THE ROLE OF DISLOCATIONS AND GRAIN BOUNDARIES IN TRANSPORT PROCESSES IN IONIC CRYSTALS

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THE ROLE OF DISLOCATIONS AND GRAIN BOUNDARIES IN TRANSPORT PROCESSES IN

IONIC CRYSTALS

P. Pratt

To cite this version:

P. Pratt. THE ROLE OF DISLOCATIONS AND GRAIN BOUNDARIES IN TRANSPORT PRO- CESSES IN IONIC CRYSTALS. Journal de Physique Colloques, 1973, 34 (C9), pp.C9-213-C9-216.

�10.1051/jphyscol:1973939�. �jpa-00215414�

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THE ROLE OF DISLOCATIONS

AND GRAIN BOUNDARIES IN TRANSPORT PROCESSES IN IONIC CRYSTALS

P. L. PRATT

Department of Metallurgy and Materials Scie~:ce, Imperial College, London SW

7 2

BP, England

Rksumk. - Apres urie breve revue des defauts introduits par deforniation plastique et leur suppression par traitenlent thermique, I'influence de la deformation plastique sur la conductivite ionique est examinee. Experimentalenlent, une augnientation aussi bien qu'une suppression de la conductivite extrinseque ont ete ob!enues en plus d'une augmentalion a tres haute temperature (region 1'). Ces effets peuvent etre expliq~les en terrnes de dislocations et de leurs interactions au cours de la deformation plastique. Dans des echantillons polycristallins proches de la densite theorique, les points de grain semblent anginenter seulernent la conductivite extrinseque et accroitre I'energie d'activation obbervee dans cette region.

Abstract.

- After a brief survey of the defects introduced by plastic deformation and of their removal by annealing, tlie influence of plastic deformation upon ionic conductivity is considered.

Both enhancement and s~~ppression of the extrinsic conduction has been found experimentally in addition to an enhancement at very high temperatures in the intrinsic region 1'. These effects can be explained in terms of dislocations and their interactions during plastic flow. In polycrystalline material of near theoretical density, the grain boundaries appear to enhance only the extrinsic conductivity and to increase the observed activation energy in tliis region.

1 . Introduction.

- There is a growing volume of evidence that tlie presence of dislocations in ionic crystals may modify their transport properties in a number of different ways. The purpose of this paper is to review tlie experimental findings and to indicate what precautions lllust be taken to tnininiise the influence of dislocations upon measurements of ionic conductivity. Since most dislocations are generated by plastic defor~iiation, the paper starts with a brief survey of the defects introduced by plastic deformation and of the way in which these defects are removed by annealing. Subsecluently the influence of dislocations and grain boundaries on ionic conductivity

is

considered.

2. Defects introduced by plastic deformation.

- At room temperature plastic deformation is not homogeneous in ionic crystals, and i t is often difficult to compare the results of dilferent workers who strain their specimens plastically by tlie same amount but produce dilyerent defect densities and distributiolls by using dilferent specimen geometries. The shape of the stress-strain curve gives

a

good idea of the nature of the dcformation process, and where possible this should be measured in all deformation experiments. F o r specimens which arc tall compared with their cross-section, conipresscd along tlie [OOI]

tall axis, three stages of work-hardening are f b u ~ i d with changes o f slope after about

4 ";;

and about

8 %

plastic co~iipression [I]. Thesc three stages represent differelit modes

of

dcform:~tion, a n d diffc- rent rates of accumulation o f dislocations ill thc

crystal, with different effects upon the transport properties, and thus it is important to know whether a crystal has been deformed into stage

I,

stage

I1

o r stage

1II.

By contrast, specimens which are squat compared with their cross-section, for example niost ionic conductivity specimens compressed along the squat axis, enter stage 111 deformation at very small plastic strains with a high rate of accumulation of dislocations and of generation of point defects.

Most of the experiments on plastic deformation of NaCl have been carried out on tall crystals with dimensions of the order of 5

x

12

x

25

m m ,

having initial dislocation densities, inside the sub-grains, of between 10' and IO"cm? The rate of increase of dislocation density is low in stage

1

and increases more rapidly in stage 11, to

a

total screw dislocation density of some

8 x

1O7/crn\af~er

8 O/;:

compression.

