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.

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 Spotlight on Alkali Metals: The Structural Chemistry of Alkali Metal Thallides

Crystals ◽  
2020 ◽  
Vol 10 (11) ◽  
pp. 1013
Author(s):  
Stefanie Gärtner
Keyword(s):  
Crystal Structure ◽  
Alkali Metal ◽  
Crystal Structures ◽  
Alkali Metals ◽  
Valence Electron ◽  
Oxidation States ◽  
Valence Electron Concentration ◽  
Base Metals ◽  
Charge Balancing

Alkali metal thallides go back to the investigative works of Eduard Zintl about base metals in negative oxidation states. In 1932, he described the crystal structure of NaTl as the first representative for this class of compounds. Since then, a bunch of versatile crystal structures has been reported for thallium as electronegative element in intermetallic solid state compounds. For combinations of thallium with alkali metals as electropositive counterparts, a broad range of different unique structure types has been observed. Interestingly, various thallium substructures at the same or very similar valence electron concentration (VEC) are obtained. This in return emphasizes that the role of the alkali metals on structure formation goes far beyond ancillary filling atoms, which are present only due to charge balancing reasons. In this review, the alkali metals are in focus and the local surroundings of the latter are discussed in terms of their crystallographic sites in the corresponding crystal structures.

Thermal Properties of an Incompletely Degenerate Fermi Gas

1936 ◽  
Vol 32 (1) ◽  
pp. 108-111 ◽  
Author(s):  
N. F. Mott
Keyword(s):  
Thermal Properties ◽  
Specific Heat ◽  
Electron Gas ◽  
Electronic States ◽  
Fermi Gas ◽  
Paramagnetic Susceptibility ◽  
Free Electrons ◽  
Periodic Field ◽  
Degenerate Fermi Gas ◽  
Image Position

The purpose of this note is to calculate the specific heat and paramagnetic susceptibility of an electron gas obeying the Fermi-Dirac statistics for all temperatures, including those temperatures for which the gas is partially degenerate. The results are applicable to the electrons in a metal, whether free or moving in a periodic field, provided only that the number of electronic states per gram atom with energy between E and E + dE can be expressed in the formas for free electrons.

scholarly journals Structural simplicity and complexity of compressed calcium: electronic origin

2014 ◽  
Vol 70 (3) ◽  
pp. 423-428 ◽  
Author(s):  
Valentina F. Degtyareva
Keyword(s):  
Valence Electron ◽  
Interaction Model ◽  
Outer Core ◽  
Electron Number ◽  
Fermi Sphere ◽  
Simple Cubic ◽  
Valence Electrons ◽  
Cubic Structure ◽  
Structural Simplicity ◽  
Tetragonal Cell

A simple cubic structure with one atom in the unit cell found in compressed calcium is counterintuitive to the traditional view of a tendency towards densely packed structures with an increase in pressure. To understand this unusual transformation it is necessary to assume electron transfer from the outer core band to the valence band, and an increase of valence electron number for calcium from 2 to ∼ 3.5. This assumption is supported by the Fermi sphere–Brillouin zone interaction model that increases under compression. The recently found structure of Ca-VII with a tetragonal cell containing 32 atoms (tI32) is similar to that in the intermetallic compound In5Bi3with 3.75 valence electrons per atom. Structural relations are analyzed in terms of electronic structure resemblance. Correlations of structure and physical properties of Ca are discussed.

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.

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