A Quantum Chemical Interpretation of Compressibility in Solids (original) (raw)
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Local compressibilities in crystals
Physical Review B, 2000
An application of the atoms in molecules theory to the partitioning of static thermodynamic properties in condensed systems is presented. Attention is focused on the definition and the behavior of atomic compressibilities. Inverses of bulk moduli are found to be simple weighted averages of atomic compressibilities. Two kinds of systems are investigated as examples: four related oxide spinels and the alkali halide family. Our analyses show that the puzzling constancy of the bulk moduli of these spinels is a consequence of the value of the compressibility of an oxide ion. A functional dependence between ionic bulk moduli and ionic volume is also proposed.
Bonding in molecular crystals from the local electronic pressure viewpoint
Molecular Physics, 2015
The spatial distribution of the internal pressure of an electron fluid, which spontaneously arises at the formation of a molecule or a crystal, is linked to the main features of chemical bonding in molecular crystals. The local pressure is approximately expressed in terms of the experimental electron density and its derivatives using the density functional formalism and is applied to identify the bonding features in benzene, formamide and chromium hexacarbonyl. We established how the spatial regions of compression and stretching of the electron fluid in these solids reflect the typical features of chemical bonds of different types. Thus, the internal electronic pressure can serve as a bonding descriptor, which has a clear physical meaning and reveals the specific features of variety of the chemical bonds expressing them in terms of the electron density.
Physics and Chemistry of Minerals, 2006
The Bader topological analysis has been applied to ab initio computed electron densities of beryl, in order to clarify its mechanism of compression. Full structural optimization and total energy (E) calculations were performed at different cell volumes (V c ). The pressure at each volume and the equation of state were estimated from the first and second derivatives of the resultant E(V c ) curve. The total (negative) potential energy of the crystal, sum of both attractive and repulsive electrostatic terms, was found to systematically decrease (i.e., it moved to more negative values) up to the highest pressure considered (28.4 GPa), indicating that interelectronic and internuclear repulsions are not the only terms controlling the compressibility, at least in the pressure range investigated. Electronic kinetic energy increases as the cell volume is reduced, leading to a parallel increase of the total energy. Both structure at equilibrium and compressibility are therefore due to the balance between the opposing kinetic and potential energy terms. The Bader theory has been used to identify the topological atoms within the structure and to calculate their properties, with particular attention to the forces driving the structural relaxation at high pressure. On a qualitative basis, the obtained results are expected to be transferable to the discussion of compressibility of other mineral phases.
The atomic and group compressibility
Journal of Molecular Structure: THEOCHEM, 2005
Using classical definition of compressibility and the electrostatic attractive force in an atom, a new atomic property, which is called Atomic Compressibility (b) is introduced for atoms. This parameter is calculated for 45 atoms and it is shown that in those cases for which the effective atomic polarizabilities are available (H, C, N, O, F, S, Cl, Br, I), the obtained atomic compressibilities have a linear relation with polarizabilities. Then for a molecule, Group Compressibility (Gb) is defined as the summation of atomic compressibilities of constituted atoms in the molecule. For a wide range of molecules with different functional groups, which their experimental polarizabilities are given in literature, group compressibilities are calculated. A plot of group compressibility vs. polarizability shows considerable linearity (the correlation coefficient is 0.996648).
Pressure dependence of the compressibility of alkali halides
European Physical Journal B, 1985
The parameterC 1=[∂(1/K T )/∂P]T , which describes the pressure variation of the compressibility, has been examined correlating the thermodynamical and interatomic potential approaches employing fewer approximations than has been usual heretofore. General expressions have been derived forC 1 by including the thermal correction terms, which have generally been ignored in previous studies concerning thermal properties of ionic crystals. The parameterC 1 has also been related to the Grüneisen parameter, γ, using a relation given earlier. The applicability of the derived equations is investigated and discussed for alkali halides employing few realistic potential forms. A good general accord is found with the available experimental data, which exhibits an essential improvement over other theoretical determinations.