The moving screw dislocatiolls leave trails of debris, in the form of vacancy clusters and edge dislocation dipoles, oriented in [I001 directions

in

the slip plane.

The density of edge dislocations and debris is about 10 tilnes that of screw dislocations during stage 11.

By measuring the change in bulk density of the crystals during deformation the rate of accuniulation of point defects can bc estimated, although it is difficult lo dislinguisli between vavancies and interstitials in tliis way. Both species should be formed as a consequence of thc geometry of the deformation process, although in the alkali halides tlie life-time of' the intcrstitinls is likely to be very short at room temperature. Interpr-cling tlic long-term change of density produced by p l ~ ~ s t i c deformation in tcrms

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1973939

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C9-2 14 P. L. PRATT

of vacancy pairs alone leads to a concentration of 1018/cc after 8 O/, conlpression.

Other factors which affect both the dislocation density and distribution, and hence the shape of the stress-strain curve include the purity of the specimens, their orientation with respect to the compression axis, and the temperature and strain-rate during the defor- mation [2], [3]. For material of very high purity, the initial yield stress is very low

(-

10 N/cm2), and it is easy to deform specimens while preparing them for measurement of their transport properties.

The damage put in by plastic deformation can be removed by annealing for long periods at elevated temperatures. Most of the change in bulk density due to deformation, and the dislocation debris, anneal out in a few hours at 2500-350 OC, before tlie dislocations theniselves are affected. Depending upon the strain, and the stage reached in the stress-strain curve, dislocations polygonise into sub-boundaries, and start to anneal out, i n the temperature range 400°-500 OC. However, the sub-boundaries once for- med, are remarkably stable and very long annealing times at temperatures not far removed from tlie melting point are needed to restore the original pro- perties of the material

;

in NaCl 1 h at 700 OC is insufficient to do this.

Comparing the behaviour of LiF with that of NaCl similar screw dislocation densities are achieved at 8 % compression, and, on annealing, the density starts to decrease, but with little polygonisation at 4000-500 OC. However, as with NaCI, 1 h at 800 OC is insufficient to eliminate all of the dislocations put in by plastic deformation and several days annealing are required for this to occur.

3. The influence of deformation upon ionic conduc- tivity in single crystals. - Two conflicting effects are found as a result of plastic deformation when ionic conductivity is measured at low temperatures (up to 200 OC) in the extrinsic region. Deformation enhances the conductivity temporarily, the well-known Gyulai-Hartly effect, since some of the point defects generated are available to carry charge. The pheno- menon is most pronounced with deformations in stage I1 of the stress-strain curve where the rate of defect production is at its greatest, and transient increases of 100 to

1

000 times have been seen. A short-lived component lasting some milliseconds is associated with interstitials, while the vacancy contri- bution may last up to half an hour or longer, depending upon the temperature of measurement. Against this enhancement, deformation at room temperature sup- presses the steady-stage conductivity [4], [5], [6], and a low temperature anneal at 160 OC, after room tem- perature deformation, gave an even longer suppres- sion [5]. For NaCl no suppression was found if the deforniation temperature exceeded 220 OC, while for KBr the suppression induced at room temperature survived a three-day anneal at 550 OC or above.

This suppression has been attributed in part to sweep- up of charge carriers by the moving dislocations and in part to precipitation of divalent impurity cations and their charge-compensating cation vacancies at or close to the dislocations. Only the removal of the excess length of dislocation line put in by the defor- mation will release the charge carriers to contribute to the conductivity, and the difficulty of doing this was noted in the previous section.

A further effect of plastic deformation is found in the high temperature intrinsic region 1'. Although different workers report slightly different values for the slope of region I, any one group shows consistent values for both pure and doped crystals

;

the slope of region I' however increases with increasing defor- mation [6], [7], [8] within stage I of the stress-strain curve, but decreases for deformations larger than 4

%,

at least in tall crystals of NaCI. This enhanced conduc- tivity can be largely annealed out in 24 h at 700 OC, and is probably annealing to some extent during the course of the conductivity run to high temperature.

Since it appears only in region I' where anion motion is aiding conduction, the effect is interpreted as being due to anion motion in those dislocations put in by deformation which survive the conductivity run.

The significance of the reduction of this enhancement in region I' by deformation into stage 11, where dis- location intersection generates point defects, is not clear. Perhaps polygonisation into subgrain boun- daries is aided by these point defects during the conduc- tivity run so that the network of dislocations enhancing anion motion is reduced.

