Theoretical debye-waller factors for the (100) and (110) surfaces of tungsten

The ratios of the atomic mean square displacements at the (100) and (110) surfaces to those in the bulk have been calculated as a function of temperature for the body-centered cubic crystal tungsten. The calculations have been carried out for a slab-shaped crystal in which the atoms interact through central potentials up to fourth neighbors and through a harmonic angle-bending interaction involving pairs of nearest neighbors. The required averages over the two-dimensional Brillouin zone were obtained using sets of special points which are most efficient in finding such averages. A comparison between the theoretical results and the available experimental data is given.