Analytical representations of the Mössbauer recoilless fraction,Debye-Waller factors,lattice energies,and heat capacities

Simple analytical expansions are given for the recoilless fraction in Mössbauer spectroscopy, the Debye-Waller factor in X-ray scattering, and the lattice energy and heat capacity of solids. While this problem has been discussed in an earlier paper [1], computer technology has now advanced to the point that direct evaluations of the simple expansions of these quantities are useful for quick curve fitting to experimental data at any desired temperature, and these expansions are easier to evaluate than using graphs to estimate recoilless fractions and Debye temperatures. We compare this approach with a polynomial expansion in terms of Bernoulli numbers, which has only a limited domain of convergence. We explicitly evaluate the convergence of these Debye integral expansions as a function of the number of terms used and the time required.This work was prepared with the support of the U.S. Department of Energy, Grant No. DE-FG02-85 ER 45199.     

Inhomogeneous lattice distortions in the Zn0.99Cd0.01Se crystal

The structural state of a Zn_0.99Cd_0.01Se crystal at temperatures of 78 and 300 K has been investigated using thermal neutron diffraction. It has been found that the diffraction patterns of the crystal contain diffuse scattering regions in the vicinity of the basic structure reflections, which are independent of temperature. It has been shown that the effects of diffuse scattering are caused by transverse displacements of lattice atoms, which are induced by impurities of the Cd²⁺ ions whose sizes substantially exceed the sizes of the Zn²⁺ ions. The obtained results have been used to construct a picture of the influence of cadmium ions on the structural state of the crystal under study.     

The static Debye-Waller factor of defect-induced lattice displacements

The attenuation of Bragg scattering intensities due to static displacements is discussed for interstitially dissolved point-defects. It is shown that in the single defect approximation the static Debye-Waller factor (DWF) exp (–2L) decreases linearly with the defect concentrationc and quadratically with the scattering-vectorK (for smallK andc). From a model calculation of the displacements around H in Nb the static DWF is shown to be primarily due to the displacements closest to the impurity. Therefore the measurement of the static DWF can be used as a method to determine these displacements. From X-ray measurements of the integrated Bragg intensities of NbH _x single crystals we obtained the displacements of the four nearest neighbours around a tetrahedral interstitial site to beu ₁=0.1Å. This is in good agreement with the results of our model calculation.     

Structural and optoelectronic properties of Mg substituted ZTe (Z=Zn,Cd and Hg)

Wide band gap semiconductor alloys, Mg_xZ_1−xTe (Z=Zn, Cd and Hg), are investigated over a full range of Mg compositions (0≤x≤1) using density functional theory (DFT). The variation in the lattice constant of Mg_xZ_1−xTe is linear with the composition x, and all these alloys obey Vegrd's law. The CdTe (6.50 Å) and MgTe (6.44 Å) are lattice matched compounds, therefore the lattice constant of MgCdTe decreases slightly with the concentration x, whereas the lattice constant also decreases for MgHgTe but increases for MgZnTe. It is due to the fact that Mg has larger size than Zn and smaller size than Cd and Hg. The band gap of these compounds are calculated using the modified Becke–Johnson (mBJ) exchange potential as LDA and GGA are not effective in producing the experimental band gap of a strongly correlated electron system. The calculated band gaps of these compounds cover the range 0–3.5 eV and are consistent with the experimental band gaps. The band gaps exhibit nonlinear behavior or bowing effect with the change in concentration. The frequency dependent optical properties like dielectric functions, and indices of refraction of these ternary systems are also calculated and discussed.     

Self-consistent Debye-Waller factors of the electron solid on liquid helium

Based on the self-consistent field formalism we propose a shear-mode self-consistency for the high-frequency Debye-Waller factors (HFDWF) of the electron solid bound on a free surface of liquid helium. Our results are qualitatively in agreement with the empirical DW factor determined by Fisher, Halperin, and Platzman with the experiment of Grimes and Adams. We also report the analysis of the HFDWF according to the Lindemann law.     

