Binary structure

The classical computer tomography (CT), including the medical one, has already been demonstrated its efficiency in many practical applications. At the same time, the request of the all-round survey of the object, which is usually unattainable, makes it important to find alternative approaches with less rigid restrictions to the number of projections and accessible views for observation. In the last time, it was understood that one effective way to withstand the extreme lack of data is to introduce a priori knowledge based upon classical inverse theory (including Maximum Entropy Method (MEM)) of the solution of ill-posed problems [1-6]. As shown in [6] for objects with binary structure, the necessary number of projections to get the quality of image restoration compared to that of CT using multistep reconstruction (MSR) method did not exceed seven and eould be reduced even further. 

Often the a priori knowledge about the structure of the object under restoration consists of the knowledge that it contains two or more different materials or phases of one material. Then, the problem of phase division having measured data is quite actual. To explain the mathematical formulation of this information let us consider the matrix material with binary structure and consider the following potentials ... 

Fig. 3.7 Plot of the D parameter of cations (DJ against the D parameter of anions (Da) for selected binary structures. Compounds with homoatomic bonds are excluded.

By XPS spectra, Endo et al. [96] confirmed that formation of binary structure prevented Pd atoms from oxidation in the AuPd and PtPd bimetallic nanoparticles which exhibited higher catal5hic activity than monometallic ones. Wang et al. [112]. characterized PtCu bimetallic alloy nanoparticles Ijy XPS. XPS revealed that both elements in the nanoparticles are in zero-valence and possess the characteristic metallic binding energy. 

It is also obvious that power consumption should be rationally calculated taking into account the reconstruction processes of chemical bonds, i.e. via the values of bond energy -for binary structures, and reduction energy - for more complex molecules and radicals (E). 

When we apply the initial model to double compounds with ionic-covalent and metallic bonds, the calculations were made based on the equation (2) for 45 binary structures in the assumption of paired inter-atomic interaction. The results of some of them are given in table... 

In simple binary structures, in which no other relevant coordinations (or bonds) can be considered, the ratio m/n will be equal to the stoichiometric compositional ratio. For instance, we will write NaCl6/6 to represent the hexa-coordination (in this case octahedral coordination) of Cl around Na (and vice versa) in sodium chloride. Similarly we will have ZnS4/4 PH3/1 CsCl8/8 CaF8/4 UCI9/3 etc. Moreover, it is possible to add modifiers to the coordination numbers in order to specify not only topological but also geometrical characteristics of the primary coordination sphere. 

In the p vs. e diagram every structure type is generally characterized by its own individually shaped space-filling curve. The space-filling curves, however, of all binary structures belonging to one homeotect structure set coincide with one curve (see 3.9.2). 

Analysis of the dependence of the behaviour of alloy systems on the properties of the component elements. In an examination of the binary structure types containing more than five representatives, Villars and Girgis (1982) observed that 85% exhibited the following regularities ... 

Hetero-atomic clusters, moreover, may be derived from the binary structures mainly through the introduction of late transition or earlier post-transition elements. Examples of ternary alloys containing such structures are the alkali metal salts of centred clusters In10Me10 (Me = Ni, Pd, Pt), Tl12 Me12- (Me = Mg, Zn, Cd, Hg), etc. The crystal structure of the phase Na T Cdi x)27 (0.24 < x < 0.33)... 

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