Lattice compression

In practice, however, the electron-hole symmetry relation (16) is never perfectly satisfied. There are deviations due to small corrections neglected in the spectrum (2). Following a lattice compression, the electron spectrum is altered and these deviations magnify under pressure and tend to suppress the logarithmic singularity (17) T, thus rapidly decreases and even vanishes above some critical pressure (Fig. 5). 

Kikegawa T, Iwasaki H (1983) An X-ray diffraction study of lattice compression and phase transition of crystalline phosphorus. Acta Cryst B39 158-164... 

We now consider the anomaly in the lattice compression observed at 77 K around 4.5 GPa. The of CeCue was reported to decrease with increasing pressure with a rate of dTm/dP = — 20 K GPa (Suzuki et al., 1985). Considering this result and Tm = 168 K at ambient pressure, we obtain a speculative P-T phase diagram, which is shown in Figure 8 (Oomi et al., 1988a). It is surprising that the point (T = 77 K, P = 4.5 GPa) falls on the line which is extrapolated from the data mentioned above. In other word, the anomaly is considered to correspond to... 

The lattice compression of Ce Kondo compoimds has been reported by many authors (Kagayama et al., 1990 Vedel et al., 1986). For example, the pressure dependence of volume of CeRh2Si2 was reported (Ohashi et al., 2003a), in which the value of IZ/Vo changes continuously with pressure. Taking the p-T curves at high pressure into account, this compound is considered to show a continuous valence transition having Bq = 139 GPa and Bo = 2.2. 

There have been quite a number of discrepancies in the compression curves of CeAl2. A discontinuous change in the pressure dependence of lattice constant at room temperature was observed by some authors (Bartholin et al., 1980 Croft and Jayaraman, 1979) around 6 GPa. But other authors did not find it below 20 GPa (Barbara et al., 1986 Vedel et al., 1986). The origin of these discrepancies seems to be a complicated issue, but it may originate mainly from the lattice compression at nonhy-drostatic condition by solidification of pressme medium. 

The lattice compression is highly anisotropic, in which the c-axis is the hardest among the three axes. The linear compressibilities are in the order, Kj, > Ka > k. Figure 68 shows the temperature dependence of the linear thermal expansion coefficients along the three crystal axes, a, (f = a, b, and c) at ambient pressure. The a curves are found to be largely different among each crystal axis. The values of and are positive and have a maximum around 105 and 75 K with values of 200 and 73 X 10 K , respectively. On the other hand, aj, is negative below... 

Figure 2 shows the leucite lattice parameters as a function of SiOj addition. Lattice parameters for the control sample are matched with reported values, whereas in SiOj-added samples, the c parameter decreases and a parameter increase compared with those in the control sample. This indicates that SiOz addition induces a lattice compression along the c-axis. However, regardless of S1O2 addition the c/a lattice ratio is always close to 1.046 this value is lower with respect to the previously reported ones (1.050) . At higher temperature (not shown), the c/a lattice ratio systematically decreases, indicating a compression along the c-axis caused to the transformation into cubic phase, as it has been described elsewhere. ... 

A more direct proof of a pressure induced structural change results from X-ray scattering data described in the contribution of Als-Nielsen. Diffraction data taken below and above 7Cs show a drastic increase in the positional coherence length from about ten to more than 50 lattice spacings and a discontinuity of the lattice compressibility, indicative of a second order transition /29,30/. Reflectivity data indicate a drastic decrease in head group dimensions and increase in electron density above tCs /31/. This can be explained by a dehydration and ordering of head groups observed also for the low temperature phases of bilayer vesicles /32/. 

Figure 12.8. Raman shift of the Ge-Ge mode as a function of lattice compression. The symbols for excitation energies are the same as in Figure 12.7. The solid curve corresponds to the least squares fit to the experimental data.

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