| NONIUS
CAD4/MACH3
User manual |
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Introduction
Reflections
locating and centering
Orientation
matrix determination and indexing
Other
routines provided for operator convenience
Reflection locating
Locating
reflections, SEARCH PHOTO
Procedure
for locating reflections, SEARCH PHOTO
Reflection centering
Centering
reflections, SETANG DETTH SET4
Procedure
for centering reflections, SETANG DETTH SET4
Orientation
matrix determination and indexing
Introduction
Matrix
determination based upon known cell parameters, RAMCEL
Matrix
determination based upon setting angles, INDEX and INDCON
Index
utility programs, REIND LS and RINDEX
Unit-cell
least-squares refinement with constraints, CELDIM
Matrix transformation, TRANS
Procedure for matrix
determination
Other
convenient routines, SCAN TH OTPLOT ANIVEC LEARN
General
scanning routine, SCAN
Calculating
h,k,l limits and number of reflections, TH
Omega
- theta profile plot, OTPLOT
Analysis
of anisotropic mosaic crystals, ANIVEC
Learnt
profile analysis, LEARN
Peak analysing method
Routines related
to
special hardware
Axial photographs,
AXIAL
Nimbus
search, NIMBUS
Texture
analysis, TEXIN TEXOUT TEXCOL
Introduction
The crystal orientation group consists of a number of routines to perform
the various operations which are necessary to prepare for data collection.
At least some of them will be needed.
Three sub-groups of commands are available:
Reflections locating
and centering
| SEARCH | Scans through reciprocal space to find and center reflections, given only a starting point. The setting angles of the reflections found are stored in the CRYSTAL file. |
| PHOTO | Locates and centers reflections observed on a Polaroid rotation photograph. The setting angles of the reflections found are stored in the CRYSTAL file. |
| SETANG | Centers reflections of which the setting angles are already known. This procedure is also integrated in SEARCH and PHOTO. |
| DETTH | Determines the theta angle independent of the zero error of the detector. The mean value for theta is placed in the list. |
| SET4 | Centers reflections at 4 equivalent positions PP, NH, NN and TN. The mean setting angles are placed in the list. |
Orientation
matrix determination and indexing
| RAMCEL | Calculates an orientation matrix, or based on unit-cell information, a direct axis direction and the setting angles of two indexed reflections, or based on the crystal orientation and the setting angles of one indexed reflection. If this sort of information is present, RAMCEL is preferred to INDEX. |
| INDEX | Produces a primitive unit cell, an orientation matrix and assigns indices to the setting angles of the reflections in the list. Requires a list of at least 3 accurately centered reflections. |
| INDCON | continues the last IND |
| REIND | Re-indexes the list of setting angles using the current orientation matrix, followed by LS |
| LS | refines the orientation matrix by a least-squares procedure using the reflection list. |
| RINDEX | Gives the (non-integer) values for the indices of the reflections, which are flagged N, without changing the matrix. |
| TRANS | Transforms or reduces the cell and re-indexes based upon the new unit-cell. |
| CELDIM | produces a constrained unit-cell. |
Other routines provided for operator convenience
SCAN
performs scan using one or two goniometer axes; the center of the scan is the current goniometer position. An intensity profile is printed.TH
calculates maximum h,k,l-values approximates the number of reflections within operator specified theta limits.OTPLOT
performs successive omega scans on reflections in the CRYSTAL file and plots the results as an omega-theta plot.ANIVEC
calculates the direction vector in case of anisotropic mosaic splitting of the crystal.LEARN
performs a learnt profile analysis on reflections in the the CRYSTAL file.AXIAL
sets up for axial oscillation photograph and conducts oscillation according to operator specifications.NIMBUS
locates and centers a particular reflection; usually when applying the high pressure cell.TEXTURE
performs texture analysis, using the texture device.Reflection locatingLocating reflections, SEARCH PHOTO
SEARCH
An automatic routine to search for and center reflections. From given a starting point, SEARCH will scan through reciprocal space to find reflections with an intensity above a level set by the operator. A novel peak/background discrimination algorithm provides the ultimate in sensitivity and adapts to the actual background intensity. The actual search, at any particular goniometer position, is by PHIK rotation using an operator specified rotation speed of 1 to 12 times 16.48 degrees/min. Thus weakly diffracting crystals can be handled at the expense of time, while normal crystals can be investigated quickly.
Up to 7 reflections may be found during one PHIK scan. These reflections are then centered and the settings put in the reflection list(the CRYSTAL file). SEARCH automatically resumes until the list is filled with 25 reflections, or until it is interrupted by setting SR=XXX1. The CRYSTAL file is not cleared by starting SEARCH, but only by an 'LK' command (see LIST entry operations ).
SEARCH can operate in two modes:
Normal mode :
A starting point in theta and chie and a phi range are given. Chie is physically limited to + 100 degrees. A spiral around the starting values theta and chie is stepped through. At each point the operator specified phi range is scanned.
Theta mode :
The theta mode is specified by a negative theta value. In this case, the search is made at constant theta over the half-sphere in reciprocal space by stepping chie scanning phi. The search continues on spheres with alternately higher and lower theta values.
The steps in chie take into account the height of the manually inserted
slit in front of the detector (SLIT, usually 4.0 mm), the actual theta
angle and the distance from the detector to the crystal (RADIUS, normally
173.0 mm, with extension bracket mounted 368.0 mm see CAD4
Geometry). The steps in theta depend on the width of the horizontally
variable aperture (9 mm for SEARCH) and the distance from the detector
to the crystal.
Operation:
The scan angle for the first OMK scan after a peak is found, is done using the setang scan parameters SWOMA and SWOMB (see Setang scan parameters). For normal crystals, use a SWOMA-angle between 0.6 and 1.0 degrees. It is important that crystals with widely profiled reflections are scanned with a large enough scan angle, because it will be difficult to analyse a profile when only the top is seen.
The program prompts 'T C P?'.
The operator must supply the starting position in theta and chie, for
the peak hunting procedure, in theta and chie and the PHIK range in degrees.
For Mo and Cu radiation theta values of 8 and 15 degrees respectively may
be suitable values to find reflections quickly. The choice will be a compromise
between speed of the hunting procedure and correctness of the unit-cell
parameters resulting after SEARCH and INDEX.
Note that if the theta is negative the theta mode is selected.
The program prompts 'Phi offset'.
The operator must supply the starting position of PHIK in degrees.
Combined with the PHIK range above, it is possible this way to search in
different phi areas.
The program prompts 'SP DF?'.
The operator must specify the speed of the PHIK scan in units ranging
from 1 to 12. Then the scan speeds range from 1*16.48 to 12*16.48 deg/min.
Normally 12 is used as input value (implicitely 197.8 deg/min). Lower speeds
can be used to search on weakly diffracting crystals. The operator must
also specify a discrimination factor for the peak/background discrimination
routine. A proper value in case of a low background would be 1. Higher
values will decrease the sensitivity, but will reduce the time spent in
trying to center diffuse, weak or noise peaks. Experience will develop
a feeling for the optimum value.
Examples SEARCH dialogue:
| normal mode | theta mode |
| CD0> SEARCH<CR> | CD0> SEARCH<CR> |
| T C P? 8 15 180<CR> | T C P? -8 15 120<CR> |
| Phi offset? 0<CR> | Phi offset? 0<CR> |
| SP DF? 12 1.5<CR> | SP DF? 10 2.5<CR> |
Terminal output is controlled by the switch register (see Terminal output).
SR=2XXX-Profile output during centering.
SR=1XXX-Centering information.
SR=X4XX-Phie scan profile output.
PHOTO
An automatic routine to search for and center reflections which have been observed on a Polaroid rotating crystal photograph (see List entry).
PHOTO is a special SEARCH routine. For its starting values it looks in the CRYSTAL file for reflections having angle status equal P. These reflections were found on a Polaroid rotation photograph and entered into the list using LPH (see List entry). The setting angles of these reflections are known apart from PHIK. PHOTO searches for these reflections over a phi range of 360 degrees in a number of scans. The number of PHIK scans depend on the value of chie and is assigned by the program.
Following the scan, the first reflection found is centered and the setting angles are written into the CRYSTAL file. The routine continues until it has treated each reflection flagged with a P. Following the centering the angle status is set to S.
Operation:
After the reflection has been located it will be centered automatically
by SETANG; the OMK scan angle chosen in this procedure is controlled indirectly
by the operator through SETPAR (see Setang
parameters).
The program prompts 'SP DF?'.
The operator must supply the scan speed for the phi rotation and the
peak/background discrimination factor (see SEARCH).
Example PHOTO dialogue:
CD0> PHOTO<CR>
SP DF? 8,3.0<CR> (see Note below)
Terminal output is controlled by the switch register (see Optional terminal output). SR=2XXX-Profile output. SR=1XXX-Centering information.
If a reflection is not found, program prints: LISTNR 'NOT
FOUND'
iii. Notes on the use of SEARCH and PHOTO If SEARCH or PHOTO succeeds in finding peaks, but fails to center the reflections, it is advised to check the contents of SETPAR and GONCON. All diagnostic output obtainable with SR=X4XX should also been examined carefully. To avoid waste of time optimizing weak reflections, it is advised to use larger DF values in PHOTO than normally appropriate for SEARCH.