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.     

Calculation of electrical resistivity of Mg,Cd, and Zn in solid and liquid state. local pseudopotential approximation

Pseudopotential method, thermodynamic perturbation theory, and the formula due to Ziman are used for calculating the temperature dependence of the electrical resistivity of solid and liquid Mg, Cd, and Zn. In solid metals, a system of Einstein oscillators is chosen as the ground state, and in melts, solid spheres are chosen. Electrical resistivity of a solid metal is represented by a sum of a diffusion and a continuous contribution, with the latter practically completely determining the temperature dependence of electrical resistivity. The local pseudopotential approximation is found to be sufficiently correct for calculating the electrical resistivity of Mg; however, it gives lower values of electrical resistivities of Cd and Zn, which is due to neglecting hybridization effects.Translated from Izvestiya Vysshikh, Uchebnykh Zavedenii, Fizika, No. 3, pp. 93–100, March, 1984.     

Ordering behaviors of Cd−Mg and Cd−Zn alloys with the h.c.p.-type structure

The structure dependent energy and the ordering energy for an h.c.p.-type binary alloy composed of simple metals are derived from a basis of the method of pseudopotentials. The expressions of the energies are characterized by the long-range and short-range order parameters.The long-range ordering energy is calculated for alloys in the Cd?Mg system. The numerical results reproduce well the fact that the Cd?Mg system has the B19-type ordered phase around the stoichiometric composition of MgCd and the D0₁₉-type ones around Mg₃Cd and MgCd₃. The calculated local ordering energies explain successfully the existence of a short-range order in the Cd?Mg system and also the insolubility between Cd and Zn.     

Zn,Cd对CaTiO3：Pr3+的发光性质的影响

采用高温固相反应合成CaTiO₃:Pr³⁺、Zn₂TiO₄、Ca_0.7Zn_0.3-xCd_xTiO₃:Pr³⁺(x=0.01,0.03,0.05,0.07,0.09,0.1)红色系列粉末状发光材料。经X射线衍射检测其结构,CaTiO₃结构为正交晶系,其结果与JCPDS标准卡(42-423)相符。Zn₂TiO₄结构属立方晶系,结果与JCPDS标准卡(25-1164)一致。Ca_0.7Zn_0.3-xCd_xTiO₃:Pr³⁺(x=0.01,0.03,0.05,0.07,0.09,0.1)由两种物相组成,一种为CaTiO₃,另一种为Zn₂TiO₄。检测了材料的激发光谱和发射光谱。发现,在CaTiO₃:Pr³⁺中加入适量Zn可形成Zn₂TiO₄相,使材料的激发光谱在324nm附近的吸收增强。少量Cd可进入Zn₂TiO₄晶格,增强激发光谱在324nm附近的吸收,同时提高发射光谱的强度;但过量的Cd的加入会导致发射光谱强度下降。     

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.     

The results of study of the anisotropy of free-electrons momenta distribution in Mg,Zn, and Cd by means of the positron annihilation method

The angular correlation of annihilation radiation was measured for single crystals of Mg, Zn, and Cd in seven crystallographic direction. The results of distribution of thez-component of the conduction electron momenta were compared with the crossectional-area distribution of the double Brillouin zone for two directions [0001] and . The results were analyzed also by the Mijnarend's method. The distributions of the electron momenta densities in the [0001] and [ ] directions are preliminarily discussed. Supported by Instytut Niskich Temperatur i Badan Strukturalnych Polskiej Akademii Nauk we Wrocławiu (Institute for Low Temperature and Structure Research, Polish Academy of Sciences in Wroclaw, Poland).     

