Explicit Gibbs free energy equation of state applied to the carbon phase diagram

Fried, Laurence E.; Howard, W. M.

doi:10.1103/physrevb.61.8734

Cited by 153 publications

(84 citation statements)

References 50 publications

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“…The two points for carbon appear at high temperatures, above 4000 K. Therefore, experimental investigations of the carbon equilibrium conditions required applications of special techniques. The published papers refer to either gas-solid (graphite) equilibrium (Marshall and Norton 1950, Clarke and Fox 1969, Lee and Sanborn 1973, Leider et al 1973, Baker 1982, Lee and Choi 1998, Havstad and Ferencz 2002, Joseph et al 2002, Miller et al 2008 or equilibrium for liquid-graphite-diamond (Fried and Howard 2000, Ghiringhelli et al 2005, Savvatimskiy 2005, Wang et al 2005, Ghiringhelli et al 2008, Yang and Li 2008, Umantsev and Akkerman 2010. The liquid-gas phase boundary was given little attention with the exception of Bundy et al (1996).…”

Section: Carbon Phase Diagrammentioning

confidence: 99%

On thermodynamic equilibrium of carbon deposition from gaseous C-H-O mixtures: updating for nanotubes

Jaworski

Zakrzewska

Pianko‐Oprych

2017

Reviews in Chemical Engineering

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AbstractExtensive literature information on experimental thermodynamic data and theoretical analysis for depositing carbon in various crystallographic forms is examined, and a new three-phase diagram for carbon is proposed. The published methods of quantitative description of gas-solid carbon equilibrium conditions are critically evaluated for filamentous carbon. The standard chemical potential values are accepted only for purified single-walled and multi-walled carbon nanotubes (CNT). Series of C-H-O ternary diagrams are constructed with plots of boundary lines for carbon deposition either as graphite or nanotubes. The lines are computed for nine temperature levels from 200°C to 1000°C and for the total pressure of 1 bar and 10 bar. The diagram for graphite and 1 bar fully conforms to that in (Sasaki K, Teraoka Y. Equilibria in fuel cell gases II. The C-H-O ternary diagrams. J Electrochem Soc 2003b, 150: A885–A888). Allowing for CNTs in carbon deposition leads to significant lowering of the critical carbon content in the reformates in temperatures from 500°C upward with maximum shifting up the deposition boundary O/C values by about 17% and 28%, respectively, at 1 and 10 bar.

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Section: Carbon Phase Diagrammentioning

confidence: 99%

On thermodynamic equilibrium of carbon deposition from gaseous C-H-O mixtures: updating for nanotubes

Jaworski

Zakrzewska

Pianko‐Oprych

2017

Reviews in Chemical Engineering

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“…This result was inferred from the comparison of the specific volumes of liquid and solid carbon computed from ab initio molecular dynamics. Empirical potentials (22)(23)(24)(25) have also been used to investigate melting of carbon with different degrees of success. In general, empirical potentials lack predictive power over large density variations and, more specifically, important discrepancies between ab initio calculations and empirical potentials have been recently found, e.g., for the existence of a liquid͞liquid phase transition at low pressure (20,24,26).…”

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confidence: 99%

Carbon under extreme conditions: Phase boundaries and electronic properties from first-principles theory

Correa

Bonev

Galli

2006

Proc. Natl. Acad. Sci. U.S.A.

