Alkali Halide Solid Solutions Research Articles

Epifluorescence microscopy study of a quadruple node of triple junctions of grain boundaries in a Eu2+-decorated highly textured composite of (Cl, Br)(K, Rb) and I(K, Rb) solid solutions.

The structural nature and geometry, as well as the lattice-relative orientation, of an arrangement of crystal defects in a highly textured Eu2+-doped composite of two alkali-halide solid solutions was studied by epifluorescence microscopy (EFM) using the doping ion as a fluorochrome. A three-dimensional reconstruction and a skeleton type model, as built from a sequence of EFM images of different optical cross-sections of this arrangement, are presented. Structurally, this arrangement is a quadruple node (QN) of triple junctions of grain boundaries. The QN core geometry is that of a tetragonal tristetrahedron (TTTH), centred at the QN site, whose tetrahedron vertices and edges are on the QN triple junctions and grain boundaries, respectively, whereas the tristetrahedron tetragonal axis is nearly parallel to the lattice [001]-axis. The measured values of the angles between triple junctions and between the grain boundaries forming them are reported. The distinct chemical compositions of the composite solid solutions are discussed to be responsible, in last instance, for the tristetrahedron departure from a cubic configuration. Collaterally, certain families of translationally periodic almost-parallel (TPAP)-wall-like regions which consist of TPAP-columns of TPAP-spindle-like singularities, as well as certain zigzag arrays of columns of this like, existing into the QN grains, are reported to be observed. Three-dimensional reconstructions of typical individuals of these families and arrays as well as of their constituent parts are presented and geometrically analysed. These families and arrays are discussed to be families of tilt subboundaries, whose constituent dislocations are decorated by cylindrical second-phase europium di-halide precipitates, and regularly faceted tilt subboundaries, respectively. Crystal growing and sample preparation, composite structural characterisation by powder and single-slab X-ray diffraction (PXRD and SSXRD, respectively), microscopy and fluorescence-cube unit optics, image processing, electronic three-dimensional reconstruction and measuring methodologies, are all described in detail.

Study of Alkali Halide Solid Solutions by Scanning Electron Microscopy and X-ray Diffraction

Study of Alkali Halide Solid Solutions by Scanning Electron Microscopy and X-ray Diffraction

Composition dependence of glow peak temperature inKCl1−xBrx doped with divalent cations

Thermoluminescence measurements ofβ-irradiatedEu2+- andCa2+-dopedKCl1−xKBrx solid solutions excited at room temperature have been carried out to identify the effect ofcomposition on the glow peaks. A typical glow peak has been distinguished foreach composition. A linear dependence of its temperature on the compositionx has been found. These results indicate that for divalent impurity-doped alkalihalide solid solutions these glow peak temperatures are mostly dependent onthe lattice constant of the host than on the size of the anion or impurity cation.

Dynamic and Static Disorder of Alkali Halide Solid Solutions studied by Temperature-dependent Extended X-Ray-Absorption Fine Structure

Interatomic potential of ionic bonds in alkali halide solid solutions has been studied by temperature dependent EXAFS (extended X-ray absorption fine structure). As a typical ionic bond in alkali halide solid solutions, K–Br bond of KCl 0.8 Br 0.2 and KBr 0.2 I 0.8 solid solutions have been focused. The K–Br bond was contracted for KCl 0.8 Br 0.2 , while it was elongated for KBr 0.2 I 0.8 , as compared to that in KBr. The longer K–Br bond was softer and less anharmonic than the shorter K–Br bond. We could explain this bond length dependence of the force constants in terms of the interatomic potential of the K–Br bond. The static disorder also increased with the K–Br bond length.

A New Approach to the Evaluation of Thermodynamic Properties of Nonideal Solid Solutions by the Molecular Dynamics Method: A Mixing Model of Alkali Halide Solid Solution

We present a new approach to evaluating the intracrystalline thermodynamic properties of solid solutions by combining the molecular dynamics (MD) method and a chemical thermodynamic approach. The coordination type of ions in alkali halide solid solutions (A, B)X is classified into 7 types Xn(n=0–6) for halide ions and into 13 types An(n=0–12) and Bn(n=0–12) for cations, depending on the kind and the coordination number of the nearest cation. Entropy of mixing for a nonideal solid solution was formulated by using the configurational entropy of coordination types. The equilibrium concentration of coordination types is expressed by equilibrium reactions among coordination types. The equilibrium constants in the solid solution of the system NaCl–KCl were then calculated by the MD method and the excess free energies of mixing were obtained by calculation. The asymmetric nature of the solvus curve of the system NaCl–KCl is well demonstrated and the temperature of the apex of the solvus agrees well with experimental data.

