The Physical and Thermodynamic Functions of Borides

  • N.Yu. Filonenko State Establishment “Dnipropetrovsk Medical Academy of Health Ministry of Ukraine”
Keywords: borides, Gibbs energy, entropy, enthalpy, heat capacity, fluctuation process


In the paper the physical properties and thermodynamic functions of borides Х2В (Х=W, Mo, Mn, Fe, Co, Ni та Cr) are studied with accounting for fluctuation processes. We use the microstructure analysis, the X-ray structural and the durometric analyses to determine the physical properties of alloys. In the paper it is determined the phase composition and physical properties of borides. In this paper for the first time it is determined the thermodynamic functions of borides using the Hillert and Staffansson model with accounting for the first degree approximation of high-temperature expansion for the free energy potential of binary alloys. We obtain the temperature dependences for such thermodynamic functions as Gibbs free energy, entropy, enthalpy and heat capacity Ср along with their values at the formation temperature for Х2В (Х=W, Mo, Mn, Fe, Co, Ni та Cr). The approach under consideration enables to give more thorough from the thermodynamic point of view description of borides formed from the liquid. The outcomes of the thermodynamic function calculation for borides are in good agreement with experimental data and results of other authors.


[1] A. Friedrich, B. Winkler, E.A. Juarez-Arellano, L. Bayarjargal, Materials 4, 1648 (2011).
[2] G. V. Samsonov, T. I. Serebryakova, V. A. Neronov, Borides (Atomizdat, Moscow, 1999).
[3] Yu. B. Kuzma, Crystal chemistry of borides (Vishcha school, Kiev, 1983).
[4] C. T. Zhou, J. D. Xing, B. Xiao, J. Feng, X. J. Xie, Y. H. Chen, Computational Materials Science 44, 1056 (2009).
[5] M. Sekar, N. V. Chandra, S. Shekar, G. Shwetha, G. Vaitheeswaran, V. Kanchana, Journal of Alloys and Compounds 654, 554 (2016).
[6] B. Halemans, P. Wollemans, J.R. Roos, Metallkd 85 (10), 676 (1994).
[7] Weihua Sun, Yong Du, Shuhong Liu, Baiyun Huang, and Chao Jiang, Journal of Phase Equilibria and Diffusion 31 (4), 357 (2010).
[8] P. K. Liao and K. E. Spear, Bulletin of Alloy Phase Diagrams 9 (4), 452 (1988).
[9] H. Duschanek and P. Rogl, Critical Journal of Phase Equilibria 16 (2), 150 (1995).
[10] O. Teppa and P. Taskinen, Materials Science and Technology 9, 205 (1993).
[11] Edmund Storms and Barbara, Journal of Physical Chemistry 8 (4) 318 (1977).
[12] B. Xiao, J. Feng, C. T. Zhou, J. D. Xing, X. J. Xie, Y. H. Cheng, R. Zhou, DFT theory Physica B. 405, 1274 (2010).
[13] S. V. Tverdokhlebova, Visnyk dniprovskogo. Nat. Un-tu. Ser. Fizika. Radiotelektronika (12/1), 100 (2007).
[14] A. S. Pomelnikova, M. N. Shipko, M A Stepovich, Surface. X-ray, synchronous and neutron studies 3, 99 (2011).
[15] M. Hillert, L. Staffonsson, Acta Chemica Scandinavica 24 (10), 3618 (1970).
[16] M. I. Shakhparonov, Introduction to the molecular theory of solutions (State Publishing House of Technical and Theoretical Literature, Moscow, 1956).
[17] L. Zhirifalko, Statistical physics of the solid body (Mir, Moscow, 1975).
[18] Richard A. Roble and David R. Waldbaum Thermodynamic Properties of Minerals and Related Substances at 298.15°K (25.0°C) and One Atmosphere (1.013 Bars) Orton memorial library the OHIO State University 155 S. Oval Drive. 1970, p. 262.
[19] SGT data for pure elements A T Dinsdale NPL Materials Center, Division of Industry and Innovation, National Physical Laboratory, Teddington, Middlesex, TW11 0LW, UK. P. 174.
[20] Y. Q. Liua, X. S. Zhao, J. Yanga, J. Y. Shenb, Journal of Alloys and Compounds 509, 4805 (2011).
[21] K. E. Spear and P. K. Liao, System Alloy Phase Diagrams 9 (4) 457 (1988).
[22] Y. Yang, Y. A. Chang, Intermetallics 13, 121 (2005).
[23] Yongcheng Liang, Zheng Zhong, Wenqing Zhang, Computational Materials Science 68, 222 (2013).
[24] Tatsuya Tokunaga, Hiroshi Ohtani; And Mitsuhiro Hasebe, SystemMaterials Transactions 46 (6) 1193 (2005).
[25] Wei-Hua Sun, Yong Du, Yi Kong, Hong-HuiXu, Wei Xiong, Shu-Hong Liu Int. J. Mat. Res. (Formerly Z. Metallkd.) 100, 59 (2009).
[26] J. Miettinen, G. Vassilev, Metallurgy and Materials 59 (2) 601 (2014).
[27] P. K. Liao and K. E. Spear, Bulletin of Alloy Phase Diagrams 7 (6), 543 (1986).
[28] N.Yu. Filonenko, Physics and Chemistry of Solid State (Ukr.) 12 (2), 370 (2011).
[29] Hiroshi Ohtani, Mitsuhiro Hasebe, and Taiji Nishizawa, Ternary Phase Diagram. Transactions ISIJ. 28, 1043 (1988).
[30] Y. Q. Liua, X. S. Zhao, J. Yanga, J. Y. Shenb, Journal of Alloys and Compounds 509, 4805 (2011).
[31] P. K. Liao and. K.E Spear, Bulletin of Alloy Phase Diagrams 7 (3) 232 (1986).
[32] J. Miettinen, G. Vassilev, Archives of metallurgy and materials 59 (2) 601 (2014).
[33] I. P. Bazarov, Thermodynamics (Higher School, Moscow, 1991).
[34] Bing Wang, Li Xiang, Xu Yuan Wang, and Yu Feitu, J. Phys. Chem. C. 115, 2142935 (2011).
[35] S. Sato and O. J Kleppa, Metallurgical Transactions B-Process Metallurgy 13 (2), 251 (1982).
[36] M. Mihalkovic, M. Widom, Physical Review 70 (14), 144107 (2004).
[37] B. V. Mikhajlovskij, V. I. Goryacheva, I.B. Kutsenok, Zhurnal Fizicheskoj Khimii 73 (4). 763 (1999).
[38] Bing Wang, De Yu Wang, Zhenxiang Cheng, Xiaolin Wang and Yuan Xu Wang Chem. Phys. Chem. 14, 1245 (2013).
[39] Raju S. et al., Asian Nuclear Prospects 1 (2012).
[40] Konga Yi, Xiongb Wei, Haibo Guoc, Weihua Suna, Yong Dua, Yichun Zhoud CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 34, 245 (2010).
How to Cite
Filonenko, N. (2017). The Physical and Thermodynamic Functions of Borides. Physics and Chemistry of Solid State, 18(1), 58-63.
Scientific articles