Euclidean Patterns in Non-Euclidean Tilings |
The CrystalMaker file links on the EPINET 3D network pages are text files formatted to be read directly into the CrystalMaker software. Downloading and opening a file within CrystalMaker gives a 3D image similar to those shown in the 3D Network pages. User options within CrystalMaker allow the images to be rotated in 3D, viewed as blue–red stereo images, etc.
Caveat: These images should be treated with some caution, as current implementations of CrystalMaker force edge connections according to metric distance criteria only. This means some images have spurious edges and vertex degrees larger than the correct vertex degree entries in the relevant 3D Framework page.
The CrystalMaker files are formatted with pseudo–atoms of atomic number 1,2,3… etc., for true network vertices. Rare–earth pseudo–atoms are appended to represent all edge mid–points to assist the model–building within CrystalMaker. Duplicate vertices are sometimes listed by CrystalMaker.
Here is an example file:
NOTE refined by Systre from s2223_FG.pgr TITL s2223_FG_3_1_D_0 MODL 1 SPGR 208 CELL 24.852800 24.852800 24.852800 90.000000 90.000000 90.000000 VIEW 0.583 1.603 0.301 DCUE 0.2 0 1 BKCL 1 1 1 BRAD 0.8 0.9 COLS 1 SHCL 1 BNCL 0.5 0.41 0.95 BMAX H La 6.21820000 BMAX He Ce 4.39839585 XYZR -0.1 1.1 -0.1 1.1 -0.1 1.1 TYPE H 0.010000 0.097510 0.677410 1.000000 He 0.010000 0.097510 0.677410 1.000000 La 0.010000 0.097510 0.677410 1.000000 Ce 0.010000 0.097510 0.677410 1.000000 ATOM H H 0.000000 0.500000 0.250000 He He 0.000000 0.500000 0.250000 H H 0.000000 0.500000 -0.250000 He He -0.250000 0.750000 0.250000 La La 0.000000 0.500000 0.000000 Ce Ce -0.125000 0.625000 0.250000
In this example file the essential crystallographic description is contained in the space group entry, the unit cell geometry and the vertex positions.
The space group entry listed by standard 3D space group number from the International Tables for Crystallography:
SPGR 208
The unit cell geometry, listed in the form a, b, c, alpha, beta, gamma:
CELL 24.852800 24.852800 24.852800 90.000000 90.000000 90.000000
The vertex positions:
ATOM H H 0.000000 0.500000 0.250000 He He 0.000000 0.500000 0.250000 H H 0.000000 0.500000 -0.250000 He He -0.250000 0.750000 0.250000 La La 0.000000 0.500000 0.000000 Ce Ce -0.125000 0.625000 0.250000
Here the vertices are H and He, and edge midpoints are La and Ce. The crystal coordinates are the 3 real numbers listed in each row. One of the H positions is redundant, leaving 2 essential vertex positions, and 2 distinct edge midpoints. If you have CrystalMaker, you can readily read this data by loading the file in CrystalMaker, and checking the crystallographic description using the “Edit… Structure…” command.