Roughening transition of high-index crystal faces: the case of copper

The thermal variation of atomic beam diffraction intensities on (1, 1, 2n + 1) faces of Cu is discussed for large n. the dramatic decrease of intensity at about 600K is attributed to a roughening transition, above which the steps are fuzzy. The steps are assumed to repel themselves with a repulsion energy proportional to (2n+1)-2, of elastic or electrostatic nature or both. The main parameter of the theory is the energy W0 of a kink on a step. Experimental data are consistent with a value of W0 between 0.2 and 0.3 eV, in agreement with very rough theoretical evaluations. Predictions are presented concerning the lineshape of diffraction spectra in the high-temperature rough phase, where intensities cannot be written as delta functions. The Bragg peak intensity vanishes just below the roughening transition temperature, TR, as exp(-constant*(TR-T)-12/), where the constant depends on the particular Bragg peak.