Mass transport along grain boundary pipelines in KBr

MASS TRANSPORT ALONG GRAIN BOUNDARY PIPELINES IN KBr*

L. B. HARRIS? and J. L. SCHLEDERER?

Dislocation electrodecoration with silver at temperatures near 200°C provides direct evidence for the existence of pipelines in tilt grain boundaries in KBr, but the pipelines do not correlate with dislocation cores and do not determine a dislocation core mobility. Mass transport is anisotropic, the mobility ratio parallel and perpendicular to the pipelines, ~11 1 pi, being of the order of 102, with ~1 being approximately equal to the mobility pt in the crystal lattice. Silver penetrates irregularly in the pipeline direction at different parts of a boundary, apparently as a result of 2 factors: intrinsic variations in the physical substructure of the boundary, and the precipitation of divalent impurity at the boundary.

TRANSPORT DE MASSE LE LONG DES PIPELINES DE JOINTS DE GRAINS

L’electrodecoration des dislocations aveo de l’argent a des temperatures voisines de 200°C met directe- ment en evidence l’existence de pipelines dans les joints de grains de torsion dans KBr, mais ces pipelines ne sont pas en correlation aveo les noeuds de dislocations et ne determinent pas une mobilite de ceux-ci. Le transport de masse est anisotrope, le rapport de mobilite parallelement et perpendiculairement aux pipelines, ~11 1 ,ul, &ant de l’ordre de 102, avec ~1 apparemment Bgal It la mobilite pL1 dans le reseau du cristal. L’argent penetre irr&ulierement dans la direction des pipelines aux differentes parties d’un joint, ceci Btant apparemment dn a deux facteurs: les variations intrinseques dans la sous-structure physique du joint, et la precipitation au joint d’impurete bivalente.

MASSETRANSPORT ENTLANG KORNGRENZEN-PIPELINES IN KBr

Elektrodekoration van Versetzungen mit Silber bei etwa 200°C gibt direkte Hinweise auf die Existenz van Pipelines in Kippkorngrenzen in KBr; die Pipelines sind jedoch nicht mit den Versetzungskernen korreliert und sie bestimmen nicht eine Beweglichkeit im Versetzungskern. Der Massetransport ist anisotrop. Das Verhaltnis der Beweglichkeiten parallel und senkrecht zur Pipeline, ~11 1~1 ist van der GroDenordung 10s. Dabei ist ,a~ etwa gleich der Beweglichkeit ,ut im Kristallgitter. Silber wandert in verschiedenen Teilen der Korngrenze in der Pipeline-Richtung unterschiedlich weit. Dieses Verhaltnis ist anscheinend von zwei Faktoren beeinflu0t: gittereigene Anderungen der physikalischen Substruktur der Korngrenze und Ausscheidungen zweiwertiger Verunreinigungen an den Korngrenzen.

INTRODUCTION

It is well known that atoms diffuse preferentially

along grain boundaries, but the mechanisms respon-

sible are only qualitatively understood. For metals

Turnbull and Hoffman(l) postulated enhanced pipe

diffusion along the cores of grain boundary disloca-

tions, a concept justified by the anisotropy of self-

diffusion measured in tilt grain boundaries.‘2) A

subsequent observation that the activation energy

for grain boundary diffusion varied with mis-

orientation anglet3) was not explicable in terms of

dislocation core diffusion, but this difficulty has since

been resolved by showing that the variation with

m&orientation angle was only apparent and that it

resulted from use of inadequate theory to analyse

data.c4) The contribution of pipe diffusion to total

matter transport is usually inferred from experimental

data by adopting the idealized low-angle model

which regards a tilt boundary as a sequence of

equally spaced pure edge dislocations.(l)

In ionic crystals rapid pipe diffusion has been

similarly inferred from experimental data by use of

the same low-angle model,c5) though it must be

recognized that mass transport mechanisms will

differ from those in metals owing to the presence of

It has been recently shown@) that the low-temper-

ature dislocation structure of alkali halide crystals

can be decorated if one avoids the high temperature

heat treatment required in other decoration methods.(Q)

Instead, a strong electric field drives metal ions,

usually silver, from evaporated electrodes into the

dislocation structure so that the preferential mass

transport aIong structural inhomogeneities is made

directly visible. Since silver decoration has been observed several mm inside sub-boundaries in

crystals in which penetration into the crystal lattice is

completely negligible, it was thought that such

electrodiffusion, combined with autoradiography to

obtain quantitative data, would be suitable for

probing grain boundary structure in alkali halides.

