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.
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.
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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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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