Solid State Communications, Vol. 22, pp. 161163, 1977. Pergamon Press. Printed in Great Britain

SURFACE SEGREGATION AND DIFFUSION IN CALCIUM—DOPED NaC1*

L,B. Harris and N.T. litunSchool of Physics, University of New South Wales,

P.O. Box 1, Kensington, N.S.W. 2033, Australia

(Received 12 November 1976 by R.H. Silsbee)

An attempt has been made to detect near—surface diffusion in calcium—doped NaCl caused by non—equilibrium segregation of the calcium im-purity to the surface during the formation of the surface doublelayer. The effect is observable above 400°C, but below this tempera-ture appears to be inhibited by bulk precipitation.

The n~ar—surface diffusion anomaly observed diffusion, the difference in the jump frequenciesin metals is apparently due to the vacancy grad— of tracer ions into the two types of vacancy prolent produced near the surface when the latter ducing changes that do not affect the overall shapeacts as a vacancy sink (source) after the temp— of the diffusion profile. Since prolonged anneal—erature of the specimen has been changed

2. It ing leads to apparently homogeneous bghaviour,is doubtful whether such a mechanism is effective even when inhomogeneities are present , it is mrin ionic solids3, but there are other methods ofproducing a surface vacancy gradient. For ex— \ample, the electric potential between the sur— -

face and bulk of an alkali halide crystal causes Idivalent cation impurity to segregate to thesurface4, thus producing a variation in vacancyconcentration that ought, in principle, to giverise to near—surfacediffusion. The equilibrium Ispace—charge

4surface layer is, in fact, only afew tin thick , which means that its influence is /unlikely to be detected. However, the effect ofnon—equilibrium segregation, causedby impurity 5 1O~m f Ca

2moving towards the surface under the driving 0

force produced by the surface electrostatic po— ~ c 2

tential, extends further into the specimen and - x 10 m. astands a greater chance of being observed. The ~ \aim of the present work was to determine the X

effect (if any) of such surface segregation on \ \the diffusion profile. x

The isoelectric temperature below which a ~, \~calcium impurity migrates to the surface of a \NaCl crystal is of the order of 500°C for a~ - \impurity level of l0~ mole fraction (m.f.) , 5the surface excess of calcium steadily increasing ~with decrease of temperature below this value5.Diffusion measurement poses great problems be—low 300°C, so the range of investigation isestablished as between 300° and 500°C, which is -

in the extrinsic region where transport is de-termined by the charge—compensating cationvacancies introdu~c~d by the calcium impurity.At sufficient distance from the surface, local °0

charge equilibrium ensures that the concentra—tion of calcium ions equals the concentration of I 0o~ocation vacancies, whereas the excess of calcium 0 50 100ions at the surface is accompanied by a deficiencyin cation vacancies4. In an intermediate region DISTANCE x (pm)lies the zone of non—equilibrium segregation 22where a non—uniform distribution of calcium ions Fig. 1. Na diffu8ion profile at 423°C, t — 48h.and of cation vacancies is to be expected. It is Full lines rep~esrt equ. (I) withnot necessary to distinguish between free and D — 1.5 x~0~ m Is (pure) andassociated vacancies since both contribute to 5.8 x 10 m Is (doped).

Present address: Department of Metallurgy & Materials Science,

Imperial College of Science and Technology, ~‘rince Consort Road,London, SW7 2BP,

161

162 SURFACE SEGREGATIONAND DIFFUSION IN CALCIUM—DOPEDNaC1 Vol. 22, No. 3

portant that diffusion time be kept relatively by the dotted curve. The difference between ob—sho~. In the present work penetration profiles served values of activity and those obtained fromof Na tracer in NaC1 crystals containing lO~ the erfc fit to experimental points at greaterm.f. of calcium impurity were obtained in the penetration is given by the single crystal curve

temperature range 3500_5000C after a diffusion in fig. 2. This difference cannot be fitted to

time t of 48h, using normal sectioning and an exponential function of x, such as would resultcounting techniques. Diffusion took place from from an equilibrium space—charge surface layer4,a source of constantconcentratiom c, the profile but is reasonably close to an erfc plot.being fitted to the equation Reduced activity near the surface was quite

1 general for doped specimens at 423°C, as illustra~-c = c

0 erfc [x/(4Dt) .J ted by the curve shown in fig. 2 for a bicrystalAs—grown specimens with cleaved surfaces were specimen containing a 100 grain boundary normalused without pre—amneal in order to ~nsure that to the surface tra~er layer. Average calcium con—surface segregation took place during the diffu— tent was again 10 m.f., and it is seen that thesion experiment, effect of the grain boundary is to allow the re—

The effect sought was clearly observed at a duction in activity to penetrate further into thetemperature of 423°C. Fig. 1 shows penetration specimen. However, the variation with tengerature

was not straightforward. From 4000 to 500 C sur-face segregation decreased. Values of activitynear the surface at 500°C were still below those

\ expected for the erfc curve, but only to a mild\ extent, and there was no peak such as seen in

— \ fig. 1. This behaviour is consistent with that\ observe~ previously on surface segregation of

