Solid, regular

Equilibrium in any reaction is determined by a compromise between tendency toward minimum energy f golf balls roll downhill ) and tendency toward maximum randomness. Reaction (29) and reaction (30) both involve increase in randomness since the regular solid lattice dissolves or melts to become part of a disordered liquid state. Both reactions produce ions. But reaction (29) proceeds readily at 25°Q whereas reaction (30) does not... 

The regular tetrahedron is a simple yet elegant geometric form. The ancient Greeks identified it as one of only five regular solids that can be placed inside a sphere so that every vertex touches the surface of the sphere. The Greeks had no idea, however, of the importance that tetrahedral shapes have for the chemical processes of life. 

Unlike the tetrahedron and the octahedron, which are regular solids with four and six equivalent vertices, respectively, the trigonal bipyramid has two sets of vertices that are not equivalent. The axial vertices have three close neighbors, whereas the equatorial vertices have two close neighbors (the axial vertices) and two more that are farther away (the other two equatorial vertices). This nonequivalence of the vertices of a trigonal bipyramid has several important consequences... 

Figure 4.10 (a)-(i) Phase diagrams of the hypothetical binary system A-B consisting of regular solid and liquid solution phases for selected combinations of Q q and Qs°l. The entropy of fusion of compounds A and B is 10 J K 1 mol-l while the melting temperatures are 800 and 1000 K. 

Ihe present paper is intended to review the most important literature in this field and to extend the theory from the widely accepted ideal solid solutions to the more general models of regular solid solutions ( 5), with and without ordering (6 ) or substitutional disorder (2, b, 1). 

Distribution Laws And Regular Solid Solutions. For so-called regular solid solutions (15), Equation (9) still holds but by definition the expression for their enthalpy of mixing is ... 

Figure 4. Distribution of the ionic compounds AX and BX over the solid phase and the aqueous phase for different values of the distribution parameter D under the assumption that AX and BX form homogeneous regular solid solutions with a negative value for the interaction parameter W.

Substitutional Disorder In Regular Solid Solutions. Most simple ionic solutions in which substitution occurs in one sublattice only are not ideal, but regular 2, J3) Most complex ionic solid solutions in which substitution occurs in more than one sublattice are not only regular in the sense of Hildebrand s definition (15) but also exhibit substitutional disorder. The Equations describing the activities of the components as a function of the composition of their solid solutions are rather complex ( 7, V7, 1 ), and these can be evaluated best for each individual case. Both type II and type III distributions can result from these conditions. 

This solid solution still makes up the bulk of the solid particles after equilibration in an aqueous solution (59), since solid state diffusion is negligible at room temperature in these apatites (60), which have a melting point around 1500°C. These considerations and controversial results justify a thermodynamic analysis of the solubility data obtained by Moreno et al (58 ). We shall consider below whether the data of Moreno et al (58) is consistent with the required thermodynamic relationships for 1) an ideal solid solution, 2) a regular solid solution, 3) a subregular solid solution and 4) a mixed regular, subregular model for solid solutions. 

Figure 9. Ultimate activities of OHA and FA at the spinodal compositions in the model of regular solid solutions.

In a theoretical study, Chorny and Krasuk(4) analysed the diffusion process in extraction from simple regular solids, assuming constant diffusivity. 

FIGURE 9.3 Example of a van t Hoff Plot showing regular (solid lines) and irregular (dashed lines) behavior. 

There is a fifth Platonic regular solid too the dodecahedron, which... 

In practice the structure of any given polymer sample is by no means as regular as the above classification would imply and in most cases defies description in terms of recognizable structural elements. For example, Wunderlich64 shows examples of cobweb structures which can be found in polymers. Clearly, for the purposes of research specific structures have been identified and studied - but this does not mean that a regular solid of macroscopic dimensions may be contracted with these structures. In polymers therefore, we always have to deal with statistical assemblies of elements more or less precisely defined as e.g. lamellar crystal, fibrous crystals, tie chains etc. 

Figure B.2 shows polyhedra commonly encountered. The five Platonic (or regular) solids are shown at the top. Beside the octahedron and cube, the octahedron is shown inside a cube, oriented so the symmetry elements in common coincide. These solids are conjugates one formed by connecting the face centers of the other. The tetrahedron is its own conjugate, because connecting the face centers gives another tetrahedron. The icosahedron and pentagonal dodecahedron are conjugates. The square antiprism and trigonal...

Thompson, D A. W. 1925 On the thirteen semi-regular solids of Archimedes, and on their development by the transformation of certain plane configurations. Proc. R. Soc. Lond. A 107, 181-188. 

The function x can be represented in x by a sum of regular solid harmonic functions,... 

The complementary potential Ad or generalized Madelung term is expanded in regular solid harmonics as... 

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