* Received November 4, 1970. t School of Physics, University of New South Wales,

Kensington, N.S.W. 2033, Australia. ACTA METALLURGICA, VOL. 19, JULY 1971 517

factors peculiar to the ionic lattice: electrically

charged defects and the marked influence at low

temperatures of trace divalent impurity ions. For

ionic crystals and oxides it has been stated that all

data is consistent with the model of a grain boundary

made up of dislocation pipes,@) but it is still not

clear under what conditions enhanced diffusion along

structural defects takes place in the class of ionic

crystals on which most experimental work has been

done, the alkali halides.“) For this reason it is not

possible for the theory of ionic conductivity to allow

for dislocation effects in the calculation of mobilities

and diffusion constants.

578 ACTA Ml4:TAI,LPIIGICA, VOL. 10. 1971

direction of pull during growth

Y

(a) -2

-I Y

(b) x4

FIG. 1. (a) As-grown boundary with dislocations along z-axis. (b) Specimens wibh dislocation length perpendicular to applied field. (c) Specimens with dislocation

length parallel to applied field.

Initial investigations have been confined to a moderate

tilt angle in order to check the assumptions implicit

in the low-angle model. The use of an electric field

means that one obtains mobility data rather than

thermal diffusion data, but information obtained

about the mobility ,u of a charged carrier is often

applicable to its diffusion coefficient D since, other

things being equal, these two quantities are related

by the IEinstein relation p 1 D = q 1 fkT, where T is

absolute temperature, E is Boltzmann’s constant, q

is the charge on a migrating carrier and f is a corre-

lation factor. Further, mobilities in ionic crystals

can be measured at much lower relative temperatures

than are accessible to diffusion experiments in either

ionic crystals or metals.

EXPERIMENTAL

Bicrystals of potassium bromide, pulled from a

melt of analytical grade stock under dry nitrogen,

were prepared by the split-seed method so as to

contain a symmetrical boundary plane with the axis

of rotation along a (100) direction and a tilt angle

nominally equal to 10”. Using a wet-string saw(lO)

t,wo types of specimen, each approximately 2.5 x

2.5 x 0.3 cm, were cut from the bicrystal ingots.

These are represented by b and c of Fig. 1 in which a

shows the location of coordinate axes inside the ingot,

the x-axis pointing along the dislocation pipelines of

the as-grown boundary. Specimens b had pipelines

running transverse to the electric field applied by the

electrodes A and K, whilst specimens c were cut so

that pipeline direction coincided with field direction.

Electrodes were small silver circles, approximate

area 0.5 cm2, vacuum-evaporated onto surfaces

polished on cloth moistened wit,h water-alcohol solu-

tion. Silver from anode A was injected into the

crystal by positive stabilized kilovolts applied to A.

K was a low-potential cathode, usually surrounded

by an evaporated-silver guardring in order to

eliminate surface conduction during conductivity

measurement.

Electrodiffusion was carried out in a small shielded

oven in which specimen temperature was stabilized

to better than 1°C by means of a thermistor sensor

and phase control through a silicon-controlled

rectifier. Dry nitrogen was slowly flushed through

the oven, which was designed for operation up to

250°C. The electric field was applied after the speci-

men reached steady temperature, the subsequent

current through the specimen being monitored by

vibrating-capacitor electrometer.

Penetration of isotope ll”Ag into the specimen was

determined by removing layers from the anode sur-

face of the crystal and, at frequent set intervals,

preparing an autogram of the freshly exposed surface.

Successive layers were removed until no further

radioactive blackening of the emulsion was obtained.

A standard schedule was used in the preparation and

processing of autoradiograms, including a 4 hr

contact period between emulsion and crystal surface,

in order to reduce random variations in photographic

density. Penetration was observed only along the

grain boundary line, not into the lattice. The density

of blackening along this grain boundary line was

converted to a chart recording, representing pene-

tration of electrodiffused silver, by a recording,

microphotometer.

