A New Condition of Formation and Stablity of All Crystalline Systems in a Good Agreement with Experimental Data

2015 ◽  
Vol 11 (3) ◽  
pp. 3224-3228
Author(s):  
Tarek El-Ashram
Keyword(s):  
Experimental Data ◽  
Brillouin Zone ◽  
Electron Concentration ◽  
Free Electron ◽  
Lattice Point ◽  
Valence Electron ◽  
Fermi Gas ◽  
Valence Electron Concentration ◽  
Fermi Sphere ◽  
Good Agreement

In this paper we derived a new condition of formation and stability of all crystalline systems and we checked its validity andit is found to be in a good agreement with experimental data. This condition is derived directly from the quantum conditionson the free electron Fermi gas inside the crystal. The new condition relates both the volume of Fermi sphere VF andvolume of Brillouin zone VB by the valence electron concentration VEC as ;𝑽𝑭𝑽𝑩= 𝒏𝑽𝑬𝑪𝟐for all crystalline systems (wheren is the number of atoms per lattice point).

Theoretical modification of Hume Rothery condition of phase stability in a good agreement with experimental data

2015 ◽  
Vol 9 (3) ◽  
pp. 2503-2508
Author(s):  
Tarek El Ashram
Keyword(s):  
Experimental Data ◽  
Electron Concentration ◽  
Phase Stability ◽  
Valence Electron ◽  
Fermi Gas ◽  
Valence Electron Concentration ◽  
Fermi Sphere ◽  
Cubic Systems ◽  
Hexagonal Systems ◽  
Good Agreement

We presented in this paper a theoretical modification of Hume Rothery condition of phase stability in good agreement with experimental data. This modification is derived directly from the quantum conditions on the free electron Fermi gas inside the crystal. The new condition relates both the volume of Fermi sphere VF and volume of Brillouin zone VB by the valence electron concentration VEC as ;                              for tetragonal and hexagonal systems and as;     for cubic systems.

scholarly journals CRYSTALLINE ACCOMMODATION LAW EXPLAINS THE CRYSTALLINE STRUCTURE OF MATERIALS

2017 ◽  
pp. 5069-5075
Author(s):  
Dr. Tarek El Ashram
Keyword(s):  
Crystalline Structure ◽  
Valence Electron ◽  
Fermi Gas ◽  
Quantum States ◽  
Valence Electron Concentration ◽  
Primitive Cell ◽  
Free Electrons ◽  
Fermi Sphere ◽  
Crystalline Materials ◽  
Different Shapes

All crystalline materials crystallize in one of seven crystalline systems which have different shapes and sizes. Why crystalline materials take particular forms of crystals and what make the atoms arrange themselves in these forms. Actually, until now there is no well defined law can account for the crystalline structure of materials. Here we show that the crystalline accommodation law, which is theoretically derived and experimentally verified, can explain the crystalline structure of all types of phases. This law is derived directly from the quantum conditions on the free electrons Fermi gas inside the crystal. The new law relates both the volume of Fermi sphere VF and volume of Brillouin zone VB to the valence electron concentration VEC as,    for all crystalline systems and phases, where n is the number of atoms per lattice point or primitive cell. Also because of this law, we introduce the occupied electronic quantum states notation (OEQS), which determine the number of occupied zones in the valence band.

scholarly journals Magnetic and Structural Transitions Tuned through Valence Electron Concentration in Magnetocaloric Mn(Co1–xNix)Ge

2018 ◽  
Vol 30 (4) ◽  
pp. 1324-1334 ◽  
Author(s):  
Qingyong Ren ◽  
Wayne D. Hutchison ◽  
Jianli Wang ◽  
Andrew J. Studer ◽  
Stewart J. Campbell
Keyword(s):  
Electron Concentration ◽  
Valence Electron ◽  
Valence Electron Concentration ◽  
Structural Transitions

Thermoelectric Properties of Ru2Si3-Based Chimney-Ladder Phases

2007 ◽  
Vol 561-565 ◽  
pp. 463-466 ◽  
Author(s):  
Kyosuke Kishida ◽  
Akira Ishida ◽  
Katsushi Tanaka ◽  
Haruyuki Inui
Keyword(s):  
Crystal Structures ◽  
Thermoelectric Properties ◽  
Electron Concentration ◽  
Valence Electron ◽  
Valence Electron Concentration ◽  
Compositional Range ◽  
Wide Compositional Range ◽  
P Type ◽  
Semiconducting Behavior

The variations of the crystal structures and thermoelectric properties of the Ru1-xRexSiy chimney-ladder phases were studied as a function of the Re concentration. A series of chimney-ladder phases with a compositional formula of Ru1-xRexSi1.539+0.178x are formed in a wide compositional range, 0.14 ≤ x ≤ 0.76. The composition of the chimney-ladder phase is systematically deviated from the idealized composition satisfying the valence electron concentration rule: VEC=14. Measurements of thermoelectric properties reveal that the chimney-ladder phases exhibit n-type semiconducting behavior at low Re concentrations and p-type semiconducting behavior at high Re concentrations, which are well consistent with the prediction based on the deviation of the composition of the chimney-ladder phase from the idealized composition.

Electronic Structure of Ru2 Si3

1991 ◽  
Vol 234 ◽  
Author(s):  
P. Pecheur ◽  
G. Toussaint
Keyword(s):  
Electronic Structure ◽  
Transition Metal ◽  
Metal Atom ◽  
Electron Concentration ◽  
Valence Electron ◽  
Tight Binding ◽  
Transition Metal Atom ◽  
Valence Electron Concentration ◽  
Tight Binding Method ◽  
The Stability

ABSTRACTThe electronic structure of Ru2Si3 has been calculated with the empirical tight binding method and the recursion procedure. The calculation strongly indicates that there exists a gap in the structure, which makes Ru2Si3 semiconducting, as found experimentally and explains the stability of the chimney-ladder phases for a valence electron concentration per transition metal atom smaller than 14.

Sign in / Sign up

Export Citation Format

Share Document