Lattice dimension

Angstrom unit, A A unit of length equivalent to 10" cm, (10 °m). Used to describe molecular and lattice dimensions and wavelengths of visible light. 

To obtain a reliable value of from the isotherm it is necessary that the monolayer shall be virtually complete before the build-up of higher layers commences this requirement is met if the BET parameter c is not too low, and will be reflected in a sharp knee of the isotherm and a well defined Point B. For conversion of into A, the ideal adsorptive would be one which is composed of spherically symmetrical molecules and always forms a non-localized film, and therefore gives the same value of on all adsorbents. Non-localization demands a low value of c as c increases the adsorbate molecules move more and more closely into registry with the lattice of the adsorbent, so that becomes increasingly dependent on the lattice dimensions of the adsorbent, and decreasingly dependent on the molecular size of the adsorbate. 

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... 

Substituting A1 atoms for Ga atoms does not change the lattice dimensions, which are determined by the size of As, the largest atom of this set. Here, the lower electronegativity of A1 relative to Ga leads to more ionic character and a smaller band gap. 

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. 

The basic instrumentation used for spectrometric measurements has already been described in the previous chapter (p. 277). Methods of excitation, monochromators and detectors used in atomic emission and absorption techniques are included in Table 8.1. Sources of radiation physically separated from the sample are required for atomic absorption, atomic fluorescence and X-ray fluorescence spectrometry (cf. molecular absorption spectrometry), whereas in flame photometry, arc/spark and plasma emission techniques, the sample is excited directly by thermal means. Diffraction gratings or prism monochromators are used for dispersion in all the techniques including X-ray fluorescence where a single crystal of appropriate lattice dimensions acts as a grating. Atomic fluorescence spectra are sufficiently simple to allow the use of an interference filter in many instances. Photomultiplier detectors are used in every technique except X-ray fluorescence where proportional counting or scintillation devices are employed. Photographic recording of a complete spectrum facilitates qualitative analysis by optical emission spectrometry, but is now rarely used. 

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. 

X-ray crystallography has provided the crystal type and lattice dimensions for numerous solids. In this technique, high-energy x-rays strike the crystal and are diffracted in a pattern characteristic of the particular lattice type. Complex mathematical... 

Figure 6.55 Distortion of TiOg octahedron in the tetragonal BaTiOs (top) and possible orientations of the polar axis when an electric field is applied along the pseudo-cubic (001) direction of BaTi03 (middle). Polar axes are shown by arrows inside each cube. Phase transitions in BaTiOj accompanied by changes in (a) dielectric constant (b) spontaneous polarization (c) heat capacity and (d) lattice dimensions (bottom).

X-ray diffraction patterns of the metal hydrides were obtained to determine the effect of dissolved hydrogen on the lattice dimensions and to confirm that the sample had not undergone decomposition. Results are presented in Table III. The R2Co7 materials are similar crystallographically to the RCo materials in the following respects ... 

In certain circumstances it may be possible to use accurate values of lattice dimensions as criteria of the purity of a substance. If the... 

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. 

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