Experiment showed that the electrodecoration

process proceeded slowly at 15O”C, whilst above

300°C the dislocation structure was not clearly

distinguished owing to movement of silver into the

lattice. Hence the operating temperature range was

chosen to be around 2OO”C, which is below the range

expected to be available to thermal diffusion

experiments.

RESULTS AND DISCUSSION

Silver movement along tilt boundaries was found

to be strongly anisotropic. With a potential difference

of 5 kV held for 24 hr across a specimen 0.35 cm

thick, radioactive silver was readily detected in

samples cut as in Fig. l(c) at penetrations of 0.1 cm,

whilst for specimens cut as in Fig. l(b), with the

dislocation pipelines transverse to the field direction,

no silver penetration was recorded in either the grain

boundary or the crystal lattice. In fact, traces of

silver could be observed optically in the transverse

HARRIS ANL> SCHLEDEKEK: MASS TRASSPORT SLOKG GRAIN BOUSDSRY PIPELINES 579

pipelines at penetrations of 25 ,D but could not be distinguished from background by autoradiography. This means that the mobility in the grain boundary parallel to the dislocation lines, pii, is close to 2 orders of magnitude larger than the mobility in the grain boundary perpendicular to the dislocation lines,

PI. A consequence of this large anisotropy is illu&rated in Fig. 2 which shows a grain boundary, on the anode surface outside the electrode region, whose pipelines were as in Fig. 1 (b). The white diffuseness is

silver decorat,ion which has been carried by grain boundary conduction parallel to the surface along pipelines t,ransverse to the direction of the applied field. This represents extensive mass transport induced by a small component of edge-effect field, whilst the much larger applied field perpendicular to the pipelines produced no measurable penetrat,ion into t,he boundary.

FIG. 2. Line of silver in grain boundary of type b (Fig. 1) on surface outside electrode. The silver has electrodiffused from anode electrode (beyond right edge of

print) along pipelines parallel to surface, 150°C.

The decorated structure obtained when the field is parallel to the dislocations is shown in Fig. 3, which unequivocally confirms that a tilt grain boundary consists of a large number of parallel pipelines. To observe this structure at high magnification (and short focal length) the crystal was deliberately split at the boundary- by thermal shock produced by air- quenching from 200°C. The surface of a cracked half-crystal only partially reproduces the original boundary structure, but one feature clearly established was that the silver pipelines were formed of discrete particles which decreased in numbers in passing from the anode to the cathode. These particles appeared to be spherical, as shown in Fig. 4, and relatively large compared with the radius of a disIooation or the width of a grain boundary.

On the basis of the low-angle model, a symmetrical 10” tilt boundary is made up of edge dislocations lying along a ilOO? tilt axis with a regular spacing of

Frc. 3. Silver electrodecoration travelling downwards in pipelines of tilt grain boundary. 225”C, 24 hr at 6 kV/am.

approximately 6 times the lattice parameter. The simple pipe diffusion model assumes that each dislocation core contributes equally to overall mass transport,. The spacing between visibly decoratted pipelines, as in Fig. 4, was Borne 100 times larger than this, which means that silver is not transported equally along all boundary dislocations and that the simple model is not operative. Actual behavior, in fact, turns out to be further complicated by a large scale irregularity of conduction over and above that responsible for the pipeline structure of Figs. 3 and 4. From microdensitometer profiles of the autoradio- graphic density along the length of a grain boundary, examples of which are given in Fig. 5, adjacent sections of the grain boundary were found to vary considerably in the extent to which they would admit migrating silver ions. Such large scale irregularity was common to the whole temperature range 150-230°C.

Two factors can be linked with irregular conduction in the pipeline direction. The first is the existence at

the boundary of points of apparently poor registration

between the tilted latt,ices. Such points could some-

times be located on an as-grown boundary a$ a

FIG. 4. Larger magnification of decorated pipelines in Fig. 3 as seen on one half of cracked grain boundary plane. Caution: variations in size of decoration particles are

produced by out-of-focus and diffraction affects.