4. The influence of grain boundaries upon ionic conductivity.

-

In this section some preliminary results of a study of the ionic conductivity of poly- crystalline NaCI, by Dr. M. S. Stucke at Imperial College [8j, will be compared with the resi~lts for the effects of deformation on single crystals. If disloca- tions can act as preferred paths for conduction

in

ionic crystals then grain boundaries probably should also. The difficulty of demonstrating this unequi- vocably lies in the difficulty of preparing sound polycrystalline material of tlieoretical density. For hot-pressed powders, Cabant.

[9]

has shown the importance of pre-drying the powder to eliminate water. .For dried powders, tlie polycrystalline compacts were transparent, and showed no enhancement of anion diffusion at l~igli temperatures, whereas for undried powders the compacts were opaque and anion diffusion was enhanced.

I n our work single crystals of NaCl were grown

from dried powders with

a

range of divalent cation

additions. and their ionic conductivity was measured

to provide a basis for comparison, figure 1. The

results are in fairly good agreement with earlier

workers, and show the features typical of NaCl

in

this temperature range. The total divalent cation

concentration increases in the order

⁽⁽

A

))

to

⁽⁽

B

^B)

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o C r y s t a l 'A'

0 I t

1 1 1 2 1 3 1 1 1 5 1 6 1 7

FIG.

I . - Conductivity of pure and doped single crystals of NaCI.

to

⁽⁽C c,,.

Some of the crystals were powdered, sieved

to 37-150 pm particle size and hot pressed in vacuum at 250 OC after drying the powder. These compacts were transparent and of theoretical density, with a grain size in the range 120-300 pm. Other specimens were extruded at 250 OC in air straight from the single crystal boule, and these were transparent with a grain size of 800 pm Both types of specimen showed an enhanced extrinsic conduction, which annealed out during the conductivity run at about 400

^OC,

figure 2. To avoid this transient enhancement all

polycrystalline specimens were annealed at 600 "C after fabrication, but unfortunately the hot-pressed specimens became opaque during this anneal, and in the pure material

⁽⁽

A

⁾⁾

the grain size increased with the removal of sub-grain boundaries. The extruded specimens remained transparent and never showed subgrain boundaries so that it is difficult to account for the transient enhancement (Fig. 2) in terms of microstructural features.

Both extruded and hot-pressed specimens of mate- rial

⁽⁽

A

^)),

after annealing, showed enhanced conduc- tivity in the extrinsic region, figure 3, without any

( e x t e n d e d 1

FIG.

3 . - Conductivity of ^c(A )) polycrystals prepared by hot-pressing and by extruding.

obvious change in the intrinsic region. The curve for the extruded material rejoins that for the single crystal in region I, with no change in region It, whereas that for the hot-pressed material rejoins the single crystal curve only in region

1'.

There is no evidence for a dependence of the enhancement in region I1 upon grain size, at least for hot-pressed material in the range 120-300

pm,

although the extruded material of 800 pm grain size showed a much smaller increase in region

11. For

both materials the activation energy

o A n n e a l e d 8 7 0 ° K

in region

I1

is about 0.8 eV compared with 0.69 eV

U n a n n e a i e d

for single ~ r y ~ t n l s . Results for the doped materials,

((

B

⁾⁾

and

⁽⁽

C

^n,

show a smallcr enchancement in the extrinsic region, with a

dependence

upon grain size

12 13 1 L 1 %

1 , 0 0 0 l T I K I

in

⁽⁽ B ⁾⁾

especially

Sol-

the sma1:cr sizes. Thc 1101-

FIG, 2. - Conductivity of llo,-pressed polycrysta~line NaC]

presscd compacts showed no grain growth during thc

before and after annealing. anneal

at 600

" C , but

is

was

ir~~possiblo to cxtrudc

t h c

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C9-2 16

P.

L.

PRATT

C Single C r y s t a l

+ 15pm graln size 'c' p o l y c r y s t a l

0.8 eV, like

⁽⁽

A

)),

the association region 111 appears t o extend in

⁽⁽

C

⁾⁾

to much higher temperatures.

