Temperature and Pressure Effect on the Structural Properties of W and W–Fe Alloys
Main Article Content
Abstract
In this study, the Statistical Moment Method (SMM) is applied to investigate the structural properties of the W-Fe alloy at temperatures up to 3000 K and pressures up to 20 GPa. Analytical expressions for the free energy are derived, along with explicit formulas for structural quantities such as lattice constants and volume, taking into account the effects of anharmonicity. The results obtained from the SMM show good agreement with existing theoretical calculations and experimental data. This method demonstrates strong potential for further extension to the study of elastic properties, thermodynamic quantities, and the melting temperature of the W–Fe alloy in future work.
Keywords:
W metal, W15Fe1 alloy, W14Fe2 alloy, structural properties, thermodynamic properties, temperature, high pressure, statistical moment method
References
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[4] D. Y. Jiang, W. B. Xiao, D. S. Liu, S. Q. Liu, Structural Stability, Electronic Structures, Mechanical Properties and Debye Temperature of W–Re Alloys: A First-Principles Study, Fusion Eng. Des., Vol. 162, 2021,
pp. 112081.
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[6] G. A. Dosovitskiy, S. V. Samoilenkov, Thermal Expansion of Ni–W, Ni–Cr, and Ni–Cr–W Alloys Between Room Temperature And 800 °C, Int. J. Thermophys., Vol. 30, No. 6, 2009, pp. 1931-1937.
[7] B. X. Liu, L. J. Huang, L. Geng, Fabrication and Superior Ductility of Laminated Ti–Tibw/Ti Composites by Diffusion Welding, J. Alloys Compd., Vol. 602, 2014, pp. 187-192.
[8] Y. D. Kim, N. L. Oh, S. T. Oh, I. H. Moon, Thermal Conductivity of W–Cu Composites at Various Temperatures, Mater. Lett., Vol. 51, No. 5, 2001, pp. 420-424,
[9] F. Klein, A. Litnovsky, X. Y. Tan, J. G. Julian, M. Rasinski, C. Linsmeier, M. Bram, J. W. Coenen, Smart Alloys as Armor Material for DEMO: Overview of Properties and Joining to Structural Materials, Fusion Eng. Des.,
Vol. 166, 2021, pp. 112272.
[10] D. Y. Jiang, W. Hu, W. B. Xiao, H. Q. Wan, K. R. He, S. Q. Liu, Structural, Electronic, Mechanical and Thermodynamic Properties of Antiperovskites Ti3Inx (X = C and N) Ceramics: a First-Principles Study, Vacuum, Vol. 204, 2022, pp. 111340.
[11] S. Biswas, First-Principles Investigation of the Metal–Insulator Transitions in Ti-Substituted Tetragonal Rutile VO2, Vacuum, Vol. 212, 2023, pp. 111994.
[12] Y. Zhuang, Z. Y. Zou, B. Lu, Y. J. Li, D. Wang, M. Avdeev, S. Q. Shi, Understanding the Li Diffusion Mechanism and Positive Effect of Current Collector Volume Expansion in Anode-Free Batteries, Chin. Phys. B, Vol. 29, 2020, pp. 068202.
[13] N. Tang, V. V. Hung, Investigation of the Thermodynamic Properties of Anharmonic Crystals by Momentum Method. I. General Results for Face-Centred Cubic Crystals, Phys. Status Solidi B, Vol. 149, No. 2, 1988,
pp. 511-519, https//doi.org/10.1002/Pssb.2221490212.
[14] K. M. Jindo, S. R. Nishitani, V. V. Hung, Hcp–Bcc Structural Phase Transformation of Titanium: Analytic Model Calculations, Phys. Rev. B, Vol. 70, No. 18, 2004, pp. 184122, https//doi.org/10.1103/Physrevb.70.184122.
[15] V. V. Hung, N. T. Hai, Investigation of the Elastic Moduli of Face- and Body-Centered Cubic Crystals, Comput. Mater. Sci., Vol. 14, 1999, pp. 261-266, https//doi.org/10.1016/S0927-0256(98)00117-7.
