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Propagation of elastic waves in continuous media - dynamic elasticity
International Tables for Crystallography (2013). Vol. D, Section 1.3.4, pp. 86-89 [ doi:10.1107/97809553602060000902 ]
... the past, although the measurements could not be very precise. A way of proceeding frequently used now is to excite a mechanical wave in the crystal and measure its propagation velocity or the wavelength associated with a particular frequency. One method consists in sending a train ...
Resonance technique
International Tables for Crystallography (2013). Vol. D, Section 1.3.4.6.2, p. 88 [ doi:10.1107/97809553602060000902 ]
... 1.3.4.6.2. Resonance technique The use of the resonance technique is a well established approach for determining the velocity of sound in a gas by observing nodes and antinodes of a system of standing waves produced in the so-called ...
Introduction
International Tables for Crystallography (2013). Vol. D, Section 1.3.4.6.1, p. 88 [ doi:10.1107/97809553602060000902 ]
... Introduction As mentioned in Section 1.3.4.1, the elastic constants of a material can be obtained by the elastic response of the ... dynamic elastic constants. When one measures the elastic response of a material to external static forces, work is done and heat ... thermal equilibrium with its surroundings, which can be considered as a heat reservoir. In this case, the measured elastic constants ...
Experimental determination of elastic constants
International Tables for Crystallography (2013). Vol. D, Section 1.3.4.6, pp. 88-89 [ doi:10.1107/97809553602060000902 ]
... Introduction | | As mentioned in Section 1.3.4.1, the elastic constants of a material can be obtained by the elastic response of the ... dynamic elastic constants. When one measures the elastic response of a material to external static forces, work is done and heat ... thermal equilibrium with its surroundings, which can be considered as a heat reservoir. In this case, the measured elastic constants ...
Tetragonal crystals (classes , , )
International Tables for Crystallography (2013). Vol. D, Section 1.3.4.5.3, pp. 87-88 [ doi:10.1107/97809553602060000902 ]
Tetragonal crystals (classes , , ) 1.3.4.5.3. Tetragonal crystals (classes , , ) In tetragonal crystals, there are six independent elastic stiffnesses, , , , , and (Section 1.1.4.10.4 ). (i) The wavevector is parallel to [001]. The Christoffel determinant reduces to The three solutions are given in Table 1.3.4.6. Table 1.3.4.6| | Velocity of propagation when the wavevector is parallel ...
Hexagonal crystals
International Tables for Crystallography (2013). Vol. D, Section 1.3.4.5.2, p. 87 [ doi:10.1107/97809553602060000902 ]
Hexagonal crystals 1.3.4.5.2. Hexagonal crystals In hexagonal crystals, there are five independent elastic stiffnesses, , , , , and (Section 1.1.4.10.4 ). (i) The wavevector is parallel to [001]. The Christoffel determinant reduces to The solutions are given in Table 1.3.4.4. Table 1.3.4.4| | Velocity of propagation when the wavevector is parallel to [001] (hexagonal ...
Cubic crystals
International Tables for Crystallography (2013). Vol. D, Section 1.3.4.5.1, p. 87 [ doi:10.1107/97809553602060000902 ]
... are given in Table 1.3.4.1. These results are valid for a wave propagating in any direction in an isotropic medium. Table ...
Relation between velocity of propagation and elastic stiffnesses
International Tables for Crystallography (2013). Vol. D, Section 1.3.4.5, pp. 87-88 [ doi:10.1107/97809553602060000902 ]
... are given in Table 1.3.4.1. These results are valid for a wave propagating in any direction in an isotropic medium. Table ...
Polarization of the elastic waves
International Tables for Crystallography (2013). Vol. D, Section 1.3.4.4, p. 87 [ doi:10.1107/97809553602060000902 ]
Polarization of the elastic waves 1.3.4.4. Polarization of the elastic waves The Christoffel determinant has three roots and the Christoffel matrix, being Hermitian with real coefficients, has three real eigenvalues and three orthogonal eigenvectors. The wavevector q, therefore, encompasses three waves with vibration vectors , , which are perpendicular to one another. In ...
Dynamic elastic stiffnesses
International Tables for Crystallography (2013). Vol. D, Section 1.3.4.3, pp. 86-87 [ doi:10.1107/97809553602060000902 ]
... stiffnesses Equation (1.3.4.7) may be written This shows that in a dynamic process only the sums can be measured and not ...
