title: ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ¿ÑÑÐ³Ð¸Ñ ÑÐ²Ð¾Ð¹ÑÑÐ² ÑÑÐ¿ÐµÑÐ¸Ð¾Ð½Ð½ÑÑ ÐºÑÐ¸ÑÑÐ°Ð»Ð»Ð¾Ð² Ð¼Ð¾Ð½Ð¾ÐºÐ»Ð¸Ð½Ð½Ð¾Ð¹ ÑÐ¸Ð¼Ð¼ÐµÑÑÐ¸Ð¸
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Investigation of elastic properties of superionic crystals of monoclinic symmetry
Creators: name: ÐÐ°Ð»Ð¸Ð¼Ð°ÑÐ´Ð°Ð½Ð¾Ð², ÐÐ°Ð´Ð¸Ð¼
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2024
Subjects: ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ ÐÑÐ¸ÑÑÐ¾ÑÑÐµÐ»Ñ
Ð¸Ð½ÑÐµÑÑÐµÑÐ¾Ð¼ÐµÑÑ Ð¤Ð°Ð±ÑÐ¸-ÐÐµÑÐ¾
Ð¼Ð°Ð½Ð´ÐµÐ»ÑÑÑÐ°Ð¼-Ð±ÑÐ¸Ð»Ð»ÑÑÐ½Ð¾Ð²ÑÐºÐ¾Ðµ ÑÐ°ÑÑÐµÑÐ½Ð¸Ðµ ÑÐ²ÐµÑÐ°
Christoffel equation
Fabry-Perot interferometer
brillouin light scattering

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿ÑÐµÐ´ÑÑÐ°Ð²Ð»ÑÐµÑ ÑÐ¾Ð±Ð¾Ð¹ ÑÐµÑÐµÐ½Ð¸Ðµ Ð¿ÑÑÐ¼Ð¾Ð¹ Ð¸ Ð¾Ð±ÑÐ°ÑÐ½Ð¾Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸ ÐºÑÐ¸ÑÑÐ°Ð»Ð»Ð¾Ð°ÐºÑÑÑÐ¸ÐºÐ¸ Ð´Ð»Ñ ÑÐ»ÐµÐ´ÑÑÑÐ¸Ñ ÑÐ¸ÑÑÐµÐ¼: ÐºÑÐ±Ð¸ÑÐµÑÐºÐ°Ñ, ÑÑÐ¸Ð³Ð¾Ð½Ð°Ð»ÑÐ½Ð°Ñ, ÑÑÐ¸ÐºÐ»Ð¸Ð½Ð½Ð°Ñ ÑÐ¸Ð½Ð³Ð¾Ð½Ð¸Ð¸. Ð ÑÐ°ÑÑÐ½Ð¾ÑÑÐ¸, Ð±ÑÐ»Ð¸ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ñ ÐºÑÐ¸ÑÑÐ°Ð»Ð»Ñ ÐºÑÐ±Ð¸ÑÐµÑÐºÐ¾Ð¹ ÑÐ°Ð·Ñ: NaCl Ð¸ ÐºÑÐ¸ÑÑÐ°Ð»Ð»Ð° Ð½Ð°ÑÑÐ¸Ð¹-Ð²Ð¸ÑÐ¼ÑÑÐ¾Ð²Ð¾Ð³Ð¾ ÑÐ¸ÑÐ°Ð½Ð°ÑÐ° Na1/2Bi1/2TiO3 (NBT), ÑÑÐ¸Ð³Ð¾Ð½Ð°Ð»ÑÐ½Ð¾Ð¹ ÑÐ°Ð·Ñ: Î±-ÐºÐ²Ð°ÑÑ SiO2. ÐÑÐ¾Ð±ÑÐ¹ Ð¸Ð½ÑÐµÑÐµÑ Ð¿ÑÐµÐ´ÑÑÐ°Ð²Ð»ÑÐ»Ð° Ð²Ð¾Ð·Ð¼Ð¾Ð¶Ð½Ð¾ÑÑÑ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ñ ÑÐµÑÐµÐ½Ð¸Ñ Ð¾Ð±ÑÐ°ÑÐ½Ð¾Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸ ÐºÑÐ¸ÑÑÐ°Ð»Ð»Ð¾Ð°ÐºÑÑÑÐ¸ÐºÐ¸ Ð´Ð»Ñ ÐºÑÐ¸ÑÑÐ°Ð»Ð»Ð¾Ð² Ð¼Ð¾Ð½Ð¾ÐºÐ»Ð¸Ð½Ð½Ð¾Ð¹ ÑÐ¸Ð¼Ð¼ÐµÑÑÐ¸Ð¸, Ð² ÑÐ°ÑÑÐ½Ð¾ÑÑÐ¸ ÑÑÐ¿ÐµÑÐ¸Ð¾Ð½Ð½Ð¾Ð³Ð¾ ÐºÑÐ¸ÑÑÐ°Ð»Ð»Ð° CsDSeO4 ÐÑÐ¸ÑÑÐ°Ð»Ð»Ñ NBT ÑÐ°ÑÑÐ¼Ð°ÑÑÐ¸Ð²Ð°Ð»Ð¸ÑÑ Ð½Ð°Ð¸Ð±Ð¾Ð»ÐµÐµ Ð¿Ð¾Ð´ÑÐ¾Ð±Ð½Ð¾ ÐºÐ°Ðº Ð¿ÑÐ¸Ð¼ÐµÑ ÑÐ¸ÑÑÐµÐ¼Ñ, Ñ Ð½ÐµÑÑÐ¸Ð²Ð¸Ð°Ð»ÑÐ½Ð¾Ð¹ Ð¿Ð¾ÑÐ»ÐµÐ´Ð¾Ð²Ð°ÑÐµÐ»ÑÐ½Ð¾ÑÑÑÑ ÑÐ°Ð·Ð¾Ð²ÑÑ Ð¿ÐµÑÐµÑÐ¾Ð´Ð¾Ð². ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ¿ÑÑÐ³Ð¸Ñ ÑÐ²Ð¾Ð¹ÑÑÐ² NBT ÑÐ²Ð»ÑÐµÑÑÑ Ð¿ÑÐ¸Ð½ÑÐ¸Ð¿Ð¸Ð°Ð»ÑÐ½Ð¾ Ð²Ð°Ð¶Ð½ÑÐ¼, Ð¿Ð¾ÑÐºÐ¾Ð»ÑÐºÑ Ð½Ð°Ð±Ð»ÑÐ´Ð°ÐµÐ¼ÑÐµ Ð½ÐµÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸ ÐºÑÐ¸ÑÑÐ°Ð»Ð»Ð¸ÑÐµÑÐºÐ¾Ð¹ ÑÐµÑÐµÑÐºÐ¸ ÑÐ²ÑÐ·Ð°Ð½Ñ Ñ Ð´ÐµÑÐ¾ÑÐ¼Ð°ÑÐ¸ÐµÐ¹. ÐÐ¾ÑÑÐ¾Ð¼Ñ Ð² ÐºÐ°ÑÐµÑÑÐ²Ðµ Ð¼ÐµÑÐ¾Ð´Ð° Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ð¹ Ð±ÑÐ»Ð¾ Ð²ÑÐ±ÑÐ°Ð½Ð¾ Ð¼Ð°Ð½Ð´ÐµÐ»ÑÑÑÐ°Ð¼-Ð±ÑÐ¸Ð»Ð»ÑÑÐ½Ð¾Ð²ÑÐºÐ¾Ðµ ÑÐ°ÑÑÐµÑÐ½Ð¸Ðµ ÑÐ²ÐµÑÐ°, Ð² ÐºÐ¾ÑÐ¾ÑÐ¾Ð¼ Ð¸ÑÑÐ»ÐµÐ´ÑÐµÑÑÑ ÑÐ°ÑÑÐµÑÐ½Ð¸Ðµ Ð½Ð° Ð´Ð»Ð¸Ð½Ð½Ð¾Ð²Ð¾Ð»Ð½Ð¾Ð²ÑÑ Ð°ÐºÑÑÑÐ¸ÑÐµÑÐºÐ¸Ñ ÑÐ¾Ð½Ð¾Ð½Ð°Ñ. Ð Ð½Ð°ÑÑÐ¾ÑÑÐµÐ¹ ÑÐ°Ð±Ð¾ÑÐµ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ñ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ ÐÐÐ  ÑÐ²ÐµÑÐ° Ð¿ÑÐ¸ ÑÐµÐ¼Ð¿ÐµÑÐ°ÑÑÑÐµ 843 Ð, Ð¾ÑÐ²Ð°ÑÑÐ²Ð°ÑÑÐ¸Ð¹ ÐºÑÐ±Ð¸ÑÐµÑÐºÑÑ ÑÐ°Ð·Ñ ÐºÑÐ¸ÑÑÐ°Ð»Ð»Ð° Ð½Ð°ÑÑÐ¸Ð¹-Ð²Ð¸ÑÐ¼ÑÑÐ¾Ð²Ð¾Ð³Ð¾ ÑÐ¸ÑÐ°Ð½Ð°ÑÐ°. Ð ÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð¼ ÑÐ°Ð±Ð¾ÑÑ ÑÑÐ°Ð»Ð¾ ÑÐµÑÐµÐ½Ð¸Ðµ Ð¿ÑÑÐ¼Ð¾Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸ ÐºÑÐ¸ÑÑÐ°Ð»Ð»Ð¾Ð°ÐºÑÑÑÐ¸ÐºÐ¸: Ð¿Ð¾Ð»ÑÑÐµÐ½Ð¸Ðµ Ð¿Ð¾Ð²ÐµÑÑÐ½Ð¾ÑÑÐµÐ¹ ÑÐ°Ð·Ð¾Ð²ÑÑ ÑÐºÐ¾ÑÐ¾ÑÑÐµÐ¹ Ð¿Ð¾ Ð¸Ð¼ÐµÑÑÐ¸Ð¼ÑÑ Ð´Ð°Ð½Ð½ÑÐ¼ ÐºÐ¾ÑÑÑÐ¸ÑÐ¸ÐµÐ½ÑÐ¾Ð² ÑÐ¿ÑÑÐ³Ð¸Ñ Ð¼Ð¾Ð´ÑÐ»ÐµÐ¹ ÐºÑÐ¸ÑÑÐ°Ð»Ð»Ð°, Ð° ÑÐ°ÐºÐ¶Ðµ ÑÐµÑÐµÐ½Ð¸Ðµ Ð¾Ð±ÑÐ°ÑÐ½Ð¾Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸: Ð¿Ð¾Ð»ÑÑÐµÐ½Ð¸Ðµ ÑÐµÐ½Ð·Ð¾ÑÐ° Ð¼Ð¾Ð´ÑÐ»ÐµÐ¹ ÑÐ¿ÑÑÐ³Ð¾ÑÑÐ¸ Ð¿Ð¾ ÑÐ½ÑÑÑÐ¼ Ð² ÑÐ¾Ð´Ðµ ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐ° Ð·Ð½Ð°ÑÐµÐ½Ð¸ÑÐ¼ Ð°ÐºÑÑÑÐ¸ÑÐµÑÐºÐ¸Ñ ÑÐºÐ¾ÑÐ¾ÑÑÐµÐ¹ Ð² ÐºÑÐ¸ÑÑÐ°Ð»Ð»Ðµ. ÐÐ°Ð¿Ð¸ÑÐ°Ð½ ÐºÐ¾Ð´ Ð´Ð»Ñ Ð¾Ð´Ð½Ð¾Ð·Ð½Ð°ÑÐ½Ð¾Ð³Ð¾ ÑÐ¾Ð¾ÑÐ²ÐµÑÑÑÐ²Ð¸Ñ ÑÑÐ¸Ñ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð². ÐÐ±ÑÐµÐºÑ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ â ÐºÑÐ¸ÑÑÐ°Ð»Ð»Ñ NaCl, NBT, SiO2, CsDSeO4. ÐÑÐµÐ´Ð¼ÐµÑ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ â Ð°ÐºÑÑÑÐ¸ÑÐµÑÐºÐ¸Ðµ ÑÐ¾Ð½Ð¾Ð½Ñ Ð² ÐºÑÐ¸ÑÑÐ°Ð»Ð»Ðµ, ÑÐµÐ½Ð·Ð¾Ñ Ð¼Ð¾Ð´ÑÐ»ÐµÐ¹ ÑÐ¿ÑÑÐ³Ð¾ÑÑÐ¸ Ð¸ Ð¿Ð¾Ð²ÐµÑÑÐ½Ð¾ÑÑÑ ÑÐ°Ð·Ð¾Ð²ÑÑ ÑÐºÐ¾ÑÐ¾ÑÑÐµÐ¹.
