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SUMMARY:Department of Materials Science &amp\; Metallurgy Goldsmiths' Semi
 nars: From Graphs to Regular Structures - Prof. Michael Treacy\, Departmen
 t of Physics\, Arizona State University
DTSTART:20241205T153000Z
DTEND:20241205T170000Z
UID:TALK225166@talks.cam.ac.uk
CONTACT:Caroline Teagle
DESCRIPTION:Refreshments and cakes will be available!\n\nThe connectivity 
 of covalently bonded compounds can be described fully by a list of atoms (
 vertices) and their bonded neighbours (edges). Such a list is a mathematic
 al graph containing no information about 3D Cartesian space. Thus\, a grap
 h tells us nothing about the structure (topology) of the material. If the 
 vertex elements are known\, structural inferences can be made by embedding
  the graph in 3-dimensional space by computational methods using known bon
 ding properties.\n\nIn this talk\, I describe how such a graph-theoretic a
 pproach was used to enumerate a database of hypothetical crystalline zeoli
 te frameworks. Because zeolites are tetrahedral silicate framework structu
 res\, their graphs are 4-coordinated – each vertex is connected to exact
 ly four others. The number of possible graphs is finite for a fixed number
  of unique tetrahedral vertices\, N\, in a given space group symmetry. How
 ever\, it grows combinatorially as N increases\, limiting this approach to
  the simplest structures with low N. I will discuss some 3-periodic and 2-
 periodic examples from the zeolite database\, which has about 10 million e
 ntries. In collaboration with Prof Mike O’Keeffe at ASU\, ideas learned 
 in the zeolite work have been extended to investigate hypothetical polycat
 enated molecular and crystalline materials. These include hypothetical kno
 tted\, linked\, interlocked\, interthreaded\, and woven structures\, bring
 ing the research within the bounds of knot theory! These catenated structu
 res can make beautiful models. The presence of mechanical bonds gives thes
 e materials unusual mechanical properties. This work focuses on the low-tr
 ansitivity structures\, with just one or two types of vertex and one type 
 of edge\, as these may be the easiest to synthesize in the laboratory. Les
 sons learned in the catenane work have shed light on some of the roadblock
 s encountered in the earlier zeolite enumeration work.\n
LOCATION:Goldsmiths' 2 &amp\; https://zoom.us/j/96836714124
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