Abstract
A group of binary Sn-xAg alloys (x = 0.5, 1.5, 2.5, 3.5, 4.5, 5.5 and 6.5 wt%) has been produced by a single copper roller melt-spinning technique. In this study the interaction between Fermi sphere and Brillouin zone and Hume-Rothery condition of phase stability have been verified. It is found that by increasing valence electron concentration VEC the diameter of Fermi sphere 2kF increases which leads to the increase in the diameter of Brillouin zone which arises from the decrease in volume of the unit cell. It is found that the electrical resistivity increases by increasing VEC due to the decrease in relaxation time τ with increasing VEC. Also it has been confirmed that the correlation between Young’s modulus and the axial ratio c/a of β-Sn unit cell.
Highlights
Valence electron concentration (VEC) plays an important role on the structure and properties of alloys
It is found that by increasing valence electron concentration VEC the diameter of Fermi sphere 2kF increases which leads to the increase in the diameter of Brillouin zone which arises from the decrease in volume of the unit cell
A pseudo-gap of density of states around the Fermi level will arise. This is the HumeRothery condition of phase stability i.e., KB = 2kF where KB is the diameter of Brillouin zone and kF is the radius of Fermi sphere
Summary
Valence electron concentration (VEC) plays an important role on the structure and properties of alloys. This is the HumeRothery condition of phase stability i.e., KB = 2kF where KB is the diameter of Brillouin zone and kF is the radius of Fermi sphere It is found by [6] that the most important factor for the formation of stable quasicrystals is the valence electron concentration. 2π dhkl where N/V is the total number of electrons per unit volume in the alloy, m is the effective mass, ħ is the reduced Plank’s constant and dhkl is the interplanar distance Another example of the importance of VEC is the connection which has been observed by [4,7] between Young’s modulus and the axial ratio c/a of the tetragonal unit cell of -Sn in which Young’s modulus increases by increasing the axial ratio. Rapid solidification has been used in the present work to prevent rejection of extra solute atoms and prevent precipitation, from a solid solution
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