Solid ideal

The ideal solid erystal eomprises a rigid lattiee of ions, atoms or moleeules, the loeation of whieh are eharaeteristie of the substanee. The regularity of the internal strueture of this solid body results in the erystal having a eharaeteristie shape smooth surfaees or faees develop as a erystal grows, and the planes of these faees are parallel to atomie planes in the lattiee. 

Solid + Liquid Equilibria in Less Ideal Mixtures We should not be surprised to find that the near-ideal (solid + liquid) phase equilibria behavior shown in Figures 8.20 and 8.21 for (benzene + 1,4-dimethylbenzene) is unusual. Most systems show considerably larger deviations. For example, Figure 8.22 shows the phase diagram for. vin-C Hw +. The solid line is the fit of the... 

A further important property which may be shown by a non-Newtonian fluid is elasticity-which causes the fluid to try to regain its former condition as soon as the stress is removed. Again, the material is showing some of the characteristics of both a solid and a liquid. An ideal (Newtonian) liquid is one in which the stress is proportional to the rate of shear (or rate of strain). On the other hand, for an ideal solid (obeying Hooke s Law) the stress is proportional to the strain. A fluid showing elastic behaviour is termed viscoelastic or elastoviseous. 

A true fluid flows when it is subjected to a shear field and motion ceases as soon as the stress is removed. In contrast, an ideal solid which has been subjected to a stress recovers its original state as soon as the stress is removed, The two extremes of behaviour are therefore represented by ... 

The possibility of the expression of the entropy of hydrogen as the sum of these terms was first noted by Giauque, who observed that it indicated the formation of nearly ideal solid solutions between symmetrical and antisymmetrical hydrogen and the retention of the quantum weight 9 for the latter. 

Solubility equilibria are described quantitatively by the equilibrium constant for solid dissolution, Ksp (the solubility product). Formally, this equilibrium constant should be written as the activity of the products divided by that of the reactants, including the solid. However, since the activity of any pure solid is defined as 1.0, the solid is commonly left out of the equilibrium constant expression. The activity of the solid is important in natural systems where the solids are frequently not pure, but are mixtures. In such a case, the activity of a solid component that forms part of an "ideal" solid solution is defined as its mole fraction in the solid phase. Empirically, it appears that most solid solutions are far from ideal, with the dilute component having an activity considerably greater than its mole fraction. Nevertheless, the point remains that not all solid components found in an aquatic system have unit activity, and thus their solubility will be less than that defined by the solubility constant in its conventional form. 

In this case, the melting point of the ideal solid solution should increase linearly as the ration of B/A increases. However, it usually does not. 

The difference between the chemical potential of a pure and diluted ideal gas is simply given in terms of the logarithm of the mole fraction of the gas component. As we will see in the following sections this relationship between the chemical potential and composition is also valid for ideal solid and liquid solutions. 

In the ideal solid solution model used, the enthalpy and entropy of oxidation are independent of composition. 

Figure 2. Idealized solid tumor, after Jain.45 It has been partly cut away to reveal the complex network of blood vessels.

As a first approximation, we may assume that /Agci//AgBr is equal to unity (ideal solid solution) and that the activity ratio of the species in the fluid may be replaced by the concentration ratio... 

The phenomena of surface precipitation and isomorphic substitutions described above and in Chapters 3.5, 6.5 and 6.6 are hampered because equilibrium is seldom established. The initial surface reaction, e.g., the surface complex formation on the surface of an oxide or carbonate fulfills many criteria of a reversible equilibrium. If we form on the outer layer of the solid phase a coprecipitate (isomorphic substitutions) we may still ideally have a metastable equilibrium. The extent of incipient adsorption, e.g., of HPOjj on FeOOH(s) or of Cd2+ on caicite is certainly dependent on the surface charge of the sorbing solid, and thus on pH of the solution etc. even the kinetics of the reaction will be influenced by the surface charge but the final solid solution, if it were in equilibrium, would not depend on the surface charge and the solution variables which influence the adsorption process i.e., the extent of isomorphic substitution for the ideal solid solution is given by the equilibrium that describes the formation of the solid solution (and not by the rates by which these compositions are formed). Many surface phenomena that are encountered in laboratory studies and in field observations are characterized by partial, or metastable equilibrium or by non-equilibrium relations. Reversibility of the apparent equilibrium or congruence in dissolution or precipitation can often not be assumed. 

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 For Simple Ideal solid solutions. If a solid solution of Formula (2) is in eguilibrium with an agueous phase (ag), the distribution of A and B ions between the agueous phase and the solid phase (s) can be represented by ... 

Figure 2. Distribution of the ionic components AX and BX over the solid components 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 ideal solid solutions and that the solid phase is homogeneous.

Distribution Laws for Complex Ideal Solid Solutions. Let AnX and BnX be two ionic compounds which form a series of solid solutions of the Formula ... 

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. 

EQUILIBRIUM BETWEEN AN IDEAL SOLID SOLUTION AND AN IDEAL LIQUID SOLUTION... 

In Chapter 13 we discussed briefly the solid-liquid equilibrium diagram of a feldspar. Feldspar is an ideal, solid solution of albite (NaAlSiaOg) and anorthite (CaAlSi20g) in the solid state as well as an ideal, liquid solution of the same components in the molten state. The relationships that we have developed in this chapter permit us to interpret the feldspar phase diagram (Figure 13.4) in a quantitative way. 

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