Procedure for locating reflections, SEARCH PHOTO
SEARCH
In both modes the SEARCH routine explores the reciprocal space in a systematical manner. The chie and theta angles at which the PHIK rotation has to be done are generated from the values specified by the operator and result in the search patterns depicted below.
Initially, SEARCH uses an aperture which has a diameter of 9mm in the horizontal direction. Therefore, steps in theta are chosen to be equal to (5/RADIUS)*(180/pi) degrees. (RADIUS and SLIT are taken from the GONCON list, Chapter VII, section D). The effective vertical diameter of the aperture depends on the size of the manually inserted slit. Note: Be sure that GONCON contains values corresponding with the hardware.
The steps, SI, in chie(in radians) are generated according to the following expression, which depends on theta.
SI = arctan (SLIT + 2.0)/[RADIUS * sin(2*THETA)]
The position of chie and theta are limited to the following ranges:
-85.5 < chie < 85.5 and 1.5 < theta < 75.0
When positions are generated which lie outside these ranges, the PHIK rotation is not executed and the next positions of chie and theta are calculated. The new values are again compared with the ranges allowed. If necessary, new positions are generated, etc. When the operator specifies the starting values outside the ranges mentioned above, the SEARCH routine generates values for chie and theta until the conditions are met. Then a PHIK rotation is done.
SEARCH and PHOTO
During a phi scan 96 dumps of the intensity are made. The aim of the phi range selection is to achieve that one reflection takes approximately 1/96 of the scan. Therefore the phi range(PANG) specified by the operator is covered in a number of steps, depending again on the chie angle. The expression used for the number of steps (M) is given below.
M = integer (PANG*cos(CHIE)/40 + 0.5)
Thus, with PANG = 180(degrees) the actual chie being 80 and 0, give
the values 1 and 5 to M, respectively. Analysis of the phi scan profile
is done in the subroutine SPEAK. It uses a procedure in which the results
of one scan are doubled as shown here:
Intensity evaluation of PHIK scan dumps for peak location.
This procedure results in 2 single and 95 double dumps. Now the double dump with the highest intensity is selected and the intensity of that dump is named PEAK. The background BG is determined from the remaining dumps. Then PEAKF = PEAK - BG. The discrimination level (D) is calculated from the background using the empirical formula (derived by Monte Carlo method):
D = 0.9709*BG + 4.3658*BG**0.5 + 2.6733.
However, the BG is calculated from less than 96 locations. Therefore the discrimination factor, DF, is supplied by the operator. DF should be equal to about 1 or higher. If the crystal investigated produces a high background D will get the value of BG. In such cases values for DF should have the value 3 or higher. If PEAKF > D*DF, a peak is located. Optional output is provided, when SR=X4XX is set (see Optional terminal output).
Up to 7 peaks may be found and analysed from one PHI scan. The positions found are subsequently centered by the centering subroutine SETSUB.
Notes on the procedure for SEARCH and PHOTO
If SEARCH or PHOTO succeeds in finding peaks, but fails to center the reflections, it is assumed to check the contents of SETPAR and GONCON. All diagnostic output obtainable with SR=X4XX should also been examined carefully. Using this information it will be possible to position the supposed reflections from the keyboard and check with large aperture and scan angle their presence. If a reflection appears on the edge of the PHIK-scan, generally a larger SWOMA and APTA will allow these to be centered. For finding weaker reflections a smaller value for SP will help and for centering weak reflections QFAC must be increased. To avoid waste of time optimizing weak reflections not visible on the polaroid film, it is advised to use larger values for DF (PHOTO) than normally appropriate when using SEARCH. If a particular reflection found on a polaroid film cannot be found, do verify your all seems to be right, try again using smaller values for both SP and DF.
Centering reflections, SETANG DETTH SET4
SETANG
An automatic routine to center reflections.
SETANG uses the list of reflections in the CRYSTAL file, except for the reflections with index flag N. Reflections with angle status of 'A' are centered. The new position overwrites the old and the angle status is set to 'S'. Operation:
No other input than the command 'SETANG' is required. Scan angles and apertures are chosen by the program.
SETANG centers all of the reflections in the list with angle status of 'A' and changes that status to 'S' to suppress unintended recentering. The operator must change 'S' to 'A' with LCA if further centering is desired. During goniometer alignment the reflections should be recentered after each adjustment.
Note: When the theta angle status is set to 'T', the theta angle in the list is not changed by SETANG.
Terminal output is controlled by the switch register (see Optional terminal output). SR=2XXX-Profile output. SR=1XXX-Centering information.
Selection of switch register=1000 is useful during goniometer alignment. The output provides one significant digit more than is requested normally.
Note: The profile output is useful for detecting abnormal or twinned reflections. It should be stressed, that for matrix determination and alignment the centering procedure SETANG needs to be repeated at least once to obtain accurate angles. This is due to the iterative character of procedure.
DETTH
The DETTH routine is a simplified SETANG routine. It only determines the theta angle, independent of the zero error of the detector position. After the normal centering procedure (described above) is carried through, DETTH conducts an omega scan at the NN position (negative theta, negative HKL). The difference between the omega values of the original reflection and of the NN reflection is an accurate measure for theta.
The theta value thus obtained is put in the list and the theta angle status is set to 'T'. Upon subsequent recentering using SETANG or DETTH the theta value stored will not be changed unless the status is changed by the operator again (see Status codes).
SET4
A routine to produce optimized setting angles for the reflections, except for the reflections with index flag N. The SET4-routine uses the reflections from the CRYSTAL file. These reflection(s) are centered at position PP and at the positions NH, NN and TN, and the appropriate mean setting angles are calculated. These angles are placed in the CRYSTAL file and the angle status IRSANG is set to Q. The measurements are done in an time-saving sequence; thus the sequence of the measurements is not always the same.
PP position in the list: THETA, (HKL), PSI NH negative hkl: THETA, -(HKL), PSI TN theta negative: -THETA, (HKL), PSI+180 (see chapter II) NN neg.hkl; neg.theta: -THETA, -(HKL), PSI+180 ( ,, ,, )
NH, TN and NN are effected by omega and theta changes; when theta > abs (THNEG (max)) the reflection is not used.
Example SET4 output:
CD0>
SET4<CR>
| 7 | 105.838 | TN | -17.613 | 13.582 | 179.7 | 303.6 |
| 7 | 17.607 | NN | ||||
| 7 | -17.616 | NH | ||||
| 7 | 17.600 | TN | ||||
| 7 | 17.609 Q | T |
7 TN
7 NN 13.544 105.842
0.2 331.3
7 NH 13.584 -74.176
-179.7 283.4
7 TN 13.536 -74.165
-0.2 317.7
7 T Q 52.694
57.071 -103.873 13.303 17.680
-74.165
CD0>
General comment on negative theta-values: in 3-circle convention PP,
etc. are given by:
| PP | theta, phib, chib | (hkl) |
| NN | -theta, phib, chib | -(hkl) |
| NH | theta, phib+180, -chib | -(hkl) |
| TN | -theta, phib+180, -chib | (hkl) |
With PP and TN the same reflection is measured, but the directions of the beams are reversed. (moreover the crystal is 'reflected' with respect to the horizontal plane, compared to psi+180 at +theta, but when we associate directions with psi, we need not consider this detail. It would play a role when corrections for inhomogeneity of the primary beam were applied, which is a rather uncommon procedure.) This leads to the conclusion that a psi of 180 degrees has to be attributed to the bisecting position -theta,phib,chib. (for +theta,phib,chib, psi is 0 by definition.) In DATCOL it is checked whether positioning of AA (alternative angles) is faster, when theta is negative.
Procedure for centering reflections SETANG DETTH SET4
The same reflection centering procedure is used in SEARCH, PHOTO, SETANG, DETTH, SET4 and orientation control of DATCOL (see Data collection). The differences in the procedures depend primarily upon how the original reflecting position was determined. SEARCH systematically scans reciprocal space until a reflection is found. Each reflection is centered when it is found and the centered position is stored in the CRYSTAL file. Reflections which were observed on a Polaroid rotation photograph, and entered into the CRYSTAL file with the LPH command, are first located under PHOTO control by means of a PHIK scan and subsequently centered. SETANG and DETTH are more general centering routines. They only center reflections in the reflection list, which have status code 'A'. DETTH is used to determine the theta angle independent of the zero position of the detector.
When setting angles are known, these are entered into the list with the command LI. When an orientation matrix exists, they are entered by the command LH (see List entries). SETANG is normally used to center the reflections in the list, then the orientation matrix can be determined or refined. SETANG should be used to recenter the reflections in the list each time the crystal moves or is moved.
Data collection orientation control periodically checks a strong reflection or a reflection flagged 'O' for crystal movement. If necessary, all reflections flagged 'O' and 'R' are recentered, the new settings are stored, the orientation matrix is redetermined and data collection resumes (see Reflection list).
Centering a reflection means accurate determination of the setting angles for the reflecting position. It involves both setting the crystal to the best reflecting position and measuring that position.
Centering a reflection after finding it by SEARCH or PHOTO usually involves an exploratory omega scan through the starting position to locate the reflection using the 9mm aperture. Centering of reflections which have been entered into the list using LI and/or LH, starts with an omega/2-theta scan using an aperture specified by the operator through SETPAR. If the program being used is not SEARCH or PHOTO, the status of the scan information is checked. Valid scan information (scan angle, scan speed, attenuator setting) will be used and thus overrules SETPAR data. The other parameters will be determined. The scan intensity profile is analysed (see Peak analysis). The center of gravity of the peak is determined. Based on the intensity ration of 2:1 for wavelength LAM1 and LAM2, the theoretical peak LAM1 position is calculated as an offset from the center of gravity. Omega is set to the LAM1 position.
