Showing papers on "Lattice energy published in 1989"

Structural phase transition and high-pressure elastic behavior of III-V semiconductors

Abstract: We have expressed the Gibbs free energy for III-V compound semiconductors as a function of pressure and charge transfer through three-body interactions. The lattice energy in it has been represented by a three-body potential consisting of the long-range Coulomb and three-body interactions, and the short-range van der Waals attraction and overlap repulsion, effective up to the second-neighbor ions. We have depicted the phase diagrams and found that the abrupt volume collapses at the phase-transition pressures agree fairly well with the observed data. The phase-transition pressures (17.0, 4.0, 17.1, 18.0, 1.0, and 11.0 GPa) obtained by us are in close agreement with the experimental data (18.5, 6.7, 22.0, 8.4, 2.2, and 10.8 GPa) for almost all the semiconductors (GaAs, GaSb, GaP, InAs, InSb, and InP) under consideration. The elastic stiffness constants (${C}_{11}$) have been found to increase with pressure while the shear moduli (${C}_{11}$-${C}_{12}$)/2 and ${C}_{44}$ decrease with it, and this feature is consistent with the experimental observations.

Thermodynamic studies of clathrate hydrates

Abstract: Thermodynamic studies of clathrate hydrates, mainly of structures I and II, are considered in this review which is based on 147 references There are two main subjects The first is the host lattice energy and the guest-host interaction energy, both of these quantities being related to the enthalpy of dissociation and composition of the hydrates The second subject concerns orientational ordering phenomena occurring in both host and guest, as reflected in the low temperature heat capacity The classical theoretical treatment of clathrate formation has been reconsidered on the basis of recent experimental results Particular emphasis has been given to orientational ordering since this topic is undoubtedly central to clarifying the nature of clathrate hydrates

Lattice models of polymer fluids: Monomers occupying several lattice sites. II. Interaction energies

Abstract: Nearest neighbor nonbonded van der Waals interaction energies are appended to the description of lattice models of flexible polymers in which monomers have specific structures and may cover several lattice sites. A formally exact representation is derived for the free energy of multicomponent system of these structured self and mutually avoiding lattice polymers with nearest neighbor van der Waals interactions. Systematic expansions of the free energy are developed in powers of the inverse of the lattice coordination number and the van der Waals energies using the mean field Flory–Huggins approximation as the zeroth order reference. Diagrammatic rules are given for the evaluation of energies, and the free energy of a binary blend is calculated to second order beyond Flory–Huggins theory for polymers with monomers having differing sizes and shapes. The accompanying paper compares these results with experiment and applies them to analyze heats of mixing of blends, their temperature and composition dependenc...

Crystal structures of methylene bromide and methylene iodide

Abstract: The crystal structures of the three solid phases of methylene iodide and the stable phase of deuterated methylene bromide have been determined using the neutron powder profile structure refinement technique. For CH2I2, both phase I at 50K and phase III at 16K, and for CD2Br2, the stable phase at 15K, have eight molecules per unit cell on general sites of the monoclinic space group C2/c. The structure of CH2I2, phase II, has been determined at 16K, 30K, 50K and 255K. This phase is face centred orthorhombic, space group Fmm2, with four molecules per unit cell on sites with C 2v symmetry. Molecular bond lengths and angles are given for all structures. The lattice energy of each structure has been calculated using an empirical potential. Phase II is found to be the most stable phase for CH2I2, but the energy differences between all three phases are small.

Correlation of glass transition temperature and molecular weight: A model based on the principle of corresponding states

Abstract: The molecular weight dependence of the glass transition temperatures of polystyrene, polyα-methyl styrene, polyisopropylα-methyl styrene, polymethylmethacrylate, polyvinylchloride, poly-isobutylene, polyisoprene, and poly-N-octadecylmaleimide is described by an equation developed from the Principle of Corresponding States. A statistical analysis is used to test the adequacy of the equation, and it is shown that from a statistical point of view the three molecular parameters, Se/Sm, e/e, and Ce/Cm, characterizing, respectively, the ratios of contact area, lattice energy, and segmental mobility of end groups relative to repeating segments along the chain, will adequately describe the data. It is also shown that in one limit the equation reduces to the well-known Ueberreiter-Kanig result, which for most cases is a good first approximation to the data. The molecular weight-TG data were used to estimate the depression of the glass transition temperature of polystyrene and polymethylmethacrylate by a series of plasticizers. It was concluded that in the absence of important changes in the molecular structure within a homologous series of polymers, the Principle of Corresponding States can be employed to describe the molecular weight dependence of glass transition temperature over the entire range of available data.

Accelerated convergence treatment of R-n lattice sums

Abstract: The accuracy and speed of evaluation of R−n lattice sums are dramatically improved by taking a Fourier transform of the long-range portion of the sum. The mathematical basis of the method for a composite lattice is reviewed. Formulas for practical evaluation of the sums in any crystal structure are given for n = 1 to 10.

Computer simulation studies of zeolite structure and stability

Abstract: This paper describes applications of the lattice energy minimization method to studies of zeolite structure and relative stability. Particular attention is paid to the effect of the presence of aluminium on the stability of different structures.

