The 44 lattice characters come in two types - all-acute reduced cells and all-obtuse ones - and
the search skips the type-1 characters whenever the reduced beta is within the angle tolerance of
90 degrees, because at that point the two types are no longer distinguishable and only the type-2
statement of a character is safe to test. But a cell whose reduced beta really is 90 within
tolerance can itself reduce EITHER way, and an all-acute one then matches no character at all: the
type-1 ones were skipped and the type-2 ones are written for the obtuse setting. It falls through
to triclinic, and a centred lattice loses its centring.
Measured on a C-centred monoclinic crystal whose reduced beta sits 0.07 degrees from 90. Its
free-refined cell came back acute or obtuse depending on the last digits of the refinement - a
sub-pixel change in the beam centre was enough - and with it the lattice was read as C-centred
monoclinic or as triclinic, and the run merged in C2 or in P1 with twice the asymmetric unit. In
the obtuse setting the character matches with residuals of 0.01 to 0.14 degrees against a 3 degree
tolerance, at every geometry tried; there was never any doubt about the lattice, only about which
side of the boundary the reduction landed on.
So when nothing matched and the cell is acute with beta at the boundary, present it in the obtuse
setting and match once more. Negating a and c leaves the lattice and beta alone and turns alpha
and gamma into their supplements. The second attempt runs only where the first found nothing, so
no lattice that is classified today can be re-classified by this.
leonarski_f
996d8e7d41