X-ray diffraction studies of RbBr-RbI mixed crystals

Mixed crystals of RbBr and RbI have been prepared from melt. Using an X-ray diffractometer powder patterns have been recorded. The lattice constants show slightly positive deviations from Vegard’s law. From the integrated intensities, the mean Debye-Waller factor has been determined. The Debye-Waller factor shows a highly non-linear composition dependence with positive deviations from linearity, the values for intermediate compositions exceeding those for the end members. The Debye temperatures calculated from the Debye-Waller factors show a non-linear composition dependence with negative deviations from linearity.     

X-ray determination of mean Debye-Waller factors and Debye temperatures of the K x Rb(1−x)Br mixed crystal system

The integrated intensities of Bragg reflections have been measured for mixed crystals in the K _x Rb_(1−x)Br system with an x-ray powder diffractometer. From the intensities, the mean Debye-Waller factors are determined. The Debye-Waller factors are corrected for static contribution and Debye temperature values are determined for the entire composition range. The x-ray Debye temperatures follow the Kopp-Neumann equation closely.     

Growth and X-ray studies of (NaCl)x(KCl)y−x(KBr)1−y single crystals

Ternary mixed crystals of NaCl, KCl and KBr were grown by the melt method for the first time. Densities and refractive indices of all the grown crystals were determined and also used for the estimation of the bulk composition in the crystal. Lattice parameters and thermal parameters like Debye-Waller factor, mean square amplitude of vibration, Debye temperature and Debye frequency were determined from the X-ray powder diffraction data. The observed lattice parameters showed the existence of two phases in crystals with NaCl content greater than 0.1 mole fraction. The thermal parameters show a highly non-linear composition dependence. The results are reported.     

Debye-Waller factor of lead nitrate

The X-ray Debye-Waller factors and Debye temperatures of lead nitrate single crystals taken in the powder form have been determined by measuring integrated intensities of selected Bragg reflections at different temperatures. The characteristic specific Debye temperature has been compared with the value obtained from elastic constant data.     

无序晶态合金的电阻率

基于Baym原则,将Ziman型液态金属电阻理论推广到晶态金属及替代式的无序合金系统,给出了电阻率的一般表达式,讨论了它们的低温和高温行为。低温下用德拜晶格振动模型,无序晶态系统的电阻率可表为ρ=ρ₀+ρ_d(T/Θ)²+ρ_i(T/Θ)⁵,与实验一致。高温下,考虑到Debye-Waller因子及多声子效应,电阻率趋向饱和。用独立原子振动近似得到的简单公式与实验资料的比较表明:类似Nb这种电阻率的高温非线性偏离可以在本文的模型中自然地得到说明。     

X-ray determination of the Debye-Waller factors and Debye temperatures of AgCl and AgBr

The integrated intensities of Bragg reflections are measured for AgCl and AgBr at room temperature using an x-ray powder diffractometer. The Debye-Waller factors and Debye temperatures are evaluated.     

X-ray determination of the mean Debye-Waller factors,amplitudes of vibration and Debye temperatures of six crystals with CsCl structure

From the integrated intensities of Bragg reflections measured at room temperature with an x-ray powder diffractometer, the mean Debye-Waller factorB, the average r.m.s. amplitude of vibration (ū ²)^1/2 and the Debye temperatureθ, have been determined for six crystals with the CsCl structure. The energy of formation of a Schottky pair in these crystals has been estimated from an empirical relation between the x-ray Debye temperature and the energy of formation.     

Debye-Waller effects in atom-surface scattering

The temperature sensitivity of helium atom reflection from NaF ranges from slight in the quantum regime (long wavelength, near-glancing incidence) to considerable in the classical regime (short wavelength, near-normal incidence). The latter is describable by the Debye-Waller theory only over a limited range of angles. In this range, no Beeby well-depth correction is required. The surface Debye temperature of the NaF is found to be 425 ± 20 K.     

An experimental investigation of the elastic scattering of He and H2 from Ag(111)

Experimental diffraction probabilities for 63 meV He and 66 meV H₂ scattering from Ag(111) along the 〈112̄〉 direction are reported. Debye-Waller experiments for the He/Ag(111) system yield a mean well depth of 9.3 meV and an effective surface Debye temperature of 253 K.     

X-ray determination of the mean Debye-Waller factors,amplitudes of vibrations and the Debye temperatures of CdO,PbS and MnS

Integrated intensities of Bragg reflections of CdO, PbS and MnS have been measured at room temperature using an x-ray powder diffractometer. From a least square treatment of the intensity data the mean Debye-Waller factor, the mean amplitude of vibration and the Debye temperature have been evaluated. Calculations were made using scattering factors pertaining to neutral atoms as well as doubly ionised ions. The results from the two sets of calculations agreed within limits of errors.     

Temperature dependence of the Mössbauer effect on Sn-119 doped metallic lead

After perfecting a technique to manufacture extremely pure, homogeneous, smallconcentration Sn in Pb samples, we have measured the Debye-Waller factor over the temperature range of 4 to 300 K. Our data show some evidence of a line broadening between 4 and 50 K which may be accounted for by the spin-density wave model of lead proposed by A. Overhauser. [1]. Between 77 K and room temperature, we find a temperature dependence to the recoilless fraction consistent with a Debye model (Debye temperature = 107(2) K). Moreover, we find no evidence of a sudden precipitous falloff of the recoilless fraction, as was reported by Schechter et al. in 1989. The origin of this difference is discussed.This work was prepared with the support of the US Department of Energy, Grant No. DE-FG02-85ER45199.     

