Mass transport along grain boundary pipelines in KBr

MASS

TRANSPORT

ALONG

GRAIN

L. B. HARRIS?

BOUNDARY

PIPELINES

IN KBr*

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 disMass transport is anisotropic, the location cores and do not determine a dislocation core mobility. mobility ratio parallel and perpendicular to the pipelines, ~111pi, 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 directement 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, ~111,ul, &ant de l’ordre de 102, avec ~1 apparemment Bgal It la mobilite pL1dans 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, ~111~1 ist van der Silber wandert in GroDenordung 10s. Dabei ist ,a~ etwa gleich der Beweglichkeit ,ut im Kristallgitter. 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.

factors

INTRODUCTION It is well known

along grain boundaries, sible are only

but the mechanisms

qualitatively

understood.

Turnbull

and Hoffman(l)

along the cores of grain boundary

tions,

a concept

diffusion

justified

measured

in

subsequent

observation

for

boundary

grain

orientation dislocation been

postulated

enhanced

tilt

grain

that

the

diffusion

core diffusion,

that

m&orientation

angle was only

resulted

from

use of inadequate

data.c4)

The contribution

of trace

ionic crystals

and oxides

crystals

and diffusion

with

ature

to analyse to total

work has been

For this reason it is not to allow

of mobilities

shown@) that the low-temper-

structure

of alkali

halide

crystals

if one avoids the high temperature

heat treatment required in other decoration methods.(Q) Instead, a strong electric field drives metal ions, silver,

from

structure

evaporated so that

electrodes

into

the preferential

the mass

recognized

crystals in which penetration

transport

been

along

transport aIong structural inhomogeneities is made directly visible. Since silver decoration has been observed several mm inside sub-boundaries in

mass

has

diffusion

in the class of ionic

similarly inferred from experimental data by use of the same low-angle model,c5) though it must be that

diffusion

place

constants.

can be decorated

usually

pipe

For

but it is still not

enhanced

effects in the calculation

dislocation

dislocation

rapid

takes

It has been recently

and that it

equally spaced pure edge dislocations.(l) crystals

pipes,@)

on which most experimental

for dislocation

at low

ions.

with the model of a grain boundary

defects

data by adopting the idealized low-angle model which regards a tilt boundary as a sequence of ionic

impurity

possible for the theory of ionic conductivity

of

has since

the variation

electrically

influence

it has been stated that all

done, the alkali halides.“)

mis-

matter transport is usually inferred from experimental

In

divalent

up of dislocation

structural

A

energy

of pipe diffusion

temperatures

lattice:

marked

clear under what conditions

in terms

theory

ionic

the

of self-

with

apparent

the

made

activation

but this difficulty

by showing

and

data is consistent

pipe

boundaries.‘2) varied

to

defects

disloca-

by the anisotropy

anglet3) was not explicable

resolved

respon-

For metals

diffusion

peculiar

charged

that atoms diffuse preferentially

mechanisms

will

differ from those in metals owing to the presence * Received November 4, 1970.

t School of Physics, University of New Kensington, N.S.W. 2033, Australia. ACTA METALLURGICA, VOL. 19, JULY

South 1971

of

Wales,

completely negligible, it electrodiffusion, combined obtain

quantitative

probing

grain boundary

517

into the crystal lattice is was thought that such with autoradiography to

data,

would

structure

be

suitable

in alkali

for

halides.

ACTA

578 direction

Ml4:TAI,LPIIGICA,

polished

of pull during growth

tion.

1971

on cloth moistened

Silver

crystal

Y

10.

VOL.

from

by positive

-2

by

an

surface

kilovolts

cathode,

evaporated-silver

eliminate

was injected

stabilized

K was a low-potential

(a)

wit,h water-alcohol A

anode

applied

usually

guardring

conduction

solu-

into

surrounded

in

during

the

to A.

order

to

conductivity

measurement. Electrodiffusion

-I

(b) x4

oven in which

Y

and

phase

250°C. men

tilt angle in order to check the assumptions

reached

in the low-angle

about

diffusion

absolute

factor.

information

obtained

D since, other

coefficient

p 1 D = q 1fkT, E is Boltzmann’s

of isotope ll”Ag into the specimen

was

by removing

of the crystal layers

processing contact

of

a symmetrical

nominally t,wo types

boundary

equal

to 10”.

of specimen,

2.5 x 0.3 cm,

were

cut

These are represented shows the location

including

a

4 hr

only

constant,

of blackening

along

pulled

under

q

crystals in either

from

a

dry nitrogen,

method

so as to

plane with the axis and a tilt angle

a wet-string

each

approximately

from

the

converted

was observed this grain

to a chart of

boundary

recording,

electrodiffused showed

the

by

the

line was

representing

silver, that

along

The density

a

pene-

recording,

electrodecoration

bicrystal

distinguished lattice.

owing to movement

Hence the operating

of silver into the

temperature

range was

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

to

be

available

to

thermal

diffusion

experiments.

saw(lO) 2.5 x

RESULTS

ingots.

Silver movement

by b and c of Fig. 1 in which a

of coordinate

further

process proceeded slowly at 15O”C, whilst above 300°C the dislocation structure was not clearly

direction Using

no

line, not into the lattice.

experiments

split-seed

along a (100)

until

grain boundary

in ionic

bromide, stock

removed

in photographic

Penetration

Experiment

of potassium

were

density.

