RING DIFFUSION IN METALS

In studying self-diffusion in copper[^1] it was found that the mechanism of exchange of two atoms of places requires much more work than the work corresponding to the observed activation energy. From this it was concluded that the mechanism of diffusion is the migration of a “hole.”

The latter mechanism, in Seitz’s opinion[^2], is confirmed by interesting experiments in which, during diffusion, motion was found of a marker at the boundary between copper and brass (70–30) toward the brass[^3]. Similar phenomena were observed in 5 other metallic systems[^4].

In the paper under review[^5] the author generalizes the exchange mechanism of diffusion and shows that such a generalization frees this mechanism from the defects that had compelled preference to be given to the mechanism of hole migration.

Schemes of ring diffusion are shown in the figure for the simplest lattices. In general, any number of atoms may be involved in a ring. The exchange mechanism considered earlier may be called a 2-ring; in the general case diffusion may occur by an \(n\)-ring. If it is required that the transition of an atom along the ring take place so that from its own site the atom moves to the nearest one, then for a face-centered lattice the 3-ring and 4-ring shown in the figure will be possible, and for a body-centered lattice only the 4-ring.

It is assumed that during motion along the ring the remaining atoms are displaced so as to reduce, as far as possible, the work of rotating the ring.

The author has calculated the activation energy required for ring diffusion. This energy is identified with the magnitude of the potential barrier that the ring must overcome in its rotation. The calculation is made taking into account the Coulomb interaction and the repulsive exchange action of the positive ions. In the calculation it was assumed that the electron density remains unchanged during rotation of the ring.

If for the 2-ring it had previously[^1] been found that the Coulomb interaction gives an activation heat of \(250\,000\ \text{cal/mol}\) (in subsequent calculations—

in the work of the same authors this figure was reduced by approximately half; then for a 4-ring this value falls to 24,000 calories if the remaining atoms are rigidly fixed, and to 8,000 calories if the 10 atoms nearest to the ring can mix.

Thus, for diffusion along a 4-ring, Coulomb repulsion is already a completely insignificant obstacle to diffusion by exchange of sites.

As for the exchange interaction, in a 4-ring it is only about \(1\frac{1}{2}\) times smaller than in a 2-ring (about 90,000 cal/mole for copper).

n-rings of diffusion: a—2-ring in a face-centered lattice; b—4-ring in a face-centered lattice; c—3-ring in a face-centered lattice; d—4-ring in a body-centered lattice.

These conclusions lead the author to the conclusion that, at least from the energetic point of view, diffusion by the exchange mechanism does not contradict experiment.

Zener points out\(^3\) that a number of factors (including the Kirkendall experiments) do not fit into Zener’s theory. At the same time, he considers the mechanism proposed by this author to be interesting and at least partially relevant to the diffusion process.

A. K.

CITED LITERATURE

1. H. B. Huntington, F. Seitz, Phys. Rev. 61, 315 (1942).
2. Acta Crystallographica 3, 355 (1950).
3. A. D. Smigelskas, E. O. Kirkendall, Trans. Am. Inst. Min. Eng. 171, 130 (1947).
4. Da Silva and Mehl, unpublished; cited in\(^3\).
5. C. Zener, Acta Crystallographica 3, 346 (1950).