Total valence electron concentration

Similar classification criteria may be made by using the total valence-electron concentration previously defined (see equation 4.27) and defining, according to Parthe (1995) the tetrahedral structure equation ... 

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 parameter the total valence electron concentration, VEC, 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. 

We define the valence electron concentration per anion, VEC(X), as the total number of all valence electrons in relation to the number of anionic atoms ... 

Figure 4.26. Optimum values, in accordance with Wade s rules and as summarized by Miller et al. (2002), of the valence electron concentration VEC (total number of electrons divided by the cluster atom number) as a function of the number of cluster atoms for closo and nido deltahedra. On the left the values computed for the main group elements and on the right those relevant to the transition metals.

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. 

To solve for the Fermi energy we must return to Eq. (B7). First consider the case NIk — 0, i.e., no states in the band gap. Then the total number of electrons in the system is NWi (the total valence-band density of states) and thus n + (ATv, — p) = Nyt, orp = nsn , the intrinsic concentration. Thus,... 

Since difference electron densities, deformation densities or valence electron densities are not observable quantities, and since the Hohenberg-Kohn theorem64 applies only to the total electron density, much work has concentrated on the analysis of p(r). The accepted analysis method today is the virial partitioning method by Bader and coworkers67, which is based on a quantum mechanically well-founded partitioning of the molecular... 

The role of subexcitation electrons is most important when the irradiated medium contains small amounts of impurity molecules the excitation energy ha) 0j (or the ionization potential I ) of which is below h(o0l. Such additive molecules can be excited or ionized by the subexcitation electrons the energy of which is between h(o 0j and fuom, and, consequently, the relative fraction of energy absorbed by an additive will be different from what it should be if the distribution of absorbed energy were solely determined by the relative fraction of valence electrons of each component of the mixture.213 214 According to estimates of Ref. 215, this effect is observed when the molar concentration of the additive is of the order of 0.1%. This selective absorption with ionization of additives has been first pointed out by Platzman as an explanation for the increase in the total ionization produced by alpha particles in helium after small amounts of Ar, C02, Kr, or Xe were added (the so-called Jesse effect).216... 

Electron density maps based on theoretical calculations (methods in parentheses) are given in [22] (SCF-MO [23] also for the highest occupied MO 5ai), in [24] (SCF and Cl also for the three valence orbitals), in [10] (SCF-Xa-SW for the valence orbitals and the total valence shell), in [25] (SCF and SCGF [self-consistent group function]), and in [26] (united atom). The Laplacian V p of the charge density p showed four local concentrations of electronic charge in the valence shell of the central P atom in accordance with the VSEPR (valence shell electron pair repulsion) model [27] for this latter model and its application to PH3, see [28 to 31]. 

It is a trivial consequence of the mass conservation and charge conservation that an increase of P leads to an increase of the O content (i.e. of 6 = [0"j — [Vq] + [Vjjj] — [M ]) in MOi+ and a decrease of total electron concentration in conduction and valence bands (cf. [e ] — [h ]). The changes with regard to the individual defect concentrations as stated above, only follow in conjvinction with the individual mass action laws. The P theorem applies in the case of simple defect chemistry. In the case of exotic associates (e.g. Mj in M+X") the tendencies c i compete so that it may become invalid. 

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)... 

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