Density, thermodynamic

The composition to the melting point is estimated to be 65% Na AlF, 14% NaF, and 21% NaAlF [1382-15-3], The ions Na" and F ate the principal current carrying species in molten cryoHte whereas the AIF is less mobile. The stmctural evidences are provided by electrical conductivity, density, thermodynamic data, cryoscopic behavior, and the presence of NaAlF in the equiUbtium vapor (19,20). 

Silicon dioxide, one of the products of this interaction, is insoluble in pure alkali metal halides and separates from the molten medium owing to the difference in densities. Thermodynamic analysis of the processes of molten iodide purification with different halogenating agents shows that their effectiveness reduces in the sequence SH4 > HI >h [294], An obvious advantage of silicon halides for the purification of halide melts used for singlecrystal growth is the fact that their use does not result in the appearance of additional impurities in the purified melts, since these processes are usually performed in quartz (Si02) vessels-reactors. 

One last concept must be considered with respect to the thermodynamic aspects of solubility—the condition of equilibrium in mixtures that contain two or more phases. What specific conditions must be met for a particular mixture to be regarded as being in thermodynamic equilibrium A particularly important requirement is that the chemical potential of each component must be the same in all the phases that are present. Numerous boundary conditions apply to this requirement, which have been discussed elsewhere [34]. By introducing the concepts of field and density thermodynamic variables, Griffiths and Wheeler were able to restate the condition of equilibrium for heterogeneous mixtures in a particularly simple, rigorous, and elegant form [35,36]. 

Properties of Liquids 4 3.1 Thermodynamic Properties of Liquids 43.1.1 Liquid Densities... 

Properties of Gases 4 4.1 Thermodynamic Properties of Gases 4.4.1.1 Gas Density... 

Two simulation methods—Monte Carlo and molecular dynamics—allow calculation of the density profile and pressure difference of Eq. III-44 across the vapor-liquid interface [64, 65]. In the former method, the initial system consists of N molecules in assumed positions. An intermolecule potential function is chosen, such as the Lennard-Jones potential, and the positions are randomly varied until the energy of the system is at a minimum. The resulting configuration is taken to be the equilibrium one. In the molecular dynamics approach, the N molecules are given initial positions and velocities and the equations of motion are solved to follow the ensuing collisions until the set shows constant time-average thermodynamic properties. Both methods are computer intensive yet widely used. 

Density functional theory from statistical mechanics is a means to describe the thermodynamics of the solid phase with information about the fluid [17-19]. In density functional theory, one makes an ansatz about the structure of the solid, usually describing the particle positions by Gaussian distributions around their lattice sites. The free... 

Ire boundary element method of Kashin is similar in spirit to the polarisable continuum model, lut the surface of the cavity is taken to be the molecular surface of the solute [Kashin and lamboodiri 1987 Kashin 1990]. This cavity surface is divided into small boimdary elements, he solute is modelled as a set of atoms with point polarisabilities. The electric field induces 1 dipole proportional to its polarisability. The electric field at an atom has contributions from lipoles on other atoms in the molecule, from polarisation charges on the boundary, and where appropriate) from the charges of electrolytes in the solution. The charge density is issumed to be constant within each boundary element but is not reduced to a single )oint as in the PCM model. A set of linear equations can be set up to describe the electrostatic nteractions within the system. The solutions to these equations give the boundary element harge distribution and the induced dipoles, from which thermodynamic quantities can be letermined. 

The critical pressure, critical molar volume, and critical temperature are the values of the pressure, molar volume, and thermodynamic temperature at which the densities of coexisting liquid and gaseous phases just become identical. At this critical point, the critical compressibility factor, Z, is ... 

Molality is used in thermodynamic calculations where a temperature independent unit of concentration is needed. Molarity, formality and normality are based on the volume of solution in which the solute is dissolved. Since density is a temperature dependent property a solution s volume, and thus its molar, formal and normal concentrations, will change as a function of its temperature. By using the solvent s mass in place of its volume, the resulting concentration becomes independent of temperature. 

We shall devote a considerable portion of this chapter to discussing the thermodynamics of mixing according to the Flory-Huggins theory. Other important concepts we discuss in less detail include the cohesive energy density, the Flory-Krigbaum theory, and a brief look at charged polymers. 

Next we consider how to evaluate the factor 6p. We recognize that there is a local variation in the Gibbs free energy associated with a fluctuation in density, and examine how this value of G can be related to the value at equilibrium, Gq. We shall use the subscript 0 to indicate the equilibrium value of free energy and other thermodynamic quantities. For small deviations from the equilibrium value, G can be expanded about Gq in terms of a Taylor series ... 

The mineralogical, structural, physical, and thermodynamic properties of the various crystalline alumiaa hydrates are Hsted ia Tables 1, 2, and 3, respectively. X-ray diffraction methods are commonly used to differentiate between materials. Density, refractive iadex, tga, and dta measurements may also be used. 

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