A THEORETICAL PREDICTION OF MOLECULAR AND CRYSTAL STRUCTURES

Leonid G. Kreidik¹ and George P. Shpenkov²

¹Department of Physics, Technical University, 220027 Minsk, Belarus,
²Institute of Mathematics and Physics, Technical University, 85-796 Bydgoszcz, Poland gshp@atr.bydgoszcz.pl

Keywords: Haüy's molecules, wave equation solutions, intra-atomic space, crystal structure

Analyzing the structure of crystals at the end of 18^th century, R.J. Haüy [1] has came to the conclusion that it is necessary to consider atoms as elementary molecules, internal structure of which is closely related to the crystal shape of solids. Particles, constituent these elementary molecules, must be coupled by strong bonds, which we call the multiplicative bonds. Then it is reasonable the ordinary molecules with relatively weak bonds to call the composite or additive molecules; e.g. if deuterium D is the multiplicative molecule then the hydrogen molecule H₂ is the additive one.

As masses of atoms are multiple to the neutron (hydrogen atom) mass then, following Haüy's ideas, it was reasonable to suppose that the atom, as the elementary Haüy's molecule, is the neutron multiplicative molecule. According to this model, using the wave equation, the problem on distribution of matter (neutrons) in the elementary Haüy's molecules has been solved.

When spherical polar coordinates are used, distribution of particles in the wave space of the atom (independently on a kind of an atomic model) is determined by the relative radius r, the polar angle q, and the azimuth angle j. Solutions of wave equations in spherical fields are represented in the form of product of the four functions: . Here, is the radial component, defining spherical shells of the atomic space on which are extremes and zeros of distribution of matter; is the polar component, it defines cones of the polar distribution of extremes and zeros, distinguishing at the spherical shells the circles-parallels of extremes and zeros; is the azimuth component, it gives the azimuth coordinates of extremes and zeros at the circles-meridians of extremes and zeros. The time component characterizes time oscillations of the distributions.

The actual picture of distribution of nodes-extremes, corresponding to Haüy's elementary molecules, is presented in Table 1. Principal azimuth nodes of the wave space of the atom are marked by ordinal numbers. These numbers coincide with the ordinal numbers of elements of Mendeleev's periodic table. Number of neutrons, localized in one node, are equal to or less than two. Collateral nodes, designated in the Table 1 by smaller white circles, are partially vacant, these provide conditions for interatomic movement of neutrons or protons. For example, one of the isotopes of ₁₄Si has four spherical neutron shells (see Table 1), principal nodes of which are completed (contain 28 neutrons), but two collateral nodes of the outer shell are vacant. The lasts determine semiconductor properties of ₁₄Si.

Assuming that all neutrons of the atom participate in scattering of incident waves or particles, the calculation of the specific density of probability of scattering a_m for these cases has been carried out. A result of this calculation is a_m =0.1955 cm²g^-1 [2], that is in accordance with the experimental value a_m =0.20 cm²g^-1 for short X-ray for all practically targets [3]. Calculations of possible effective cross-sections of the neutron and a-particle scattering on atomic neutrons-nodes are also in conformity with the experiment [2]. Such an agreement with experience gives the base to assume that X-ray reflection occurs on individual neutrons and an image of X-ray diffraction defines the space distribution of neutrons in atoms as if these were the elementary Haüy's molecules.

General formulae of lines of optical and roentgen spectra follow from the multiplicative model of atom. In a case of the hydrogen atom the formula of the optical spectrum is transferred into the Balmer's formula. The spectral formula of coherent transitions describes experimental K-lines of X-ray spectrum essentially more precisely than it allows the experimental Moseley's law [2], etc.

On the basis of elementary multiplicative Haüy's molecules, it is easy to predict the possible structures of both the crystals and additive molecules that is presented in the extended report.

1. R.G. Haüy, Essai d'une theorie sur la structure des crystaux, Paris, (1784).
2. L.G. Kreidik, G.P. Shpenkov, Alternative Picture of the World, V.1-3, Bydgoszcz (1996).
3. S. Flugge, ed., Hadbuch der Physik, Encyklopedia of Physics, V.30, Springer-Verlag (1957).