On the Applicability of Lindemann’s Law for the Melting of Alkali Metals

Shanker, J.; Anand, K.; Sharma, B. K.; Vijay, A.

doi:10.1007/s10765-020-02751-3

Cited by 9 publications

(5 citation statements)

References 34 publications

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“…417 For Na the same model 418 yielded T mel ≅ 961 K at P ≅ 31 GPa in reasonably good agreement with the experimental data. However, as noted by Shanker, 419 the second-order expression for γ and K′ leads to negative values at really high (infinite) pressure which is unphysical. The value γ = 1/2 is the minimum value for that pressure, 420,421 a result based on Thomas−Fermi theory.…”

Section: Lindemann-based and Related Approachesmentioning

confidence: 92%

“…However, as noted by Shanker, the second-order expression for γ and K ′ leads to negative values at really high (infinite) pressure which is unphysical. The value γ = 1/2 is the minimum value for that pressure, , a result based on Thomas–Fermi theory .…”

Section: The Influence Of Pressurementioning

confidence: 94%

“…The authors suggested that the discrepancies are possible due to the inadequacy of the Lindemann rule for some metals. 419 Stacey obtained from thermodynamic considerations d ln T mel /d ln V = 2γ, 398 which leads to T mel −1 (dT mel /dP) = 2/(AK + BP). Solving this expression in the same way, the results for Cu, Mg, Zn, Au, and Ag agree to a large extent with experimental and ab initio data, while for Al the agreement is better than the results of both Ashini et al and Kholiya and Chandra.…”

Section: Lindemann-based and Related Approachesmentioning

confidence: 99%

“…Comparable results were obtained using the alternative expression T mel − T 0 T mel 0 − T 0 = K ( K 0 ′ + 1 ) K 0 ( K ′ + 1 ) with T 0 a reference temperature as given by Kholiya and Chandra using the same parameters. The authors suggested that the discrepancies are possible due to the inadequacy of the Lindemann rule for some metals . Stacey obtained from thermodynamic considerations d ln T mel /d ln V = 2γ, which leads to T mel –1 (d T mel /d P ) = 2/( AK + BP ).…”

Section: The Influence Of Pressurementioning

confidence: 99%

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Melting Is Well-Known, but Is It Also Well-Understood?

de With

2023

Chem. Rev.

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Contrary to continuous phase transitions, where renormalization group theory provides a general framework, for discontinuous phase transitions such a framework seems to be absent. Although the thermodynamics of the latter type of transitions is wellknown and requires input from two phases, for melting a variety of one-phase theories and models based on solids has been proposed, as a generally accepted theory for liquids is (yet) missing. Each theory or model deals with a specific mechanism using typically one of the various defects (vacancies, interstitials, dislocations, interstitialcies) present in solids. Furthermore, recognizing that surfaces are often present, one distinguishes between mechanical or bulk melting and thermodynamic or surface-mediated melting. After providing the necessary preliminaries, we discuss both types of melting in relation to the various defects. Thereafter we deal with the effect of pressure on the melting process, followed by a discussion along the line of type of materials. Subsequently, some other aspects and approaches are dealt with. An attempt to put melting in perspective concludes this review.

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Section: Lindemann-based and Related Approachesmentioning

confidence: 92%

Section: The Influence Of Pressurementioning

confidence: 94%

Section: Lindemann-based and Related Approachesmentioning

confidence: 99%

Section: The Influence Of Pressurementioning

confidence: 99%

See 2 more Smart Citations

Melting Is Well-Known, but Is It Also Well-Understood?

de With

2023

Chem. Rev.

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“…Equation (10) gives dT m /dP at ambient pressure equal to 61KGPa -1 for MgCu. Melting slope of a material decreases with the increase in pressure because gamma decreases and bulk modulus increases with the increasing pressure [51].…”

Section: Methods Of Analysismentioning

confidence: 99%

Untitled

2023

RDMS

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A simple analytical method has been developed using the Grover-Saxena equation of state to determine pressure-volume-temperature relationships, bulk modulus and its pressure derivative, Debye temperature, Grüneisen parameter and melting curve of the intermetallic compound MgCu. We have considered a wide range of pressures up to 50GPa, and temperatures up to 1000K. The effect of temperature has been taken into account in terms of the thermal pressure estimated from the Anderson formula. The results are compared with those obtained by earlier workers using the ab initio calculations based on the density functional theory. The Roy-Sarkar model recently developed for the density dependence of Debye frequency based on the first-principles has been used in the present study to investigate variations of Debye temperature and Grüneisen parameter with pressure and temperature. Melting curve for MgCu has been predicted using the Roy-Sarkar model for the density dependence of gamma in the Lindemann law. The simple analytical methods used in the present study are capable of making rapid estimations of the thermoelastic properties and melting curve for MgCu.

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