[16] T. D. Cuong, N. Q. Hoc, A. D. Phan, N. T. Thao, N. D. Trung, Theoretical Predictions of Melting Behaviors of Hcp Iron up to 4000 Gpa, Phys. Rev. B, Vol. 106, No. 9, 2022, pp. 094103, https//doi.org/10.1103/Physrevb.106.094103.
[17] C. H. Phuong, V. V. Hung, Influence of Temperature and Pressure on the Lattice Constant of Srtio3 Perovskite by the Statistical Moment Method with Improved Interatomic Potential, Math. Phys., Vol. 38, No. 3, 2022, https//doi.org/10.25073/2588-1124/Vnumap.4706.
[18] N. Q. Hoc, T. T. Nga, N. N. Thang, B. L. Ngoc, N. T. Ngoc, L. T. Lam, Toward Better Understanding of Anharmonic Structural, Thermodynamic, and Elastic Properties of Casio3_33 Perovskite Under Extreme Conditions Via Statistical Moment Method, Materialia, Vol. 34, 2024, pp. 102105,
https//doi.org/ 10.1016/J.Mtla.2024.102105.
[19] S. Baty, L. Burakovsky, D. Preston, Topological Equivalence of the Phase Diagrams of Molybdenum and Tungsten, Crystals, Vol. 10, No. 1, 2020, pp. 20, https//doi.org/10.3390/Cryst10010020.
[20] E. Y. Tonkov, E. G. Ponyatovsky, Phase Transformations of Elements Under High Pressure. Boca Raton, FL: CRC Press, 2004, pp. 253-265.
[21] M. Zhang, X. Wang, Y. Chen, H. Cai, H. Li, D. Jiang, Theoretical Study of Mechanical and Thermodynamic Properties of W–Fe Alloys: Promising Ultra-High Temperature Alloy Materials, Vacuum, Vol. 222, 2024,
pp. 113047, https//doi.org/10.1016/J.Vacuum.2024.113047.
[22] N. Tang, V. V. Hung, Investigation of the Thermodynamic Properties of Anharmonic Crystals by Momentum Method. IV, The Limiting of Absolute Stabi0, lity and the Melting Temperature of Crystals, Phys. Status Solidi B, Vol. 162, No. 2, 199, pp. 379-385, https//doi.org/oi: 10.1002/Pssb.2221620207.
[23] M. N. Magomedov, The Calculation of the Parameters of the Mie–Lennard-Jones Potential, High Temp., Vol. 44, No. 4, 2006, pp. 513-529, https//doi.org/10.1134/S0018151X06040099.
[24] K. D. Litasov, P. N. Gavryushkin, P. I. Dorogokupets, I. S. Sharygin, A. Shatskiy, Y. Fei, S. V. Rashchenko,
Y. V. Seryotkin, Y. Higo, K. Funakoshi, E. Ohtani, Thermal Equation of State to 33.5 Gpa and 1673 K and Thermodynamic Properties of Tungsten, J. Appl. Phys., Vol. 113, 2013, pp. 133505.
[25] D. Y. Jiang, Q. Zhou, L. Xue, T. Wang, J. F. Hu, First-Principles Study of the Phase Stability and Mechanical Properties of Binary W–Mo Alloys, Fusion Eng. Des., Vol. 130, 2018, pp. 56-61.
[26] K. D. Litasov, P. N. Gavryushkin, P. I. Dorogokupets, I. S. Sharygin, A. Shatskiy, Y. Fei, S. V. Rashchenko,
Y. V. Seryotkin, Y. Higo, K. Funakoshi, E. Ohtani, Thermal Equation of State to 33.5 Gpa and 1673 K and Thermodynamic Properties of Tungsten, J. Appl. Phys., Vol. 113, 2013, pp. 133505.
[27] Y. Wang, D. Chen, X. Zhang, Phonon Softening and Phase Transitions in Metals Under Pressure, Phys. Rev. Lett., Vol. 84, 2000, pp. 3220.
[28] S. Xiang, F. Xi, Y. Bi, J. A. Xu, H. Geng, L. Cai, F. Jing, J. Liu, Elastic and Thermodynamic Properties of Bcc Tungsten Under High Pressure, Phys. Rev. B, Vol. 81, 2010. pp. 014301.