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Tensors
International Tables for Crystallography (2013). Vol. D, Section 1.10.4, pp. 253-262 [ doi:10.1107/97809553602060000909 ]
... is the group of nonsingular integer matrices S satisfying where T means the transpose. For a lattice corresponding to a quasiperiodic ... tensor of elastic stiffnesses c gives the relation between stress T and strain S. The stress tensor is a physical tensor ... . The tensor is zero. Other examples are given in Janssen (1997). 1.10.4.5.2. Elasticity tensor | | (See Section 1.3.3.2 .) ...
Piezoelectric tensor for a three-dimensional octagonal quasicrystal
International Tables for Crystallography (2013). Vol. D, Section 1.10.4.6.4, pp. 258-259 [ doi:10.1107/97809553602060000909 ]
Piezoelectric tensor for a three-dimensional octagonal quasicrystal 1.10.4.6.4. Piezoelectric tensor for a three-dimensional octagonal quasicrystal A quasicrystal with octagonal point group 8/mmm(831mm) will not show a piezoelectric effect because the point group contains the central inversion. We consider here the point group 8mm(83mm) which is a ...
Elasticity tensor for a two-dimensional octagonal quasicrystal
International Tables for Crystallography (2013). Vol. D, Section 1.10.4.6.3, pp. 257-258 [ doi:10.1107/97809553602060000909 ]
Elasticity tensor for a two-dimensional octagonal quasicrystal 1.10.4.6.3. Elasticity tensor for a two-dimensional octagonal quasicrystal The point group of the standard octagonal tiling is generated by the 2D orthogonal matrices In the tensor space one has the following transformations of the basis vectors; they are denoted by ij for ...
EFG tensor for Pcmn
International Tables for Crystallography (2013). Vol. D, Section 1.10.4.6.2, p. 257 [ doi:10.1107/97809553602060000909 ]
EFG tensor for Pcmn 1.10.4.6.2. EFG tensor for Pcmn The electric field gradient tensor transforms as the product of a reciprocal vector and a vector. In Cartesian coordinates the transformation properties are the same. The point group for the basic structure of many IC phases of the family of A2BX4 compounds ...
Metric tensor for an octagonal three-dimensional quasicrystal
International Tables for Crystallography (2013). Vol. D, Section 1.10.4.6.1, p. 257 [ doi:10.1107/97809553602060000909 ]
Metric tensor for an octagonal three-dimensional quasicrystal 1.10.4.6.1. Metric tensor for an octagonal three-dimensional quasicrystal From the Fourier module for an octagonal quasicrystal in 3D the generators of the point group can be expressed as 5D integer matrices. They are and and span an integer representation of the point ...
Determining the independent tensor elements
International Tables for Crystallography (2013). Vol. D, Section 1.10.4.6, pp. 257-262 [ doi:10.1107/97809553602060000909 ]
Determining the independent tensor elements 1.10.4.6. Determining the independent tensor elements In the previous sections some physical tensors have been studied, for which in a number of cases the number of the independent tensor elements has been determined. In this section the problem of determining the invariant tensor elements themselves will ...
Electric field gradient tensor
International Tables for Crystallography (2013). Vol. D, Section 1.10.4.5.3, pp. 256-257 [ doi:10.1107/97809553602060000909 ]
Electric field gradient tensor 1.10.4.5.3. Electric field gradient tensor As an example, we consider a rank-two tensor, e.g. an electric field gradient tensor, in a system with superspace-group symmetry Pcmn(00[gamma])1s. The Fourier transform of the tensor is nonzero only for multiples of the vector (including zero ...
Elasticity tensor
International Tables for Crystallography (2013). Vol. D, Section 1.10.4.5.2, p. 256 [ doi:10.1107/97809553602060000909 ]
... theory of quasicrystals. Phys. Rev. B, 48, 7003-7010. Lubensky, T. C., Ramaswamy, S. & Toner, J. (1985). Hydrodynamics of icosahedral ... Rev. B, 32, 7444-7452. Socolar, J. E. S., Lubensky, T. C. & Steinhardt, P. J. (1986). Phonons, phasons and dislocations ...
Piezoelectric tensor
International Tables for Crystallography (2013). Vol. D, Section 1.10.4.5.1, pp. 255-256 [ doi:10.1107/97809553602060000909 ]
... . The tensor is zero. Other examples are given in Janssen (1997). References Janssen, T. (1997). Tensor properties of incommensurate phases. Ferroelectrics, 203, ...
Determining the number of independent tensor elements
International Tables for Crystallography (2013). Vol. D, Section 1.10.4.5, pp. 255-257 [ doi:10.1107/97809553602060000909 ]
... . The tensor is zero. Other examples are given in Janssen (1997). 1.10.4.5.2. Elasticity tensor | | (See Section 1.3.3.2 .) As ... elasticity theory of quasicrystals. Phys. Rev. B, 48, 7003-7010. Janssen, T. (1997). Tensor properties of incommensurate phases. Ferroelectrics, 203, ...
