Extension of Lindemann’s Formula to Study the Pressure Dependence of Melting Temperature

Arafin, Sayyadul; Singh, Ranjit; George, A. K.

doi:10.1007/s10765-012-1227-8

Cited by 18 publications

(11 citation statements)

References 14 publications

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“…It is very useful to characterize the atomic vibrations in both solids and liquids. θ D also plays a significant role in geophysical studies of rocks and minerals to investigate the structural stability, bonding strength between constituent elements, structure defect availability including dislocations in crystalline structures of mineral grains, pores, micro‐cracks, and the density . The values of θ D can be determined precisely from low‐temperature measurements of the specific heat .…”

Section: Resultsmentioning

confidence: 99%

“…θ D also plays a significant role in geophysical studies of rocks and minerals to investigate the structural stability, bonding strength between constituent elements, structure defect availability including dislocations in crystalline structures of mineral grains, pores, micro‐cracks, and the density . The values of θ D can be determined precisely from low‐temperature measurements of the specific heat . In addition to the heat capacity measurements method, θ D can be predicted from the average acoustic wave velocity v m using the following expression

θ_{normalD} = \frac{ℏ}{k_{B}} {[(\frac{6 π^{2} N K v_{m}^{3}}{V})]}^{1 / 3}

where

ℏ = h false/ 2 π

, h is the Planck constant; k B is the Boltzmann constant, N is the number of unit cells in the volume V of the crystal, and K is the number of atoms per unit cell.…”

Section: Resultsmentioning

confidence: 99%

“…The melting temperature T m and its pressure dependence are important information required for the thermal characterization of materials including minerals and rocks . It can be predicted using the elastic constants based on empirical formulas .…”

Section: Resultsmentioning

confidence: 99%

“…[62] The values of θ D can be determined precisely from low-temperature measurements of the specific heat. [62,63] In addition to the heat capacity measurements method, θ D can be predicted from the average acoustic wave velocity v m using the following expression [59] Table 4. Pressure dependence of the acoustic wave velocities V p , V s 1 , and V s 2 (in km s À1 ) in three directions [100], [110], and [111] for MgCa intermetallic compound with CsCl-type structure.…”

Section: Sound Velocity and Debye Temperature Of The Aggregate Materialsmentioning

confidence: 99%

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High‐Pressure Effect on Elastic Constants and Their Related Properties of MgCa Intermetallic Compound

Daoud

Bouarissa

Benmakhlouf

et al. 2020

Physica Status Solidi (b)

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Structural parameters, elastic constants, and their related properties of MgCa with a cubic CsCl‐type structure under high pressure up to 16 GPa are investigated using the pseudopotential plane‐wave approach in the framework of the density functional theory as implemented in the CASTEP code. The results indicate that MgCa possesses a brittle nature below 1.4 GPa and begins to be prone to ductility when the pressure goes beyond this value. The tetragonal shear parameter is found to vanish at around 7 GPa. The analyses of the anisotropy factors show that MgCa is highly anisotropic. The magnitude of the anisotropy increases monotonically with applied pressure. The single crystal azimuthal anisotropy for longitudinal and transverse waves is determined. The variation of the longitudinal and shear‐wave velocities with the direction of propagation is estimated at 0 and 16 GPa pressure. The Cauchy condition is found to be strongly violated, reflecting the important contribution from the noncentral many‐body forces in the crystal. In addition, the specific heat capacity CV and the entropy S at elevated temperatures up to 600 K are studied. At zero‐pressure and T = 300 K, our calculation yields values of CV ≈ 47.31 J mol−1 K−1 and S ≈ 66.06 J mol−1 K−1.

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Section: Resultsmentioning

confidence: 99%

θ_{normalD} = \frac{ℏ}{k_{B}} {[(\frac{6 π^{2} N K v_{m}^{3}}{V})]}^{1 / 3}

where

ℏ = h false/ 2 π

, h is the Planck constant; k B is the Boltzmann constant, N is the number of unit cells in the volume V of the crystal, and K is the number of atoms per unit cell.…”

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Sound Velocity and Debye Temperature Of The Aggregate Materialsmentioning

confidence: 99%

See 2 more Smart Citations

High‐Pressure Effect on Elastic Constants and Their Related Properties of MgCa Intermetallic Compound

Daoud

Bouarissa

Benmakhlouf

et al. 2020

Physica Status Solidi (b)

View full text Add to dashboard Cite

show abstract

“…Gabbro is mainly composed of calcium plagioclase, pyroxene and olivine minerals. The percentage of olivine present in the gabbro of the Oman ophiolite ranges from 18% to 44% [15].…”

Section: Oman Ophiolitementioning

confidence: 99%