Lattice Parameters Theoretical

Xhe theoretical methods described in this section are those appearing with minor exceptions in the FI2X and MOFM IBM 7O9O programs.  

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Superconducting transition temperature Lattic parameters Theoretical density Resistivity near Residual resistance ratio Coherence lengths... 

Fig.7 shows an example of the type of fit we obtain between experiment and theory. The experiment pattern was recorded in a CCD camera, and energy filtering was not used. The experimental and theoretical patterns are processed by a line detection program. To save computation times, only selected areas of the experimental pattern are matched. The areas are selected based on their sensitivity to lattice parameters. 

XRD measurements showed that the compound has a cubic lattice with the lattice parameter a = 0.6443 nm and metal atom arrangement of the fluorite type (space group Fm3m). Theoretical studies of its X-ray absorption spectra were conducted soon after its discovery by Orgaz and Gupta [35]. 

Fig. 13. Lattice parameters of the actinide and rare earth nitrides and arsenides. Full circles and triangles represent experimental values open circles and triangles, the theoretical values, for actinides and rare earths (from )...

Self-consistent energy band calculations have now been made through the LMTO method for all of the NaCl-type actinide pnictides and chalcogenides . The equation of state is derived quite naturally from these calculations through the pressure formula extended to the case of compounds . The theoretical lattice parameter is then given by the condition of zero pressure. 

Figure 13 also shows the results from the Dirac equation. Here the trend is reproduced very well as far as Pu with a minimum at UN. The reason that the theoretical lattice parameters have increased significantly for Pu and Am is that the fully relativistic f-bands consist of both j = 5/2 and j = 7/2 bands. Spin-orbit coupling is of the order of the band width and, with increasing atomic number, the j = 5/2 band fills preferentially. The... 

Characterization.— The LSFTO powder was calcined at a series of temperatures (1250, 1300, and 1400°C) in air to investigate phase purity and densification behavior. X-ray diffraction (XRD) powder patterns are shown in Fig. 1. The sample is single phase after heating at 1250°C. At the higher sintering temperatures, the lines become sharper and the density increases. The density measured by the Archimedes method was 90.3% relative to theoretical value after annealing at 1400°C for 10 h. The XRD pattern sintered at 1400°C was completely indexed with a cubic unit cell with lattice parameter a = 3.898(8) A and V= 59.2(6) A3. The weak XRD peaks at 31, 43, 55, and 65° 20 are also from the perovskite phase and arise from a small amount of WL radiation in the incident beam. 

The shift of the A line in the epilayers has been connected with the variation of the lattice parameters of GaN [1,11,12], The shift of this line was also measured in samples subjected to hydrostatic pressure (see Datareview A3.1). Combination of all these data permits one to obtain the whole series of excitonic deformation potentials [6,16], Two sets of data are available which are consistent with each other and are given in TABLE 1. The discrepancies between them are linked to the differences in the values of the stiflhess coefficients of GaN used by the authors. Gil and Alemu [6] in their work subsequent to the work of Shan et al [16] used data not available when Shan et al calculated their values. The notations are the same and are linked to the relationship with the quasi cubic model of Pikus and Bir [17], Deformation potentials as and a6 have been obtained by Alemu et al [8] who studied the anisotropy of the optical response in the growth plane of GaN epilayers orthorhombically distorted by growth on A-plane sapphire. For a detailed presentation of the theoretical values of deformation potentials of GaN we refer the reader to Suzuki and Uenoyama [20] who took the old values of the stiflhess coefficients of GaN [21]. 

Another contribution to variations of intrinsic activity is the different number of defects and amount of disorder in the metallic Cu phase. This disorder can manifest itself in the form of lattice strain detectable, for example, by line profile analysis of X-ray diffraction (XRD) peaks [73], 63Cu nuclear magnetic resonance lines [74], or as an increased disorder parameter (Debye-Waller factor) derived from extended X-ray absorption fine structure spectroscopy [75], Strained copper has been shown theoretically [76] and experimentally [77] to have different adsorptive properties compared to unstrained surfaces. Strain (i.e. local variation in the lattice parameter) is known to shift the center of the d-band and alter the interactions of metal surface and absorbate [78]. The origin of strain and defects in Cu/ZnO is probably related to the crystallization of kinetically trapped nonideal Cu in close interfacial contact to the oxide during catalyst activation at mild conditions. A correlation of the concentration of planar defects in the Cu particles with the catalytic activity in methanol synthesis was observed in a series of industrial Cu/Zn0/Al203 catalysts by Kasatkin et al. [57]. Planar defects like stacking faults and twin boundaries can also be observed by HRTEM and are marked with arrows in Figure 5.3.8C [58],... 

The LDA results describe the experimental trends quite well. It is noticed, that the distances X-X and A-X as well as the lattice parameters are underestimated for AuSb2 and FeS2, a typical effect of the local density approximation. The theoretical unit cell of SIP2 is slightly expanded in comparison to the experimental result, which was assumed to be a high pressure phase [7]. All position parameters u are reproduced with sufficient precision. 

Figure 5. Small-angle X-ray scattering data fix>m a polymerized cubic phase in the DDAB / water / methyl methacrylate system. The abscissa is s=2 sin 0 / X, in A l, where 6 is half the scattering angle and X (=1.54A) is the wavlength of the radiation used. The vertical lines give the theoretical peak positions for an Im3m lattice with a lattice parameter of 1ISA. The maximum at s =...

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