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topology
     

PNS (Periodic Nodal Purfaces) and PES (Periodic Equi Purfaces) are generated by short Fourier summations, involving only a small set of Structurefactors (SF) in reciprocal space. The choice of reflections near the origin of reciprocal space and of characteristic intrinsic symmetry for a particular space group reduces the sometimes enormous amount of detail a structure may contain to its general features.

 

tessalation of an PNS (S. Leoni)

The roots of the resulting density spaces generate a family of continuous, orientable, 3D-periodic surfaces PNS (closely related to minimal surfaces) partitioning euclidean space into non-intersecting subspaces. There is an intriguing relation between the distribution of chemical interacting units and orientation of principal interactions with PNS.
Based on PNS we investigate reconstructive phase transitions, diffusion problems, and hypothetical structure modeling.

 

Light and hard materials, author: Dr. S. Leoni
© / Author S. Leoni

Selected literature:

S. Leoni and R. Nesper
Elucidation of simple pathways for reconstructive phase transitions using periodic equi-surfaces (PES) descriptors. II. The strontium disilicide transition
Solid State Sciences 2003, 5, 95-107
abstract | pdf

R. Nesper, S. Leoni
On tilings and patterns on hyperbolic surfaces and their relation to structural chemistry
Chemphyschem. 2001, 2 (7), 413-422
abstract   full text (pdf) (WILEY interscience)

S. Leoni, R. Nesper,
Elucidation of simple pathways for reconstructive phase transitions using periodic equi- surface (PES) descriptors. The silica phase system. I. Quartz-tridymite
Acta Cryst. A. 2000, 56, 383-393 html/pdf/video

PNS - definition & history:

H.G. von Schnering, R. Nesper
Nodal surfaces of Fourier series: fundamental invariants of structured matter
Zeitschrift für Physik B, 1991, 83, 407-412.

H.G. von Schnering, R. Nesper
The curvature of chemical structures
Colloq. Phys.(C7, Int. Workshop Geom. Interfaces, 1990), C7-383-C7-396.

H.G. von Schnering, R. Nesper
Natural adaptation of chemical structures on curved surfaces
Angew. Chem. 1987, 99, 1097-119

R. Nesper, H.G. von Schnering
Periodic potential surfaces in crystal structures
Angew. Chem. 1986 98, 111-13

 

 

 

 

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