Hardness physical structural commonality

Commonality in the Basis of the Physical Structures of Hardness and Electronegativity... 

The naturally occurring dioxide exists in three crystal forms anatase, rutile and brookite. While rutile, the most common form, has an octahedral structure. Anatase and brookite have very distorted octahedra of oxygen atoms surrounding each titanium atom. In such distorted octahedral structures, two oxygen atoms are relatively closer to titanium than the other four oxygen atoms. Anatase is more stable than the rutile form by about 8 to 12 kJ/mol (Cotton, F.A., Wilkinson, G., Murillo, C.A and M Bochmann. 1999. Advanced Inorganic Chemistry, 6 ed, p. 697, New York John Wiley Sons) Other physical properties are density 4.23g/cm3 Mohs hardness 5.8 g/cm ( anatase and brookite) and 6.2 g/cm ( rutile) index of refraction 2.488 (anatase), 2.583 (brookite) and 2.609 (rutile) melts at 1,843°C insoluble in water and dilute acids soluble in concentrated acids. 

Weathering in older soils produces decreasing permeabilities due to in situ secondary mineral formation and the development of hard pans and argillic horizons. Such zones of secondary clay and iron-oxides are clearly evident in the increased aluminum and iron at a depth of a meter in the Panola regolith (Figure 3). Low permeabilities in such features are commonly related to the absence of continuous pores due to the formation of thick cutans of clay (O Brien and Buol, 1984). This process is enhanced by physical translocation and collapse of saprolite structures (Torrent and Nettleton, 1978). 

The complex phase which is fundamental to gauge theory is commonly defined in terms of symmetry groups without consideration of its physical meaning, which emerges most clearly in its characterization of the quantum wave functions. Whereas phase relationships between point particles are hard to imagine, they appear naturally in wave structures. With respect to electrons and other chemical entities a wave model in terms of complex wave functions is therefore the most satisfactory physical model. The complex phase represents the fundamental attribute of non-classical systems and the major difference between classical particles and quantum waves. Simulation of chemical systems based on real basis sets is essentially classical. It is therefore wrong, although fashionable, to refer to such simulations as quantum chemistry. 

Two questions arise naturally from this emerging taxonomy of liquid behavior. First, is structural order in core-softened fluids hard sphere or water-like Second, is it possible to seamlessly connect the range of liquid behavior from hard spheres to water like by a simple and common potential by simply changing a physical parameter ... 

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