When the intensity is too low, too high or the profile is too narrow (< 6/96*scan angle) or too wide (> 60/96*scan angle) a message is printed and the reflection is rejected.
Now, a theta scan is done using APMIN (usually 1.3mm width) to position the detector more accurately. The theta scan angle (delta Theta) is chosen to match the area covered by the previous omega scan with the 9mm aperture (10mm is used by the program to be sure that the reflection is found).
deltaTheta = (1/2)*(360/2pi)*(10/RADIUS) degrees
Again the reflection profile is analysed and the calculated offset of the center of gravity is applied to theta.
Measuring the position of the reflection involves measuring the actual position of the reflection on the detector. A method has been developed to determine this position. This method uses two slanted slits at angles of +45 and -45 degrees to the horizontal plane. These slits will be positioned in front of the detector automatically, controlled by the aperture encoding system.
Two theta scans are done through the reflection, one with each slit. Here the scan angle deltaTheta is defined as:
deltaTheta = (1/2)*(360/2pi)*[(SLIT + 0.5)/RADIUS] degrees
This expression sets the vertical area covered by the skew slits to be equal to the area covered by SLIT. The reflection profiles are analysed and the offset of the centers of gravity are determined. GRAV1 and GRAV2 are the offsets from the beginning of the scan calculated from the first and second scan with the slanted slits, respectively (cf. figure below).
Fig. X.3. Theta area covered by scans with slanted slits.
These offsets GRAV1 and GRAV2 (fractions of the scan angle), are used to calculate both the distance from the horizontal plane and the offset in theta.
theta offset = 0.5*(GRAV1 + GRAV2 - 1.0)*deltaTheta degrees
distance from hor. plane = (GRAV1 - GRAV2) * deltaTheta degrees
When the reflection is not in the horizontal plane (h.NE.0) the crystal will be rotated around the primary beam. The rotation required (alpha) amounts to:
alpha = arctan[sin h/(sin(2THETA)*cos h)] degrees
New setting angles are calculated for this reflection. If ABS h < 0.6 the setting angles calculated on basis of the above corrections will be stored in the list. If ABS h > 0.6 a new omega scan is done to verify the calculated position. When the results are accepted, the calculated settings are written in the CRYSTAL file. If the results are not acceptable, the theta scans using the slanted slits will be repeated, etc. If the reflection is too weak for accurate centering, the message LISTNR 'weak' is printed, the settings if present in the list will not be refreshed and the scan status is set to 'W'. If during SEARCH or PHOTO a reflection turns out to be too weak it will simply be ignored. Too many reflections found 'weak' during SEARCH or PHOTO may be an indication that the SETPAR parameters should be optimized to match the properties of the crystal being investigated (Cf. Chapter VIII, section G). If the reflection intensity is too high(even with the attenuator) to be measured accurately, the message LISTNR 'strong' is printed. If the reflection profile is too narrow or too wide (see specifications given above), the message LISTNR 'noise' is printed. Scan information which was determined will be written into the list for optimization of subsequent recentering, but the scan status will be modified accordingly (see IRSSCN).
Orientation Matrix determination and indexing
There are two primary routines available for initial orientation matrix determination, namely RAMCEL and INDEX. RAMCEL requires detailed information concerning the crystallographic unit-cell and information about the crystal orientation. INDEX only requires a number (>3) of reflections. These reflections should have been centered by SETANG, SEARCH or PHOTO.
If unit-cell information is available, and if one or two reflections can be located, based on experience or photographic data, RAMCEL can be used. It gives the user control of the final orientation matrix.
INDEX can be used in different modes both interactive and non-interactive. INDEX works towards a primitive crystallographic cell. This cell by convention is normalized such that A<B<C and the angles are all acute or all obtuse. Such a cell may not be appropriate for the system under investigation, though it will enable locating reflections after indexing. A different cell and set of indices might produce a matrix with smaller standard deviations. In other words, both routines, RAMCEL and INDEX, are convenient tools which must not be used blindly. The primitive cell used by the program to orient the crystal in reciprocal space may bear no relationship at all to the cell and indices derived by conventional methods. In general, the larger the celldimensions are, e.g. some large proteins, the less likely the indexing routines are to produce the expected or correct cell. It is important to note here that in this event, externally calculated indices may not correspond to the same reflections. The program doesnot use systematic absences or other symmetry related phenomena in its cell calculations.
A transformation routine gives the user control of the above problem by enabling the primitive cell to be transformed. Indices and a matrix corresponding to the new cell are then produced.
Additional routines enable indexing of new reflections in the list or re-indexing(REIND) the entire list based on the current cell and least-squares refinement(LS) of the matrix following the addition of reflections to the list or following recentering all reflections in the list after adjustment of the crystal.
Matrix determination based upon known cell parameters, RAMCEL
RAMCEL enables the operator to calculate the orientation matrix R based on unit-cell parameters and some information from the mounted crystal. Then, the matrix R will normally be used to locate additional reflections to be put in the list for further centering and matrix refinement. A reciprocal matrix B is calculated from the specified cell constants. This matrix must be rotated to match the orientation of the crystal as it is mounted on the goniometer head.
If U represents the rotation matrix, R can be written as R = U*B.
In determining U, three distinct cases are encountered:
1. The crystal is mounted along a direct rotation axis (u, v, w). The reflecting position and indices of one additional reflection should be known.
2. The crystal is mounted along a reciprocal rotation axis (h, k, l). This is known as the top-reflection. The reflection position and indices of one additional reflection should be known.
3. The reflecting position and indices of two different reflections should be known (not both may be top-reflections).
The idea is that two vectors in B space are related to two vectors in R space. Only the directions of these vectors are considered. The included angle in B space should be equal to the included angle in R space; the difference between these two angles is denoted as EPS. EPS must be approximately zero. Otherwise the calculation is not valid. EPS is printed for verification. The second vector in R space is adjusted to make the angles equal, then the rotation U is calculated. Finally R is calculated and printed.
It should be realized that there are two possible solutions, only one of which is presented. The other solution will be given if all indices of the second reflection are inverted. The two reflections given above will obviously fit both solutions, but in general, only one of the two grids will fit the crystal. The correct solution is the one that gives accurate settings for other observable reflections. Position several characteristic reflections with command 'HP' and examine these using SCAN.
Operation:
RAMCEL prompts 'A B C alp bet gam?' The operator must supply the unit-cell constants a, b and c in Angstroms and the angles alpha, beta and gamma in degrees. The program will then ask 'R T N?'. The operator must typ
R Direct rotation axis case. The program will promt 'U V W?'. The operator must supply the direct cell indices. The program will prompt 'H K L T P O K?'. The operator must supply the indices of any known reflection outside the direct rotation axis and the kappa geometry position theta, phik, omk and kappa in degrees.
T Top-reflection case. The program prompts 'H K L?'. The operator must supply the indices of the top reflection. The program then prompts 'H K L T P O K?' as above.
N Case of two known reflections. The program prompts twice for 'H K L T P O K?'
RAMCEL then prints EPS, the calculated orientation matrix R and NIGGLI matrix S. The NIGGLI matrix may be used to derive space group information.
Notes pertaining to the example given on the next page: Ramcel top-reflection case.
In this example of the use of RAMCEL, a reflection at CHIE=90 was chosen as the top-reflection. This reflection, the 4,0,0, was centered manually:
THETA was set to the expected value, PHIK=0, OME=THETA, CHIE=90. The reflection was located by scanning in OMEGA, then the horizontal arc of the goniometer head was adjusted to obtain OME = THETA. The procedure was repeated with PHIK=90 and the other arc.
A reflection at CHIE=0 was chosen as the other reflection. This reflection, either the 0,4,0 or the 0,0,4, was located manually:
THETA was set to the expected value, PHIK=0, OME=THETA, CHIE=0. The reflection was located by rotating PHIK until it was found. The position was measured using command MK.
The unit-cell parameters and cell angles are entered first. Then the 'T' for the top-reflection case and the indices of the top reflection. Next the index and position of the second reflection are typed in. The resultant matrix is tested by HP for the 0,4,0. The aperture is set to 9mm and the shutter opened. If the reflection was not present, the wrong index was used for the second reflection. Having verified the matrix, the operator may now proceed to fill the list with reflections to be centered using LH. These reflections must be centered with SETANG. The crystal will then be ready for data collection.
