The first systematic error treated is that due to the absorption of X-rays by a combination of the passage of X-rays through the capillary, mother liquor and crystal. The treatment is an empirical one, based on the measurement of the intensity of a single reflection near χ 90° which is rotated around the diffraction vector. The correction data must be obtained by measuring no less that 17 intensities of the chosen reflection, spaced roughly equally around the φ circle. The intensity values, obtained from the diffractometer, and processed by programs like NICNAK and DIFDAT, are placed in the bdf with a reflection code of 2. The reflection code is item 1018 in the bdf and should not be confused with the reflection rcode, item 1308. The correction data is normalized to the largest intensity as 1.0 and the reciprocal of each value is stored as an absorption correction factor, a function of φ. Each measured reflection is then treated by the following empirical scheme:

AI is the impinging beam absorption correction.

AD is the diffracted beam absorption correction.

C is the χ angle for the reflection.

P is the φ angle for the reflection.

T is the θ angle for the reflection.

D is the correction to φ as a function of χ.

PD is the pesudo φ angle for the diffracted beam.

D = T cos(C) as χ goes to zero, D goes to θ.

PI = P + D

PD = P - D

PI and PD are arguments which are used to obtain absorption corrections AI and AD from the original φ spin table. These absorption corrections, AI and AD approximate the absorption due to the entering and exiting path lengths. The reflection absorption correction applied is the average (AI + AD)/2

This quantity is applied to the intensity and estimated standard deviation in intensity of all the reflections in the bdf.

The second systematic error treated is decay of intensity due to the destruction of the crystal during its exposure to the ionizing radiation. In order to establish a basis for this correction it is necessary that a number of reflections be specified as "monitors" or "standards" which are measured and remeasured during the course of the data collection. The exposure time can be obtained in one of two ways. The diffractometer simply records the time in seconds since the beginning of data collection. This value is stored as item 1014 in logical record lrrefl:. If this quantity is not stored then the reflection sequence number, item 1027, must be present. This number is multiplied by the average seconds per reflection which the user must supply in the ABSCAL input line. The exposure time measurements are then used to establish another empirical correction, in this case by fitting a function by least-squares. Different decay functions are provided in ABSCAL. One is a function of exposure time alone, the others are functions of exposure time and θ, the diffraction angle.

Since the decay of crystals may be anisotropic it is prudent to choose several strong monitor reflections with quite different θ angles. The functions which are provided are:

Type 1 S = +t +

Type 2 S = +tT + +T + +

Type 3 S = +t +T +tT +,

where S is the scale correction, to are the coefficients determined by a least-squares fitting of the observed monitor reflections, t is the exposure time in hours, and T is the θ angle in radians of the monitor reflection.

Every monitor reflection is treated, initially, by assuming that the Type 1 relationship holds. Then all the monitor reflections are treated together according to the type of relationship specified by the user. In the application stage the coefficients for the combined funtion will be used to scale measured intensitites and estimated standard deviation in intensities for reflections in the bdf. Either all reflections or just those specified in an apply line will be treated.

A bdf containing raw integrated intensity data such as that prepared by the use of programs NICNAK, ADDREF or DIFDAT is used as input to ABSCAL. This bdf should contain measurements of the absorption correction reflection and of a series of decay monitor reflections. If this is not the case, line input may be used to place the φ-spin data in memory while the coefficients of the absorption decay function may be specified as well. In the more usual case in which the correction reflections are included in the bdf, the absorption correction table is stored for the first encountered reflection of Type 2. The monitor reflections are loaded into memory and the least-squares fitting done to determine the coefficients in the specified decay equation.

On a second pass through the input bdf an output bdf is written containing the intensity data rescaled using the information developed from the absorption and monitor reflections. Provisions have been made to either retain or delete the scaling reflections from the output file. There is also a method for treating only part of the data and simply passing the untreated reflections to the output file. This is done to allow one to compensate for a discontinuity in the data due to a crystal change or some other major disruption in the data collection process.

In order to be successfully used, ABSCAL must have the following quantites in the input bdf in logical record lrrefl:

IDN Item

1 Miller indicies

1005 observation angle φ

1006 observation angle χ

1007 observation angle ψ

1008 observation angle 2θ

1014 crystal exposure time in seconds

1018 reflection code as 0/1/2 for (regular intensity measurement) / (decay monitor intensity measurement) / (φ spin absorption intensity measurement)

1027 reflection sequence number

1300 observed integrated intensity

1301 estimated standard deviation of the integrated intensity

Either 1014 or 1027 may be present in the file. If only 1027, the reflection sequence number is present, the time in seconds per exposure must be given in the ABSCAL line.

Reads the input archive bdf

Optionally writes a corrected, edited, archive bdf

ABSCAL deca 1 nopu

In this example the absorption corrections will be calculated if there are reflections of code 2 in the input bdf. The decay corrections used will be of Type 1, RS= +t + if there are reflections of code 1 in the bdf. The nopu signal will cause all the monitoring reflections to be transfered to the output bdf. Since they will have been scaled, a following run of ABSCAL should show that all the absorption factors and decay scales have been reduced to 1.0 within noise.

ABSCAL noab deca 3

decay 1.0 3.6 2.1-4 3.0-5 7.1-8

apply 100 3000 5.0 15.0

In this example no absorption corrections will be made. All reflections will be rescaled by the scale factors formed from the relationship RS= +t +T +Tt + . In this case the values of through will not determined by a least-squares analysis of the code 1 reflections, rather, the values of through supplied in the decay line will be used. In addition, only reflections between 100 and 3000 on the input bdf will be modified and within that region only those with T (2θ) between 5.0° and 15.0°. This last feature is provided to enable the user to cope with discontinuites in the data.