Adiabatic switching applied to realistic crystalline solids: Vacancy-formation free energy in copper

Koning, Maurice de; Antonelli, Alex

doi:10.1103/physrevb.55.735

Cited by 54 publications

(62 citation statements)

References 17 publications

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“…To evaluate the free energy differences, we use the method of de Koning and Antonelli [20,21] based on a thermodynamic analysis that is not specific to any particular thermostat. De Koning and Antonelli considered a system of interest S 1 that is coupled to a thermostat S 2 and to an external work source W. The system S 1 must be in thermal equilibrium with S 2 at temperature T , while the extended system S 1 ∪ S 2 must be isolated except for the coupling to W through the variable λ .…”

Section: A Methodologymentioning

confidence: 99%

Thermodynamic properties of average-atom interatomic potentials for alloys

Nöhring

2016

Modelling Simul. Mater. Sci. Eng.

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The atomistic mechanisms of deformation in multicomponent random alloys are challenging to model because of their extensive structural and compositional disorder. For embedded-atom-method interatomic potentials, a formal averaging procedure can generate an average-atom EAM potential and this average-atom potential has recently been shown to accurately predict many zero-temperature properties of the true random alloy. Here, the finite-temperature thermodynamic properties of the average-atom potential are investigated to determine if the average-atom potential can represent the true random alloy Helmholtz Free Energy as well as important finite-temperature properties. Using a thermodynamic integration approach, the average-atom system is found to have an entropy difference of at most 0.05 k B /atom relative to the true random alloy over a wide temperature range, as demonstrated on FeNiCr and Ni 85 Al 15 model alloys. Lattice constants, and thus thermal expansion, and elastic constants are also well-predicted (within a few percent) by the average-atom potential over a wide temperature range. The largest differences between the average atom and true random alloy are found in the zero temperature properties, which reflect the role of local structural disorder in the true random alloy. Thus, the average-atom potential is a valuable strategy for modeling alloys at finite temperatures.

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Section: A Methodologymentioning

confidence: 99%

Thermodynamic properties of average-atom interatomic potentials for alloys

Nöhring

2016

Modelling Simul. Mater. Sci. Eng.

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“…In this situation, the minimal energetic cost is equal to the difference of Helmholtz free energies. Thereby, one of the many applications of such optimal finite-time processes is the estimation of free-energy differences [5][6][7][8][9][10]. A major breakthrough in this problem was achieved by Jarzynski [11] and Crooks [12].…”

Section: Introductionmentioning

confidence: 99%

Degenerate optimal paths in thermally isolated systems

Acconcia

Bonança

2015

Phys. Rev. E

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We present an analysis of the work performed on a system of interest that is kept thermally isolated during the switching of a control parameter. We show that there exists, for a certain class of systems, a finite-time family of switching protocols for which the work is equal to the quasistatic value. These optimal paths are obtained within linear response for systems initially prepared in a canonical distribution. According to our approach, such protocols are composed of a linear part plus a function which is odd with respect to time reversal. For systems with one degree of freedom, we claim that these optimal paths may also lead to the conservation of the corresponding adiabatic invariant. This points to an interesting connection between work and the conservation of the volume enclosed by the energy shell. To illustrate our findings, we solve analytically the harmonic oscillator and present numerical results for certain anharmonic examples.

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“…Problems of the latter type can be addressed very efficiently and accurately using the AS technique [4][5][6][7][8][9][10]. In principle, this method allows the determination of the free-energy dependence on an external parameter in a Hamiltonian of interest from a single MD or MC simulation, without relying on any uncontrollable approximations.…”

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confidence: 99%

“…+ m In the study of thermodynamic properties of materials [1,2], free-energy calculation is a unique application of computer simulation techniques. For this purpose, the coupling parameter formalism [2,3] provides a powerful and robust framework which underlies state-of-the-art techniques such as thermodynamic integration (TI) [2] and adiabatic switching (AS) [4][5][6][7][8][9][10]. Standard application of this approach involves the evaluation of reversible work along a path connecting a physical system of interest to a reference.…”

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confidence: 99%

Optimized Free-Energy Evaluation Using a Single Reversible-Scaling Simulation

1999

Self Cite

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We present a method, for highly efficient free-energy calculations by means of molecular dynamics and Monte Carlo simulations, which is an optimized combination of coupling parameter and adiabatic switching formalisms. This approach involves dynamical reversible scaling of the potential energy function of a system of interest, and allows accurate determination of its free energy over a wide temperature interval from a single simulation. The method is demonstrated in two applications: crystalline Si at zero pressure and a fcc nearest-neighbor antiferromagnetic Ising model. PACS numbers: 02.70.Lq, 02.70.Ns, 65.50. + m In the study of thermodynamic properties of materials [1,2], free-energy calculation is a unique application of computer simulation techniques. For this purpose, the coupling parameter formalism [2,3] provides a powerful and robust framework which underlies state-of-the-art techniques such as thermodynamic integration (TI) [2] and adiabatic switching (AS) [4][5][6][7][8][9][10]. Standard application of this approach involves the evaluation of reversible work along a path connecting a physical system of interest to a reference. Usually, the path is constructed using a composite Hamiltonian H͑l͒ coupling the two systems through a parameter l. Upon varying l the coupled system evolves along a reversible trajectory, changing continuously from the system of interest to the reference. The reversible work done by the generalized force ≠H͞≠l along this path is then equal to the free-energy difference between the systems. While this approach is very powerful, it is not optimal in that only the initial and final points on the trajectory correspond to physically relevant systems. The information gathered at the intermediate states of the path has no physical meaning, serving only to connect the end points of the path. As a consequence, one obtains only one value of the desired free energy per simulation.In this Letter we describe a formulation which fully utilizes all the information available along a reversible path and thereby allows the evaluation of free energies over a wide temperature interval from a single simulation. This approach, which effectively exploits both the coupling parameter formalism and the adiabatic switching technique, is based on the use of a specific path which is defined by the introduction of a scaling factor l in the potential energy function of the physical system of interest. The fundamental difference from the usual coupling approach is that for this particular path all intermediate states provide physically relevant information. In fact, an exact relation between the partition functions of the original and the scaled systems shows that all the states along the scaling path correspond to the original physical system at different temperatures. The combination of this reversiblescaling concept with the dynamical variation of l within the adiabatic switching method results in a highly optimized technique with a significant efficiency gain without loss of accuracy.The idea of determ...

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Adiabatic switching applied to realistic crystalline solids: Vacancy-formation free energy in copper

Cited by 54 publications

References 17 publications

Thermodynamic properties of average-atom interatomic potentials for alloys

Thermodynamic properties of average-atom interatomic potentials for alloys

Degenerate optimal paths in thermally isolated systems

Optimized Free-Energy Evaluation Using a Single Reversible-Scaling Simulation

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