Adjusting the melting point of a model system via Gibbs-Duhem integration: Application to a model of aluminum

Sturgeon, J.B.; Laird, Brian B.

doi:10.1103/physrevb.62.14720

Cited by 96 publications

(81 citation statements)

References 16 publications

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“…The approach has been shown [64] to yield results consistent with simulation methods based upon thermodynamic-integration calculations of free energies for bulk solid and liquid phases (e.g. [65]). For Au and Ag the melting point was estimated from an extrapolation to zero growth rate of the velocity versus undercooling behavior [54], while the melting point for the Pb potential was quoted in [61].…”

Section: The Capillary Fluctuation Methodsmentioning

confidence: 64%

Atomistic and continuum modeling of dendritic solidification

Hoyt

2003

Materials Science and Engineering: R: Reports

398

220

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Section: The Capillary Fluctuation Methodsmentioning

confidence: 64%

Atomistic and continuum modeling of dendritic solidification

Hoyt

2003

Materials Science and Engineering: R: Reports

398

220

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“…When a coupling parameter λ is introduced within the expression of the potential energy of the system, then a set of Generalised Clapeyron equations can be derived [31,167,168]. For two phases at coexistence:…”

Section: Hamiltonian Gibbs Duhem Integrationmentioning

confidence: 99%

Determination of phase diagrams via computer simulation: methodology and applications to water, electrolytes and proteins

Vega¹,

Sanz

Abascal

et al. 2008

J. Phys.: Condens. Matter

278

452

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Abstract. In this review we focus on the determination of phase diagrams by computer simulation with particular attention to the fluid-solid and solid-solid equilibria. The methodology to compute the free energy of solid phases will be discussed. In particular, the Einstein crystal and Einstein molecule methodologies are described in a comprehensive way. It is shown that both methodologies yield the same free energies and that free energies of solid phases present noticeable finite size effects. In fact this is the case for hard spheres in the solid phase. Finite size corrections can be introduced, although in an approximate way, to correct for the dependence of the free energy on the size of the system. The computation of free energies of solid phases can be extended to molecular fluids. The procedure to compute free energies of solid phases of water (ices) will be described in detail. The free energies of ices Ih, II, III, IV, V, VI, VII, VIII, IX, XI and XII will be presented for the SPC/E and TIP4P models of water. Initial coexistence points leading to the determination of the phase diagram of water for these two models will be provided. Other methods to estimate the melting point of a solid, as the direct fluid-solid coexistence or simulations of the free surface of the solid will be discussed. It will be shown that the melting points of ice Ih for several water models, obtained from free energy calculations, direct coexistence simulations and free surface simulations, agree within their statistical uncertainty. Phase diagram calculations can indeed help to improve potential models of molecular fluids. For instance, for water, the potential model TIP4P/2005 can be regarded as an improved version of TIP4P. Here we will review some recent work on the phase diagram of the simplest ionic model, the restricted primitive model. Although originally devised to describe ionic liquids, the model is becoming quite popular to describe the behaviour of charged colloids. Besides the possibility of obtaining fluid-solid equilibria for simple protein models will be discussed. In these primitive models, the protein is described by a spherical potential with certain anisotropic bonding sites (patchy sites).

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“…These empirical interatomic potentials fitted to the so-called mechanical properties of the materials usually have no guarantees to give good results for the nonmechanical properties, such as melting temperatures. 31,32 As the second step of this approach, the ab initio melting temperature is computed by correcting the approximate T ref m . We perform two independent molecular-dynamics simulations for solid and liquid using the reference potential and a small 128-atom supercell.…”

mentioning

confidence: 99%

Melting temperature of tungsten from twoab initioapproaches

Wang

Walle

2011

Phys. Rev. B

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We have calculated the melting temperature of tungsten by two ab initio approaches. The first approach can be divided into two steps. In the first step, we simulate a large coexisting solid and liquid system by the classical embedded-atom method potential and obtain an approximate melting temperature. In the second step, we compute the accurate melting temperature by performing the ab initio free-energy corrections. The second approach is to perform a direct ab initio molecular-dynamics simulation for the coexisting solid and liquid system using the constant particle number, pressure, and enthalpy ensemble. In the second approach, the simulation is carried out entirely using a density-functional theory Hamiltonian, and no other approximations are imposed. However, the simulation is performed using a relatively small supercell. The results obtained from two ab initio approaches can provide a check for each other. Our results show that they are in good agreement with each other and also in reasonably good agreement with the experimental value. Computer simulation of solid-liquid equilibrium can be traced back to the 1950s.1 Thanks to the increasing power of modern supercomputers, it has recently become possible to calculate the melting properties of materials using accurate ab initio methods. There are two commonly used computational approaches introduced in previous studies to obtain the melting temperature of a material. The first one is the so-called thermodynamic integration approach. [2][3][4][5][6][7] In this approach, the Gibbs free energies are calculated ab initio for solid and liquid, and the melting transition is determined by the equality of the Gibbs free energies of two phases. The second approach is the direct simulation of the solid-liquid coexistence, i.e., the so-called coexistence approach. [8][9][10][11][12][13][14][15][16][17][18] In this approach, the temperature adjusts spontaneously during the simulation to provide a two-phase equilibrium that satisfies the equality of Gibbs free energies of solid and liquid. In this paper, we use a recently proposed [19][20][21][22] hybrid approach combining the above two approaches. An approximate melting temperature is first obtained by coexisting solid and liquid simulation using an empirical potential. Next, the ab initio melting temperature is obtained by applying free-energy corrections akin to thermodynamic integration in the limit of small perturbations. This approach has been applied to get the melting properties of Fe, 19 Cu, 20 Ta, 21 and Mo 22 for a wide pressure range. The advantage of this last approach is its moderate computational costs compared with the other two approaches.As the melting point is a quantity that is very sensitive to small inaccuracies in the Hamiltonian used, the use of accurate ab initio methods is desired. However, such methods are computationally demanding, and the accuracy is limited by sampling and system size convergence. The ability to internally check the accuracy of the results is therefore crucial. In the presen...

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Adjusting the melting point of a model system via Gibbs-Duhem integration: Application to a model of aluminum

Cited by 96 publications

References 16 publications

Atomistic and continuum modeling of dendritic solidification

Atomistic and continuum modeling of dendritic solidification

Determination of phase diagrams via computer simulation: methodology and applications to water, electrolytes and proteins

Melting temperature of tungsten from twoab initioapproaches

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