Theoretical Evaluation of Electrical Resistivity with Bloch-Gruneisen Function

Year 2025, Volume: 14 Issue: 2, 115 - 123, 31.08.2025

Melek Gökbulut , Elif Somuncu

https://doi.org/10.54187/jnrs.1667993

Abstract

In this study, a simple and efficient analytical formula is presented to calculate the generalized Bloch-Gruneisen function. The proposed analytical formula for the generalized Bloch-Gruneisen function is corrected for non-integer and integer values of parameter 𝑚. Note that the Bloch-Gruneisen function is preferred to calculate thermal conductivity and electrical resistivity of solid materials. It has been demonstrated that the offered analytical formula gives very correct results of semiconductor and superconductivity for a wide range of temperatures. As an example, the Bloch-Gruneisen function of MgB2 material, which is envisioned as an alternative superconducting wire for advanced fusion reactors, has been calculated and compared with theoretical calculations and experimental data. The results obtained for m=3.5 were found to be in excellent agreement with the experimental data, with a maximum deviation of approximately 1.26%. The results demonstrated that the analytical formula can be satisfactorily used for solid materials.

Keywords

Bloch-Gruneisen function , debye temperature , electrical resistivity , magnesium diboride , superconductivity

References

• A. Grünebohm, A. Hütten, A. E. Böhmer, J. Frenzel, I. Eremin, R. Drautz, I. Ennen, L. Caron, T. Kuschel, F. Lechermann, D. Anselmetti, T. Dahm, F. Weber, K. Rossnagel, G. Schierning, A unifying perspective of common motifs that occur across disparate classes of materials harboring displacive phase transitions, Advanced Energy Materials 13 (30) (2023) 2300754.
• H. Zhang, W. Zhong, X. Yu, B. Yue, F. Hong, Electronic phase transitions and superconductivity in ferroelectric S n2 P2 Se6 under pressure, Physical Review B 109 (2024) 214517.
• N. S. Piro, A. S. Mohammed, S. M. Hamad, Electrical resistivity measurement, piezo resistivity behaviour and compressive strength of concrete: a comprehensive review, Materials Today Communications 36 (2023) 106573.
• R. Singh, M. Ahmad, A. Caceres, R. Eybel, M. Medraj, The influence of defects on hydrogen-induced electrical resistivity changes in Fe-based systems: A first-principles study, International Journal of Hydrogen Energy 126 (2025) 429-438.
• E. Eser, H. Koç, Investigations of temperature dependences of electrical resistivity and specific heat capacity of metals, Physica B:Condensed Matter 492 (2016) 7–10.
• I. A. Ansari, Numerical solution of Bloch–Gruneisen function to determine the contribution of electron–phonon interaction in polycrystalline MgB2 superconductor, Physica C: Superconductivity 470 (11-12) (2010) 508–510.
• I. A. Ansari, The Analytical Solution of Incomplete Gamma Function to Determine the Electrical Resistivity at Normal State for MgB2 Superconductor, Journal of Physics: Conference Series 1172 (2019) 012028.
• I. A. Ansari, C. Rao, Evaluation of Bloch–Gruneisen Function to Determine the Electrical Resistivity for Pure Nano-MgB2, Superconductor Materials Research Proceedings 22 (2022) 13-17.
• A. Poddar, B. Bandyopadhyay, P. Mandal, D. Bhattacharya, P. Choudhury, U. Sinha, B. Ghosh, Studies of transport properties of MgB2 superconductor, Physica C: Superconductivity 390 (2003) 191–196.
• B. Mamedov, I. Askerov, A new algorithm for accurate evaluation of the generalized Bloch–Gruneisen function and its applications to MgB2 superconductor, Physics Letters A 362 (2007) 324–326.
• Z. Hu, J. Deng, H. Li, M. Ogunbunmi, X. Tong, Q. Wang, D. Graf, Robust three-dimensional type-II Dirac semimetal state in SrAgBi. Npj Quantum Materials 8 (2023) 20.
• Z. Dogan, T. Mehmetoglu. An approach to improve energy performance of electric vehicle:Theoritical evaluation of electric motor winding heat capacity and electrical resistivity using Debye and Bloch-Gruneisen approximations, International Journal of Hydrogen Energy 41 (42) (2016) 19265-19268.
• Z. Dogan, T. Mehmetoglu, An analytical evaluation method of the temperature dependence of resistive losses in electric motors, Journal of Power Technologies 103 (2) (2023) 118-122.
• C. Buzea, T. Yamashita, Review of the superconducting properties of MgB2, Superconductor Science and Technology 14 (11) (2001) R15.
• J. Nagamatsu, N. Nakagawa, T. Muranaka, Y. Zenitani, J. Akimitsu, Superconductivity at 39 K in magnesium diboride, Nature 410 (2001) 63.
• S. Giannelli, G. Montenero, A. Ballarino, Investigation of Splice Resistances of High-Current MgB2 Cables Operated in Liquid and Helium Gas, IEEE Transactions on Applied Superconductivity, 27 (4) (2017) 4802505.
• C. Guo, H. Wang, X. Cai, W. Luo, Z. Huang, Y. Zhang, Q. Feng, Z. Gan, High performance superconducting joint for MgB2 films, Physica C: Superconductivity and its applications 584 (2021) 1353863.
