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 / , rcode, reflection multiplicity, symmetry reinforcement factor and phase restriction code may be calculated, interpolatedscattering factors may be inserted into the bdf and systematically-absent reflections may be marked or removed.

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 using Difrac (Flack, Blanc Schwarzenbach, 1991). The ciffile may be read by CIFIO or the sfifile by REFM90 to create an Xtal bdf. This process compactly loads all of the necessary raw experimental data onto a bdf in a diffractometer-independent way which preserves all essential information concerning the data-gathering process. In a preliminary scan through the bdf, REFCAL determines whether the data in the input bdf are complete and in which of the forms (raw counts, net intensities, | | or | |) they are present.

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 STARTX .

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 appl / naps options on the REFCAL line control the application of the scale factors to all intensity data in the form of | | , or | |. Raw counts and net intensities are NOT modified.

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 the instabilitycoefficients b and 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. b and m may be estimated either before or after the reference reflections are scaled. In the first approach, specified by the befr option in the REFCAL line, the values of b and m obtained are subject to all the variations in reference reflections that occur during the course of measurement such as crystal degradation. In the second approach, specified by the default aftr option on the REFCAL linc, b and m will be subject only to those fast changing variations in the reference intensities which have not been removed by the overall rescaling process.

The calculation of the instability coefffcicnts b and m is controlled by the inst option on the REFCAL line with the value of o as follows:

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 n.[e.s.d.(| |)] 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 obst n specification. Zero is allowed and means that all reflections will be given an rcode = 1. Each reflection is tested to see if under the specified space group it would be systematically absent. If absent, the reflection is either rejected or included in the bdf marked with an rcode of 5.

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 rawi , neti , fsqr or frel options on the REFCAL line.

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 STARTX ) may be used to calculate interpolated atomic scattering factor values for each reflection. A four-point interpolation procedure is used (Rollett, 1965). The interpolated values are stored with each reflection. This option is invoked by the ffac signal on the REFCAL line. The advantage of interpolated atomic scattering factors is that they provide for more precise structure factor calculations with programmes such as FC and CRYLSQ . The disadvantage is that the size of the bdf is increased substantially and the extra precision is usually unwarranted for routine structure analyses.

	Warning
	Users must use this option if R -factors of less than 0.04 are anticipated.

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 REFM90 , STARTX , REFCAL and ADDATM to create a bdf with | | data from an archived data set in SCFS 90 format. REFM90 is neccssary to read the SCFS file; STARTX to calculate the direct and reciprocal cell metrics, load the scattering factor tables, atomic radii, and to check the symmetry information; REFCAL to calculate the reflection information as detailed above and ADDATM to generate the symmetry constraints.

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 REFM90 , STARTX , and REFCAL to load a bdf with net intensity data from diffractometer data produced in SCFS 90 format by the DIFRAC programme. The sgname line is necessary in STARTX as this information is not stored with the raw diffractometer data. Even if symmetry information were present in the SCFS file, it is still necessary to run STARTX in update mode to calculate and store the cell metrics, find the atomic radii, etc. and to check the symmetry information.