Construction of primitive cells of the cubic syngony on the basis of the molecular acoustics method

Abstract

Abstract Topicality of the present article is connected with introduction of new verifying condition, which is required for estimation of structures of cores of the “elementary” lattices of the body-centred cell and face-centred cell (these lattices were proposed in accordance with the Bravais theory), on the basis of theoretical calculations of the ultrasonic velocities, which are directed along the edges of the selected cells and which are verified with the help of the experimental data that were obtained in accordance with the molecular analysis method. The purpose of the present investigation was as follows: to carry out evaluation of the core structures of the elementary and primitive cells of the body-centred and face-centred cell of the crystal lattice of the cubic syngony (for alpha iron and cuprum) in respect of their conformity with methods of the molecular acoustics. The method of the present investigation is based on comparison of values of the ultrasonic velocities (longitudinal velocity, transversal velocity, and velocity within the rod), which were calculated on the basis of the relevant theory and which are transmitted over edges of the primitive cell that is constructed (for alpha iron and cuprum), with the values of these velocities of the ultrasound, which were obtained experimentally with the help of the molecular acoustics method for these materials. Introduction of the additional criterion (requirement) in respect of selection of the least cell on the basis of the molecular analysis has made it possible to draw the conclusion that cores of the “elementary” cells of the body-centred and face-centred crystal lattices, which are determined in accordance with the Bravais theory and which are assumed as the basis of the analysis with the help of the analytic geometry method, are inconsistent with actually existing mechanism of transmission of the ultrasound over the interatomic bonds (edges of the cell). In addition, this conclusion has made it possible to reveal new type (that is, a new syngony), which is the basis of the core structure of these “elementary” cells. The theoretically calculated ultrasound velocities, which are directed along the edges of the primitive cell of the new type (for alpha iron and for cuprum), have been coincident with high accuracy with the values of the longitudinal and transversal sound velocity, as well as with the sound velocity within the rod, which were experimentally established with the help of the molecular acoustics method.