Stability of crystal structures

Hydrogen bonds play an important part in determining such properties as solubility, melting points, and boiling points, and in affecting the form and stability of crystal structures. They play a crucial role in biological systems. For ex-... 

Structure at high temperatures. A distorted perovskite would be expected to transform to the cubic structure at high temperatures. The Born model of ionic solids with the appropriate repulsive and van der Waals parameters can explain the relative stabilities of crystal structures in partly covalent solids, an ionicity parameter would have to be used to predict the preferred crystal structure (see Chapter 1, Section 1.3). 

Hiickel calculations have been employed extensively in other approaches such as the angular overlap model and the method of moments developed by Burdett and coworkers. Stabilities of crystal structures, pressure- and temperature-induced transitions, dynamical pathways in reactions and other phenomena have been analysed using angular overlap models. Thus, the electronic control of rutile structures and the stability of the defect structure of NbO have been examined (Burdett, 1985 Burdett Mitchell, 1993). In the case of NbO, the structure is stable at involving the formation... 

INFLUENCE OF POLARIZATION ON STABILITY OF CRYSTAL STRUCTURE, IONIC DISSOCIATION AND VOLATILITY... 

Cellulose is a polymer that meets these requirements as an adhesive. However, due to its semicrystalline structure, highly hydrogen-bonded cellulose cannot be dissolved easily in conventional solvents, and it cannot be melted before it burns. This is because the attractive forces and stability of crystal structures are greater than those that result from interaction between polymer and solvent. Hence, cellulose itself is not suitable for use as an adhesive. The same can be said of regenerated cellulose. In order to make cellulose soluble or meltable, the hydrogen bonds must be broken (i.e., cellulose molecules must be more flexible and possess high entropy, so that they can be separated easily). 

Charge transfer between the constituent atoms is thought to be important for the stability of crystal structures. In our previous work [1] the transferred charge in the case of ARNi and AlNia was estimated from Auger parameter measurements. In the present study, performing non relativistic spin-restricted and spin-unrestricted DVY molecular orbital calculations of model cluster we obtain more detailed information on the particular orbitals involved in the charge transfer processes. 

The structural importance of the quantitative lattice theory of ionic crystals discussed above lies in the light which it throws on the stability of crystal structures and the conditions which determine the appearance of different structures in substances chemically closely related, on the types of binding which occur in different structures, and on questions of solubility. We may consider these several points separately. 

Zhi et al. [31] reported the effect of the precipitator concentration on the activity of mesoporous Cu-Ce-La mixed oxide catalyst. They concluded that the precipitator concentration influences the activity of catalyst via the stability of crystal structure and mesoporous structure. 

Note also that all the structures discussed above, are determined for bulk materials. If normal thermodynamic conditions are close to the limit of stability of a given phase, then even small external influences (e.g. grinding of the crystals) can change its structure. The effect of particle size on stability of crystal structure of pure cobalt has been studied [36], showing that while common hep allotrope of Co is stable in the bulk, particles with diameters of 100-200 A have a/cc structure and those of 20-50 A have a bcc lattice. In these structures, the particles the minimum of surface free energy, which yields a stable equilibrium configuration of atoms with minimal internal energy. 

Relative stability of crystal lattices The hard-sphere model introduced by Born and Madelung was later used to understand the relative stability of crystal structures. Some structures, typical of binary oxides, are represented in Fig. 1.1. An important parameter is the ratio r+/r between the cation and the anion ionic radii (r+ and r, respectively). When cations... 

Factors Influencing the Stability of Crystal Structures 5.1. Electrochemical Factor... 

Generally the name of a compound should correspond to the most stable tautomer (76AHCS1, p. 5). This is often problematic when several tautomers have similar stabilities, but is a simple and reasonable rule whose violation could lead to naming phenol as cyclohexadienone. Different types of tautomerism use different types of nomenclature. For instance, in the case of annular tautomers both are named, e.g., 4(5)-methylimidazole, while for functional tautomerism, usually the name of an individual tautomer is used because to name all would be cumbersome. In the case of crystal structures, the name should reflect the tautomer actually found therefore, 3-nitropyrazole should be named as such (97JPOC637) and not as 3(5)-nitropyrazole. 

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. 

The presence of the foreign cation stabilizes the crystal structure of a - Mn02 compounds. This manganese dioxide modification (more exactly it is not a real MnOz modification, since the structure contains a considerable proportion of foreign atoms) can be heated to relatively high temperatures (300 - 400 °C) without destruction of the lattice. Although Thackeray et al. reported the synthesis of cation-and water- free a - MnOz [49, 50J, which is reported to be stable up to 300 °C without destruction of the [2 x 2] tunnel structure, it is commonly believed that a small,... 

The Sodium Chloride and Cesium Chloride Structures.—The agreement found between the observed inter-atomic distances and our calculated ionic radii makes it probable that the crystals considered are built of only slightly deformed ions it should, then, be possible, with the aid of this conception, to explain the stability of one structure, that of sodium chloride, in the case of most compounds, and of the other, that of cesium chloride, in a few cases, namely, the cesium and thallous halides. 

Many complex ions, such as NH4+, N(CH3)4+, PtCle", Cr(H20)3+++, etc., are roughly spherical in shape, so that they may be treated as a first approximation as spherical. Crystal radii can then be derived for them from measured inter-atomic distances although, in general, on account of the lack of complete spherical symmetry radii obtained for a given ion from crystals with different structures may show some variation. Moreover, our treatment of the relative stabilities of different structures may also be applied to complex ion crystals thus the compounds K2SnCle, Ni(NH3)3Cl2 and [N(CH3)4]2PtCl3, for example, have the fluorite structure, with the monatomic ions replaced by complex ions and, as shown in Table XVII, their radius ratios fulfil the fluorite requirement. Doubtless in many cases, however, the crystal structure is determined by the shapes of the complex ions. 

The Relative Stability of Alternative Structures of Ionic Crystals.—... 

Both thermodynamic and kinetic factors need to be considered. Take, for instance, acetic acid. The liquid contains mostly dimer but the crystal contains the catemer and no (polymorphic) dimer crystal has ever been obtained. Various computations (R. S. Payne, R. J. Roberts, R. C. Rowe, R. Docherty, Generation of crystal structures of acetic acid and its halogenated analogs , J. Comput. Chem, 1998, 19,1-20 W. T. M. Mooij, B. P. van Eijck, S. L. Price, P. Verwer, J. Kroon, Crystal structure predictions for acetic acid , J. Comput. Chem., 1998, 19, 459-474) show the relative stability of the dimer. Perhaps the dimer is not formed in the crystal because it is 0-dimensional and as such, not able to propagate so easily to the bulk crystal as say, the 1-dimensional catemer. 

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