Component isomorphous

Mol% of first Type of component isomorphism Chain conformation... 

Monomer giving isomorphous copolymers component isomorphism Chain conformation Techniques Refs. 

A binary alloy of two components A and B with nearest-neighbour interactions respectively, is also isomorphic with the Ising model. This is easily seen on associating spin up with atom A and spin down with atom B. There are no vacant sites, and the occupation numbers of the site are defined by... 

Consider, for definiteness, a set of otherwise identical lowest-level components of a system, so that the hierarchy is a tree of constant depth. Since we assume that the components are all identical, the only distinction among the various nodes of the hierarchy consists of the structure of the subtrees. Now suppose we have a tree T that consists of /3 subtrees branching out from the root at the top level. We need to determine the number of different interactions that can occur on each level, independent of the structure of each subtree i.e. isomorphic copies of trees do not contribute to our count. We therefore need to find the number of nonisomorphic subtrees. We can do this recursively. 

Specific Heats of Solid Mixtures.—The specific heat of a homogeneous solid mixture of solid components is not usually additively composed of the specific heats of the latter. W. Spring (1886) found that the total heat capacity of alloys of lead and tin was always greater than the sum of those of the components, but above the melting-point the two were equal. A. Bogojawlensky and N. Winogradoff (1908) find, however, that the heat capacities of the isomorphous mixtures ... 

In the four isomorphous structures the different guest components are located in a similar crystalline environment. Since the species involved are of nearly identical... 

Once a suitable crystal is obtained and the X-ray diffraction data are collected, the calculation of the electron density map from the data has to overcome a hurdle inherent to X-ray analysis. The X-rays scattered by the electrons in the protein crystal are defined by their amplitudes and phases, but only the amplitude can be calculated from the intensity of the diffraction spot. Different methods have been developed in order to obtain the phase information. Two approaches, commonly applied in protein crystallography, should be mentioned here. In case the structure of a homologous protein or of a major component in a protein complex is already known, the phases can be obtained by molecular replacement. The other possibility requires further experimentation, since crystals and diffraction data of heavy atom derivatives of the native crystals are also needed. Heavy atoms may be introduced by covalent attachment to cystein residues of the protein prior to crystallization, by soaking of heavy metal salts into the crystal, or by incorporation of heavy atoms in amino acids (e.g., Se-methionine) prior to bacterial synthesis of the recombinant protein. Determination of the phases corresponding to the strongly scattering heavy atoms allows successive determination of all phases. This method is called isomorphous replacement. 

Also important are exchange-promotional structural interactions that determine isomorphism, solubility of components in solid, liquid and molecular media [2],... 

In particular, electron transfer results in that phosphoric acid molecules present in ATP, NADP and NADPN contain oxygen atoms in the form of O". Spatial-energy interactions (including isomorphic) are objectively expressed both at similar and opposite electrostatic charge of atoms-components. Such interactions can also take place between two heterogeneous atoms, if only their PE-parameters are roughly equal, and geometric shapes of orbitals are similar or alike. 

Complete 100% isomorphism, complete isomorphous replacement of atoms-components ... 

Sorption processes are influenced not just by the natures of the absorbate ion(s) and the mineral surface, but also by the solution pH and the concentrations of the various components in the solution. Even apparently simple absorption reactions may involve a series of chemical equilibria, especially in natural systems. Thus in only a comparatively small number of cases has an understanding been achieved of either the precise chemical form(s) of the adsorbed species or of the exact nature of the adsorption sites. The difficulties of such characterization arise from (i) the number of sites for adsorption on the mineral surface that are present because of the isomorphous substitutions and structural defects that commonly occur in aluminosilicate minerals, and (ii) the difference in the chemistry of solutions in contact with a solid surface as compound to bulk solution. Much of our present understanding is derived from experiments using spectroscopic techniques which are able to produce information at the molecular level. Although individual methods may often be applicable to only special situations, significant advances in our knowledge have been made... 

Almost all the crystalline materials discussed earlier involve only one molecular species. The ramifications for chemical reactions are thereby limited to intramolecular and homomolecular intermolecular reactions. Clearly the scope of solid-state chemistry would be vastly increased if it were possible to incorporate any desired foreign molecule into the crystal of a given substance. Unfortunately, the mutual solubilities of most pairs of molecules in the solid are severely limited (6), and few well-defined solid solutions or mixed crystals have been studied. Such one-phase systems are characterized by a variable composition and by a more or less random occupation of the crystallographic sites by the two components, and are generally based on the crystal structure of one component (or of both, if they are isomorphous). 

Now let us consider the fixed point set of the C -action. In the case of A/"s, the obvious component of the fixed point set is Afs which corresponds to the set of a point of the form ( /,0) G A/s- There exist other components, and this shows that A/s is not exactly the same as T Afs- These components are described as follows. By definition E, ) G A/s is a fixed point if and only if there exists an isomorphism between ( , ) and E,t ). This... 

Now that we can determine overall compositions on a ternary diagram, we can retnm to the issue of representing temperature in the diagram. As mentioned earlier, the temperature axis is perpendicular to the compositional, triangular plane, as shown in Figure 2.16 for the case of three components that form a solid solution, a. Recall that in order to form solid solutions, the components must generally have the same crystal structure. Such substances are said to be isomorphous. 

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