Thermodynamic properties of solids

Table 2. Physical and Thermodynamic Properties of Solid Hydrogen...

A large number of techniques have been used to investigate the thermodynamic properties of solids, and in this section an overview is given that covers all the major experimental methods. Most of these techniques have been treated in specialized reviews and references to these are given. This section will focus on the main principles of the different techniques, the main precautions to be taken and the main sources of possible systematic errors. The experimental methods are rather well developed and the main problem is to apply the different techniques to systems with various chemical and physical properties. For example, the thermal stability of the material to be studied may restrict the experimental approach to be used. 

Finally, it is not appropriate to derive thermodynamic properties of solid solutions from experimental distribution coefficients unless it can be shown independently that equilibrium has been established. One possible exception applies to trace substitution where the assumptions of stoichiometric saturation and unit activity for the predominant component allow close approximation of equilibrium behavior for the trace components (9). The method of Thorstenson and Plummer (10) based on the compositional dependence of the equilibrium constant, as used in this study, is well suited to testing equilibrium for all solid solution compositions. However, because equilibrium has not been found, the thermodynamic properties of the KCl-KBr solid solutions remain provisional until the observed compositional dependence of the equilibrium constant can be verified. One means of verification is the demonstration that recrystallization in the KCl-KBr-H20 system occurs at stoichiometric saturation. 

In application of this method to solubility data (8) in the KCl-KBr- O system at 25°C, it is found that equilibrium is in general not attained, though some mid-range compositions may be near equilibrium. As the highly soluble salts are expected to reach equilibrium most easily, considerable caution should be exercised before reaching the conclusion that equilibrium is established in other low-temperature solid solution-aqueous solution systems. It is not appropriate to derive thermodynamic properties of solid solutions from experimental distribution coefficients unless it can be demonstrated that equilibrium has been attained. 

In the early part of this century, many types of solid electrolyte had already been reported. High conductivity was found in a number of metal halides. One of the first applications of solid electrolytes was to measure the thermodynamic properties of solid compounds at high temperatures. Katayama (1908) and Kiukkola and Wagner (1957) made extensive measurements of free enthalpy changes of chemical reactions at higher temperatures. Similar potentiometric measurements of solid electrolyte cells are still made in the context of electrochemical sensors which are one of the most important technical applications for solid electrolytes. 

Holder J. and Granato A. V. (1969). Thermodynamic properties of solid containing defects. Phys. Rev., 182 729-741. 

Thermodynamic. The thermodynamic properties of elemental plutonium have been reviewed (35,40,41,43—46). Thermodynamic properties of solid and liquid Pu, and of the transitions between the known phases, are given in Table 5. There are inconsistencies among some of the vapor pressure measurements of liquid Pu (40,41,43,44). 

Calorimetric measurements of specific heats and related thermodynamic properties of solid high polymers represent a fundamental approach to the attainment of an understanding of the solid state. Any... 

In table 5, we list the thermodynamic properties of solid biphenyl at 300 K for all eight potential models. The heat of vapourization AHvap was obtained from the expression. 

Using differential scanning calorimetry (DSC) (or, less directly, differential thermal analysis (DTA)) (see Section 2.8.5., above) it is possible to measure several of the thermodynamic properties of solids and of solid state reactions. The DSC response is directly proportional to the heat capacity, Cp, of the sample, so that by use of a calibrant it is possible to obtain values of this fundamental thermodynamic property, at a particular temperature, or as an average over a specified temperature range. Other thermodynamic properties are readily derived from such measurements ... 

Table V-11 Thermodynamic properties of solid monoclinic Zr02...

A knowledge of the vibration spectrum of oscillation of ions and electrons in a crystal at different temperatures and external fields solves, to some extent, the problem of the thermodynamic properties of solids. The value of the internal energy U, the specific heat cy, and other thermodynamic functions is expressed directly in terms of the density of the frequency distribution g(u) and the average energy of the oscillators ... 

The introduction of new methods [12-17], which have been semiempirlcally extended also to the liquid and solid phases [17], seems to have opened the way for a more effective study of the thermodynamic properties of solids, and particularly of semiconductors. 

Althou, in principle, the general theory is superior to the band theory, the appropriate techniques for its application are not yet developed sufficiently well and a unified approach to a quantitative description of the structures and the physical properties of crystals is still lacking. The less generally valid band theory can at present give clearer and more convincing explanations of changes in the physical properties of crystals caused by variations in the temperature, pressure, magnetic and electric fields intensities, impurity concentrations, etc. However, many problems encoimtered in the study of chemical bonds in crystals cannot be considered within the framework of the standard band theory. They include, for example, determination of the elastic, thermal, and thermodynamic properties of solids, as well as the structure and properties of liquid and amorphous semiconductors. 

MOLECULAR ENERGY STATES AND THE THERMODYNAMIC PROPERTIES OF SOLID ISOTOPIC METHANES. 

Shortly after the discovery of Isotopes Fajans ( recognized that the thermodynamic properties of solids, which depend on the frequencies of atomic and molecular vibrations, must be different for isotopes. This idea was put into quantitative form Independently by Stern ( ) and Lindemann (, ) ... 

In summary, IGC is a simple, relatively inexpensive approach using standard GC instrumentation to obtain the surface thermodynamic properties of solids. The theoretical interpretation of the experimental resnlts is now well established, and the deduction of acid-base properties of materials can now be regarded as being routine. IGC provides a complementary method to the nse of wetting Uqnids, insomuch as it probes the microscopic properties of the solid surface, (as the probe molecules are invariably small and in the gaseous phase, and are at infinite dilntion, i.e. there is no interaction between adjacent probe molecules on the solid snrface or in the gas phase), while the use of liquids in techniques such as dynamic contact angle analysis probes the macroscopic properties. 

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