Calculation of the Average Potential of a Wigner Solid

Zhang Yue

doi:doi:10.11648/j.ijecs.20180303.12

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Calculation of the Average Potential of a Wigner Solid

Zhang Yue

Published in International Journal of Education, Culture and Society (Volume 3, Issue 3)

Received: 24 June 2018 Accepted: 9 July 2018 Published: 8 August 2018

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Abstract

The paper corrects a few errors occurring in the calculations of CALLAWAY J on the average potential of a Wigner solid. With respect to the monoatomic bcc and fcc metals, a theory of calculating the average potentials of them is established, and the theoretical results demonstrate that the average potential is directly proportional to the reciprocal of the lattice constant of the crystal. Moreover, the paper performs a great deal of calculations of the average potentials of various bcc and fcc metals, and obtains a lot of numerical results which are valuable for applications.

Published in	International Journal of Education, Culture and Society (Volume 3, Issue 3)
DOI	10.11648/j.ijecs.20180303.12
Page(s)	49-52
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

Wigner Solid, Poisson’s Equation, Average Potential, Lattice Constant

References

[1]	HALL G L. Correction to Fuchs’ calculation of the electrostatic energy of a Wigner solid [J]. Phys Rev B, 1979, 19(8): 3921 - 3932.
[2]	CALLAWAY J, GLASSER M L. Fourier Coefficients of Crystal Potentials [J]. Phys Rev, 1958, 112(1): 73–77.
[3]	HATKE A T, Yang Liu, Engel L W, et al. Microwave spectroscopic observation of a Wigner solid within the 1 / 2 fractional quantum effect [J]. Phys. Rev. B, 2017, 95 (4): 045417.
[4]	MONARKHA YURIY. Subharmonic phonon-ripplon coupling in the 2D Wigner solid on superfluid helium [J]. Europhysics Letters, 2017, 118 (6): 67001.
[5]	CALLAWAY J. Quantum Theory of the Solid State (Second Edition) [M]. San Diego: Academic Press, INC., 1991:16-19.
[6]	REES D G, BEYSENGULOV N R, LIN J J, and KONO K. Stik-Slip Motion of the Wigner Solid on liquid Helium [J]. Phys. Rev. Lett., 2016, 116(20): 206801.
[7]	KLEINMAN L. Comment on the average potential of a Wigner solid [J]. Phys Rev B, 1981, 24(12): 7412–7414.
[8]	HALL G L. Response to “Comment on the average potential of a Wigner solid” [J]. Phys Rev B, 1981, 24(12): 7415–7418.
[9]	BRADBURY T C. Mathematical Methods with Applications to Problems in Physical Sciences [M]. New York: John Wiley & Sons, 1984:109-110.
[10]	ASHCROFT N W, MERMIN N D. Solid State Physics [M]. San Francisco: Holt, Rinehart and Winston, 1976.
[11]	YOU X Z. Ionic Polarizability [J]. Chinese Science Bulletin, 1974, 19(9):419–423.

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APA Style

Zhang Yue. (2018). Calculation of the Average Potential of a Wigner Solid. International Journal of Education, Culture and Society, 3(3), 49-52. https://doi.org/10.11648/j.ijecs.20180303.12

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ACS Style

Zhang Yue. Calculation of the Average Potential of a Wigner Solid. Int. J. Educ. Cult. Soc. 2018, 3(3), 49-52. doi: 10.11648/j.ijecs.20180303.12

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AMA Style

Zhang Yue. Calculation of the Average Potential of a Wigner Solid. Int J Educ Cult Soc. 2018;3(3):49-52. doi: 10.11648/j.ijecs.20180303.12

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@article{10.11648/j.ijecs.20180303.12,
  author = {Zhang Yue},
  title = {Calculation of the Average Potential of a Wigner Solid},
  journal = {International Journal of Education, Culture and Society},
  volume = {3},
  number = {3},
  pages = {49-52},
  doi = {10.11648/j.ijecs.20180303.12},
  url = {https://doi.org/10.11648/j.ijecs.20180303.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijecs.20180303.12},
  abstract = {The paper corrects a few errors occurring in the calculations of CALLAWAY J on the average potential of a Wigner solid. With respect to the monoatomic bcc and fcc metals, a theory of calculating the average potentials of them is established, and the theoretical results demonstrate that the average potential is directly proportional to the reciprocal of the lattice constant of the crystal. Moreover, the paper performs a great deal of calculations of the average potentials of various bcc and fcc metals, and obtains a lot of numerical results which are valuable for applications.},
 year = {2018}
}

