High-pressure thermal expansion, bulk modulus, and phonon structure of diamond

Xie, Ju; Chen, S. P.; Tse, John S.; Gironcoli, Stefano de; Baroni, Stefano

doi:10.1103/physrevb.60.9444

Cited by 93 publications

(65 citation statements)

References 32 publications

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“…As reported in ref. 37, acoustic branches of the phonon dispersion are rather flat near the Brillouin zone boundaries. In addition, the frequencies of the transverse acoustic branches near the L and X symmetry points have a maximum as a function of pressure.…”

Section: Discussionmentioning

confidence: 92%

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

Correa

Bonev

Galli

2006

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

217

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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Section: Discussionmentioning

confidence: 92%

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

Correa

Bonev

Galli

2006

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

217

122

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“…There has been particular attention to the thermodynamics of crystals, whose harmonic free energy can be obtained from phonon frequencies computed by standard DFT methods [5][6][7][8][9][10][11]. The ab initio treatment of liquid-state thermodynamics is also important, and thermodynamic integration has been shown to be an effective way of calculating the DFT free energy of liquids [1,3,4].…”

Section: Introductionmentioning

confidence: 99%

Iron under Earth’s core conditions: Liquid-state thermodynamics and high-pressure melting curve fromab initiocalculations

2002

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Ab initio techniques based on density functional theory in the projector-augmented-wave implementation are used to calculate the free energy and a range of other thermodynamic properties of liquid iron at high pressures and temperatures relevant to the Earth's core. The ab initio free energy is obtained by using thermodynamic integration to calculate the change of free energy on going from a simple reference system to the ab initio system, with thermal averages computed by ab initio molecular dynamics simulation. The reference system consists of the inverse-power pair-potential model used in previous work. The liquid-state free energy is combined with the free energy of hexagonal close packed Fe calculated earlier using identical ab initio techniques to obtain the melting curve and volume and entropy of melting. Comparisons of the calculated melting properties with experimental measurement and with other recent ab initio predictions are presented. Experiment-theory comparisons are also presented for the pressures at which the solid and liquid Hugoniot curves cross the melting line, and the sound speed and Grüneisen parameter along the Hugoniot. Additional comparisons are made with a commonly used equation of state for high-pressure/high-temperature Fe based on experimental data.

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“…Only a handful of publications, [3][4][5] however, have taken proper account of subtleties that cannot be ignored. The results of zerotemperature ground-state electronic structure calculations are not directly comparable with experimental measurements that include zero-point phonon effects, and are often taken at room temperature.…”

Section: Introductionmentioning

confidence: 99%

“…The temperature and phonon effects can modify the calculated bulk modulus by up to 20% ͑see Table I͒, invalidating any comparison of theory and experiment that does not take them into account, and explaining the frequently reported overestimation of bulk moduli. [6][7][8][9] Although these effects are known and have been evaluated satisfactorily, [3][4][5] they are still frequently overlooked. One of the two main aims of this paper is to show how, by generalizing the work of Ref.…”

Section: Introductionmentioning

confidence: 99%

Ab initiocalculations of bulk moduli and comparison with experiment

Gaudoin

Foulkes

2002

Phys. Rev. B

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Bulk moduli appear readily accessible in electronic structure calculations, but the calculated values are often substantially greater than experimental bulk moduli. This discrepancy is the result of an unfair comparison of calculated and experimental results: many workers ignored the zero-point and finite-temperature effects that are present in experiments but absent from most calculations. These effects can alter bulk moduli by up to 20%. We show how good approximations to the required corrections may be obtained with little effort. We also deal with the statistical errors and biases in quantities derived from the noisy energy-volume curves produced by quantum Monte Carlo simulations.

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High-pressure thermal expansion, bulk modulus, and phonon structure of diamond

Cited by 93 publications

References 32 publications

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

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

Iron under Earth’s core conditions: Liquid-state thermodynamics and high-pressure melting curve fromab initiocalculations

Ab initiocalculations of bulk moduli and comparison with experiment

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