Crystallographic Topology 2: Overview and Work in Progress

Conference · Sun Aug 01 00:00:00 EDT 1999

OSTI ID:4618

Johnson, C K

This overview describes an application of contemporary geometric topology and stochastic process concepts to structural crystallography. In this application, crystallographic groups become orbifolds, crystal structures become Morse functions on orbifolds, and vibrating atoms in a crystal become vector valued Gaussian measures with the Radon-Nikodym property. Intended crystallographic benefits include new methods for visualization of space groups and crystal structures, analysis of the thermal motion patterns seen in ORTEP drawings, and a classification scheme for crystal structures based on their Heegaard splitting properties.

• Research Organization: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE Office of Energy Research (ER) (US)
• DOE Contract Number: AC05-96OR22464
• OSTI ID: 4618
• Report Number(s): ORNL/CP-102063; TRN: AH200114%%233
• Resource Relation: Conference: Conference on Trends in Mathematical Physics, Knoxville, TN (US), 08/1998; Other Information: PBD: 1 Aug 1999
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
ATOMS
CLASSIFICATION
CRYSTAL STRUCTURE
CRYSTALLOGRAPHY
PHYSICS
SPACE GROUPS
TOPOLOGY
VECTORS