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Estimates for the displacement of the phase equilibrium lines for small carbon particles containing from several hundred to several tens of thousands of atoms are made, and an error analysis of the uncertainties in these estimates is derived and evaluated using available experimental data. Hugoniot calculations for methane, benzene, polyethylene, and polybutene, based on a carbon particle surface energy adjusted equation of state, are in better agreement with shock pressure-volume and temperature data than those obtained with a bulk carbon equation of state. The results suggest that carbon particles, of order 103–104 atoms, can exist in the liquid state at lower temperatures than bulk carbon.

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Underground nuclear explosions, even though they are thoroughly contained, invariably produce spallation. This mass of earth and rock, kicked up by the initial shock wave, falls back within a second or two. It is possible that the surface waves observed from explosions originate from the impact of this material. This hypothesis has been investigated, first, by estimating the spall impulse from accelerometer data, computing the surface wave amplitudes consistent with this impulse, and comparing the results with observed amplitudes and, second, by performing computer explosion simulation experiments with and without spallation and comparing the amplitudes of the resulting surface waves. The comparison of the amplitudes consistent with the spall momentum with the observed Rayleigh amplitudes at ranges of 50-500 km indicates that the spall has sufficient impulse to account for these waves. The computer simulation experiments show that the Rayleigh amplitudes corresponding to realistic inelastic spallation have several times the amplitude 'of Rayleigh waves computed from purely elastic behavior. The surface wave for the spallation case is also delayed relative to the wave from the elastic source. Many studies [Brune et al., 1963; Press et al., 1963; Liebermann and Pomeroy, 1969; Evernden, 1969] have confirmed the development of an effective discriminant between earthquakes and explosions based on a comparison of the excitation of long-period surface waves Me and short-period body waves mo. However, the process by which an underground explosion generates surface waves is not well understood. Theoretical solutions for approximate explosionlike sources have been worked out for the case of linear elastic behavior [Lamb, 1904; Harkrider, 1964; ToksSz et al., 1964; Thiruvenkatachar and Visw,anathan, 1969; Tanyi, 1966; Alterman and Aboudi, 1969]. The actual material behavior in the neighborhood of the explosion is of course inelastic and highly nonlinear tRodcan, 1971]. If one could assume that the inelastic region of a contained underground explosion remained well below the surface, one would have some justification for using the linear approximation in the study of surface wave generation. In the case of a nuclear explosion it is unlikely that this assumption is ever valid, because of the phenomenon of surface spallation [Rinehart, 1960; Eider and Chilton, 1964; Eisler Copyright ¸ 1973 by the American Geophysical Union. et al., 1966; Chilton et al., 1966; Perret, 1971]. Spallation occurs when the compression shock from the explosion strikes the surface and refleets as a tension pulse traveling back into the rock. At some depth the tensile stress in the downward traveling wave exceeds the sum of the tensile strength of the rock, the lithostatic stress, and the compressive stress remaining in the tail end of the upward traveling compression wave. At that depth the rock parts and traps a substantial part of the shock wave momentum in a layer of rock, which flies up from the surface. The parting of the rock forms new surfaces,...

A much simplified model of nonequilibrium soot phase mixture kinetics is derived for use in hydrodynamic computation. This model is based on a review of existing shock and detonation soot recovery experiments as well as the available data on the carbon phase diagram. It yields a time and pressure–temperature path dependent value for the nonequilibrium diamond fraction of the soot mixture. Approximate methods for computing the detonation products pressure for the kinetics derived mixture of diamond and graphite are discussed. The proposed model increase in hydrodynamic computation cost is negligible.