Optical study of the phase separation in alkali halide solid solutions

Abstract Thin crystals of Na1−xKxI:Tl+ solid solutions with thicknesses of 0.1 ∼ 10 μm have been produced and their phase separation has been observed in both regions of the exciton band and Tl+ impurity band. An intermediate band of Tl+ was recognized in the absorption spectrum of Na0.5K0.5I:Tl+. A precursor phenomenon was found as a temporal change of the intensity ratio of two Tl+ emission bands.

Theoretical Interpretation of EXAFS Results for the Relaxation in Mixed Crystals

AbstractUsing EXAFS technique it is possible to measure the relaxation of the nearest neighbours around a substitutional defect and at a finite concentration one obtains distinctly two types of nearest‐neighbour distances in a binary solid solution. A relation is derived containing a single parameter for the variation of these two types of nearest‐neighbour distances with concentration which predicts the results successfully both, for alkali halide solid solutions and covalently bonded tetrahedral solid solutions of zincblende structure. The parameter is calculated for alkali halide solid solutions using information of the perfect crystals only.

On Lattice Parameters and Enthalpies of Mixing of Alkali Halide Solid Solutions

AbstractA simple unified approach to the calculation of enthalpies of mixing and deviations of lattice parameters from Vegard's rule is presented. No experimental information about the solid solution is required and the results are insensitive to small experimental errors of the relevant parameters (r, x) of the pure components. In many cases this model is superior to more sophisticated theories in reproducing experimental data of mixed crystals. The main shortcomings of these theories with respect to lattice spacings are discussed.

Lattice Dilatation in High‐Concentration Binary Solid Solutions

AbstractA simple extension of Huang's theory of lattice dilatation for low concentration is found to reproduce Retger's law of additivity of molar volume. Deviation from the law is accounted for by considering the elastic strength of the defect to be concentration dependent and an attempt is made to calculate the elastic strength of the defect from the parameters of the perfect crystal. The method is then used to predict the concentration dependence of volume over the entire concentration range of eight alkali halide solid solutions and two metallic alloys and fairly good agreement is obtained.

A Co‐Ordinated Approach to the Calculation of Lattice Parameter and Heat of Formation for Alkali Halide Solid Solutions

AbstractExperimentally observed deviations of the lattice parameter from Vegards' law in alkali halide solid solutions are predicted from the boundary condition on the equation for the heat of formation. This also simultaneously makes the latter consistent with experimental results. The theory uses no experimental information of the solid solution and only the perfect crystal information is sufficient. The model is employed here to calculate the lattice parameter and heat of formation of ten alkali halide solid solutions over the entire concentration range. The agreement with the experimental results is quite satisfactory.

A Theory of Hardening in Concentrated Alkali Halide Solid Solutions

The activation energy to move a dislocation through randomly distributed solute ions was calculated as a function of applied stress, solute ion concentration and line tension of the dislocation, by using a statistical method. The interaction between a dislocation and solute ions is calculated on the basis of elasticity theory (size misfit). Critical resolved shear stress, activation volume and dislocation velocity-stress exponent were determined as a function of temperature and concentration, by assuming that the thermally activated deformation is expressed by the Arrhenius equation. The theoretical results were compared with experimental data of KC1–KBr solid solution measured from 4.2 K to 293 K and close agreement was obtained, except for a range of low concentrations at low temperatures.

Infrared absorption spectra of bef 2−4 in alkali halide solid solutions : Relative intensities and site stability

The infrared absorption spectra of solid solutions of the type M 2-BeF 2− 4/(KCl, KBr, and KI) have been investigated. Bands associated with anion sites of T d, C 2v, and C 3v symmetry have been identified. The relative populations of the ion pair site configurations are discussed in terms of the Atypical Cell model and an energy-entropy competition. Utilizing an expression derived from solution theory, {|∂μ/∂ Q 3}|and ṽ 3 0 of the isolated BeF 2− 4 ion have been calculated to be 186 cm 3 2 sec −1 and 890 cm −1, respectively.