EXPERIMENTAL

contain

set intervals,

in order to reduce random variations

ionic crystals or metals.

of rotation

at frequent

of the freshly exposed surface.

are related

microphotometer.

to diffusion

the

and,

autoradiograms,

can be measured at much lower relative temperatures

by

layers from the anode sur-

period between emulsion and crystal surface,

than are accessible

were prepared

electrometer.

where T is

carrier and f is a corre-

mobilities

grade

being

subsequent by

tration

Bicrystals

the

monitored

preparing an autogram

carrier is often

these two quantities

melt of analytical

temperature,

the specimen

Successive

but

Further,

up to

radioactive blackening of the emulsion was obtained. A standard schedule was used in the preparation and

is the charge on a migrating lation

through

field

to its diffusion

temperature,

flushed

for operation

than

data rather

,u of a charged

being equal,

was slowly

mobility

data,

by the IEinstein relation

sensor

silicon-controlled

The use of an electric

one obtains

the mobility

applicable things

model.

steady

Penetration

implicit

a

was designed

through

determined face

through

nitrogen

which

vibrating-capacitor

have been confined to a moderate

Initial investigations

thermal

was stabilized

The electric field was applied after the speci-

current 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.

control

Dry

the oven,

that

temperature

to better than 1°C by means of a thermistor rectifier.

means

was carried out in a small shielded

specimen

axes inside the ingot,

AND

to be strongly anisotropic. of 5 kV held

DISCUSSION

along tilt boundaries

was found

With a potential difference

for 24 hr across

a specimen

0.35 cm

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

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,

that pipeline

no silver penetration was recorded in either the grain boundary or the crystal lattice. In fact, traces of

direction

coincided

with field direction.

Electrodes were small silver circles, approximate area 0.5 cm2, vacuum-evaporated onto surfaces

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, A consequence of this large anisotropy is PI. 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 airquenching 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 pipelines of tilt grain boundary.

travelling downwards in 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 autoradiographic 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

between the tilted latt,ices. times

be located

on

poor registration

Such points could some-

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,

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 temperaturedo 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

VOL.

19,

1971

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 : determination 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 oorresponding to a just discernible blackening of the audiogram 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 ,ullbut 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 therefore 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

‘, Extrapolated \

lo-lo

1, 14

\

\

\

I 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~tui’fb (“C) ___225 210 200 190 180 I70

‘-I, (cm) 1.78 x 10-l 1.41 1.42 1.27 1.14 0.76

fk9 (cm2 V-l see-‘) 7.0 x lo-” 5.55 5.6 5.0 4.4 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 trendselective penetration of silver into a particular region

ALONG

GRAIN

BOUSDARY

PIPELINES

581

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~~rerange. 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 ,uaof 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,, 1p,_ 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.

ACTA

582

NETALLCRGICA,

VOL.

The present

work has described

mass transport

structure-sensitive. diffusion

is usually analyzed

isotropic.

of grain and

to be aware that

is possible, since grain boundary in terms of theoriePJ7)

which assume a grain boundary and

a form

that is both anisotropic

It is important

this type of behavior

The

present

to be both uniform

work

also

shows

that

anisotropy

in mass transport is not necessarily directly

associated

with migration

cores.

Dislocation

grain boundary of additional excluded.

down individual

cores

are invoked

example,

it

curvature

of a grain boundary

diffusion

ratme,

centration

dislocation to

interpret

diffusion in metals, but the possibility structure-sensitive

For

and

dependence

also

factors has

must not be

been

noted

that

in metal enhances

that

the

of impurity

low-level

the con-

diffusion occurs at

progressively

lower levels for smaller tilt angles,(18) a

fact

explicable

readily

if the

197

I

REFERENCES

CONCLUSION

boundary

19,

impurity

diffuses

in

localized regions of higher than average concentration.

1. I). TURNBULL~~~R. E. HOFFMAN, A&M&.2,419 (1954). 2. R. E. HOFFMAN. Acta Met. 4. 97 (19561. 3. W. R. UPTRE&IVE and M.-i. S&NO&, Trans. Am. Sot. Metals 50, 1031 (1958). 4. R. F. CANON and J. P. STARK, J. appl. Phys. 40, 4361 (19691. 5. k. L. ‘MODIENTand R. B. GORDON,.J. appl. Phys. 35,2489 (19641. 6. G. B. GIBBS and J. E. HARRIS, Interjaces, Proceeding8 of International Conference, Melbourne, Aumsust, 1969, p. 53. _ Butterworths (1969). 7. K. R. R~aos and RI. WCTTIG, J. appl. Phys. 40, 4682 I19691. 8. L. B. HARRIS, AppZ. Phys. Lett. 13,154 (1968). 9. S. AMELINCKX. Acta Met. 6. 34 (1958). 10. L. B. HARRIS,‘J. Phys. (SC& In&um~) 2, 432 (1969). 11. L. B. HARRIS, J. appl. Phys. 41, 1883 (1970). 12. A. D. LECLAIRE, Br. J. uppl. Phys. 14, 351 (1963). 13. G. KCMBARTZKI and K. TROMMEN, X5. Phys. 184, 355 (1965). 14. L. B. HARRIS, J. R. HANSCOMB and J. L. SCHLEDERER, Phys. Lett. 32A, 163 (1970). 15. B. J. WUE~SCH and T. VASILOS, J. Am. G’emm. Sot. 49, 433 (1966). 16. J. C. FISHER, J. a&. Phvs. 22. 74 (1951). 17. R. T. P. WmPPLi,APhiZ. kag. 45, li25 (i954). 18. A. E. AVSTIN and N. A. RICHARD, J. appl. Phys. 32, 1462 (1961). \----I

\----I.