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By J. Leliwa-Kopystynski and Roman Teisseyre (Eds.)

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Extra resources for Constitution of the Earth's Interior

Sample text

8), any two constants appearing in the interaction potential can be replaced by the quantities ρ0 and K0, convenient for direct measurements. 6 for the derivation of the Murnaghan and MurnaghanBirch equations. 8). 5). 2. The potential of Bardeen £/(r)= - - ? -*. 9) is used for the description of alkaline metals. The first two terms correspond to the Coulomb attraction between nuclei and electrons and to the energy of electron gas, and the term proportional to r - 3 includes the shielding, exchange and correlation energies.

4 2-2,,|- (,8, 2 , In particular, for various values of the parameters n and δ we obtain the following formulas (which can also be derived quite independently): I. The formula of Slater (1939) for n = 0 V d2p dV2 2 dV where the correction Ö can be expressed by the Poisson coefficient σ. A simple justification of this relation was given by Zeldovitch and Rayzer (1966). The highest vibration frequency vmaK can be estimated as follows: y velocity of acoustic waves c0 . Of- maK . minimum wavelength comparable to the lattice constant r0 Since ,2 dp _ dp c g o c - ^ = -VT2/ 2 A1/ dg dV and V d = -jj-or r 0 oc F 1 / 3 where Λ^ is the number of molecules in the volume V and the coefficient a depends on the lattice structure, we have c .

18), describing a Hugoniot adiabat which is explicitly independent of the internal energy and thus also of temperature. 4 x Fig. 1. 21) with experimental data, according to Prieto and Renero (1976). 8 1 1 09 ID ^ Fig. 2. Pressure p versus relative density 1—ρ0/ρ for eight media, according to Prieto and Renero (1980). 22) and to is the nondimensional temperature corresponding to the nondimensional pressure pfi. The numerical coefficients in eqn. 21) result from the assumption that the quantities 34 EQUATIONS OF STATE m = where κ KCVQ0B C h.

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