 Solution

ID: past-exam-of-the-materials-science-course-of-the-university-of-cambridge/2022/paper-1/2/b/iii/solution

D = D_{0} e^{- Q / (k_{B} T)}

. Eliminating the prefactor with two temperatures gives

Q = \frac{k _{B} l n ( D _{600} / D _{300} )}{1/ T _{300} - 1/ T _{600}} ⟹ Q = 0.795 eV = 76.7 kJ mo l^{- 1} .

573.15

and

873.15 K

. Because the input is a vacancy diffusion coefficient, this is a migration activation energy inferred from that diffusivity; an additional vacancy-formation energy should not automatically be added.

 New to topics? Read the docs here!