| | | | | |ed |
|Zirconium |Zr |Т=1135К |4 |8 |body-centered|
|Niobium |Nb |+0,72 |5 |8 |body-centered|
|Molybde-num |Mo |+1,91 |6 |8 |body-centered|
|Ruthenium |Ru |+22 |7 |9 |volume-center|
| | | | | |ed |
|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-center|
| | | | | |ed |
|Cadmium |Cd |+0,67 |3 |9 |volume-center|
| | | | | |ed |
|Caesium |Cs |-7,80 |1 |8 |body-centered|
|Lanthanum |La |-0,80 |2 |9 |volume-center|
| | | | | |ed |
|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-center|
| | | | | |ed |
|Praseodymium |Pr |+0,71 |1 |9 |volume-center|
| | | | | |ed |
|Neodymium or |Nd |+0,97 |5 |9 |volume-center|
| | | | | |ed |
|Neodymium |Nd |+0,97 |1 |9 |volume-center|
| | | | | |ed |
|Gadolinium or |Gd |-0,95 |2 |9 |volume-center|
| | | | | |ed |
|Gadolinium |Gd |T=1533K |3 |8 |body-centered|
|Terbium or |Tb |-4,30 |1 |9 |volume-center|
| | | | | |ed |
|Terbium |Tb |Т=1560К |2 |8 |body-centered|
|Dysprosium |Dy |-2,70 |1 |9 |volume-center|
| | | | | |ed |
|Dysprosium |Dy |Т=1657К |2 |8 |body-centered|
|Erbium |Er |-0,341 |1 |9 |volume-center|
| | | | | |ed |
|Thulium |Tu |-1,80 |1 |9 |volume-center|
| | | | | |ed |
|Ytterbium or |Yb |+3,77 |3 |9 |face-centered|
|Ytterbium |Yb |+3,77 |1 |9 |face-centered|
|Lutecium |Lu |-0,535 |2 |9 |volume-center|
| | | | | |ed |
|Hafnium |Hf |+0,43 |3 |9 |volume-center|
| | | | | |ed |
|Hafnium |Hf |Т=2050К |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 |volume-center|
| | | | | |ed |
|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 |2 |9 |face-centered|
|Thallium or |Tl |+0,24 |3 |18 |volume-center|
| | | | | |ed |
|Thallium |Tl |+0,24 |4 |9 |volume-center|
| | | | | |ed |
|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)
Z is an assumed number of electrons released by one atom to
the conductivity zone.
Z kernel is the number of external electrons of the atomic
kernel on the last shell.
The lattice type is the type of the metal crystal structure
at room temperature and, in some cases, at phase transition
temperatures (1).
Conclusions
In spite of the rough reasoning the table shows that the greater
number of electrons gives the atom of the element to the
conductivity zone, the more positive is the Hall’s constant. On
the contrary the Hall’s constant is negative for the elements
which have released one or two electrons to the conductivity
zone, which doesn’t contradict to the conclusions of Payerls. A
relationship is also seen between the conductivity electrons (Z)
and valency electrons (Z kernel) stipulating the crystal
structure.
The phase transition of the element from one lattice to
another can be explained by the transfer of one of the external
electrons of the atomic kernel to the metal conductivity zone or
its return from the conductivity zone to the external shell of
the kernel under the influence of external factors (pressure,
temperature).
We tried to unravel the puzzle, but instead we received a
new puzzle which provides a good explanation for the physico-
chemical properties of the elements. This is the “coordination
number” 9 (nine) for the face-centered and volume-centered
lattices.
This frequent occurrence of the number 9 in the table
suggests that the densest packings have been studied
insufficiently.
Using the method of inverse reading from experimental values
for the uniform compression towards the theoretical calculations
and the formulae of Arkshoft and Mermin (1) to determine the Z
value, we can verify its good agreement with the data listed in
Table 1.
The metallic bond seems to be due to both socialized
electrons and “valency” ones – the electrons of the atomic
kernel.
Literature:
1) Solid state physics. N.W. Ashcroft, N.D. Mermin. Cornell
University, 1975
2) Characteristics of elements. G.V. Samsonov. Moscow, 1976
3) Grundzuge der Anorganischen Kristallchemie. Von. Dr. Heinz
Krebs. Universitat Stuttgart, 1968
4) Physics of metals. Y.G. Dorfman, I.K. Kikoin. Leningrad, 1933
5) What affects crystals characteristics. G.G.Skidelsky. Engineer №
8, 1989
Appendix 1
Metallic Bond in Densest Packing (Volume-centered and face-centered)
It follows from the speculations on the number of direct bonds ( or
pseudobonds, since there is a conductivity zone between the
neighbouring metal atoms) being equal to nine according to the number
of external electrons of the atomic kernel for densest packings that
similar to body-centered lattice (eight neighbouring atoms in the
first coordination sphere). Volume-centered and face-centered lattices
in the first coordination sphere should have nine atoms whereas we
actually have 12 ones. But the presence of nine neighbouring atoms,
bound to any central atom has indirectly been confirmed by the
experimental data of Hall and the uniform compression modulus (and
from the experiments on the Gaase van Alfen effect the oscillation
number is a multiple of nine.
Consequently, differences from other atoms in the coordination
sphere should presumably be sought among three atoms out of 6 atoms
located in the hexagon. Fig.1,1. d, e shows coordination spheres in
the densest hexagonal and cubic packings.
[pic]
Fig.1.1. Dense Packing.
It should be noted that in the hexagonal packing, the triangles of
upper and lower bases are unindirectional, whereas in the hexagonal
packing they are not unindirectional.
Literature:
Introduction into physical chemistry and chrystal chemistry of semi-
conductors. B.F. Ormont. Moscow, 1968.
Appendix 2
Theoretical calculation of the uniform compression modulus (B).
B = (6,13/(rs|ao))5* 1010 dyne/cm2
Where B is the uniform compression modulus
Ao is the Bohr radius
rs – the radius of the sphere with the volume being equal to the volume
falling at one conductivity electron.
rs = (3/4 (n ) 1/3
Where n is the density of conductivity electrons.
Table 1. Calculation according to Ashcroft and Mermine
|Element |Z |rs/ao |theoretical |calculated |
|Cs |1 |5.62 |1.54 |1.43 |
|Cu |1 |2.67 |63.8 |134.3 |
|Ag |1 |3.02 |34.5 |99.9 |
|Al |3 |2.07 |228 |76.0 |
Table 2. Calculation according to the models considered in this paper
|Element |Z |rs/ao |theoretical |calculated |
|Cs |1 |5.62 |1.54 |1.43 |
|Cu |2 |2.12 |202.3 |134.3 |
|Ag |2 |2.39 |111.0 |99.9 |
|Al |2 |2.40 |108.6 |76.0 |
Of course, the pressure of free electrons gases alone does not
fully determine the compressive strenth of the metal,
nevertheless in the second calculation instance the theoretical
uniform compression modulus lies closer to the experimental one
(approximated the experimental one) this approach (approximation)
being one-sided. The second factor the effect of “valency” or
external electrons of the atomic kernel, governing the crystal
lattice is evidently required to be taken into consideration.
Literature:
Solid state physics. N.W. Ashcroft, N.D. Mermin. Cornell
University, 1975
Grodno
March 1996
G.G. Filipenko
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