Crystal structure elements, phase transitions

Vasylechko, L. O. Crystal chemistry and phase transitions in complex oxides of rare earth elements with perovskite structure. Dr. Sd. Thesis. The Ivan Franko Natl. Univ. of Lviv, 2005, 343. (in Ukrainian). 

Hetero-atomic clusters, moreover, may be derived from the binary structures mainly through the introduction of late transition or earlier post-transition elements. Examples of ternary alloys containing such structures are the alkali metal salts of centred clusters In10Me10 (Me = Ni, Pd, Pt), Tl12 Me12- (Me = Mg, Zn, Cd, Hg), etc. The crystal structure of the phase Na T Cdi x)27 (0.24 < x < 0.33)... 

Another important contribution by Landau is related to symmetry changes accompanying phase transitions. In second-order or structural transitions, the symmetry of the crystal changes discontinuously, causing the appearance (or disappearance) of certain symmetry elements, unlike first-order transitions, where there is no relation between the symmetries of the high- and low-temperature phases. If p(x, y, z) describes the probability distribution of atom positions in a crystal, then p would reflect the symmetry group of the crystal. This means that for T> T p must be consistent with... 

The 17 rare-earth metals are known to adopt five crystalline forms. At room temperature, nine exist in the hexagonal closest packed structure, four in the double c-axis hep (dhep) structure, two in the cubic closest packed structure and one in each of the body-centered cubic packed and rhombic (Sm-type) structures, as listed in Table 18.1.1. This distribution changes with temperature and pressure as many of the elements go through a number of structural phase transitions. All of the crystal structures, with the exception of bep, are closest packed, which can be defined by the stacking sequence of the layers of close-packed atoms, and are labeled in Fig. 18.1.1. 

Considerable interest centres on the Mantle constituting, as it does, more than half of the Earth by volume and by weight. Attention has been focussed on several problems, including the chemical composition, mineralogy, phase transitions and element partitioning in the Mantle, and the geophysical properties of seismicity, heat transfer by radiation, electrical conductivity and magnetism in the Earth. Many of these properties of the Earth s interior are influenced by the electronic structures of transition metal ions in Mantle minerals at elevated temperatures and pressures. Such effects are amenable to interpretation by crystal field theory based on optical spectral data for minerals measured at elevated temperatures and pressures. 

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