|Abstract or Summary
- 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
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.
- File scanned at 300 ppi (Monochrome) using Capture Perfect 3.0 on a Canon DR-9050C in PDF format. CVista PdfCompressor 4.0 was used for pdf compression and textual OCR.
- description.provenance : Approved for entry into archive by Patricia Black(email@example.com) on 2012-07-25T15:51:16Z (GMT) No. of bitstreams: 1HruschkaMichaelArchimedes2005.pdf: 11689087 bytes, checksum: 3a339c151bad9067321ac11679018042 (MD5)
- description.provenance : Made available in DSpace on 2012-07-25T15:53:23Z (GMT). No. of bitstreams: 1HruschkaMichaelArchimedes2005.pdf: 11689087 bytes, checksum: 3a339c151bad9067321ac11679018042 (MD5) Previous issue date: 2005-04-26
- description.provenance : Submitted by Eric Hepler (firstname.lastname@example.org) on 2012-07-03T01:46:31ZNo. of bitstreams: 1HruschkaMichaelArchimedes2005.pdf: 11689087 bytes, checksum: 3a339c151bad9067321ac11679018042 (MD5)
- description.provenance : Approved for entry into archive by Patricia Black(email@example.com) on 2012-07-25T15:53:23Z (GMT) No. of bitstreams: 1HruschkaMichaelArchimedes2005.pdf: 11689087 bytes, checksum: 3a339c151bad9067321ac11679018042 (MD5)