Improved van der Waals potentials for alkali halide crystals

Improved values of the van der Waals energy coefficients are presented for 16 alkali halides using more recent electronic polarizabilities and, for each ion, three alternative values of the effective number of electrons. The statistical method of calculating interionic potentials is used to obtain the correlation energy at small interionic separations and the values are scaled to fit the van der Waals energy at large separation. The resultant correlation energy as a function of interionic separation is fitted to both a cubic polynomial and a cr^?6 analytic form. The extent to which the van der Waals interactions are quenched by ionic overlap is derived and contrasted with Catlow et al. work on this effect.     

Interionic potentials for alkali halide crystals derived by the hybrid Thomas-Fermi-Dirac method

The first results of a systematic study of interatomic potentials in sixteen alkali halides derived using the hybrid Thomas-Fermi-Dirac method are presented. Both the basic method and modifications to (a) correct the exchange energy to exclude the self-exchange part and (b) scale the kinetic and exchange energy terms are employed. The interactions between ion pairs are calculated at a set of interionic distances in a range corresponding to ± 30% deviations from the appropriate measured equilibrium separation. In this way a tabular function for the lattice energy/ion pair is constructed and predicted values of the equilibrium nearest neighbour interionic distance, the equilibrium lattice energy/ion pair and the Smith stiffness parameter are found numerically. The derived short-range interactions between ion pairs are fitted over the whole range to the analytic form A exp($\text{?R}\text{ρ}$) + CR^?6. It is shown that the use of an expression for the lattice energy/ion pair involving these analytic forms introduces significant errors in the predicted physical parameters.     

Interionic potentials in alkali halides and their use in simulations of the molten salts

After an outline of work on rare-gas systems, which serves as a target for parallel work on alkali halides, and an initial brief survey of those parts of this parallel work for which results have been obtained, interionic potential models for alkali halides are considered in some detail. The rigid ion potentials of Fumi and Tosi are discussed and then a major part of the section is devoted to deriving a new set of polarizable ion potentials, which incorporate the ideas behind the lattice dynamical shell model. Extensions which include many-body terms in the potentials are considered briefly and finally the information which can be obtained from alkali halide diatomic molecules is discussed.

In the third section methods of computer simulation for ionic liquids are outlined, concentrating on the molecular dynamics method, and some of the properties which can be obtained by analysing the ion trajectories are listed. Results from simulations, including some new work on LiF, NaCl and RbI, are reviewed.     

Third-order elastic constants for 2:2 chalcide crystals possessing the sodium chloride structure

Third-order elastic constants of 45 chalcide crystals having the sodium chloride structure are reported using Born-Mayer potential model. We have considered repulsive interaction up to second nearest neighbours. The temperature coefficients of the third-order elastic constants have also been computed for these crystals. As is the case for NaCl-type alkali halides we find that C₁₁₁, C₁₁₂, C₁₆₆ are negative and C₁₄₄ are positive for 2:2 chalcide crystals possessing the NaCl-type structure. We have found that a₁₂₃, a₄₅₆ and a₁₄₄ are negative whereas a₁₁₂ and a₁₆₆ are positive, once again in agreement with the situation found for the alkali halides a₁₁₁ values are positive for alkali halides whereas they are both positive and negative depending upon the interionic distance for the chalcide crystals. We have found that the nature of the variation of C⁰_αβγ with interionic separation is similar for alkali halides and for the 2:2 chalcides having the NaCl-structure. We have also computed the values of the pressure derivatives of second-order elastic constants for MgO, CaO, and SrO which agree well with the experimental values indicating the satisfactory nature of our computed data for C_αβγ.     

Evaluation of the spectroscopic constants of the modified rittner potential by the Simon-Parr-Finlan technique

A critical examination is shown of the modified Rittner potential by use of the Simon-Parr- Finlan (SPF) technique, including contributions from the polarisability of ions and the van der Waals term. We develop an equation for the SPF constants, which are related to spectroscopic constants and the polarisability of the constituent ions. Our analysis indicates excellent agreement for the dissociation energies of 20 alkali halides with available experimental data. We also cite theoretical values of the SPF coefficients Y₂₀ and Y₁₁ for the 20 alkali halides; these also compare favourably with experimental data.     