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TY  - JOUR
T1  - Calculation of the Average Potential of a Wigner Solid
AU  - Zhang Yue
Y1  - 2018/08/08
PY  - 2018
N1  - https://doi.org/10.11648/j.ijecs.20180303.12
DO  - 10.11648/j.ijecs.20180303.12
T2  - International Journal of Education, Culture and Society
JF  - International Journal of Education, Culture and Society
JO  - International Journal of Education, Culture and Society
SP  - 49
EP  - 52
PB  - Science Publishing Group
SN  - 2575-3363
UR  - https://doi.org/10.11648/j.ijecs.20180303.12
AB  - The paper corrects a few errors occurring in the calculations of CALLAWAY J on the average potential of a Wigner solid. With respect to the monoatomic bcc and fcc metals, a theory of calculating the average potentials of them is established, and the theoretical results demonstrate that the average potential is directly proportional to the reciprocal of the lattice constant of the crystal. Moreover, the paper performs a great deal of calculations of the average potentials of various bcc and fcc metals, and obtains a lot of numerical results which are valuable for applications.
VL  - 3
IS  - 3
ER  -

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Author Information

Zhang Yue

College of Physics and Information Science, Hunan Normal University, Changsha, China

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Plain Text BibTeX RIS

APA Style

Zhang Yue. (2018). Calculation of the Average Potential of a Wigner Solid. International Journal of Education, Culture and Society, 3(3), 49-52. https://doi.org/10.11648/j.ijecs.20180303.12

Copy | Download

ACS Style

Zhang Yue. Calculation of the Average Potential of a Wigner Solid. Int. J. Educ. Cult. Soc. 2018, 3(3), 49-52. doi: 10.11648/j.ijecs.20180303.12

Copy | Download

AMA Style

Zhang Yue. Calculation of the Average Potential of a Wigner Solid. Int J Educ Cult Soc. 2018;3(3):49-52. doi: 10.11648/j.ijecs.20180303.12

Copy | Download

@article{10.11648/j.ijecs.20180303.12,
  author = {Zhang Yue},
  title = {Calculation of the Average Potential of a Wigner Solid},
  journal = {International Journal of Education, Culture and Society},
  volume = {3},
  number = {3},
  pages = {49-52},
  doi = {10.11648/j.ijecs.20180303.12},
  url = {https://doi.org/10.11648/j.ijecs.20180303.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijecs.20180303.12},
  abstract = {The paper corrects a few errors occurring in the calculations of CALLAWAY J on the average potential of a Wigner solid. With respect to the monoatomic bcc and fcc metals, a theory of calculating the average potentials of them is established, and the theoretical results demonstrate that the average potential is directly proportional to the reciprocal of the lattice constant of the crystal. Moreover, the paper performs a great deal of calculations of the average potentials of various bcc and fcc metals, and obtains a lot of numerical results which are valuable for applications.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Calculation of the Average Potential of a Wigner Solid
AU  - Zhang Yue
Y1  - 2018/08/08
PY  - 2018
N1  - https://doi.org/10.11648/j.ijecs.20180303.12
DO  - 10.11648/j.ijecs.20180303.12
T2  - International Journal of Education, Culture and Society
JF  - International Journal of Education, Culture and Society
JO  - International Journal of Education, Culture and Society
SP  - 49
EP  - 52
PB  - Science Publishing Group
SN  - 2575-3363
UR  - https://doi.org/10.11648/j.ijecs.20180303.12
AB  - The paper corrects a few errors occurring in the calculations of CALLAWAY J on the average potential of a Wigner solid. With respect to the monoatomic bcc and fcc metals, a theory of calculating the average potentials of them is established, and the theoretical results demonstrate that the average potential is directly proportional to the reciprocal of the lattice constant of the crystal. Moreover, the paper performs a great deal of calculations of the average potentials of various bcc and fcc metals, and obtains a lot of numerical results which are valuable for applications.
VL  - 3
IS  - 3
ER  -

Copy | Download