Example RAMCEL dialogue:
CD0> SCAN<CR>
MM? O<CR>
SA N R? 1 1<CR>
1 1111
1111
23470999789878937549653322333635859522
1111112379264226748124787646479363940271070121185
010995902595979965476813802002857680290630996093
1 0 1 0 N 1 15
CD0> MK<CR>
THETA = 16.15 PHIK = 90.73 OMK = 16.16 KAPPA
=
0.00
CD0> RAMCEL<CR>
A B C alp bet gam? 7.65,7.88,11.08,90.,90.,90.<CR>
R T N? T<CR>
H K L? 4,0,0<CR>
H K L T P O K? 0 0 4 16.16 90.73 16.16 0<CR>
EPS= 0.00
R11= 0.000000 R12= -0.002617 R13= -0.090245
R21= -0.000000 R22= 0.126893 R23= -0.001150
R31= 0.130719 R32= 0.000000 R33=
0.000000
S11= 58.5226 S22= 62.0949 S33=122.7673
S32= -0.0001 S31= -0.0000 S21=
-0.0001
A= 7.6500 B=
7.8800 C= 11.0800
Alp= 90.0001 Bet= 90.0000 Gam=
90.0000 Vol=
667.9294
CD0> HP<CR>
H K L? 0 4 0<CR>
CD0> SAP<CR>
<CR>
(to select the 9 mm aperture)
CD0> SO<CR>
CD0>
Matrix determination based upon setting angles, INDEX and INDCON
INDEX produces a primitive cell, a corresponding orientation matrix and it assigns indices to the reflecting positions stored in the CRYSTAL file.
Example INDEX dialogue (mode #1 (SR=7600)):
CD0> INDEX<CR>
Enter axis limit in Angstrom [ 116.3]<CR>
Information ? (Y/N) [N] <CR>
Index-Status: HHHHHHHHHHHHHHHH/////////
Nr S H K
L Dev-Ang dTh
dPh dCh 0.0090129
1 H 3.001 -1.999 1.999
0.0201 -0.000 -0.083 0.014 0.0001394
2 H 2.002 -1.001 -3.000
0.0307 -0.003 -0.005 -0.030 0.0002479
3 H 3.998 0.004 -1.995
0.0471 0.010 -0.048 -0.006 0.0006244
4 H 3.997 4.001 4.007
0.0871 -0.004 -0.093 -0.011 0.0007295
5 H 5.001 2.996 2.989
0.1233 0.005 0.144 0.013
0.0009989
6 H -0.999 -2.998 2.001
0.0207 0.003 0.023 -0.011 0.0001815
7 H 0.995 -4.001 0.999
0.0546 0.002 0.061 0.043
0.0004105
8 H 3.009 0.005 3.004
0.0873 -0.012 0.157 0.066 0.0007721
9 H 3.002 -1.999 1.998
0.0498 -0.000 -0.157 0.041 0.0003416
10 H 2.996 -3.002 1.997
0.0350 0.004 0.093 0.026
0.0003336
11 H 0.999 -3.005 -0.002 0.0449
-0.007 0.025 0.042 0.0004087
12 H 0.998 -4.000 3.004
0.0470 -0.004 0.093 0.018 0.0004586
13 H -2.996 -5.000 -2.999 0.0437
0.002 -0.020 -0.039 0.0003552
14 H 3.000 -0.999 -2.000 0.0187
0.001 -0.014 0.013 0.0001370
15 H -0.998 -4.000 0.002 0.0372
-0.001 -0.003 -0.037 0.0002331
16 H 3.002 2.998 1.004
0.0878 0.001 -0.024 -0.085 0.0004827
Reciprocal axis matrix
Direct axis matrix
0.011927 -0.059046 -0.049186
-2.932516 9.036276 7.205751
0.071514 0.029826 -0.056197
-9.998953 4.902071 -4.28748
0.053951 -0.061433 0.050456
-9.038591 -3.693645 6.894207
Niggli-values
Sigma direct axis matrix
142.1768 142.3919 142.8692
0.003645 0.003553 0.002703
42.7112 42.8070
42.7240 0.002735 0.002665
0.002028
0.004590 0.004473 0.003403
Cell parameters
Sigma cell parameters
11.9238 11.9328
11.9528 0.0033
0.0026 0.0042
72.5752 72.5212
72.5260 0.0232
0.0264 0.0197
0.299454 0.300352 0.300272
0.000387 0.000440 0.000328
Volume= 1505.8270
0.7981
Index-Status: HHHHHHHHHHHHHHHH/////////
Next solution? (Y/N) [N] <CR>
CD0>
Explanation:
When during INDEX, REIND or LS SR=X2XX is set, the indices calculated are printed as real parameters with 3 decimal digits. After each h,k,l, the angle between the real scattering vector and the scattering vector calculated from the final orientation matrix is printed. It will be apparent that this angle should be as low as possible (finally for all reflections well below 0.1). In the columns dTh, dPh and dCh the difference between the real angle and the angle based on the orientations matrix is given. The header value in the header in the last column is 10 % of the shortest vector in the R matrix; the values below are the lenght of the difference vector between the real scattering vector and the one as calculated from the current R matrix. When this value is greater than the value in the header, the status of this reflection is changed to N and the message try REIND is printed after the cell dimensions. However, when INDEX is first used on preliminary data of a crystal, the angles will be larger. Recentering the reflections in the list will generally show a remarkable improvement. If not, there may be reflections in the list which have not properly been centered due to being in a streak, your crystal may move, etcetera. The reciprocal axis matrix printed is the final orientation matrix (see Kappa Geometry, section F). If the DETERMINANT equals one, this matrix will be identical to the preliminary matrix (apart from eventual interchange of columns). The Niggli-values (metric tensor) are:
a.a b.b c.c b.c a.c a.b
Cell parameters are a, alpha, cos(alpha) in the first column, b, beta, cos(beta) and c, gamma, cos(gamma), in the second and third column, respectively. The sigma-values printed are those derived by the least-squares procedures. They provide an additional possibility to judge on the quality of the final orientation matrix.
Note: Reflections in the CRYSTAL file, with index status 'N' are not used in the indexing operation. The indexing routine can operate in three Modes, depending on the response to the questions: 'Information ? (Y/N) [N]' and later 'Cell dimensions?' 1. Completely automatic 2. Interactive with primary vector changes allowed 3. Interactive with optionally primary vector changes allowed and grid search
SR=X2XX controls output of floating point indices (see Optional Terminal Output.)
*** Mode 1 --Automatic--
The question 'Information ? (Y/N) [N]' must be answered with <CR> or N<CR>. With SR=7600 all output is sent to the terminal. For an explanation of the procedure is referred to section F of this Chapter.
*** Mode 2 --Interactive with vector changes--
The question 'Information ? (Y/N) [N]' must be answered with Y<CR>. With SR=7600 all output is sent to the terminal. The primary vectors in reciprocal space are determined according to the algorithm described in section F of this Chapter and the primary vector components are printed as columns in the matrix. 27 shortest vectors with unique orientation are printed in the following form: Vector number, X,Y,Z components in reciprocal space, reciprocal vector length, composing two vectors from the reflection list(connected by '+' or '-') and H,K,L based on the current orientation matrix.
The question 'Print short vector angles?' must be answered by Y<CR> or N<CR>. Following an affirmative response a matrix is printed. This matrix displays the angles between short vectors and cosines of the angles. In the upper right-hand triangle the angles and in the lower left-hand triangle the cosines of the angles.
The question 'Change vectors?' must be answered by Y<CR> or N<CR>. After a negative response the program will continue as described in section F of this Chapter. After an affirmative response the operator must enter three 3 vector numbers (Cf. the list of shortest vectors). Any modification in the vectors will cause the question 'print vectors?' to be posed. Since the modification changed the current orientation matrix, the vector list will only show differences in calculated H,K,L.
Hereafter the operator may 'Change vectors?' again and so on, if considered necessary. Then the program continues as described in section F of this Chapter.
*** Mode 3 --Interactive with optionally vector changes and grid search--
The question 'Information ? (Y/N) [N]' must be answered with Y<CR> and SR=X1XX must be set before the number of short vectors is entered through the keybord. With SR=7700 all output is sent to the terminal.
The main dialogue is similar to the dialogue of Mode 2. After the negative response to the question 'Change vectors?', however, the question 'Cell dimensions?[D,R,N]' is posed.
If no dimensions of the unit-cell are available 'N' must be entered. Following the answers 'D' or 'R' the operator has to supply the cell dimensions in direct or reciprocal space, respectively. In both cases the determinant of the corresponding reciprocal matrix is calculated and, if cell dimensions were supplied, compared with the determinant of the current primary vector matrix. The results are printed and again it is allowed to 'Change vectors?'. If you have changed vectors a new determinant of the primary matrix is calculated and the results are printed.
If you do not want to change vectors and if the calculated Ratio is > 1.0, you are asked to 'Enter delta?'. Delta is the limit used in the grid search routine to allow for a certain deviation of both vector length and cosines of vector angles. The default value is 0.025. The output consists of a sequence number, a primary vector identifier and the indices specifying which vector in the current matrix corresponds with that primary vector in the user determined grid. The program tries to find the primary vector lengths of the user determined cell within the range specified by Delta using the matrix currently stored. Every time a third vector is found it tries to set up the specified grid using all combinations of first and second primary vectors found.
If one consistent set of vectors is found (with vector identifiers 1,2,3 and sequence numbers oo,pp,qq) the message 'oo,pp,qq Change these vectors if you want' is printed. If, at this point, the operator wishes to continue with the standard indexing routine SR=XXX1 must be set. On the other hand, entering a slash will continue the search.
If no other set is found 'Enter vector numbers' is printed. The operator should then type any set of sequence numbers 'oo pp qq'. Note that the storage capacity of this list of indices is limited to 54 entries. If this capacity is exceeded by the program, then the last entry for each vector identifier will be overwritten.
A new orientation matrix is now set up and the next output conforms to the output of Mode 1.