These results suggest that the conduction in the intrinsic region is but little affected by the presence of good grain boundaries, in general agreement with CabanC's diffusion results. The major role of these boundaries is to enhance extrinsic conduction pro- cesses although the mechanism of this enhancement is not yet clear. It is difficult to compare o u r results with those of earlier workers [lo], since they produced opaque compacts from undried powders by pressing in air a t room temperatures to only 95-97.9

"/,

of theoretical density. In these porous specimens enhanced extrinsic conductivity was found which varied inver- sely with the grain size.

I I I I I I I

I

11 1 2 1 3 1 1 1 5 1 6 1 7

1,0001T I O K - ' ~

Acknowledgments.

-

I would like to express

FIG. 4.

-

Conductivity of (( B ))and (( C )) polycrystals prepared

my thanks to Dr. M. S. Stucke for permission to

by hot-pressing.

quote his results prior to their publication elsewhere, and to the Science Research Council for the provision doped crystals successfully. While

⁽⁽

B

⁾⁾

shows an of a Research Studentship while lie was carrying out extrinsic region I1 with a n activation energy of about the work.

References

[I]

DAVIDGE,

R. W. and

PRATT, P.

L., PIrys. Stot. Sol. 6 (1964) [6]

BROWN,

N. and

JACOBS,

P. W. M., J. P11)~siclrre 34 (1973)

759. suppl. C I .

[2]

EVANS,

A. G. and

PRATT, P.

L., Pl~il. Mcig. 21 (1970) 951. [7]

KIRK,

D. L. and

PRATT, P.

L., PYOC. Brit. Ceratir. SOC. 9 [3]

ARGON,

A. S.,

NIGAM,

A. K. and

PADAWEK, G.,

Phil. (1967) 215.

Mug. 25 (1972) 1095. [S]

STUCKE,

M .

S., Ph.

D. Thesis London University, 1971.

[4]

FISCHBACH,

D. 9. and NOWICK,

A.

S., J. PIIJ~s. C I I ~ I I I . Sol. ^[9]CAB AN^, J., J. Clrittt. PIrys. 59 (1962) 1135.

2 (1957) 226. [lo]

GRAHAM,

H. C.,

TALLAN,

N. M . and

RUSSELL,

R., J. AIII.

[S]

TAYLOR, A., Ph.

D. Thesis Birmingham University, 1958. Cvroti~. Sac. 50 (1967) 156.

DISCUSSION P. W. M. JACOBS.

-

I noticed that the enhance-

ment of the intrinsic conductivity of a single crystal is greater for the crystal that had been deformed t o a smaller extent. What is the explanation of this

?

Also would you expect this effect to vary with the material

?

In similar experiments with KBr we found the conductivity to increase with the amount of deformation up to 5.5 %.

There is another interesting way of introducing dislocations into a crystal and that is by heating a suitable crystal through its phase transition tempe- rature. In experiments

(:)

on RbCIO, we found that the conductivity showed a peak after passing through the transition temperature. Also on cooling tlirough the phase transition temperature, the material became polycrystalline and then exhibited a higher conduc- tivity than the single crystal in agreement with tlie results of Professor Pratt on NaC1.

P. L. PRATT.

-

The enhancement of the intrinsic conductivity appears to depend upon whether the deformation extends to stage

1

o r stage 2 on the

work hardening curve. In stage

1

the enhancement increases with increasing deformation, but as soon as stage 2 is reached the enhancement decreases rapidly.

The explanation of this difference is not clear but since the onset of stage 2 varies with different mate- rials then tlie enhancement of the intrinsic conducti- vity would be expected to vary with the material.

It seems that i n your KBr crystals 5.5 "/, is still in stage

I .

R. J . F R I A U I . .

-

For the polycrystalline samples, there

^{I S}

a considerably enhanced conduct~vity for both the extruded and hot pressed samples. Docs thls enhanced conductivity anneal out a t li~gli tempe- ratures

?

In other words, if the conductivity is mca- sured with increasing temperature up to a temperature near the mclting point, are the same conductiv~ty results obtained on decreasing the temperature

?

P. L. PRATT.

-

The conductivity enliancemcnt is

permanent.

Although the niecl~anism and the sipni- ficance of the activation energy are not clear

i t

is possible that the activation energy includes the heat

(*I Frances E. Bates and p, W. M. ~ ~i n course ~ of publi- ~ b

of solution of some species and that cation vacancies

~ ,

cation.