Refining the Results of the Electronic Theory of Reflection of Metals

Konstantin Ludanov

doi:doi:10.11648/j.wjap.20200501.12

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Refining the Results of the Electronic Theory of Reflection of Metals

Konstantin Ludanov

Received: 26 May 2020 Accepted: 5 June 2020 Published: 4 July 2020

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Abstract

The article provides an accurate analytical approximation of the expressions of the known results of the electronic theory of reflection of metals, i.e. for the spectral and integrated reflectivity of and (Drude and Hagen-Rubens formulas, as well as the formulas of Ashkinass, Foote, Eckert and Drake, which are fragments of power series). Compact closed expressions for and are obtained, and published experimental data on the reflectivity of the polished metal surface in new coordinate systems are processed and analyzed: (ln)^-2~λ and ln()^-1~ T. It turned out that the experimental data on in the new coordinates clearly “lie” on the straight lines, which in the general case do not pass through the origin, which required introducing into the expression a new parameter − λ_о, taking into account the difference between the "optical" conductivity σ_о(ω) from the electrical σ_е, where l_о constant specific to each of the metal (for example, Ag, and Al: λ_о>0, for Ni and W: λ_о= 0, for Au and Cu: λ_{_о}<0). In obtaining the final formula for a new mathematical derivation scheme was used, starting with an analysis of a pair of equivalent expressions of the complex refractive index of the metal — much more justified and brief.

DOI	10.11648/j.wjap.20200501.12
Published in	World Journal of Applied Physics (Volume 5, Issue 1, March 2020)
Page(s)	15-20
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Electronic Theory of Reflection of Metals, Normal Spectral Reflectivity, Optical Conductivity, Approximation of Power Series, Processing of Experimental Data

References

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[2]	Zener C. Nature, 132, 968 (1953).
[3]	Roberts S. Electronics (translation), No. 1 (1955).
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[5]	Edwards J. Heat Transfer (Translation), No. 1 (1962).
[6]	Edwards J., de Volo. Heat Transfer (Translation), No. 3 (1965).
[7]	Handbook of heat exchangers. (M.: Energoatomizdat: 1987).
[8]	Sokolov A. V. Optical properties of metals (M: FM: 1961).
[9]	Khrustalev B. A. Radiation properties of solids. Review, IFJ, XVIII, No. 4 (1970).
[10]	Garbuni M. Physics of optical phenomena. (Moscow: Energy: 1967).
[11]	Ginzburg V. L., Motulevich G. P. Physics – Uspekhi, LV, No. 4 (1955).
[12]	Blokh A. G., Zhuravlev Yu. A., Ryzhikov L. N. Radiation heat transfer. Handbook (Moscow: Energoatomizdat: 1991).
[13]	Vinogradov V. N., Gai E. V., Rabotnov N. S. Analytical approximation of data in nuclear and neutron physics (Moscow: Energoatomizdat: 1987).
[14]	Ludanov K. I. Method of obtaining approximate formulas // «EUREKA: Physics and Engineering» (Mathematical sciences) No. 2, p. 72-78 (2018).
[15]	Emissive properties of solid materials. Directory. Ed. A. E. Sheidlin (Moscow: Energy, 1974).
[16]	Siegel R., Howell J. Heat transfer by radiation (Moscow: World: 1975).
[17]	Ludanov K. I. Closed solution of the Schmidt-Eckert problem of determining the temperature dependence of the integral reflectivity of metals in the normal direction // Abstracts at the XI School-Seminar of Academician A. I. Leontyev. (May 20-25, 2001. Sainct-Petersburg, Russia).
[18]	Helfgott, Zeits. f. Physik. 49, 555 (1928).
[19]	Novitsky L. A., Stepanov B. M. Optical properties of materials at low temperatures (Moscow: Mechanical Engineering: 1978).
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Konstantin Ludanov. (2020). Refining the Results of the Electronic Theory of Reflection of Metals. World Journal of Applied Physics, 5(1), 15-20. https://doi.org/10.11648/j.wjap.20200501.12

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Konstantin Ludanov. Refining the Results of the Electronic Theory of Reflection of Metals. World J. Appl. Phys. 2020, 5(1), 15-20. doi: 10.11648/j.wjap.20200501.12

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Konstantin Ludanov. Refining the Results of the Electronic Theory of Reflection of Metals. World J Appl Phys. 2020;5(1):15-20. doi: 10.11648/j.wjap.20200501.12

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@article{10.11648/j.wjap.20200501.12,
  author = {Konstantin Ludanov},
  title = {Refining the Results of the Electronic Theory of Reflection of Metals},
  journal = {World Journal of Applied Physics},
  volume = {5},
  number = {1},
  pages = {15-20},
  doi = {10.11648/j.wjap.20200501.12},
  url = {https://doi.org/10.11648/j.wjap.20200501.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.wjap.20200501.12},
  abstract = {The article provides an accurate analytical approximation of the expressions of the known results of the electronic theory of reflection of metals, i.e. for the spectral and integrated reflectivity of  and  (Drude and Hagen-Rubens formulas, as well as the formulas of Ashkinass, Foote, Eckert and Drake, which are fragments of power series). Compact closed expressions for  and  are obtained, and published experimental data on the reflectivity of the polished metal surface in new coordinate systems are processed and analyzed: (ln)-2~λ and ln()-1~ T. It turned out that the experimental data on  in the new coordinates clearly “lie” on the straight lines, which in the general case do not pass through the origin, which required introducing into the expression  a new parameter − λо, taking into account the difference between the "optical" conductivity σо(ω) from the electrical σе, where lо constant specific to each of the metal (for example, Ag, and Al: λо>0, for Ni and W: λо= 0, for Au and Cu: λо a new mathematical derivation scheme was used, starting with an analysis of a pair of equivalent expressions of the complex refractive index of the metal — much more justified and brief.},
 year = {2020}
}

