Liquid-Liquid Phase Transformation in Carbon

Abstract

A first order phase transition is found in liquid carbon using atomistic simulation methods and Brenner's bond order potential. The phase line is terminated by a critical point at 8801 K and 10.56 GPa and by a triple point on the graphite melting line at 5133 K and 1.88 GPa. The phase change is associated with density and structural changes. The low-density liquid is predominantly sp bonded with little sp 3 character. The high-density liquid is mostly sp 3 bonded with little sp character. This is the first nonempirical evidence of a liquid-liquid transition between thermodynamically stable fluids.[ S0031-9007(99) . This careful work on the melting of graphite by Togaya suggests that the slope of pressure-temperature ͑P-T ͒ melting line is discontinuous at the temperature maximum, and hence at least three stable phases coexist at this point. The most likely conclusion is that this point is a triple point and the carbon phase diagram exhibits a LLPT.Though somewhat exotic, LLPT's have been suggested in liquid S, Ga, Se, Te, I 2 , Cs, and Bi [4]. Recent experiments [5] and molecular dynamics (MD) calculations [6] have shown evidence of a first order transition between metastable phases of supercooled water.The purpose of this Letter is to report the findings of a MD simulation of liquid carbon showing clear evidence of a LLPT. The LLPT line in carbon is mapped out, including the critical point at high T and the triple point at low T . The low-density liquid (LDL) phase has different local structure than the high-density liquid (HDL) phase. An order parameter sensitive to this local order change is defined and examined as a function of T and P. This is the first time that atomic simulations have directly observed a first order LLPT between two distinct thermodynamically stable liquid phases in carbon or any other material.To describe the carbon-carbon interaction, the hydrocarbon potential model developed by Brenner [7] is used. The Brenner potential falls in a class of empirical potentials known as bond-order potentials having the simple formwhere f R and f A are exponential functions representing the repulsive and attractive terms, respectively, in the bond energy. Although a sum over bond energies (͕bonds͖ is the set of all bonds), this is not a pair potential. The so-called bond-order factor b ij is a many-body factor and depends on bond angles, torsional angles, bond lengths, and atomic coordination in the vicinity of the bond. This many-body nature of b ij allows bond energy to depend on the local environment in such a way so as to produce the correct geometry and energy for many different carbon structures including graphite and diamond.The simulations are performed mostly on 512 particle systems using a constant (cubic) volume ͑V ͒ and temperature MD. A number of calculations were done with 4096 particles to check for finite-size effects. The equations of motion are integrated using a velocity-Verlet algorithm [8] with temperature controlled via the Nóse-Hoover thermostat [9]. To control integration errors,...

A geometric model for cold water and liquid–liquid transitions

“…This transition has also been reported from molecular dynamics simulations [5] and a scaling formalism [6]. Experimental results also report a liquid-liquid transition in phosphorus in the stable phase [7].…”

“…As in the solid state [34], the slope of the liquid-liquid coexistence line in the pressure versus temperature diagram is positive [5,6] and, according to Le Chatelier's principle, the lower density phase must present the largest entropy. In the absence of the HB net entropy, the model we propose could be thought of as a mean-field treatment of Brenner's potential, used to describe carbon, and for which bond energies depend on the local environment in such a way as to produce the correct geometries and energies of the known carbon structures [5,35]. Is is not clear whether it would be necessary to consider additional entropy terms, because of the mean-field treatment.…”

“…Graphite is less dense, but of higher entropy. Experimental and theoretical results [3,5,6] point to the possibility of a liquid-liquid phase transition, between a high density liquid phase (dominated by sp 3 hybridized atoms) and a low density liquid phase (dominated by sp hybridized atoms in the case of MD simulations [5] and by sp 2 hybridized atoms in a scaling formalism model [6]). As in the solid state [34], the slope of the liquid-liquid coexistence line in the pressure versus temperature diagram is positive [5,6] and, according to Le Chatelier's principle, the lower density phase must present the largest entropy.…”

“…Experimental and theoretical results [3,5,6] point to the possibility of a liquid-liquid phase transition, between a high density liquid phase (dominated by sp 3 hybridized atoms) and a low density liquid phase (dominated by sp hybridized atoms in the case of MD simulations [5] and by sp 2 hybridized atoms in a scaling formalism model [6]). As in the solid state [34], the slope of the liquid-liquid coexistence line in the pressure versus temperature diagram is positive [5,6] and, according to Le Chatelier's principle, the lower density phase must present the largest entropy. In the absence of the HB net entropy, the model we propose could be thought of as a mean-field treatment of Brenner's potential, used to describe carbon, and for which bond energies depend on the local environment in such a way as to produce the correct geometries and energies of the known carbon structures [5,35].…”

“…The relevant systems must have open molecular coordination environments at low pressures, and may either be liquids associated through a hydrogen-bond net, water being the main example [2], or substances for which the different possibilities for hybridyzed eletronic orbitals imply structures of different densities, as in the case of carbon [3][4][5][6].…”