5 In thermal equilibrium at temperature T, a crystal with N atoms can have a certain number n of lattice sites vacant, g

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5 In Thermal Equilibrium At Temperature T A Crystal With N Atoms Can Have A Certain Number N Of Lattice Sites Vacant G 1 (31.24 KiB) Viewed 18 times

5 In thermal equilibrium at temperature T, a crystal with N atoms can have a certain number n of lattice sites vacant, giving a structure with N + n sites in total. Obtain an expression for the number of ways, 92, in which this situation can arise by considering the different arrangements of the n vacant sites chosen from N+n possibilities. kint and that the internal energy U= ne, find an expres- Assuming that S sion for the vacancy concentration n/N by minimising the Helmholtz free energy <= 1 eV. F=U-TS. Estimate the vacancy concentration in copper at 1300K if € (In this estimation we are assuming that the volume does not change, and provided the pressure is small (atmospheric) this is not a major approximation.) Why has it been suggested that you use the Boltmann rather than the Gibbs expression for entropy when formally the latter is set up specifically for this 'canonical' case?