Some Basic Properties and Their Measurement

A solid phase responds to a small applied stress by undergoing a small elastic deformation. When the stress is removed, the solid returns to its initial shape and the properties return to those of the unstressed solid. Under these conditions of small stress, the solid has an equation of state just as a fluid does, in which p is the pressure of a fluid surrounding the solid (the hydrostatic pressure) as explained in Sec. 2.3.4. The stress is an additional independent variable. For example, the length of a metal spring that is elastically deformed is a unique function of the temperature, the pressure of the surrounding air, and the stretching force. 

however, the stress applied to the solid exceeds its elastic limit, the response is plastic deformation. This deformation persists when the stress is removed, and the unstressed solid no longer has its original properties. Plastic deformation is a kind of hysteresis, and is caused by such microscopic behavior as the slipping of crystal planes past one another in a crystal subjected to shear stress, and conformational rearrangements about single bonds in a stretched macromolecular fiber. Properties of a solid under plastic deformation depend on its past history and are not unique functions of a set of independent variables an equation of state does not exist. 

---

CHAPTER 2 SYSTEMS AND THEIR PROPERTIES 2.3 Some Basic Properties and Their Measurement... 

This chapter begins by explaining some basic terminology of thermodynamics. It discusses macroscopic properties of matter in general and properties distinguishing different physical states of matter in particular. Virial equations of state of a pure gas are introduced. The chapter goes on to discuss some basic macroscopic properties and their measurement. Finally, several important concepts needed in later chapters are described thermodynamic states and state functions, independent and dependent variables, processes, and internal energy. 

Ultrasonics is in many ways the ideal measurement method for fat crystallization studies. The ultrasonic properties of a fat are strongly sensitive to solids content and can be measured in opaque fats and through container walls. In the present work I will describe the basic physics of ultrasonic waves, their interactions with matter (particularly with semi-solid fats), and their measurement. I will then describe ultrasonic studies of fat crystallization in bulk and emulsified fats. Finally I will use some measurements of the effect of applied shear on fat crystallization as an illustration of a study that could not be easily undertaken by other methods. 

Abstract. Investigation of P,T-parity nonconservation (PNC) phenomena is of fundamental importance for physics. Experiments to search for PNC effects have been performed on TIE and YbF molecules and are in progress for PbO and PbF molecules. For interpretation of molecular PNC experiments it is necessary to calculate those needed molecular properties which cannot be measured. In particular, electronic densities in heavy-atom cores are required for interpretation of the measured data in terms of the P,T-odd properties of elementary particles or P,T-odd interactions between them. Reliable calculations of the core properties (PNC effect, hyperfine structure etc., which are described by the operators heavily concentrated in atomic cores or on nuclei) usually require accurate accounting for both relativistic and correlation effects in heavy-atom systems. In this paper, some basic aspects of the experimental search for PNC effects in heavy-atom molecules and the computational methods used in their electronic structure calculations are discussed. The latter include the generalized relativistic effective core potential (GRECP) approach and the methods of nonvariational and variational one-center restoration of correct shapes of four-component spinors in atomic cores after a two-component GRECP calculation of a molecule. Their efficiency is illustrated with calculations of parameters of the effective P,T-odd spin-rotational Hamiltonians in the molecules PbF, HgF, YbF, BaF, TIF, and PbO. 

Isotope dilution mass spectrometry (IDMS) can be considered as a special case of the internal standard method the internal standard that is used is an isotopomer of the compound to be measured, for example a deuterated derivative. Note that an internal standard is necessary for every compound to be measured. This internal standard is as close as possible to perfection since the only property that distinguishes it from the compound to be measured is a slight mass difference, except for some phenomena that involve the labelled atoms, such as the isotopic effect. In that case, we have an absolute reference, that is the response coefficients of the compound and of the standard are identical. This method is often used to establish standard concentrations. The basic theory of this method rests on the analogy between the relative abundance of isotopes and their probability of occurrence [23]. 

Some substances with very weakly basic properties are only partially ionized in sulfuric acid and it is possible to measure their degree of ionization and hence obtain their basicity constants by means of cryo-scopic, conductimetric, and spectroscopic measurements. A number of nitro-compounds have been carefully studied by several different methods. It may be seen in Table IX that the results obtained by the differ-... 

