The Kramers-Langevin stochastic equation governing desorption is derived microscopically in the case where the adatom is coupled to the lattice vibrations of the solid substrate, and in the limit where the adatom mass is much larger than the atomic mass of the substrate. The systematic potential $V_{\mathrm{eff}}$ and the friction coefficient $\eta$ are calculated, with the help of a local harmonic approximation, in terms of the microscopic binding potential $V$ and of the local static surface compressibility $\chi$ of the isolated substrate. $\eta$ is found to be position dependent. It is shown that, for a given chemisorption potential $V$, two regimes may occur, depending on the value of $\chi$. For "hard" substrates, the Kramers equation holds, but $\eta$ may have significant space variations. For "soft" substrates, a dynamic instability of the local deformation of the substrate around the adatom appears at a particular value of the adatom position. This effect exhibits an intrinsic hysteresis and induces a large energy loss. It leads, in spite of the large value of the mass ratio, to the breakdown of the Kramers approximation.

• Received 17 December 1976

DOI:https://doi.org/10.1103/PhysRevB.18.545