Lattice parameter characteristic

To rationalize the units, g is divided by the lattice parameter, a of each carbide. The final parameter (g /a) = characteristic vibrational energy density has the units of energy per volume (GPa) which is the same as the hardness units. The correlation of this with hardness is shown in Figure 10.3. The correlation is good especially when it is considered that the hardness numbers for carbides scatter as much as 30 percent. 

Figure 5.8. Lanthanide Ln203 oxides (cubic cI80-Mn2O3 type, on the left side) and Pb alloys (LnPb3, cubic cP4-type, on the right). The trends of the lattice parameter and of the heat of formation are shown (see the text and notice the characteristic behaviour of Eu and Yb). A schematic representation of the energy difference between the divalent and trivalent states of an ytterbium compound is shown. Apromff represents the promotion energy from di- to trivalent Yb metal, A,//11, and Ar/Ynl are the formation enthalpies of a compound in the two cases in which there is no valence change on passing from the metal to the compound the same valence state (II or III) is maintained.

The character of the pattern does not alter when the angle of inclination of the specimen to the beam is changed. Thus the geometry of a polycrystalline pattern is a set of lengths, Hhki, i.e. set of inter-planar distances dhki characteristic of the crystal lattice. Polycrystal-type electron diffraction patterns provided a complete three dimensional set of diffraction reflections, however, two or more reflections, with different hkl can overlap in one ring of the pattern, especially in the cases where the material studied has large lattice parameters. 

The lattice parameters for the polymorphic MaOs obtained by various investigators are compared in Table 4. The different polymorphic forms show characteristic M—0 streaching frequencies in the infrared between 500 and 600 cm i. These M—O frequencies were found (75) to vary linearly with the lattice parameter a of the oxides. 

Identification of unknown crystal structures and determination of phase fields by X-rays can be problematical if the characteristic patterns of the various phases are quite similar, for example in some b.c.c. A2-based ordered phases in noble-metal-based alloys. However, in many cases the characteristic patterns of the phases can be quite different and, even if the exact structure is not known, phase fields can still be well established. Exact determination of phase boundaries is possible using lattice-parameter determination and this is a well-established method for identifying solvus lines for terminal solid solutions. The technique simply requires that the lattice parameter of the phase is measured as a function of composition across the phase boimdary. The lattice parameter varies across the single-phase field but in the two-phase field becomes constant. Figure 4.12 shows such a phase-boundary determination for the HfC(i i) phase where results at various temperatures were used to define the phase boundary as a fimction of temperature (Rudy 1969). As can be seen, the position of is defined exactly and the method can be used to identify phase fields across the whole composition range. 

The XRD powder patterns of V-containing silicalite samples indicate in all cases the presence of only a pentasyl-type framework structure with monoclinic lattice symmetry, characteristic of silicalite-1 no evidence was found for the presence of vanadium oxide crystallites. The analysis of cell parameters of VSU545 does not indicate significant modifications with respect to those found for pure silicalite-1. This is in agreement with that expected on the basis of the small amount of V atoms present in V-containing silicalite. 

Consider now a one-dimensional lattice of parameter /. The distance of each atomic jump depends on the rate of de-excitation once the adatom is excited and is translating along the lattice. This de-excitation process can be described by a characteristic life time r in the symmetric random walk, as in many other solid state excitation phenomena. The initial position of the adatom is taken to be the origin, denoted by an index 0. The adatom accomplishes a jump of distance il if it is de-excited within (i — i)l and (i + i)l, where / is the lattice parameter, or the nearest neighbor distance of the one-dimensional lattice, and i is an integer. The probability of reaching a distance il in one jump is given by... 

YPd2Sb was reported to be isotypic with the crystal structure of MnCu2Al with a lattice parameter a = 0.6691 (Ishikawa et al., 1982 powder diffraction). The sample was prepared by levitation melting followed by annealing at 1173 K for several days. Riani et al. (1995) confirmed the crystallographic characteristics for this compound, MnCu2Al type, a = 0.6691. 

MCrX3 (M = Li—Cs X = halide) have been reviewed770 and mass spectrometric studies of the compositions of MCrCl3 (M = K or Cs) vapours have been reported and the thermodynamic characteristics for the evaporation of these compounds determined.776 Electrode potential data for Cr11 in KCl-LiCl melts have been reported.78 CsCrI3 has been obtained by melting Csl and Crl2 (1 1) in a sealed, evacuated quartz tube. The lattice parameters of this compound have been determined and compared with those of other compounds of this formula type.79... 

Ungar and Zeng [33] have comprehensively summarized the research on strictly monodisperse materials from their first synthesis in 1985 until 2001. From the earliest studies it became apparent that, due to the monodisper-sity of the materials, the thickness of the lamellar crystals formed is always an integer fraction of the extended chain length (allowing for any chain tilt), such that the polymers always crystallize in the extended chain form or fold exactly in half (once-folded), or in three (twice-folded), etc. This behavior means that, when the alkanes are crystallized at a particular temperature, the entire lamellar population has very closely the same thickness and stability. The use of such an ultra-pure system to study the impact of thickness on lattice parameters removes many of the problems inherent to polymers, whilst maintaining the most important characteristic of chain length. 

Figure 15. Graphitization of nanocrystalline graphene precursors (see Fig. 9). Chemical structures (dots represent heteroatoms or methyl groups) and stacking order are given as a function of characteristic temperatures. The polymerization and aromatization are reflected in the average lattice parameters which can be extracted from X-ray diffraction data. The correlation between the axis parameters indicates the shrinking of the cell volume [75].

The lattice parameters of nonstoichiometric uranium oxides, quenched from 1100° C., were determined within the composition range U02 to U4Og. Two separate linear relations for the lattice parameter as a function of oxygen content were obtained one characteristic of U02+2. and the other of U409 J/. The two functions are a0 = 5.4705 - 0.094 x (0 < x < 0.125) and a0 = 5.4423 + 0.029 y (0 < y < 0.31). Helium displacement densities were determined for some samples the values obtained are consistent with an oxygen interstitial model for U02+a. and an oxygen vacancy model for U409 y ... 

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