First-principles study of ground- and metastable-state properties of XO (X = Be,Mg, Ca,Sr, Ba,Zn and Cd)

The evolution of the local atomic order of an amorphous Ni₄₆Ti₅₄ alloy produced by mechanical alloying as a function of temperature was studied by synchrotron X-ray diffraction (XRD) and differential scanning calorimetry (DSC) techniques. XRD measurements at several temperatures (25 °C, 350 °C, 412 °C, 430 °C, 450 °C and 515 °C) were performed and analyzed using the reverse Monte Carlo (RMC) simulations method or the Rietveld refinement procedure. The experimental total structure factor for samples at 25 °C and 350 °C, which are amorphous in nature, were simulated by using the RMC method, and the local structures of the alloy at both temperatures were determined, indicating a decrease in its density as the temperature increases. At 412 °C, the XRD pattern shows a partially crystalline sample, indicating that the crystallization process is in progress. At 430 °C, 450 °C and 515 °C, the XRD measurements indicate the presence of two crystalline phases, NiTi and NiTi₂, whose structural parameters (lattice parameters, coherently diffracting domains (CDD) sizes, microstrains and relative amount of phases) were determined using the Rietveld refinement procedure. DSC measurements at different heating rates furnished the crystallization temperature, enthalpy and activation energy of the crystallization process, and these values are similar to those found in other amorphous alloys of the Ni-Ti system. They also showed the existence of a second exothermic process, which was related to diffusive processes in the crystalline phases, which could be associated with the changes in the CDD sizes happening from 450 °C to 515 °C.     

速效救心丸中Ca,Mg,Fe,Cu,Zn的测定及Ca/Mg,Cu/Zn比值分析

本文采用火焰原子吸收分光光度法测定了速效救心丸中Ca ,Mg ,Fe,Cu ,Zn五种金属元素的含量 ,并对速效救心丸中Ca/Mg ,Cu/Zn含量比值进行了分析研究。结果表明 ,速效救心丸中含有丰富的Ca,Mg ,Fe ,Cu ,Zn元素 ,元素含量Ca>Fe >Mg >Zn >Cu ,它为探讨速效救心丸中Ca ,Mg ,Fe ,Cu ,Zn与治疗冠心病之间的关系提供了有用的数据。     

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.     

EFG sign for Sn in Zn,Cd, and Sb

Mössbauer spectroscopy on ion-implanted sources of¹¹⁹Cd in single-crystals was applied to study the electric field gradients (EFG) at¹¹⁹Sn in three non-cubic metals. The signs and magnitudes determined are in agreement with presently known systematics. The measured isomer shifts and the recoilless fractions are discussed.     

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.     

Matrix reactions of Zn,Cd and Mg atoms with NO2. Infrared spectra of M+NO2− species

Matrix reactions of Mg, Zn and Cd atoms and NO₂ have been performed. Infrared absorptions in the 1220 cm^?1 range show isotopic shifts appropriate for M⁺NO₂^? species. Bands near 950 cm^?1 in the zinc experiments are attributed to a different ion-pair structural isomer.     

Theoretical study of local lattice structure of Mn in perovskite fluorides A2MF4 (A=K, Rb; M=Mg, Zn, Cd) series

A theoretical method for investigating the inter-relation between the molecular structure and electronic structure has been established on the basis of the 252×252 complete energy matrices for a 3d⁵ configuration ion in a tetragonal ligand field. By means of this method, which is independent of the X-ray diffraction, the local structure of the paramagnetic Mn²⁺ ion in perovskite fluorides A₂MF₄ (A=K, Rb; M=Zn, Mg, Cd) are determined directly by analyzing the EPR spectrum of octahedral Mn²⁺ center in A₂MF₄ crystals and the optical absorption spectrum of the (MnF₆)⁴⁻ cluster. It is shown that, comparing with the octahedral cubic structure, the local micro-structure in the vicinity of Mn²⁺ displays an elongated distortion when and a compressed distortion when , and ΔR vs. as well as ΔR vs. in the distortion region is, respectively, approximately linear. Simultaneously, the theoretical zero-field-splitting parameters , and are in good agreement with the experimental values.