Temperature dependence of the lattice

The dependence of birefringence on the temperature seems to be correlated to the temperature dependence of the lattice parameters ratio c/a shown in Fig. 102. 

At high temperatures, the module of the pyroelectric constants of both compounds increases more significantly and reaches an extremum at about 480K. Fig. 113 shows the temperature dependence of the pyroelectric coefficients. This phenomenon could be related to the change in dilatation mechanism that was observed while investigating the temperature dependence of the lattice parameters (see Fig. 102). 

Fig. 38. Temperature dependence of the lattice constants a, b, c and the unit cell volume V of [Fe(2-pic)3]Cl2 CH3OH. The solid lines are calculated using the parameter values of Table 20. According to Ref. [39]...

Figure 30 shows the temperature dependence of the lattice parameters of GdPt, obtained by x-ray powder diffraction. The estimated values of the spontaneous magnetoelastic... 

In the first stage of this work we studied the kinetics of saturation of fullerite Cgo with He at room temperature and at pressures close to 105 Pa., The temperature dependences of the lattice parameter of Cgo being saturated with helium was investigated within the temperatures interval of 30-300 K under warm-up and cool-down conditions. 

The salt undergoes a crystalline transition from tetragonal to cubic at 412 K AH for the transition is 2.49 kJ mol-1. The temperature dependence of the lattice parameters and thermal expansion coefficient has been carefully studied.100... 

The temperature dependence of the lattice parameters a and c of ZnO were measured by Khan [25] and Reeber [26] and are displayed in Fig. 1.7. For low temperatures (T < 200 K) ZnO exhibits a very small thermal expansion. For temperatures higher than 300 K, the thermal expansion of the a and c axis are linearly dependent on T, which means that the thermal expansion... 

Figure 4.11 Temperature dependence of the lattice constant of Ni nanoparticles in the Ni/Si02 catalyst in the single gas medium (H2) and in the reaction mixture H2 + CO at the stationary occurrence of the syngas methanation. The abscissa shows the temperature of the catalyst granules as measured with a thermocouple [3].

Since there is only little side group reorientation the transition is connected with small anomalies of the temperature dependence of the lattice parameters (Fig. 25). 

Figure 21.5 shows the Tc in superlattices determined by the Raman data, variable-temperature XRD, and the phase-field model, as a function of the BaTiOs and SrTiOs layer thicknesses. The XRD measurements provide data on the temperature dependence of the lattice parameters, and the observed noticeable change in the slope of the out-of-plane c-axis lattice parameter due to the... 

The thermal expansion of solids depends on their structure symmetry, and may be either isotropic or anisotropic. For example, graphite has a layered structure, and its expansion in the direction perpendicular to the layers is quite different from that in the layers. For isotropic materials, ay w 3 a . However, in anisotropic solid materials the total volume expansion is distributed unequally among the three crystallographic axes and, as a rule, cannot be correctly measured by most dilatometric techniques. The true thermal expansion in such case should be studied using in situ X-ray diffraction (XRD) to determine any temperature dependence of the lattice parameters. 

Figure 13 Temperature dependence of the lattice parameters of [Fe(phen)2(NCS)2] ( ) and [Fe(btz)2(NCS)2] (O). Reproduced with permission from ref 48.

The peculiar temperature and composition dependence of the valence of chemically collapsed phases of SmS was first observed in the system Sm1 xGdxS (55). Recently a phase diagram in the (x, T)-plane has been proposed for this system (41) as well as for CeTh alloys (44). When cooled below about 200 K the chemically collapsed phases of SmS show a dramatic lattice expansion, in some cases with explosive character (55) and disintegration of the crystal into a black powder. An example of this transition towards a more divalent state of Sm on cooling in SmAs 18 S 82 and Sm 81 Y19S is shown in Fig. 22 and 23, where we show the data of Poliak et al (63). The temperature dependent configurational mixing of Sm ions which is directly visualized in the XPS data is the source of the anomalous temperature dependence of the lattice constant. No detailed analysis of the dependence of the Sm 4/lineshape on temperature... 

Fig. 22. Temperature dependence of the lattice constant of pure SmS, SmAs and chemically collapsed Sm.g1Y.19S and SmS.82As.i8. Note the anomalous expansion of the collapsed phases on cooling (Ref. 63).

Figure 4. left Projection of the crystal structure of FA2AsF6 perpendicular to the stacks at 300 K (top) and 120 K (bottom), and right temperature dependence of the lattice parameters of FA2AsF6. ... 

Skanthakumar S, Loong CK, Soderholm L, Nipko J, Richardson JW Jr, Abraham, MM, Boatner LA (1995) Anomalous temperature dependence of the lattice parameters in H0PO4 and H0VO4 rare earth quadrapolar effects. J Alloys Compd 225 595-598... 

Temperature dependencies of the lattice parameters of LSTGO-8, normalized to the perovskite-like cell, have nonlinear and anisotropic character (fig. 4). A small decrease in the cell volume (AV = -0.09 %) occurs at the phase transition. 

Figure 6. Temperature dependencies of the lattice parameters in Lao65Caoo4TiOs,...

The phase changes that occur in BaTiOs are characterized by an expansion of the original cubic lattice in the direction of the spontaneous polarization and a contraction in the perpendicular direction. The temperature dependence of the lattice parameters of BaTiOs in the four phases is shown in Figure 31.9. 

Also YbPdln shows the typical behavior of an intermediate-valent compoimd. The magnetic susceptibility was measured up to about 1000 K (Cirafici et al. 1985). The intermediate-valent behavior is also evident from the temperature dependence of the lattice parameters. A significant anomaly is detected only for the c parameter, while a increases linearly. 

FIGURE 4 Low-temperature dependencies of the lattice parameters of (pseudo)-tetragonal (T), monoclinic (M), orthorhombic (O), and rhombohedral (Rh) PrAlOj phases, obtained on cooling and heating (solid and open symbols, respectively). The lines are guides for the eye. For the LT-V phase below 110 K, both monoclinic and tetragonal lattice parameters are shown (Vasylechko, unpublished data). 

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