Effects of Linear Deformation on Relaxation Time and Some Fermi Properties of Metals

G.e Adesakin ,E.o Aliyu ,O Olubosede ,Om Osiele ,E.b Faweya ,O G Edenma

doi:10.7176/jnsr/9-8-04

Abstract

In this work, a model for computing the relaxation time, Fermi velocity and Fermi temperature of deformed metals was developed based on free electron theory. This study generalized the work of Kiejna and Pogosov (2000) due to the shortcomings of the electron density parameter of deformed metals. They failed to account for metal dilation by assuming a constant value for the Poisson ratio of metals which leads to neglect of the uniaxial strain (deformation) in their computation. This causes the electron density parameter of both deformed and undeformed metals to be equal. The result obtained in this work revealed that there is an agreement between the experimental and computed values of the Fermi velocity, Fermi temperature and relaxation time of some of the metals calculated which shows the validity of the model used in the study. The experimental value used in this work is theoretically obtained by substituting the experimental value of Fermi energy obtained from solid state Physics by Charles Kittel (1976) into the model used in the computation. The Fermi velocity, Fermi temperature and relaxation time of all the metals subjected to different deformation decreases as deformation increases. This seems to suggest that as deformation increases the collision frequency between the interacting electron decreases which forces the relaxation time, Fermi velocity and Fermi temperature to decrease as deformation increases. This behavior could also be due to an increase in the inter-atomic spacing between the interacting electrons in the metals during deformation which reduces the strength of interaction between the electrons in metal and their-by forces the relaxation time, Fermi velocity and Fermi temperature to decrease as deformation increases. Keywords: relaxation time, Fermi velocity, Fermi temperature, mean free path, deformation, Fermi surface DOI : 10.7176/JNSR/9-8-04 Publication date : April 30 th 2019

Highlights

Metals achieve structural stability by letting their valence electrons roam freely through the crystal lattice
The experimental value used in this work is theoretically obtained by substituting the experimental value of Fermi energy obtained from solid state Physics by Charles Kittel (1976) into the model used in the computation of the Fermi velocity in this work
The trend exhibited by metals in figure 2 could be due to the fact that as deformation increases the temperature and mean free path between the interacting electrons in metals increases which causes the frequency of collision between the interacting electrons to decrease and their by forces the Fermi velocity to decrease as deformation increases

Summary

Introduction

Metals achieve structural stability by letting their valence electrons roam freely through the crystal lattice. Kiejna and Pogosov (1999), theoretically determined the effect of deformation on the surface properties of metal, based on stabilized jellium model, and derived modified equations for the stabilization energy of the deformed Wigner Seitz cell as a function of the bulk electron density and the given deformation.

Results

Conclusion