International Tables for Crystallography (2013). Vol. D, Section 1.3.4, pp. 86-89 [ doi:10.1107/97809553602060000902 ]
... the past, although the measurements could not be very precise. A way of proceeding frequently used now is to excite a mechanical wave in the crystal and measure its propagation velocity or the wavelength associated with a particular frequency. One method consists in sending a train ...
Resonance technique
International Tables for Crystallography (2013). Vol. D, Section 1.3.4.6.2, p. 88 [ doi:10.1107/97809553602060000902 ]
... 1.3.4.6.2. Resonance technique The use of the resonance technique is a well established approach for determining the velocity of sound in a gas by observing nodes and antinodes of a system of standing waves produced in the so-called ...
Introduction
International Tables for Crystallography (2013). Vol. D, Section 1.3.4.6.1, p. 88 [ doi:10.1107/97809553602060000902 ]
... Introduction As mentioned in Section 1.3.4.1, the elastic constants of a material can be obtained by the elastic response of the ... dynamic elastic constants. When one measures the elastic response of a material to external static forces, work is done and heat ... thermal equilibrium with its surroundings, which can be considered as a heat reservoir. In this case, the measured elastic constants ...
Experimental determination of elastic constants
International Tables for Crystallography (2013). Vol. D, Section 1.3.4.6, pp. 88-89 [ doi:10.1107/97809553602060000902 ]
... Introduction | | As mentioned in Section 1.3.4.1, the elastic constants of a material can be obtained by the elastic response of the ... dynamic elastic constants. When one measures the elastic response of a material to external static forces, work is done and heat ... thermal equilibrium with its surroundings, which can be considered as a heat reservoir. In this case, the measured elastic constants ...
Tetragonal crystals (classes , , )
International Tables for Crystallography (2013). Vol. D, Section 1.3.4.5.3, pp. 87-88 [ doi:10.1107/97809553602060000902 ]
Tetragonal crystals (classes , , ) 1.3.4.5.3. Tetragonal crystals (classes , , ) In tetragonal crystals, there are six independent elastic stiffnesses, , , , , and (Section 1.1.4.10.4 ). (i) The wavevector is parallel to [001]. The Christoffel determinant reduces to The three solutions are given in Table 1.3.4.6. Table 1.3.4.6| | Velocity of propagation when the wavevector is parallel ...
Hexagonal crystals
International Tables for Crystallography (2013). Vol. D, Section 1.3.4.5.2, p. 87 [ doi:10.1107/97809553602060000902 ]
Hexagonal crystals 1.3.4.5.2. Hexagonal crystals In hexagonal crystals, there are five independent elastic stiffnesses, , , , , and (Section 1.1.4.10.4 ). (i) The wavevector is parallel to [001]. The Christoffel determinant reduces to The solutions are given in Table 1.3.4.4. Table 1.3.4.4| | Velocity of propagation when the wavevector is parallel to [001] (hexagonal ...
Cubic crystals
International Tables for Crystallography (2013). Vol. D, Section 1.3.4.5.1, p. 87 [ doi:10.1107/97809553602060000902 ]
... are given in Table 1.3.4.1. These results are valid for a wave propagating in any direction in an isotropic medium. Table ...
Relation between velocity of propagation and elastic stiffnesses
International Tables for Crystallography (2013). Vol. D, Section 1.3.4.5, pp. 87-88 [ doi:10.1107/97809553602060000902 ]
... are given in Table 1.3.4.1. These results are valid for a wave propagating in any direction in an isotropic medium. Table ...
Polarization of the elastic waves
International Tables for Crystallography (2013). Vol. D, Section 1.3.4.4, p. 87 [ doi:10.1107/97809553602060000902 ]
Polarization of the elastic waves 1.3.4.4. Polarization of the elastic waves The Christoffel determinant has three roots and the Christoffel matrix, being Hermitian with real coefficients, has three real eigenvalues and three orthogonal eigenvectors. The wavevector q, therefore, encompasses three waves with vibration vectors , , which are perpendicular to one another. In ...
Dynamic elastic stiffnesses
International Tables for Crystallography (2013). Vol. D, Section 1.3.4.3, pp. 86-87 [ doi:10.1107/97809553602060000902 ]
... stiffnesses Equation (1.3.4.7) may be written This shows that in a dynamic process only the sums can be measured and not ...
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