St. Petersburg scientists have developed a mathematical model of the processes occurring during the propagation of heat in ultrapure crystals. This will open up prospects for the creation of new materials for use in cooling circuits of various equipment. They talked about this on the pages of Continuum Mechanics and Thermodynamics magazine. The research was supported by a grant from the Russian Science Foundation (RSF).
Materials can conduct heat due to their internal structure. Atoms in any solid matter at a temperature other than absolute zero vibrate about their equilibrium position. Such movement can propagate in space from one atom to another. In order to more conveniently describe the processes of transferring vibrational energy, scientists have introduced a new quasiparticle (a particle that can be considered simultaneously as a wave) - a phonon.
For this, the properties of phonons are used in solid state physics. As the temperature rises, the amplitude of atomic vibrations in the crystal lattice increases. The heated atoms emit more phonons. Phonons are transferred through the crystal lattice, and atoms throughout the material begin to vibrate with greater amplitude. An increase in the vibration amplitude of the atoms of the crystal lattice corresponds to an increase in the temperature of the solid.
The existing theory of heat transfer states that phonons transfer thermal energy in solids - by analogy with how photons transfer light energy. Also, this theory takes into account that phonons can be scattered due to collisions with crystal lattice defects. During its scattering, the phonon can change the direction of motion, thereby complicating the process of heat transfer. This theory describes well the propagation of heat in bodies containing a large number of defects, but it does not work well in the case of ultrapure crystals (real crystals, the number of defects in which is minimal).
Scientists from Peter the Great's SPbPU have created a mathematical model that describes the transfer of thermal energy in solids on the basis of the theory of ballistic thermal conductivity that they are developing. This theory considers defect-free crystals as a collection of particles connected by bonds that can stretch and contract. When carrying out calculations using this model, scientists found out that heat transfer in ultrapure crystals is associated with the free propagation of phonons. The existing theories of heat transfer are inapplicable in this case.
Propagation of thermal disturbance in a square lattice performing transverse vibrations / Anton Krivtsov / indicator.ru
Researchers have yet to complete the creation of the theory of ballistic thermal conductivity, and in their current work they described the mathematical apparatus that underlies it. Using the example of a superpure crystal, scientists have shown that the model they created describes well the alleged properties of a physical system, but in some aspects contradicts the classical theory. If scientists succeed in showing that the mathematical apparatus they have created is capable of describing the effects observed in reality better than the existing model, then in the future it will be able to replace the classical theory. SPbPU researchers, together with colleagues from the Berlin Technical University, are already preparing for an experiment that will test the predictions of the new theory.
“Soon we will create a theory of ballistic heat propagation in ultrapure materials. The theory will make it possible to develop efficient methods of heat removal using the unique thermal properties of ultrapure materials, which are already possible to obtain using modern technologies. This will open up prospects for the creation of new materials for use in cooling circuits of various equipment,”says one of the authors of the study, Corresponding Member of the Russian Academy of Sciences, Doctor of Physical and Mathematical Sciences, Professor Anton Krivtsov.
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