Solid-phase specific heat

Liquid- and Solid-Phase Specific Heat For an incompressible liquid or solid, the density is constant, so that... 

Fig. 63. Magnetic phase diagnun of TbH(D)2 exhibiting the existence region for the two commensuiate phases (a) and (b) and the incommensurate phase (c) (note the overlap regions ). Crosses, neutron data open circles, resistivity data open squares, susceptibility data, solid diamonds, specific heat data (Vajda et al. 1993).

Here U = T — T )Cp/L is the appropriately rescaled temperature field T measured from the imposed temperature of the undercooled melt far away from the interface. The indices L and 5 refer to the liquid and solid, respectively, and the specific heat Cp and the thermal diffusion constant D are considered to be the same in both phases. L is the latent heat, and n is the normal to the interface. In terms of these parameters,... 

Generally, a phase transition is triggered by an external stress which most commonly is a change in temperature or pressure. Properties that can change discontinuously include volume, density, specific heat, elasticity, compressibility, viscosity, color, electric conductivity, magnetism and solubility. As a rule, albeit not always, phase transitions involve structural changes. Therefore, a phase transition in the solid state normally involves a change from one to another modification. 

Even when complete miscibility is possible in the solid state, ordered structures will be favored at suitable compositions if the atoms have different sizes. For example copper atoms are smaller than gold atoms (radii 127.8 and 144.2 pm) copper and gold form mixed crystals of any composition, but ordered alloys are formed with the compositions AuCu and AuCu3 (Fig. 15.1). The degree of order is temperature dependent with increasing temperatures the order decreases continuously. Therefore, there is no phase transition with a well-defined transition temperature. This can be seen in the temperature dependence of the specific heat (Fig. 15.2). Because of the form of the curve, this kind of order-disorder transformation is also called a A type transformation it is observed in many solid-state transformations. 

Because the melting point of sodium metal is about 98° C (a bit lower than the boihng point of water), it is heated into a liquid phase and then transported in rail tank cars, where it cools and solidifies. When it arrives at its destination, heating coils in the tanks warm it back to the liquid stage, and it is then stored for use. Because sodium has a high specific heat rating, a major use is as a liquid coolant for nuclear reactors. Even though sodium (both solid and liquid) is extremely reactive with water, it has proven safe as a coolant for nuclear reactors in submarines. 

However, most of the examples quoted in these earlier papers do not include the higher melting-point elements such as W, where a detailed treatment shows that the total entropy (at least of the solid phases) must include many other components such as the electronic specific heat, anharmonicity terms and the temperature dependence of 9d (Grimwall et al. 1987, Moroni et al. 1996). An estimate for the Debye temperature of the high-temperature 0 phase was included in the seminal... 

The large phase shifts t 2 give a large enhancement of the resistivity when transitional metals are dissolved in other metals. A survey for solid metals is given by Friedel (1956), and for solutions of Fe and Co in liquid germanium and tin by Dreirach et al (1972). The resonance will also enhance the electronic specific heat and the Pauli paramagnetism, but these quantities cannot be treated quantitatively without including correlation as shown in Chapter 3. 

Cps specific heat capacity of solid phase at constant pressure... 

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