Site occupation, crystallographic

I Site-occupatioH parameters. A complete description of a system requires detailed knowledge about the occupancy of all available sites by all die participating species. However, with K constituents and N sites, this leads to different configurations, which is computationally unrealistic. A usefid approximation is to use average site-occupation parameters, for equivalent crystallographic sites. 

Virtually all of the reported structural data on titanium alloy hydrides and deuterides indicate that the solute atoms occupy tetrahedral interstitial sites in the metal lattice. Neutron diffraction data obtained for deuterium in Ti/34 atom % Zr and in Ti/34 atom % Nb (17) indicate tetrahedral site occupancy in the bcc /3-phase. Similarly, data reported for deuterium in Ti/19 atom % V and in Ti/67 atom % Nb (18) indicate tetrahedral site occupancy in the fee 7-phase. Crystallographic examination of the 7-phase Ti-Nb-H system (19) reveals that increasing niobium content linearly increases the lattice parameter of the fee 7-phase for Nb contents ranging from 0 to 70.2 atom %. Vanadium, on the other hand, exerts the opposite effect (6) at H/M = 1.85, the 7-phase lattice parameter decreases with increasing vanadium contents. 

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. 

Some of the uncertainties concerning site occupancy assignments of iron cations might be alleviated if comparisons could be made between measurable parameters for different cations in the same coordination site. One such correlation is suggested by the isomer shift parameter for coexisting Fe2+ and Fe3+ ions in similar coordination environments in a mineral, particularly when the two cations occupy the same crystallographic position in the crystal structure. 

Toraya s WPPD approach is quite similar to the Rietveld method it requires knowledge of the chemical composition of the individual phases (mass absorption coefficients of phases of the sample), and their unit cell parameters from indexing. The benefit of this method is that it does not require the structural model required by the Rietveld method. Furthermore, if the quality of the crystallographic structure is poor and contains disordered pharmaceutical or poorly refined solvent molecules, quantification by the WPPD approach will be unbiased by an inadequate structural model, in contrast to the Rietveld method. If an appropriate internal standard of known quantity is introduced to the sample, the method can be applied to determine the amorphous phase composition as well as the crystalline components.9 The Rietveld method uses structural-based parameters such as atomic coordinates and atomic site occupancies are required for the calculation of the structure factor, in addition to the parameters refined by the WPPD method of Toraya. The additional complexity of the Rietveld method affords a greater amount of information to be extracted from the data set, due to the increased number of refinable parameters. Furthermore, the method is commonly referred to as a standardless method, since the structural model serves the role of a standard crystalline phase. It is generally best to minimize the effect of preferred orientation through sample preparation. In certain instances models of its influence on the powder pattern can be used to improve the refinement.12... 

The technique of channeling-enhanced X-ray emission (CHEXE) has enabled cation site occupancies to be determined in various minerals, including transition metal ions in spinels and ferromagnesian silicates (Taftp, 1982 Taftp and Spence, 1982 Smyth and Taftp, 1982 McCormick etal., 1987). The method, which is based on relative intensities of X-ray peaks measured on crystals with diameters as small as 50 nm under the electron microscope, is particularly useful for determining site occupancies of minor elements with concentrations as low as 0.05 atom per cent in a structure. The most important criterion for the determination of element distribution in a mineral by this technique is that the cation sites should lie on alternating crystallographic planes. In order to make quantitative site population estimates, additional information is required, particularly the occupancy of at least one element in one of the sites or in another site that lines up with one of the sites of interest (McCormick et al., 1987). For example, cation site occupancies by CHEXE measurements have been determined from X-ray peak intensity ratios of Si to Ni, Mn, Cr and Fe in forsterite, as well as thermal disordering of these cations in heated olivines (Smyth and Taftp, 1982). 

IR-11.4.2 Indication of site occupancy IR-11.4.3 Indication of crystallographic sites IR-11.4.4 Indication of charges... 

Many other examples of the use of site occupancy factors could be cited, especially in mineralogy, where most natural crystals have a mixed population of atoms occupying the various crystallographic cites. 

The structure of the compounds was probed by XRPD (Philips PW Diffractometer with graphite monochromator) The measured integrated intensities were used for the refinement of the unit cell dimensions, the atomic coordinates, the site occupancies and the isotopic thermal factor related to a crystallographic model developed by XRD123, a publically available software (internet address http //www.polito.it/Ulisse/Corsi/TLC/F0620/materiali). 

As the crystallographic site occupancy is concerned, in inverse spinels all Li ions reside in octahedral coordination sites, while the transition metal ions (TMI) can occupy both octahedral and tetrahedral sites. The results obtained are reported in Table 1 they suffer a limitation due to the fact that the XRPD technique can discriminate between ion and Co ... 

Desorption isotherms for the hydrides of LaNi eAlo,] and LaNij sAlo.s are presented and values for the enthalpy and entropy changes of the hydriding reactions are calculated from the vant Hoff plots of log P vs, i/T. A crystallographic model of LaNij Al is shown and consideration of the nearest neighbor atom distribution leads to a rationalization of the observed linear relationship between the enthalpy change, aH, and the aluminum composition. Brief discussions of methods to predict dissociation pressures or interstitial site occupation are included. The cubic and hexagonal ABs phases are compared and, finally, the application of these alloys in chemical heat pump systems is noted. 

Note that the correct site occupancy factor instructions of Al(l) and Al(2) (both in PART 1) are 20.5000 and not 21.0000,as they lie on the crystallographic twofold axis. 

In the case of inverse ferrites (or in any case where more than one type of cation occupies the same set of crystallographic sites), ordering phenomena can be expected (Gorter, 1954). In inverse ferrites, octahedral site occupancy by two kinds of cations (divalent and trivalent) can lead to long-range order, where successive (001) layers of octahedral sites are occupied alternately by D and T cations. In this case, there are two ionic sublattices (Fuentes, Aburto Valenzuela, 1987) on octahedral sites. Fig. 2.4. 

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