Authors: George Davenport and Syd Hall
Contact: Syd Hall, Crystallography Centre, University of Western Australia, Nedlands 6907, Australia
ADDREF adds measured reflection data to the archive bdf and converts them into different structure factor coefficients. ADDREF can also create reflection data, expand or contract an existing reflection record, and merge reflection records. Options include the insertion of interpolated form factors into the reflection record, the removal of systematically absent reflections, and the calculation and application of the Lorentz-polarization factor for a range of geometries.
Most crystallographic calculations require reflection information to be present in the bdf. The basic reflection data includes the Miller indices, sin / , reflection multiplicity, the symmetry reinforcement factor (epsilon), phase restriction codes and |F| relative. Other quantities such as |F|, reflection weights, the Lorentz-polarization factor, scale group number, and interpolated scattering factors may be added as the user requires.
Up to five sources of input may be used (input lines
and/or up to four binary data files) or dummy reflection
records may be generated from the cell dimensions within
specified limits of h, k, l, and sin
. Generated data
is useful for calculating structure factors when only the
atomic parameters are available. When more than one input
source is used, it is vital that each source have the same
set of reflections and refer to the same compound. This
The sources of reflection data, as well as the specific items, are specified using combinations of bdfin and hklin lines. One hklin line is allowed, and one bdfin line per input bdf is allowed. These lines can be in any order, but an important caveat applies. That is, if a data item is specified as coming from two different sources (e.g. if the Miller indices are given on an hklin line and also on a bdfin line), the item will be taken from the source specified first.
For convenience, a
remove line has also been
provided. For cases in which a large number of items are to
be taken from an input bdf, it may be easier to specify
those items which are not to be output than those items
which are to be output. The
remove line may thus be
used in conjunction with a
bdfin line (using the
Items on bdfin, hklin, remove, and c (continuation) lines may be specified in two ways. A set of four-letter mnemonics are available for the most commonly used quantities. For more involved applications, items can be specified using their identification numbers as listed in the BDF section at the back of the manual.
The printed output contains a list of items from each
source, along with the status of each item. The status
refers to possible user errors, such as a duplicate request
for an item or the absence of an item on the given source.
A list of data for each reflection is given, for either a
specified number of reflections or all reflections,
depending on the user's choice. A list of items contained
in the reflection record of the output bdf is given, along
with the maxima and minima of the data for those items. In
addition, the maximum magnitudes of the Miller indices and
the maximum and minimum values of sin
for the output
bdf are stored in
ADDREF tests each reflection to see if it is systematically absent under the space group symmetry given. Systematically absent reflections are either rejected from the file or marked with an rcode of 5 and these must not be included in the bdf as observed reflections. Inclusion of such reflections will cause the Fourier transform to show incorrect symmetry. To ensure that no
duplicate reflections are present on the bdf, the
Reflection status codes (rcode)
The values of rcode which are recognised for most XTAL calculations are as follows:
Note that rcodes are assigned by SORTRF and retained by ADDREF.
Generate hkl data
Occasionally it is necessary to produce a file
containing 'dummy' reflection data. Measured diffraction
data may not be available for input but reflections are
needed in order to calculate structure factors with
programs such as
The minimum contents of the
When running SORTRF after ADDREF make sure that, in
addition to specifying the sort order code, the
ADDREF provides many options for reducing the data to be stored in the output archive bdf. It is a "two pass" program. During the first pass, statistical information on the reflection data is calculated and written to a scratch file. During the second pass, reflection data processing is completed and the results are written to the output archive bdf.
The following calculations may be performed:
Algorithms for the common 1/Lp factors are available. In the equations below refers to the reflection diffraction angle, and to the diffractometer angle for the monochromator crystal.
The formulae used for polarization are those described by Azaroff (1955), Hope (1971), and Vincent & Flack (1980). The general expression for polarization of a twice-diffracted beam is
P = (1-B)( 2 + ) + B( 2 + ) / [(1-B) +B]
where , the polarization ratio is = 2 for an ideal mozaic crystal and = |cos 2 | for an ideal crystal. B is the fraction of the intensity with the electric field parallel to the plane of the monochromator (Azaroff's notation is ). This direction is given by the cross product of the vector in the direction of the source beam and the normal to the monochromator crystal plane. In a standard X-ray diffractometer the source beam is unpolarized and B=0.5. is the monochromator angle and is the angle between 2 planes of diffraction (i.e. planes, containing the incident and reflected rays of the monochromator and the sample).
