Any lattice in which the hydrogen atoms would be translationally identical (Bravais lattice) would have metallic properties. In the present paper the energy of a body‐centered lattice of hydrogen is calculated as a function of the lattice constant. This energy is shown to assume its minimum value for a lattice constant which corresponds to a density many times higher than that of the ordinary, molecular lattice of solid hydrogen. This minimum—though negative—is much higher than that of the molecular form. The body‐centered modification of hydrogen cannot be obtained with the present pressures, nor can the other simple metallic lattices. The chances are better, perhaps, for intermediate, layer‐like lattices.
REFERENCES
1.
It was J. D. Bernal who first put forward the view that all substances go over under very high pressures into metallic or valence lattices.
2.
E. L.
Hill
remarks in a “Note on the Statistics of Electron Interaction
” (Physik. Zeits. Sowjetunion
7
, 447
(1935
)) that the expressions “parallel spin” and “antiparallel spin” should be replaced by “parallel spin Z components” and “antiparallel spin Z components,” respectively. The former expressions are not quite equivalent with the latter ones according to the general formalism of the statistical interpretation of quantum mechanics and can be used only as an abbreviation for them. (This is done in the present paper also.) We believe that Dr. Hill’s further remarks concerning the papers of this reference are based on a misunderstanding.3.
Interesting quantum‐mechanical considerations on this point have been put forward by F. Hund (International Conference on Physics, October 1934, London).
4.
To be given in Section 3.
5.
for Li see reference 2 (IV) and
J.
Millman
, Phys. Rev.
47
, 286
(1935
)., Phys. Rev.
6.
Cf. Eq. (11), reference 2 (II). The energy in (3) is in Rydberg units Ry and the length in Bohr units.
7.
The reason for this is that only for this form were we able to perform the integrations.
8.
This differs from the case for Li.
9.
We emphasize this point since doubts have been raised whether the correlation energy actually exists.
10.
11.
12.
Cf. e.g., E. Schrödinger, Geiger‐Scheel Handbuch der Physik, Vol. X.
13.
A.
Reis
, 2
, 57
(1920
);14.
This corresponds also to the ideas developed by
L.
Pauling
, J. Am. Chem. Soc.
53
, 1367
(1931
);15.
The calculated nearest distance for the metallic form is 1.5A.
16.
17.
Such polymorphic transitions induced by pressure in solids are described by
P. W.
Bridgman
, Rev. Mod. Phys.
7
, 1
(1935
).18.
19.
Diamond is a valence lattice, but graphite is a layer lattice (
A. W.
Hull
, Phys. Rev.
10
, 661
(1917
)).Yellow arsenic and phosphorus are evidently molecular lattices, black phosphorus a layer lattice (
R.
Hultgren
and B. E.
Warren
, Phys. Rev.
47
, 808
(1935
)), and metallic As is also only approximately a simple lattice.The red, monoclinic selenium can be said to form a molecular lattice (
F.
Halla
, F.
Bosch
, and E.
Mehl
, Zeits. f. Physik. Chemie
B11
, 455
(1930
)),while the metallic modification is a thread lattice (
A. J.
Bradley
, Phil. Mag.
48
, 477
(1924
)).The situation seems to be most complicated with tin. Grey tin forms a diamond lattice, but shows otherwise no similarity to the valence lattice of diamond, while the metallic lattice has a rather complicated structure (
H.
Mark
and M.
Polanyi
, Zeits. f. Physik
18
, 75
(1923
)).
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1935
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