Change of the lattice parameter

Although MIL-47, and especially MIL-53(A1), had been found on many occasions to dynamically respond to adsorption of particular compounds, referred to as breathing [35] in the literature, in these liquid phase conditions, only minor changes of the lattice parameters have been observed. A study of xylene separations in vapor phase on MIL-5 3(A1) shows that breathing profoundly influences the shape of the obtained breakthrough profiles as a function of adsorbate concentration [97]. 

Fig. 7. Relative change of the lattice parameter in TS-6 along the chain direction as a function of conversion X. Indices m and p refer to monomer and polymer, respectively. The full curve is derived from a continuous dilatometric measurement the dashed curve is calculated according to Ref. by minimizing the elastic energy assuming a ratio Ep/E = 5.0 for the elastic constants of polymer and monomer, respectively. Open circles are X-ray data from Ref. crosses represent data from optical absorption studies...

Anharmonicity effects in nanocrystals Materials properties, especially the physical properties, are dependent on temperature. A change in the lattice parameters of crystalline materials is expected when population of the different levels for each normal mode is influenced by variation in temperatures. Therefore, any change of the lattice parameters with temperature is attributed to the anharmonicity of the lattice potential. Raman spectroscopy is a great tool to investigate these effects. The Raman spectra of various nanocrystals as well as other amorphous or crystalline materials show changes in line position and bandwidth with temperature. These changes manifest in shift of line position and a change in line width and intensity. 

The negative Langevin susceptibility Xju hardly varies with concentration x for both components in Ag Pti-. It more or less compensates for the positive orbital contribution Xvv e corresponding atom. A variation in xSia with concentration should primarily arise from the change of the lattice parameter with concentration (Banhart et al. 1986). It seems that this effect is not very pronounced for Ag Pti-jr. 

In fact, the structure of the RB2C phases is very similar to that of the RB4 phases, as shown by their analogous X-ray powder diffraction diagrams and the same indexes being identified. The difference between the two phases represents only the changes of the lattice parameters, the parameters a and c diminish by about 4.5% and 7 to 9%,... 

The crystal in Fig. 5.34 illustrates the concept of isomorphism, the possibility that two different motifs fit into the same crystal. For polymers isomorphism of repeating units is most important. Isomorphism of complete chains is seldom possible. Polyfvinyl fluoride) that fits into a crystal of poly(vinylidene fluoride) provides a rare exception. The repeating-unit isomorphism can be separated into three types Type 1 occurs when both homopolymers have die same crystal structure, and a smooth change of the lattice parameters occurs on changing the concentration. An example of type 1 repeating-unit isomorphism is poly(vinylidene fluoride-co-vinyl fluoride). Type 2 is also called isodimorphism and occurs if the homopolymers have different crystal structures. A change in structure occurs at an intermediate concentration. Type 3 occurs if one homopolymer does not crystallize by itself, but participates in the crystal of the other. 

Changes of the lattice parameters 4.1. Anomalies of the Debye-Waller factor ... 

Changes of the lattice parameters and bond lengths with the oxygen nonstoichiometry the structural T O transformation... 

Fig. 12. Dependence of the lattice parametets on oxygen nonstoicliiometry (a) a-parameter, (b) 6-parameter (c) c-parameter. NPD after Cava et al. (1990) (solid squares), at r=5K (compare table 3a) Jorgensen et al. (1990b) (open circles), NPD at RT. Note the abrupt change at the phase transition (x=6.35-6.45) of the Zr-gettered samples of Cava et al. The vertical shift of the two groups of data is due to the different temperatures. The vertical lines show the boundaries of changes of the lattice parameters. The onset of superconductivity for the Zr-gettered samples is x = 6.45, that for the quenched samples is x 6.35.

The total relative change of the lattice parameters in the x=6.0-6.99 range is large -1.15% for the a-axis, +0.72% for the 6-axis, -1.64% for the c-axis, and -1.85% for the unit cell volume. The a- and 6-parameters as well as the orthorhombicity have a linear dependence on oxygen only in the underdoped range x = 6.5-6.75. The large number of measured compositions allows to measure the deviation from hnearity. At x = 6.75 the... 

Relative changes of the lattice parameters and apical bond with doping... 

Lanthanum ions introduced into alumina structure, decrease the solubility of copper and chromium ions, thus, providing the decrease of the mineralizing effect. Copper and chromium ions not involved in the support structure, yield an extra quantity of copper chromite, which enriches coirespondingly the solid solution of CUAI2O4 and CuCr204 spinels, providing the change of the lattice parameter. 

The change of the lattice parameter of a fixed sample at low temperature is... 

This proves that only the extended tr-electron system of the diacetylene backbone is responsible for the enhanced polarizability. This conclusion is supported by the experimental analysis for three orthogonal directions in TS single crystals shown in Fig. 9.33 [75]. The minor variations for the two orthogonal directions (2) and (3) can be explained by the changes of the lattice parameters. In contrast, the change of the respective lattice parameters with polymer content does not suffice to explain the change of Ae. ... 

---