DOI: 10.18503/1995-2732-2026-24-3-100-107
Abstract
The aim of this study is to substantiate the hypothesis that the Seebeck coefficient can be used as an indicator of changes in the internal energy of a material. The study formulates and solves the problem of determining an analytical relationship between the Seebeck coefficient and the change in internal energy of an amorphous soft magnetic ribbon by jointly solving the equations of the first law of thermodynamics for an isochoric process, the equations relating the amount of heat to temperature during heating or cooling, and the equation formalizing the Seebeck effect. The calculations and graphical relationships have been based on experimental results obtained by measuring the thermal electromotive force (TEMF) and determining the Seebeck coefficients of an amorphous ribbon using the authors’ methodology. Heating and cooling experiments on the investigated amorphous ribbon specimens have been performed using the PocketJaw module of the Gleeble 3500 system with a specially designed assembly. It has been theoretically substantiated that the Seebeck coefficient is directly proportional to the TEMF and inversely proportional to unity minus the ratio of the changes in the internal energies of the cold and hot ends of the specimen, as well as to the temperature of the hot end of the specimen. It has been shown that the Seebeck coefficient characterizes the ratio of changes in the internal energies of the cold and hot ends of the specimen under thermal exposure and can be used as a structure-dependent parameter characterizing the initial internal energy state of an amorphous ribbon. It has been experimentally confirmed that there is no direct dependence between the Seebeck coefficient and the change in internal energy. The possibility of using the method for determining and analyzing Seebeck coefficients to characterize the initial internal energy state of the surfaces of an amorphous ribbon has been demonstrated.
Keywords
Finemet-class amorphous soft magnetic ribbon, thermal electromotive force, Seebeck coefficient, change in internal energy, thermal exposure.
For citation
Chukin M.V., Koptseva N.V., Efimova Yu.Y. Relationship Between the Seebeck Coefficient and the Internal Energy of the Finemet-Class Amorphous Soft Magnetic Ribbon. Vestnik Magnitogorskogo Gosudarstvennogo Tekhnicheskogo Universiteta im. G.I. Nosova [Vestnik of Nosov Magnitogorsk State Technical University]. 2026, vol. 24, no. 3, pp. 100-107. https://doi.org/10.18503/1995-2732-2026-24-3-100-107
1. Ginne S.V. Amorphous metallic materials: regularities and conditions of amorphization. Epokha nauki [Era of science]. 2025;(41):25-32. (In Russ.)
2. Huang B., Yang Y., Wang A.D. et al. Saturated magnetization and glass forming ability of soft magnetic Fe-based metallic glasses. Intermetallics. 2017;84:74-81. DOI: 10.1016/j.intermet.2017.01.003.
3. Starodubtsev Yu.N., Belozerov V.Ya. Magnitnye svoistva amorfnykh i nanokristallicheskikh splavov [Magnetic properties of amorphous and nanocrystalline alloys]. Yekaterinburg: Ural University Publishing House, 2002, 366 p. (In Russ.)
4. Tsepelev S., Starodubtsev Yu.N., Zelenin V.A. et al. Dilatometric analysis of the nanocrystallization process of the Fe72.5Cu1Nb2Mo1.5Si14B9 soft magnetic alloy. Fizika metallov i metallovedenie [Physics of metals and metallography]. 2017;118(6):584-588. (In Russ.)
5. Zhai X.B., Zhu L., Zheng H. et al. Optimization of crystallization, microstructure and soft magnetic properties of Fe-B-Cu alloys by rapid cyclic annealing. Journal of Alloys and Compounds. 2018;768(5):591-597. DOI: 10.1016/j.jallcom.2018.07.272.
6. Yoshizawa Y., Yamauchi K. Fe-based soft magnetic alloys composed of ultrafine grain structure. Materials Transactions. 1990;31:307-314. DOI: 10.2320/matertrans1989.31.307.
7. Herzer G. Nanocrystalline soft magnetic alloys. Handbook of Magnetic Materials. 1997;10:415-462. DOI: 10.1016/S1567-2719(97)10007-5.
8. Yoshizawa Y., Oguma S., Yamauchi K. New Fe-based soft magnetic alloys composed of ultrafine grain structure. Journal of Applied Physics. 1988;64:6044-6046. DOI: 10.1063/1.342149.