The general expression for the integrated polarization of mosaic/perfect crystal is
= (1-C) + C .
where C is the monochromator perfection factor (the fraction of the monochromator crystal considered to be perfect) and and the kinematic and dynamical components of the polarization. RLP is the reciprocal of Lp.
X-ray powder, no monochromator
RLP1 = 2sin sin 2 / (1 + 2 )
X-ray single crystal, no monochromator
RLP2 = 2sin 2 / (1 + 2 )
X-ray single crystal, with monochromator and perfection factor, perpendicular setting
In the perpendicular monochromator setting, the rotation axis of the monochromator crystal is perpendicular to the normal to the equatorial plane of the diffractometer (ie. 2 axis), such that the plane of the incident beam and the beam reflected by the monochromator is perpendicular to the plane of the beam reflected by the monochromator and the beam reflected by the crystal under study. Rho, as defined by Azaroff, is 90°. If the source beam incident on the monochromator is unpolarized then B=0.5. For a perfectly polarized beam B=0. for this setting. This is the CAD4 setting.
T1 = (1 - C) ((1-B) 2 + 2 ) / (B +(1-B) 2 )
T2 = C( 2 + (1-B)cos2 ) / (B + (1-B)cos2 )
RLP3 = sin2 / (T1 + T2)
X-ray single crystal, with monochromator and perfection factor, parallel setting
For the equatorial, or normal, monochromator setting, the rotation axis of the monochromator is parallel to the normal to the equatorial plane of the diffractometer (ie. 2 axis) such that the incident beam, the beam reflected by the monochromator and the beam reflected by the crystal under study all lie in the same plane. If the source beam incident on the monochromator is unpolarized then B=0.5. For a perfectly polarized beam B=1. for this setting. This is the Nicolet setting.
T1 = (1 - C) (B + (1-B) 2 2 ) / (B + (1-B) 2 )
T2 = C(B + (1-B) 2 cos2 ) / (B + (1-B)cos2 )
RLP4 = sin2 / (T1 + T2)
Neutron powder (no polarization)
RLP1 = 2sin sin 2
Neutron single crystal
RLP2 = 2sin 2
title CREATION OF AB INITIO REFLECTION RECORD ADDREF dset 1 ffac list reduce itof rlp2 hklin skip hkl rcod irel sigi absf eval remove irel sigi hkl p6122 0 1 1 1 22004.8 4043.4 1.0 3.0 hkl p6122 0 1 4 1 387.4 205.5 1.0 1.0 hkl p6122 0 1 5 1 6735.0 1110.5 1.0 3.0 :...................................reflection data omitted for brevity hkl p6122 2 2 7 1 358.1 98.2 1.0 0.3 hkl p6122 2 2 8 1 384.3 78.1 1.0 0.3 hkl p6122 2 3 3 1 2275.6 247.0 1.0 2.0
The ADDREF line specifies that interpolated form
factors are to be inserted in
title Contraction of the reflection record ADDREF bdfin all remove absf tbar extf
To decrease the size of a large archive
bdf, first check to see which items are in
title Merging of reflection data ADDREF bdfin file a all bdfin file ddd absf eval
Suppose the input archive bdf contains
reflection information about a compound and the bdf with
title EXAMPLE USE OF CONTINUATION LINES ADDREF dset 1 hklin hkl frel sigf fcal 1000 1001 1002 c 1003 rcod tbar hkl 1 1 1 40 5 56 289 33 256 4 0.1
The preceding example illustrates the use of c lines. Note that some items are specified using ID numbers and some are specified using four-letter mnemonics.
title Generate reflection data to sin(theta)/lambda=.5 ADDREF limits *4 0.5 hklgen hkl frel title Complete data preparation sequence STARTX cell 11.52 11.21 4.92 90 90.833 90 288.0 cellsd .012 .011 .005 0.0 .0005 0.0 sgname -p 2yab :p21/a celcon o 12 celcon c 28 celcon h 24 DIFDAT cad attenu 5. genscl 3 SORTRF order khl aver 1 cull 1.5 print 1500 pakfrl ADDREF dset 1 list 7 ffac lpin friedel reduce itof rlp2 xray bdfin hkl irel sigi rcod ifri sfri rcdf remove irel sigi ifri sfri
In this example a run of