Thermodynamics of laser evaporation of polycrystalline graphite Sergei I. Kudryashov,* Nikita B. Zorov, Aleksandr A. Karabutov and Yurii Ya. Kuzyakov Department of Chemistry, M. V. Lomonosov Moscow State University, 119899 Moscow, Russian Federation. Fax: +7 095 939 0701 The change in recoil pressure of polycrystalline graphite as the radiation intensity increases during laser pulse evaporation is The change in recoil pressure of polycrystalline graphite as the radiation intensity increases during laser pulse evaporation is related to the movement of the surface as a dynamic system along the curve of the liquid±vapour equilibrium above the triple related to the movement of the surface as a dynamic system along the curve of the liquid±vapour equilibrium above the triple point of the phase diagram of carbon. point of the phase diagram of carbon. Carbon nanostructures have recently become one of the most interesting objects for various fields of natural science due to their unusual topological, electric and chemical properties. 1,2 Nanospheres and nanotubes are the metastable state of carbon in the form of clusters, occupying an intermediate position between small molecules and macroscopic material. New forms of material, which have no analogs in nature and which possess unique properties, can be obtained at the level of clusters. 3 Presently, the optothermodynamic method 4 is the only means of studying the thermodynamics of metastable states of carbon in the range of high temperatures and pressures. This ability is related to the unique ability of powerful pulse lasers to heat a substance to hundreds of thousands degrees and to develop a recoil pressure of several hundred megabar. 5 It is known that the equilibrium solid state of carbon under normal conditions is graphite, which evaporates by a thermal mechanism owing to the metallic character of its thermal and electric conductivity as determined by the absence of a forbidden band between the valence and conductivity band of the valence p-electrons in its band spectrum. 6 The laser surface evaporation of graphite is quasi-stationary if the intensity of incident light I L is lower than the threshold of explosive boiling of carbon (10 10 W cm 72 ) 7 ; this is based on the assumption that the local thermodynamic equilibrium is controlled by the usual thermodynamic variables and described by the thermodynamics of non-equilibrium processes. This allows one, starting from the known thermophysical and optical parameters of the material, to establish the correspondence between thermodynamic variables (pressure of saturated vapour p and temperature T ) of the phase diagram and the analogous parameters of the material upon its evaporation. 8 Thus, the instant recoil pressure P rec corresponds to the pressure of unsaturated vapour at the given instant temperature of the surface and can be expressed 7 as: P rec = r vap V vap V vap = rV evap V vap taking into account the continuity equation on the surface: rV evap = r vap V vap where V vap is the velocity of sound in the vapour, V evap is the velocity of the evaporation front in the substance, r is the condensed phase density and r vap is the vapour density. The main equation of the quasi-stationary approximation, relating the saturated vapour pressure and the temperature in the surface layer to the parameters of laser radiation and individual characteristics of the medium, is (17R)I L V vap /H gas (p,T )= P(T )= P 0 exp[7l (RT )] which is obtained from the boundary condition of the Stephan's problem, 7 taking into account the expression for the recoil pressure and neglecting the heat flow to the bulk medium compared to the heat flow to the surface (which maintains evaporation). Here P 0 is the parameter characterizing the change in pressure as the temperature increases, l is the heat of evaporation, R is the reflection coefficient and H gas istheheatof transition from the solid-phase state under normal conditions to the gaseous state at the given p and T. In this work polycrystalline graphite (PCG) with a density of r = 1.7 g cm 73 , consisting of weakly bound graphite grains 0.1 to 100 mm in size, each of which is a batch of individual crystallites ranging 50 to 500 A, was used as a carbon target for evaporation. 9 The dynamics of evaporation of PCG is determined by the reflection coefficient of radiation R and the heat of transition of the material from the solid-phase to the gaseous state, H gas . The reflection coefficient of PCG under normal conditions is 0.6, 10 but decreases to 10±20% of the initial value on heating the surface to its melting point 7 and becomes equal to 0.1. The heat of transition of the medium from the solid-phase state under normal conditions to the gaseous state at the given p and T in the range of the liquid±vapour phase equilibrium between the triple (T tr = 4100 K, P tr = 100 atm) and critical points (T cr = 6800 K, P cr = 2220 atm) changes from 5.1Â10 5 to 7.8Â10 5 J mol 71 , and the average heat of evaporation of graphite, l(p,T )=2.5Â10 5 J mol 71 , is equal to the jump in enthalpy of the medium under transition defined by the equilibrium curve. 8 The opticoacoustic setup described in refs. 11 and 12 was used in the experiments. The graphite target was evaporated by irradiation with a Nd:YAG laser (l =532 nm) with a pulse duration (FWHM) of 10 ns and a pulse frequency of 0.9 Hz. An integral amplitude of the longitudinal acoustic compression wave (ablative component) for a half-time of the compression pulse for various values of radiation intensity in the I L range of (0.1±2.5)Â10 8 W cm 72 was measured by a 180 Mendeleev Commun. 1996 Mendeleev Commun., 1996, 6(5), 180–181 Mendeleev Communications