Crystal structure Thermodynamic properties

Chapter 5 summarizes the crystal field spectra of transition metal ions in common rock-forming minerals and important structure-types that may occur in the Earth s interior. Peak positions and crystal field parameters for the cations in several mineral groups are tabulated. The spectra of ferromagnesian silicates are described in detail and correlated with the symmetries and distortions of the Fe2+ coordination environments in the crystal structures. Estimates are made of the CFSE s provided by each coordination site accommodating the Fe2+ ions. Crystal field splitting parameters and stabilization energies for each of the transition metal ions, which are derived from visible to near-infrared spectra of oxides and silicates, are also tabulated. The CFSE data are used in later chapters to explain the crystal chemistry, thermodynamic properties and geochemical distributions of the first-series transition elements. 

M. Dirand, M. Bouroukba, V. Chevallier, D. Petitjean, E. Behar, V, Ruffier-Meray (2002). J. Chem. Eng. Data, 47, 115-143. Normal alkanes, multialkane synthetic model mixtures, and real petroleum waxes Crystallographic structures, thermodynamic properties, and crystallization. 

Dirand, M., Bouroukba, M., Chevallier, V., Petitjean, D., Behar, E., and Ruffier—Meray, V., Normal Alkanes, Multialkane Synthetic Model Mixtures, and Real Petroleum Waxes Crystallographic Structures, Thermodynamic Properties, and Crystallization, /. Chem. Eng. Data, 47,115-143, 2002. 

Volume 1 General Problems and Electron Structure of Crystals Volume 2 Crystal Structure, Lattice Properties, and Chemical Bonds Volume 3 X-Ray and Thermodynamic Investigations Volume 4 Semiconductor Crystals, Glasses, and Liquids... 

The second and the third volumes deal with the correlation between the nature of chemical bonds and the physical properties of crystals, particularly lattice dynamics, and thermodynamic and thermochemical parameters. The second volume is concerned mainly with crystal structure, physical properties, and lattice dynamics. The first part of the third volume reports extensive data on electron distributions and on the effective charges of ions deduced from x-ray diffraction and spectroscopic investigations. The second part of the third volume is concerned mainly with thermodynamic and thermochemical investigations of semiconductor crystals. This part includes also papers concerned with the thermodynamic stability of crystals. 

A central challenge for atomic level simulations of minerals is to be able to model the crystal structure, thermodynamics and atom transport. Clearly, if the same technique is employed then the underlying relationships between these properties can be examined. There are two atomistic simulation techniques that have been used to model these three properties for minerals, lattice dynamics (LD) and molecular dynamics (MD). The aim of this chapter is to describe these techniques and show, via a series of examples, how these methods can be applied. 

The perfect shape of crystals reflects their inner regular construetion from a highly ordered array of molecirles. The structure of a crystal determines thermodynamic properties and can make the erystal as a whole chiral, even if it is built from achiral components. In this section, some special properties of crystals will be looked at which allow for mirror symmetry breaking or amplification, focussing on phase behavioiu studies. Most models discussed here work by imequally distributing enantiomers into different phases. Thus, the net amoimt of both enantiomers stays constant but enrichment in one phase can provide a local enviromnent of high asynunetry. 

General reviews of the structure and properties of liquid crystals can be found in the following G. H. Brown, J. W. Doane, and V. D. Neff. "A Review of the Structure and Physical Properties of Liquid Crystals." CRC Press, Cleveland, Ohio, 1971 P. J. Collings and M. Hind, Introduction to Liquid Crystals. Nature s Delicate Phase of Matter," Taylor and Francis, Inc., Bristol. Pennsylvania, 1997 P. J. Collins, "Liquid Crystals. Nature s Delicate Phase of Matter," Princeton University Press. Princeton. New Jersey, 1990. A thermodynamic description of the phase properties of liquid crystals can be found in S. Kumar, editor, "Liquid Crystals in the Nineties and Beyond, World Scientific, Riven Edge, New Jersey, 1995. 

A number of other thermodynamic properties of adamantane and diamantane in different phases are reported by Kabo et al. [5]. They include (1) standard molar thermodynamic functions for adamantane in the ideal gas state as calculated by statistical thermodynamics methods and (2) temperature dependence of the heat capacities of adamantane in the condensed state between 340 and 600 K as measured by a scanning calorimeter and reported here in Fig. 8. According to this figure, liquid adamantane converts to a solid plastic with simple cubic crystal structure upon freezing. After further cooling it moves into another solid state, an fee crystalline phase. 

A large number of compounds of pharmaceutical interest are capable of being crystallized in either more than one crystal lattice structure (polymorphs), with solvent molecules included in the crystal lattice (solvates), or in crystal lattices that combine the two characteristics (polymorphic solvates) [122,123]. A wide variety of structural explanations can account for the range of observed phenomena, as has been discussed in detail [124,125]. The pharmaceutical implications of polymorphism and solvate formation have been recognized for some time, with solubility, melting point, density, hardness, crystal shape, optical and electrical properties, vapor pressure, and virtually all the thermodynamic properties being known to vary with the differences in physical form [126]. 

Liquid crystals are thermodynamic phases composed of a great many molecules. These molecules, termed mesogens, possess a free energy of formation, of course. LCs (their structure, properties, everything that gives them their unique identity), however, are not defined at the level of the constituent molecules any more than a molecule is defined at the level of its constituent atoms. LCs are supermolecules. How do they differ from supramolecular... 

What was the distinction between quantum chemistry and chemical physics After the Journal of Chemical Physics was established, it was easy to say that chemical physics was anything found in the new journal. This included molecular spectroscopy and molecular structures, the quantum mechanical treatment of electronic structure of molecules and crystals and the problem of chemical binding, the kinetics of chemical reactions from the standpoint of basic physical principles, the thermodynamic properties of substances and calculation by statistical mechanical methods, the structure of crystals, and surface phenomena. 

In the same chapter (Chapter 5), as an introduction to the paragraphs dedicated to the various groups of metals, the values relevant to a number of elementary properties have been collected. These are atomic properties (such as metallic and ionic radii, ionization energies, electronegativities, Mendeleev number, chemical scale, Miedema parameters, etc.), crystal structure and lattice parameters data of the allotropes of the elements, and selected thermodynamic data (melting and boiling temperatures and enthalpies, etc.). All these data indeed represent reference values in the discussion of the alloying behaviour of the elements. 

The theory developed for perfect gases could be extended to solids, if the partition functions of crystals could be expressed in terms of a set of vibrational frequencies that correspond to its various fundamental modes of vibration (O Neil 1986). By estimating thermodynamic properties from elastic, structural, and spectroscopic data, Kieffer (1982) and subsequently Clayton and Kieffer (1991) calculated oxygen isotope partition function ratios and from these calculations derived a set of fractionation factors for silicate minerals. The calculations have no inherent temperature limitations and can be applied to any phase for which adequate spectroscopic and mechanical data are available. They are, however, limited in accuracy as a consequence of the approximations needed to carry out the calculations and the limited accuracy of the spectroscopic data. 

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