Susceptibility pressure dependence

Uranium metal is weaMy paramagnetic, with a magnetic susceptibility of 1.740 X 10 A/g at 20°C, and 1.804 x 10 A/g (A = 10 emu) at 350°C (51). Uranium is a relatively poor electrical conductor. Superconductivity has been observed in a-uranium, with the value of the superconducting temperature, being pressure-dependent. This was shown to be a result of the fact that there are actually three transformations within a-uranium (37,52). 

In a solution where a nonzero volume change between the electronic isomers, HS and LS, is encountered, the position of the spin equilibrium will depend on pressure. The volume change, usually denoted here AF°, may be obtained from the study of the pressure dependence of equilibrium properties such as the magnetic susceptibility or the electronic spectrum. In favorable cases, A F° values may be derived from the amplitude of sound absorption observed in ultrasonic relaxation measurements of a spin equilibrium as will be shown in the... 

Calcium carbonate solubility is also temperature and pressure dependent. Pressure is a 6r more important fector than temperature in influencing solubility. As illustrated in Table 15.1, a 20°C drop in temperature boosts solubility 4%, whereas the pressure increase associated with a 4-km increase in water depth increases solubility 200-fold. The large pressure effect arises from the susceptibility of the fully hydrated divalent Ca and CO ions to electrostriction. Calcite and aragonite are examples of minerals whose solubility increases with decreasing temperature. This unusual behavior is referred to as retrograde solubility. Because of the pressure and temperature effects, calcium carbonate is fer more soluble in the deep sea than in the surfece waters (See the online appendix on the companion website). 

The pressure dependence of other properties can be used to calculate AV°. Because the volume differences between the spin states are relatively large, pressures of up to only 1000-3000 atm are sufficient to cause a significant shift in the spin equilibrium. Observation of the change in the electronic absorption spectrum, for example, enables calculation of A V°, with the help of certain assumptions and ancillary experiments (19). The extinction coefficients for absorption by the two isomers must be obtained. In the simplest model they are assumed to be independent of pressure. In one approach (19) they were found by examination of the temperature dependence of the electronic absorption spectrum. This required knowledge of the temperature dependence of the spin-equilibrium constant, which was obtained from the temperature dependence of the susceptibility observed in the Evans NMR experiment. Clearly a more direct measurement is preferable. 

Figure 11 Pressure dependence of the spin susceptibility, d In yjdp, versus temperature for three representative organic metals. (From Ref. 79.)...

The very large pressure coefficient of the susceptibility (Fig. 14a) and conductivity in the metallic regime (d In room temperature [6]) raises a serious problem for the comparison with theory, which usually computes constant-volume temperature dependences. Hence the temperature dependence at constant pressure that is observed in actual experiments must be transformed into constant-volume data since the change of volume (due to the thermal expansion) cannot be ignored between 300 and 50 K. No detailed determinations of the constant-volume resistivity have been performed so far. However, a crude estimate of the intrinsic temperature dependence can be performed using the thermal expansion and the pressure dependence of the a axis at various temperatures [59] (Fig. 14b). 

Figure 14 (a) Pressure dependence of the spin susceptibility x (T,T)-l/2 from NMR data. (From Ref. 41b.) (b) Constant-pressure and constant-volume temperature dependences of the resistivity of (TMTSF)2AsF6 derived point by point from the constant-pressure data of Fig. 12. The lattice parameters are from Ref. 33 and the pressure coefficient of the conductivity from Ref. 57.

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The pressure dependence of susceptibility and relaxation rate experiments... 

The expression above does not indicate any pressure-dependence in the molar susceptibility. However, the observed decrease in susceptibility with increased pressure is consistent with the fact that NOt has a tendency to dimerize, and that dimerization is favored by higher pressure. The dimer has no unpaired electrons, so the dimerization reaction effectively reduced the number of paramagnetic species. 

Saturation magnetization M0, Curie temperature Tc, high-field susceptibility Xht anc the pressure dependences of M0 and Tc for Fej alloys (Beille et al. 1979). 

Fig. 165. Temperature dependence of the AC susceptibility of CcjNij at various pressures. The insert shows the pressure dependence of Neel temperature. From Umeo et al. (1996a).

Besides the isomer shift, the experimental linewidth and the electric field gradient, information about the crystal-field anisotropy can also be obtained from Yb Mossbauer spectroscopy, as shown by Bonville et al. (1990) and Bonville and Hodges (1985) for YbCuAl. Furthermore, YbCuAl was investigated by Yb Mossbauer spectroscopy at pressures up to ISOkbar. The data give strong evidence for a valence transition towards the 4f (Yb ) configuration. At 4.2 K the transition is completed at about SOkbar (Schdppner et al. 1986). This behavior is paralleled by the pressure-dependent susceptibility measurements (Klaasse et al. 1977). 

Fig. 19. Pressure dependence of the Curie temperature of YbNiSn (from Cornelius et al. 1995). Inset experimental ac-susceptibility signal in units of nanovolts at 0.8 GPa after subtraction of a temperature-dependent background.

Fig. 54. Normalized pressure dependences of inverse (as T 0) susceptibility Xo > position of x( ) maximum, inverse square root of low-T resistivity coefficient, and...

Fig. 44. Left panel Calculated pressure dependence of spin Ms orbital Mi) and total moment Ms + Mi). Right panel Pressure dependence of calculated longitudinal susceptibility. The steep drop at is caused by the loss of intra-band transitions due to finite resolution. The enhancement of xo under pressure for small suggests the...

However, subsequent measurements of the electrical resistivity (Haen and Lethuillier, 1975 Abou Aly et al., 1975 Lethuillier and Haen, 1975) and the pressure dependence of (DeLong et al., 1975) were performed which may prove difficult to reconcile with a simple ionic behavior for Pr impurities in LaSns. The electrical resistivity measurements show weak minima in the vicinity of 10-20 K at a Pr concentration of greater than, or the order of, lOat.%. The resistivities also exhibit a local maximum around 7.5 K for Pr concentrations less than 80 at.%, which is the lowest Pr concentration where the resistivity maximum and the Neel temperature (as determined by static susceptibility measurements) coincide. For Pr concentrations well below 80 at.%, the resistivity maximum and the rapid decrease in the resistivity below 7.5 K have been associated with a thermal depopulation of the CEF excited states of Pr. 

Recently, DeLong et al. (1976) reported measurements of the depression of T, the magnetic susceptibility, specific heat and pressure dependence of for (LaSm)Sn3 alloys. The extremely large value of the initial depression of Tc was confirmed by ac susceptibility and specific heat measurements in the superconducting state. 

P < 15 kbar) on the YbAh susceptibility (dY/d < 1-5 x 10" emu/gm-kbar) Sales, 1974). The magnetic susceptibility of YbAb is temperature independent at low temperatures (0.6 x emu/mole), but increases with increasing temperatures reaching a maximum of 5.5 x 10 emu/gm at 850 K (Klasse et al., 1973). At room temperature the susceptibility of YbAl2 is strongly pressure dependent with d /dP = 2 x 10 emu/mole-kbar (Sales, 1974). 

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