On the problem of crystal metallic lattice in the densest packings of chemical elements valency.The electrons in zone of conductivity. (стр. 1 из 2)
Dear Sirs.
Thank you for your assistance.
ON THE PROBLEM OF CRYSTAL METALLIC LATTICE IN THE DENSEST PACKINGS OF CHEMICAL ELEMENTS
Yours faithfully, Н.G FILIPENKА
http://home.ural.ru/~filip/
Grodno
Abstract
The literature generally describes a metallic bond as the one formed by means of mutual bonds between atoms' exterior electrons and not possessing the directional properties. However, attempts have been made to explain directional metallic bonds, as a specific crystal metallic lattice.
This paper demonstrates that the metallic bond in the densest packings (volume-centered and face-centered) between the centrally elected atom and its neighbours in general is, probably, effected by 9 (nine) directional bonds, as opposed to the number of neighbours which equals 12 (twelve) (coordination number).
Probably, 3 (three) "foreign" atoms are present in the coordination number 12 stereometrically, and not for the reason of bond. This problem is to be solved experimentally.
Introduction
At present, it is impossible, as a general case, to derive by means of quantum-mechanical calculations the crystalline structure of metal in relation to electronic structure of the atom. However, Hanzhorn and Dellinger indicated a possible relation between the presence of a cubical volume-centered lattice in subgroups of titanium, vanadium, chrome and availability in these metals of valent d-orbitals. It is easy to notice that the four hybrid orbitals are directed along the four physical diagonals of the cube and are well adjusted to binding each atom to its eight neighbours in the cubical volume-centered lattice, the remaining orbitals being directed towards the edge centers of the element cell and, possibly, participating in binding the atom to its six second neighbours /3/p. 99.
Let us try to consider relations between exterior electrons of the atom of a given element and structure of its crystal lattice, accounting for the necessity of directional bonds (chemistry) and availability of combined electrons (physics) responsible for galvanic and magnetic properties.
According to /1/p. 20, the number of Z-electrons in the conductivitiy zone has been obtained by the authors, allegedly, on the basis of metal's valency towards oxygen, hydrogen and is to be subject to doubt, as the experimental data of Hall and the uniform compression modulus are close to the theoretical values only for alkaline metals. The volume-centered lattice, Z=1 casts no doubt. The coordination number equals 8.
The exterior electrons of the final shell or subcoats in metal atoms form conductivity zone. The number of electrons in the conductivity zone effects Hall's constant, uniform compression ratio, etc.
Let us construct the model of metal - element so that external electrons of last layer or sublayers of atomic kernel, left after filling the conduction band, influenced somehow pattern of crystalline structure (for example: for the body-centred lattice - 8 ‘valency’ electrons, and for volume-centered and face-centred lattices - 12 or 9).
ROUGH, QUALITATIVE MEASUREMENT OF NUMBER OF ELECTRONS IN CONDUCTION BAND OF METAL - ELEMENT. EXPLANATION OF FACTORS, INFLUENCING FORMATION OF TYPE OF MONOCRYSTAL MATRIX AND SIGN OF HALL CONSTANT.
(Algorithm of construction of model)
The measurements of the Hall field allow us to determine the sign of charge carriers in the conduction band. One of the remarkable features of the Hall effect is, however, that in some metals the Hall coefficient is positive, and thus carriers in them should, probably, have the charge, opposite to the electron charge /1/. At room temperature this holds true for the following: vanadium, chromium, manganese, iron, cobalt, zinc, circonium, niobium, molybdenum, ruthenium, rhodium, cadmium, cerium, praseodymium, neodymium, ytterbium, hafnium, tantalum, wolfram, rhenium, iridium, thallium, plumbum /2/. Solution to this enigma must be given by complete quantum - mechanical theory of solid body.
Roughly speaking, using the base cases of Born- Karman, let us consider a highly simplified case of one-dimensional conduction band. The first variant: a thin closed tube is completely filled with electrons but one. The diameter of the electron roughly equals the diameter of the tube. With such filling of the area at local movement of the electron an opposite movement of the ‘site’ of the electron, absent in the tube, is observed, i.e. movement of non-negative sighting. The second variant: there is one electron in the tube - movement of only one charge is possible - that of the electron with a negative charge. These two opposite variants show, that the sighting of carriers, determined according to the Hall coefficient, to some extent, must depend on the filling of the conduction band with electrons. Figure 1.
