Elastic Reflection of Atoms from Crystals

The reflection of atoms by a crystal surface is examined by a modification of the Born collision method. The fraction of reflections in which all the normal coordinates of the crystal remain unaltered is found to be approximately $U=e^{-\frac{3{\pi }^2\left(\frac{m_A}{m_B}\right){\left(\frac{t_A}{\Theta }\right)}^2\left(\frac{t_B}{\Theta }\right)}{(1+\frac{4\pi d}{\lambda })}}.$ $m_A$, $m_B$ are the masses of the reflected atom $A$ and of the lattice atoms, respectively. The energy of atom $A$ is $k{t}_A$. The temperature of the lattice is $t_B$. $\Theta$ is the characteristic temperature of the lattice. $d$ is the distance in which the mutual repulsion between atom $A$ and lattice atoms falls to one e'th its value. $\lambda$ is the de Broglie wave-length of atom $A$. For reflection of H atoms on LiF at room temperature, $U$ is estimated to be 0.9. When $\Theta$ and $t_A$ are comparable, those normal coordinates are found to be most readily excited which have the lowest frequency.