Incommensurate modulation
In case of
- unknown spacegroup and cell, AND
- existence of reflection subsets that are offset from each other by a fractional displacement (not rotation!) in reciprocal space
you will find in IDXREF.LP a table like
***** RESULTS FROM LOCAL INDEXING OF 201 DIFFERENCE VECTOR CLUSTERS ***** MAXIMUM MAGNITUDE OF INDEX DIFFERENCES ALLOWED 8 MAXIMUM ALLOWED DEVIATION FROM INTEGRAL INDICES 0.050 MIMINUM QUALITY OF INDICES FOR EACH CLUSTER IN A SUBTREE 0.80 NUMBER OF CLUSTER SUBTREES 4 MERGE_TREE= 0.20 merged subtrees are marked by * NODES number of nodes belonging to subtree DIFF_VEC number of difference vectors in subtree ORIGIN_INDICES fractional indices of tree origin ORIGIN_COORDINATES reciprocal space coordinates of tree origin LENGTH length of tree origin vector (1/A) SUBTREE NODES DIFF_VEC ORIGIN_INDICES ORIGIN_COORDINATES LENGTH * 1 148 154546 0.00 0.00 0.00 0.000000 0.000000 0.000000 0.000000 2 29 27949 0.13 -0.43 0.00 0.005978 -0.002899 0.000329 0.006652 3 22 20055 -0.13 0.43 0.00 -0.005989 0.002904 -0.000323 0.006664
Inclusion of reflection subsets (subtrees) into the subsequent analysis of LATTICE BASIS (cell parameters and orientation) and CLUSTER INDICES is influenced by MERGE_TREE (default 0.2). That value can be set higher (e.g. 0.5) to merge less subtrees, or lower (e.g. 0.1) to merge more subtrees (the merged ones then also get a * in the first column above). Merging more subtrees will lead to longer cell parameters, and fractional CLUSTER INDICES.
Another indication of subtrees is in the table
***** RESULTS FROM LOCAL INDEXING OF 3000 OBSERVED SPOTS *****
MAXIMUM MAGNITUDE OF INDEX DIFFERENCES ALLOWED 8
MAXIMUM ALLOWED DEVIATION FROM INTEGRAL INDICES 0.050
MIMINUM QUALITY OF INDICES FOR EACH SPOT IN A SUBTREE 0.80
NUMBER OF SUBTREES 96
SUBTREE POPULATION
1 1081
2 846
3 836
4 29
5 15
6 12
7 10
8 10
9 9
10 8
which informs in this example that there are two subtrees of substantial size after the main subtree on which the subsequent indexing is based. However, that table also shows rotationally separated lattices!
In this example, we see a case of incommensurate modulation, with a vector 0.13 -0.43 0.00 and its opposite -0.13 0.43 0.00, meaning we have satellite reflections around each reflection of the main lattice. In reciprocal space, this looks like
