown for the preannealed bicrystal at the same temperature in figure 2. Neither of these forms of extra penetration can, however, be observed on a penetration plot when diffusion time t is large. The dashed curve in figure 2 is a replot of the only known penetration profile for Na' diffusion in a NaCl bicrystal that has been published to illustrate the lack of enhanced grain boundary diffusion. It was, in fact, originally contrasted [9] with a profile that exhibited a large grain boundary tail caused by NaOH contamination. In figure 2, however, the dashed curve is seen to stop at the point where the boundary tails of the present work begin. Hence present measurements are not in conflict with the failure to detect boundary diffusion in this particular instance.

The values of D' 6 and

P

obtained at 623 K from the curve plotted in figure 2 are 4.4 x m3/s and 13. These are considerably lower than earlier values of

C7-368 L. B. HARRIS is not yet clear whether this decrease is due to the

improvement in counting technique or to use of a tracer deposition method that prevents water getting onto the specimen surface. In any case the values of

D'

6 and

p

obtained on as-grown bicrystals show considerable scatter. Values of D for as-grown single crystals, by contrast, are usually independent of the specimen used. The points giving the top curve in figure 4 were obtained from equation (3) for a diffusion time t of 120 h, the longer time giving a smaller sub- structure tail than those seen in figure 3. To reduce scatter in

D'

6 , an attempt was made to produce a standard as-grown bicrystal specimen by holding cleaved samples for 75 h at 900 K before allowing them to cool with the annealing oven. This reduced both the scatter and the value of

D'

6, but completely consistent results could be obtained only when the specimens were taken from the same ingot. The two lower curves in figure 4 were obtained from a set of preannealed specimens from one bicrystal ingot.

FIG. 4. -Variation of 22Na diffusion parameters with perature. 0 D, top left ordinate ; D' 6, right ordinate ;

bottom left ordinate.

tem-

x

D,

Two points emerge from figure 4, of which the first concerns the low experimental values of

P.

It is usually suggested that observation of grain boundary diffusion by sectioning is best carried out for values of

P

>

10 [14]. The lowest values of

P

in figure 4 is 1, the grain boundary tail from which this value was calculated being that shown for 696 K in figure 2. In general, values of

P

varied between 1 and 15, which gives the range within which experiments on

the alkali halides might be expected t o operate. The second point concerns the apparent anomalous increase in grain boundary diffusion between 700 and 725 K. This increase has been observed on other specimens apart from those giving rise to figure 4, and can therefore be regarded as well established. Since

D

measured in single crystals is well behaved in this temperature range, such behaviour appears to be an impurity effect specific to the boundary. Evidence that 700 K is a temperature at which there is a relatively minimal amount of enhanced diffusion is also provided by quenched specimens, annealed for 75 h at 900 K and then cooled to room temperature in 15 min. Enhanced diffusion could not be detected at 700 K on such specimens, the values of

D'

6 being below the limit of detection (< 3 x lo-" m3/s) in other work [8] that failed to detect enhanced sodium diffu- sion.

4.2 ULTRAMICROSCOPY AND LIGHT-SCATTERING.

-

The distribution of ultramicroscopic centres in as- grown bicrystals, using configuration (a) of figure 1, was always influenced by boundary segregation. The surface density in figure 5, representing the number of specks per mm2 seen by an objective with a depth of field of 5 pm inside the specimen, corresponds to volume density similar to that observed previously in pure NaCl [16], the boundary peak value being about twice that in the bulk crystal. The boundary layer over which there is a significant increase in density is at least 100 pm thick.

GRAIN BOUNDARY

0 0.5 1.0 1.5

DISTANCE (rnrn)

FIG. 5. - Distribution of ultramicroscopic centres across grain boundary in as-grown bicrystal.

DISTANCE (mm )

FIG. 6. -Intensity profile of light scattered from as-grown bicrystal. - measured, X calculated.

being effectively 400 pm wide. The crosses in figure 6 demonstrate that this broad profile is produced by a narrower distribution of scattering centres, the crosses being in fact calculated from a scan across a profile of identical shape to that in figure 5 by a collecting slit 400 pm wide. It is seen that the crosses closely outline the experimental profile and, hence, that the distribution of both types of centre is very similar.

Many experimental profiles on as-grown bicrystals were less regular than those seen in figures 5 and 6 . Such profiles contained asymmetrical pumps, or subsidiary peaks or dips, that changed in shape as observation was shifted to different parts of the boundary. In general, the annealing processes that reduced boundary diffusion also reduced the grain boundary profile, while slow cooling from high temperature sharpened the peak. The profile width could never, however, be reduced to a value less than 20 p.

Since it is known [17] that most of the centres observed by ultramicroscopy and light-scattering are precipitates, and since the specimens used in this work are nominally pure, it is of some interest to attempt to identify the impurities responsible for this precipitation. Analysis of one of the specimens used to obtain the grain boundary curves in figure 4 is given in table I, the impurity levels shown being entirely typical of the crystals used in this work. The major metallic impurity is potassium, but the major divalent impurity contributing to extrinsic transport is calcium. It may be assumed that the impurities listed in table I are those involved in the segregation processes described in this section.

