Similarity measures orientation dependent

As noted in Section 7.2, the RB44Si2 samples that can be grown are not single crystals but are polycrystalline. Therefore, we note that there is sample/measurement (configuration of electrodes and preferred orientation) dependence and this is reflected in differences in the absolute values of the resistivity for the different lanthanide phases. However, the To of crystals are similar and should be considered to be close to the intrinsic values. That is, To is a microscopic parameter reflective of the localization length which is dependent on intrinsic disorder throughout the compound, while po in Eq. (3) will cumulatively reflect contributions from the grain boundaries. The values of po and Tq are listed in Table 5. 

For certain minerals with multiple element substitutions on lattice sites, electron channeling experiments can provide estimates of site occupancy using a similar thin-film analysis technique. This latter approach, termed ALCHEMI, utilises an orientational dependence of X-ray emission from specific elements on crystallographic sites. Conventional thin-film analyses, which measure the concentration of elements in a sample, do not require specific, known orientations of a sample, and are best obtained from randomly-oriented or non-Bragg diffracting crystals and with a convergent beam which minimises channeling effects. 

Recently, it has been demonstrated that confocal Raman microscopy can be employed to obtain information on the phase, growth direction and radial crystallographic orientation of GaN nanowires [46, 47]. Fan et al. have demonstrated the orientation-dependent micro-Raman measurements on single wurtzite CdS nano wires with an average diameter of 60 nm [48]. The Raman spectra of nanowires were compared with those of bulk ribbon. As opposed to the Raman spectra fi om the bulk samples, the intensity of most Raman bands of the nanowires exhibited significant dependence on the polarization of the excitation with respect to the nanowire axis. The Raman bands were found to be polarized along the longitudinal axis because of the shape-induced depolarization effect, similar to... 

Molecular quantum similarity measures, as formulated in integral (1), are dependent on the relative position of both studied molecules in space. Consequently, a procedure capable of arranging the molecular coordinates needs to be established. Two methodologies have been implemented to deal with this question the maximal similarity rule (MSR) [71], which considers that the optimal orientation corresponds to the one that maximizes the value of integral (1) and the topo-geometrical superposition algorithm... 

This expression looks similar to the definition of P2 (Eq. 2.10). If ( = 0° is the deformation direction, then the value of / varies from 0 in a randomly oriented system to 1 in a perfectly oriented system, and is -0.5 when the chosen crystal axis is perpendicular to the fiber axis. The number of Hermans orienfation functions that need to be evaluated for a complete description of orientation depends on the unit cell two for an orthorhombic and up to five for a triclinic unit cell [1]. Figure 2.11 shows an example of the evaluation of the degree of orientation in uniaxially oriented samples. Figure 2.11b is the azimuthal trace of one of the crystalline reflections in the diffraction pattern (Fig. 2.3a) [40,68], A practical measure of parallelism or orientation given by expression 2.14 is sometimes useful ... 

---