Equilibrium Concentration of Impurities on the Surface of a Crystal

The equilibrium concentration of impurities on the surface of a solid is examined. Weakly bound impurity atoms concentrate at the surface in preference to the bulk, while strongly bound impurity atoms dilute at the surface relative to the bulk. Calculations are made explicitly for neon and krypton atoms on the argon (100) surface. At $\frac{{\mathrm{T}}_m}{3}$ (28°K), where ${\mathrm{T}}_m$ is the melting temperature, the (100) surface neon concentration is ${10}^4$ higher than the bulk concentration, and the krypton concentration is 2×${10}^{-3\mathrm{}}$ smaller than in the bulk. At low temperatures the surface impurities cannot equilibrate with the bulk in a reasonably short period of time. However, at $\frac{T_m}{3}$, the surface neon concentration can exceed the bulk concentration by a factor of 10 within about a week; the time required is 10 min at $\frac{1}{2}{T}_m$. The concentration of impurity atoms at the surface may play an important role in determining the properties of the surface.