Example 1 INDEX dialogue mode #1 (SR=7600):
CD0> INDEX<CR>
Enter axis limit in Angstrom [ 116.3]<CR>
Information ? (Y/N) [N] <CR>
Index-Status: HHHHHHHHHHHHHHHHHHHHH////
Nr S H K
L Dev-Ang dTh
dPh dCh 0.0072334
1 H 0.000 -5.000 6.000
0.0083 0.001 0.005 -0.007 0.0001195
2 H -0.000 -4.000 5.000
0.0029 0.001 0.002 0.002
0.0000567
3 H 0.000 -2.001 8.000
0.0095 -0.002 -0.008 -0.005 0.0001284
4 H 0.000 -1.000 8.000
0.0008 0.000 0.001 -0.000 0.0000145
5 H 0.000 2.000 7.002
0.0064 -0.002 -0.004 -0.005 0.0001265
6 H 1.000 5.000 1.000
0.0073 -0.001 0.001 -0.007 0.0001037
7 H 1.000 4.000 2.000
0.0076 0.003 0.001 0.008
0.0001494
8 H 1.000 4.000 -0.001
0.0035 0.000 0.004 -0.001 0.0000448
9 H 1.000 3.000 5.999
0.0033 0.002 0.003 0.001
0.0000922
10 H 1.000 0.000 7.998
0.0038 0.004 0.004 0.001
0.0001908
11 H 1.000 -2.999 6.001
0.0077 0.001 0.008 0.004
0.0001008
12 H 1.000 -4.000 4.001
0.0046 0.000 0.003 0.003
0.0000569
13 H 1.000 -4.001 1.000
0.0102 -0.003 -0.005 0.009 0.0001639
14 H 2.000 -4.000 -0.001 0.0031
0.001 -0.004 -0.001 0.0000644
15 H 2.000 -2.000 1.000
0.0045 0.001 -0.007 0.003 0.0000589
16 H 2.000 -2.000 4.000
0.0089 -0.002 0.007 -0.008 0.0001448
17 H 2.000 2.000 1.000
0.0080 -0.001 -0.005 -0.008 0.0001065
18 H 2.000 2.000 3.001
0.0041 -0.000 -0.006 0.003 0.0000508
19 H 2.000 3.001 1.002
0.0113 -0.004 -0.018 0.003 0.0002343
20 H 1.999 0.000 3.999
0.0042 0.004 0.006 0.003
0.0001905
21 H 1.000 -3.001 5.001
0.0073 -0.004 -0.006 -0.005 0.0001935
Reciprocal axis matrix
Direct axis matrix
0.019553 0.070421 0.064585
-0.154360 -0.149664 3.483218
0.003899 -0.117999 0.032294
3.269563 -6.521198 -0.133642
0.288125 -0.001949 0.004250
11.965130 7.155701 -0.908827
Niggli-values
Sigma direct axis matrix
12.1790 53.2339
195.1944 0.000227 0.000154
0.000200
-7.4215 -6.0835
0.0058 0.000375 0.000255
0.000330
0.000671 0.000456 0.000590
Cell parameters
Sigma cell parameters
3.4898 7.2962
13.9712 0.0002
0.0003 0.0006
94.1752 97.1676
89.9870 0.0035 0.0042
0.0038
-0.072806 -0.124772 0.000227
0.000061 0.000073 0.000067
Volume= 352.0106
0.1325
Index-Status: HHHHHHHHHHHHHHHHHHHHH////
Next solution? (Y/N) [N] <CR>
CD0>
Example 2 INDEX dialogue mode #1 (SR=7600):
CD0> INDEX<CR>
Enter axis limit in Angstrom [ 116.3]<CR>
Information ? (Y/N) [N] <CR>
Index-Status: HHHHHHHHHHHHHHHHHH/HHH///
Nr S H K
L Dev-Ang dTh
dPh dCh 0.0068505
1 H 0.004 2.001 -3.997
0.0696 0.007 -0.230 -0.032 0.0004181
2 H 1.000 1.998 -2.001
0.0273 0.004 -0.009 -0.027 0.0001351
3 H -3.010 1.008 0.010
0.1675 -0.046 -0.132 0.103 0.0012775
4 H -3.013 -1.006 -1.001 0.0554
-0.051 0.013 0.054 0.0011501
5 H 0.001 1.002 -1.997
0.0763 0.004 -0.261 0.030 0.000234
6 H -1.012 0.000 -1.010
0.0730 -0.053 -0.038 0.064 0.0012040
7 H 0.999 0.001 -2.000
0.0322 0.002 -0.025 -0.030 0.0001052
8 H -1.015 0.002 -2.014
0.2130 -0.065 -0.199 0.151 0.0015815
9 H -0.001 -0.999 -2.000 0.0479
0.003 -0.057 -0.011 0.0001531
10 H 2.000 -0.001 -0.002 0.0633
0.002 -0.055 -0.033 0.0001873
11 H 0.002 3.003 1.002
0.0353 -0.012 -0.032 0.014 0.0003028
12 H 1.000 2.999 -0.001
0.0198 0.003 0.003 -0.020 0.0001164
13 H -0.002 4.999 1.994
0.0491 0.008 0.030 -0.039 0.0004134
14 H 2.995 3.999 1.996
0.0454 0.018 0.037 -0.027 0.0005093
15 H 3.993 3.000 1.998
0.0435 0.022 0.043 -0.004 0.0005802
16 H -2.996 -3.003 -3.998 0.0503
0.006 0.051 0.010 0.0004117
17 H 4.996 -1.999 -0.995 0.0336
0.019 0.011 0.032 0.0004753
18 H -3.996 3.000 -2.005 0.0594
0.006 0.002 -0.059 0.0004735
20 H 0.998 -7.998 -1.004 0.0308
0.007 -0.021 -0.023 0.0003879
21 H 0.999 -8.001 -0.004 0.0239
-0.002 -0.015 -0.019 0.0002814
22 H 0.000 -7.999 -1.999 0.0045
0.005 0.001 0.004 0.0001032
Reciprocal axis matrix
Direct axis matrix
-0.057791 -0.048845 -0.028099
-8.391244 -8.231930 2.659024
-0.056669 0.059630 0.008656
-7.106956 8.679410 4.441591
0.018267 0.030463 -0.061875
-5.976285 1.842937 -13.189819
Niggli-values
Sigma direct axis matrix
145.2480 145.5687 213.0837
0.005965 0.006254 0.011807
-0.1150 -0.0945
-0.0018 0.002429 0.002546
0.004807
0.004990 0.005232 0.009877
Cell parameters
Sigma cell parameters
12.0519 12.0652
14.5974 0.0065
0.0029 0.0092
90.0374 90.0308
90.0007 0.0317
0.0564 0.0364
-0.000653 -0.000537 -0.000012
0.000553 0.000984 0.000634
Volume= 2122.5806
1.3743
Index-Status: HHHHHHHHHHHHHHHHHH/HHH///
Next solution? (Y/N) [N] <CR>
CD0>
Example INDEX dialogue mode #2 (SR=7600):
CD0> INDEX<CR>
Enter axis limit in Angstrom [ 116.3]<CR>
Information ? (Y/N) [N] y<CR>
CD0>
Orientation matrix:
R11= .005060 R12= .123911 R13= .019565
R21= .006177 R22= .027372 R23= -.087840
R31= -.130110 R32= .006135 R33= -.003402
27 Short vectors:
nr x*
y* z*
d* from to h
k l
1 -.019561 .087834 .003400
.008109 20 -25 .00 .00 -1.00
2 -.143473 .060494 -.002733
.024251 14 -15 .00 -1.00 -1.00
3 .123911 .027366 .006123
.016140 1 -19 .00 1.00
.00
4 .104331 .115202 .009540
.024247 6 -7 .00 1.00 -1.00
5 -.084773 -.203066 -.012944 .048590
1 -2 .00 -1.00 2.00
6 -.034057 .181841 -.123280
.049424 7 -8 1.00 .00 -2.00
7 -.163023 .148292 .000662
.048567 21 -24 .00 -1.00 -2.00
8 .182546 -.236095 -.004036
.089080 4 -16 .00 1.00 3.00
9 .065262 .290857 .016306
.089123 11 -17 .00 1.00 -3.00
10 .024752 -.081537 -.133540 .025094
9 -12 1.00 .00 1.00
11 -.070389 -.297032 .113653 .106100
5 -6 -1.00 -1.00 3.00
12 .158036 -.154439 .129372
.065564 23 -24 -1.00 1.00 2.00
13 .089879 .209237 -.117134
.065579 7 -20 1.00 1.00 -2.00
14 -.118714 -.021089 -.136198 .033088
9 -16 1.00 -1.00 .00
15 .267312 -.033057 .008907
.072628 12 -13 .00 2.00 1.00
16 .109190 .121251 -.120518
.041149 21 -22 1.00 1.00 -1.00
17 -.272347 .027061 .121147