Physical Review B
Extended x-ray absorption fine-structure studies have been performed at the Zn K and Cd K edges for a series of solid solutions of wurtzite Zn 1−x Cd x S samples with x = 0.0, 0.1, 0.25, 0.5, 0.75, and 1.0, where the lattice parameter as a function of x evolves according to the well-known Vegard's law. In conjunction with extensive, large-scale first-principles electronic structure calculations with full geometry optimizations, these results establish that the percentage variation in the nearest-neighbor bond distances are lower by nearly an order of magnitude compared to what would be expected on the basis of lattice parameter variation, seriously undermining the chemical pressure concept. With experimental results that allow us to probe up to the third coordination shell distances, we provide a direct description of how the local structure, apparently inconsistent with the global structure, evolves very rapidly with interatomic distances to become consistent with it. We show that the basic features of this structural evolution with the composition can be visualized with nearly invariant Zn-S 4 and Cd-S 4 tetrahedral units retaining their structural integrity, while the tilts between these tetrahedral building blocks change with composition to conform to the changing lattice parameters according to the Vegard's law within a relatively short length scale. These results underline the limits of applicability of the chemical pressure concept that has been a favored tool of experimentalists to control physical properties of a large variety of condensed matter systems.
Structure factors and compressibilities of liquid metals
physica status solidi (b), 1982
A shouldered hard sphere interatomic potential is used to evaluate, within the mean spherical approximation, the expsrimental structure factors of 13 liquid metals. For 10 metals, a positive shoulder of the potential is more appropriatz than a squara well potential. A parabolic well potential is also tried and in many cases a, repulsive tail is obtained. The isothsrmal compressibility and the electrical resistivity for some metals are calculatad. A good agreement with experimental values is achieved, especially when a n electronic contribution is introduced for the compressibility. Un potentiel interatomique perturb6 par une marche rkpulsive ou par un puits carrB ib B t 4 utilish pour Bvaluer, nu moyen de I'approxirnation M.S.A., le facteur de structure de 13 m6tanx liqnides. Pour 10 metaux, la marche repulsive rend mieux compte de I'experience. Une perturbation de forme parabolique a Bgalement BtB essay&, e t la conclusion est analogue. La rbsistivite a 6M calculke pour quelques mBtaux, ainsi que la compressibilite isotherme. On obtient un accord satisfaisant avec les valeurs expkrimentales, surtout quand une contribution Blectronique est introdnite pour la compressibilitk.
Physical Review, 1967
Atomic radii in metals at O'K are calculated from shock-wave equation-of-state measurements, and are compared with the radii of various free-atom electron orbitaLs obtained from Hartree-Pock calculations. For metals from the long periods of the periodic table having less than half-6lled conduction bands, the Z dependence of the experimental atomic radii and of the Hartree-Fock, free-atom orbital radii are found to be essentially identical at all pressures. This allows the identi6cation of the dominant contribution to the e8ective interatomic interaction. In these metals it is found that the presence of a signi6cant population in the d band appears to result in a low compressibility. An unusually high compressibility observed for the normally trivalent rare-earth metals is then taken as evidence of the promotion of a sd electron to a 4 f shell under compression. Interactions between closed electron shells in metals are estimated from the experimental equations of state of the rare gases and their isoelectronic alkali halides. In the experimental pressure range, interactions between these closed-shell cores are found to be important only for the rare-earth metals, where an observed stiffening of the Hugoniot is identi6ed as resulting from core interactions. The limits of validity of Thomas-Fermi-like equation-of-state calculations are discussed. Under normal conditions of temperature and pressure, the interatomic spacings and compressibilities of *Work performed under the auspices of the U. S. Atomic Energy Commission.
Journal of Superhard Materials, 2008
A strong correlation relationship has been established between the structure and specific Gibbs free energy of the substance atomization on the one hand, and the substance hardness and volume com pressibility on the other. In the framework of the model proposed hardness is directly proportional to the specific Gibbs free energy per bond in isodesmic crystals. An application of a correction coefficient to the ionic component of chemical bonds allows one to evaluate the hardness of compounds having both the covalent (polar and nonpolar) and ion bonds. In the framework of the suggested approach we have been the first to correctly calculate the temperature dependence of the hardness by the example for diamond and cubic boron nitride.