Average magnetic valence

SPD singular point detection (method) (ZJ average magnetic valence... 

Here (i) is the number of 3d electrons in the Fe spin-up band, (ii) Z, is the chemical valence of atom i, (iii) Nip is the number of electrons in the unpolarized s-p conduction bands and (iv) (Zn,) is the average magnetic valence of the compounds, which for the pseudotemaries considered by Christides et al. (1991b) has the form... 

In Bai.2Mn80i6 the average manganese valence is + 3.7, and both types of ion are found in high-spin states [130]. This compound shows magnetic ordering at Tn =... 

Hohenberg and Kohn have proved generally that the total ground state energy E of a collection of electrons in the presence of an externally applied potential (e.g. the valence electrons in the presence of the periodic potential due to the cores in a lattice), when no net magnetic moment is present, depends only on the average density of electrons n(R). By this proof, n(R) becomes the fundamental variable of the system (as it is in the Thomas-Fermi theory ). Variational minimization of the most general form of E, with respect to n lends to the Hartree-Fock equations formalism. 

Solid-state sulfide compounds MMo2S4 (M = V, Cr, Fe, Co) contain infinite chains of Mo4S6 clusters with intracluster Mo-Mo distances (2.756-2.989 A) and intercluster distance (2.960 A) for the cobalt derivative (112). As the valence of M is +2, judging from magnetic measurements, and the average oxidation state of molybdenum +3, the CVE for M2Mo4S8 is 12. This agrees with five intracluster and one intercluster... 

Matsunaga (15) applied the magnetic techniques of Eischens and Selwood and the chemisorption and chemical techniques of Voltz and Weller to a series of chromia-alumina catalysts. He found that in the limit of low chromia contents, where Eischens and Selwood deduced a two-dimensional distribution of chromium ions, treatment with oxygen at 450°C. resulted in an average valence number of six for all of the chromium ions in the sample. 

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