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| Element | (cubic metres /K) | Z (number) | Z kernel (number) | Lattice type | |
| Natrium | Na | -2,30 | 1 | 8 | body-centered |
| Magnesium | Mg | -0,90 | 1 | 9 | volume-centered |
| Aluminium Or | Al | -0,38 | 2 | 9 | face-centered |
| Aluminium | Al | -0,38 | 12 | face-centered | |
| Potassium | K | -4,20 | 1 | 8 | body-centered |
| Calcium | Ca | -1,78 | 1 | 9 | face-centered |
| Calciom | Ca | T=737K | 2 | 8 | body-centered |
| Scandium Or | Sc | -0,67 | 2 | 9 | volume-centered |
| Scandium | Sc | -0,67 | 1 | 18 | volume-centered |
| Titanium | Ti | -2,40 | 1 | 9 | volume-centered |
| Titanium | Ti | -2,40 | 3 | 9 | volume-centered |
| Titanium | Ti | T=1158K | 4 | 8 | body-centered |
| Vanadium | V | +0,76 | 5 | 8 | body-centered |
| Chromium | Cr | +3,63 | 6 | 8 | body-centered |
| Iron or | Fe | +8,00 | 8 | 8 | body-centered |
| Iron | Fe | +8,00 | 2 | 14 | body-centered |
| Iron or | Fe | Т=1189K | 7 | 9 | face-centered |
| Iron | Fe | Т=1189K | 4 | 12 | face-centered |
Cobalt or | Co | +3,60 | 8 | 9 | volume-centered |
| Cobalt | Co | +3,60 | 5 | 12 | volume-centered |
| Nickel | Ni | -0,60 | 1 | 9 | face-centered |
| Copper or | Cu | -0,52 | 1 | 18 | face-centered |
| Copper | Cu | -0,52 | 2 | 9 | face-centered |
| Zink or | Zn | +0,90 | 2 | 18 | volume-centered |
| Zink | Zn | +0,90 | 3 | 9 | volume-centered |
| Rubidium | Rb | -5,90 | 1 | 8 | body-centered |
| Itrium | Y | -1,25 | 2 | 9 | volume-centered |
| Zirconium or | Zr | +0,21 | 3 | 9 | volume-centered |
| Zirconium | Zr | 4 | 8 | body-centered | |
| Niobium | Nb | 5 | 8 | body-centered | |
| Molybde-num | Mo | +1,91 | 6 | 8 | body-centered |
| Ruthenium | Ru | +22 | 7 | 9 | volume-centered |
| Rhodium Or | Rh | +0,48 | 5 | 12 | face-centered |
| Rhodium | Rh | +0,48 | 8 | 9 | face-centered |
| Palladium | Pd | -6,80 | 1 | 9 | face-centered |
| Silver or | Ag | -0,90 | 1 | 18 | face-centered |
| Silver | Ag | -0,90 | 2 | 9 | face-centered |
| Cadmium or | Cd | +0,67 | 2 | 18 | volume-centered |
| Cadmium | Cd | +0,67 | 3 | 9 | volume-centered |
| Caesium | Cs | -7,80 | 1 | 8 | body-centered |
| Lanthanum | La | -0,80 | 2 | 9 | volume-centered |
| Cerium or | Ce | +1,92 | 3 | 9 | face-centered |
| Cerium | Ce | +1,92 | 1 | 9 | face-centered |
| Praseodymium or | Pr | +0,71 | 4 | 9 | volume-centered |
| Praseodymium | Pr | +0,71 | 1 | 9 | volume-centered |
| Neodymium or | Nd | +0,97 | 5 | 9 | volume-centered |
| Neodymium | Nd | +0,97 | 1 | 9 | volume-centered |
| Gadolinium or | Gd | -0,95 | 2 | 9 | volume-centered |
| Gadolinium | Gd | T=1533K | 3 | 8 | body-centered |
| Terbium or | Tb | -4,30 | 1 | 9 | volume-centered |
| Terbium | Tb | 2 | 8 | body-centered | |
| Dysprosium | Dy | -2,70 | 1 | 9 | volume-centered |
| Dysprosium | Dy | 2 | 8 | body-centered | |
| Erbium | Er | -0,341 | 1 | 9 | volume-centered |
| Thulium | Tu | -1,80 | 1 | 9 | volume-centered |
| Ytterbium or | Yb | +3,77 | 3 | 9 | face-centered |
| Ytterbium | Yb | +3,77 | 1 | 9 | face-centered |
| Lutecium | Lu | -0,535 | 2 | 9 | volume-centered |
| Hafnium | Hf | +0,43 | 3 | 9 | volume-centered |
| Hafnium | Hf | 4 | 8 | body-centered | |
| Tantalum | Ta | +0,98 | 5 | 8 | body-centered |
| Wolfram | W | +0,856 | 6 | 8 | body-centered |
| Rhenium | Re | +3,15 | 6 | 9 | |
| Osmium | Os | <0 | 4 | 12 | volume centered |
| Iridium | Ir | +3,18 | 5 | 12 | face-centered |
| Platinum | Pt | -0,194 | 1 | 9 | face-centered |
| Gold or | Au | -0,69 | 1 | 18 | face-centered |
| Gold | Au | -0,69 | 9 | face-centered | |
| Thallium or | Tl | +0,24 | 3 | 18 | volume-centered |
| Thallium | Tl | +0,24 | 4 | 9 | volume-centered |
| Lead | Pb | +0,09 | 4 | 18 | face-centered |
| Lead | Pb | +0,09 | 5 | 9 | face-centered |
Where Rh is the Hall’s constant (Hall’s coefficient)