Partial order among the 14 Bravais types of lattices: basics and applications

Grimmer, H.

doi:10.1107/s2053273314027351

Cited by 10 publications

(16 citation statements)

References 12 publications

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“…It is often assumed, see e.g. Grimmer (2015), that the small monoclinic distortions of the crystal structure of -Fe 2 O 3 observed at room temperature are due to the magnetic ordering. This idea is in agreement with the Landau description of phase transitions (Landau & Lifschitz, 1969) assuming that the symmetry of the paramagnetic phase (at high temperature) and the symmetry of the magnetically ordered phase (at low temperature) should show a group-subgroup relation.…”

Section: Introductionmentioning

confidence: 99%

Deformations of the α-Fe₂O₃ rhombohedral lattice across the Néel temperature

Fabrykiewicz

Stękiel

Sosnowska

et al. 2017

Acta Crystallogr B Struct Sci Cryst Eng Mater

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High-resolution synchrotron radiation powder diffraction patterns of -Fe 2 O 3 measured between room temperature and 1100 K, i.e. above the Né el temperature T N = 950 K, have been analyzed. The integral breadths of the Bragg peaks show a hkl-dependent anisotropy, both below and above T N . This anisotropy can be quantitatively described by using a statistical peakbroadening model [Stephens (1999). J. Appl. Cryst. 32, 281]. Model calculations show that the rhombohedral -Fe 2 O 3 lattice is deformed and the deformation leads to a monoclinic lattice with the unique monoclinic axis along the hexagonal [110] direction both below and above T N . The monoclinic symmetry of bulk -Fe 2 O 3 is compatible with -Fe 2 O 3 nanowire growth along the [110] direction reported in Fu et al.

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Section: Introductionmentioning

confidence: 99%

Deformations of the α-Fe₂O₃ rhombohedral lattice across the Néel temperature

Fabrykiewicz

Stękiel

Sosnowska

et al. 2017

Acta Crystallogr B Struct Sci Cryst Eng Mater

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“…the specializations of the metric that promote the lattice symmetry to a higher holohedry. These specializations have recently been reviewed in great detail by Grimmer (2015); we give here just one example to emphasize how misleading are the metric restrictions frequently found in textbooks.…”

Section: Can the Lack Of Symmetry Impose Restrictions?mentioning

confidence: 99%

“…On the other hand, to exclude only the 90 for is not enough. If the cell parameters define a primitive unit cell and = cos À1 (Àa/2c), then the lattice is actually oB (orthorhombic with a B-centred cell, , then the lattice is actually hR (rhombohedral); if c 2 + 3b 2 = 9a 2 and c = À3a cos or a 2 + 3b 2 = 9c 2 and a = À3c cos , then the lattice is again hR (rhombohedral) (data from Table 9.4.3.1 in ITA9; unit cells of type mI, mC, mA and mF are all easily converted into each other so that the above conditions for mI can be transformed into the setting of any of the other three types of unit cell; see also Grimmer, 2015).…”

Section: Can the Lack Of Symmetry Impose Restrictions?mentioning

confidence: 99%

The ash heap of crystallography: restoring forgotten basic knowledge

Nespolo

2015

J Appl Cryst

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A critical analysis of some basic notions often overlooked in crystallographic education is presented to correct some common oversights occurring both in the literature and in textbooks. The crystal forms (face forms), defined in terms of their geometric eigensymmetry, are 47 in number, not 48 as often found in the literature. The split of the dihedron into dome and sphenoid calls for the consideration of the physical properties of the faces building a form; in that case, however, the same criterion should be used for all forms. By taking the handedness of the faces as representative of the physical properties of the faces, the occurrence of 130 crystallographic face forms (97 affine face forms and 33 enantiomorphic pairs) is demonstrated. Next, the correct use of non-coprime Miller indices when a centred unit cell is adopted is shown, and the inconsistent multiplication of Miller indices in the Bravais–Friedel–Donnay–Harker law is pointed out. A geometric derivation of the reflection conditions is reviewed. Finally, the inconsistent presentation of metric restrictions imposed by the structural symmetry is pointed out and corrected.

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“…Grimmer & Nespolo (2006) have studied the effects of metric specializations of lattices and collected the results in a path through Bravais types of lattice ( Fig. 3 therein); this has been reviewed and extended by Grimmer (2015), who analysed in detail the metric specializations leading to a higher lattice symmetry, and exploited by Nespolo et al (2014) to study the effect of merohedric twinning on the diffraction pattern.…”

Section: Non-standard Settings Of Space Groups: Alternative Settings mentioning

confidence: 99%

The crystallographic chameleon: when space groups change skin

Nespolo

Aroyo

2016

Acta Cryst Sect A

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Volume A of International Tables for Crystallography is the reference for space-group information. However, the content is not exhaustive because for many space groups a variety of settings may be chosen but not all of them are described in detail or even fully listed. The use of alternative settings may seem an unnecessary complication when the purpose is just to describe a crystal structure; however, these are of the utmost importance for a number of tasks, such as the investigation of structure relations between polymorphs or derivative structures, the study of pseudo-symmetry and its potential consequences, and the analysis of the common substructure of twins. The aim of the article is twofold: (i) to present a guide to expressing the symmetry operations, the Hermann-Mauguin symbols and the Wyckoff positions of a space group in an alternative setting, and (ii) to point to alternative settings of space groups of possible practical applications and not listed in Volume A of International Tables for Crystallography.

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Partial order among the 14 Bravais types of lattices: basics and applications

Cited by 10 publications

References 12 publications

Deformations of the α-Fe₂O₃ rhombohedral lattice across the Néel temperature

Deformations of the α-Fe₂O₃ rhombohedral lattice across the Néel temperature

The ash heap of crystallography: restoring forgotten basic knowledge

The crystallographic chameleon: when space groups change skin

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Partial order among the 14 Bravais types of lattices: basics and applications

Cited by 10 publications

References 12 publications

Deformations of the α-Fe2O3 rhombohedral lattice across the Néel temperature

Deformations of the α-Fe2O3 rhombohedral lattice across the Néel temperature

The ash heap of crystallography: restoring forgotten basic knowledge

The crystallographic chameleon: when space groups change skin

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Product

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Deformations of the α-Fe₂O₃ rhombohedral lattice across the Néel temperature

Deformations of the α-Fe₂O₃ rhombohedral lattice across the Néel temperature