The <i>ISOTILT</i> software for discovering cooperative rigid-unit rotations in networks of interconnected rigid units

Campbell, Branton J.; Stokes, Harold T.; Averett, Tyler B.; Machlus, Shae; Yost, Christopher

doi:10.1107/s1600576721009353

Cited by 3 publications

(1 citation statement)

References 20 publications

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“…It can be seen that all octahedra in the structure display the same angle of tilt, as we now believe to be favoured. It is now possible to confirm that structure using the computer program ISOTILT (Campbell et al, 2018(Campbell et al, , 2021. ISOTILT finds two acceptable modes of tilting (rigid unit modes) associated with irrep S 3 (a,0,0,0), which in one certain combination have all the octahedra display (very nearly) the same angle of tilt; in this way, the structure from Whittle et al (2015), here Fig.…”

Section: The Probable Structure Of Bnn At Room Temperaturementioning

confidence: 83%

Structures and phase transitions in barium sodium niobate tungsten bronze (BNN)

Whittle¹,

Howard²,

Schmid³

2021

Acta Crystallogr Sect B

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The room-temperature structure of the filled tetragonal tungsten bronze, Ba2NaNb5O15 (BNN), has been the subject of a number of studies, and these studies have given an almost corresponding number of different results. From a group theoretical examination of the different possibilities and a review of the published experimental results we conclude that the room-temperature structure is that proposed by Labbé et al. [J. Phys. Condens. Matter (1989), 2, 25–43] in the space group Bbm2 (Ama2 in standard setting) on a 2\sqrt{2}a × \sqrt{2}a × 2c cell. Upon heating, the structure remains ferroelectric but becomes tetragonal (space group P4bm) at 550 K, then paraelectric (space group P4/mbm) at and above 860 K.

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Section: The Probable Structure Of Bnn At Room Temperaturementioning

confidence: 83%

Structures and phase transitions in barium sodium niobate tungsten bronze (BNN)

Whittle¹,

Howard²,

Schmid³

2021

Acta Crystallogr Sect B

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Theoretical and computational improvements to the algebraic method for discovering cooperative rigid-unit modes

Campbell¹,

Stokes²,

Averett³

et al. 2021

J Appl Cryst

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A linear-algebraic algorithm for identifying rigid-unit modes in networks of interconnected rigid units has recently been demonstrated. This article presents a series of enhancements to the original algorithm, which greatly improve its conceptual simplicity, numerical robustness, computational efficiency and interpretability. The improvements include the efficient isolation of constraints, the observation of variable-block separability, the use of singular value decomposition and a quantitative measure of solution inexactness.

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SUBGROUPS: a computer tool at the Bilbao Crystallographic Server for the study of pseudo-symmetric or distorted structures

Tasci,

Elcoro,

Perez-Mato

et al. 2024

J Appl Crystallogr

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SUBGROUPS is a free online program at the Bilbao Crystallographic Server (https://www.cryst.ehu.es/). It permits the exploration of all possible symmetries resulting from the distortion of a higher-symmetry parent structure, provided that the relation between the lattices of the distorted and parent structures is known. The program calculates all the subgroups of the parent space group which comply with this relation. The required minimal input is the space-group information of the parent structure and the relation of the unit cell of the distorted or pseudo-symmetric structure with that of the parent structure. Alternatively, the wavevector(s) observed in the diffraction data characterizing the distortion can be introduced. Additional conditions can be added, including filters related to space-group representations. The program provides very detailed information on all the subgroups, including group–subgroup hierarchy graphs. If a Crystallographic Information Framework (CIF) file of the parent high-symmetry structure is uploaded, the program generates CIF files of the parent structure described under each of the chosen lower symmetries. These CIF files may then be used as starting points for the refinement of the distorted structure under these possible symmetries. They can also be used for density functional theory calculations or for any other type of analysis. The power and efficiency of the program are illustrated with a few examples.

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The ISOTILT software for discovering cooperative rigid-unit rotations in networks of interconnected rigid units

Cited by 3 publications

References 20 publications

Structures and phase transitions in barium sodium niobate tungsten bronze (BNN)

Structures and phase transitions in barium sodium niobate tungsten bronze (BNN)

Theoretical and computational improvements to the algebraic method for discovering cooperative rigid-unit modes

SUBGROUPS: a computer tool at the Bilbao Crystallographic Server for the study of pseudo-symmetric or distorted structures

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