Point symmetry, from crystal data

However, its was found possible to infer all four microscopic tensor coefficients from macroscopic crystalline values and this impossibility could be related to the molecular unit anisotropy. It can be shown that the molecular unit anisotropy imposes structural relations between coefficients of macroscopic nonlinearities, in addition to the usual relations resulting from crystal symmetry. Such additional relations appear for crystal point group 2,ra and 3. For the monoclinic point group 2, this relation has been tested in the case of MAP crystals, and excellent agreement has been found, triten taking into account crystal structure data (24), and nonlinear optical measurements on single crystal (19). This approach has been extended to the electrooptic tensor (4) and should lead to similar relations, trtten the electrooptic effect is primarily of electronic origin. 

Structural data are available for several Ayp/to-pentaboranes which are BsHg2L adduct species77 . Shore and coworkers have determined the crystal and molecular structure of BjHg 2 P(CH3)2 77a. The structure is a shallow pyramid (C3 point symmetry) with basal borons distorted from a square pyramid. The two trimethyl-... 

Raman spectra on CsF 3 XeOF4 have shown the presence of the [Xe303F,3]-ion 160). This consists of three XeOF4 molecules bonded equivalently to a central F" ion. The expected point symmetry is C3v. The proposed formulation is supported by 160-180 isotope substitution experiments. X-ray powder photography showed 160) that the compound is isostructural with CsF 3 IF5 161), but definitive confirmation of the structure has had to wait for a single crystal study, the data from which are outlined below (Fig. 10). 

In this case, x = 0.3047 as follows from the structure data. To the best of our knowledge only computer code CRYSTAL [23] allows one to include the space-group information in input data so that any occupied Wyckoff position can be presented by one representative. In the other computer codes the coordinates of all atoms in the PUC are introduced and the point symmetry of the structure is found by the code itself and used in calculations. Prom this example it is seen that the necessary information for structures requires the use not only of the database but also IT. 

The R2O28O4 series (R = La Lu, Y) forms isostructural orthorhombic (1222) crystals (Ballestracci and Mareschal, 1967). The structure of the lanthanum compoimd (a = 4.2681 A, b = 4.1938 A and c = 13.720 A) has been refined from X-ray powder diffraction data by Fahey (1976). The refinement confirmed the earlier results by Ballestracci and Mareschal (1967) concerning the (RO)"" -type layer stmcture and showed that the lanthanum atom is coordinated by four oxygens from the (RO) layer and two oxygens from different sulfate groups. The R-O distances are 2.40 and 2.41 A in the (RO) layer and 2.36 A when sulfate oxygens are involved. The point symmetry around lanthanum is C2. 

The chemical bonding and the possible existence of non-nuclear maxima (NNM) in the EDDs of simple metals has recently been much debated [13,27-31]. The question of NNM in simple metals is a diverse topic, and the research on the topic has basically addressed three issues. First, what are the topological features of simple metals This question is interesting from a purely mathematical point of view because the number and types of critical points in the EDD have to satisfy the constraints of the crystal symmetry [32], In the case of the hexagonal-close-packed (hep) structure, a critical point network has not yet been theoretically established [28]. The second topic of interest is that if NNM exist in metals what do they mean, and are they important for the physical properties of the material The third and most heavily debated issue is about numerical methods used in the experimental determination of EDDs from Bragg X-ray diffraction data. It is in this respect that the presence of NNM in metals has been intimately tied to the reliability of MEM densities. 

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