X-ray determination of the mean Debye-Waller factors and Debye temperatures of KCl-RbCl mixed crystals

Integrated intensities of Bragg reflections have been measured for KCl-RbCl mixed crystals with various compositions and the data used to evaluate the mean Debye-Waller factors and the Debye temperatures. The composition dependence of the Debye-Waller factor is highly nonlinear with positive deviations from linearity while that of the Debye temperature is slightly nonlinear with negative deviations from linearity. Using an empirical relationship between the Debye temperature and the molar volume, the average values of the Gruneisen parameter for some mixed crystal systems are obtained.     

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.     

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.     

Melting temperatures of some alkali halide mixed crystal systems

The melting points in the KCl-KBr, RbCl-RbBr and KBr-RbBr mixed crystal systems have been measured using the microscopic method. In all the three systems, melting points vary nonlinearly with composition, with negative deviations from linearity and maximum deviation at about the equimolar concentration. The observed composition dependence of the melting points is explained qualitatively in terms of the enhanced concentration of point defects and dislocations in mixed crystals.     

An analysis of the temperature and pressure dependence of the electrical resistivity in lead

The volume dependence of the high temperature electrical resistivity has been treated in detail for lead. Volume changes caused by external pressure as well as thermal expansion have been considered. Experiments on the volume dependence of the effective electron mass have been reanalysed with an inclusion of electron-phonon interaction. Finally, we have found no experimental support for a net effect from a Debye-Waller factor and multi-phonon processes.     

Effect of lattice strain on the Debye-Waller factors of Mg, Zn and Cd

Lattice strains in Mg, Zn and Cd powders produced by grinding have been analyzed by X-ray powder diffraction. The lattice strain (ɛ) and Debye-Waller factor (B) are determined from the half-widths and integrated intensities of the Bragg reflections. In all three cases viz. Mg, Zn and Cd, the Debye-Waller factor is found to increase with the lattice strain. From the correlation between the strain and effective Debye-Waller factor, the Debye-Waller factors for zero strain have been estimated for Mg, Zn and Cd. The variation of energy of vacancy formation as a function of lattice strain has been studied.     

Temperature and pressure dependence of some thermal characteristics of magnesium

The theoretical values of the Debye-Waller factor, specific heat and the phonon dispersion relations as functions of temperature for magnesium are derived from a simple model of lattice dynamics proposed by Czachor for hexagonal crystals.. The pressure dependence of the dispersion curves is also derived. The theoretical results have been found to be in very good agreement with experimental data available.     

Debye-Waller factor of gold

The temperature dependence of the exponent of Debye-Waller factor of gold for the temperature range extending from 50 to 900°K has been studied using a theoretical model where the interactions are treated in realistic manner. The results are found to be in reasonable agreement with the experimental ones.     

The influence of the substrate on the Debye-Waller factor of very thin films

The temperature dependence of the Debye-Waller factor of very thin undisturbed films is studied. It is found that if interaction between the substrate and the film does not exist the Debye-Waller factor diverges, with the exception of the case of zero absolute temperature, so that under these conditions resonance recoilless absorption and emission of X- and-rays or neutrons by the nucleus of the film cannot occur. In the presence of interaction between the film and substrate the Debye-Waller factor is finite; its temperature dependence was determined.     

Local structure of nanopowders of refractory nitrides used to increase the critical current of high-temperature superconductors

The effect of dispersivity on the local-structure features in ZrN nanocrystals has been investigated by X-ray absorption (EXAFS) spectroscopy. The Debye-Waller factors and bond lengths have been determined for Zr-N and Zr-Zr coordination spheres. It is found that a decrease in the nanoparticle size leads to an increase in the static Debye-Waller factor for the Zr-Zr bond. The scale of changes is comparable with the increase in the Debye-Waller factor upon heating from 15 to 77 K.     

Electrical deviations from Matthiessen's rule in A Ag:Au alloy

Electrical resistivity of Ag:0.29 at % Au alloy has been measured and explained theoretically with the aim of understanding the deviations from Matthiessen's rule. The anisotropy in the electron-phonon interaction, the recoil of the impurity, mass-changes, nearest neighbour radial and angular force-constant-changes and Debye-Waller factors have been taken into consideration.     

