# BSU bulletin. Mathematics, Informatics

Bibliographic description:
Mantatov V. V.
A LINEAR CORRELATION BETWEEN THE ANHARMONIC COEFFICIENT AND THE SOFTENING TEMPERATURE OF VITREOUS SOLIDS // BSU bulletin. Mathematics, Informatics. - 2017. №4. . - С. 48-55.
Title:
A LINEAR CORRELATION BETWEEN THE ANHARMONIC COEFFICIENT AND THE SOFTENING TEMPERATURE OF VITREOUS SOLIDS
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Codes:
DOI: 10.18101/2304-5728-2017-4-48-55UDK: 532.2
Annotation:
In the article using the model of delocalized atoms we first showed a linear correlation between the anharmonic coefficient and the softening temperature of some vitreous solids.

The anharmonicity of lattice vibrations leads to a total thermal pressure, which stretches the interatomic bonds. Thermal pressure is compensated by external and internal pressures. Internal pressure, which is the main component of thermal pressure in liquid and solids, is equal to the derivative of internal energy by volume at a constant temperature, and represents the elastic response of the lattice to external influences. The internal energy consists of the binding energy of atoms and molecules that form a solid body. The internal pressure, which is the main component of the thermal pressure in the liquid and solid, is equal to the derivative of internal energy by volume at a constant temperature and represents the elastic response of the lattice to external influences. In the approximation up to the limiting deformation Hooke's law is valid; using the proposed model we have found the value of maximum thermal pressure. Here the limiting deformation of the interatomic bond is proportional to the reciprocal of the anharmonic coefficient. Further, taking into account the equation of state, we reveal a linear correlation of the reciprocal of squared anharmonic coefficient with the softening temperature of vitreous solids.
According to this model, it can be assumed that the elementary act of the process of vitreous solids softening and plastic deformation is the maximum deformation of the interatomic bond.
Keywords:
model of delocalized atoms; non-crystalline solids; linear correlation, glass transition temperature; maximum deformation of the interatomic bond; anharmonicity.
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