Abstract
In this study, the temperature dependence of resistivity of some solids were investigated with the analyticalexpressions of Bloch-Gruneisen function using binomial expansion theorem. The contributions of electron-phonon interaction to the electrical resistivity of metals have taken into account in this method. Therefore, the analysis of change in resistivity with temperature was performed with the Bloch-Gruneisen functions. Programs in the system Mathematica were constructed in accordance with the analytical equations obtained for the generalized Bloch-Gruneisen function. Resistivity values at the different temperatures were calculated for tin metal and Sn-doped indium oxide compound. Reliability of the using method is tested by applications to these solids
References
- Gruneisen E., 1933. The Temperature Dependence of the Electrical Resistance of Pure Metals, Annalen der Physik (Leipzig), 16: 530.
- Pinski F.J., Allen P.B., Butler W.H., 1981. Calculated electrical and thermal resistivities of Nb and Pd, Physical Review, B23(10): 5080-5096.
- Igasaki Y., Mitsuhashi H., 1980. The effects of substrate bias on the structural and electrical properties of TiN films prepared by reactive r.f. sputtering, Thin Solid Films, 70(1): 17-25.
- Igasaki Y., Mitsuhashi H., 1983. Origin of negative temperature coefficient of resistivity in polycrystalline Ti N films, Journal of Applied Physics, 54(2): 836-840.
- Igasaki Y., Mitsuhashi H., 1987. Polynomial expression of the bloch-grüneisen integral - application to an analysis of the resistivity-temperature variation of metals, Physica Status Solidi A, 99(2): K111-K115.
- White G.K., Woods S.B., 1959. Electrical and Thermal Resistivity of the Transition Elements at Low Temperatures, Philosophical Transactions of the Royal Society A, 251(995): 273-302.
- Deutsch M., 1987. An accurate analytic representation for the Bloch-Gruneisen integral, Journal of Physics A, 20(13): L811.
- Cvijovic D., 2011. The Bloch–Gruneisen Function of arbitrary order and its series representations, Theoretical and Mathematical Physics, 166(1): 37–42.
- Kamalakar M.V, Raychaudhuri A.K, 2012. Modification in electrical transport with a change in geometry from a nanowire to a nanotube of copper: effect of the extra surface, New Journal of Physics, 14(2012), 043032: 13pp.
- Mamedov B.A., Askerov I.M., 2007. A new algorithm for accurate evaluation of the generalized Bloch–Gruneisen function and its applications to MgB2 superconductor, Physics Letters A, 362: 324-326.
- Guseinov I.I., Mamedov B.A., 2002. Evaluation of overlap integrals with integer and noninteger n Slater-type orbitals using auxiliary functions, Journal of Molecular Modeling, 8: 272-276.
- Gradshteyn I.S., Ryzhik I.M., 2007. Tables of Integrals, Series and Products, Academic Press, New York, p. 1171.
- Karamargin M.C., Reynolds C.A., Lipschultz F.P., Klemens P.G., 1972. Thermal and Electrical Conductivity of Pure Tin from 4.5 to 77 °K, Physical Review B, 5(8): 2856-2863.
- Li Z.Q., Lin J.J., 2004. Electrical resistivities and thermopowers of transparent Sn-doped indium oxide films, Journal of Applied Physics, 96(10): 5918-5920.
- İskender Askeroğlu e-posta: iskender.askeroglu@gop.edu.tr
Bloch-Gruneisen Fonksiyonu ile Bazı Katıların Elektriksel Özdirencinin Sıcaklığa Göre Değişiminin Analitik İncelenmesi
Abstract
Özet: Bu çalışmada, binomial açılım teoremi kullanılarak Bloch-Gruneisen fonksiyonunun analitik ifadeleri ile bazı katıların özdirencinin sıcaklığa bağlılığı incelendi. Bu yöntemde, metallerin elektriksel özdirencine elektron-fonon etkileşim katkısı dikkate alındı. Bu sebeple, özdirencin sıcaklığa göre değişmesinin Bloch-Gruneisen fonksiyonları ile analizine yer verildi. Genelleştirilmiş Bloch-Gruneisen fonksiyonu için elde edilen analitik bağıntılar doğrultusunda Mathematica programlama dilinde program oluşturuldu. Kalay metali ve Sn katkılı indiyum oksit bileşiği için farklı sıcaklıklarda özdirenç değerleri hesaplandı. Kullanılan metodun geçerliliği, bu katılara uygulamalarıyla birlikte test edildi.
