Lattice dimension structure

It is important to note that, for important sub-cases of case /), which will be discussed in more detail in Sect. 2.4, there is a low extent of disorder entropy effects, if any, are small and changes of the lattice dimensions are absent or small. These particular disordered forms are not considered as mesomorphic. In such cases, the limiting models which are fully ordered or fully disordered may be designated respectively as ordered or disordered crystalline modifications, if their consideration is useful for the structural description of a polymeric material. Note... 

The crystal structures of two compounds are isotypic if their atoms are distributed in a like manner and if they have the same symmetry. One of them can be generated from the other if atoms of an element are substituted by atoms of another element without changing their positions in the crystal structure. The absolute values of the lattice dimensions and the interatomic distances may differ, and small variations are permitted for the atomic coordinates. The angles between the crystallographic axes and the relative lattice dimensions (axes ratios) must be similar. Two isotypic structures exhibit a one-to-one relation for all atomic positions and have coincident geometric conditions. If, in addition, the chemical bonding conditions are also similar, then the structures also are crystal-chemical isotypic. 

Disordered structures belonging to the class (i) are interesting because, in some cases, they may be characterized by disorder which does not induce changes of the lattice dimensions and of the crystallinity, and a unit cell may still be defined. These particular disordered forms are generally not considered as mesomorphic modifications. A general concept is that in these cases the order-disorder phenomena can be described with reference to two ideal structures, limit-ordered and limit-disordered models, that is, ideal fully ordered or fully disordered models. 

In all such circumstances the problem which presents itself is, in the first place, that of distinguishing between the different possible causes of line-broadening and then, if a definite verdict on this point can be given, to attempt quantitative interpretation in terms of this factor, be it crystal size, or the extent of the variation of lattice dimensions, or the periodicity of structural irregularities or thermal movements. 

Crystallographic data for CdSexTe x, from X-ray powder diffraction. Stoichiometries from relative amounts of starting materials, and from Vegard s law. Percentages of cubic and hexagonal structures estimated from powder diffraction intensities. Lattice dimensions in parentheses are literature data. 

As molecular packing calculations involve just simple lattice energy minimizations another set of tests have focused on the finite temperature effects. For this purpose, Sorescu et al. [112] have performed isothermal-isobaric Monte Carlo and molecular dynamics simulations in the temperature range 4.2-325 K, at ambient pressure. It was found that the calculated crystal structures at 300 K were in outstanding agreement with experiment within 2% for lattice dimensions and almost no rotational and translational disorder of the molecules in the unit cell. Moreover, the space group symmetry was maintained throughout the simulations. Finally, the calculated expansion coefficients were determined to be in reasonable accord with experiment. 

This intermolecular potential for ADN ionic crystal has further been developed to describe the lowest phase of ammonium nitrate (phase V) [150]. The intermolecular potential contains similar potential terms as for the ADN crystal. This potential was extended to include intramolecular potential terms for bond stretches, bond bending and torsional motions. The corresponding set of force constants used in the intramolecular part of the potential was parameterized based on the ab initio calculated vibrational frequencies of the isolated ammonium and nitrate ions. The temperature dependence of the structural parameters indicate that experimental unit cell dimensions can be well reproduced, with little translational and rotational disorder of the ions in the crystal over the temperature range 4.2-250 K. Moreover, the anisotropic expansion of the lattice dimensions, predominantly along a and b axes were also found in agreement with experimental data. These were interpreted as being due to the out-of-plane motions of the nitrate ions which are positions perpendicular on both these axes. 

There are no indications that the molybdenum oxides considered exhibit variations of lattice dimensions which would indicate extended homogeneity ranges. They form well developed crystals which give excellent x-ray photographs and they are stable in air up to about 200° C. The crystal structures of all of them have now been studied. They often possess a basic structure, which provides a basis for classification. Such a classification is illustrated in Table II here the known tungsten and mixed molybdenum-tungsten oxides have also been listed, since they fit naturally into such a scheme. 

Atomic and molecular displacement under constraint. Thermal expansion and compressibility are large and anisotropic. Sometimes structural data have been extrapolated from the room temperature (RT) down to low temperature (LT) simply by considering changes in lattice dimensions. This has led to disappointing results since, even in the absence of a phase transition, molecular shapes and orientations may change substantially. Similarly, if we find an isostatic pressure at room temperature whose effect is equivalent to a given temperature decrease at ambient pressure for, say, the chain contraction, the equivalence will not usually match for, say, the... 

If this plot is extrapolated to do = 0.335 nm for a fully graphitic structure, the Tafel slope is exactly RT/F, for this carbon, at this temperature. This supports the belief that the Tafel slope is sensitive to the d0 lattice dimension of the carbon. For any carbon that is not fully graphitized, the observed Tafel slopes result from mixtures of contributions of the two types of surfaces, disordered and ordered. As the amount of disorder decreases, the Tafel slope more closely approaches the expected values for the basal structure of the carbon. 

One of the most special aspects of cellulose polymorphy is the transformation from I to II. The conversion of the parallel-packed cellulose I structures to an antiparallel cellulose II structure is interesting because it can occur without loss of the fibrous form. This transformation is widely thought to be irreversible, although there are several reports [231-233] of regenerated cellulose I. The observation that there are two different forms of cellulose III and of IV is also remarkable. The two subforms of each allomorph have essentially identical lattice dimensions and at least similar equatorial intensities. Other intensities are different, particularly the meridional intensities, depending on whether the structures were prepared initially from cellulose I or II. The formation of the III and IV structures is reversible and the preceding polymorph (I or II) results. 

Another type of solid-solution formation is encountered when two ions as a pair can replace two other ions in a crystal lattice. Grimm and Wagner pointed out that such a twofold replacement can occur if the two salts have the same type of chemical structure and crystallize in the same type of crystal with lattice dimensions not too dissimilar. An apt example is barium sulfate, which can form solid solutions... 

The crystal structures of the azides have been reviewed by Choi [14] and tables of lattice dimensions are provided. He points out that the crystal structures of the metal azide hydrates are quite different fi-om those of the anhydrous forms. He also notes a correlation between structure and impact sensitivity to explosion, which increases with the asymmetry of the azide ion, in the sequence ... 

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