description: This work represents a solution to the direct and inverse problem of crystal acoustics for the following systems: cubic, trigonal, triclinic system. In particular, crystals of the cubic phase: NaCl and sodium-bismuth titanate crystal Na1/2Bi1/2TiO3 (NBT), trigonal phase: Î±-quartz SiO2 were studied. Of particular interest was the possibility of using a solution to the inverse problem of crystal acoustics for crystals of monoclinic symmetry, in particular the superionic crystal CsDSeO4. NBT crystals were considered in most detail as an example of a system with a nontrivial sequence of phase transitions. The study of the elastic properties of NBT is fundamentally important, since the observed instabilities of the crystal lattice are associated with deformation. Therefore, Mandelstam-Brillouin light scattering was chosen as a research method, in which scattering by long-wave acoustic phonons is studied. In this work, we studied light MBR at a temperature of 843 K, covering the cubic phase of a sodium-bismuth titanate crystal. The result of the work was the solution of the direct problem of crystal acoustics: obtaining phase velocity surfaces from the available data on the coefficients of elastic moduli of the crystal, as well as the solution of the inverse problem: obtaining the tensor of elastic moduli from the values of acoustic velocities in the crystal taken during the experiment. Code has been written to unambiguously match these parameters. The object of research is crystals of NaCl, NBT, SiO2, CsDSeO4. The subject of the study is acoustic phonons in a crystal, the tensor of elastic moduli and the surface of phase velocities.