Temperature Variation Of Debye-Waller Factors Research Articles

Effective real-space correlations of crystal lattice vibrations

Effective phonon fields coupled to a temperature-dependent permeability tensor are introduced to model empirical thermodynamic functions of crystal lattices and the temperature variation of Debye-Waller factors inferred by X-ray, γ-ray or neutron diffraction. The permeabilities generate a varying Debye temperature and a temperature-dependent spectral cutoff in the partition function as well as an effective temperature-dependent oscillator mass, to be calculated from diffraction and heat capacity data. The zero-point internal energy of the phonon field is extracted from low-temperature Debye-Waller B-factor measurements. The varying spectral cutoff, Debye temperature and oscillator mass determine the temperature evolution of real-space correlation functions. Closed integral representations are derived for the effective two-point function correlating isotropic lattice vibrations in monatomic cubic crystals as well as for the reduced four-point function correlating fluctuations around the mean-squared atomic displacement. The correlations are long-range with power-law tails and become oscillatory at low temperature. The formalism is illustrated with the correlation functions of copper.

Temperature Variation of Debye-Waller Factor and Mean Square Displacement for bcc Metals Using Density Based Pseudopotential

Temperature Variation of Debye-Waller Factor and Mean Square Displacement for bcc Metals Using Density Based Pseudopotential

Temperature variation of Debye-Waller factor of KNO3

Temperature variation of Debye-Waller factor of KNO3

A Temperature Variation of Debye-Waller Factor for Alkali and Noble Metals

Debye-Waller factors at different temperatures of four alkali and three noble metals have been computed on the basis of a screened shell phenomenological model. The theoretical values are compared with existing experimental data. Particularly for lithium and potassium, most recent experimental information has been included. A critical examination of the results reveals a satis­factory agreement between the theoretical and experimental findings.

Temperature Variation of Debye-Waller Factors in Molybdenum and Tungsten

Temperature Variation of Debye-Waller Factors in Molybdenum and Tungsten

Temperature Variation of Debye-Waller Factors in Molybdenum and Tungsten

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A model for lattice dynamics of face centred cubic metals

A lattice dynamical model for the face-centred-cubic (FCC) metals has been proposed by incorporating the ion-ion central and angular and the electron-ion interactions through well known theories. The model satisfies the translational invariance and the condition for the internal force equilibrium of the lattice. The application of this model has revealed fairly well the phonon dispersion curves and the temperature variation of Debye-Waller factor and electrical resistivity of copper.

Lattice vibrations and Debye-Waller factors in f.c.c. metals

Frequencyvs. wave vector dispersion relations along three principal symmetry directions [00ζ], [0ζζ] and [ζζζ] and temperature variation of Debye-Waller factors in five face-centred cubic metals, copper, silver, gold, nickel and aluminium, have been computed on the basis of a lattice-dynamical model which considers short-range pairwise forces effective up to second neighbours and long-range Coulomb forces on the lines of Krebs model, and also describes the ionic lattice to be in equilibrium in a medium of electrons. A comparison of theoretical results obtained with the experimental findings indicates that the model gives a reasonably satisfactory description of the lattice-dynamical behaviour in face-centred cubic metals.