Publication: Equilibrium fluid-solid coexistence of hard spheres
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2012-04-16
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American Physical Society
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Abstract
We present a tethered Monte Carlo simulation of the crystallization of hard spheres. Our method boosts the traditional umbrella sampling to the point of making practical the study of constrained Gibbs’ free energies depending on several crystalline order parameters. We obtain high-accuracy estimates of the fluid-crystal coexistence pressure for up to 2916 particles (enough to accommodate fluid-solid interfaces). We are able to extrapolate to infinite volume the coexistence pressure [p_(co) = 11.5727(10)k_(B)T/σ^(3)] and the interfacial free energy [γ_({100}) = 0.636(11)k_(B)T/σ^(2)].
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© 2012 American Physical Society. We thank K. Binder, C. de Vega, L. G. MacDowell, B. Lucini, and D. Yllanes for enlightening discussions. Simulations were carried out at BIFI. We acknowledge support from MICINN, Spain, through research Contracts No. FIS2009-12648-C03, No. FIS2008 01323, and from UCM-Banco de Santander. B. S. was supported by the FPU program.
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[1] B. J. Alder, T. E. Wainwright, J. Chem. Phys., 27, 1208 (1957)
-- W. W. Wood, J. D. Jacobson, ibid., 27, 1207 (1957).
[2] P. N. Pusey, W. van Megen, Nature, (London) 320, 340 (1986).
[3] P. N. Pusey, W. van Megen, P. Bartlett, B. J. Ackerson, J. G. Rarity, S. M. Underwood, Phys. Rev. Lett., 63, 2753 (1989).
[4] V. N. Manoharan, M. T. Elsesser, D. J. Pine, Science, 301, 483 (2003)
-- S. C. Glotzer, M. J. Solomon, Nature Mater., 6, 557 (2007).
[5] E. Bianchi, J. Largo, P. Tartaglia, E. Zaccarelli, F. Sciortino, Phys. Rev. Lett., 97, 168301 (2006).
[6] F. Sciortino, A. Giacometti, G. Pastore, Phys. Rev. Lett., 103, 237801 (2009).
[7] M. P. Allen, D. J. Tildesley, Computer Simulation of Liquids (Oxford University Press, New York, 1989), 2nd ed.
[8] E. Zaccarelli, C. Valeriani, E. Sanz, W. C. K. Poon, M. E. Cates, P. N. Pusey, Phys. Rev. Lett., 103, 135704 (2009).
[9] B. A. Berg, T. Neuhaus, Phys. Rev. Lett., 68, 9 (1992).
[10] F. Wang, D. P. Landau, Phys. Rev. Lett., 86, 2050 (2001).
[11] V. Martín-Mayor, Phys. Rev. Lett., 98, 137207 (2007).
[12] V. J. Anderson, H. N. W. Lekkerkerker, Nature (London), 416, 811 (2002).
[13] C. Vega, E. Sanz, J. L. F. Abascal, E. G. Noya, J. Phys. Condens. Matter, 20, 153101 (2008).
[14] N. B. Wilding, A. D. Bruce, Phys. Rev. Lett., 85, 5138 (2000).
[15] J. R. Errington, J. Chem. Phys., 120, 3130 (2004).
[16] W. G. Hoover, F. H. Ree, J. Chem. Phys., 49, 3609 (1968).
[17] D. Frenkel, A. J. C. Ladd, J. Chem. Phys., 81, 3188 (1984).
[18] J. M. Polson, E. Trizac, S. Pronk, D. Frenkel, J. Chem. Phys., 112, 5339 (2000).
[19] C. Vega, E. G. Noya, J. Chem. Phys., 127, 154113 (2007).
[20] A. J. C. Ladd, L. V. Woodcock, Chem. Phys. Lett., 51, 155 (1977).
[21] E. G. Noya, C. Vega, E. de Miguel, J. Chem. Phys., 128, 154507 (2008).
[22] T. Zykova-Timan, J. Horbach, K. Binder, J. Chem. Phys., 133, 014705 (2010).
[23] See Supplemental Material at http://link.aps.org/ supplemental/10.1103/PhysRevLett.108.165701 for simulation details, intermediate results, and snapshots of particle configurations.
[24] R. L. Davidchack, J. Chem. Phys., 133, 234701 (2010).
[25] A. Cacciuto, S. Auer, D. Frenkel, J. Chem. Phys., 119, 7467 (2003).
[26] Y. Mu, A. Houk, X. Song, J. Phys. Chem. B, 109, 6500 (2005).
