Author: H.D. Flack, Laboratoire de Cristallographie, University of Geneva 4, CH-1211 Geneve 4, Switzerland
REFCAL treats reflection raw intensity and background, net intensity | | or | | data
REFCAL processes intensity data coming from single
crystal diffractometer measurements. The programme uses
data already placed on the input bdf in the form (a) raw
counts and associated experimental details, (b) net
intensities and associated experimental details, (c) |
or (d) |
| values. The reference
reflections can be analysed both for long-term drift and to
determine the short term stability of the measurements. The
input data are transformed in a downhill cascade manner:
raw intensitics --> net intensities > |
| and output according to
option. The Lorentz-polarization factor, sin
reflection multiplicity, symmetry reinforcement factor
and phase restriction code may be calculated,
The recommended method of placing raw diffractometer
data on the bdf is first to transform a
diffractometer-specific file into a CIF or SCFS90 (Standard
Crystallographic File Structure 90, Brown, 1991) format
Difrac (Flack, Blanc Schwarzenbach,
When REFCAL is run the input bdf must also contain
all cell, symmetry and cell content information pertinent
to the compound. This implies that the input bdf must
contain the data generated by
When using the input of raw net intensity data, the inut bdf should contain the following information concerning the experimental method of intensity measurement: type of radiation used, mean wavelength of radiation, temperature of intensity measurements, minimum and maximum sin / of intensity measurement, total number of reflections measured, minimum and maximum values of h, k and l used in data collection, Miller indices of reference reflections, crystal shape information as either (a) Miller indices of faces and their distances and e.s.d.s from centre, or (b) the radius of a spherical crystal or (c) the radius and length of a cylindrical crystal, detector deadtime and e.s.d., wavelength of filter absorption edge, for each attenuator filter: its reciprocal transmission factor with e.s.d and index; incident beam polarization characteristics viz polarization ratio, and e.s.d., dihedral angle between diffraction planes of the sample and monochromator, incident beam half-width, wavelength and intensity weights of spectral line components.
For raw intensities, the data for each reflection should contain the following information. h, k, l, peak count, high- and low-angle background counts, Flack, Blanc & Schwarzenbach coefficients, crystal-based azimuthal angle, elapsed time of measurement, attenuator filter index, scale factor index, reference reflection index, background scanning mode, total scan width, scan type, total horizontal and vertical detector aperture.
For net intensities, the data for each reflection should contain the following information h,k,l, net intensity and its e.s.d., crystal-based azimuthal angle, elapsed time of measurement, attenuator filter index, scale factor index, reference reflection index, background scanning mode, total scan width, scan type, total horizontial and vertical detector aperture. The net intensity is that derived from the raw peak counts by subtraction only of the background but without any other correction factor being applied to it.
For | | input, the data for each reflection should contain h,k,l, | | and its e.s.d. | | may be obtained from the net intensity by applying all systematic corrections. For | | input, the data for cach reflection should contain h,k,l, | | and its e.s.d.
REFCAL can undertake an analysis of reference reflections. These are specified reflections whose intensities are remeasured at regular intervals These measurements are used for two purposes: (a) The establishment of a set of scale factors based on the counts of the reference reflections to compensate all reflections for any drift over the data gathering process, (b) The calculation of instability constants which are based on the spread and perhaps the trend of the measuremcnt of the reference reflections.
During the course of the data treatment, the sets of interspersed reference reflection measurements (in the form of reference index, net intensity, its e.s.d., elapsed time of measurement and set index) are stored in memory. Each set contains at most one measurement of each reference reflection although all references need not be present in each set. Reference reflections separated by non-reference reflections in the sequence of measurements belong to different sets of reference reflections.
No more than 30 different reflections may be designated as reference reflections. Under option the user may specify whether the reference reflections, once they have been used in the scaling and stability calculation, should be removed from the bdf or kept as observed reflections for later use (such as merging) with the other intensity measurements.
