Mineral isotropic

Aluminosilicates. These silicates consist of frameworks of silica and alumina tetrahedra linked at all corners to form three-dimensional networks familiar examples are the common rock-forming minerals quartz and feldspar. Framework silicates generally form blocky crystals, more isotropic... 

In the case of most nonporous minerals at sufficiently low-shock stresses, two shock fronts form. The first wave is the elastic shock, a finite-amplitude essentially elastic wave as indicated in Fig. 4.11. The amplitude of this shock is often called the Hugoniot elastic limit Phel- This would correspond to state 1 of Fig. 4.10(a). The Hugoniot elastic limit is defined as the maximum stress sustainable by a solid in one-dimensional shock compression without irreversible deformation taking place at the shock front. The particle velocity associated with a Hugoniot elastic limit shock is often measured by observing the free-surface velocity profile as, for example, in Fig. 4.16. In the case of a polycrystalline and/or isotropic material at shock stresses at or below HEL> the lateral compressive stress in a plane perpendicular to the shock front... 

Such a mechanism is not incompatible with a Haven ratio between 0.3 and 0.6 which is usually found for mineral glasses (Haven and Verkerk, 1965 Terai and Hayami, 1975 Lim and Day, 1978). The Haven ratio, that is the ratio of the tracer diffusion coefficient D determined by radioactive tracer methods to D, the diffusion coefficient obtained from conductivity via the Nernst-Einstein relationship (defined in Chapter 3) can be measured with great accuracy. The simultaneous measurement of D and D by analysis of the diffusion profile obtained under an electrical field (Kant, Kaps and Offermann, 1988) allows the Haven ratio to be determined with an accuracy better than 5%. From random walk theory of ion hopping the conductivity diffusion coefficient D = (e /isotropic medium. Hence for an indirect interstitial mechanism, the corresponding mobility is expressed by... 

If the diffusion medium is isotropic in terms of diffusion, meaning that diffusion coefficient does not depend on direction in the medium, it is called diffusion in an isotropic medium. Otherwise, it is referred to as diffusion in an anisotropic medium. Isotropic diffusion medium includes gas, liquid (such as aqueous solution and silicate melts), glass, and crystalline phases with isometric symmetry (such as spinel and garnet). Anisotropic diffusion medium includes crystalline phases with lower than isometric symmetry. That is, most minerals are diffu-sionally anisotropic. An isotropic medium in terms of diffusion may not be an isotropic medium in terms of other properties. For example, cubic crystals are not isotropic in terms of elastic properties. The diffusion equations that have been presented so far (Equations 3-7 to 3-10) are all for isotropic diffusion medium. 

In an isotropic medium, D is a scalar, which may be constant or dependent on time, space coordinates, and/or concentration. In anisotropic media (such as crystals other than cubic symmetry, i.e., most minerals), however, diffusivity also depends on the diffusion direction. The diffusivity in an anisotropic medium is a second-rank symmetric tensor D that can be represented by a 3 x 3 matrix (Equation 3-25a). The tensor is called the diffusivity tensor. Diffusivity along any given direction can be calculated from the diffusivity tensor (Equation 3-25b). Each element in the tensor may be constant, or dependent on time, space coordinates and/or concentration. 

For simplicity, the melt inclusion is assumed to be (i) spherical, and (ii) concentric with the spherical crystal shell (Figure 4-33). Furthermore, the host mineral is assumed to be isotropic in terms of diffusion. The concentric assumption and the isotropic assumption are rarely satisfied. Nonetheless, for order of magnitude estimate, these assumptions make the problem easy to treat. 

Solid sphere For isotropic diffusion in a spherical mineral of radius a with uniform initial concentration Cq and zero surface concentration, Ar diffusion profile is as follows (Equation 3-68g) ... 

Often it is necessary to treat diffusion between different layers as three dimensional diffusion. For isotropic minerals such as garnet and spinel (including magnetite), diffusion across different layers may be considered as between spherical shells, here referred to as "spherical diffusion couple." Oxygen diffusion in zircon may also be treated as isotropic because diffusivity c and that Tc are roughly the same (Watson and Cherniak, 1997). If each shell can be treated as a semi-infinite diffusion medium, the problem can be solved (Zhang and Chen, 2007) as follows ... 

A full treatment of this problem is unavailable. The simplest case would be a bimineralic rock. The mineral grains are randomly distributed with variable grain sizes. Even if both minerals are diffusionally isotropic, all grains of the same mineral are equal in size and shape, and the mineral grains are regularly spaced, the problem still has not been solved. One complication is that grain boundary diffusion is much more rapid than volume diffusion. 

When either arsenolite or senarmontite is sublimed on to mica, it is deposited in oetahedra, respectively isotropic and birefringent, oriented so that similar dimensions of the crystal meshes coincide,8 for example -. As4Oe 13-54, Sb406 13-64, mica 13-66 A. Such orientation appears only to occur with minerals of ionic structure 9 and when both substances concerned have heteropolar linkings,10 so that the phenomenon is said to provide evidence of this type of linking. 

Carbon form microscopically distinguishable carbonaceous textural components of coal and coke, exuding mineral carbonates recognized by reflectance, anisotropy, and morphology derived from the organic portion of coal and can be anisotropic or isotropic (ASTM D-5061). 

The possible presence of isotropic materials, including fiberglass, diatomaceous earth, perlite or any isometric mineral has been eliminated. The substance is anisotropic. The following possibilities exist ... 

Teeth fulfill very specific functions and it can be safely assumed that the tooth structure is finely tuned for this purpose. The dentin structure is clearly anisotropic, with all the mineralized fibrils being located on one plane, and all the tubules oriented perpendicular to this plane. It is therefore most surprising that in terms of microhardness, dentin is isotropic. This has recently been confirmed in a careful study in which root dentin microhardness was measured at the same precise location in three orthogonal directions [33],... 

A linear relationship between isotropic 2H chemical shift (6H) and 0---0 distance (r0...o) has also been established [77] for several metal phosphates and minerals. Similarly, for carboxylic acid protons, SH has been shown [78] to depend linearly on r0...0, and for several trihydrogen selenites, SH was shown [79] to correlate linearly with r0...0 and rH...0 distances. 

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