9. Zhu L. Modulating the crystallization process of Fe82B12C6 amorphous alloy via rapid annealing. Journal of Alloys and Compounds. 2019;785(5):328-334. DOI: 10.1016/j.jallcom.2019.01.209.
10. Khonik V.A. Structural relaxation and the resulting plastic flow of metallic glasses below the glass transition temperature: from phenomenological to microscopic understanding. Vestnik TGU [Vestnik of Tomsk State University]. 2010;15(3):789. (In Russ.)
11. Chen H.S. Structural relaxation in metallic glasses. Amorfnye metallicheskie splavy [Amorphous metallic alloys]. Moscow: Metallurgiya, 1987, 584 p. (In Russ.)
12. Krakhmalev P.V. Struktura i svoistva magnitomyagkikh amorfnykh splavov na osnove zheleza i kobalta pri termicheskoi, mekhanotermicheskoi i termomagnitnoi obrabotke: dis. kand. tekhnich. nauk [Structure and properties of soft magnetic amorphous iron- and cobalt-based alloys under thermal, thermomechanical and thermomagnetic treatment. Ph.D. dissertation]. Saint Petersburg, 1999. 142 p.
13. Hodge I.M. Structural Relaxation. In: Classical Relaxation Phenomenology. Springer, Cham, 2019, pp. 197–222. DOI: 10.1007/978-3-030-02459-8_11.
14. Bitzek E., Koskinen P., Gähler F., Moseler M., Gumbsch P. Structural Relaxation Made Simple. Physical Review Letters. 2006;97:170201. DOI: 10.1103/PhysRevLett.97.170201.
15. Barysheva T.B. Vtoroe nachalo termodinamiki i entropiya: Metodicheskoe posobie [The second law of thermodynamics and entropy: a methodological guide]. Ed. by Chernoutsan A.I. Moscow: Publishing Center of Gubkin University of Oil and Gas, 2017, 32 p. (In Russ.)
16. Novikov S.V. Termoelektricheskie svoistva nanokristallicheskikh silitsidov khroma i margantsa: dis. kand. fiz.-mat. nauk [Thermoelectric properties of nanocrystalline chromium and manganese silicides. Ph.D. dissetation]. Saint Petersburg, 2014, 168 p.
17. Petrov A.L., Gavrilyuk A.A., Zubritsky S.M. Struktura i svoistva neuporyadochennykh tverdykh tel: uchebnoe posobie [Structure and properties of disordered solids: textbook]. Irkutsk: Irkutsk State University Publishing House, 2004, 70 p. (In Russ.)
18. Arseneva A.D., Vedyaev A.V., Vasilyeva R.P. et al. Termoeds v amorfnykh ferromagnitnykh splavakh [Thermoelectric power in amorphous ferromagnetic alloys]. Vestnik Moskovskogo universiteta. Seriya 3. Fizika. Astronomiya [Vestnik of Moscow University. Series 3: Physics. Astronomy]. 1991;(3):71-75. (In Russ.)
19. Melnikova N.V., Egorushkin V.E., Bobenko N.G. et al. Density of electronic states and thermoelectric power in carbon nanotubes with impurities and structural disorder. Izvestiya vysshikh uchebnykh zavedenii. Fizika [Russian Physics Journal]. 2012;55(11):24-34. (In Russ.)
20. Chukin M.V., Efimova Yu.Yu., Koptseva N.V. Determination of the heterogeneity of cold-rolled strip properties by thermoelectric power. Part 1. Development of a research methodology. Chernye metally [Ferrous Metals]. 2026;60-66. (In Russ.)
21. Chukin M.V., Koptseva N.V., Efimova Yu.Yu. Determination of the heterogeneity of cold-rolled strip properties by thermoelectric power. Part 2. Investigation of the relationship between hardness and thermoelectric power. Chernye metally [Ferrous Metals]. 2026;(3):22-29. (In Russ.)
22. Chukin M.V., Koptseva N.V., Efimova Yu.Yu. et al. Thermoelectric nondestructive assessment of residual stresses in cold-rolled steel strip. Vestnik Magnitogorskogo gosudarstvennogo tekhnicheskogo universiteta im. G.I. Nosova [Vestnik of Nosov Magnitogorsk State Technical University]. 2026; 24(1):88-99. (In Russ.)

