System, crystal right-handed

There is not generally accepted rule for the choice of the coordirrate system for right-handed and left-handed quartz crystals. Coordinate jc-axis is chosen generally in the direction of electrical a-axis and z-axis is in the direction of the optical c-axis. Cady and several other authors use right-handed coordinate system for right-handed quartz and left-handed coordinate system for left-handed quartz. On the contrary. 

Fig. 34. Orthorhombic system. (See also Fig. 25.) a. Unit cell type.. (H.COO),Sr.2HsO. Cla8s222. Left-and right-handed crystals, c. 1-Brom, 2-hydroxy-naphthalene. Class 222. d. Picric acid, Class mm. e. Oxalic acid. Class mmm. /. C,Br. Class mmm.

The parameters of Hamiltonians (1) and (2) are determined in our approach by pure theoretical way using different quantum chemical models and calculations unlike the traditional fitting the experimental thermodynamic and dielectric data. Our method of the many-pseudospin clusters [ 1,4] seems to be the most reliable way of determination. The latter are obtained in this case within the static approximation from the system of equations for a typical crystal fragment (cluster) for all possible proton distributions on H-bonds. The left-hand side of any equation expresses the cluster total energy in terms of Jy, while the right-hand side is determined by means of the quantum chemical calculation of this energy. 

Regardless of which tools were used in the indexing of the powder diffraction pattern, the most reliable solution should result in the minimum discrepancies in the series of simultaneous equations (Eq. 5.5 or its equivalent for a different crystal system) constructed with the observed 20 substituted into the left hand side and the assigned index triplets and refined unit cell dimensions substituted into the right hand side of each equation. While the minimum combined discrepancy is easily established algebraically, e.g. as the sum of the squared differences... 

A standard set of reference axes and equations to describe spontaneous strains is now well established (Schlenker et al. 1978, Redfern and Salje 1987, Carpenter et al. 1998a). The orthogonal reference axes, X, Y and Z, are selected so that Y is parallel to the crystallographic y-axis, Z is parallel to the normal to the (001) plane (i.e. parallel to c ) and X is perpendicular to both. The +X direction is chosen to conform to a right-handed coordinate system. Strain is a second rank tensor three linear components, cn, 622 and 33 are tensile strain parallel to X, Y and Z respectively and co, 623, eu are shear strains in the XZ, YZ and XY planes, respectively. The general equations of Schlenker et al. (1978) define the strains in terms of the lattice parameters of a crystal (a, b, c, a, P, y, where P is the reciprocal lattice angle) with respect to the reference state for the crystal ( , bo, Co, cto, Po,Yo) ... 

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