Simple binary materials

One way of combining the responses is shown across the top of the figure. We form a sum of responses or force-flux relations for component A by itself, do the same for component B by itself, and then face the question how will A and B interfere and make their combined response different from the simple sum of their in-isolation responses This method can employ eqn. (12.8)  

The method was used in Chapter 14 and quickly showed the general form of the result there sought, but left open the matter of properly quantifying the interactions of A and B. 

The reason that box (ii) also becomes vacant lies in the exchange process if we treat atoms as spherical and the substrate is isotropic, all effects of such an exchange must be isotropic, so that effects linked to the nonhydrostatic 

Consequences of the second approach are that we usually do not need eqn. (12.8) in its full form. For the joint field, eqn. (12.7) is general enough, 

In a sense we treat the material as a gas dissolved in a continuum. The continuum part is chemically inert but responds in the classical way to the total stress field, both the mean stress and the deviatoric stress and their gradients it supports the whole of the nonhydrostatic stress components. The gas part has a completely different mobility coefficient, and the idea of its being affected by the deviation of the stress state from hydrostatic is rejected. 

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Although irreversible thermodynamics neatly defines the driving forces behind associated flows, so far it has not told us about the relationship between these two properties. Such relations have been obtained from experiment, and famous empirical laws have been established like those of Fourier for heat conduction, Fick for simple binary material diffusion, and Ohm for electrical conductance. These laws are linear relations between force and associated flow rates that, close to equilibrium, seem to be valid. The heat conductivity, diffusion coefficient, and electrical conductivity, or reciprocal resistance, are well-known proportionality constants and as they have been obtained from experiment, they are called phenomenological coefficients Li /... 

The conclusion is that even for a simple binary material, we should not look for a single factor K constructed from and K as in eqn. (14.9). 

The distinction now being emphasized between a-terms and star-terms was shown diagrammatically in Figure 15.3b with black and white arrows. It is a distinction easy to make in (A, B)X compounds and less easy to make in simple binary materials. One purpose of this review chapter is to identify aspects that are not yet fully worked out, that are currently fuzzy, and binary materials such as alloys are one such aspect. Clearly, to some extent binary alloy behavior can be described as joint behavior with some interdiffusive... 

The conclusion is that for simple binary materials, to work with K and with a joint velocity field and an exchange velocity field, is the preferred approach, as it is for materials of type (A, B)X. It seems that even when no stoichiometry constraint operates, to use an atom-for-atom scheme for describing changes of composition is an efficient way to work. 

The majority of bacteria reproduce-by simple binary fission the circular chromosome divides into two identical circles which segregate at opposite ends ofthe cell. At the same time, the cell wall is laid down in the middle ofthe cell, which finally grows to produce two new cells each with its own wall and nucleus. Each ofthe two new cells will be an exact copy of the original cell from which they arose and no new genetic material is received and none lost. 

Consider the material balance for a simple binary distillation column. A simple column has one feed, two products, one reboiler and one condenser. Such a column is shown in Figure 9.5. An overall material balance can be written as ... 

However, it became evident in the post-war period that, valuable as they were, these band-structure concepts could not be applied even qualitatively to key systems of industrial interest notably steels, nickel-base alloys, and other emerging materials such as titanium and uranium alloys. This led to a resurgence of interest in a more general thermodynamic approach both in Europe (Meijering 1948, Hillert 1953, Lumsden 1952, Andrews 1956, Svechnikov and Lesnik 1956, Meijering 1957) and in the USA (Kaufman and Cohen 1956, Weiss and Tauer 1956, Kaufman and Cohen 1958, Betterton 1958). Initially much of the work related only to relatively simple binary or ternary systems and calculations were performed largely by individuals, each with their own methodology, and there was no attempt to produce a co-ordinated framework. 

The quest for higher transition temperatures in superconductors took a strange turn when ceramic materials, possessing good, room-temperature metallic conductivity, were investigated. A study of simple binary compounds such as ZrN (Tc = 10.7 K), NbC (Tc =... 

Whereas the development of crystalline, open-frameworks based upon silicates, phosphates and related materials has progressed at an ever increasing pace, the synthesis of simple binary oxides with periodic open stmctures has been less sue-... 

Chemistry. We shall assume rather simple chemistry. In some of the discussion, the material will be as simple as ice, that is to say of a single, fixed composition and at other times we shall consider binary mixtures such as the sulfide (Zn, Fe)S—which can be thought of as a mixture of ZnS and FeS—or a polymer mixture of trifluorethylene and tetrafluorethylene. With such a binary material, there is the possibility of variation in composition within a sample. One might say that the purpose of the book is to learn to understand how nonhydrostatic stress can affect such variations in composition. 

In addition to the extremely wide variety of simple binary spinels, it is possible to prepare many solid solutions series. The major advantage of forming solid solutions is that their physical properties vary continuously with composition, thus leading to the possibility of material design for specific applications. The cations forming spinel solid solutions appear in Table 2.4. Solid solutions involving the substitution of one divalent cation by another, or by a combination of divalent cations, are first discussed. 

In this and the following chapter, we will describe the most important simple (binary) crystal structures found in ceramic materials. You need to know the structures we have chosen because many other important materials have the same structures and because much of our discussion of point defects, interfaces, and processing will use these materials as illustrations. Some, namely FeSi, TiOi, CuO, and CU2O, are themselves less important materials and you would not be the only ceramist not to know their structure. We include these oxides in this discussion because each one illustrates a special feature that we find in oxides. These structures are just the tip of the topic known as crystal chemistry (or solid-state chemistry) the mineralogist would have to learn these, those in Chapter 7, and many more by heart. In most examples we will mention some applications of the chosen material. 

Schottky defects do not change the composition of the material. The concentration of Schottky defects in a crystal is deduced using standard statistical mechanics that appears in most thermodynamics textbooks (because it is such a clear application of basic thermodynamics). For most ceramics, we just need the result from the calculation. Notice that charge is not mentioned and the derivation assumes a pure simple binary compound, like MgO or NiAl. 

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