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.     

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 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 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.     

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.     

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.     

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.     

Mechanoluminescence induced by elastic deformation of coloured alkali halide crystals using pressure steps

During the elastic deformation of coloured alkali halide crystals, the bending segments of dislocations capture F-centre electrons lying in the expansion region of edge dislocations, to the states of dislocation band. After the separation from interacting F-centres, the captured electrons move together with the bending segments of dislocations and also drift along the axis of dislocations and subsequently the radiative electron–hole recombinations, owing to both the processes of captured-electron movement, give rise to the light emission. The generation rate of electrons in the dislocation band and the mechanoluminescence (ML) intensity initially increase with time, attain maximum value at a particular time, and then they decrease with time. The intensity I_m corresponding to the peak of ML intensity versus time curve and the total intensity I_T of ML increase with the applied pressure and also with the density of F-centres in the crystals. At low temperature, both I_m and I_T increase with temperature and at higher temperature they decrease with increasing temperature due to the thermal bleaching of F-centres and also due to the decrease in luminescence efficiency. Thus, both I_m and I_T are optimum for a particular temperature of the crystals. For longer time duration, the ML intensity decreases exponentially with time in which the decay time is equal to the lifetime of interacting F-centres. Expressions derived for the different characteristics of ML are able to explain the experimental results. It is shown that the time constant for rise of pressure, lifetime of the interacting F-centres or damping time of dislocation segments, and the activation energy can be determined from the ML measurements.     

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.     

Debye temperature of alkali halide crystals

The Debye temperature _D is calculated from the elastic constants for 18 alkali halide crystals. Comparison of the results with calorimetric data _D reveals an agreement within the experimental error. The temperature dependence of _D is determined for NaCl, NaBr, KCl, and KBr crystals from the elastic constants, and this dependence is compared with the calorimetric data.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 3, pp. 89–94, March, 1971.     

Morphology of alkali halide thin films

Two alkali halide adsorbate-substrate systems were investigated by atomic force microscopy (AFM) working in contact mode. Adsorbate film orientation relative to the substrate was determined from the arrangement of the atomic steps of the substrate and the edges of the forming islands. In this work we present experimental results obtained for systems: NaCl/LiF(0 0 1) and LiF/NaCl(0 0 1), which exhibit a strong tendency of the self-assembly into regular structures.     

Dielectric properties of RbCl-RbBr mixed crystals

A systematic measurement of dielectric constant and loss on RbCl-RbBr mixed crystals in various compositions has been carried out in the frequency range 100 Hz to 100 kHz and in the temperature range from room temperature to 320°C. From these measurements the static dielectric constant, the Szigeti charge, the conductivity and the activation energy for conduction are evaluated. All these properties show a nonlinear composition dependence. Semiempirical equations proposed earlier are employed to evaluate the dielectric constant as a function of composition. The validity of these relations is also discussed.     

Microhardness studies in alkali halide mixed crystals

Microhardness measurements done in KCl, KBr and in different compositions of KCl-KBr mixed crystals show that it varies nonlinearly with composition. In order to investigate the nature of defects, several techniques such as etching, ionic conductivity and dielectric loss have been employed which showed that the mixed cristals of KCl-KBr are more defective, containing a high concentration of dislocations, low-angle grain boundaries and vacancies as compared to the end products KCl and KBr. These imperfections appear to be responsible for the nonlinear variation of microhardness in mixed crystals. The microhardness studies also revealed that the difference in size of the ions constituting the mixed system are responsible for the internal strains which in turn give rise to imperfections affecting the microhardness of mixed crystals.     

Pressure effects in Debye-Waller factors and in EXAFS

Anharmonic correlated Einstein model (ACEM) and statistical moment method (SMM) have been developed to derive analytical expressions for pressure dependence of the lattice bond length, effective spring constant, correlated Einstein frequency and temperature, Debye-Waller factors (DWF) or second cumulant, first and third cumulants in Extended X-ray Absorption Fine Structure (EXAFS) at a given temperature. Numerical results for pressure-dependent DWF of Kr and Cu agree well with experiment and other theoretical values. Simulated EXAFS of Cu and its Fourier transform magnitude using our calculated pressure-induced change in the 1st shell are found to be in a reasonable agreement with those using X-ray diffraction (XRD) experimental results.     

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.     

The fractional ionic character of alkali and silver halide crystals

The fractional ionic character of alkali and silver halide crystals is defined in terms of the deviations from the additivity rule for polarizabilities of ions. The electronic polarizabilities of ions are calculated using an empirical relationship according to which the electronic polarizability of an ion can be assumed to be directly proportional to the cube of its radius. The calculated ionicities indicate that the alkali halides are nearly or more than 90% ionic and silver halides are much less ionic which is also evident from the Phillips ionicity scale.     

Correlation between deformation bleaching and mechanoluminescence in coloured alkali halide crystals

The present paper reports the correlation between deformation bleaching of coloration and mechanoluminescence (ML) in coloured alkali halide crystals. When the F-centre electrons captured by moving dislocations are picked up by holes, deep traps and other compatible traps, then deformation bleaching occurs. At the same time, radiative recombination of dislocation captured electrons with the holes gives rise to the mechanoluminescence. Expressions are derived for the strain dependence of the density of colour centres in deformed crystals and also for the number of colour centres bleached. So far as strain, temperature, density of colour centres, E _a and volume dependence are concerned, there exists a correlation between the deformation bleaching and ML in coloured alkali halide crystals. From the strain dependence of the density of colour centres in deformed crystals, the value of coefficient of deformation bleaching D is determined and it is found to be 1.93 and 2.00 for KCl and KBr crystals, respectively. The value of (D+χ) is determined from the strain dependence of the ML intensity and it is found to be 2.6 and 3.7 for KCl and KBr crystals, respectively. This gives the value of coefficient of deformation generated compatible traps χ to be 0.67 and 1.7 for KCl and KBr crystals, respectively.     

Mechanoluminescence excitation in alkali halide crystals and colouration decay in microcrystalline powders

The mechanoluminescence (ML) of NaCl, NaBr, NaF, LiCl and LiF crystals ceases at 105, 58, 170, 151 and 175°C respectively. Both the temperatureT _c at whichML disappears and the temperatureT _s required to induce a particular percentage of colouration decay in a given time, decreases with increasing nearest neighbour distance in alkali halide crystals. This perhaps suggests that similar processes cause the disappearance ofml in alkali halide crystals and the colouration decay in their microcrystalline powders. It is shown that mobile dislocations may cause the leakage of surface charge and the decay of colouration in microcrystalline powders.     

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.