Crystal structure and phase stability

CRYSTAL STRUCTURE AND PHASE STABILITY IN Fei Co FROM AB INITIO THEORY... 

A. I. Abrikosov, P. James, O. Eriksson, P. Soderlind, A. V. Ruban, H. L. Skriver, and B. Johansson, Magnetically induced crystal structure and phase stability in FecCoi c, Phys. Rev. B (to be published). 

In this chapter, developments in the understanding of mullite over the last few decades are reviewed. A discussion of crystal structures and phase stability is presented to provide the reader with an overview of certain characteristics of this material. The next part of this chapter examines the effect of process chemistry on the synthesis and microstructure of mullite. The role of various synthetic methods that are used to modify mullite formation will be discussed, followed by a compilation of selected materials properties. 

Crystal Structure and Phase Stability in Fei.xCOx from Ab Initio... 

Pressure-induced phase transitions in the titanium dioxide system provide an understanding of crystal structure and mineral stability in planets interior and thus are of major geophysical interest. Moderate pressures transform either of the three stable polymorphs into the a-Pb02 (columbite)-type structure, while further pressure increase creates the monoclinic baddeleyite-type structure. Recent high-pressure studies indicate that columbite can be formed only within a limited range of pressures/temperatures, although it is a metastable phase that can be preserved unchanged for years after pressure release Combined Raman spectroscopy and X-ray diffraction studies 6-8,10 ave established that rutile transforms to columbite structure at 10 GPa, while anatase and brookite transform to columbite at approximately 4-5 GPa. 

Park, J.G. and Cormack, A.N. Crystal defect structures and phase stability in Ba hexaaluminates. 5 Solid State Chem. 1996,121, 278-290. 

Pettifor s structure maps additional remarks. We have seen that in a phenomenological approach to the systematics of the crystal structures (and of other phase properties) several types of coordinates, derived from physical atomic properties, have been used for the preparation of (two-, three-dimensional) stability maps. Differences, sums, ratios of properties such as electronegativities, atomic radii and valence-electron numbers have been used. These variables, however, as stressed, for instance, by Villars et al. (1989) do not always clearly differentiate between chemically different atoms. 

Chapter 6 therefore deals in detail with this issue, including the latest attempts to obtain a resolution for a long-standing controversy between the values obtained by thermochemical and first-principle routes for so-called lattice stabilities . This chapter also examines (i) the role of the pressure variable on lattice stability, (ii) the prediction of the values of interaction coefficients for solid phases, (iii) the relative stability of compounds of the same stoichiometry but different crystal structures and (iv) the relative merits of empirical and first-principles routes. 

V. Milman, B. Winkler, J. A. White, C. J. Pickard, M. C. Payne, E. V. Akhmatskaya, and R. H. Nobes, Electronic Structure, Properties, and Phase Stability of Inorganic Crystals A Pseudopotential Plane-Wave Study, hit. 

Factors similar to those in sedimentary processes are involved in metamorphic reactions. The susceptibility of a cation in a mineral to dissolution and recrystallization in a new phase depends on the relative stability of the ion in each crystal structure and the ease of removal of the ion from the structure. Thus, kinetic and thermodynamic factors again determine the fractionation of... 

Phase X has been observed in a number of studies on hydrous potassium-bearing systems (Trpnnes, 1990, 2002 Inoue et al., 1998a Luth, 1997). Its stability relations have been studied by Konzett and Fei (2000), who found that it breaks down between 20 GPa and 23 GPa at 1,500-1,700 °C. Its breakdown products were reported by Konzett and Fei (2000) to be K-hollandite, y-Mg2Si04, majorite, Ca-perovskite, and fluid. Hence, phase X is not succeeded by another hydrous potassic solid phase, and is therefore the hydrous potassic (solid) phase with the highest-pressure stability. The crystal structures of phase X and some related phases were determined by Yang et al. (2001). 

Upon release of supersaUiration, the initially dissolved compound will be separated from the solution and form a secondary phase, which could be either oil, amorphous solid, or crystalline solid. Crystalline materials are solids in which molecules are arranged in a periodical three-dimensional pattern. Amorphous materials are solids in which molecules do not have a periodical three-dimensional pattern. Under some circumstances with very high supersaturation, the initial secondary phase could be a liquid phase, i.e., oil, in which molecules could be randomly arranged in three-dimensional patterns and have much higher mobility than solids. Generally, the oil phase is unstable and will convert to amorphous material and/or a crystalline solid over time. At a lower degree of supersaturation, an amorphous solid can be generated. Like the oil, the amorphous solid is unstable and can transform into a crystalline solid over time. Even as a crystalline solid, there could be different solid states with different crystal structures and stability. The formation of different crystalline solid states is the key subject of polymorphism, which will be mentioned below and... 

A typical ab initio (first principles) calculation for lithium intercalation consists of two steps (i) energy calculation at 0 K to determine the ground states and relative energy difference between crystal structures and (ii) the construction and calculation of a free energy model to determine the phase stability at non-zero temperature. Dahn ef al. [37], Ceder ef al. [38] and Benco ef al. [41] all reported that the electrode potentials of transition metal oxides could be very well predicted by this method. In addition, Ceder ef al. constructed (on a theoretical basis) the phase diagram of IiCoO2 [40, 42,... 

In summary, we calculate that the low clinoenstatite is not stable under hydrostatic conditions and enstatite has a comparatively small stability field. The energy differences are so small that they are within the reliability of the simulations and thus the precise positions of the phase boundaries are not well located. The primary reason for this problem is the reliability of the potential models. Hence, calculating phase relationships represents the most difficult challenge for free energy minimization techniques. However, the simulations do provide valuable insights into the mechanisms of phase transitions and the effect of pressure and/or temperature on the crystal structures and the relative phase stabilities. 

It is quite difficult to explain this difference in the behavior of similar compounds. The factors which can account for these differences in the evaporation mechanisms can be reduced to two. First, we have the presence of intermediate phases which are less rich in Se or Te, and which are not observed in the bismuth—sulfur system [20-22]. The presence of intermediate phases, even though they decompose peritectically below the meltii points of Bi2X3, should stabilize bismuth selenide and telluride against thermal dissociation. Secondly, bismuth selenide and telluride have one type of crystal structure and bismuth sulfide has a different structure. The telluride and selenide have layered lattices and the sulfide has a chain lattice but with some sulfur atoms outside the chains [23, 24]. It is natural to assume that such sulfur atoms are bound less strongly to the lattice and this accounts for the ease of thermal dissociation in bismuth sulfide. 

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