How Do Crystals Melt?

Phillpot, Simon R.; Yip, Sidney; Wolf, D.

doi:10.1063/1.4822877

Cited by 119 publications

(53 citation statements)

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“…Previous efforts in MD simulations attempted to relate the thermodynamic melting to the Lindemann criterion ͑vibrational instability͒ and Born ͑mechani-cal͒ instability. 48,49 In MD simulations of a Lennard-Jones fcc system, superheating of ⌰ md ϩ ϳ0.20 corresponds to Lindemann's parameter ␦ L ϳ0.22 ͑fractional root-mean-square displacement͒ and near-zero shear moduli of a bulk system. 49 It is not surprising that both criteria are satisfied at the kinetic limit of superheating.…”

Section: Discussionmentioning

confidence: 99%

Maximum superheating and undercooling: Systematics, molecular dynamics simulations, and dynamic experiments

et al. 2003

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The maximum superheating and undercooling achievable at various heating ͑or cooling͒ rates were investigated based on classical nucleation theory and undercooling experiments, molecular dynamics ͑MD͒ simulations, and dynamic experiments. The highest ͑or lowest͒ temperature T c achievable in a superheated solid ͑or an undercooled liquid͒ depends on a dimensionless nucleation barrier parameter ␤ and the heating ͑or cooling͒ rate Q. ␤ depends on the material: ␤ϵ16␥ sl 3 /(3kT m ⌬H m 2 ) where ␥ sl is the solid-liquid interfacial energy, ⌬H m the heat of fusion, T m the melting temperature, and k Boltzmann's constant. The systematics of maximum superheating and undercooling were established phenomenologically as ␤ϭ(A 0 Ϫb log 10 Q) c (1Ϫ c ) 2 where c ϭT c /T m , A 0 ϭ59.4, bϭ2.33, and Q is normalized by 1 K/s. For a number of elements and compounds, ␤ varies in the range 0.2-8.2, corresponding to maximum superheating c of 1.06 -1.35 and 1.08 -1.43 at Q ϳ1 and 10 12 K/s, respectively. Such systematics predict that a liquid with certain ␤ cannot crystallize at cooling rates higher than a critical value and that the smallest c achievable is 1/3. MD simulations (Q ϳ10 12 K/s) at ambient and high pressures were conducted on close-packed bulk metals with Sutton-Chen many-body potentials. The maximum superheating and undercooling resolved from single-and two-phase simulations are consistent with the c -␤-Q systematics for the maximum superheating and undercooling. The systematics are also in accord with previous MD melting simulations on other materials ͑e.g., silica, Ta and ⑀-Fe͒ described by different force fields such as Morse-stretch charge equilibrium and embedded-atom-method potentials. Thus, the c -␤-Q systematics are supported by simulations at the level of interatomic interactions. The heating rate is crucial to achieving significant superheating experimentally. We demonstrate that the amount of superheating achieved in dynamic experiments (Qϳ10 12 K/s), such as planar shock-wave loading and intense laser irradiation, agrees with the superheating systematics.

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Section: Discussionmentioning

confidence: 99%

Maximum superheating and undercooling: Systematics, molecular dynamics simulations, and dynamic experiments

et al. 2003

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“…That is, the bcc(112)͗110͘S3 plane is a twin boundary, and bcc(111)͗110͘S3 and bcc(221)͗110͘S9 planes are a mismatched grain boundaries. As discussed in previous works, 2,30) melting starts heterogeneously from interfaces such as the surface or grain boundary. Hence, it is reasonable to assume that only atoms near the mismatched grain boundary fluctuated markedly and that premelting was observed at a temperature close to the melting point.…”

Section: Premelting In the Symmetric Tilt Boundariesmentioning

confidence: 99%

A Molecular Dynamics Study of the Energy and Structure of the Symmetric Tilt Boundary of Iron