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TY  - JOUR
T1  - Refining the Results of the Electronic Theory of Reflection of Metals
AU  - Konstantin Ludanov
Y1  - 2020/07/04
PY  - 2020
N1  - https://doi.org/10.11648/j.wjap.20200501.12
DO  - 10.11648/j.wjap.20200501.12
T2  - World Journal of Applied Physics
JF  - World Journal of Applied Physics
JO  - World Journal of Applied Physics
SP  - 15
EP  - 20
PB  - Science Publishing Group
SN  - 2637-6008
UR  - https://doi.org/10.11648/j.wjap.20200501.12
AB  - The article provides an accurate analytical approximation of the expressions of the known results of the electronic theory of reflection of metals, i.e. for the spectral and integrated reflectivity of  and  (Drude and Hagen-Rubens formulas, as well as the formulas of Ashkinass, Foote, Eckert and Drake, which are fragments of power series). Compact closed expressions for  and  are obtained, and published experimental data on the reflectivity of the polished metal surface in new coordinate systems are processed and analyzed: (ln)-2~λ and ln()-1~ T. It turned out that the experimental data on  in the new coordinates clearly “lie” on the straight lines, which in the general case do not pass through the origin, which required introducing into the expression  a new parameter − λо, taking into account the difference between the "optical" conductivity σо(ω) from the electrical σе, where lо constant specific to each of the metal (for example, Ag, and Al: λо>0, for Ni and W: λо= 0, for Au and Cu: λо a new mathematical derivation scheme was used, starting with an analysis of a pair of equivalent expressions of the complex refractive index of the metal — much more justified and brief.
VL  - 5
IS  - 1
ER  -

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Author Information

Konstantin Ludanov

Department No 5, Institute for Renewable Energy of NASU, Kiev, Ukraine

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APA Style

Konstantin Ludanov. (2020). Refining the Results of the Electronic Theory of Reflection of Metals. World Journal of Applied Physics, 5(1), 15-20. https://doi.org/10.11648/j.wjap.20200501.12

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ACS Style

Konstantin Ludanov. Refining the Results of the Electronic Theory of Reflection of Metals. World J. Appl. Phys. 2020, 5(1), 15-20. doi: 10.11648/j.wjap.20200501.12

Copy | Download

AMA Style

Konstantin Ludanov. Refining the Results of the Electronic Theory of Reflection of Metals. World J Appl Phys. 2020;5(1):15-20. doi: 10.11648/j.wjap.20200501.12

Copy | Download

@article{10.11648/j.wjap.20200501.12,
  author = {Konstantin Ludanov},
  title = {Refining the Results of the Electronic Theory of Reflection of Metals},
  journal = {World Journal of Applied Physics},
  volume = {5},
  number = {1},
  pages = {15-20},
  doi = {10.11648/j.wjap.20200501.12},
  url = {https://doi.org/10.11648/j.wjap.20200501.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.wjap.20200501.12},
  abstract = {The article provides an accurate analytical approximation of the expressions of the known results of the electronic theory of reflection of metals, i.e. for the spectral and integrated reflectivity of  and  (Drude and Hagen-Rubens formulas, as well as the formulas of Ashkinass, Foote, Eckert and Drake, which are fragments of power series). Compact closed expressions for  and  are obtained, and published experimental data on the reflectivity of the polished metal surface in new coordinate systems are processed and analyzed: (ln)-2~λ and ln()-1~ T. It turned out that the experimental data on  in the new coordinates clearly “lie” on the straight lines, which in the general case do not pass through the origin, which required introducing into the expression  a new parameter − λо, taking into account the difference between the "optical" conductivity σо(ω) from the electrical σе, where lо constant specific to each of the metal (for example, Ag, and Al: λо>0, for Ni and W: λо= 0, for Au and Cu: λо a new mathematical derivation scheme was used, starting with an analysis of a pair of equivalent expressions of the complex refractive index of the metal — much more justified and brief.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Refining the Results of the Electronic Theory of Reflection of Metals
AU  - Konstantin Ludanov
Y1  - 2020/07/04
PY  - 2020
N1  - https://doi.org/10.11648/j.wjap.20200501.12
DO  - 10.11648/j.wjap.20200501.12
T2  - World Journal of Applied Physics
JF  - World Journal of Applied Physics
JO  - World Journal of Applied Physics
SP  - 15
EP  - 20
PB  - Science Publishing Group
SN  - 2637-6008
UR  - https://doi.org/10.11648/j.wjap.20200501.12
AB  - The article provides an accurate analytical approximation of the expressions of the known results of the electronic theory of reflection of metals, i.e. for the spectral and integrated reflectivity of  and  (Drude and Hagen-Rubens formulas, as well as the formulas of Ashkinass, Foote, Eckert and Drake, which are fragments of power series). Compact closed expressions for  and  are obtained, and published experimental data on the reflectivity of the polished metal surface in new coordinate systems are processed and analyzed: (ln)-2~λ and ln()-1~ T. It turned out that the experimental data on  in the new coordinates clearly “lie” on the straight lines, which in the general case do not pass through the origin, which required introducing into the expression  a new parameter − λо, taking into account the difference between the "optical" conductivity σо(ω) from the electrical σе, where lо constant specific to each of the metal (for example, Ag, and Al: λо>0, for Ni and W: λо= 0, for Au and Cu: λо a new mathematical derivation scheme was used, starting with an analysis of a pair of equivalent expressions of the complex refractive index of the metal — much more justified and brief.
VL  - 5
IS  - 1
ER  -

Copy | Download