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VERSION:2.0
PRODID:-//University of Liverpool Computer Science Seminar System//v2//EN
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DTSTAMP:20260922T101400Z
UID:Seminar-MIF-1397@lxserverM.csc.liv.ac.uk
ORGANIZER:CN=Othon Michail:MAILTO:Othon.Michail@liverpool.ac.uk
DTSTART:20221216T140000
DTEND:20221216T150000
SUMMARY:MIF Series
DESCRIPTION:Semen Gorfman: The algorithms of target transformation of basis vectors of crystal lattice.\n\nThe crystal lattice is the mathematical object that describes the long-range order (three-dimensional periodicity) of crystal structures. The lattice is set by non-coplanar vectors (also known as basis vectors), whose linear combinations with the integer coordinates describe the position of individual lattice points. While the lattice parameters (the lengths and the angles between the basis vectors) are often used as one of the fingerprints of a crystal structure, the choice of basis vectors is not ambiguous. Specifically, one and the same lattice can be created by an infinitely large number of sets of basis vectors. Transformation of basis vectors is the key mathematical operation that appears to be useful for the comparison of polymorphs crystal structures, phase transitions analysis, the understanding of twinning laws, indexing of X-ray diffraction peaks, and lattice reduction. While such operations are often built into larger computer programs and serve as only small blocks, the need for stand-alone algorithms of specific transformation of basis vectors of a crystal lattice still exist. The goal of this presentation is to introduce a simple numerical approach for the transformation of lattice basis vectors to a specific target: in the first case, one of the new basis vectors is aligned to a predefined lattice direction. In the second case (for a three-dimensional lattice) two of the basis vectors are brought to the lattice “plane” with specific Miller indices. Two, three and multidimensional versions of the algorithms will be presented. The applications for the simulation of zone planes and the transformation of a unit cell setting will be shown.\n\nhttps://www.csc.liv.ac.uk/research/seminars/abstract.php?id=1397
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