580 ACTA METALLURGICA, VOL. 19, 1971

123456 0 istance along boundary (mm)

FIG. 5. Profiles of silver density along grain boundary (meeaured as photographic density) for different temperatures and different depths below anode surface. Profiles were obtained from microdenaitometer scans on autoradiograms, and all have same vertical sensitivity. Profiles at same temperature do rxx? have same vertical

scale zero.

segment, of distinct boundary curvature in the y-z plane (Fig. 1 ), silver decoration being strong in the curved segment and relatively sparse elsewhere. By contrast, high quality boundaries-characterized as being difficult to etch and difficult to observe optically but which appeared quite straight in the y-x plane under a low-power microscope-appeared to contain a fine veil of silver spread uniformly along the entire length of the boundary covered by the anode. Closer

examination showed, however, that silver penetration was more pronounced wherever there were slight corrugations or small deviations in the boundary, This correlation between structure and penetration was always found to exist at temperatures below 200°C but above 200°C the connection became less definite. Curvature of the grain boundary requires, in the simplest case, extra edge dislocations with Burgers vectors different from those in a straight boundary, so that possibilities for misfit are increased. The behavior typified in Figs. 3 and 5 may be understood if a boundary is regarded as a chain of high quality segments, each segment being a narrow semi-coherent plane of strong bonding containing regularly spaced

dislocations as in the idealized model, linked together by sections of open or incoherent structure. Grain boundary conduction, operating primarily in the misfit regions of the boundary, will be intrinsically structure-sensitive. There will be no possibility of obtaining a ~sIocation core mobility, since any measured mobility wiI1 be only slightly influenced by movement along the regularly spaced dislocations. This model allows for the development of relatively large silver aggregates in the pipelines, apparently by neutralization of vacancies since it was found that the conductivity of all specimens containing grain boundaries monotonically deereased. This decrease in conductivity was observed even for those specimens where subsequent microscope observation showed that silver decoration had travelled right through the grain boundary to the cathode. Thus there is no evidence for intensification of the local electric field in the boundary, which would be accompanied by increasing conductivity and early breakdown of the crystal.

The existence of a second factor became apparent during measurements of the mobility of the electrodiffused silver. There are various experimental methods for obtaining mass transport data in grain boundaries,(12) but only one was suited to quantitative autoradiography on the present crystals : determi- nation of penetration depth d. Measurement of the angle $ made by concentration contours at the boundary was possible in principle, but in practice 4 was too small to be useful. Penetration depth, however, varied greatly in magnitude at different parts of the boundary, and so it was decided to measure the peak penetration depth a!,, taken as the value oorre- sponding to a just discernible blackening of the audio- gram emulsion along part of the bounda_ry line. Knowing the applied field and the time of application one can calculate the corresponding mobility ,uzr, defined as the corresponding velocity per unit field, The average penetration depth, which gives the more meaningful average mobility ,ull but which is less easy to obtain, need not be measured if the irregular penetration retains its character over the range of temperatures used so that peak penetration remains proportional to average penetration, and ,us is there- fore proportional to p,,. Under these circumstances a plot of p,T against l/T will give a straight line whose slope determines the activation enthalpy for mobility of silver in KBr grain boundaries.

Peak penetration d, was measured on a number of samples after the same standard treatment: applied voltage 5 kli, specimen thickness 0.31 cm, electrodiffusion time 45 hr, deposited silver layers of the

HARRIS ANI, SCHLEDEKER: MASS TRANSPORT ALONG GRAIN BOUSDARY PIPELINES 581

‘, Extrapolated \

\ \

\

lo-lo 1 ,

\ \ \ \ \ I

14 2-O 22

1O’iT ( “K j’

Fro. 6. Temperature dependence of grain boundary mobilit,y ,I,, compared in magnitude and slope with that

of lattice mohilit,y pr.