.089582 22 -24 -1.00 -2.00 -1.00
18 -.177567 .242164 -.125908 .106026
24 -25 1.00 -1.00 -3.00
19 .281898 -.127067 .135418
.113951 8 -24 -1.00 2.00 2.00
20 .168084 -.142068 -.130715 .065522
9 -14 1.00 1.00 2.00
21 -.238539 -.154988 .244646 .140774
21 0 -2.00 -2.00 1.00
22 .321097 -.302802 .128718
.211361 20 -21 -1.00 2.00 4.00
23 -.228393 -.142592 -.015559 .072738
10 -14 .00 -2.00 1.00
24 .172555 -.248549 .256218
.157200 7 0 -2.00 1.00 3.00
25 -.075359 -.303346 .243980 .157224
24 0 -2.00 -1.00 3.00
26 -.252812 -.060777 .117725 .081467
18 -21 -1.00 -2.00 .00
27 .276970 -.133310 .265763
.165114 6 0 -2.00 2.00 2.00
Print short vector angles? y<CR>
vector angles ( cosine degrees )
1
2 3 4
5 6 7
8 9
1 .00 54.66 90.00 54.66
144.81 35.89 35.20 154.82 25.19
2 .58 .00 144.66 109.33
90.14 62.06 19.46 150.52 79.86
3 .00 -.82
.00 35.33 125.19 90.00 125.20 64.82 64.80
4 .58 -.33
.82 .00 160.53 62.06 89.86 100.15 29.47
5 -.82 .00 -.58
-.94 .00131.45 109.61 60.38 170.00
6 .81 .47
.00 .47 -.66 .00 48.54
137.16 42.85
7 .82 .94
-.58 .00 -.34 .66
.00 169.98 60.39
8 -.90 -.87 .43
-.18 .49 -.73 -.98
.00 129.62
9 .90 .18
.43 .87 -.98 .73
.49 -.64 .00
10 -.57 -.33 .00
-.33 .46 .02 -.46
.51 -.51
11 -.83 -.16 -.39
-.80 .90 -.91 -.45
.58 -.92
12 -.70 -.81 .50
.00 .29 -.87 -.86
.85 -.43
13 .70 .00
.50 .81 -.86 .87
.29 -.43 .85
14 .00 .57 -.70
-.57 .40 .42 .40
-.30 -.30
15 -.33 -.96 .94
.58 -.27 -.27 -.82 .70
.10
16 .44 -.25 .63
.77 -.72 .74 .00
-.14 .67
17 .30 .87 -.85
-.52 .24 -.01 .74
-.63 -.09
18 .83 .80 -.39
.16 -.45 .91 .90
-.92 .58
19 -.53 -.92 .75
.31 .00 -.66 -.87
.80 -.16
20 -.70 -.81 .50
.00 .29 -.27 -.86
.85 -.43
21 -.24 .41 -.68
-.69 .59 -.60 .19
-.07 -.51
22 -.78 -.90 .55
.00 .32 -.80 -.96
.94 -.47
23 -.33 .58 -.94
-.96 .82 -.27 .27
-.10 -.70
24 -.68 -.66 .32
-.13 .37 -.94 -.74
.75 -.48
25 -.68 -.13 -.32
-.66 .74 -.94 -.37
.48 -.75
26 .00 .73 -.89
-.73 .51 -.27 .51
-.38 -.38
27 -.44 -.77 .63
.25 .00 -.74 -.72
.67 -.13
vector angles ( cosine degrees )
10 11
12 13 14
15 16 17
18
1 124.60 146.03 134.69 45.30 89.98109.50
63.66 72.47 33.98
2 109.21 99.28 144.27 89.88 55.29164.17
104.67 29.96 37.05
3 89.95 112.98 60.24 60.25 134.23 19.51
51.31 148.05 112.97
4 109.13 142.94 90.10 35.75 124.67 54.84
39.96 121.20 80.73
5 62.38 25.49 73.23 149.41 66.31105.69
136.28 75.94 116.92
6 88.71 154.99 150.24 29.75 65.14105.70
42.62 90.64 25.00
7 117.68 116.92 149.42 73.21 66.26144.70
89.87 42.68 25.49
8 59.06 54.24 32.03 115.18 107.30 45.31
97.79 129.31 156.43
9 120.89 156.44 115.16 32.03 107.25 84.31 48.12
95.09 54.25
10 .00 81.87 91.09 88.86
53.92 79.03 73.90 122.00 98.17
11 .14 .00 53.63 168.67
90.83 95.22 150.31 75.20 134.05
12 -.02 .59 .00
120.48 135.33 45.34 109.18 114.31 168.67
13 .02 -.98 -.51
.00 88.93 76.54 18.37 115.51 53.62
14 .59 -.01 -.71
.02 .00131.14 88.61 73.72 56.00
15 .19 -.09 .70
.23 -.66 .00 63.83 154.19 130.16
16 .28 -.87 -.33
.95 .02 .44 .00 132.55
67.62
17 -.53 .26 -.41
-.43 .28 -.90 -.68
.00 65.99
18 -.14 -.70 -.98
.59 .56 -.64 .38
.41 .00
19 -.01 .30 .95
-.20 -.80 .89 -.01 -.63
-.89
20 .82 .19
.48 .01 .02 .70
.33 -.85 -.57
21 -.44 .74 .19
-.86 -.03 -.56 -.98 .81
-.21
22 .21 .55
.97 -.42 -.59 .78 -.18
-.58 -.98
23 .19 .64 -.23
-.70 .66 -.78 -.74
.70 .09
24 -.15 .70 .97
-.66 -.70 .53 -.52 -.19
-.95
25 -.15 .95 .66
-.97 -.25 -.07 -.93 .35
-.70
26 -.38 .53 -.21
-.67 .29 -.84 -.85
.95 .17
27 -.28 .38 .95
-.33 -.90 .74 -.22 -.39
-.87
vector angles ( cosine degrees )
19 20
21 22 23
24 25 26
27
1 122.24 134.69 103.90 141.59 109.51132.97 132.98 89.98
116.32
2 157.31 144.25 65.55 154.72 54.84130.98
97.64 43.44 140.08
3 41.17 60.25 132.66 56.44 160.50 71.30
108.69 152.86 51.27
4 72.21 90.11 133.76 90.12 164.17 97.62
130.97 136.53 75.28
5 89.88 73.22 54.07 71.23 35.30
68.15 42.12 59.16 89.90
6 131.17 105.75 127.02 143.22 105.71159.68 159.69 105.50
137.35
7 150.44 149.40 78.80 163.54 74.31137.89 111.86
59.12 136.30
8 36.57 32.05 94.07 19.20 95.68
41.12 61.28 112.26 48.12
9 99.34 115.16 120.39 118.28 134.70118.71 138.88 112.24
97.75
10 90.80 35.04 115.87 77.75 79.14 98.86
98.90 112.12 106.02
11 72.38 79.28 42.13 56.81 49.83
45.32 17.56 58.03 67.66
12 19.07 61.18 79.27 14.12 103.47 13.29
49.08 102.11 18.37
13 101.42 89.39 149.19 114.90 134.65130.92 166.71 132.34
109.15
14 143.30 88.96 91.46 126.09 48.92134.04 104.36
72.91 153.70
15 27.41 45.37 123.95 38.48 140.99 58.00
94.26 147.02 42.44
16 90.79 71.03 167.56 100.61 137.53121.63 157.69 148.11
102.58
17 129.16 148.69 36.38 125.57 45.62101.02 69.34
17.51 112.65
18 152.93 124.99 102.28 168.23 84.78162.45 134.69 80.49
150.30
19 .00 56.47 96.54 19.35 122.09
30.83 67.91 119.61 17.24
20 .55 .00 121.41 47.06
103.48 72.32 90.83 132.38 72.80
21 -.11 -.52 .00
89.39 44.01 66.19 33.06 23.07 82.61
22 .94 .68
.01 .00 105.03 26.13 57.08 111.28 28.92
23 -.53 -.23 .72
-.26 .00 94.27 58.00 32.98 116.20
24 .86 .30
.40 .90 -.07 .00 37.39
89.17 22.34
25 .38 -.01 .84
.54 .53 .79 .00 54.19
58.41
26 -.49 -.67 .92
-.36 .84 .01 .59
.00 105.31
27 .96 .30
.13 .88 -.44 .92
.52 -.26 .00
Change vectors? y<CR>
Enter vector numbers 1 11 14<CR>
Orientation matrix:
R11= .128971 R12= .118850 R13= .019565
R21= .033549 R22= .021196 R23= -.087840
R31= -.123975 R32= .136244 R33= -.003402
27 Short vectors:
nr x*
y* z*
d* from to h
k l
1 -.019561 .087834 .003400
.008109 20 -25 .00 .00 -1.00
2 -.143473 .060494 -.002733
.024251 14 -15 -.50 -.50 -1.00
3 .123911 .027366 .006123
.016140 1 -19 .50 .50
.00
4 .104331 .115202 .009540
.024247 6 -7 .50 .50 -1.00
5 -.084773 -.203066 -.012944 .048590
1 -2 -.50 -.50 2.00
6 -.034057 .181841 -.123280
