Thermodynamic properties of crystallization

The theoretical calculation of the thermodynamic properties of condensed phases is still in an early stage of development and only the simplest models can be treated quantitatively. For solids the simplest useful theory, that of Debye, assumes that the distribution of vibration frequencies among the atoms in the solid is the same as that of the frequencies of vibration of a continuous medium. The errors introduced by this hypothesis are difficult to estimate. Some progress has, however, been made recently in the direct evaluation of the thermodynamic properties of crystal lattices without having to liken them to continuous media.f... 

Thermodynamic Properties of Crystals in Relation to the Nature and Energy of... 

THERMODYNAMIC PROPERTIES OF CRYSTALS IN RELATION TO THE NATURE AND ENERGY OF THE INTERATOMIC INTERACTION ... 

There is little doubt that direct experimental determination of the heats of atomization, heats of formation of compounds, free energies, and other thermodynamic properties of crystals can provide the basis for theoretical calculations of the bond energies, which are used to establish the nature of bonds. 

Of the next eleven books listed, " comments will be passed on only five. The text by Eyring et fl/. includes consideration of the thermodynamic properties of crystals, black-body radiation, dielectric, diamagnetic, and paramagnetic properties of matter, real gases, equilibrium properties of liquids, liquid mixtures, and surface chemistry. 

FIGURE 18.5 Peter J. W. Debye (1884-1966) was a Dutch-American physical chemist who made important advances in the understanding of ionic solutions and dipoles in molecules. He also formulated an acceptable theory of the thermodynamic properties of crystals at low temperatures. He was awarded the 1936 Nobel Prize in chemistry for his work. 

Before we can discuss in detail the simulation of adsorption and diffusion in zeolites using atomistic simulation we must ensure that the methods and potentials are appropriate for modelling zeolites. The work of Jackson and Catlow reviewed in the previous section shows the success of this approach. Perhaps the most critical test is to apply lattice dynamics and model the effect of temperature as any instability will cause the calculation to fail. Thus we performed free energy minimization calculations on a range of zeolites to test the methodology and applicability to zeolites. As noted in Section 2.2, the extension of the static lattice simulation technique to include the effects of pressure and temperature leading to the calculations of thermodynamic properties of crystals and the theoretical background to this technique have been outlined by Parker and Price [21], and this forms the basis of the computer code PARAPOCS [92] used for the calculations. 

Thermodynamic properties of crystals near 0°K (equation of state, compressibility. ..). 

The quasiharmonic approximation studied in Sects.5.2,3 gives reasonable results for the thermodynamic properties of crystals in which the anhar-monicity is weak and the force constants are renormalized by thermal expansion only. In crystals with very strong enharmonic interactions, however, this approximation breaks down. Examples are the vibrations in rare-gas solids, in particular solid helium, soft modes in ferro-electric phase transitions and melting processes. For these cases a method has been developed, the self-consistent harmonic approximation (SCHA), which allows a qualitative description of the effects of strong anharmonicity. 

An extensive treatment of the thermodynamic properties of second-order phase transitions in magnetic crystals has been given by K. P. Belov, Magnetic Transitions, Consultants Bureau, Enterprises, Inc., New York, 1961. 

One of the first attempts to calculate the thermodynamic properties of an atomic solid assumed that the solid consists of an array of spheres occupying the lattice points in the crystal. Each atom is rattling around in a hole at the lattice site. Adding energy (usually as heat) increases the motion of the atom, giving it more kinetic energy. The heat capacity, which we know is a measure of the ability of the solid to absorb this heat, varies with temperature and with the substance.8 Figure 10.11, for example, shows how the heat capacity Cy.m for the atomic solids Ag and C(diamond) vary with temperature.dd ee The heat capacity starts at a value of zero at zero Kelvin, then increases rapidly with temperature, and levels out at a value of 3R (24.94 J-K -mol-1). The... 

Jorgensen et al. has developed a series of united atom intermolecular potential functions based on multiple Monte Carlo simulations of small molecules [10-23]. Careful optimisation of these functions has been possible by fitting to the thermodynamic properties of the materials studied. Combining these OPLS functions (Optimised Potentials for Liquid Simulation) with the AMBER intramolecular force field provides a powerful united-atom force field [24] which has been used in bulk simulations of liquid crystals [25-27],... 

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. 

The very high friction-sensitivity, particularly of large crystals, and brisance on explosion are to be expected from the thermodynamic properties of the salt. Its great sensitivity, even under water, renders it unsuitable as a practical detonator [1], Spontaneous explosions dining interciystalline transformations have been observed, or on crystallisation from hot water [2], A safe method of preparing solutions in aqueous THF for synthetic purposes is available [3],... 

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. 

Wood B. I (1980). Crystal field electronic effects on the thermodynamic properties of Fe minerals. In Advances in Physical Geochemistry, vol. 1, S. K. Saxena (series ed.). New York-Heidelberg-Berlin Springer-Verlag. 

Wood B. I and Strens R. G. J. (1972). Calculation of crystal field splittings in distorted coordination polyhedra Spectra and thermodynamic properties of minerals. Min. Mag, 38 909-917. 

New applications of the MOLPAK/WMIN computational method for estimating crystal densities of energetic materials have been investigated in collaboration with Prof. Herman L. Ammon and his co-workers at the University of Maryland. Finally, thermodynamic properties of HCTD and PCU have been determined by Prof. G. J. Kabo and his colleagues at Belarussian State University, Minsk, Belarus. 

V. Crystal Structures and Thermodynamic Properties of Simple Actinide Binary 106... 

Table 4.2. Structure and thermodynamic properties of some plastic crystals"... 

In one patented process (19) a m-p-xylene fraction is produced from xylene mixtures by distillation, and is subsequently cooled to about —70° F. to produce p-xylene crystals, which are removed in high purity by filtering or centrifuging. The yield of p-xylene is limited by eutectic formation with m-xylene. As the mixture behaves as an ideal solution, the yield and temperature level can be calculated from the thermodynamic properties of xylenes, which were reported by Kravchenko (12). 

The object of this study was to investigate more closely the influence of a plasticizer on the crystallization behavior of bisphenol A polycarbonate and to deduce some fundamental thermodynamic properties of the polymer. 

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