Pulsed Nuclear Double Resonance in Alkali-Halide Solid Solutions

The nuclear magnetic double resonance technique has been used to study the first order quadrupole splittings of the NMR lines due to Na nuclei surrounding the substitutional impurities in NaCl single crystals. By studying the angular variation, signals observed are assigned to (0, 0, 1) Na sites around the Br - impurities in NaCl-NaBr solid solutions, and to (0, 0, 1) Na and (1, 1, 1) Na sites close to the I - impurities in NaCl-NaI crystal. The electric field gradients on these sites are found from the quadrupole frequency ν Q obtained from our experiments and the nuclear quadrupole moment Q =0.1×10 -24 cm 2 for Na nucleus:

Activités thermodynamiques des constituants dans les solutions solides d'halogénures alcalins

Thermodynamical activities of constituants in alkali-halide solid solutions are calculated by exploiting solid solution demixion gaps, solidus-liquidus curves or by calorimetric measurements. Results are compared and methods discussed.

Electronic polarizability and magnetic susceptibility of alkali-halide crystals: A phenomenological discussion in terms of interacting ions

Individual ion values of the electronic and magnetic susceptibilities deduced, on a phenomenological way, from the alkali halides and multicomponent alkali-halide solid solutions are discussed in the scope of a recent theoretical investigation based on an individual interacting ion model. The two approaches entirely agree and strongly support the view of alkali-halide crystals including non-negligible interactions between the ions.

Lattice theory of alkali halide solid solutions-I. Heat of formation

A statistical theory for the composition dependence of the heat of formation of alkali halide solid solutions has been developed on the basis of the substitutional impurity model of Dick and Das. Numerical results are presented for all pairs of binary alkali halide systems. Good agreement with experimental values is found over the entire composition range for seven out of eight systems for which experimental data are available. The overall agreement is better than for any of the previously developed theories of other authors.

Nuclear-Quadrupole Effects in Alkali-Halide Solid Solutions

Nuclear-Quadrupole Effects in Alkali-Halide Solid Solutions

Lattice theory of alkali halide solid solutions - II. Entropy of mixing and solid solubility

The theory of kinetics of short range order for an AB alloy containing vacancies of Kidin and Shtremel is criticized and an alternative set of equations of motion for the probabilities of atom-atom pairs and atom-vacancy pairs is proposed. Formulae are derived for the equilibrium probabilities which are consistent with the quasi-chemical theory and it is shown that the equilibrium state of atom-atom pairs implies the equilibrium state of atom-vacancy pairs. The integration of the equations of motion for the case of a quenching experiment in which the degree of short range order increases with time shows that the approach to equilibrium cannot be described by a simple exponential, in qualitative agreement with experiment. The study of the initial relaxation times gives also results in qualitative agreement with experiment. It is proposed that restrictive conditions that relate the equilibrium energy parameters to the energy of motion parameters should apply if the system is ever going to reach the state of thermodynamic equilibrium.

Lattice theory of alkali halide solid solutions - I. Heat of formation

Lattice theory of alkali halide solid solutions - I. Heat of formation

Analysis of the vapour pressure of KCl + RbCl solid solutions

The vapour pressure of alkali halide solid solutions is described in terms of the quasi-harmonic theory of lattice vibrations. The solutions are assumed to be completely disordered and contributions from defects are neglected; the validity of these assumptions is discussed. The vapour pressures of several compositions in the KCl + RbCl systems have been analyzed and values obtained for the static lattice energy U12 and the geometric mean frequency of the lattice vibrations νg. In addition, the thermodynamic functions of mixing have been obtained in the usual way. Appreciable fractions of dimeric species exist in the gaseous alkali halides and an essential step in the analyses is the calculation of the monomer partial pressures from the primary experimental data. The enthalpy of formation of the solutions at T∼800°K is smaller than the experimental uncertainties but is probably positive with values not exceeding a few 100 cal/mole. The excess entropy of mixing at 800 °K is also positive and of the order of a few tenths cal/mole.