Back
 JAMP  Vol.9 No.1 , January 2021
A Simple Approach to Compute Interatomic Force Constant for Mono and Diatomic Semiconductors
Abstract: In this paper, a mathematical relation was found between interatomic Hooke’s force constant and both the bulk modulus and interatomic distance in solid crystals, considering that the forces which have effect on an atom are only those resulted from the neighboring atoms, and the forces are subject to Hooke’s law as the deflections of atoms from their equilibrium positions are very small. This work has been applied on some solid semiconducting crystals of diatomic primitive cell, including crystals of mono-atomic primitive cell automatically, by using linear statistical fitting with computer programming and, then, using mathematical analysis, proceeding from the vibrational dispersion relation of solid linear lattice, these two methods have been used in the process in order to support each other and for the result to be satisfying and reasonable. This is a contribution to the process of using computer programming in physics to facilitate mathematical analyses and obtain the required relations and functions by designing and developing appropriate computer programs in line with the macro and micro natures of materials. The importance of this is in enhancing our understanding of the interatomic actions in cells and of the crystal structure of materials in general and semiconductors in particular, as it is a step of the initial steps to facilitate the process of calculating energies and extracting mathematical relations between correlation energy and temperature as well as between sub-fusion and fusion energies with temperature.
Cite this paper: Joghlaf, M. , Ababou, Y. and Sayouri, S. (2021) A Simple Approach to Compute Interatomic Force Constant for Mono and Diatomic Semiconductors. Journal of Applied Mathematics and Physics, 9, 11-20. doi: 10.4236/jamp.2021.91002.
References

[1]   Tapia Goazalez, J., Villanueva Lopez, C., Peon-Escalante, R., Quintal, R., Medina, J., Penunuri, F. and Avilves, F. (2015) The Bond Force Constant and Bulk Modulus of Small Fullerenes Using Density Functional Theory and Finite Element Analysis. Journal of Molecular Modeling, 21.
https://doi.org/10.1007/s00894-015-2649-6

[2]   Santiago-Perez, D.G., de Leon-Perez, F., Mora-Ramos, M.E. and Perez-Alvarez (2008) Force Constants and Dispersion Relations in GaN. PIERS Online, 4, 187-190.
https://doi.org/10.2529/PIERS071005121557

[3]   Kot, M., Nagahashi, H. and Szymczak, P. (2014) Elastic Moduli of Simple Mass Spring Models. Springer-Verlag, Berlin, Heidelberg.
https://doi.org/10.1007/s00371-014-1015-5

[4]   Dolocan, V., Dolocan, A. and Dolocan, V.O. (2008) Relation of Interatomic Forces in Solids to Bulk Modulus, Cohesive Energy and Thermal Expansion. Modern Physics Letters B, 22, 2481-2492.
https://doi.org/10.1142/S0217984908017096

[5]   Kittel, C. (1996) Introduction to Solid State Physics. 7th Edition, John Wiley & sons, Inc., New York.

[6]   Ashcroft, N.W. and Mermin, N.D. (1976) Solid State Physics. Holt Rin, and Win., New York.

[7]   Brillouin, L. (1946) Wave Propagation in Periodic Structures: Electric Filters and Crystal Lattices. Originally Published by the McGraw-Hill Book Company, Inc. (Dover Phoenix Editions, Inc., 2003)

[8]   Rössler, U. (2009) Solid State Theory: An Introduction. 2nd Revised and Extended Edition, Springer, Dordrecht, Heidelberg, London, New York, Springer-Verlag, Berlin, Heidelberg.

[9]   Quinn, J.J. and Yi, K.-S. (2009) Solid State Physics: Principles and Modern Applications. Springer-Verlag, Berlin, Heidelberg.

[10]   Semat, H. and Albright, J. (1972) Introduction to Atomic and Nuclear Physics. Holt, Rin. and Win. C., USA.

[11]   Adachi, S. (2004) Handbook on Physical Properties of Semiconductors. Vol. 3, II-VI Compound Semiconductors, Kluwer Academic Publishers group, Dordrecht.

[12]   Razeghi, M. (2006) Fundamentals of Solid State Engineering. 2nd Edition, Springer Science + Business Media, Evanston.

[13]   Elliott, S.R. (1998) The Physics and Chemistry of Solids. John Wiley & Sons, Ltd., England.

 
 
Top