215

122

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At high pressure and temperature, the phase diagram of elemental carbon is poorly known. We present predictions of diamond and BC8 melting lines and their phase boundary in the solid phase, as obtained from first-principles calculations. Maxima are found in both melting lines, with a triple point located at Ϸ850 GPa and Ϸ7,400 K. Our results show that hot, compressed diamond is a semiconductor that undergoes metalization upon melting. In contrast, in the stability range of BC8, an insulator to metal transition is likely to occur in the solid phase. Close to the diamond͞liquid and BC8͞liquid boundaries, molten carbon is a low-coordinated metal retaining some covalent character in its bonding up to extreme pressures. Our results provide constraints on the carbon equation of state, which is of critical importance for devising models of Neptune, Uranus, and white dwarf stars, as well as of extrasolar carbon-rich planets.phase transitions ͉ melting ͉ high pressure ͉ molecular dynamics ͉ metalization E lemental carbon has been known since prehistory, and diamond is thought to have been first mined in India Ͼ2,000 years ago, although recent archaeological discoveries point at the possible existence of utensils made of diamond in China as early as 4,000 before Christ (1). Therefore, the properties of diamond and its practical and technological applications have been extensively investigated for many centuries. In the last few decades, after the seminal work of Bundy and coworkers (2) in the 1950s and '60s, widespread attention has been devoted to studying diamond under pressure (3). For example, the properties of diamond and, in general, of carbon under extreme pressure and temperature conditions are needed to devise models of outer planet interiors (e.g., Neptune and Uranus) (4-6), white dwarfs (7, 8) and extrasolar carbon planets (9).Nevertheless, under extreme conditions the phase boundaries and melting properties of elemental carbon are poorly known, and its electronic properties are not well understood. Experimental data are scarce because of difficulties in reaching megabar (1 bar ϭ 100 kPa) pressures and thousands of Kelvin regimes in the laboratory. Theoretically, sophisticated and accurate models of chemical bonding transformations under pressure are needed to describe phase boundaries. In most cases, such models cannot be simply derived from fits to existing experimental data, and one needs to resort to first-principles calculations, which may be very demanding from a computational standpoint.It has long been known that diamond is the stable phase of carbon at pressures above several gigapascal (2). Total energy calculations (10, 11) based on Density Functional Theory (DFT) predict a transition to another fourfold coordinated phase with the BC8 symmetry ¶ at Ϸ1,100 GPa and 0 K, followed by a transition to a simple cubic phase at pressures Ͼ3,000 GPa. These transitions have not yet been investigated experimentally, because the maximum pressure reached so far in diamond anvil cell experiments on carbon is 140 GP...

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“…The theory does not introduce a new phase diagram of carbon but uses already existing data on phase boundaries of the diamond, graphite, and liquid phases [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Specifically, we will be using the database of [4] for the low-temperature region ð0 À 3000 KÞ and the thermodynamic calculations of [8] for the high-temperature region ð3000 À 6000 KÞ of the phase diagram. The theory has proven to be able to analyze a variety of systems [27,28]; it provides a universal approach to a variety of processes and has an important advantage of analyzing both stability and transformation kinetics incorporating the thermodynamic and dynamic data into a unified scheme.…”

Section: Continuum Methods Of Phase Transitionsmentioning

confidence: 99%

“…Despite the tremendous technical difficulties of experimental studies (temperatures of up to 10,000 K and pressures of 100-1000 GPa) the phase diagram of carbon has been created [1][2][3]. Thermodynamic databases helped develop fairly good bulk-thermodynamic free-energy functions that reproduce the low-temperature portion of the carbon phase diagram [4]. Because of the experimental difficulties, the theoretical (density functional) and numerical (MC and MD) methods of study of carbon phases gained popularity in the scientific community [5][6][7][8][9][10][11][12][13][14][15] graphite, diamond, and liquid carbon, although there is a number of high energy phases, e.g.…”

Section: Carbon Phasesmentioning

confidence: 99%

Continuum theory of carbon phases

Umantsev

Akkerman

2010

Carbon

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Explicit Gibbs free energy equation of state applied to the carbon phase diagram

Cited by 153 publications

References 50 publications

On thermodynamic equilibrium of carbon deposition from gaseous C-H-O mixtures: updating for nanotubes

On thermodynamic equilibrium of carbon deposition from gaseous C-H-O mixtures: updating for nanotubes

Carbon under extreme conditions: Phase boundaries and electronic properties from first-principles theory

Continuum theory of carbon phases

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