Polyhedral volumes

Volume per oxygen in a unit cell, A. e Polyhedral volume of a coordination site, A. ... 

Polyhedral volume plotted against isomer shift for Fe3+-bearing coordination sites in minerals. 

We thank Dr. L. W. Finger for providing the program for computing polyhedral volumes and polyhedral distortion parameters from a set of atomic coordinates in a unit cell (114). Mineral spectroscopic research on terrestrial and planetary minerals is supported by the National Aeronautics and Space Administration (NASA grant number NSG-7604). 

There is a general correlation of decreasing A0 with increasing average metal-oxygen distances in the mineral structures hosting the Cr3+ ions (Schmetzer, 1982). Also, Cr3+ ions in coordination sites with higher polyhedral volumes (see Appendix 7) also tend to have lower A0 values. 

First, the sizes of coordination sites, as gauged by mean metal-oxygen distances or polyhedral volumes (Appendix 7), decrease in the order... 

Polyhedral volume, the volume of a coordination polyhedron (Hazen and Finger, 1982, Appendix HI, p. 103). 

The motivation for this approximation is found in the following cases a. For all polyhedral volumes containing an inscribed sphere of radius r, for some k 5 Zkr f (pkr / M ... 

This chapter concerns carboranes (carbaboranes), which are boron clusters with at least one carbon atom as part of the polyhedral cage. Published studies on carboranes before 1981 were reviewed in GOMC (1982) and between 1982 and 1992 in COMC (1995). The present review covers the period of 1992 to early 2005. Unlike in previous chapters, boron hydrides with organic substituents attached to a boron atom, organopolyboron hydrides, are not discussed in this chapter. Borane clusters containing at least one non-carbon atom as part of the cage framework are reviewed in Chapters 3.03, 3.04 and 3.05 of this volume. 

Incidentally, it must be noted that, although most olivine compounds are stable (at P = 1 bar) up to the melting temperature, in some compounds polymorphic transitions are observed at temperatures below the melting point (for instance, Ca2Si04 has a transition to a monoclinic polymorph at 1120 K). Forsterite at 1 bar melts at 7) = 2163 K, whereas fayalite melts at a much lower temperature Tf = 1490 K). The significance of this difference, as shown by Hazen (1977), must be ascribed to different polyhedral thermal expansions for polyhedra containing Mg and Fe cations. Hazen (1977) pointed out that, if the curve of volumes of the members of the (Mg,Fe)2Si04 mixture is extrapolated at various... 

A general conclusion from these DPT studies on M Eio clusters of various types is that the Wade-Mingos rules [13-16] are most applicable when the Eio unit has as large a cavity as possible, i.e., when E is a relatively heavy element such as bismuth or lead. Plowever, if the Eio cavity is too small, particularly when E is arsenic or germanium, then maximizing the internal volume of the polyhedral cavity can override any electronic considerations from the Wade-Mingos rules. 

As was mentioned in the introduction, HIPEs contain an internal phase volume fraction greater than 0.74. Since this is the maximum volume which can be occupied by uniform, undeformed spherical particles, the dispersed phase droplets must either be non-uniform, i.e. polydisperse, or deformed into non-spheri-cal, polyhedral cells. 

The shape of the dispersed phase droplets was investigated experimentally by Lissant and coworker by scanning electron microscopy (SEM) on cured HIPEs of water in a styrene-based resin [5], At high internal phase volumes, droplets were indeed polyhedral, and appeared to be relatively monodisperse in size. 

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