Anahtar kelimeler: Bloch-Gruneisen teorisi, elektron-fonon etkileşmesi, elektriksel özdirenç.
The Analytical Investigation of Temperature Dependence of Electrical Resistivity Using Bloch-Gruneisen Function for Some Solids
Abstract: In this study, the temperature dependence of resistivity of some solids were investigated with the analytical expressions of Bloch-Gruneisen function using binomial expansion theorem. The contributions of electron-phonon interaction to the electrical resistivity of metals have taken into account in this method. Therefore, the analysis of change in resistivity with temperature was performed with the Bloch-Gruneisen functions. Programs in the system Mathematica were constructed in accordance with the analytical equations obtained for the generalized Bloch-Gruneisen function. Resistivity values at the different temperatures were calculated for tin metal and Sn-doped indium oxide compound. Reliability of the using method is tested by applications to these solids.
Key words: Bloch-Gruneisen theory, electron-phonon interaction, electrical resistivity.
References
- Gruneisen E., 1933. The Temperature Dependence of the Electrical Resistance of Pure Metals, Annalen der Physik (Leipzig), 16: 530.
- Pinski F.J., Allen P.B., Butler W.H., 1981. Calculated electrical and thermal resistivities of Nb and Pd, Physical Review, B23(10): 5080-5096.
- Igasaki Y., Mitsuhashi H., 1980. The effects of substrate bias on the structural and electrical properties of TiN films prepared by reactive r.f. sputtering, Thin Solid Films, 70(1): 17-25.
- Igasaki Y., Mitsuhashi H., 1983. Origin of negative temperature coefficient of resistivity in polycrystalline Ti N films, Journal of Applied Physics, 54(2): 836-840.
- Igasaki Y., Mitsuhashi H., 1987. Polynomial expression of the bloch-grüneisen integral - application to an analysis of the resistivity-temperature variation of metals, Physica Status Solidi A, 99(2): K111-K115.
- White G.K., Woods S.B., 1959. Electrical and Thermal Resistivity of the Transition Elements at Low Temperatures, Philosophical Transactions of the Royal Society A, 251(995): 273-302.
- Deutsch M., 1987. An accurate analytic representation for the Bloch-Gruneisen integral, Journal of Physics A, 20(13): L811.
- Cvijovic D., 2011. The Bloch–Gruneisen Function of arbitrary order and its series representations, Theoretical and Mathematical Physics, 166(1): 37–42.
- Kamalakar M.V, Raychaudhuri A.K, 2012. Modification in electrical transport with a change in geometry from a nanowire to a nanotube of copper: effect of the extra surface, New Journal of Physics, 14(2012), 043032: 13pp.
- Mamedov B.A., Askerov I.M., 2007. A new algorithm for accurate evaluation of the generalized Bloch–Gruneisen function and its applications to MgB2 superconductor, Physics Letters A, 362: 324-326.
- Guseinov I.I., Mamedov B.A., 2002. Evaluation of overlap integrals with integer and noninteger n Slater-type orbitals using auxiliary functions, Journal of Molecular Modeling, 8: 272-276.
- Gradshteyn I.S., Ryzhik I.M., 2007. Tables of Integrals, Series and Products, Academic Press, New York, p. 1171.
- Karamargin M.C., Reynolds C.A., Lipschultz F.P., Klemens P.G., 1972. Thermal and Electrical Conductivity of Pure Tin from 4.5 to 77 °K, Physical Review B, 5(8): 2856-2863.
- Li Z.Q., Lin J.J., 2004. Electrical resistivities and thermopowers of transparent Sn-doped indium oxide films, Journal of Applied Physics, 96(10): 5918-5920.
- İskender Askeroğlu e-posta: iskender.askeroglu@gop.edu.tr
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Makaleler |
| Authors | |
| Publication Date | June 10, 2013 |
| Published in Issue | Year 2013 Volume: 8 Issue: 1 |