.049424 7 -8 .50 -.50 -2.00
7 -.163023 .148292 .000662
.048567 21 -24 -.50 -.50 -2.00
8 .182546 -.236095 -.004036
.089080 4 -16 .50 .50 3.00
9 .065262 .290857 .016306
.089123 11 -17 .50 .50 -3.00
10 .024752 -.081537 -.133540 .025094
9 -12 .50 -.50 1.00
11 -.070389 -.297032 .113653 .106100
5 -6 -1.00 .00 3.00
12 .158036 -.154439 .129372
.065564 23 -24 .00 1.00 2.00
13 .089879 .209237 -.117134
.065579 7 -20 1.00 .00 -2.00
14 -.118714 -.021089 -.136198 .033088
9 -16 .00 -1.00 .00
15 .267312 -.033057 .008907
.072628 12 -13 1.00 1.00 1.00
16 .109190 .121251 -.120518
.041149 21 -22 1.00 .00 -1.00
17 -.272347 .027061 .121147
.089582 22 -24 -1.50 -.50 -1.00
18 -.177567 .242164 -.125908 .106026
24 -25 .00 -1.00 -3.00
19 .281898 -.127067 .135418
.113951 8 -24 .50 1.50 2.00
20 .168084 -.142068 -.130715 .065522
9 -14 1.00 .00 2.00
21 -.238539 -.154988 .244646 .140774
21 0 -2.00 .00 1.00
22 .321097 -.302802 .128718
.211361 20 -21 .50 1.50 4.00
23 -.228393 -.142592 -.015559 .072738
10 -14 -1.00 -1.00 1.00
24 .172555 -.248549 .256218
.157200 7 0 -.50 1.50 3.00
25 -.075359 -.303346 .243980 .157224
24 0 -1.50 .50 3.00
26 -.252812 -.060777 .117725 .081467
18 -21 -1.50 -.50 .00
27 .276970 -.133310 .265763
.165114 6 0 .00 2.00
2.00
Change vectors? n<CR>
Cell dimensions? [D/R/N] <CR>
Index-Status: HHHHHHHHHHHHHHHHHHHHHHHHH
Nr S H K
L Dev-Ang dTh
dPh dCh .0090059
1 H 3.000 1.000 -6.001
.0028 -.001 .002
.002 .0000565
2 H 3.000 3.999
.001 .0086 .001 -.011
-.002 .0001179
3 H 3.000 4.000 -1.000
.0050 .000 -.006
.003 .0000586
4 H 3.000 4.000 1.000
.0039 .001 -.004 -.003
.0000536
5 H 2.999 1.000 -5.000
.0084 .001 .007
.007 .0000955
6 H 2.001 2.001 -2.001
.0082 -.003 -.008 .005
.0001641
7 H 2.000 1.001 -3.001
.0052 -.002 -.007 .000
.0001071
8 H 3.000 1.000 -5.001
.0071 .000 .001
.007 .0000766
9 H 2.000 2.001 4.001
.0070 -.002 .004
.006 .0001192
10 H 3.001 -1.000 5.000
.0034 -.002 -.004 -.001
.0000895
11 H 2.999 -2.999 2.998
.0079 .006 -.005 -.007
.0002841
12 H 3.000 2.000 5.000
.0074 .000 -.004 -.007
.0000837
13 H 3.000 .000 5.999
.0042 .001 .000 -.004
.0000731
14 H 3.000 1.001 6.000
.0088 .000 .009
.005 .0001046
15 H 3.000 2.000 5.000
.0060 .000 -.006 -.004
.0000698
16 H 3.000 3.000 4.000
.0036 .001 -.005
.000 .0000715
17 H 3.000 -4.000 .001
.0069 .000 .007
.004 .0000788
18 H 3.000 -4.001 -.999
.0127 -.001 .015
.004 .0001476
19 H 3.000 .000 -5.999
.0020 .002 -.002
.000 .0000885
20 H 3.000 .000 -5.001
.0036 -.002 -.004 .002
.0000939
21 H 2.001 -2.001 -1.000
.0097 -.004 .011
.005 .0001995
22 H 3.000 -2.999 -1.999
.0105 .001 .006 -.009
.0001158
23 H 3.000 .000 -5.000
.0015 -.001 -.002 .001
.0000301
24 H 2.001 -1.000 -3.001
.0027 -.003 .000 -.003
.0001378
25 H 3.000 .000 -5.999
.0013 .002 .000 -.001
.0000756
Reciprocal axis matrix
Direct axis matrix
-.005061 .123907 -.019565
-.298974 -.363051 7.656916
-.006177 .027374
.087842 7.677235 1.695288
.379097
.130110 .006136
.003401 -2.413466 10.830228
.420250
Niggli-values
Sigma direct axis matrix
58.8496 61.9577
123.2953 .000314
.000237 .000245
-.0091 .0075
-.0081 .000449
.000339 .000351
.000578 .000436 .000451
Cell parameters
Sigma cell parameters
7.6713 7.8713
11.1038 .0002
.0004 .0004
90.0060 89.9950
90.0076 .0039
.0029 .0034
-.000104 .000088 -.000133
.000068 .000051 .000060
Volume= 670.4899
.0511
Index-Status: HHHHHHHHHHHHHHHHHHHHHHHHH
Next solution? <CR>
CD0>
Example 1 INDEX dialogue mode #3
(SR=7700):
Example 1 INDEX dialogue mode #3(SR=7700):
CD0> INDEX<CR>
Enter axis limit in Angstrom [ 116.3]:
<CR>
Information ? (Y/N) [N]: y<CR>
Orientation matrix:
R11= .005060 R12= .123911 R13= .019565
R21= .006177 R22= .027372 R23= -.087840
R31= -.130110 R32= .006135 R33= -.003402
27 Short vectors:
nr x*
y* z*
d* from to h
k l
1 -.019561 .087834 .003400
.008109 20 -25 .00 .00 -1.00
2 -.143473 .060494 -.002733
.024251 14 -15 .00 -1.00 -1.00
3 .123911 .027366 .006123
.016140 1 -19 .00 1.00
.00
4 .104331 .115202 .009540
.024247 6 -7 .00 1.00 -1.00
5 -.084773 -.203066 -.012944 .048590
1 -2 .00 -1.00 2.00
6 -.034057 .181841 -.123280
.049424 7 -8 1.00 .00 -2.00
7 -.163023 .148292 .000662
.048567 21 -24 .00 -1.00 -2.00
8 .182546 -.236095 -.004036
.089080 4 -16 .00 1.00 3.00
9 .065262 .290857 .016306
.089123 11 -17 .00 1.00 -3.00
10 .024752 -.081537 -.133540 .025094
9 -12 1.00 .00 1.00
11 -.070389 -.297032 .113653 .106100
5 -6 -1.00 -1.00 3.00
12 .158036 -.154439 .129372
.065564 23 -24 -1.00 1.00 2.00
13 .089879 .209237 -.117134
.065579 7 -20 1.00 1.00 -2.00
14 -.118714 -.021089 -.136198 .033088
9 -16 1.00 -1.00 .00
15 .267312 -.033057 .008907
.072628 12 -13 .00 2.00 1.00
16 .109190 .121251 -.120518
.041149 21 -22 1.00 1.00 -1.00
17 -.272347 .027061 .121147
.089582 22 -24 -1.00 -2.00 -1.00
18 -.177567 .242164 -.125908 .106026
24 -25 1.00 -1.00 -3.00
19 .281898 -.127067 .135418
.113951 8 -24 -1.00 2.00 2.00
20 .168084 -.142068 -.130715 .065522
9 -14 1.00 1.00 2.00
21 -.238539 -.154988 .244646 .140774
21 0 -2.00 -2.00 1.00
22 .321097 -.302802 .128718
.211361 20 -21 -1.00 2.00 4.00
23 -.228393 -.142592 -.015559 .072738
10 -14 .00 -2.00 1.00
24 .172555 -.248549 .256218
.157200 7 0 -2.00 1.00 3.00
25 -.075359 -.303346 .243980 .157224
24 0 -2.00 -1.00 3.00
26 -.252812 -.060777 .117725 .081467
18 -21 -1.00 -2.00 .00
27 .276970 -.133310 .265763
.165114 6 0 -2.00 2.00 2.00
Print short vector angles? n<CR>
Change vectors? n<CR>
Cell dimensions? [D/R/N] d<CR>
Enter A, B, C, Alp, Bet, Gam 7.6 7.8 11.1 90 90 90<CR>
Det(R1,R2,R3)= .0014914 Det(A,B,C)=
.0015197 Ratio= .9814
Enter delta: .025<CR>
1 1 1. 0.
0.
2 1 0. 1.
0.
3 2 0. 1.
0.
4 3 0. 0.
1.
