Isomorphous replacement theory

But many computations of phase-formation based on the application of pseudo-potential, quantum-mechanical techniques, statistic-thermodynamic theories are carried out now only for comparatively small number of systems, for instance [1-3], A lot of papers dedicated to the phenomenon of isomorphic replacement, arrangement of an adequate model of solids, energy theories of solid solutions, for instance [4-7], But for the majority of actual systems many problems of theoretical and prognostic assessment of phase-formation, solubility and stable phase formation are still unsolved. 

The Patterson synthesis (Patterson, 1935), or Patterson map as it is more commonly known, will be discussed in detail in the next chapter. It is important in conjunction with all of the methods above, except perhaps direct methods, but in theory it also offers a means of deducing a molecular structure directly from the intensity data alone. In practice, however, Patterson techniques can be used to solve an entire structure only if the structure contains very few atoms, three or four at most, though sometimes more, up to a dozen or so if the atoms are arranged in a unique motif such as a planar ring structure. Direct deconvolution of the Patterson map to solve even a very small macromolecule is impossible, and it provides no useful approach. Substructures within macromolecular crystals, such as heavy atom constellations (in isomorphous replacement) or constellations of anomalous scattered, however, are amenable to direct Patterson interpretation. These substructures may then be used to solve the phase problem by one of the other techniques described below. 

Two possibilities exist with respect to the disposition of the co-units. In one case the crystalline phase remains pure, i.e. the co-units are excluded from entering the crystal lattice. In the other, the co-unit is allowed to enter the lattice on an equilibrium basis. Typical examples of the latter would be akin to compound formation, or isomorphous replacement, where one unit can replace the other in the lattice. In either of these two main categories ideal conditions are first calculated and analyzed. Subsequently nonideal contributions to both phases can be considered while stiU maintaining equilibrium. There is an analogy here to solution theory and to gases, where equilibrium conditions are established first. In the next step, nonequilibrium effects in either or both phases can be brought to bear on the problem. It needs to be recognized that deviations from equilibrium in copolymers exist and are in fact important. 

A) In the area of isomorphous replacement, there is need to measure quantitatively the extent to which such elements as B, Fe, Cr, Be, and the like can replace Al, P, and Si in 3-dimensional frameworks and the extent to which they are present merely as detrital material. It should also be established how such framework substitutions vary with temperature, according to the physicochemical background theory, and whether pH and other factors can also influence the extent of genuine framework substitution. 

The ammonium theory.—In the ammonium theory of H. Davy, A. M. Ampere, and J. J. Berzelius, it was assumed. that the ammonium compounds contain a metallic radicle, NH4 (4.31,38), which may replace potassium, sodium, etc., in different salts. When ammonia unites with hydrogen chloride, the NH4-radicle is formed which unites with chlorine to form ammonium chloride in the same way that potassium united with chlorine forms potassium chloride. The ammonium theory thus corresponds with the ethyl theory of J. J. Berzelius, and J. von Liebig. The nitrogen is assumed to be quinquevalent, and this is in harmony with the work of V. Meyer and M. T. Lecco, A. Ladenburg, and W. Lossen on the quaternary ammonium baseb, and with the isomorphism of the ammonium and the potassium salts. 

Phosphoric acid was the original of the three water molecule type ,- replacement of these molecules by basic oxides in typical phosphates, investigated by Clark, led Graham to the theory of basicity. In aqueous solutions phosphoric acid has played a no less important part as an example of successive dissociation of hydrogen ions. The theory of isomorphism, enunciated by Mitscherlich and others, was founded on the phosphates and arsenates. 

In accordance with the postulated ideal of a rational reconstruction of scientific developments, structuralists often focused on cases of mere replacement, or on similarity-relations between theories, which are cashed out in terms of approximation or (semantic counterparts of) derivation under ideal conditions (Moulines 1984 Scheibe 1999 Stegmiiller 1979, 1986, ch. 4). Consequently, these conceptions do not straightforwardly translate into definitions of the concept at issue here. At the same time, structuralists tried to capture interesting possible cases of reduction, such as reduction of psychology to physiology. The first influential attempt to characterize this sort of reduction in semantic terms was made by Patrick Suppes. He basically replaced the notion of syntactic derivation by a notion of (partial) structural equivalence, which, in turn, is characterized via the notion of an isomorphism ... 

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