0018-151X/03/4104- $25.00 © 2003 MAIK “Nauka / Interperiodica” 0447 High Temperature, Vol. 41, No. 4, 2003, pp. 447–458. Translated from Teplofizika Vysokikh Temperatur, Vol. 41, No. 4, 2003, pp. 515–526. Original Russian Text Copyright © 2003 by Lomonosov, Fortov, Frolova, Khishchenko, Charakhch’yan, Shurshalov. INTRODUCTION The study of polymorphous transformations of car- bon in shock waves [1–17] is of special interest from the standpoint of the development of dynamic methods of synthesis of superhard materials [17]. In this paper, we treat one of the possible new approaches to the pro- duction of artificial diamonds, which was suggested previously [18]. This approach is based on the use of conic solid-state targets similar to those employed in problems associated with controlled thermonuclear fusion [19, 20]. The initial results of numerical simula- tion [18] were obtained disregarding the graphite-to- diamond transformation and pertained only to the study of the cumulative effect arising in the initial stage of the process of compression. We used new semiempirical wide-range equations of state for polymorphous modi- fications of carbon, as well as various models of the kinetics of phase transformation of graphite to dia- mond. The investigation was largely performed using the kinetic parameters obtained as a result of experi- ments with highly oriented quasi-single-crystal graph- ite [10]. Some calculations were performed within a model corresponding to experiments with isotropic artificial graphite [9]. All stages of the process were simulated, including the unloading. Conic targets of two types were involved, namely, those with a closed recess and with a cone smoothly changing to a channel. Note some features of real flow which are disre- garded in the formulation of the problem. The differ- ence between standard cubic diamond [1, 2] and hexag- onal modification of diamond (lonsdaleite) [4] is disre- garded, as well as the reverse transformation of diamond to graphite (graphitization) [6, 11] and the effect of thermal conductivity. Nevertheless, the sug- gested model enables one to investigate the dependence of the main characteristics of flow on the parameters of the problem and make a sound choice of such parame- ters during experiments. EQUATIONS OF STATE FOR GRAPHITE AND DIAMOND In the case of numerical simulation of unsteady- state hydrodynamic processes, one needs to know the thermodynamic properties of the medium. The employed equations of state for materials largely define the reliability of the calculation results. Given below is the model of semiempirical equations of state which we used to describe the thermodynamic characteristics of polymorphous modifications of carbon in a wide range of density and temperature in the phase diagram. The free energy F , selected as the thermodynamic potential of graphite and diamond, is represented in the form of the sum of three terms defining the elastic part of interaction at T = 0 ä (F c ) and the thermal contribu- tion of atoms (F a ) and electrons (F e ) [21], (1) The first and last components in Eq. (1) have differ- ent forms for each solid phase, and the third component has the same forms. The volume dependence of the energy of elastic interaction of diamond upon compression σ c  1 (where σ c = V 0c /V and V 0c is the specific volume of crystal at P = 0 and T = 0 K) has a conventional form [22] of expansion in powers of inverse interatomic FVT , ( 29 F c V ( 29 F a VT , ( 29 F e VT , ( 29 . + + = THERMOPHYSICAL PROPERTIES OF MATERIALS The Simulation of Transformation of Graphite to Diamond under Conditions of Dynamic Compression in a Conic Target I. V. Lomonosov 1 , V. E. Fortov 1 , A. A. Frolova 2 , K. V. Khishchenko 1 , A. A. Charakhch’yan 2 , and L. V. Shurshalov 2 1 Institute of High Energy Density, IVTAN (Institute of High Temperatures) Scientific Association, Russian Academy of Sciences, Moscow, 125412 Russia 2 Dorodnitsyn Computer Center, Russian Academy of Sciences, Moscow, 117967 Russia Received November 28, 2002 Abstract—Some results are given of numerical simulation of carbon loading in conic lead targets using alumi- num impactors moving at a velocity of 4 km/s. Semiempirical wide-range equations of state for materials and a kinetic model of nonequlibrium transformation of graphite to diamond, calibrated against the available exper- imental data, are used in the calculations. The cumulative effect on the target axis of symmetry is investigated, as well as the effect of the sample unloading after the arrival of the release wave from the rear surface of the impactor.