Perfectly crystalline solids

Brittle fracture may be considered, therefore, as two layers of atoms being pulled apart until the interatomic forces fall below their maximum (Fig. 8.82). Using this information it is possible to calculate the fracture strength of a perfect crystalline solid (a,h), e.g. 

The Third Law requires that a perfectly crystalline solid of a pure material be present at 0 Kelvin for So to equal zero. Exceptions to the Third Law occur when this is not the case. For example, AgCl(s) and AgBr(s) mix to form a... 

In the case of a perfect crystalline solid, for temperature well below the Debye temperature 0D, a c/T3 versus T graph would give a constant value c/T3 a 1 /dD. However, most crystals show deviations from the Debye s law, in particular c/T3 versus T presents a maximum. This behavior is present also in amorphous solids where the maximum is more evident and appears at temperatures higher than in crystals [40],... 

Third Law of Thermodynamics. Also referred to as the Nernst heat theorem, this law states that it is impossible to reduce the temperature of any system, via a finite set of operations, to absolute zero. For any changes involving perfectly crystalline solids at absolute zero, the change in total entropy is zero (thus, A5qk = 0). A corollary to this statement is that every substance, at T > 0 K, must have a positive and finite entropy value. The entropy of that substance is zero only at absolute zero when that substance is in pure, perfect crystalline form. See Entropy... 

In contrast to AfG° and Afl° which are relative values (representing differences between values for the compound and the elemental reference states, arbitrarily assigned to be zero), standard entropy values, S° (Frame 16, section 16.2) are absolute values. This arises because the entropy of a perfectly crystalline solid at the absolute zero of temperature has a value of zero (Frames 16 and 17), i.e. ... 

THEORETICAL SOLID STATE PHYSICS, Vol. I Perfect Unices in Equilibrium Vol. II Non-Equilibrium and Disorder, William Jones and Norman H. March. Monumental reference work covers fundamental theory of equilibrium properties of perfect crystalline solids, non-equilibrium properties, defects and disbrdered systems. Appendices. Problems. Preface. Diagrams. Index. Bibliography. Total of 1,501pp. 55 x 8)4. Two volumes. Vol. I 65015-4 Pa. 12.95... 

Some of the discussion of bonding theory will concern distorted crystals or crystals with defects then description in terms of bond orbitals will be essential. Description of electronic states is relatively simple for a perfect crystalline solid, as was shown for CsCl in Chapter 2 for these, use of bond orbitals is not essential and in fact, in the end, is an inconvenience. We shall nevertheless base the formulation of energy bands in crystalline solids on bond orbitals, because this formulation will be needed in other discussions at the point where matrix elements must be dealt with, we shall use the LCAO basis. The detailed discussion of bands in Chapter 6 is done by returning to the bonding and antibonding basis. 

Examination of the residual solid is critically important in this case. Sometimes, the residual solid may not be a perfectly crystalline solid salt. If this is the case, it is obvious that the solubility determined only represents the solubility of the particular form that is in equilibrium with the saturated solution. 

The Third Law of Thermodynamics As the temperature of a perfect crystalline solid approaches absolute zero (0 K), disorder approaches zero. 

Chapter 6, which states that the entropy of perfect crystalline solids tends towards zero as absolute zero temperature is approached. This sets a baseline against which the entropy of any substance can be determined from measured heat capacities and the relationship... 

In 1902, T. W. Richards found experimentally that the free-energy increment of a reaction approached the enthalpy change asymptotically as the temperature was decreased. From a study of Richards data, Nernst suggested that at absolute zero the entropy increment of reversible reactions among perfect crystalline solids is zero. This heat theorem was restated by Planck in 1912 in the form The entropy of all perfect crystalline solids is zero at absolute zero.f This postulate is the third law of thermodynamics. A perfect crystal is one in true thermodynamic equilibrium. Apparent deviations from the third law are attributed to the fact that measurements have been made on nonequilibrium systems. 

The difference in entropy between a state at temperature T and the perfect crystalline, solid at absolute zero is obtained by integrating Eq. (5-1) along any reversible path between the state at T and the state at absolute zero. Thus,... 

A significant starting point is provided by the third law of thermodynamics, which states that the entropy of a perfectly crystalline solid is zero at the absolute zero of temperature. The third law allows one to estimate entropy by using the following thermodynamic relation... 

On the molecular level, the entropy of a system is related to the number of accessible microslales. The entropy of the system increases as the randomness of the system increases. The third law of thermodynamics states that, at 0 K, the entropy of a perfect crystalline solid is zero. 

The second law is concerned with changes in entropy (AS). The third law of thermodynamics provides an absolute scale of values for entropy by stating that for changes involving only perfect crystalline solids at absolute zero, the change of the total entropy is zero. This law enables absolute values to be stated for entropies. 

We know that the entropy of a pure, perfect crystalline solid at 0 K is zero and that the entropy increases as the temperature of the crystal is increased. Figure 19.12 shows that the entropy of the solid increases steadily with increasing temperature up to the melting point of the solid. When the solid melts, the atoms or molecules are free... 

For perfect, crystalline solids, the entropy at 0 K is zero, Sc° = 0. Thus, absolute entropies can be calculated directly. Information to the available data is given in Table 1. For crystalline, linear macromolecnles, the derived thermodynamic functions are reported as follows... 

In Section 5.5 we discussed how calorimetry can be used to measure AH for chemical reactions. No comparable, easy method exists for measuring AS for a reaction. By using experimental measurements of the variation of heat capacity with temperature, however, we can determine the absolute entropy, S, for many substances at any temperature. (The theory and the methods used for these measurements and calculations are beyond the scope of this text.) Absolute entropies are based on the reference point of zero entropy for perfect crystalline solids at 0 K (the third law). Entropies are usually tabulated as molar quantities, in units of joules per mole-Kelvin (J/mol-K). 

This brief review has indicated many of the different kinds of defects which exist in otherwise perfect crystalline solids. Table 1 gives a classification of crystal defects. The purpose of this chapter is to briefly introduce each category of defect to give a broad picture of the complete field so that the individual chapters in this treatise may be placed in proper perspective. The classification is convenient for... 

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