Abstract
Phase equilibrium lines of hexagonal graphite (hg) and cubic diamond (cd) phases of carbon as well as a saddle-point equilibrium line between the two phase equilibrium lines are studied by first-principles total-energy calculations. The Gibbs free energies (G) of the three equilibrium lines determine the transition pressure p t = 70 kbar (0.070 Mbar) from hg phase to cd phase and the barrier height at p t of ΔG = 178 mRy/atom that stabilizes the two phases against a phase transition. The cd phase becomes unstable at V = 13.6 au3/atom (p = 26 Mbar) where the curvature at the equilibrium point of the energy curve (denoted E V (c/a) curve) goes to zero. The hg and cd phase equilibrium lines cross at V = 14.5 au3/atom where the regular hg phase (with one minimum in each E V (c/a) curve) ends and the irregular hg phase (with two minima in each E V (c/a) curve) develops. The feature of “two phase equilibrium lines cross” was not observed in our previous work [S.L. Qiu, P.M. Marcus, J. Phys.: Condens. Matter 24, 225501 (2012); S.L. Qiu, P.M. Marcus, Eur. Phys. J. B 86, 425 (2013)] where the two interacting crystal phases have a common unit cell with different c/a ratios. This work demonstrates that the saddle-point equilibrium line along with the two phase equilibrium lines are all needed for a complete description of crystal phases and their transitions under pressure.
Similar content being viewed by others
References
S.L. Qiu, P.M. Marcus, J. Phys.: Condens. Matter 24, 225501 (2012)
S.L. Qiu, P.M. Marcus, Eur. Phys. J. B 86, 425 (2013)
P.S. DeCarli, J.C. Jameson, Science 133, 1821 (1961)
F.P. Bundy, J. Chem. Phys. 38, 631 (1963)
S. Fahy, S.G. Louie, M.L. Cohen, Phys. Rev. B 34, 1191 (1986)
S. Scandolo, M. Bernasconi, G.L. Chiarotti, P. Focher, E. Tosatti, Phys. Rev. Lett. 74, 4015 (1995)
F. Bundy, W. Bassett, M. Weathers, R. Hemley, H. Mao, A. Gocharov, Carbon 34, 141 (1996)
J.B. Wang, G.W. Yang, J. Phys.: Condens. Matter 11, 7089 (1999)
L. Sun, Q. Wu, Y. Zhang, W. Wang, J. Mater. Res. 14, 631 (1999)
V.F. Britun, A.V. Kurdyumov, I.A. Petrusha, Powder Metall. Met. Ceram. 43, 87 (2004)
V.A. Davydov, A.V. Rakhmanina, S. Rols, V. Agafonov, M.X. Pulikkathara, R.L. Vander Wal, V.N. Khabashesku, J. Phys. Chem. C 111, 12873 (2007)
J.T. Wang, C. Chen, D.S. Wang, H. Mizuseki, Y. Kawazoe, J. Appl. Phys. 107, 063507 (2010)
R.Z. Khaliullin, H. Eshet, T.D. Kühne, J. Behler, M. Parrinello, Nat. Mater. 10, 693 (2011)
P. Xiao, G. Henkelman, J. Chem. Phys. 137, 101101 (2012)
S.L. Qiu, P.M. Marcus, J. Phys.: Condens. Matter 21, 435403 (2009)
P.M. Marcus, S.L. Qiu, J. Phys.: Condens. Matter 21, 125404 (2009)
P.M. Marcus, S.L. Qiu, J. Phys.: Condens. Matter 21, 115401 (2009)
P. Blaha, K. Schwarz, G.K.H. Madsen, D. Kvasnicka, J. Luitz, WIEN2k, An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties (Karlheinz Schwarz, Techn. Universität Wien, Austria, 2001), ISBN 3-9501031-1-2
P. Blaha, K. Schwarz, P. Sorantin, Comput. Phys. Commun. 59, 399 (1990)
http://en.wikipedia.org/wiki/Compact_stencil http://en.wikipedia.org/wiki/Numerical_differentiation
M. Birowska, K. Milowska, J.A. Majewski, Acta Physica Polonica A 120, 845 (2011)
M.T. Yin, M.L. Cohen, Phys. Rev. B 29, 6996 (1984)
J. Furthmuller, J. Hafner, G. Kresse, Phys. Rev. B 50, 15606 (1994)
Y.C. Wang, K. Scheerschmidt, U. Gosele, Phys. Rev. B 61, 12864 (2000)
F.D. Murnaghan, Proc. Natl. Acad. Sci. USA 30, 244 (1944)
O.L. Anderson, J. Phys. Chem. Solids 27, 547 (1966)
J. Donohue, The Structure of the Elements (Krieger, Malabar, FL, 1982)
K. Gschneidner, Solid State Phys. 16, 275 (1964)
M.S. Dresselhaus, G. Dresselhaus, P.C. Eklund, Science of Fullerenes and Carbon Nanotubes (Academic, New York, 1996)
C. Frondel, U.B. Marvin, Nature 214, 587 (1967)
Metals Handbook, 8th edn. (American Society for Metals, 1973), Vol. 8, p. 235
H.J. McSkimin Jr., P. Andreatch, J. Appl. Phys. 43, 985 (1972)
S. Fahy, S.G. Louie, Phys. Rev. B 36, 3373 (1987)
A. Janoti, S.H. Wei, D.J. Singh, Phys. Rev. B 64, 174107 (2001)
A.S. Barnard, S.P. Russo, I.K. Snook, Philos. Mag. B 82, 1767 (2002)
M. Itoh, M. Kotani, H. Naito, T. Sunada, Y. Kawazoe, T. Adschiri, Phys. Rev. Lett. 102, 055703 (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Qiu, S.L. Hexagonal graphite to cubic diamond transition from equilibrium lines and barrier calculations. Eur. Phys. J. B 87, 147 (2014). https://doi.org/10.1140/epjb/e2014-50260-8
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjb/e2014-50260-8