The applicability of thermal equilibrium as a criterion for the prediction of the distribution of vacant atomic sites in a nonisothermal crystal has been tested and found to be in error. If thermal equilibrium holds at a local position in a nonisothermal crystal, then the chemical potential of the vacancies ${\ensuremath{\mu}}_{v}$ is equal to zero, and the functional relationship for the vacancy fraction in a pure crystal is ${\overline{C}}_{v}=\mathrm{exp}(\ensuremath{-}\frac{{G}_{v}}{{k}_{B}T})$, where $T$ is the local temperature and ${G}_{v}$ is the free energy of formation of the vacancy in an isothermal crystal. This relationship has been used by various investigators studying thermomigration in metals to evaluate the thermodynamic force on a vacancy ${X}_{v}$ in making deductions about the intrinsic heats of transport for the atoms in the crystal. Consequently, if ${C}_{v}\ensuremath{\ne}{\overline{C}}_{v}$ in the nonisothermal crystal, these deductions are in error since ${X}_{v}$ contributes a term to the measured heat of transport ${Q}_{m}$. The violation of thermal equilibrium has been determined from measurements of the diffusivity of silver into pure aluminum single crystals. Enhanced vacancy fractions are found as evidenced by the reduced activation energy for diffusion of $Q=16500\ifmmode\pm\else\textpm\fi{}680$ cal/mole as compared to that of $Q=27830$ cal/mole for isothermal diffusion of silver in aluminum. The distribution which correlates the vacancy fraction in aluminum is determined and provides an explanation for the anomalous heats of transport reported for aluminum and for silver in aluminum. The vacancy fraction is given by ${C}_{v}=\mathrm{exp}(\frac{{S}_{v}}{{k}_{B}})\mathrm{exp}[\ensuremath{-}(1\ensuremath{-}\ensuremath{\gamma})\frac{{H}_{v}}{{k}_{B}{T}_{H}}]\mathrm{exp}(\ensuremath{-}\frac{\ensuremath{\gamma}{H}_{v}}{{k}_{B}T})$, where ${T}_{H}$ is the hot end temperature of a crystal in a one-dimensional gradient and $T$ is the local temperature. $\ensuremath{\gamma}$, for aluminum, is determined in this experiment to be equal to 0.353.