Theoretical assessment on mixing properties of liquid Tl–Na alloys

Thermodynamic and structural properties of mixing of molten Tl–Na alloys at 673 K have been investigated using quasi-chemical model. To understand the mixing behaviour in more detail, emphasis is placed on the role of interaction energy term, and viscosity and surface tension of the alloys have also been analysed under statistical considerations. Our study shows negative deviation from the Raoultian behaviour in the properties of Tl–Na alloy thereby indicating hetero-coordination in the Tl–Na melt at 673 K in the full range of concentration. Theoretically, computed thermodynamic data at 673 K agree very well with the corresponding experimental data. The viscosities of the alloys computed from Kaptay equation show small negative deviation and those computed from Singh and Sommer’s formulation show small positive deviation from ideal values while the Budai-Benko-Kaptay equation predicts noticeable negative deviation in Na-rich end and positive deviation in Tl-rich end of the composition. The calculations of surface tension reveal that results obtained from layered structure approach and compound formation model are in good agreement in the Na-rich side and in reasonable agreement in Tl-rich side of the composition, while those computed from Butler equation show noticeable deviations in the intermediate compositions. Both the viscosity and surface tension of liquid Tl–Na alloys increase with addition of Tl-component, viscosity having approximately linear variation with concentration. The study shows that there is non-linear variation in surface composition with bulk concentration and for most of the compositions the surface of the alloy is enriched with Na-atoms which segregate to the surface.     

The anomalous Debye-Waller factor of hydrogen in niobium as determined by quasielastic neutron scattering

The integrated intensity of quasielastic neutron scattering by protons in polycrystalline NbH_0.16 and in a single crystal of NbH_0.045 was investigated as a function of the scattering vector Q. Strong deviations from a harmonic Debye-Waller factor behavior were observed at elevated temperatures. The results show a temperature dependent delocalization of the proton extending as far as the neighboring sites of the interstitial lattice. Experiments on the single crystal indicate a directional dependent mean-square amplitude of the proton even at room temperature.     

M?ssbauer effect in superconducting tin-europium-molybdenum-sulfides

Mössbauer spectra of¹¹⁹Sn in Sn_1–z Eu _z Mo₆S₈ (z=0, 1/3, 2/3) have been measured in the temperature range 4.9 KT293 K. The spectra consist of a quadrupole doublett with unequal intensities at all temperatures. The Debye-Waller factor, the isomeric shift and the asymmetry of the intensity of the quadrupole components show irregularities between 50 K and 110 K which are interpreted as arising from a structural phase transition. The temperature dependence of the Debye-Waller factor can be approximated by a simple phonon spectrum. No quantitative explanation can be given for the large values of the asymmetry. Evidence is presented that this behavior is connected with the properties of the librational modes of the Mo₆S₈-units in the crystal.     

Developments in time domain Mössbauer spectroscopy

Time differential measurements of nuclear resonance scattering using synchrotron radiation have been performed with the low energy Mössbauer transitions of⁵⁷Fe,¹¹⁹Sn, and¹⁶⁹Tm since 1984. Various methods of filtering the nuclear energy band from the incident synchrotron radiation are now available. The possibilities of applying these methods to transition energies above 30 keV are discussed. A new technique is proposed, which is especially effective for the high energy Mössbauer transitions. It takes advantage of the different dependence of the electronic Debye-Waller factor and the Mössbauer-Lamb factor on the scattering angle.     

Adsorbate induced changes of Debye-Waller factors

The scattering of a molecular beam by a solid surface is sensitive to the vibrational properties of the surface which are changed by the presence of adsorbed molecules. In particular light adsorbates with discrete localized vibrational modes lead to discrete structures in the energy distribution of scattered particles and corresponding structures in the intensities of specular scattering as measured by the Debye-Waller factor. We investigate the dependence of the Debye-Waller factor on various parameters characterizing the adsorbate as well as the scattered particle. It turns out that the intensity of discrete structures in the Debye-Waller factor usually is small. Only in a very restricted range of parameter values one may be able to find observable effects.     

Mössbauer effect in superconducting tin-europium-molybdenum-sulfides

Mössbauer spectra of¹¹⁹Sn in Sn_1–z Eu _z Mo₆S₈ (z=0, 1/3, 2/3) have been measured in the temperature range 4.9 KT293 K. The spectra consist of a quadrupole doublett with unequal intensities at all temperatures. The Debye-Waller factor, the isomeric shift and the asymmetry of the intensity of the quadrupole components show irregularities between 50 K and 110 K which are interpreted as arising from a structural phase transition. The temperature dependence of the Debye-Waller factor can be approximated by a simple phonon spectrum. No quantitative explanation can be given for the large values of the asymmetry. Evidence is presented that this behavior is connected with the properties of the librational modes of the Mo₆S₈-units in the crystal.     

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.