LETTERS TO THE EDlTOR 651

FIG. 1. Specimen ofKC1 doped with AgNO, after X-irradia. tion (6 hr) and anneal in air. Note the decoration of dis- locations and the random precipitation ( x250). Inset:

enlarged view of random precipitates ( x 900).

follows. Suppose that a vacancy cluster captures a few gas molecules; the gas will then exert a pressure on the walls of the small cavity. This pressure will cause an elastic interaction with other vacancies in the neighbourhood, which will migrate towards it, and enIa,rge it, and so relieve the pressure.

I wish to thank Prof. W. Dekcyser for his con- tinuous interest and for helpful discussions. This work is part of a research programme supported by I.R.S.I.A. (Institut pour l’encouragement de la Recherche Scientifique dans 1’Industrie et l”Agricul- ture; Corn% d’etude de 1’Etat Solide).

S. AMELINCKX

Laboratorium Boor Iiristalkunde

Bozier 6, CAM,

Belgium

References 1. A. BOX,TAX, Aeta Met. 6, 721 (1958). 2. P. B. ~IRsCXi and J. SILCOX, in Growth and Perfection..c?f

Crysta1.c edited by Doremus, Roberts and Turnbull, p. 262. Wiley, New York (1958).

3. S. AMELINCK~, PAW. Mug. 3. 653 (1958). 4. E. AERTS, S. AMELINCKX and W. DEKEYSER, _4ctn Met. 7,

29 (1959).

Temperature gradient grainrboundary migration*

Grain boundaries have been observed to migrate in a temperature gradient towards higher tempera- tures.(2*2) This phenomenon can be explained by a mechanism similar to temperature gradient zone melting,(3) if one assumes that the grain bomdary has a finite thickness and behaves as a distinct phase. This assumption seems to be supported by the recent work of Cahn and Hilliard(4), and Inman and Tiplercs).

In order that temperature gradient zone melting may take place in a given system, certain conditions have to be fulfilled. The same condit#ions can be applied to the temperature gradient migration of a solid phase in a two phase system of appropriate geometry. These conditions are as follows:

(a) the eq~librium eon~entration of solute must be different in the two phases, at a given temperature,

(b) the equilibrium concentration of solute in one or both phases should vary with temperature,

(c) the rate of diffusion of solute in one of the phases must be substantially higher than in the other.

If we accept that for a given concentration in the bulk material the grain boundary concentration is * Received February 28, 1959.

652 ACTA METALLURGICA, VOL. 7, 1959

a function of temperature,(6) a grain boundary becomes

essentially a thin slab of “second phase” in the bulk

material. The temperature dependence of the grain

boundary concentration can be approximately

described by an equation of the form:

Cpb = AC exp (QlRT) (1)

where C,, = concentration in the grain boundary

C = concentration in the bulk

Q = difference between elastic distortion

energy due to the presence of a solute

atom in the lattice and in the grain

boundary.

R = gas constant

T = absolute temperature

A = constant

Although Q varies from one system to another, it is

always a positive quantity, and the grain boundary

concentration is always a decreasing function of

temperature.

Grain boundary migration, regardless of the nature

of the driving force, must be accompanied by mass

transfer across the grain boundary. Under approp-

riate driving forces, the rate of grain boundary

migration can be substantially higher than the rate

of self-diffusion or the rate of diffusion of most solutes

in the bulk material. It is, therefore, reasonable to

assume that the diffusion rate across grain boundaries

is substantially higher than in the bulk material.

Thus, a grain boundary fulfills all the necessary con-

ditions for temperature gradient migration with

respect to the adjacent crystals.

Let us consider a system consisting of two crystals

separated by a large angle grain boundary. In this

system, let A designate the solvent or main con-

stituent, and B all the solutes or impurities.

Let us assume that for a given concentration of

B in the bulk material, the grain boundary has

reached a concentration in B corresponding to a

temperature Tl. This concentration exceeds the

concentration in the bulk, as shown by equation (1).

Let us now impose on the system a temperature

gradient in a direction normal to the plane of the

grain boundary; which gives a temperature difference

across the grain boundary T, - T, with T, > T,

> Tl. Under these conditions the concentration of

the grain boundary in B will tend to decrease and

adjust to the value corresponding to equilibrium

between bulk and grain boundary at T, for one side,

and T, for the other side. When steady state is

reached, a concentration gradient will be established

across the grain boundary, the lower concentration

corresponding to the hotter side. B will, therefore,

diffuse toward the hotter side, where it will “dissolve”

A from the bulk. Simultaneously A will flow toward

the colder side, where it will be “rejected” into the

bulk. Mass transfer can thus be obtained across the

grain boundary, which will migrate as a result of this

process.

The above considerations, of course, implicitly

assume that the only driving force for migration to

which the grain boundary is subject is due to the

temperature gradient. In other words, under iso-

thermal conditions the grain boundary would remain

stationary.

C. ELBAUM

Division of Engineering and

Applied Physics

Harvard University, Cambridge, Mass.

References

1. H. SUZUKI, J. Phys. Sm. Japan 6, 522 (1951). 2. M. ROBERT, A. ROBILLIARD, and I’. LACOMBE; C. R. Acad.

Sci.. Paris 240. 1089 (19551. 3. W. ‘G. PFANN, Trans’. A&r. Inst. Min. (Metall.) Engrs.

203, 961 (1955). 4. J. W. CAHN, and J. E. HILLIARD, J. Chem. Phys. 28, 258

(1958). 5. k C: INMAN and H. R. TIPLER, Actn Met. 6, 73 (1958). 6. D. MCLEAN, Grain Boudaries in Metals, p. 116-120.

Clarendon Press, Oxford (1957).

* Received March 5, 1959.