Kalitkin and Kuz'mina approximation

Quantum-statistical calculations of shock Hugoniots of 83 elements and several molecular compounds are approximated by simple formulas with high accuracy (0.05% on particle velocity). These approximations are valid for porosities m from 1 to 10 and pressures from 10-300 Mbar to 400-1000 Mbar; here m = R / R0, R - sample density, R0 - normal state density. The approximations are given by the formulas:

D(U) = C(m) + B(m)U + A(m)U2.
lgC(m) = c + r lgm,
lgA(m) = a + p lgm
lg[ B(m) + 2(A(m)C(m))1/2 - 1 ] = b + q lgm,

where m - the porosity (from m = 1 to m = 10, m = 1 - normal state density), a, b, c, p, q, r - the coefficients. The approximations are constructed for 83 substances.

Full reference: N. N. Kalitkin, L. V. Kuz'mina, Quantum-statistical shock adiabats of porous substances, Mat. Model., 10(7), 111-123 (1998)