Crystal symmetry rising

In bulk material, the resistivity is independent of crystal orientation because silicon is cubic. However, if the carriers are constrained to travel in a very thin sheet, eg, in an inversion layer, the mobility, and thus the resistivity, become anisotropic (18). Mobility is also sensitive to both hydrostatic pressure and uniaxial tension and compression, which gives rise to a substantial piezoresistive effect. Because of crystal symmetry, however, there is no piezoelectric effect. The resistivity gradually decreases as hydrostatic pressure is increased, and then abrupdy drops several orders of magnitude at ca 11 GPa (160,000 psi), where a phase transformation occurs and silicon becomes a metal (35). The longitudinal piezoresistive coefficient varies with the direction of stress, the impurity concentration, and the temperature. At about 25°C, given stress in a (100) direction and resistivities of a few hundredths of an O-cm, the coefficient values are 500—600 m2/N (50—60 cm2/dyn). 

The crystal symmetry changes that accompany order-disorder transitions, discussed in Section 17.1.2, give rise to diffraction phenomena that allow the transitions to be studied quantitatively. In particular, the loss of symmetry is accompanied by the appearance of additional Bragg peaks, called superlattice reflections, and their intensities can be used to measure the evolution of order parameters. 

It has been demonstrated that RhBr,-doped AgBr crystals give rise to centers upon exposure to light. These rhodium(II) centers become more stable with decreasing temperatures and at 35 K it was shown that the low spin Rh center was in a Z>4 environment. However, it was believed that the Z>4/, symmetry observed for photolytically generated Rh + centers in LiH or LiD lattices was an artifact of site symmetry. It is reasonable to assume less than ideal geometry for a ion since Jahn-Teller effects will be prominent for such an electronic configuration and a static Jahn-Teller effect has been observed for Rh in a CaO matrix at 4.2... 

If the elastic constants are divided into four quadrants as shown above, one finds the constants in the upper left quadrant all involve the numbers 1 to 3. This set of constants, therefore, represents the relationships between normal stresses and normal strains. In the lower right quadrant, the only numbers are 4 to 6 and hence, involve only shear stresses and shear strains. In the upper right quadrant, which by symmetry is the same as the lower left, there is the possibility of relationships between normal stresses and shear strains and other such combinations. This implies it is possible to apply a normal stress to some bodies and obtain a shear strain or a shear stress to produce a normal strain. For many materials, these upper right quadrant constants may all be zero, but this is not always the case. For example, in some crystal symmetries, such as monoclinic, some of these components are non-zero. A similar effect can be found in angle-ply fiber composites in which, for example, a normal stress applied at an angle to the fibers can give rise to shear strains. 

Comparison of K and L, absorption spectra (cf. fig. 6a), which both involve s-p transitions, demonstrates similar smooth variations of the absorption coefficient with energy. In the L, spectrum, however, fine structures can be resolved much more clearly than in the K spectrum F = 14 eV), due to the considerably smaller total width of the L, core hole (= 5eV). The spectral shape of the L, spectra in all lanthanide metals exhibits a stair-case-like rise of the absorption at threshold. A weak minimum is located at about 20 eV above the onset (figs. 6a). The fine structure of the L, spectra reflects sensitively local s- and p-type band states and their modifications through different types of chemical bonding or crystal symmetries (Lengeler and Zeller 1984). 

Any perturbation from ideal space-group symmetry in a crystal will give rise to diffuse scattering. The X-ray diffuse scattering intensity at some point (hkl) in reciprocal space can be written as... 

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