Crystal structures and stabilities

H.W. Brinks, A. Fossdal, J.E. Fonnelpp, B.C. Hauback, Crystal structure and stability of LiAlD with TiF, additive , J. Alloys Compd. 397 (2005) 291-295. 

As the aforementioned results indicate, it is difficult to predict the molecular structure of a suitable host for Cl-MIT, so it is necessary to employ a degree of trial and error. However, it becomes easier to design the host molecule if the crystal structure and stability of the inclusion complex are predictable. 

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... 

Oxide anions (0 ) must be mobile within the oxide structure, requiring both an appropriate spacing between the metal atoms in the crystal structure and stability of the metal atom lattice. Such structural stability occurs in vanadia provided that no more than two-thirds of the V(V) atoms are reduced to V(IV) further reduction causes changes in both structure and catalytic behaviour. The partially reduced oxides (and sometimes the fully oxidized states) therefore have vacancy (coordinatively deficient) structures. 

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

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. 

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). 

One of the most important parameters that defines the structure and stability of inorganic crystals is their stoichiometry - the quantitative relationship between the anions and the cations [134]. Oxygen and fluorine ions, O2 and F, have very similar ionic radii of 1.36 and 1.33 A, respectively. The steric similarity enables isomorphic substitution of oxygen and fluorine ions in the anionic sub-lattice as well as the combination of complex fluoride, oxyfluoride and some oxide compounds in the same system. On the other hand, tantalum or niobium, which are the central atoms in the fluoride and oxyfluoride complexes, have identical ionic radii equal to 0.66 A. Several other cations of transition metals are also sterically similar or even identical to tantalum and niobium, which allows for certain isomorphic substitutions in the cation sublattice. 

The principles described in the following six sections have been deduced in part from the empirical study of known crystal structures and in part from considerations of stability involving the crystal energy. 

Crystal structure and lattice parameters 6.7.2.4.3 Thermal stability 6.7.2.4.3... 

A white pigment for rubbers and plastics characterised by high tinctorial power, fastness to light, and chemical stability. Titanium dioxide pigments are made in two crystal forms, mtile and anatase, which differ in crystal structure and crystal size. 

The cocrystal adduct TTF[Hg3(C6F4)3]2 crystallizes as orange needles by combining 1 1 carbon disulfide methylene chloride solutions of TTF and Hg3(C6F4)3 [56]. As illustrated in Fig. 5, the crystal structure is stabilized by multiple Hg—S secondary interactions which cause the TTF molecules to be sandwiched between two Hg3(C6F4)3 molecules. Spectroscopic and structural results indicate that charge transfer does not occur in this adduct and minimal conductivity is expected. 

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. 

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