The influence of solvents on the ionization equilibrium is related to their electrostatic and their solvation properties. The value of the ionization constant of an analyte is closely determined, in practice, by the pH scale in the particular solvent. It is clear that it is most desirable to have a universal scale which is able to describe acidity (and basicity) in a way that is generally valid for all solvents. It is, in principle, not the definition of an acidity scale in theory which complicates the problem it is the difficulty of approximating the measured values in practice to the specifications of the definition. The pH scale, as is common in water, is applicable only to some organic solvents (i.e., mainly those for which the solvated proton activity is compatible with the Brpnsted theory of acidity). The applicability of an analog to the pH scale in water decreases with decreasing relative permittivity of the solvents and with their increasing aprotic character. 

Dielectric constants cannot explain, quantitatively, most physicochemical properties and laws of solutions, and we shall soon see that they can become unimportant. The molecules of more polar solvents, which tend to cluster around the ions and dipole ions, produce a preferential or selective solvation that is reflected in measurements of such properties as solubility, acid—base equilibria, and reaction rates. Nonelectrostatic effects, such as the basicity of some solvents, their hydrogen-bonding, and the internal cohesion and the viscosity of mixtures, probably interfere with the electrostatic effects and thus reduce their actual influence. On the other hand, mixtures of water and nonaqueous solvents are enormously complicated systems, and their effective microscopic properties may be vastly different from their macroscopic properties, varying with the solute because of selective attraction of one of the solvents for the solute. 

Acid-base properties of oxide surfaces are employed in many fields and their relationship with PZC has been often invoked. Adsorption and displacement of different organic molecules from gas phase was proposed as a tool to characterize acid-base properties of dry ZnO and MgO [341]. Hammet acidity functions were used as a measure of acid-base strength of oxides and some salts [342]. Acidity and basicity were determined by titration with 1-butylamine and trichloroacetic acid in benzene using indicators of different pAg. There is no simple correlation between these results and the PZC. Acid-base properties of surfaces have been derived from IR spectra of vapors of probe acids or bases, e.g. pyridine [343] adsorbed on these surfaces. The correlation between Gibbs energy of adsorption of organic solvents on oxides calculated from results obtained by means of inverse gas chromatography and the acceptor and donor ability of these solvents was too poor to use this method to characterize the donor-acceptor properties of the solids [344],... 

Initially, some relevant thermodynamic and molecular properties of polar solvents are considered. Then, their dielectric properties are considered in detail. Ion solvation in these solvents is also discussed with emphasis on some non-thermo-dynamic methods of dividing experimentally measured data for electrolytes into contributions for the cation and anion. Finally, the important characteristics of the solvent in its direct interaction with the solute, namely, its acidity and basicity, are also described. 

X-ray and electron diffraction methods are applied in order to measure atomic distances in the crystal lattice and their changes. Hence, the diffraction methods are also basically suitable for measuring the strain/stress behaviour in thin films. However, since the film thickness and the crystallite size in thin films are small, some line broadening already arises from this. In order to determine what contribution the mechanical stresses have on the diffuse lines, careful analysis of the line profiles must be undertaken [148, 151]. This method is less suitable for routine determination of stresses in thin films. In some cases, it is possible though rarely applied to determine the stresses in the films through their influence on other, known film properties, at least approximately. Such properties are, for example, the position of an absorption edge [152], the Hall effect [153], electron spin resonance spectra [155] and in the case of superconducting films, variations in the critical transition temperature [156]. However, these effects can, unfortunately, also arise for other reasons, and thus these techniques can usually only be used as supplemental experiments. 

The atomic theory of matter, which was conjectured on qualitative empirical grounds as early as the sixth century BC, was shown to be consistent with increasing experimental and theoretical developments since the seventeenth century AD, and definitely proven by the quantitative explanation of the Brownian motion by Einstein and Perrin early in the twentieth century [1], It then took no more than a century between the first measurements of the electron properties in 1896 and of the proton properties in 1919 and the explosion of the number of so-called elementary particles - and their antiparticles - observed in modern accelerators to several hundred (most of which are very short lived and some, not even isolated). Today, the standard model assumes all particles to be built from three groups of four basic fermions - some endowed with exotic characteristics - interacting through four basic forces mediated by bosons - usually with zero charge and mass and with integer spin [2],... 

---