Partial valence electron concentration

ABSTRACT. For compounds with tetrahedral structure or anionic tetrahedron complex two valence electron concentration rules can be formulated which correlate the number of available valence electrons with particular features of the crystal structure. These two rules are known as the tetrahedral structure equation where the total valence electron concentration, VEC, is used as parameter and the generalized 8 - N rule where the parameter of interest is the partial valence electron concentration in respect to the anion, VEC. From the tetrahedral structure equation one can calculate the average number of non-bonding orbitals per atom and, in the case of non-cyclic molecular tetrahedral structures, the number of atoms In the molecule. An application of the generalized 8 - N rule allows the derivation of the average number of anion -anion bonds per anion or the number of valence electrons which remain with the cation to be used for cation - cation bonds and/or lone electron pairs. These rules have been used not only to predict probable structural features of unknown compounds but also to point out possible errors in composition or structure of known compounds. 

Introducing as new parameter the partial valence electron concentration in respect to the anion, VECa, defined as... 

The drawings are complemented with text blocks detailing the numerical values of the different parameters which can be calculated from the valence electron equations discussed above. On top is given the total valence electron concentration, VEC. If VEC < 4 a tetrahedral structure involving all atoms is impossible. The parameters listed below VEC are derived from the valence electron concentration of the charged anion partial structure, VEC, and the next one from the partial valence electron concentration in respect to the anion, VECa- parameter C AC, to be discussed in the next paragraph, refers to the sharing of the anions and can be calculated from the composition of the compound. Finally, on the last row one finds a classification code for the base tetrahedron, also to be discussed later on. 

The valence electron concentration may be calculated from the positive valences of the component atoms, e.g. Ni°, Cu1+, Zn2+, Ga3+ etc., the valence electron correlation is fully occupied in low valence electron concentration phases. (The possibility of partial occupation had been mentioned above.)... 

Experimentally it is found that the Fe-Co and Fe-Ni alloys undergo a structural transformation from the bee structure to the hep or fee structures, respectively, with increasing number of valence electrons, while the Fe-Cu alloy is unstable at most concentrations. In addition to this some of the alloy phases show a partial ordering of the constituting atoms. One may wonder if this structural behaviour can be simply understood from a filling of essentially common bands or if the alloying implies a modification of the electronic structure and as a consequence also the structural stability. In this paper we try to answer this question and reproduce the observed structural behaviour by means of accurate alloy theory and total energy calcul ions. 

We have seen that molecular electron density distributions are dominated by contributions of steeply falling electron densities around the nuclei, whieh we can attribute in the main to the core electrons. Superimposed on these are smaller contributions Ifom a few valence electrons, which may be bonding or nonbonding. These are loeal eharge concentrations. From the chemieal point of view the latter are the more interesting features, and if we derive the second derivative of the three-dimensional electron density, defined as the sum of partial seeond derivatives, Eq. 10.18, we can study them in more detail. 

Oxides play many roles in modem electronic technology from insulators which can be used as capacitors, such as the perovskite BaTiOs, to the superconductors, of which the prototype was also a perovskite, Lao.sSro CutT A, where the value of x is a function of the temperature cycle and oxygen pressure which were used in the preparation of the material. Clearly the chemical difference between these two materials is that the capacitor production does not require oxygen partial pressure control as is the case in the superconductor. Intermediate between these extremes of electrical conduction are many semiconducting materials which are used as magnetic ferrites or fuel cell electrodes. The electrical properties of the semiconductors depend on the presence of transition metal ions which can be in two valence states, and the conduction mechanism involves the transfer of electrons or positive holes from one ion to another of the same species. The production problem associated with this behaviour arises from the fact that the relative concentration of each valence state depends on both the temperature and the oxygen partial pressure of the atmosphere. 

The electron transfer reactions at the semiconductor/electrolyte interface occur either via the conduction band or the valence band. The total current is therefore given by the sum of four partial currents, denoted as represent electron transfer via the conduction anc valence bands, respectively, and the superscripts, a and c, indicate anodic anc cathodic processes, respectively. Let us assume nereafter that the electron transfer occurs only via the conduction band. In a simple case where the concentration of the electrolyte is sufficiently high and only the overvoltages at the Helmholtz layer (tjh) and in the space charge layer (rjsc) are important, the ica and cc can be given as follows4)... 

An X-ray photoelectron spectroscopic study of Ni(DPG)2I showed no evidence of trapped valence or any appreciable change in the charge on the metal upon oxidation.97 The site of partial oxidation and hence the electron transport mechanism is still unclear but one explanation of the relatively low conductivity is that the conduction pathway is metal centred and that the M—M distances are too long for effective orbital overlap. Electron transport could be via a phonon-assisted hopping mechanism or, in the Epstein—Conwell description, involve weakly localized electronic states, a band gap (2A) and an activated carrier concentration.101... 

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