Low-qPhonons and the Widths of Low-Energy Electron-Differaction Peaks

Low-$q$ phonons cause local distortions of the crystal lattice which cause the gaps in the electronic band structure to wobble up and down. This results in a broadening of the peaks in low-energy electron diffraction which otherwise would be much narrower than observed, according to recent calculations. The effect varies with temperature and energy as $T^{\frac{1}{2}}{E}^{\frac{3}{4}}$ in rough agreement with experiment.