The scales will be generated from the reference
reflection sets and smoothed over a specified number of
scale factors. The default smoothing range is five scale
factors forward and five scale factorsbackward. This
smoothing is necessary due to the statistical counting
fluctuations in the measured intensities. No smoothing will
occur if the smoothing range is set to 0. The
Two input lines, setscl and discon are available to control the calculation of scale factors. sctscl specifies scale factors. Scale factors which have been calculated automatically will have their calculated value overwritten by the setscl value.
discon provides a way of indicating the position of an abrupt discontinuity in the scale factor values. Abrupt scale discontinuities may occur if there is a change in the radiation source or a degradation in the crystal. A scale factor, indicated by its time on the discon line, will be understood to be the last member of a set of scale factors over which smoothing takes place. The scale factor following the one indicated on the discon line will be taken as the first of a another set used for smoothing. The smoothing function will not span the two sets. It may be necessary to make a preliminary run of REFCAL to find the discontinuities.
From the average value of the net intensity and the individual measurements, the external variance may be calculated for each reference reflection. This gives a measure of the variance over and above the variance based on counting statistics alone. The model used for the total variance of a reflection intensity is given by:
(Total e.s.d.) = (Counting e.s.d.) + | b | + | m |.(Net intensity) .
In REFCAL different estimates (as specified below) of
m are obtained by least-squares
analysis, using all reference reflections, of the
individual difference between the external and the
counting-statistics variances against the square of the
individual average net intensities.
m may be estimated either before or
after the reference reflections are scaled. In the first
approach, specified by the
The calculation of the instability coefffcicnts
m is controlled by the
No attempt will be made to calculation the values of instability constants if the reference reflections have been measured less than seven times during the data gathering procedure. Raw counts and net intensities are NOT modified by the instability calculation.
Xtal uses a system of reflection status codes
described earlier in the Primer Section. Each reflection is
tested against its e.s.d. Those reflections which show a |
| more than
|)] are coded as
rcode = 1 (observed) and those with
less than this value are coded with
rcode = 2 (less-thans). The value of
n may bc specified in the
REFCAL line by use of the
The reflection data are transformed in a downhill
cascade manner; raw intensities --> net intensities
| starting at the form of
the input data. The form of the reflection data output is
indicated by the
The net intensity is calculated from the raw intensity data according to the scheme for reducing raw peak and background counts described in Flack, Blanc & Schwarzenbach (1991) with the coefficients ; , and available on the bdf. The net intensity is that derived from the raw peak counts by subtraction only of the background but without any other correction factor being applied to it.
| | is obtained from the net intensity by applying all systematic corrections. | | is obtained from | | by treating negative | | values as zero. The calculation of the e.s.d.(| |) is carried out using the following expression:
The Lorentz-polarization factor for each reflection is calculated from the values of the polarization ratio K and the dihedral angle , the angle between the diffraction planes of the monochromator and the sample ( diffaction plane is the plane containing the incident and diffracted ray directions). Let the Bragg angle of the sample. For single crystal equatorial-plane diffractometer measurements, the Lorentz factor = L = 1/(2 sin 2 ). The expression for polarization of a twice-diffracted X-ray beam is given by:
P = + K + K ) /(1 + K ).
For diffraction by neutrons, there is no polarization. See Azaroff (1955) and Hope (1977).
The scattering factor tables present on the input bdf
(as stored by
The symmetry reinforcement factor is the integer multiplicity of a reflection intensity due to the symmetry-generated coincidence of identical diffraction vectors (i.e. direction and phase). The value of is required for the calculation of E values, normalized structure factors. In REFCAL this factor is calculated for each reflection and stored in the binary data file for use by other programmes in the system. The method is described by Stewart and Karle (1976), Iwasaki and Ito (1977); and Stewart and Karle (1977).
title Create a bdf from an SCFS 90 archive file REFM90 scfs STARTX upd REFCAL frel ADDATM upd
The above example shows the use of
title Form a bdf from an SCFS 90 diffractometer file REFM90 scfs STARTX upd sgname -C 2YC REFCAL
The above example shows the use of