Acta Crystallographica Section A Foundations and Advances, 2015
The affine and Euclidean normalizers of the subperiodic groups, the frieze groups, the rod groups... more The affine and Euclidean normalizers of the subperiodic groups, the frieze groups, the rod groups and the layer groups, are derived and listed. For the layer groups, the special metrics used for plane-group Euclidean normalizers have been considered.
Acta Crystallographica Section A Foundations and Advances, 2015
Tables of the scanning of two-dimensional space groups are presented to determine the frieze-grou... more Tables of the scanning of two-dimensional space groups are presented to determine the frieze-group symmetry of lines that transect two-dimensional crystals. It is shown how these tables can be used to predict the (001) projection symmetries of migration-related segments of coincidence site lattice tilt boundaries with [001] tilt axis.
Acta Crystallographica Section A Foundations and Advances, 2014
The form of physical property tensors of a quasi-one-dimensional material such as a nanotube or a... more The form of physical property tensors of a quasi-one-dimensional material such as a nanotube or a polymer can be determined from the point group of its symmetry group, one of aninfinitenumber of line groups. Such forms are calculated using a method based on the use of trigonometric summations. With this method, it is shown that materials invariant under infinite subsets of line groups have physical property tensors of the same form. For line group types of a family of line groups characterized by an indexnand a physical property tensor of rankm, the form of the tensor for all line group types indexed withn>mis the same, leaving only afinitenumber of tensor forms to be determined.
Acta Crystallographica Section A Foundations and Advances, 2014
The physical property coefficients that arise in a phase transition which are zero in the high-sy... more The physical property coefficients that arise in a phase transition which are zero in the high-symmetry phase and nonzero in the low-symmetry phase are calledspontaneous coefficients. For all 1601 Aizu species of phase transitions, matrices have been constructed which show the nonzero coefficients of a wide variety of magnetic and nonmagnetic physical properties including toroidal property coefficients in the high-symmetry phase and their corresponding spontaneous coefficients in the low-symmetry phase. It is also shown that these spontaneous coefficients provide for the distinction of and switching between nonferroelastic domain pairs.
Acta Crystallographica Section A Foundations and Advances, 2014
This paper presents crystallographic data of double antisymmetry space groups, including symmetry... more This paper presents crystallographic data of double antisymmetry space groups, including symmetry-element diagrams, general-position diagrams and positions, with multiplicities, site symmetries, coordinates, spin vectors, roto vectors and displacement vectors.
Acta Crystallographica Section A Foundations and Advances, 2015
The affine and Euclidean normalizers of the subperiodic groups, the frieze groups, the rod groups... more The affine and Euclidean normalizers of the subperiodic groups, the frieze groups, the rod groups and the layer groups, are derived and listed. For the layer groups, the special metrics used for plane-group Euclidean normalizers have been considered.
Acta Crystallographica Section A Foundations and Advances, 2015
Tables of the scanning of two-dimensional space groups are presented to determine the frieze-grou... more Tables of the scanning of two-dimensional space groups are presented to determine the frieze-group symmetry of lines that transect two-dimensional crystals. It is shown how these tables can be used to predict the (001) projection symmetries of migration-related segments of coincidence site lattice tilt boundaries with [001] tilt axis.
Acta Crystallographica Section A Foundations and Advances, 2014
The form of physical property tensors of a quasi-one-dimensional material such as a nanotube or a... more The form of physical property tensors of a quasi-one-dimensional material such as a nanotube or a polymer can be determined from the point group of its symmetry group, one of aninfinitenumber of line groups. Such forms are calculated using a method based on the use of trigonometric summations. With this method, it is shown that materials invariant under infinite subsets of line groups have physical property tensors of the same form. For line group types of a family of line groups characterized by an indexnand a physical property tensor of rankm, the form of the tensor for all line group types indexed withn>mis the same, leaving only afinitenumber of tensor forms to be determined.
Acta Crystallographica Section A Foundations and Advances, 2014
The physical property coefficients that arise in a phase transition which are zero in the high-sy... more The physical property coefficients that arise in a phase transition which are zero in the high-symmetry phase and nonzero in the low-symmetry phase are calledspontaneous coefficients. For all 1601 Aizu species of phase transitions, matrices have been constructed which show the nonzero coefficients of a wide variety of magnetic and nonmagnetic physical properties including toroidal property coefficients in the high-symmetry phase and their corresponding spontaneous coefficients in the low-symmetry phase. It is also shown that these spontaneous coefficients provide for the distinction of and switching between nonferroelastic domain pairs.
Acta Crystallographica Section A Foundations and Advances, 2014
This paper presents crystallographic data of double antisymmetry space groups, including symmetry... more This paper presents crystallographic data of double antisymmetry space groups, including symmetry-element diagrams, general-position diagrams and positions, with multiplicities, site symmetries, coordinates, spin vectors, roto vectors and displacement vectors.
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Papers by Daniel Litvin