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Nested Sampling for Materials

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Classical Statistical Mechanics with Nested Sampling

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Abstract

This chapter develops nested sampling into a powerful tool for the calculation of pressure-temperature phase diagrams, and demonstrates how it may be applied to single species and binary systems, including the Lennard-Jones system, a binary Lennard-Jones alloy, and an EAM model for Aluminium. A comparison to parallel tempering is also presented.

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Notes

  1. 1.

    Although \(V_u \) appears in Eq. (8.23) as an argument of \({ \Delta }_{\mathrm {NS}}\) but not of \(\widetilde{{ \Delta }}\), there is no inconsistency because (8.23) is only valid in the limit \(k_{\mathrm {B}}T/ PV_u \rightarrow 0\) where the value of \({ \Delta }_{\mathrm {NS}}\) is independent of \(V_u \).

  2. 2.

    Note that the behaviour of Lennard-Jonesium is different to that of a harmonic-crystal, where nearest neighbour atoms are connected by springs: at zero pressure the harmonic-crystal slightly favours the FCC lattice over the HCP lattice [21].

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  1. Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge, UK

    Robert John Nicholas Baldock

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Correspondence to Robert John Nicholas Baldock .

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Baldock, R.J.N. (2017). Nested Sampling for Materials. In: Classical Statistical Mechanics with Nested Sampling. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-66769-0_8

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