Crystal site occupancy

The same structure is formed in a number of binary (or ternary) phases, for which a random distribution of the two (or three) atomic species in the two equivalent sites is possible. Typical examples are the (3-Cu-Zn phase (in which the equivalent 0,0,0 A, A, A positions are occupied by Cu and Zn with a 50% probability) and the (3-Cu-Al phase having a composition around Cu3A1 (in which the two crystal sites are similarly occupied, on average by Cu, with a 75% occupation probability, and by Al, with a 25% occupation probability). A number of these phases can be included within the group of the Hume-Rothery phases (see 4.4.5). 

Essentially, sublattice models originate from the concepts of Temkin (1945) who proposed that two separate sublattices exist in a solid-state crystal for cations and anions. The configurational entropy is then governed by the site occupation of the various cations and anions on their respective sublattices. When the valence of the cations and anions on the sublattices are equal, and electroneutrality is maintained, the model parameters can be represented as described in Section 5.4.2. However, when the valence of the cations and anions varies, the situation becomes more complex and some additional restrictions need to be made. These can be expressed by considering equivalent fractions (/) which, for a sublattice phase with the formula (/, . .. )(M"", . ..), are given by... 

The earliest theoretical predictions on the state of interfaces were made by Burton, Cabrera, and Frank [11[, who demonstrated that the interface would, in most cases, be rough at the growth temperature for metal crystals. Jackson [13[ suggested a system in which the solid and liquid phases are separated by an interface with one-layer thickness, and he calculated the energy changes as a function of the ratio of site occupancy of the constituent unit on the interface. When the site occupancy ratio was 50%, the interface was rough, whereas 0 or 100% site occupancy... 

Therefore the ideal structure of Y7O6F9 can be depicted as a stacking of. .. AjBiAjBj. .. along [100], as shown in Fig. 2.36. In the real crystal, shown in Fig. 2.35, mutual correlations among these atomic planes exist. These result in structural modulation, i.e. the movement of not only anions but also cations from the ideal positions, although the dimensions of the subcells of each plane (Aj., Bj, Aj, B2) are assumed to be constant in the ideal structure, and, moreover, the site occupancy of anions is differentiated. 

The packing of anions, the coordination of the anions and cations, and the cation site occupation for a number of the common crystal structures are listed in Table 13.7... 

By varying the relative site occupancies of G and G2, inclusion compounds with different properties would result. Some progress in this direction has been achieved [30,31] and Desiraju [32], in an article entitled Matching of molecular and supramolecular symmetry. An exercise in crystal engineering , has indicated the direction of future progress. 

Cation Site Distribution, Thin-film EDS analysis can also be used to quantitatively determine the site occupancy of atoms in a known crystal structure. Atom Location by Channeling Enhanced Microanalysis (ALCHEMI) is a technique which utilises electronchanneling enhanced X-ray emission for specific atoms in a crystal when appropriately oriented relative to the incident beam [43]. The method involves no adjustable parameters, can be used on relatively small areas of sample and provides fractional occupancies of atom positions [44] Unlike X-ray diffraction which has had limited success with adjacent elements in the periodic table [e.g. 45], ALCHEMI can provide site occupancies for adjacent elements and is relatively insensitive to sample thickness or the precise electron beam orientation [44] ... 

The problems of element loss or low intensity channeling effects have been addressed by Spence et al. [59], by performing ALCHEMI experiments at low temperature (e.g. 9OK) In the latter case the atom site occupancy is not temperature dependent, but the ratio of elemental X-ray counts from a crystal in two different... 

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. 

The following assignment shows that six positional parameters (neglecting the hydrogen atoms) are required for a description of the crystal structure. The hydrogen atoms are orientationally disordered, and they occupy general position 96(g) with half-site occupancy, as indicated in the last three rows of the table. 

Crystal structure of (a) ReC>3, and (b) Na W03 (central large circle, Na+ of fractional site occupancy). 

Compositional variations of intensity of the absorption band at 23,400 to 24,000 cm-1 attributed to Ni2+/M2 site cations have provided site occupancy data for the Mg2+-Ni2+ olivines (Hu et al., 1990). The results obtained from crystal field spectra showing strong cation ordering of Ni2+ ions in the olivine Ml sites are in good agreement with estimates from crystal structure refinements (e.g. Bostrom, 1987 Ottonello etal., 1989) described later ( 6.7.1.2). 

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