DirAx Remarks

General remarks
The parameter dmax
The parameters Indexfit and Levelfit
Selection of Acceptance Level (ACL)
Obstinate Data

General Remarks

The program differs slightly from the description in the DirAx paper (Duisenberg, A.J.M.(1992). J. Appl. Cryst. 25, 92-96.) 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 t-vector 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.

The parameter Dmax

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).

The parameters IndexFit and LevelFit

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 Mo-radiation (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/'.

Selection of Acceptance Level (ACL)

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.

Obstinate Data

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