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Results for DC.creator="B." AND DC.creator="Gruber" in section 3.1.4 of volume A |
Sublattices
International Tables for Crystallography (2016). Vol. A, Section 3.1.4.6, p. 718 [ doi:10.1107/97809553602060000929 ]
... construct explicitly the matrices fulfilling (3.1.4.4). The following formulae (Gruber, 1997b) can be used: (i) If , where is a prime ... 3.1.4.5 were a square, the sublattices in cases (a) and (b) would have the same symmetry (though being different subsets of ... Introduction to the Geometry of Numbers, p. 13. Berlin: Springer. Gruber, B. (1997b). Alternative formulae for the number of ...
Conventional characters
International Tables for Crystallography (2016). Vol. A, Section 3.1.4.5, pp. 717-718 [ doi:10.1107/97809553602060000929 ]
Conventional characters 3.1.4.5. Conventional characters Lattice characters were defined in Section 3.1.4.2 by dividing the Niggli image of a certain Bravais type into components. Doing the same - instead of with the Niggli points - with the parameters of conventional cells7 of lattices of the Bravais type we obtain a division of the ...
Conventional cells
International Tables for Crystallography (2016). Vol. A, Section 3.1.4.4, pp. 715-717 [ doi:10.1107/97809553602060000929 ]
... type if and only if there exists a cell (a, b, c) in L such that (i) the centring of (a, b, c) agrees with the centring mode given in column 2 ... aP. Bravais type of latticeCentring mode of the cell (a, b, c)ConditionsLimiting casesConventional basis (a', b', c') for limiting ...
Further properties of lattices
International Tables for Crystallography (2016). Vol. A, Section 3.1.4, pp. 714-718 [ doi:10.1107/97809553602060000929 ]
... cell3 - have significant geometrical features based mainly on extremal principles (Gruber, 1989). We shall describe some of them below. If ... types and that an exact general definition does not exist. Gruber (1992) tried to base such a definition on topological concepts. ... L. It is the point provided that the vectors a, b, c describe the Niggli cell of L and fulfil ...
Topological characterization of lattice characters
International Tables for Crystallography (2016). Vol. A, Section 3.1.4.2, pp. 714-715 [ doi:10.1107/97809553602060000929 ]
... types and that an exact general definition does not exist. Gruber (1992) tried to base such a definition on topological concepts. ... L. It is the point provided that the vectors a, b, c describe the Niggli cell of L and fulfil the ... of Table 3.1.3.1 or by Tables 1 and 3 in Gruber (1992)] by perpendicular projection of the c vector onto ...
Further kinds of reduced cells
International Tables for Crystallography (2016). Vol. A, Section 3.1.4.1, p. 714 [ doi:10.1107/97809553602060000929 ]
... cell3 - have significant geometrical features based mainly on extremal principles (Gruber, 1989). We shall describe some of them below. If ... auf ihre tabellarische Berechung. J. Math. (Crelle), 41, 141-190. Gruber, B. (1989). Reduced cells based on extremal principles. Acta ...
A finer division of lattices
International Tables for Crystallography (2016). Vol. A, Section 3.1.4.3, p. 715 [ doi:10.1107/97809553602060000929 ]
... subdivision be crystallographically meaningful. Such a division was proposed by Gruber (1997a). It uses the fact that the Niggli points ... Henry & K. Lonsdale, pp. 530-535. Birmingham: Kynoch Press. Delaunay, B. N. (1933). Neuere Darstellung der geometrischen Kristallographie. Z. Kristallogr. 84, 109-149. Gruber, B. (1997a). Classification of lattices: a new step. ...
International Tables for Crystallography (2016). Vol. A, Section 3.1.4.6, p. 718 [ doi:10.1107/97809553602060000929 ]
... construct explicitly the matrices fulfilling (3.1.4.4). The following formulae (Gruber, 1997b) can be used: (i) If , where is a prime ... 3.1.4.5 were a square, the sublattices in cases (a) and (b) would have the same symmetry (though being different subsets of ... Introduction to the Geometry of Numbers, p. 13. Berlin: Springer. Gruber, B. (1997b). Alternative formulae for the number of ...
Conventional characters
International Tables for Crystallography (2016). Vol. A, Section 3.1.4.5, pp. 717-718 [ doi:10.1107/97809553602060000929 ]
Conventional characters 3.1.4.5. Conventional characters Lattice characters were defined in Section 3.1.4.2 by dividing the Niggli image of a certain Bravais type into components. Doing the same - instead of with the Niggli points - with the parameters of conventional cells7 of lattices of the Bravais type we obtain a division of the ...
Conventional cells
International Tables for Crystallography (2016). Vol. A, Section 3.1.4.4, pp. 715-717 [ doi:10.1107/97809553602060000929 ]
... type if and only if there exists a cell (a, b, c) in L such that (i) the centring of (a, b, c) agrees with the centring mode given in column 2 ... aP. Bravais type of latticeCentring mode of the cell (a, b, c)ConditionsLimiting casesConventional basis (a', b', c') for limiting ...
Further properties of lattices
International Tables for Crystallography (2016). Vol. A, Section 3.1.4, pp. 714-718 [ doi:10.1107/97809553602060000929 ]
... cell3 - have significant geometrical features based mainly on extremal principles (Gruber, 1989). We shall describe some of them below. If ... types and that an exact general definition does not exist. Gruber (1992) tried to base such a definition on topological concepts. ... L. It is the point provided that the vectors a, b, c describe the Niggli cell of L and fulfil ...
Topological characterization of lattice characters
International Tables for Crystallography (2016). Vol. A, Section 3.1.4.2, pp. 714-715 [ doi:10.1107/97809553602060000929 ]
... types and that an exact general definition does not exist. Gruber (1992) tried to base such a definition on topological concepts. ... L. It is the point provided that the vectors a, b, c describe the Niggli cell of L and fulfil the ... of Table 3.1.3.1 or by Tables 1 and 3 in Gruber (1992)] by perpendicular projection of the c vector onto ...
Further kinds of reduced cells
International Tables for Crystallography (2016). Vol. A, Section 3.1.4.1, p. 714 [ doi:10.1107/97809553602060000929 ]
... cell3 - have significant geometrical features based mainly on extremal principles (Gruber, 1989). We shall describe some of them below. If ... auf ihre tabellarische Berechung. J. Math. (Crelle), 41, 141-190. Gruber, B. (1989). Reduced cells based on extremal principles. Acta ...
A finer division of lattices
International Tables for Crystallography (2016). Vol. A, Section 3.1.4.3, p. 715 [ doi:10.1107/97809553602060000929 ]
... subdivision be crystallographically meaningful. Such a division was proposed by Gruber (1997a). It uses the fact that the Niggli points ... Henry & K. Lonsdale, pp. 530-535. Birmingham: Kynoch Press. Delaunay, B. N. (1933). Neuere Darstellung der geometrischen Kristallographie. Z. Kristallogr. 84, 109-149. Gruber, B. (1997a). Classification of lattices: a new step. ...
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