Modes of vibrations due to (U-center + additive cation impurities) in alkali halides

Local and resonant modes due to hydride ions in various alkali halides containing additive cation impurities have been computed by the Green function technique. Local vibrations due to U-centers in alkali halides have O_h symmetry. When one of the six nearest neighbour cations is replaced by an additive impurity, the site symmetry of the system is lowered from O_h to C_4v. The phonon Green functions matríx is analysed according to the irreducible representation of the point group symmetry pertaining to the substitutional impurity. We have considered the vibrations of the hydride ion and all its six nearest neighbours. Analytical expressions have been derived for various modes of vibrations. Using group theory the 21 × 21 matrix has been block diagonalized into various irreducible representations. The effect of mass changes and the changes in short-range force constants have been taken into account. The computed results of the localized modes have been compared with the available experimental results. Good agreement has been found. Theoretical results on resonant modes are also displayed, which will be of use in future experiments on these systems.     

Absorption spectra of excitons in alkali-halides in the vacuum-ultra-violet region

On the basis of the localized excitation model, the spectra of K⁺ - 3p electron excitation in potassium halides are studied theoretically by using methods of the ligand field theory and a good agreement with the experiment is obtained. Some discussions are given on the applicability of the Frenkel exciton model to the VUV spectra of other alkali halides.     

The generalised Huggins-Mayer form of born repulsive potentials for NaCl-type alkali halides

The generalised Huggins-Mayer form of Born repulsive potentials for NaCl-type alkali halides have been re-evaluated using more reliable, recently published thermodynamic data and van der Waals energy coefficients. As with older versions of these potentials excellent agreement between model and experimental values of interionic distance and cohesive energy is achieved. Further, the earlier shortcomings in the failure of the stability condition and predicted elastic constants are significantly reduced. For the majority of salts the new short-range interactions have stronger van der Waals attractions and slider repulsions. The model gives average crystal radii for the alkali ions about ~0.3 Å larger than traditional free ion radii and ~0.08 Å larger than Tosi-Fumi crystal radii. The predicted halogen crystal radii are correspondingly smaller by the same amounts.     

Estimation of van der Waals dipole-quadrupole interactions

A formula has been derived based on a variational approach for the van der Waals dipole-quadrupole interaction coefficient between two atoms or ions. The coefficients for the various ion pairs in the alkali halides have been estimated on the basis of this formula. The results agree quite well with those estimated by Mayer (J. Chem. Phys.1, 270 (1933)) using a perturbation approach. The present formula is shown to have a practical advantage over the perturbation formula.     

Analysis of melting based on the diffusional force theory for alkali halides

The theory of melting based on the concept of diffusional force given by Bosi is used for studying the melting of alkali halides. Values of thermal expansivity and the Anderson-Gruneisen parameter are used to predict the interionic separations in 16 alkali halides at melting temperatures with the help of the Anderson formula. A model for melting is developed by estimating the diffusional force from the knowledge of interionic potentials based on ultrasonic data for bulk modulus and its temperature and pressure derivatives. The model thus developed is found to yield satisfactory results in agreement with the experimental data on melting.     

The elastic constants and their temperature and pressure derivatives of AgBr-AgCl mixed crystals

The three independent second-order elastic constants and their temperature and pressure derivatives have been measured for four AgBr-AgCl mixed crystals, with 19.5, 39.1, 56.6 and 78.7 mole % AgCl, using the ultrasonic pulse-echo technique at room temperature. The explicit temperature dependence of the elastic constants is calculated and is found to be much larger than that of other NaCl structure crystals. The violation of the Cauchy relation C₁₂ = C₄₄ is found to be significant and increases between AgBr and AgCl. The high temperature limit of the Gruneisen parameter is calculated from the elastic data. A comparison is made between the elastic properties of the silver halides and the alkali halides.     

Thermally stimulated depolarization of Eu2+-cation vacancy dipoles in alkali halide single crystals

Ionic thermocurrent (ITC) measurements have been performed on eight alkali halide single crystals doped with divalent europium. In all cases, the observed ITC peaks were fitted with a mono-energetic model without to appeal to any dipole-dipole interaction. Values for the reorientation parameters have been calculated. The relationship T_M1nτ^?1 α E previously found for I–V complexes in alkali halides has been found to be very well obeyed for the experimental data obtained in this investigation. It is also reported that the logarithm of the experimentally determined energies for free dipole reorientation shows a linear dependence on the interaction distance between the Eu²⁺ ion and the surrounding halogen ions in the distorted cubic site occupied by this impurity in the alkali halides.     

Cathodo-luminescence spectra of alkali halides

Cathodo-luminescence spectra of fourteen alkali halides and of some mixed crystals of NaCl and KCl have been studied. The spectra show broad structureless bands. In some ten halides it is possible to find a strong band whose peak position shifts towards longer wavelengths as the inter-atomic distance increases. For pottasium halides the relationship λ_max=1380d, where “d” is the inter-atomic distance, holds approximately but is not generally true. A mechanism of cathodo-luminescence in alkali halides has been postulated, and an interpretation of the above band and of some NaCl bands has been made on that basis.     

