EFFECT OF PRESSURE ON DEBYE – WALLER FACTOR, DEBYE FREQUENCY, DEBYE TEMPERATURE AND MELTING TEMPERATURE OF HCP STRUCTURE CADMIUM METAL
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Abstract
Cadmium (Cd) has great potential for application in the technology of manufacturing super-strong or heat-resistant alloys. The study of the thermodynamic properties of this metal is necessary not only in the scientific field but also in many industries. However, the study of some thermodynamic quantities of Cd such as Debye frequency and temperature, Debye – waller factor (DWF) at high pressure is still limited. In this paper, we use a semi-empirical method to study some thermodynamic properties of Cd metal including Debye frequency and temperature, DWF. The anharmonic Debye model and the Lindemann’s melting law are combined to study the melting temperature of Cd metal. Numerical calculations have been performed for Cd metal up to 50 GPa. The results we obtained are in good agreement with some previous results. This study not only provides additional data on the thermodynamic properties of Cd but also brings many practical applications in scientific and industrial fields.
Keywords
Cadmium, anharmonic Debye model, Debye frequency and temperature, Debye–Waller factor, melting, high pressure, Lindemann’s melting law
Article Details
References
[2] J. F. Cannon (1974) “Behavior of the elements at high pressures” 781 J. Phys. Chern. Ref. Data, vol. 3.
[3] T. S. Tien (2022) “Analysis of Temperature-dependent Extended X-ray Absorption Fine Structure Oscillation of Distorted Crystalline Cadmium” Commun. Phys., vol. 32.
[4] N. V. Hung et al. (2014) "High-order expanded XAFS Debye Waller factors of HCP crystals based on classical anharmonic correlated Einstein model" Mod. Phys. Letters B Vol. 28.
[5] B. Li et al.(2018) “Phase transition and thermoelastic behavior of cadmium sulfide at high pressure and high temperature” J. Alloys Compd., vol. 743.
[6] B. P. Grady et al. (1996) “EXAFS Studies of Various Sulfonated and Carboxylated Cadmium Ionomers” Am. Chem. Soc., vol. 29.
[7] I. F. Vasconcelos et al. (2008) “EXAFS analysis of cadmium(II) adsorption to kaolinite Igor,” Chem. Geol., vol. 249.
[8] M. Minicucci et al. (2005) “Cadmium under High Pressure and High Temperature Conditions,” Phys. Scripta., vol. T115.
[9] D. Errandonea (2010) “The melting curve of ten metals up to 12 GPa and 1600 K,” J. Appl. Phys., vol. 108.
[10] G. Bunker (1983) “Application of the ratio method of EXAFS analysis to disordered systems,” Nucl. Instruments Methods Phys. Res., vol. 207.
[11] N. Van Hung et al. (2010) “Anharmonic correlated Debye model Debye-Waller factors,” Phys. B Condens. Matter, vol. 405.
[12] E. Grüneisen(1912) “Theorie des festen Zustandes einatomiger Elemente,” Ann. Phys., vol. 344.
[13] J. C. Graf et al. (2004) “High-Pressure Debye-Waller and Grüneisen Parameters of Gold and Copper” vol. 65.
[14] H. K. Hieu (2014) “Melting of solids under high pressure” Vacuum, vol. 109.
[15] L. Burakovsky et al. (2004) “Analytic model of the Grüneisen parameter all densities” J. Phys. Chem. Solids, vol. 65.
[16] N. V. Hung et al. (1997) “Anharmonic correlated Einstein-model Debye-Waller factors” Phys. Rev. B - Condens. Matter Mater. Phys., vol. 56.
[17] L. Burakovsky et al. (2000) “Analysis of dislocation mechanism for melting of elements: Pressure dependence” J. Appl. Phys., vol. 88.
[18] F. Lindemann (1910) “The calculation of molecular vibration frequencies” Phys. Z, vol. 11.
[19] Y. Wang et al. (2001) “Melting of iron and other metals at earth’s core conditions: A simplified computational approach” Phys. Rev. B vol. 65.
[20] P. Vinet et al. (1987) “Compressibility of solids” J. Geophys. Res. Geophys Res, vol. 92.
[21] N V. Hung et al. (2008) “Anharmonic effective potential, Local force constant and EXAFS of crystial: Theory and comparison to experiment” Int. J. Mod. Phys. B, vol 22.
[22] T. Kenichi (1997) “Structural study of Zn and Cd to ultrahigh pressures” Physical Review B - Condensed Matter and Materials Physics, vol. 56, no. 9.
[23] D. L. Martin (1961) "The Specific Heat of Hexagonal Metals at Very Low Temperatures" Proc. Phys. Soc. Vol. 78.
[24] D. Rajdev et al. (1962) "Debye Temperature for Cadmium Derived from Low-Temperature Specific-Heat Measurements" Phys. Rev. Vol. 128.
[25] C. W. Garland et al. (1960) "Elastic Constants of Cadmium from 4.2°K to 300°K" Physical Review, vol. 119 .
[26] S. Arafin et al. (2013) “Melting of metals under pressure” Physica B: Condensed Matter, vol. 419.