Impurities in nominally pure NaCl bicrystal specimen Impurity - Ca Cu Fe K Mg Mn Ni Sr A1 Cd Cr Li Si Sn Concentration (10-6 mole fraction)

-

4.5 3.0 < 1 5.0 1 1.5 < 1 0.45

<

2

<

10

<

2

<

10

<

3

e

2

5. Discussion.

-

The present observations have established that enhanced diffusion of cations can take place along grain boundaries in NaCl, and have done so in a manner that is completely compatible with previous investigations that failed to detect such diffusion. It has not yet been possible to obtain a value of D' 6 as large as that reported by another set of workers (- 6 x lo-" m3/s at 723 K [lo]), but it is probable that slow cooling of specimens from high temperatures will, by promoting boundary segrega- tion, produce larger values of D' 6 than those shown in figure 4. The top two curves of figure 4 show that cation boundary diffusion has the same characteristics (low activation enthalpy and relatively greater signi- ficance at lower temperatures) as anion boundary diffusion [8], and hence that both are similar to boundary diffusion in metals. Experimental values of D' 6 for 36C1 diffusion, which has been measured between 690 and 750 K [15], are some two orders of magnitude smaller than those shown here for "Na diffusion, while D for 36C1 is also two orders of magnitude smaller than D for "Na in the same temperature range. This emphasises the similarity between anion and cation behaviour, and also points to a possible common mechanism.

C7-370 L. B. HARRIS tration, which naturally leads to enhanced diffusion

with

D'

>

D since diffusion is increased by the addition of divalent impurity. However, from the values plotted in figure 4, it is found that for D' to be only a few times greater than D, 6 cannot be greater than 10 pm. This is much less than the profile width in figure 5. Hence, we must reject the idea of extra diffusion introduced by extrinsic vacancies associated with segregated divalent cation impurity. In any case segregation of such impurities would tend to inhibit anion boundary diffusion, which is contrary to the observation that both anion and cation diffusion are enhanced.

Since annealing broadens the light-scattering profile and at the same time reduces D' 6, it is clear that the real connection between enhanced diffusion and the formation of scattering centres is the fact that the latter are precipitates [17]. It has been demonstrated in MgO [20] and KBr [I31 that enhanced grain boundary transport is associated with boundary precipitate rather than just with boundary segregation. Further, anomalous variations in j3 and

D'

6, such as that shown in figure 4, can be explained quite naturally by the formation of second phase. It is known [17] that doping with calcium to an impurity level only

twice that shown in table I results in the formation of precipitates up to a temperature of 680 K, so that enhanced diffusion below this temperature can be related to a phase-change reaction that has been already observed. To explain the increased grain boundary diffusion above 700 K it is necessary to postulate the formation of another type of second phase, perhaps similar to those that cause light-scattering peaks [21] and conductivity changes [22] in the upper extrinsic region. Support for the existence of such a higher temperature second phase is provided by the anomaly detected near 750 K in measurements of anion diffu- sion along grain boundaries in NaCl [6]. Electro- decoration experiments [13] suggest that enhanced boundary transport takes place near precipitates only, rather than over the whole boundary layer. Hence, from the viewpoint of transport, the grain boundary appears to be strongly inhomogeneous, which explains why the effective transport width 6 is very much less than the thickness of the grain boundary region over which precipitates form. A

transport mechanism based on phase change disorder produced by a precipitation reaction would lead to enhancement of both anion and cation diffusion, as observed experimentally.

References

[I] FULLER, R. G., in Point Defects in Solids, vol. 1, editors, J. H. Crawford and L. M. Slifkin (Plenum Press, New York) 1972, p. 103.

[2] FREDERICKS, W. J., in Difusion in Solids : Recent Deve-

lopments editors A. S. Nowick and J. J. Burton (Aca-

demic Press, New York) 1975, p. 381.

[3] GIBBS, G. B. and HARRIS, J. E., in Interfaces, Proc. Internat. Conf. Melbourne, Aug. 1969, ed. R. C. Gifkins (Butterworths, Sydney) 1969, p. 53.

[4] KINGERY, W. D., J. Amer. Ceram. Soc. 57 (1974) 74. [5] BARR, L. W. and LIDIARD, A. B., in Physical Chemistry,

an Advanced Treatise, ed. W. Jost, Vol. X (Academic Press, New York) 1970, p. 152.

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Phys. 46 (1975) 1839.

[7] HARRIS, L. B. and FIASSON, J., Phys. Status Solidi (a) 33

(1976) 697.

[8] CAB AN^, J., J. Chim. Phys. 59 (1962) 1135.

191 RIGGS, K. R. and WUTTIG, M., J. Appl. Phys. 40 (1969) 4682.

[lo] GEGUZIN, Ya. E., DOBROVINSKAYA, E. R., LEV, I. E. and MOZHAROV, M. V., SOV. Phys. Solid State 8 (1967) 2599.

[ l l ] PRATT, P. L., J. Physique Colloq. 34 (1973) C9-213. [12] MCQUHAE, K. G., Ph. D. Thesis, London University, 1969. [13] HARRIS, L. B. and QUANG, P. G., Phil. Mag. 32 (1975) 1213. [14] LE CLAIRE, A. D., Brit. J. Appl. Phys. 14 (1963) 351. [15] RIGGS, K. R., Ph. D. Thesis, University of Missouri-Rolla,

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33 (1962) 383.

[17] NOTTIN, M., Acta Cryst. A 26 (1970) 636.

[18] GLEITER, H. and CHALMERS, B., Prog. Mat. Sci. 16 (1972) 1.

[19] MISTLER, R. E. and COBLE, R. L., J. Appl. Phys. 45 (1974) 1507.

[20] WUENSCH, B. J. and VASILOS, T., J. Amer. Ceram. Soc. 49 (1966) 433.

1211 BALTOG, I., GHITA, C. and GIURGEA, M., J. Phys. C : Solid State Phys. 7 (1974) 1892.

[22] KIRK, D. L. and PRATT, P. L., Proc. Brit. Ceram. Soc. 9