2008

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The temperature dependences of the energy and structure of the symmetric tilt boundary of bcc and fcc iron were investigated by molecular dynamics simulation. A large energy cusp was observed at the bcc(112)͗110͘S3 and fcc(111)͗110͘S3 grain boundary plane, which is a twin boundary, whereas it was not observed at the bcc(111)͗110͘S3 plane in spite of it having the lowest S-value. The grain boundary energy increased at the temperature close to the melting point except for the grain boundary planes that have a large energy cusp. On the other hand, it was newly founded that the grain boundary energies at the bcc(112)͗110͘S3 and fcc(111)͗110͘S3 did not increased despite such a high temperature. The increase in grain boundary energy was due to the premelting, which is a localized disorder of the atoms near the grain boundary energy. It was confirmed that the grain boundary energy is affected by the matching at the interface rather than the periodicity described by the S-value.

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“…Simulations of atomic dynamics for solids with an fcc [18,19,20,11,10] or diamond [17] structures show, among other things, the onset of a shear instability of the solid at a temperature T s , which can exceed the thermodynamic melting temperature T m by some 20%, depending on the details of the potential.…”

Section: Introductionmentioning

confidence: 99%

Molecular dynamics study of melting of the bcc metal vanadium. I. Mechanical melting

2003

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We present molecular dynamics simulations of the homogeneous (mechanical) melting transition of a bcc metal, vanadium. We study both the nominally perfect crystal as well as one that includes point defects. According to the Born criterion, a solid cannot be expanded above a critical volume, at which a 'rigidity catastrophe' occurs. This catastrophe is caused by the vanishing of the elastic shear modulus. We found that this critical volume is independent of the route by which it is reached whether by heating the crystal, or by adding interstitials at a constant temperature which expand the lattice. Overall, these results are similar to what was found previously for an fcc metal, copper. The simulations establish a phase diagram of the mechanical melting temperature as a function of the concentration of interstitials. Our results show that the Born model of melting applies to bcc metals in both the nominally perfect state and in the case where point defects are present. IntroductionOver the years, several theories explaining the mechanism of melting have been proposed. [1,2,5] This research has by now evolved to a state where a clear distinction exists between two possible scenarios for the melting transition: a first scenario of homogeneous, or mechanical melting resulting 1 from lattice instability [3,4,6] and/or a spontaneous generation of thermal defects, [7,8,9,10,11] and a second scenario of heterogeneous, or thermodynamic melting which begins at extrinsic defects such as a free surface or an internal interface (grain boundaries, voids, etc). [12,13,14,15,16] Throughout this paper we will use the term mechanical melting to describe the former case, which we consider here. In particular, we take the view proposed by Born that at the melting point a 'rigidity catastrophe' is caused by the vanishing of one of the elastic shear moduli,[3, 4] C 44 , or C ′ = (C 11 − C 12 )/2. In other words, the crystal melts once it loses its ability to resist shear. This condition determines the mechanical melting temperature, T s , of a perfectly homogeneous bulk crystal and was confirmed in extensive studies of fcc metals. [18,19,20,11,10] Tallon [4] pointed out that a mechanical instability arises when the solid expands up to a critical specific volume which is close to that of the liquid phase (melt). In the study by Wang et al. [18,19] of the mechanical melting transition of an fcc solid under external stress, it was found that volume expansion is the underlying cause of lattice instability. Kanigel et al. [11] confirmed this scenario in a simulation of fcc copper in the presence of point defects. They showed that the critical volume at which a crystal of copper melts is independent of the path through phase space by which it is reached, whether by heating of the perfect crystal or by adding point defects to expand the solid at a constant temperature [11].Solids can undergo mechanical melting only if they have no extended defects [6], a situation which is conveniently realized in three-dimensional computer simulati...

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How Do Crystals Melt?

Cited by 119 publications

References 0 publications

Maximum superheating and undercooling: Systematics, molecular dynamics simulations, and dynamic experiments

Maximum superheating and undercooling: Systematics, molecular dynamics simulations, and dynamic experiments

A Molecular Dynamics Study of the Energy and Structure of the Symmetric Tilt Boundary of Iron

Molecular dynamics study of melting of the bcc metal vanadium. I. Mechanical melting

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