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Valency

About: Valency is a research topic. Over the lifetime, 1632 publications have been published within this topic receiving 26141 citations.


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TL;DR: In this article, the conditions of glass formation are divided into two groups, namely, one puts stress on the geometry of the structure, and the other on the strength of chemical bonds.
Abstract: Studies have been made on the conditions of the formation of multicomponent glasses assuming that the one to one correspondence between the glassy state and the glass structure does hold good. This idea is strongly supported by the experimental results of the glass formation range of the systems of borate, silicate, germanate, tellurite glasses, etc.The conditions of glass formation may be divided into two groups, namely, one puts stress on the geometry of the structure, and the other on the strength of chemical bonds. The former is represented by Zachariasen's rule, and the latter by the mixed bond, and electronegativity theories etc. However, the author pointed out that the conditions regarding the bond strength are implied by those of geometry being necessary for giving glassy state.According to the picture of glass structure consisting of network and modifier ions Zachriasen's rules are to be applied to the network. The important point in this rule is that the valency of the ion of the network is equal to its coordination number, i.e. Z/S (electrostatic valency)=1. For multicomponent glasses this condition is to be extended as follows:(1) A cation whose valency is less than the coordinate number, an intermediate ion, may join in the network to take the office of a network former if the condition Z/S=1 is satisfied by making up the difference with the positive charge of an attached modifier.(2) In order to form glass at least one dimentional continuity should exist in the structure. In addition oxygen polyhedra should share corners, and the central ion of the polyhedra should be small.These conditions of glass formation are supported strongly by the experimental survey of the area of glass formation covering many polycomponent glasses.Furthermore, the glass forming range involving b-subgroup ions as Pb may be explained by the idea that Pb-ion itself helps the formation of network of four coordinated Pb.On the other hand, glass formation range changes by the influence of modifier ions. It was concluded from geometrical calculation that the radius of a modifier ion being most suitable to the network atom is 6 coordination. It the network is formed by four coordinated ions the most suitable radius ratio is Rm/Rn=2, where Rm and Rn are respectively the radii of modifier and network ions.

7 citations

Journal ArticleDOI
TL;DR: In this article, the lattice spacings of solutions of manganese, iron, cobalt and nickel in the copper-germanium $\zeta$-phase have been examined.
Abstract: According to previous work, solution of a third metal in the close-packed hexagonal $\zeta$-phases which occur at approximately 1.5 electrons per atom in certain binary copper alloys causes the lattice spacings to vary in such a way that the axial ratio remains constant at a constant valency electron:atom ratio. On the assumption that this remains true when the third metal is a transition metal of the VIIIth Group of the Periodic Table, the lattice spacings of solutions of manganese, iron, cobalt and nickel in the copper-germanium $\zeta$-phase have been examined. From the observed axialratios, the contributions of the transition metals to the conduction band of the alloy have been assessed and expressed as an effective valency value. This value, at the lower electron:atom ratios (approximately 1.39), is unity for iron, cobalt and nickel, but decreases as the electron:atom ratio rises. For manganese effective valency values at the lower electron:atom ratios vary from 1.64 to 1.42 according to manganese content; again the values decrease with increasing electron:atom ratio. The dependence of the effective valency values on transition metal content is such that, if a lattice contraction is produced by the solution of the transition metal in the binary $\zeta$-phase (cobalt, nickel) the valency decreases as the transition metal content rises. Lattice expansion (manganese) leads to the reverse effect, while the effective valency of iron, which has little effect on the lattice spacings, is virtually independent of iron content. The results are discussed in terms of transfer of electrons between the conduction band of the alloy and the virtual bound 3d states localized on the transition metal atoms in solution.

7 citations

Journal ArticleDOI
TL;DR: This paper shows a valency bound for distance-regular graphs with a relatively large, in absolute value, smallest eigenvalue, and classifies the non-bipartite distance- regular graphs with diameter at most three with smallesteigenvalue not larger than − k / 2, where k is the valency of the graph.

7 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that for any positive integer C, there are only finitely many distance-regular graphs with valency k at least three, diameter D at least six and k"2k=

7 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202377
2022190
202119
202029
201937
201829