Empirical energy parameters for structural modeling of alkali halide crystals in standard formalisms

Abstract: Potential energy parameters, describing Coulombic, van der Waals, and repulsion energies, have been established for each of the nine common alkali halide ions in two forms of the exp-6 potential, with use of the standard, ambient-stable alkali halide crystal structures for reference. The derived potential parameters fir the lattice energies of the stable NaCl-type structures to better than 1 kcal/mol and predict the lattice energies of the stable CsCl-type structures to better than 3 kcal/mol. For the unstable alkali halide structures, lattice constants are predicted to better than 0.2 {angstrom}, in general, while the lattice energies obtained are more positive than for the corresponding stable strucures and agree well with published values where available.

The role of bonding electrons in intermolecular forces; solid acetylene

Abstract: Acetylene crystallizes in orthorhombic Cmca below 133 K and in cubic Pa3 above. We calculate the lattice energy Φ, using pairwise potentials as the terms in two sums, E HFSCF, the Hartree-Fock self-consistent field MO energy with 6–31 G* basis and E disp the dispersion energy. In the latter a more extended basis was used to determine the locations and polarizabilities of the localized MOs in the molecule. The triple bond has by far the largest polarizability, that of the atomic cores being too small to contribute to E disp. Both structures were relaxed by steepest descent and do not change greatly. The results, without corrections for basis set superposition errors (BSSE), were Φ for Pa3, -24·3 kJ mol-1, for Cmca, -23·5 kJ mol-1 (experimental, -21·8 kJ mol-1), the calculated order of stability of the two structures thus being the reverse of that observed. When BSSE corrections were applied in the Pa3 calculations, too large a unit cell dimension and too small a lattice energy were obtained. The better agr...

Single-stage calculation of the total energy of compositionally modulated III-V alloys

Abstract: We consider ternary and quaternary III‐V alloys whose constituent binaries are not lattice matched. The change in energy associated with the development of a composition modulation in these alloys is calculated in a single stage, without splitting it artificially between hypothetical ‘‘chemical’’ and ‘‘elastic’’ parts, as done up to now. The calculation, which consists of a numerical minimization of the microscopic elastic energy of the valence force field model, is illustrated for InxGa1−xAs. For most modulations along low index axes, the total energy is found close to the energy calculated by the two‐stage procedure. This confirms the stabilization by strain of the bulk III‐V alloys, justifies the use of a strain‐independent ‘‘chemical’’ energy in the description of inhomogeneous alloys, and strengthens our earlier demonstration of the reduced stability of the thin epitaxial layers of these alloys.

Nuclear quadrupole coupling in hexachlorometallates A2[MCl6] and A'[MCl6], A⊕, A'2⊕ = several inorganic or organic cations, M = Sn, Pb, Te, Pt

Abstract: The electric field gradient (EFG) at the chlorine site of the hexachlorometallates A2[MCl6] and A'[MCl6], M = Sn, Te, Pb, Pt, and A⊕, A'2⊕ = alkali metal ion, hexahydrated bivalent metal ion, or organic ammonium cation, is investigated and the dependence of the EFG on the size of the cation is discussed. — For the cubic alkali hexachlorometallates the observed trend in the EFG with increasing size of the cation is corroborated by quantum mechanical calculations using the Multiple-Scattering-Xα-method (MS-Xα) and the point charge model. A correlation v(35Cl) ∼ 1/r3 is found, where r is the distance between the ions in the lattice and the chlorine nucleus considered. For hexachlorometallates with organic cations, like pyridine, piperazine, 4-picoline, ethylenediamine, 1.3-propylenediamine, and other aliphatic or aromatic amines, this 1/r3 dependence is found for the averaged 35Cl NQR frequency, too. This is due to the distortion of the [MCl6]2⊕ octahedra, caused by hydrogen bonds N—H…Cl, and to the decrease of the lattice symmetry because of non-sphericity of the cations. — A hydrogen bond has a large influence on the properties of one of the chlorine atoms of the hexachlorometallate complex. The M-Cl distance is increased and therefore the EFG at the nucleus site is decreased. However, the average of the M-Cl bond lengths or the 35Cl NQR frequencies, taken over all six chlorine atoms of a [MCl6]2⊕ complex, is not influenced by the chemical nature of the cation but only by its size or the size of the unit cell, respectively. The increase of 35Cl NQR frequency with increasing size of the cation originates from a decrease of the lattice energy.

Structure of modulated molecular crystals. VI: Lattice-energy analysis of the modulated phase of thiourea

Abstract: Calcul de l'energie reticulaire de la phase modulee unidimensionnelle de la thiouree par une modification du programme wMIN. Deux modeles permettent de decrire les interactions N-H...S

Lattice dynamics and intermolecular forces in P4Se3 derived from the Raman spectra

Abstract: The Raman-active lattice modes of crystalline P4Se3 at room temperature have been calculated in the rigid–body approximation by using estimated atom-atom potentials for the Se atoms. The agreement is satisfactory and reveals several types of couplings of the different degrees of freedom. The calculated lattice energy is of the correct order of magnitude. The potentials obtained show characteristic features which correlate with the presence of short SeSe distances in the crystal.