Solid thermodynamic description

Which of the two fragmentation theories is more appropriate has not yet been firmly established. The more recent energy-horizon theory appears to have a more solid thermodynamic basis and the theory has the potential of providing a broader description of spall fragmentation phenomena. 

All approaches are based either on the thermodynamical description of the gas-solid phase transition by classical nucleation theory or on a detailed discussion of the relevant chemical reactions leading finally to critical clusters (e.g. review by Gail, Sedlmayr, 1987d). We will refrain from a presentation of these various approaches but only list the basic molecules from which the primary condensates are likely to be formed ... 

The need to abstract from the considerable complexity of real natural water systems and substitute an idealized situation is met perhaps most simply by the concept of chemical equilibrium in a closed model system. Figure 2 outlines the main features of a generalized model for the thermodynamic description of a natural water system. The model is a closed system at constant temperature and pressure, the system consisting of a gas phase, aqueous solution phase, and some specified number of solid phases of defined compositions. For a thermodynamic description, information about activities is required therefore, the model indicates, along with concentrations and pressures, activity coefficients, fiy for the various composition variables of the system. There are a number of approaches to the problem of relating activity and concentrations, but these need not be examined here (see, e.g., Ref. 11). 

P. D. Glynn and E. J. Reardon, Solid-solution aqueous-solution equilibria Thermodynamic theory and representation, Am. J. Sci. 290 164 (1990), 292 215 (1992) H. Konigsberger and II. Gamsjager, Solid-solution aqueous-solution equilibria Thermodynamic theory and representation, Am. J. Sci. 292 199 (1992). These papers contain comprehensive discussions of the thermodynamic description of solid solutions. See also L. N. Plummer, L. Husenherg, P. I). Glynn, ami A. li. Blum. Dissolution of... 

A thermodynamic description of the defect solid state of linear high polymers. Polymer 5, 125—134 (1964). 

The new assessment for the Si-C system was primarily based on experimental SiC solubility data in liquid solution given by Scace and Slack [34], Hall [35], Iguchi [36], Kleykamp and Schumacher [37], Oden and McCune [38], and Ottem [14], Solid solubility data given by Nozaki et al. [39], Bean [40], and Newman [41] were used to determine the properties of solid solution. The eutectic composition reported by Nozaki et al. [39] and Hall [35] and peritec-tic transformation temperature determined by Scace [34] and Kleykamp [37] were also used in the thermodynamic optimization. Thermodynamic description of the SiC compound was taken from an early assessment [42]. The... 

In pursuing an accurate thermodynamic description of the three-phase, three-component system, the phase equilibrium compositions can be calculated after pressure and temperature have been fixed, since it is known from the Gibbs phase rule that there are only 2 degrees of freedom. There are five unknown compositions, assuming that the solid is crystalline and pure and that its solubility in the vapor/fluid phase is negligible. Two of these unknown mole fractions are eliminated by the constraints that the mole fractions in each phase sum up to unity. To find these three unknown mole fractions, namely, xi, X3, and y2, only three equilibrium relations are required. 

An equally remarkable feature to whidi we shall turn now is the fact that confined fluids may sustain a certain shear stress without exhibiting structural features normally pertaining to solid-like phases that is, they do not necessarily assume any long-range periodic order. We tacitly assumed this from the very beginning of this book in our development of a thermodynamic description of cuiifiiied fluids, wliich closely resembles that appropriate for solid-like bulk phases (see Section 1) (12). 

A complete thermodynamic description of a material under pressure requires knowledge of the (thermal) equation of state (EOS), for example, in the form F = V (p,T) or p = p (p,T), for the specific material, where V is usually the specific volume (the volume per unit mass) or the molar volume and p is the specific density p=l/F. For a rigid cylinder with a fixed amount of a sample enclosed by the piston, the relative change in volume V(p,T)IVo is directly related to the movement of the piston if deformations of the piston and cylinder, and leakage and friction, can be neglected. For pressures below 1 GPa and moderate temperatures these techniques are well developed for liquids and gases. However, for higher pressures and variable temperatures the encapsulation of the sample and the deformation of the pressure vessel need special attention. The state of the art for encapsulated solids corresponds to a precision of only 500 p.p.m. (parts per million) in V/Vq or 3 per... 

The thermodynamic description of an electrified solid-liquid interphase is similar to that of nonionic systems with one important difference—the description requires the introduction of electrochemical parameters the thermodynamic charge and the electrical potential difference between the solid phase considered and a reference electrode. 

It was first observed by Geilikman et al. (1993) that a porosity diffusion process is predicted by the equations of motion associated with this thermodynamic description in the limit when the inertial terms and bulk attenuation are assumed small. Under these assumptions, the equations of motion may be written as follows (Spanos, 2(X)1) first, for the solid, including a source term ... 

The third example involves growth of a crystalline salt phase from the saturated solution. The thermodynamic description again is inadequate for describing the detailed states of the solid. The relatively anhydrous chloride ion readily deposits into the surface lattice but the sodium ion must be dehydrated to form NaCl. This means that water must be diffused away from the surface during solidification. The white cast of salt, termed veiling, involves solution incorporation during growth with a subsequent diffusion of the solvent out of the crystal. 

Surprisingly, there is no complete Calphad assessment of this system available in the literature. [1989Kau] calculated 6 isotherms for the ternary system by combining available thermodynamic descriptions for the binary systems. Some of the modeling was quite primitive by present standards, particularly with respect to the a phase, which was modeled as a substitutional solid solution as opposed to the compound energy model that is used currently. Nevertheless, the calculated and experimental isothermal section for 900°C were in reasonable quahtative agreement. Sadly, the same could not be said for the sections at 600°C. 

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