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D = Γα²/6 applies to any diffusing species in any cubic lattice. Show that this is true for vacancy diffusion in a pure FCC metal. (hint: consider two adjacent {111} planes and determine what fraction of all possible jumps result in the transfer of a vacancy between the two planes. Is the same result obtained by considering adjacent {100} planes?

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Answer:

The explanation is shown below

Explanation:

The equation is by a three dimensional analysis. This yields the equation:

[tex]D = \frac{1}{6} \lamba ^{2}T[/tex]

In cubic lattices, the jump distance is a fraction of the lattice constant represented as:

[tex]\lamba = fa_{O}[/tex]

the total jump frequency is given by:

[tex]R = \beta W[/tex]

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