\ \~ calcium , and fits in with the idea that the elec—

~ trostatic potential responsible for the surface\ \ impurity layer decreases with increase of

~ —\ \ temperature4. The trouble with this explanation

\ \~ is that decrease of temperature below 400°C should\ ‘,~ lead to increased cal~ium at the surface, as has

\ \ in fact been observed , whereas the diffusion ex—

x \ periments apparently indicate the opposite. The— \ \~ diffusion profile at 350°C coincided almost corn—

\ ‘t,~ pletely with an erfc curve, while penetration\ \ profiles between 3500 and 400°C deviated only\ \~ slightly, in an irregular manner, from an erfc

(_) \ ~\ curve. Clearly, some intervening influence dis—\ \ rupts the regularity observed above 400°C and

— \ leads to elimination of near—surface diffusion

at lower temperatures.X X\ X It is known that calcium diffuses to the sur—

\\ face above 400°C, as evidenced by the progressive

I ~x~x-I

0 20 40

DISTANCE x (pm)x—~--—x———-

Fig. 2. Difference between expected and actual 2 — ~tracer activity as a function of pene— Xtration for single crystal (x) and bi—crystal (~) specimens at 423°C,t = 48h. Full lines represent eqn. (1). W /

z xprofiles at this temperature, from a nominally 8pure and a doped crystal under the same experi— 1 --mental conditions, that have been fitted to eqn,(1). For the pure specimen the small extra corn—poment of fast diffusion observed in the profiletail beyond 40 pm has been attributed to an in—homogeneous distribution of residual impuritywithin the bulk6. In the doped specimen thiscomponent is submerged by the larger component of 0 I ________

diffusion introduced by the extra vacancies that 0 20 40compensate for the calcium impurity, though thefact that there is experimental scatter about the DISTANCE X (pm)erfc curve shows that the distribution of vacan-cies (and of impurity) is not uniform. The most Fig. 3. Surface vacancy concentration at 423°Cstriking feature of the doped profile, however, assuming the deficiency in near—surfaceis the greatly reduced activity immediately be— activity exactly represents the deficiencyneath the surface that results in the peak shown in cation vacancies.

Vol. 22, No. 3 SURFACE SEGREGATION AND DIFFUSION IN CALCIUM—DOPED NaCl 163

surface formation of CaO on calciu~ doped NaC1 effects of such impurity migration to penetratespecimens annealed in air at 450°C . This must more deeply into the specimen (fig, 2). Note~ reconciled with the fact that diffusion of that near—surface diffusion in metals is assumed

Na is determined by the cation vacancy concen— to operate by the contrary mechanism wherebytration, If it is assumed that the decrease in vacancies drag impurities to the surface

2,measured tracer activities near the surface It has been noted that 400°C is the minimumcorresponds to a decrease in cation vacancy con— temperature needed to completely dissolve precipi—centration, then the single—crystal curve of fig. tates in calcium doped NaCl, an annealing time of2 can be re—interpreted as shown in fig. 3. The 18 h being effective at this temperature 8,continuous line in fig. 3 corresponds to the Hence, there will be second—phase nucleation sitesequation and/or precipitates within the specimen at temp-

eratures below 400°C, and if it is accepted thatc = c’ (1 + erf [x/(4Dt)~J} (2) these can drastically reduce the range over which

which is the equation that represents out—diffu— the surface is a potent influence on impuritysion at the surface, x = 0. However, the value segregation, then the change in form of the di—of D associated with this out—diffusion for the ffusion profile below 400°C becomes explicable.single ystal specimen of figs. 2 and 3 is It has been found that enhanced grain boundary5 x 10 m2/s, which is an order of magni~de diffusion of cations.is determined by the ~tatesmaller than the diffusion coefficient of Na of the impurity segregated at the boundary . Itinto the specimen. It is, therefore, reasonable is to be expected that diffusion near the sur—to associate this slow out—diffusion with vacancy face will similarly depend on the chemical statedrag by calcium impurities migrating to the sur— of the impurity in the surface layer and on pre-face, the consequence being a vacancy depletion viods thermal treatment of the specimen. Thislayer adjacent to the surface. Enhanced trans— is being investigated.port within a grain boundary would allow the

REFERENCES

1. MORTLOCK, A,J,, Trans. Met. Soc. AIME ~L 1963 (1968).2. HANNEMAN, R.E. and ANTHONY, T.R,, Acts Met, 17, 1133, (1969).3. KINGERY, W.D., J. Amer. Ceram. Soc. 57, 74, (1974),4. KLIEWER, K.L. and KOEHLER, J.S., Phys. Rev. 140, A1226, (1965).5. KUMMER, J.T. and YOUNGS, J.D., J. Phys. Chem. 67, 107, (1963).6. HARRIS, L.B. and FIASSON, .1., Phys. Status Solidi (a) 33, 697, (1976).7. YACAHAN, H. J., Phys. Status Solidi (b), 56, 429, (1973)8. NOTTIN, M,, Acta Crystallogr, A26, 636, (1970).9. HARRIS, L.B., J. Physique (to be published).