4.5. ADDREF: Load reflection data

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.

4.5.1. Overview

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 constitutes a lrrefl: merging feature. Also worth noting is that the input archive bdf must contain all cell, symmetry, and cell content information pertinent to the compound. In other words, the input archive bdf must contain the data generated by STARTX or any subsequent calculation.

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 all option) to trim unneeded items from the reflection record (see Examples).

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 lrdset: of the output bdf for use by other programs.

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 program SORTRF (with average specified) should be run after (or, in some cases, before) ADDREF.

Reflection status codes (rcode)

The values of rcode which are recognised for most XTAL calculations are as follows:

  1. "observed" reflection (ie. Y>= nY)

  2. "less than" reflection (ie. Y< nY)

  3. unreliable reflection not used in refinement or R factors

  4. Friedel-related value is missing when data stored as Friedel pairs

  5. systematically absent

Note that rcodes are assigned by SORTRF and retained by ADDREF.

4.5.2. Calculations Performed

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 FC. Reflection data may be generated by entering the hklgen line. It should be emphasised that ADDREF only limits the data to the boundaries of the defined limits (see ADDREF line). ADDREF will remove systematically absent reflections (due to symmetry) but for crystal classes higher that orthorhombic it will generate redundant reflections. These are easily removed from the bdf by applying the sort/merge routine SORTRF immediately following ADDREF. Using SORTRF to average the generated data (option aver 1 ) will ensure that only a unique set of reflections remain. It is good policy always to run SORTRF after ADDREF, especially if the reflection generation feature is used.

The minimum contents of the lrrefl: record are the packed hkl word, sin/, the packed phase-code/multiplicity/epsilon word and structure factor coefficient (this can be Frel, Frel squared or Irel). The input hklgen line must contain the codes hkl and either frel , f2rl or irel . This line may also contain any of the other option codes if they are needed, but remember that all values, except those calculated by ADDREF (e.g. rlp or the interpolated form factors), will stored on the bdf as 0. Note that it is possible to generate the Friedel equivalent reflections for noncentrosymmetric space groups by entering the frie code on the ADDREF line.

When running SORTRF after ADDREF make sure that, in addition to specifying the sort order code, the aver 1 and the merged coefficient ( frel , f2rl or irel ) are also entered. Note that if Friedel equivalent data is to be preserved the pakfrl or sepfrl code must be entered on the SORTRF line. Form Factor usage (Important!)

The lrscat: are present in the Archive (stored by STARTX). These may be used to calculate interpolated form factor values which are stored in each reflection record.This option is invoked by the ffac option on the ADDREF line. This provides more precise structure factors with programs such as FC, CRYLSQ etc. The disadvantage is that the size of the archive bdf is increased substantially and the extra precision is often unwarranted for routine structure analyses. This option should be used for precision analyses or when R-factors of less than 0.04 are anticipated. Data Reduction

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:

  • transform Miller indices

  • generate hkl data

  • calculate sin/

  • calculate the multiplicity and reinforcement factor, and phase restriction code

  • determine if reflection is systematically absent for this space group

  • apply Bayesian statistics to weak data

  • interpolate the scattering factors and store reflection packets

  • obtain max/min h, k, l, sin/, and other quantities

  • calculate and apply 1/Lp for all geometries and radiation

  • convert input function of F to requested output function of F

  • calculate the standard deviation in the chosen F function Lorentz-polarization corrections

Algorithms for the common 1/Lp factors are available. In the equations below refers to the reflection diffraction angle, and m to the diffractometer angle for the monochromator crystal.

Lorentz factor= 1/(2sin 2)for single crystal
 = 1/(2sin 2 sin )for powder

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 = Ki(1-B)(cos2 cos22+sin2) + B(sin2 cos22+cos2) / [(1-B)Ki+B]

where Ki, the polarization ratio is Kk = cos22m for an ideal mozaic crystal and Kd = |cos 2m| 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 E). 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. m 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

Pi = (1-C) Pk + C Pd.

where C is the monochromator perfection factor (the fraction of the monochromator crystal considered to be perfect) and Pk and Pd the kinematic and dynamical components of the polarization. RLP is the reciprocal of Lp.

X-ray powder, no monochromator

RLP1 = 2sin sin 2 / (1 + cos22)

X-ray single crystal, no monochromator

RLP2 = 2sin 2 / (1 + cos22)

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)cos22m + Bcos22) / (B +(1-B) cos22m)

T2 = C(Bcos22 + (1-B)cos2m) / (B + (1-B)cos2m)

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)cos22 cos22m) / (B + (1-B)cos22m)

T2 = C(B + (1-B)cos22 cos2m) / (B + (1-B)cos2m)

RLP4 = sin2 / (T1 + T2)

Neutron powder (no polarization)

RLP1 = 2sin sin 2

Neutron single crystal

RLP2 = 2sin 2 Calculation of Sigma(F) from Intensity data

The calculation of (F) is straightforward except where F is close to zero or negative. To avoid the asymptotic form of this conversion, the following expression is used in ADDREF.

F = (RLP I) / (F + {F2 + RLP I}1/2)

4.5.3. File Assignments

  1. Reads lrcell: and symmetry data from the input archive bdf

  2. Writes updated file to the output archive bdf

  3. Optionally, reads reflection data form specified (on bdfin) bdf

4.5.4. Examples

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 lrrefl:, and that all reflections are to be listed. The reduce line indicates that relative intensities and their sigmas are to be converted to relative F's and (F)'s; the Lp factor is to be calculated by method 2 (spectrometer with Eulerian cradle geometry and 2 scan). The hklin line specifies the items which are found on hkl lines. Note that the user has labeled the hkl lines with the compound identification, so skip must be used to ignore this data. The remove line indicates that irel and sigi are to be excluded from the output bdf (they are used, however, in the conversion to frel and sigf , so they must be specified on the hklin and hkl lines.

title Contraction of the reflection record
bdfin all
remove absf tbar extf

To decrease the size of a large archive bdf, first check to see which items are in lrrefl: of the file. Then check (carefully) to see which items are no longer necessary to keep in the bdf. Use the remove line to get rid of these, as in the procedure above. The input archive bdf is read. The absorption correction, extinction correction, and mean radiation path length will be removed from lrrefl: of the bdf by the lines above.

title Merging of reflection data
bdfin file a all
bdfin file ddd absf eval

Suppose the input archive bdf contains reflection information about a compound and the bdf with extension DDD contains a bdf with different reflection information about the same compound. The preceding sequence of lines will merge certain items from both bdf's and output them to the output archive bdf.

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
limits *4 0.5
hklgen hkl frel
title Complete data preparation sequence
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
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 STARTX, DIFDAT, SORTRF, and ADDREF is combined to produce a bdf with F values in logical record lrrefl: for a unique asymmetric set of reflections including the Friedel related pairs.

4.5.5. References