• D. Patel, A. Matsumoto, H. Kumakura, M. Maeda, S.H. Kim, M. S. A. Hossain, S. Choib, J. H. Kim, MgB2 for MRI application: Dual sintering induced performance variation in in situ and IMD processed MgB2 conductors, Journal of Materials Chemistry C (7) (2020) 2507-2516.
• D. Matera, M. Bonura, R. Cerny, S. M. Walker, F. Buta, D. LeBoeuf, X. Chaud, E. Giannini, C. Senatore, High-field superconductivity in C-doped MgB2 bulk samples prepared by a rapid synthesis route, Scientific Reports 10 (2020) 17656.
• T. Prikhna, V. Sokolovsky, V. Moshchil, Bulk MgB2 Superconducting materials: technology, properties, and applications Materials 17 (11) (2024) 2787.
• Y. Hishinuma, A. Kikuchi, Y. Iijima, Y. Yoshida, T. Takeuchi, A. Nishimura, Fabrication of MgB2 superconducting wires as low activation superconducting materials for an advanced fusion reactor application, Fusion Engineering and Design 81 (20-22) (2006) 2467–2471.
• Q. Cai, Q. Guo, Y. Liu, Z. Ma, H. Li, W. Qiu, D. Patel, H. Jie, J.H. Kim, M. Somer, E. Yanmaz, A. Devred, V. Luzin, A. Fatehmulla, W. A. Farooq, D. Gajda, Y. Bando, Y. Yamauchi, S. Pradhan, S.A. Hossain, Doping-induced isotopic Mg11B2 bulk superconductor for fusion application, Energies 10 (3) (2017) 409.
• F. Cheng, Y. Liu, Z. Ma, M. S. Al Hossain, M. Somer, Improved superconducting properties in the Mg11B2 low activation superconductor prepared by low-temperature sintering, Scientific Reports 6 (2016) 25498.
• P. Gao, Y.X. He, H.J. Ma, V.A. Anvar, J.F. Huang, X.F. Pan, C. Zhou, A. Nijhuis, J.G. Li, J.G. Qin, W. J. Wang, M. Yu, H. Jin, DC performance and AC loss of sub-size MgB2 CICC conductor for fusion magnet application, Nuclear Fusion 62 (5) (2022) 056014.
• W. Wang, Y. Wu, Y. He, P. Gao, A. Nijhuis ve J. Qin, Heat Transfer Analysis of MgB2 Coil in Heat Treatment Process for Future Fusion Reactor, IEEE Transactions on Applied Superconductivity, 33 (5) (2023) 4200605.
• K. Konstantopoulou, J. Hurte, J. Fleiter, A. Ballarino, Electro-Magnetic Performance of MgB2 Cables for the High Current Transmission Lines at CERN, IEEE Transactions on Applied Superconductivity 29 (5) (2019) 4802205.
• N. Bairagi, V. L. Tanna, D. Raju, Preliminary design and analysis of 20 K helium cooled MgB2 based superconducting current feeder system for tokamak application, IEEE Transactions on Applied Superconductivity 32 (6) (2022) 4802305.
• N. Bairagi , D. Sonara, H. Nivamat , V. L. Tanna, U. Prasad, D. Raju, Copper electroplating technique for development of HTS current leads bottom joints using MgB2 wires, Physica C: Superconductivity and its Applications 601 (2022) 1354108.
• N. Bairagi, V. L. Tanna, H. Nimavat, D. Sonara, R. Panchal, A. Garg, Test results of a prototype HTS current lead with MgB2 and NbTi superconducting joints, IEEE Transactions on Applied Superconductivity 33 (4) (2023) 4801408.
• N. Bairagi, V. L. Tanna, H. Nimavat, D. Sonara, A. Garg, R. Panchal, Feasibility study of HTS current leads with MgB2 shunt for tokamak application, IEEE Transactions on Applied Superconductivity 34 (5) (2024) 4800804.
• I. Gradshteyn, I. Ryzhik, Tables of Integrals, Series and Products, in: A. Jeffery, D.Zwillinger (Eds.), 7th Edition, Elsevier Academic Press, New York, 1980.
• M. N. Mathews, M. A. Esrick, Z. Y. Teoh, J. K. Freericks, A Physicist’s Guide to the solution of Kummer's Equation and Confluent Hypergeometric Functions, Condensed Matter Physics 25 (3) (2022) 33203.
• Y. Kong, O. Dolgov, O. Jepsen, O. Anderson, Electron-phonon interaction in the normal and superconducting states of MgB2, Physical Review B 64 (2) (2001) 020501.
• A. Bharathi, S.J. Balaselvi, S. Kalavathi, G.L.N. Reddy, V. Sankar Sastra, Y. Hariharan, T.S. Radhakrishnan, Carbon solubility and superconductivity in MgB2, Physica C: Superconductivity 370 (4) (2002) 211–218.
• C. Adelmann, On the extraction of resistivity and area of nanoscale interconnect lines by temperature-dependent resistance measurements, Solid State Electronics 152 (2019) 72–80.
• V.A. Gasparov, N.S. Sidorov, I.I. Zverkova, S.S. Khassanov, M.P. Kulakov, Electron Transport, Penetration Depth, and the Upper Critical Magnetic Field in ZrB12 and MgB2, Journal of Experimental and Theoretical Physics 101 (1) (2005) 98–106.
• M. Susner, M. Bhatia, M. Sumption, E. Collings, Electrical resistivity, Debye temperature, and connectivity in heavily doped bulk MgB2 superconductors, Journal of Applied Physics 105 (2009) 103916.
• M. C. T. D. Müller, S. Blügel, C. Friedrich, Electron-magnon scattering in elementary ferromagnets from first principles: Lifetime broadening and band anomalies. Physical Review B 100 (2019) 045130.
• P. K. G. Bedi, Superconducting critical temperature and isotope effect in the presence of electron-phonon,electron-paramagnon and electron-electron interactions in rhodium. Physica C: Superconductivity and its applications 596 (2022) 1354049.