Heat capacity anomaly in UO2 in the vicinity of 1300 K: an improved description based on high resolution X-ray and neutron powder diffraction studies

X-ray and neutron powder diffraction studies of UO₂ were performed under controlled oxygen partial pressure between room temperature and 1673 K. More than 40 neutron diffraction patterns were recorded. The thermal expansion coefficient of UO₂ and the temperature dependence of Debye-Waller factors for oxygen and uranium atoms were determined. The dependence of Debye-Waller factors as a function of temperature is linear and the thermal expansion coefficient follows the classical Debye regime within the temperature range 300-1000 K. Above 1200 K, a departure from this quasi-harmonic behavior is clearly observed. Both an abnormal increase of the thermal expansion and of the oxygen sublattice disorder are evidenced. The departure of the lattice parameter from a linear thermal variation is found to be thermally activated with an effective activation energy close to 1 eV, very similar to the activation energy already found for the electrical conductivity. This new result suggests that polarons may affect the mean lattice parameter. A new thermodynamic model is then proposed to explain the heat capacity thermal variation by only three contributions: harmonic phonons, thermal expansion and polarons.     

Multiphonon contribution to the structure factor of metals

The structure factor of Na is calculated including two-phonon terms and the Debye-Waller factor. The result is compared with the one-phonon approximation usually employed to evaluate the electronic transport coefficients. This multiphonon contribution can amount to 13 per cent at the melting point and 10 per cent at room temperature in the transport sensitive region of wave vector 1.5 k_F < q < 2 k_F, where k_F is the Fermi wave vector. We conclude that calculations of electronic transport coefficients of metals intended to attain a precision better than 10 per cent above the Debye temperature must take into account the contributions of the Debye-Waller factor and the two phonon terms.     

Lattice Dynamics of Some Fcc F-Shell Metals

A model pseudopotential depending on an effective core radius but otherwise parameter free is used to study the binding energy, equation of state, ion-ion interaction, phonon dispersion curves (q-space and r-space analysis), phonon density of states, Debye temperature, mode Grüneisen parameters, dynamical elastic constants, Debye-Waller factor, mean-square displacement, Debye-Waller temperature parameter and propagation velocities of elastic waves of some fcc f-shell metals La, Yb, Ce, and Th. The contribution of the s-like electrons is calculated in the second-order perturbation theory for the model potential while d- and f-like electron is taken into account by introduction of repulsive short-range Born-Mayer term. Very recently proposed screening function due to Sarkar et al. has been used to obtain the screened form factor. The parameter of the potential is evaluated by zero pressure condition. Which is independent of any fitting procedure. An excellent agreement between theoretical investigations and experimental findings prove the ability of the potential for d- and f-shell metals exclusively.     

X-ray determination of the Debye-Waller factors and Debye temperatures of europium monochalcogenides

X-ray powder diffractograms of EuS and EuTe have been recorded. The integrated intensites have been measured and corrected for TDS. From an analysis of the intensity data, Debye-Waller factors and Debye temperatures have been evaluated.     

Lattice variation and thermal parameters of gel grown KDP crystals added with some ammonium compounds

Pure and impurity added (with NH₄Cl, NH₄NO₃, NH₄H₂PO₄, and (NH₄)₂SO₄) KDP single crystals were grown by the gel method using silica gels. X-ray diffraction data were collected for powder samples and used for the estimation of lattice variation and thermal parameters like Debye-Waller factor, mean-square amplitude of vibration, Debye temperature and Debye frequency. The thermal parameters do not vary in a particular order with respect to impurity concentration. The results obtained are reported and discussed.     

Vibrational dynamics and surface structure of Bi(111) from helium atom scattering measurements

The Bi(111) surface was studied by elastic scattering of helium atoms at temperatures between 118 and 423 K. The observed diffraction patterns with clear peaks up to third order were used to model the surface corrugation using the eikonal approximation as well as the GR method. Best fit results were obtained with a rather large corrugation height compared to other surfaces with metallic character. The corrugation shows a slight enhancement of the surface electron density in between the positions of the surface atoms. The vibrational dynamics of Bi(111) were investigated by measurements of the Debye-Waller attenuation of the elastic diffraction peaks and a surface Debye temperature of (84 ± 8) K was determined. A decrease of the surface Debye temperature at higher temperatures that was recently observed on Bi nanofilms could not be confirmed in the case of our single-crystal measurements.     

X-ray diffraction and colour centre studies on RbCl-RbBr mixed crystals

X-ray diffraction and colour centre studies have been carried out on RbCl-RbBr mixed crystals. The lattice constant closely follows the linear form of Vegard’s law. The mean Debye-Waller factor shows a highly nonlinear composition dependence. The composition dependence of the F-band peak position is slightly nonlinear but that of the F-band half-width is highly nonlinear. The Ivey-Mollow relation holds for this system with an index of 2.5. The ‘size effect’ is found to have a dominant effect on the F-band width.     

X-ray determination of the mean amplitudes of vibration and debye temperatures of some rare earth monochalcogenides

The x-ray diffraction intensities of Bragg reflections have been measured at room temperature for thulium selenide, samarium sulphide, samarium selenide and samarium telluride. On the basis of a common amplitude approximation, the Debye-Waller factor, the mean amplitude of vibration and the Debye temperature have been evaluated. The values of the Debye temperatures and mean amplitudes of vibration are 176±16°K, 0·185 ± 0·017 Å (TmSe), 155 ± 7°K, 0·244 ± 0·012 Å (SmS), 153 ± 14°K, 0·221 ± 0·020 Å (SmSe) and 151 ± 20°K, 0·204 ± 0·027 Å (SmTe).