A method for predicting the anharmonicity constants ωeχe of halides of sodium

A method is proposed for estimation of the vibrational anharmonicity constants ω_eχ_e of diatomic molecules. The procedure involves fitting of the potential energy curve obtained by the RKRV method with that obtained by using the 5-parameter Hulburt-Hirschfelder potential function. We have predicted values of ω_eχ_e for alkali halides for which accurate data are not available.     

The photoelectron spectra of gaseous silver halides

Ionization potentials have been determined for gaseous AgCl, AgBr and AgI using He(I) photoelectron spectroscopy. The solids were vaporized directly into the photon beam from a heated substrate. Molecular orbitals were assigned to observed spectral bands based upon simple molecular orbital arguments, band intensity relationships and observed spin—orbital splitting. The spectra of the gaseous silver halides are more complex than those of other diatomic halides as a result of Ag(d)-X(π) interactions which occur in these molecules.     

Dispersion of the stress optic coefficient of the alkali halides

The dispersion of the stress optic coefficient C=n³/2 (q₁₁?q₁₂) of the alkali halides, NaCl, KCl, KBr and KI have been measured from the visible to the ultraviolet region. In general the value of “C” decreases with wavelength for all crystals. While the dispersion is only a few per cent in the visible region of wavelengths, it is enormous in the ultraviolet. NaCl shows a dispersion of about 100% from 5800 to 2400 Å; KCl about 200% from 5000 to 2400 Å; KBr about 300% from 5000 to 2400 Å; and KI about 400% from 5000 to 2800 Å. Also the potassium halides exhibit a change in sign of their “C” values in the ultraviolet. In KCl the sign reversal occurs at about 2550 Å; in KBr at 2760 Å and in KI at 3380 Å. Below these wavelengths, the potassium halides belong to the same class inMueller's classification as sodium chloride. The theory ofRamaseshan andSivaramakrishnan based on the assumption that a stress causes a change in the frequencies and oscillator strengths of atoms is unable to explain the observed behaviour of the alkali halides. On the other hand, the mere variation of the ionic refractivities with wavelength is also unable to explain the observed dispersion onMueller's theory. One is forced to assume that the strain polarisability constantK inMueller's theory varies with wavelength. When “K” is calculated from the experimentally observed values of “C”, it is found to increase with decreasing wavelength for all alkali halides. The variation with wavelength of “K” for all the alkali halides can be fitted up well by a formula of the type given byRamaseshan andSivaramakrishnan. Hence it appears that the total dispersion ofC can be explained only when we take into account the variation with wavelength of 1. theLorentz andCoulomb contributions fromMueller's theory and 2. the strain polarisability constant fromRamaseshan andSivaramakrishnan's theory.     

The role of halide ions on the electrochemical behaviour of iron in alkali solutions

Active dissolution and passivation of transition metals in alkali solutions is of technological importance in batteries. The performance of alkaline batteries is decided by the presence of halides as they influence passivation. Cyclic voltammetric studies were carried out on iron in different sodium hydroxide solutions in presence of halides. In alkali solutions iron formed hydroxo complexes and their polymers in the interfacial diffusion layer. With progress of time they formed a cation selective layer. The diffusion layer turned into bipolar ion selective layer consisted of halides, a selective inner sublayer to the metal side and cation selective outer layer to the solution side. At very high anodic potentials, dehydration and deprotonation led to the conversion of salt layer into an oxide.     

Neutral beam sputtering of positive ion clusters from alkali halides

Neutral argon atom beams of 15 keV energy have been used to sputter alkali halides and the ejected positive ions have been analysed in energy, mass and angular distribution.

The use of a neutral beam, rather than an ion beam, minimizes surface charge and the deflection of ejected ions by electrostatic interaction with a charged incident beam.

A cluster component of the form K₂Cl⁺, K₃Cl⁺ ₂ and higher members of the series is found for all alkali halides studied.     

Formation time of F centers in alkali halides

It is argued that in most alkali halides an appreciable fraction of the self-trapped excitons may undergo non-radiative transitions from vibrationally excited states of B_3u to the A_1g state during the relaxation of the self-trapped excitons created by ionizing radiation. Numerical calculations show that the non-radiative transition probabilities, from vibrational levels of B_3u near or above the crossing point of the A_1g and B_3u potential curves to the A_1g state, are consistent with the observed formation times of F centers in various alkali halides. The exceptional case of KI is also discussed.