The mean-square amplitude of vibration of silicon at 293 K has been determined by a lattice-dynamical procedure. A Born–von Kármán model has been used to fit phonon dispersion data from inelastic neutron-scattering measurements. The force-constant model included the first six nearest neighbors in the diamond-type lattice. The least-squares results from the fitting of the force constants were used to carry out variance analyses of properties dependent on the harmonic model. The density of phonon states was determined by sampling an even mesh of 5.7 billion points in the unique part of the Brillouin zone. Moments of the frequency distribution up to eighth order are tabulated. The frequency distribution function was used to calculate a $〈u_{\mathrm{LD}}^2〉$ for silicon. The result is $0.005941\pm 0.000021{\AA }^2.$ An Einstein-type potential of Dawson and Willis was used to extract an anharmonic force constant from the temperature dependence of neutron-diffraction measurements of silicon carried out by Batterman and co-workers. These measurements were restricted to the weak reflections from the (222), (442), and (622) diffracting planes. With the use of the lattice-dynamical value for the vibrational amplitude of silicon the result for the ${\beta }_{\mathrm{DW}}$ anharmonic constant is $18.58\pm 0.27{\mathrm{N}\mathrm{}\mathrm{m}}^{\mathrm{-}1}{\AA }^{-1}.$

• Received 16 July 1998

DOI:https://doi.org/10.1103/PhysRevB.60.284