# Considerations to determine the mass of atoms (ions) of crystalline substance

### Abstract

We consider the importance of numerical value of the mass of the hypothetical atom (ion) crystal, which through the medium of of that mass are calculated numerical values of other physical characteristics. In particular it is the determination of the characteristic X-ray Debye temperature or medium quadratic dynamic displacement of atoms from the equilibrium position the thermal vibration of their movement. It is often calculated the average or taken numerical value of the mass of the hypothetical atom of matter. In its turn the magnitude of this value depends on how it calculate. The article provides examples of the atomic masses of crystals type , , in solids type or , and more complex structures such and . Authors of the article bring mathematical equations calculating the value of and consolidated atomic masses for diatomic and triatomic structure of cubic system. In particular, for diatomic structures such and an average atomic mass, where і – atomic mass of sodium and chloride molecules, respectively. In previous studies the authors by radiographic high temperature methods investigated the physical properties of the aforementioned alloys, ionic crystals and iso-type structures ( ) and ( ). In this case they had to count, to some extent, the average atomic mass. The calculation results of averages and consolidated atomic masses in the article for hexaboride and dodecaboride given only for extreme masses of molecules. First atomic mass are calculated in relative units of mass, and then, if necessary, can be found inside the mass of the hypothetical atoms. In the tables is presented part of such calculations. Typically the average atomic mass is larger than the resulted mass. For izostructures consisting of atoms of small mass difference it is proposed to use average mass of the hypothetical atoms. For structures with large difference of atoms mass it is proposed to use the reduced mass at research of acoustic branches of vibration spectrum, especially in the temperature that is below the characteristic temperature. In this case, there is no need calculate the atomic mass, because it was determined the exponent of temperature multiplying Deby: , where – mean-square displacement of an atom from equilibrium position, – the angle of diffraction, – the wavelength of X-rays.

### References

Umanskij, I.S. (1967). Rentgenohrafij metallow. Moskwa: Metallurgij (in Russian).

Kriwohlaz, M.A. (1967). Teorija rassejanija rentgenovskih luchej i teplovyh nejtronov real'nymi kristallami. «Nauka». Moskva: fizmat literatura (in Russian).

Mirkin, L.I. (1961). Spravochnik po rentgenostrukturnomu analizu polikristallov. Moskwa: Fizmatgiz (in Russian).

*Scientific Messenger of LNU of Veterinary Medicine and Biotechnologies. Series: Food Technologies*,

*19*(75), 40-44. https://doi.org/10.15421/nvlvet7508

This work is licensed under a Creative Commons Attribution 4.0 International License.