[27] L. A. Fernández, V. Martín-Mayor, D. Yllanes, Nucl. Phys., B807, 424 (2009).
[28] V. Martín-Mayor, B. Seoane, D. Yllanes, J. Stat. Phys., 144, 554 (2011).
[29] G. M. Torrie, J. P. Valleau, Chem. Phys. Lett., 28, 578 (1974)
-- J. Comput. Phys., 23, 187 (1977)
-- C. Bartels, Chem. Phys. Lett., 331, 446 (2000).
[30] P. R. ten Wolde, M. J. Ruiz-Montero, D. Frenkel, Phys. Rev. Lett., 75, 2714 (1995).
[31] M. Schrader, P. Virnau, K. Binder, Phys. Rev. E, 79, 061104 (2009).
[32] K. Binder, B. Block, S. K. Das, P. Virnau, D. Winter, J. Stat. Phys., 144, 690 (2011).
[33] P. J. Steinhardt, D. R. Nelson, M. Ronchetti, Phys. Rev. B, 28, 784 (1983).
[34] S. Angioletti-Uberti, M. Ceriotti, P. D. Lee, M. W. Finnis, Phys. Rev. B, 81, 125416 (2010).
[35] M. Biskup, L. Chayes, R. Kotecký, Europhys. Lett., 60, 21 (2002).
[36] K. Binder, Physica (Amsterdam), 319A, 99 (2003).
[37] L. G. MacDowell, V. K. Shen, J. R. Errington, J. Chem. Phys., 125, 034705 (2006).
[38] P. G. Bolhuis, D. Frenkel, S.-C. Mau, D. A. Huse, Nature (London), 388, 235 (1997).
[39] J. S. van Duijneveldt, D. Frenkel, J. Chem. Phys., 96, 4655 (1992).
[40] Particles i and j are neighbors if r_(ij) < 11.5σ. In the ideal fcc structure, for all particle densities relevant to us, this choice includes only the nearest-neighbors shell.
[41] Equation (7) behaves as an animal’s tether: only if (say) |ˆǪ_(6)–Ǫ_(6)(R)|»1√Nα is the penalty large. Note as well that Eqs. (7) and (8) generalize straightforwardly to the case of more than two quasiconstraints.
[42] A magnitude A is additive if NA is extensive: gluing together systems 1,2 (with N^(i) particles and A = A^(i) , i = 1, 2), results in a total system with N = N^(1) + N^(2) particles and NA = N^(1) A^(1) + N^(2) A^(2) (plus subdominant corrections such as surface effects ≈ N^( 2/3). C is additive to a great accuracy for coexisting fluid and fcc phases, because the average number of neighbors Nb is very similar in both phases (5% difference, with negligible effects on additivity in our N range, as compared with surface effects). Q_(6) is additive only if one of the subsystems, say i = 1, is a liquid so that Q^(1)_( 6) ≈ 1/ √N ð1Þ p (Q6 is a pseudo-order parameter, i.e., a strictly positive quantity which is of order 1= ffiffiffiffi N p in a disordered phase). For studies of interfaces on larger systems, it would be advisable to choose exactly additive order parameters.
[43] D. Ruelle, Statistical Mechanics (Benjamin, New York, 1969).
[44] Our runs for N ≤ 2916 are, at least, 100τ long (τ is the integrated autocorrelation time [50], computed for Q_(6) and v [28]). For N = 2916, but only at S = 0.4, we find metastability with a helicoidal configuration (however, its contribution to final quantities is smaller than statistical errors). Metastabilities arise often for N = 4000, at intermediate S (yet, a careful selection of starting configurations yields a ∇Ω_(N) with smooth S dependency).
[45] A. M. Ferrenberg, R. H. Swendsen, Phys. Rev. Lett., 61, 2635 (1988).
[46] C. Borgs, R. Kotecký, Phys. Rev. Lett., 68, 1734 (1992).
[47] The tethering approach should not induce artificial interfaces. In fact, mathematically, the interfacial free energy is defined through the ratio of two partition functions with different boundary conditions. The tethered potential does not change the partition function [with any boundary conditions, see Eq. (5)].
[48] K. Binder, Phys. Rev. A, 25, 1699 (1982).
[49] A. Billoire, T. Neuhaus, B. A. Berg, Nucl. Phys., B413, 795 (1994).
[50] A. D. Sokal, in Functional Integration: Basics and Applications (1996 Cargèse School), edited by C. DeWitt- Morette, P. Cartier, and A. Folacci (Plenum, New York, 1997).