TABI.E 1. Peak penetration d, in pipeline dire&ion after 16,000 V/cm applied for 45 hr, and corresponding mobility p, _-.. I-

Tempera~t ui’fb ‘-I, fk9 (“C) (cm) (cm2 V-l see-‘)

___-

225 1.78 x 10-l 7.0 x lo-” 210 1.41 5.55 200 1.42 5.6 190 1.27 5.0 180 1.14 4.4 I70 0.76 3.0

same specific activity and constant processing conditions for the autoradiograms, each experiment being repeated on a different sample t,o check reproduoibility. Values of CE, and p, at, several ten~peratures are given in Table 1. The corresponding plot of ,upT against l/T at the top of Fig. 6 has a systematic curvature, which shows t.hat no activation enthalpy can be obtained. The reason for this curvature must be that the structure-sensitive nature of the grain boundary conduction varies systematically with temperature, a conclusion supported by the shapes of the curves seen in Fig. 5. These show that silver is impelled strongly into 3 separate sectors of the boundary at 225”C, less st’rongly into 2 major regions at 21O”C, whilst, at 19O’C the profiles peak over a single short section. This was a general systematic trend- selective penetration of silver into a particular region

at lower temperatures, more extensive but irregular penetration at higher tem~ratures-and it must

result from some factor other than the intrinsic dislocation structure of the boundary, which is quite unaffected by low temperature activation. The most likely cause is precipit.ation of divalent impurity, since this is a process which is not only active at these temperatures(13) but which is also capable of changing the boundary structure. Such impurity tends to segregate to low energy sites near the boundary, resulting in local preferential nucleation and the formation of misfit interfaces between matrix and precipit~ate. It may be that divalent impurity is directly responsible for the open pipelines of high mobility (Fig. 3), but in any case the environment of migrating ions near precipitates will change markedly over the experime~ltal ~~mperat~~re range. There will also be a continuous change in the concentration of charge-carrying vacancies as impurity ions transform into an electrically neutral phase, and vice versa. Since silver ions almost certainly move by a cation vacancy process, this accounts for the more general spread of silver into the boundary at higher temperatures.

Experimental values of Iattice mobility ,ua of silver in KBr single crystals are available;(14) they give the straight line shown in Fig. 6. To first order this line may be extrapolated (dashed line) to lower temperatures, where it is seen that values of grain boundary mobility in the pipeline direction, assuming ,u~ w p,,, is some 2 orders of magnitude larger than lattice mobility ,uE. This means that the enhancement factor for grain boundary mobility over that in the Iattice is much less than the value of 106 observed. for diffusion in metals, a fact similarly noted for grain boundary diffusion promoted by segregated impurity in IWg0.(15) It was shown earlier that the ratio p,, 1 p,_ is approximately 2 orders of magnitude, so it is reasonable to conclude that pui is not greatsly different from pr.

The activation enthafpy for latt,ice mobility pl, derived from the straight line of Fig. 6, is 0.67 eV, which is the same value as tha.t for cation vacancy mobilit,y. In the present experiments the average penetration depth will vary more rapidly with temperature than peak penetration d,, and hence a graph of~~~!Z’ against l/T could become a st,raight line over a limited telnperature range. Preparations are under way to measure the average penetration, using the sectioning method in conjunction with counting techniques, to determine whether this is so, and if so, to check whether the activation enthalpy for pipeline mobility SO obtained is related to that for vacancy mobility.

582 ACTA NETALLCRGICA, VOL. 19, 197 I

CONCLUSION

The present work has described a form of grain

boundary mass transport that is both anisotropic and

structure-sensitive. It is important to be aware that

this type of behavior is possible, since grain boundary

diffusion is usually analyzed in terms of theoriePJ7)

which assume a grain boundary to be both uniform

and isotropic. The present work also shows that

anisotropy in mass transport is not necessarily directly

associated with migration down individual dislocation

cores. Dislocation cores are invoked to interpret

grain boundary diffusion in metals, but the possibility

of additional structure-sensitive factors must not be

excluded. For example, it has been noted that

curvature of a grain boundary in metal enhances the

diffusion ratme, and also that the low-level con-

centration dependence of impurity diffusion occurs at

progressively lower levels for smaller tilt angles,(18) a

fact readily explicable if the impurity diffuses in

localized regions of higher than average concentration.

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_

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Mass transport along grain boundary pipelines in KBr