( sin omega cos phi )
( sin omega sin phi )
( cos omega )
These sections may be plotted as stereograms. The position of peaks is given for all symmetry related positions in both polar and Eulerian angles.
Options are provided in the program for writing the calculated rotation to a map file, which can be read by the program on another occasion for plotting, peak searching etc (options MAP, READ). The results of the first stage of the calculation (ALMN) may also be saved for subsequent rotation function summations on different grids (SAVE, SUM). A list of peaks may be read in, and all symmetry related peaks generated (option PEAK).
Compared to the Crowther program (ALMN), this program is a little slower but a self rotation function in polar angles is easier to understand. This program can also be used to calculate a small part of the rotation function on a fine grid (down to 1 degree steps). However, the crystal symmetry is expressed less fully in polar angle space than in Eulerian angle space, so for cross-rotation functions the Eulerian program is normally more appropriate.
CROSS, CRYSTAL, END, FIND, JOIN, LABIN, LIMITS, MAP, NOPRINT, PEAK, PLOT, READ, RESOLUTION, SAVE, SELF, SUM, TITLEThe following keywords are compulsory: SELF/CROSS, CRYSTAL, LABIN.
This card is COMPULSORY for each hklin set (one for self-rotation, two for cross-rotation). The first subkeyword FILE (or NUMBER) indicates whether this CRYSTAL card refers to crystal 1 or to crystal 2.
ncode orthogonalisation code for this crystal
= 1, orthogonal x y z along a,c*xa,c* (Brookhaven, default)
= 2 b,a*xb,a*
= 3 c,b*xc,b*
= 4 a+b,c*x(a+b),c*
= 5 a*,cxa*,c (Rollett)
FILE sets the crystal number, 1 or 2 (default 1). The syntax is any one of FILE 1 or FILE 2.
iphi1 iomega1 ikappa1 start points in degrees
iphi2 iomega2 ikappa2 stop points in degrees
nphi nomega nkappa intervals in degrees
(Default = 0 180 5 0 180 5 0 180 5.
This covers the basic asymmetric unit at 5 degree intervals).
If the keyword NOTITLE is present, the maps are plotted with no labels or titles: this may be useful for publication purposes. The plots are not normally useful if a small part of the function is being calculated.
If the keyword DASHED is present, the arc will be dashed with repeat and dash length as specified (in multiples of the radius of the stereogram). Default values for <repeat> and <dash> are 0.05, 0.025. Up to 30 JOIN commands may be given.
Warning: this option is primarily intended for self-rotation functions, and probably will not work sensibly if the kappa sections are split into two sections or half sections.
Note that although the program attempts to interpolate the positions of peaks, this may not be very accurate in regions where the peaks are very spread out (kappa near 0) or on the edges of the map.
If the keyword RMS is present, then the peak threshold is <peak> * RMS density, otherwise <peak> is the absolute threshold in the scaled map.
If the keyword OUTPUT is present, the unique peaks will be output to a file whose name may also be given (default filename or logical name PEAKS). The keyword RMS must precede OUTPUT if both are present.
If more than one of these symmetries is present, additional symmetry is generate by their combination. The asymmetric units required are given in the following table:
Symmetry Asymmetric unit
-------- omega phi kappa
no symmetry 180 360 180
1. 180 - omega, 180 + phi 90 360 180
or 180 180 180
2. 180 - omega, -phi 90 360 180
or 180 180 180
3. 180 - omega, 180 - phi 90 360 180
or 180 -90) 180
to +90)
4. omega, 180 + phi 180 180 180
In the program, the PLOT option will always try to plot a complete stereogram of all kappa sections. In the absence of symmetry, each kappa section is split into two hemispheres, omega 0 to 90 and omega 90 to 180. For symmetries 1, 2 and 3, only the hemisphere omega 0 to 90 is plotted. For symmetry 4, the two quarter spheres phi 0 to 180 for omega 0 to 90 and omega 90 to 180 are plotted together in the same circle. The PLOT option is not normally useful if only a small part of the asymmetric unit is calculated.
+ two internal scratch files
polarrfn hklin tpfktrunc.mtz
mapout tself.map
plot self.plt
<< eof
TITLE T-PFK self-rotation R=29A, 5 - 7 A
SELF 29
RESOLUTION 7 5
CRYSTAL FILE 1 ORTH 1 BFAC -20 SYMMETRY P21
LABIN FILE 1 F=FP SIGF=SIGFP
LIMITS 0 180 5 0 180 5 0 180 5
MAP
PLOT 10 10
FIND 2 20 RMS OUTPUT peaks.dat
eof
#!/bin/csh -f
#
# Self-rotation function
#
set resolution = 15 3
set radius = 20
set u1af = {$scr0}/u1afobs_fc117
# Calculate whole map, & search for peaks
polarrfn hklin {$u1af} mapout u1aself << eof-1
title U1A Self-Rotation function, resolution ${resolution} radius ${radius}
self ${radius}
resolution ${resolution}
crystal file 1 bfac -20
labin file 1 F=FP SIGF=SIGFP
limits 0 180 5 0 180 5 0 180 5
map
find 5 100
eof-1
# Now plot just the kappa = 180 deg section
plot:
polarrfn hklin {$u1af} mapin u1aself plot u1aself << eof-2
title U1A Self-Rotation function, resolution ${resolution} radius ${radius}
self ${radius}
resolution ${resolution}
crystal file 1 bfac -20
labin file 1 F=FP SIGF=SIGFP
limits 0 180 5 0 180 5 0 180 5
read 180 180
plot 10 10
eof-2
polarrfn hklin tpfktrunc
hklin2 uniqsfpfk.mtz
mapout tcross.map
<< eof
TITLE T-PFK cross-rotation R=29A, 5 - 7 A
CROSS 29
RESOLUTION 7 5
CRYSTAL FILE 1 ORTH 1 BFAC -20 SYMMETRY 4
LABIN FILE 1 F=FP SIGF=SIGFP
CRYSTAL FILE 2 ORTH 1 BFAC -20 SYMMETRY 1
LABIN FILE 2 F=FC SIGF=FC
LIMITS 0 180 5 0 360 5 0 180 5
MAP
FIND 10 20
eof