DirAx Remarks
General remarks
The parameter dmax
The parameters Indexfit and Levelfit
Selection of Acceptance Level (ACL)
Obstinate Data
The program differs slightly from the description in the DirAx paper
(Duisenberg, A.J.M.(1992). J. Appl. Cryst. 25, 9296.)
but the essentials are still the same.
Main differences concern the parameters LevelFit and IndexFit (see
The parameters Indexfit and Levelfit).
Unlike the DOS
version the UNIX versions cannot be interrupted during the tvector
generating process, there is no need for this as the UNIX computers are
much faster.
For the same reason the random selection of triplets is only applied with
more than 25 reflections.
Dmax should exceed amply the maximum expected axis length in order not to
miss this axis, but it should not be very much larger than twice this
length to avoid unnecessary calculations and erroneous results. The
default value is set to 80 Å which proved adequate for most of our
problems (example 2 uses Dmax=160).
In the paper LevelFit and IndexFit are defined as RELATIVE criteria (p 96,
last line 1st column and 1st line 2nd column). Now both parameters are
used in the ABSOLUTE sence. They refer to distances in reciprocal space
(reciprocal Å) and not any more to fractions of level spacings or
to fractions of indices respectively.
IndexFit is a factor: IndexFit*LevelFit is used as the criterion for
fitting the indices.
If LevelFit corresponds to realistic errors (see below) IndexFit should
not differ too much from 2.
 Actually, for LevelFit the precision of the setting angles
('delta_angle') should be taken into account. DT, DO and DC,
the absolute errors in reciprocal space in reciprocal Å, are given
by:

DT = (2/λ) * Δθ,
DO = (2/λ) * sin(θ) * Δω,
DC = (2/λ) * sin(θ) * Δχ_{B},
with all delta's in radians and
Δω = Δφ_{B} *
cos(χ_{B}),
(Subscript B for 'Bisecting'). The corresponding vectors,
DT, DO and DC,
form a "monoclinic cell" with unique angle
(90+θ) between DT and DO.
The maximal combined error D is given by:
 D = √( DT*DT + DO*DO + DC*DC + 2*DO*DT*sin(θ) ),
from D = DT  DO + DC, the longest body
diagonal of the "cell".
Example: for Moradiation (λ=0.71Å), θ=15° and errors
of 0.01° in θ and ω,
and 0.03 in χ_{B} we have (if we are not
mistaken): DT = 1/2034, DO = 1/7859,
DC = 1/2620 and therefore D = 1/1514
reciprocal Å, so 1/1000 is a good choice here. (We prefer writing
1/1514 to 0.000660501 because this is easier to visualize, and to
emphasise the reciprocal nature of the magnitudes.)
 But in general it is unnecessary to go through these calculations:
simply start with the default value of 1/1000 and if this does not work
try 1/500, or 1/2000; all this is not very critical. Too large a LevelFit
is worse than a too small one, i.e.: 1/1000 is better than 1/500, mostly.
NOTE: only the denominator of LevelFit is to be put in, not the symbols
'1/'.
The program selects ACL for the geometrical correct solution with the
maximum number of fitting reflections. Usually this is
crystallographically correct too, but sometimes a lower solution is
better, as may occur with twin lattices or an incommensurate structure,
where a super lattice may accomodate more or even all reflections.
Therefore solutions from lower ACL's are presented too and you may prefer
one of those although (or just because!) it produces more aliens.
With poor setting angles use a less strict LevelFit (1/500). Start with a
higher IndexFit and decrease it later, but be careful with a too lenient
IndexFit, especially with twins, because an apparently correct but
actually false (super) lattice may be found.
On the other hand, with multiple lattices narrower criteria for LevelFit
and IndexFit may be required to discriminate reflections almost on regular
lattice points. A good procedure here is to start with LevelFit 1/3000 (if
your setting angles permit this!  with a CAD4 use SET4), and then to
lower the IndexFit gradually until a satisfactory solution appears.
Whether a solution is crystallographically acceptable or not can NOT be
decided by DirAx: it gives only geometrically possible solutions.
The suggested values for the parameters in this instruction are in no way
sacrosanct and seldom very critical, fortunately: try others to become
experienced with the method.
DirAx