Fig. 9.21. Resistivity of lithium versus density (Fortov et al. 2001). The legend of points includes the initial temperature and the maximum pressure, and numbers near the points show the calculated temperature.

tion of sodium into the dielectric state was reported by Fortov et al. (2001). The dramatic changes in the atomic and electron structure of lithium and

sodium obtained in the quantum mechanical calculations by Neaton and Ashcroft (1999, 2001) indicate strong electron–phonon interaction. This suggests the possibility of superconductivity at relatively high temperatures (Christensen and Novikov 2001).

The transition to the dielectric state is predicted not only for the alkali metals. Self–consistent augmented–plane–wave calculations by McMahan and Albers (1982) predict that nickel should transform from a metal to an insulator at a pressure of 34 TPa, and then revert back to a metal at 51 TPa. This prediction still requires experimental confirmation.

9.4Ionization by pressure

The e ect of pressure–induced ionization is most pronounced in the case of hydrogen. Figure 9.5 shows the data on the quasi–isentropic compression of liquid and gaseous hydrogen in planar 1 and cylindrical 2 geometries (Fortov et al. 2003) together with the results of the compression in the light–gas gun 5 (Weir et al. 1996a) and the results of explosive cylindrical compression in an axial magnetic field 3 (Hawke et al. 1978) and 4 (Pavlovskii et al. 1987). Because of the small molecular weight, the multiple shock compression of hydrogen is accompanied by relatively weak heating – even at maximum pressures of 0.1–1 TPa, the typical values of the temperature do not exceed T = 104 K, which favors the regime of

“cold” ionization. For hydrogen compressed to densities of ρ 0.01–1.2 g cm−3 and heated to T 104 K at pressures below 1.5 TPa, a wide spectrum of plasma states was realized, characterized by a fully developed ionization, α 1, and a high electron concentration, ne 2 · 1023 cm−3. At maximum compressions, the plasma is degenerate, neλ3e < 200, and is strongly nonideal both with respect to Coulomb (γ 10) and to interatomic (nara3 1) interactions.

It is interesting that the extrapolation of the simplest plasma models to this region of strong nonideality leads to the thermodynamic instability of Debye– H¨uckel models (the “Coulomb collapse” indicated by the arrow DP in Fig. 9.5) and to the divergence of the Spitzer formula (arrow SP). The first of these approximations is depicted by the DHA curve in Fig. 9.5 and predicts the “pressure– induced ionization” at densities approximately two orders of magnitude lower than the experimental values. The shock compression leads to the overlap of the wavefunctions for neighboring atoms and, hence, to the percolation conductivity mechanism suggested by Likal’ter (1998, 2000), which is described in terms of the density–dependent reduction of the ionization potential (see the discussion of the percolation model in Chapter 4).

A decrease in the ionization potential with density is also predicted by the Mott model (Mott and Davis 1979), which was used by Ebeling et al. (1991) to construct a semiempirical broad–range model of ionization equilibrium and transport properties (curve M in Fig. 9.5) of compressed and hot matter,

The parameters a, R and ∆ were chosen to reproduce experimental data on pressure–induced ionization of alkali metals. One can see that the proposed approximations provide a good qualitative description of experimental results.

By using the ring (Debye) approximation in a big canonical ensemble of statistical mechanics (curve LDH) to describe Coulomb nonideality, one can reduce the discrepancy between the theoretical and experimental results down to one order of magnitude. The remaining disagreement can be eliminated by introducing the hard–sphere model to describe the short–range repulsion of atoms and ions (curve HS) and by taking into account the compression–induced change in the energy spectrum of atoms and ions within a simplified model discussed in Section 9.3 (curve CA). An attempt to take into account the “hopping” character of the electrical conductivity in nonideal plasmas was made by Redmer et al. (2001). The corresponding results are marked by the symbol “R” in Fig. 9.5. The QMC curve corresponds to the calculation of the conductivity by the quantum MC method (Filinov et al. 2000a,b, 2001; Mulenko et al. 2001).

Figures 9.6–9.9 display the results of the electrical conductivity of shock– compressed Xe, Ar, Kr, and He. Similar to the case of hydrogen, at “low” temperatures one can clearly see the e ect of the pressure–induced ionization occurring at higher plasma densities 1–10 g cm−3. For multielectron atoms it is also

natural to expect that, as compression is increased further, the first pressure– induced ionization will be followed by the next stages of multiple ionization. These stages should be accompanied by the emergence of new boundaries in the phase diagram. Unfortunately, experimental investigation of the regimes of multiple ionization is beyond the currently available capabilities of the explosive experimental equipment.

Along with the results of multiple (“cold”) compression, the same figures show data obtained previously (Ivanov et al. 1976; Mintsev and Fortov 1979; Mintsev et al. 1980) by measuring the electrical conductivity of singly and doubly compressed plasmas. The temperature in this case is almost one order of magnitude higher, so that the e ect of thermal ionization becomes dominant. The e ect increases with increasing molecular weight of the studied substance and is particularly clear for xenon (see Fig. 9.6). It can be seen that upon thermal ionization at T (4–10)·103 K, a high level of the electrical conductivity of 103 ohm−1cm−1 is achieved even at low densities of ρ 0.04–1 g cm−3, whereas the pressure–induced ionization can provide the same conductivity in cold (T 104 K) matter only at extremely high densities of ρ 10 g cm−3. It can also be seen that, with increasing molecular weight of substances, the relative jump in the conductivity due to pressure–induced ionization decreases and becomes as low as two orders of magnitude for xenon. It is noteworthy that the electrical conductivity of xenon plasma measured in experiments with multiple shock compression is close to that obtained under static compression in diamond anvils (crosses in Fig. 9.6).

It is important to note that some of the models discussed here lose thermodynamic stability in the parameter regime achieved in the experiments. This might be considered as an indication of a “plasma” first–order phase transition (see Chapter 5) leading to the stratification of a strongly nonideal plasma into phases characterized by di erent degrees of ionization and compressibility. A sharp increase in the electrical conductivity of a dense plasma might suggest the occurrence of such a phase transition.

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