The generalized Lindemann melting coefficient

Vopson, Melvin; Rogers, Nassina; Hepburn, I. D.

doi:10.1016/j.ssc.2020.113977

Cited by 28 publications

(25 citation statements)

References 14 publications

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“…New Lindemann coefficients δ ls have been determined for many elements represented Figure 1 reprinted from [ 77 ]. The enthalpy coefficients ε ls0 = ε gs0 of each element depending on δ ls are given in Equation (7) [ 72 ]:

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Section: Application Of Nchn Model To Liquid Elements: First-order Glass Transition During the First Cooling And Second-order Transition mentioning

confidence: 99%

Section: Figurementioning

confidence: 99%

“…The aim of this work is to predict the melting temperatures of pure elements having a Lindemann coefficient around to 0.103 with the NCHM model [ 72 , 76 ]. New values of Lindemann constants for each element [ 77 ] are used to calculate the glass transition temperature of elements at low and high heating and cooling rates, the transition temperatures of glacial phases and the various melting temperatures of Ag, Cu, Zr, Ta, Re, Ni and Co compared with those deduced from MD simulations or from crystallization enthalpy of highly supercooled liquid elements.…”

Section: Introductionmentioning

confidence: 99%

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Prediction of Second Melting Temperatures Already Observed in Pure Elements by Molecular Dynamics Simulations

Tournier

Ojovan

2021

Materials

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A second melting temperature occurs at a temperature Tn+ higher than Tm in glass-forming melts after heating them from their glassy state. The melting entropy is reduced or increased depending on the thermal history and on the presence of antibonds or bonds up to Tn+. Recent MD simulations show full melting at Tn+ = 1.119Tm for Zr, 1.126Tm for Ag, 1.219Tm for Fe and 1.354Tm for Cu. The non-classical homogeneous nucleation model applied to liquid elements is based on the increase of the Lindemann coefficient with the heating rate. The glass transition at Tg and the nucleation temperatures TnG of glacial phases are successfully predicted below and above Tm. The glass transition temperature Tg increases with the heating rate up to Tn+. Melting and crystallization of glacial phases occur with entropy and enthalpy reductions. A universal law relating Tn+ and TnG around Tm shows that TnG cannot be higher than 1.293Tm for Tn+= 1.47Tm. The enthalpies and entropies of glacial phases have singular values, corresponding to the increase of percolation thresholds with Tg and TnG above the Scher and Zallen invariant at various heating and cooling rates. The G-phases are metastable up to Tn+ because the antibonds are broken by homogeneous nucleation of bonds.

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…”

Section: Application Of Nchn Model To Liquid Elements: First-order Glass Transition During the First Cooling And Second-order Transition mentioning

confidence: 99%

Section: Figurementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Prediction of Second Melting Temperatures Already Observed in Pure Elements by Molecular Dynamics Simulations

Tournier

Ojovan

2021

Materials

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“…Where is the reduced Planck's constant (JHz -1 ), is the Boltzmann's constant (JK -1 ) and The Debye temperature is closely related to the melting temperature through Lindeman's melting criterion [56,57]. Indeed, according Lindeman, solids liquefy when the amplitude of vibration exceeds a fraction of the interatomic spacing.…”

Section: Debye and Einstein Temperaturesmentioning

confidence: 99%

“…Indeed, according Lindeman, solids liquefy when the amplitude of vibration exceeds a fraction of the interatomic spacing. The modern form of Lindeman's criterion is given by [57]:…”

Section: Debye and Einstein Temperaturesmentioning

confidence: 99%