Using Hume$-$Rothery's rules predict the relative degree of solid solubility $($very low to very high$)$ of aluminum, copper, chromium, magnesium, and zinc in nickel.

Calculate the equilibrium concentration of vacancies per cubic meter in pure silver at $700C.$ Assume the energy of formation of a vacancy in pure silver is $1\mathrm{.}10eV.$ What is the vacancy fraction at $900C?$