Questions: The Kirkendall Effect and Interdiffusion

Question 1

In Kirkendall's 1947 experiment, inert molybdenum wire markers were placed at the copper-brass interface and the couple was annealed. After annealing, the markers had moved toward the brass. What does this marker motion reveal about the diffusion mechanism?

• A. Copper diffuses faster than zinc, causing the copper side to swell and push the markers toward the brass
• B. Zinc diffuses faster than copper; the brass side loses mass faster than it gains copper, causing the interface (and markers) to shift toward the brass
• C. Both species diffuse at equal rates, and the marker motion is caused by thermal expansion of the brass
• D. The markers moved because the annealing temperature caused partial melting of the brass near the interface

Answer: (B)

Zinc diffuses faster than copper in this system. The brass (zinc-rich) side loses zinc atoms faster than it receives copper atoms; the copper side gains zinc faster than it loses copper. The original interface — marked by the inert Mo wires — therefore moves toward the brass as the brass 'shrinks' and the copper 'swells.' The key insight is that if diffusion were by direct atom exchange (every A jump paired with a B jump), both sides would maintain equal flux and the markers would not move. Marker motion is direct evidence of unequal diffusivities and a vacancy-mediated mechanism.

Question 2

In a copper-zinc diffusion couple where zinc diffuses faster, Kirkendall voids form preferentially on which side, and through what mechanism?

• A. On the copper side, where copper atoms leave gaps as they diffuse toward the zinc
• B. Equally on both sides, because diffusion always creates vacancies wherever atoms move
• C. On the zinc-rich (brass) side, where the net outflow of zinc atoms creates excess vacancies that condense into voids
• D. At the center of the diffusion zone, where the two fluxes collide and interfere

Answer: (C)

Each zinc atom jump into a vacancy displaces the vacancy in the opposite direction — the net vacancy flux is directed toward the zinc-rich side (opposite to the net zinc flux). This creates an excess of vacancies on the brass side. Above a supersaturation threshold, these vacancies condense into voids — just as excess interstitials can condense into dislocation loops. The copper side, receiving more atoms than it loses, has a vacancy deficit and no void formation. This asymmetry is the direct fingerprint of the vacancy mechanism: voids always form on the faster-diffusing side.

Question 3

If two species in a diffusion couple had exactly equal intrinsic diffusivities (D_A = D_B), no Kirkendall marker displacement or void formation would be observed.

• T. True
• F. False

Answer: True

True. The Kirkendall velocity v_K = (D_A − D_B)(∂x_A/∂x) is proportional to the diffusivity difference. When D_A = D_B, the Kirkendall velocity is zero everywhere — no net vacancy flux, no marker motion, no void formation. Each A jump is exactly matched by a B jump in the opposite direction, just as the discredited atom-exchange model predicted. The Kirkendall effect is specifically a consequence of *unequal* diffusivities, which only a vacancy mechanism can produce. This is why the observation of marker motion was decisive: it proved unequal fluxes, ruling out symmetric exchange.

Question 4

Kirkendall voids form on the side of the diffusion couple where the slower-diffusing species originated.

• T. True
• F. False

Answer: False

False — voids form on the faster-diffusing side. The faster species leaves its side more rapidly than the slower species arrives to fill the vacated sites. The net vacancy flux directed into the faster-diffusing side causes local supersaturation of vacancies, which condense into voids. In the classic copper-brass couple, zinc diffuses faster than copper, so voids form on the zinc-rich brass side. This counterintuitive result — voids form where atoms are *leaving*, not where they are *arriving* — is a direct consequence of the vacancy mechanism and is the source of reliability failures in Al-Au wire bonds and Cu-Sn solder joints.

Question 5

Explain why the Kirkendall effect disproved the atom-exchange mechanism of diffusion and what it revealed about how atoms actually move in metals.

Model answer: The atom-exchange mechanism predicted that every A atom jumping to an adjacent site would be matched by a B atom jumping back — a perfect pairwise exchange. This would produce equal and opposite fluxes for both species, so no net mass transport would occur on either side of the couple, and inert markers would never move. Kirkendall's observation that the markers shifted toward the brass proved that zinc and copper were NOT moving at equal rates. One species (zinc) was crossing the interface faster than the other. The only known atomic mechanism consistent with unequal fluxes is the vacancy mechanism: atoms move by jumping into adjacent vacancies, and the rate depends on each species' jump frequency (activation energy and attempt frequency). Unequal jump rates produce a net vacancy flux and net matter flux, explaining both the marker motion and the void formation.

The Darken equations formalized this: the interdiffusion coefficient D̃ = x_A D_B + x_B D_A is a composition-weighted average of the individual intrinsic diffusivities D_A and D_B, which are generally unequal. The vacancy mechanism predicts exactly this structure. Direct atom exchange would require D_A = D_B everywhere, contradicting Kirkendall's measurements.