Abstract
A user-friendly web-based software tool called 'ISOTILT' is introduced for detecting cooperative rigid-unit modes (RUMs) in networks of interconnected rigid units (e.g. molecules, clusters or polyhedral units). This tool implements a recently described algorithm in which symmetry-mode patterns of pivot-atom rotation and displacement vectors are used to construct a linear system of equations whose null space consists entirely of RUMs. The symmetry modes are first separated into independent symmetry-mode blocks and the set of equations for each block is solved separately by singular value decomposition. ISOTILT is the newest member of the ISOTROPY Software Suite. Here, it is shown how to prepare structural and symmetry-mode information for use in ISOTILT, how to use each of ISOTILT's input fields and options, and how to use and interpret ISOTILT output.
Highlights
In a material whose crystal structure consists of or includes an interconnected network of rigid units, the identification of possible cooperative rigid-unit modes (RUMs) is important for understanding and controlling its phase transitions, phonon dynamics and structure-sensitive physical properties
Our present objective is to introduce the user-friendly and web-based ISOTILT software tool, which implements the linear-algebraic RUM-search algorithm and its improvements reported by Campbell et al (2018, 2021)
Because each of the hexagonal tungsten bronze (HTB), tungsten bronze (TTB) and CAZO examples involve hundreds of symmetry modes, their ISOTILT outputs are too long to be displayed here, but they are available in the supporting information (SI), along with the corresponding parent CIFs
Summary
In a material whose crystal structure consists of or includes an interconnected network of rigid units (e.g. molecules, clusters or polyhedral units), the identification of possible cooperative rigid-unit modes (RUMs) is important for understanding and controlling its phase transitions, phonon dynamics and structure-sensitive physical properties. Campbell et al (2021) described a series of critical improvements to the original algorithm based on the observation that the split-passenger-atom-displacement pattern arising from a rotational symmetry mode belonging to a given irrep is a symmetry mode of that same irrep, so that such patterns enjoy special orthogonality properties. This means that the split-passenger-atom-displacement patterns arising from distinct irreps, or even from different components of the OPD of the same irrep, must be linearly independent.
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