International Tables for Crystallography (2013). Vol. D, Section 1.10.4, pp. 253-262 [ doi:10.1107/97809553602060000909 ]
... is the group of nonsingular integer matrices S satisfying where T means the transpose. For a lattice corresponding to a quasiperiodic ... tensor of elastic stiffnesses c gives the relation between stress T and strain S. The stress tensor is a physical tensor ... . The tensor is zero. Other examples are given in Janssen (1997). 1.10.4.5.2. Elasticity tensor | | (See Section 1.3.3.2 .) ...
Piezoelectric tensor for a three-dimensional octagonal quasicrystal
International Tables for Crystallography (2013). Vol. D, Section 1.10.4.6.4, pp. 258-259 [ doi:10.1107/97809553602060000909 ]
Piezoelectric tensor for a three-dimensional octagonal quasicrystal 1.10.4.6.4. Piezoelectric tensor for a three-dimensional octagonal quasicrystal A quasicrystal with octagonal point group 8/mmm(831mm) will not show a piezoelectric effect because the point group contains the central inversion. We consider here the point group 8mm(83mm) which is a ...
Elasticity tensor for a two-dimensional octagonal quasicrystal
International Tables for Crystallography (2013). Vol. D, Section 1.10.4.6.3, pp. 257-258 [ doi:10.1107/97809553602060000909 ]
Elasticity tensor for a two-dimensional octagonal quasicrystal 1.10.4.6.3. Elasticity tensor for a two-dimensional octagonal quasicrystal The point group of the standard octagonal tiling is generated by the 2D orthogonal matrices In the tensor space one has the following transformations of the basis vectors; they are denoted by ij for ...
EFG tensor for Pcmn
International Tables for Crystallography (2013). Vol. D, Section 1.10.4.6.2, p. 257 [ doi:10.1107/97809553602060000909 ]
EFG tensor for Pcmn 1.10.4.6.2. EFG tensor for Pcmn The electric field gradient tensor transforms as the product of a reciprocal vector and a vector. In Cartesian coordinates the transformation properties are the same. The point group for the basic structure of many IC phases of the family of A2BX4 compounds ...
Metric tensor for an octagonal three-dimensional quasicrystal
International Tables for Crystallography (2013). Vol. D, Section 1.10.4.6.1, p. 257 [ doi:10.1107/97809553602060000909 ]
Metric tensor for an octagonal three-dimensional quasicrystal 1.10.4.6.1. Metric tensor for an octagonal three-dimensional quasicrystal From the Fourier module for an octagonal quasicrystal in 3D the generators of the point group can be expressed as 5D integer matrices. They are and and span an integer representation of the point ...
Determining the independent tensor elements
International Tables for Crystallography (2013). Vol. D, Section 1.10.4.6, pp. 257-262 [ doi:10.1107/97809553602060000909 ]
Determining the independent tensor elements 1.10.4.6. Determining the independent tensor elements In the previous sections some physical tensors have been studied, for which in a number of cases the number of the independent tensor elements has been determined. In this section the problem of determining the invariant tensor elements themselves will ...
Electric field gradient tensor
International Tables for Crystallography (2013). Vol. D, Section 1.10.4.5.3, pp. 256-257 [ doi:10.1107/97809553602060000909 ]
Electric field gradient tensor 1.10.4.5.3. Electric field gradient tensor As an example, we consider a rank-two tensor, e.g. an electric field gradient tensor, in a system with superspace-group symmetry Pcmn(00[gamma])1s. The Fourier transform of the tensor is nonzero only for multiples of the vector (including zero ...
Elasticity tensor
International Tables for Crystallography (2013). Vol. D, Section 1.10.4.5.2, p. 256 [ doi:10.1107/97809553602060000909 ]
... theory of quasicrystals. Phys. Rev. B, 48, 7003-7010. Lubensky, T. C., Ramaswamy, S. & Toner, J. (1985). Hydrodynamics of icosahedral ... Rev. B, 32, 7444-7452. Socolar, J. E. S., Lubensky, T. C. & Steinhardt, P. J. (1986). Phonons, phasons and dislocations ...
Piezoelectric tensor
International Tables for Crystallography (2013). Vol. D, Section 1.10.4.5.1, pp. 255-256 [ doi:10.1107/97809553602060000909 ]
... . The tensor is zero. Other examples are given in Janssen (1997). References Janssen, T. (1997). Tensor properties of incommensurate phases. Ferroelectrics, 203, ...
Determining the number of independent tensor elements
International Tables for Crystallography (2013). Vol. D, Section 1.10.4.5, pp. 255-257 [ doi:10.1107/97809553602060000909 ]
... . The tensor is zero. Other examples are given in Janssen (1997). 1.10.4.5.2. Elasticity tensor | | (See Section 1.3.3.2 .) As ... elasticity theory of quasicrystals. Phys. Rev. B, 48, 7003-7010. Janssen, T. (1997). Tensor properties of incommensurate phases. Ferroelectrics, 203, ...
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