Graduate Thesis Or Dissertation
 

A new trigonal huntite material and subgroup relationships between crystallographic space groups

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  • The use of an adjacency matrix to determine distant (not maximal or minimal) subgroup and supergroup relationships between crystallographic spacegroup types is described. Full lists of space-group types that are supergroups and subgroups for every space-group type were compiled. A list of the space-group types connected to each space-group type by combined maximal subgroup! minimal supergroup paths was compiled. Each of these lists was also compiled in matrix form, showing for each pair of space-group types whether one is a subgroup of the other and how many maximal subgroup, minimal supergroup, or combination of maximal subgroup and minimal supergroup steps are required to connect them. A method for using these lists and matrices to construct shortest path subgroup/supergroup graphs between space-group types was developed. From the matrices, statistics were compiled on the number of subgroup and supergroup paths of lengths one to six between space-group types, the average, median, and expected shortest path length between space-group types, and the number of space-group types each space-group type has as subgroups and supergroups. Correlations were sought between these properties and the number of organic and inorganic crystal structures of each space-group type. It was determined that organic compounds tend to crystallize in space-space groups that have many space-group types as supergroups and few space-group types as subgroups. The 17 most prevalent organic structure space-group types, comprising 90% of organic structures, were found to be closely related (paths of length 1 or 2) by subgroup/supergroup paths to each of two space-group types: P2₁ and P2₁/c. Other space-group type were found to be related to space-group types comprising more than 90% of organic structures by paths of length one or two. Properties of graphs and frees consisting exclusively of type I or type II subgroup relationships are discussed. The subgroup relationships work was motivated by the structure determination of a new trigonal huntite material, yttrium lanthanum scandium borate. Linear and nonlinear optical properties, the structure, and the composition range of this material are discussed.
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file details HruschkaMichaelArchimedes2005.pdf 2017-08-15 Öffentlich Herunterladen