Tetragonal groups

Table 63 Character tables of some tetragonal groups and their double groups...

Thus, a symmetric tensor of rank 2 is characterized by an ellipsoid of revolution for threefold, fourfold and sixfold symmetries. With respect to piezoelectricity, the hexagonal groups impose the same conditions on the tensor as the corresponding tetragonal groups (422 <- 622,4mm 6mm, etc.). Because a piezoelectric polarization can only develop along a polar direction, the effect is zero in any direction perpendicular to a fourfold or sixfold axis. Consequently,... 

Nodal structure of the superconducting gap and impurity effects As explained before, thermodynamics and transport behaviour points to an extremely anisotropic or nodal gap function in the nonmagnetic borocarbides. A gap function compatible with reported experiments was proposed in Maki et al. (2002). It is a hybrid s - - g wave gap which is fully symmetric (Ai ) under the tetragonal group D4/, and has the form... 

Jahn-Teller distortion" occurs in LiMn204 at 7°C (280 K). This phase transition results in a transformation from the cubic space group Fd3m to the tetragonal group Mj/amd. The structural distortion results from interaction of the Jahn-Teller active species Mn + (t2 -e ), in contrast, Mn" " (t2/-e ) and Mn (t2/-e/) are not Jahn-Teller active. Because of the low temperature of this transition, and that modified spinels have in general lower transition temperatures, this mechanism may not be as relevant as others for currently used spinel materials. Related mechanisms can cause strain and structural failure, resulting in electrically disconnected particles. 

Polymorphism. Many crystalline polyolefins, particularly polymers of a-olefins with linear alkyl groups, can exist in several polymorphic modifications. The type of polymorph depends on crystallisa tion conditions. Isotactic PB can exist in five crystal forms form I (twinned hexagonal), form II (tetragonal), form III (orthorhombic), form P (untwinned hexagonal), and form IP (37—39). The crystal stmctures and thermal parameters of the first three forms are given in Table 3. Form II is formed when a PB resin crystallises from the melt. Over time, it is spontaneously transformed into the thermodynamically stable form I at room temperature, the transition takes about one week to complete. Forms P, IP, and III of PB are rare they can be formed when the polymer crystallises from solution at low temperature or under pressure (38). Syndiotactic PB exists in two crystalline forms, I and II (35). Form I comes into shape during crystallisation from the melt (very slow process) and form II is produced by stretching form-1 crystalline specimens (35). 

Kea.tlte, Keatite has been prepared (65) by the crystallisation of amorphous precipitated silica ia a hydrothermal bomb from dilute alkah hydroxide or carbonate solutions at 380—585°C and 35—120 MPa (345—1180 atm). The stmcture (66) is tetragonal. There are 12 Si02 units ia the unit cell ttg = 745 pm and Cg = 8604 pm the space group is P42. Keatite has a negative volumetric expansion coefficient from 20—550°C. It is unchanged by beating at 1100°C, but is transformed completely to cristobahte ia three hours at 1620°C. 

Inspired by experimental observations on bundles of carbon nanotubes, calculations of the electronic structure have also been carried out on arrays of (6,6) armchair nanotubes to determine the crystalline structure of the arrays, the relative orientation of adjacent nanotubes, and the optimal spacing between them. Figure 5 shows one tetragonal and two hexagonal arrays that were considered, with space group symmetries P42/mmc P6/mmni Dh,), and P6/mcc... 

The second group is the group of oxyfluorides that are derived from ferroelectric oxides by means of fluorine-oxygen substitution. The basic oxides are usually perovskite, tetragonal tungsten bronze, pyrochlore, lithium tantalate etc. [400]. 

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