Editor’s ChoiceNonequilibrium free-energy calculation of solids using LAMMPS
Graphical abstract
Introduction
The calculation of free energies and derivative thermodynamic quantities for condensed-phase systems is a common and widespread application of atomistic simulation techniques. The continuous improvement of methods and the steady increase in computational power have enabled the efficient and reliable computation of free energies for complex systems of interest in materials science, including extended defects and interfaces. Free-energy calculation methods have benefited substantially with the introduction of nonequilibrium approaches such as the adiabatic switching [1] (AS) method, which allow the calculations to be performed along explicitly time-dependent processes that can lead to significant efficiency gains compared to standard equilibrium methods. Moreover, with the derivation of Jarzynski’s equality the connection between equilibrium free-energy differences and nonequilibrium processes has been placed on a firm theoretical basis [2].
In this paper we describe the implementation of state-of-the-art nonequilibrium techniques for calculating free energies of solids in the highly optimized LAMMPS [3] (Large-scale Atomic/Molecular Massively Parallel Simulator) molecular dynamics code. Specifically, we focus on two particular kinds of nonequilibrium routes which, respectively, allow the calculation of free-energy differences between systems described by different Hamiltonians as well as the temperature dependence of the free energy of a given system Hamiltonian from a single nonequilibrium simulation. We demonstrate their application to the calculation of free energies of different crystalline structures for a classical interatomic potential model of iron [4] and discuss extensions of the approaches to the calculations of interfacial free energies, which can be readily undertaken using the methods implemented in LAMMPS [5].
The paper has been organized as follows. In Section 2 we give a short and self-contained presentation of the theoretical framework underlying the nonequilibrium processes used to compute free-energy differences between equilibrium states. In Section 3 we describe the implementation of these methods into LAMMPS, and discuss how to optimize the parameters for efficiency, using bcc iron as an example system. In Section 4 we describe the application of the methods to the study of polymorphism in iron and we end with a summary and a discussion of the extension of the methodology to more complex crystalline systems as well as surfaces and interfaces in Section 5.
Section snippets
Nonequilibrium free-energy estimation
Standard equilibrium free-energy calculations are often based on thermodynamic integration (TI), [6], [7] which is a general class of methods based on the construction of a sequence of equilibrium states on a path between two thermodynamic states of interest. The free-energy difference between two equilibrium states is then determined by computing ensemble averages of the relevant thermodynamic driving force for these states by means of a set of independent equilibrium simulations, followed by
Calculation of bulk free energy
In this section we describe the implementation of the methods described above in the widely used Molecular Dynamics code LAMMPS [3]. We demonstrate the application of the methods to the calculation of the temperature-dependent free energy of a body-centered-cubic solid described by an embedded-atom-method (EAM) [13] many-body interatomic potential model of iron developed by Meyer and Entel [4]. Free energies are calculated at zero pressure for a range of temperatures between 100 and ; the
Iron polymorphism
The formalism described in this article provides an efficient framework for computing the free energies of crystalline solids described by classical interatomic potential models. Such calculations are useful in many contexts in computational materials science. For example, a central issue in the modeling of crystalline solids is polymorphism, i.e., the thermodynamic stability of crystalline phases with different crystal structures as a function of temperature. Many materials used in engineering
Summary and discussion
In this paper a detailed account has been presented of the use of state-of-the-art nonequilibrium simulation methods to compute free energies of solids in LAMMPS using the Frenkel–Ladd [10] and Reversible Scaling [11] paths. The approach was demonstrated in free energy calculations for different polymorphs (fcc, bcc, and hcp) in a classical potential model of iron [4]. It was demonstrated that a precision of tenths of meV/atom or better can be achieved in nonequilibrium simulations for systems
Acknowledgments
This work was supported by the FAPESP grant 2010/13902-4. MK acknowledges support from FAPESP and FAPESP/CEPID 2013/00293-7. The research of RF and MA at UC Berkeley was supported by the US National Science Foundation (Grant No. DMR-1105409).
References (26)
J. Comput. Phys.
(1995)- et al.
Curr. Opin. Solid State Mater. Sci.
(2013) - et al.
Phys. Rev. Lett.
(1990) Phys. Rev. Lett.
(1997)- et al.
Phys. Rev. B
(1998) - See <http://lammps.sandia.gov/doc/fix_ti_spring.html> for documentation about the fix that implements the Frenkel–Ladd...
J. Chem. Phys.
(1935)- et al.(2001)
- et al.
J. Phys. Chem. B
(2005) J. Chem. Phys.
(2005)
J. Chem. Phys.
Phys. Rev. Lett.
J. Chem. Phys.
Cited by (145)
Multiscale modeling of irradiation-induced defect evolution in BCC multi principal element alloys
2023, Journal of Alloys and CompoundsGNN-assisted phase space integration with application to atomistics
2023, Mechanics of MaterialsCalculation of Melting Temperature Using Nonequilibrium Thermodynamic Integration Methods
2024, Advanced Theory and Simulations