1 3 4 Change these vector
numbers
if you want: /<CR>
-1 -3 4 Change these vector numbers
if you want: /<CR>
1 -3 -4 Change these vector numbers
if you want: <CR>
Nr S H K
L Dev-Ang dTh
dPh dCh .0090059
1 H -3.000 -1.000 -6.001
.0028 -.001 .002
.002 .0000565
2 H -3.000 -3.999 .001
.0086 .001 -.011 -.002
.0001179
3 H -3.000 -4.000 -1.000
.0050 .000 -.006
.003 .0000586
4 H -3.000 -4.000 1.000
.0039 .001 -.004 -.003
.0000536
5 H -2.999 -1.000 -5.000
.0084 .001 .007
.007 .0000955
6 H -2.001 -2.001 -2.001
.0082 -.003 -.008 .005
.0001641
7 H -2.000 -1.001 -3.001
.0052 -.002 -.007 .000
.0001071
8 H -3.000 -1.000 -5.001
.0071 .000 .001
.007 .0000766
9 H -2.000 -2.001 4.001
.0070 -.002 .004
.006 .0001192
10 H -3.001 1.000 5.000
.0034 -.002 -.004 -.001
.0000895
11 H -2.999 2.999 2.998
.0079 .006 -.005 -.007
.0002841
12 H -3.000 -2.000 5.000
.0074 .000 -.004 -.007
.0000837
13 H -3.000 .000 5.999
.0042 .001 .000 -.004
.0000731
14 H -3.000 -1.001 6.000
.0088 .000 .009
.005 .0001046
15 H -3.000 -2.000 5.000
.0060 .000 -.006 -.004
.0000698
16 H -3.000 -3.000 4.000
.0036 .001 -.005
.000 .0000715
17 H -3.000 4.000 .001
.0069 .000 .007
.004 .0000788
18 H -3.000 4.001 -.999
.0127 -.001 .015
.004 .0001476
19 H -3.000 .000 -5.999
.0020 .002 -.002
.000 .0000885
20 H -3.000 .000 -5.001
.0036 -.002 -.004 .002
.0000939
21 H -2.001 2.001 -1.000
.0097 -.004 .011
.005 .0001995
22 H -3.000 2.999 -1.999
.0105 .001 .006 -.009
.0001158
23 H -3.000 .000 -5.000
.0015 -.001 -.002 .001
.0000301
24 H -2.001 1.000 -3.001
.0027 -.003 .000 -.003
.0001378
25 H -3.000 .000 -5.999
.0013 .002 .000 -.001
.0000756
Reciprocal axis matrix
Direct axis matrix
.005061 -.123907 -.019565
.298974 .363051 -7.656916
.006177 -.027374
.087842 -7.677235 -1.695288
-.379097
-.130110 -.006136 .003401
-2.413466 10.830228 .420250
Niggli-values
Sigma direct axis matrix
58.8496 61.9577
123.2953 .000314
.000237 .000245
.0091 -.0075
-.0081 .000449
.000339 .000351
.000578 .000436 .000451
Cell parameters
Sigma cell parameters
7.6713 7.8713
11.1038 .0002
.0004 .0004
89.9940 90.0050
90.0076 .0039
.0029 .0034
.000104 -.000088 -.000133
.000068 .000051 .000060
Volume= 670.4899
.0511
Index-Status: HHHHHHHHHHHHHHHHHHHHHHHHH
Next solution? <CR>
CD0>
If the question 'Next solution' is answered with 'y', a new index run will be started with an other combination ofvectors used for the preliminary matrix. This will often result in the same solution, but sometimes after a few cycles an other solution can be found. Also later this still can be done (as long as the reflection list not has been changed) using the command INDCON (index continue).
Index utility programs, REIND, LS and RINDEX
These indexing routines are available separately.
REIND
This command enables the operator to match all of the reflections in the list with the current orientation matrix, by calculating the indices from the angles and placing them in the list. This is done only for reflections of which the index status is not N (see the Reflection list). When the value in the last column (the lenght of the difference vector between the real scattering vector and the one as calculated from the current R matrix) is greater than the value in the header of that column, the status of this reflection is changed to N and this reflection is omitted for further calculations.
LS
This command enables to execute the least-squares calculation. LS is usually used to obtain a new orientation matrix following recentering of the reflections in the list. The command LS can also be used to compose an orientation matrix once for three reflections the settings and the indices are known.
Notes:
1. LS is executed automatically during data collection orientation control
following recentering of the orientation reflections.
2. Only reflections in the list with index status 'H' are affected
or used by TRANS, REIND and LS.
3. If during LS one or more reflections are set to status code N, the
index status code is printed after the cell parameters.
Example LS dialogue:
CD0> LS<CR>
Nr S H K
L Dev-Ang dTh
dPh dCh 0.0090325
1 H -3.001 -5.000 4.000
0.0052 -0.003 -0.002 -0.005 0.0000932
2 H -3.001 -5.000 -4.000 0.0067
0.000 0.003 -0.006 0.0000973
3 H -3.000 5.000 -4.000
0.0029 -0.003 -0.001 -0.003 0.0000656
4 H -3.000 5.000 4.000
0.0035 -0.001 -0.003 -0.002 0.0000536
5 H -4.000 5.000 0.000
0.0031 0.002 0.002 -0.003 0.0000618
6 H -5.000 1.999 -5.000
0.0117 0.003 -0.017 -0.006 0.0001770
7 H -5.000 2.000 4.999
0.0077 0.001 -0.004 -0.007 0.0001126
8 H -6.000 2.000 0.999
0.0063 0.004 -0.020 -0.004 0.0001178
9 H -6.000 1.999 -0.000
0.0052 0.001 -0.014 -0.004 0.0000795
10 H -2.000 -6.001 1.000 0.0020
-0.004 0.002 0.000 0.0000735
11 H -2.000 -6.001 -1.000 0.0020
-0.006 0.002 0.001 0.0001038
12 H -5.000 1.000 4.999
0.0051 0.002 -0.008 -0.002 0.0000783
13 H -5.000 0.001 5.000
0.0061 0.000 -0.010 -0.002 0.0000855
14 H -5.000 3.000 2.999
0.0046 0.005 -0.005 -0.004 0.0001044
15 H -6.000 -1.000 0.001 0.0087
0.001 -0.029 -0.003 0.0001216
16 H -0.000 2.000 9.001
0.0042 -0.005 0.004 -0.001 0.0000997
17 H 0.000 2.001 -9.001
0.0052 -0.009 0.005 -0.000 0.0001664
18 H -3.000 -6.000 -0.001 0.0038
-0.001 0.004 -0.001 0.0000612
19 H -2.000 6.001 -3.000 0.0011
-0.004 0.001 0.000 0.0000720
20 H -2.000 6.000 3.001
0.0082 0.001 0.008 -0.003 0.0001220
21 H -3.000 6.000 0.000
0.0021 -0.002 0.002 -0.001 0.0000463
22 H -6.000 -2.000 -2.999 0.0071
0.005 -0.007 -0.006 0.0001404
23 H -6.000 -1.999 3.000 0.0052
0.003 -0.008 -0.003 0.0000917
24 H -6.000 -0.000 -3.999 0.0076
0.005 -0.013 -0.005 0.0001395
25 H -6.000 0.001 4.000
0.0048 0.004 -0.010 -0.002 0.0000985
Reciprocal axis matrix
Direct axis matrix
-0.011855 -0.097281 0.057759
-0.694517 0.571357 -7.597619
0.009760 0.080930 0.069444
-5.991275 4.983947 0.921938
-0.129803 0.014979 -0.000058
7.079887 8.511488 -0.006612
Niggli-values
Sigma direct axis matrix
58.5326 61.5851
122.5703 0.000150 0.000158
0.000113
-0.0028 -0.0038
0.0041 0.000271 0.000285
0.000204
0.000383 0.000403 0.000288
Cell parameters
Sigma cell parameters
7.6507 7.8476
11.0711 0.0001
0.0003 0.0004
90.0019 90.0025
89.9961 0.0029
0.0019 0.0019
-0.000033 -0.000044 0.000069
0.000050 0.000033 0.000033
Volume= 664.7057
0.0852
CD0>
The command RINDEX will give the (non-integer) values for the indices of the reflections, which are flagged N, without changing the matrix.
Unit-cell least-squares refinement with constraints, CELDIM
This program is intended to produce cell constants for publication. It has been written for the CAD4 system by Steve Rettig. The method used is a least-squares refinement with constraints, based on the theta-values of the reflections. The program uses the alpha1 wavelength from the CRYSTAL file in all calculations. H,K,L and theta are taken from the CRYSTAL file. Only reflections with angle statuscode LCA not * and with index status LCH H are used. To obtain the best results the CRYSTAL file must be filled (after data collection) with strong high-theta reflections. These reflections must be centered with SETANG and DETTH or with SET4 to determine the correct theta-values.
Only independent cell parameters are refined. Standard deviations are calculated for the cell parameters, the unit-cell volume and for the density (if density=1).
Input parameters
Cell-type, Extrapolation, Weight, Density:
Cell-type = 1 TRICLINIC
2 MONOCLINIC
3 ORTHORHOMBIC
4 TETRAGONAL
5 CUBIC
6 HEXAGONAL
7 RHOMBOHEDRAL(PRIMITIVE LATTICE) (standard settings, ie. b unique for
monoclinic and c unique for hexagonal systems)
Extrapolation = 0 (usually) 1 For Nelson-Riley extrapolation (works well with Cu radiation over a wide range of theta values)
Weight = 0 unit weights 1 sin(theta) 2 tan(theta) 3 sin(theta)**2 4 sin(two-theta)**2 5 1/(2*cos(theta)**2 /sin(theta) +cos(theta)**2/the ta)
Density = 0 no density calculation to be done 1 calculate density if Density=1 program requests: Z Mol-weight, sigma-Mw: Z = number of formula weights per unit cell Mol-weight = formula weight sigma-Mw = error in formula weight (for calculation of error in density)
lit: Nelson, J.B., and Riley, D.P. (1945). Proc. Phys. Soc., 57, 160.
Example 1 CELDIM dialogue:
CD0> CELDIM<CR>
Unit cell refinement with constraints.
Cell-type, Extrapolation, Weight,
Density:
2 0 0 0<CR>
15 reflections
MONOCLINIC
15.4231
8.4135 9.0383
90.0000 102.8049
90.0000
rank = 4
mean deviation = 0.00005
end of cycle 1
sigmasquared = 1.944249E-09
rank = 4
mean deviation = 0.00004
end of cycle 2
sigmasquared = 1.701229E-09
refl h k l
theta-obs theta-cal diff
wt minimize
1 -7 5 0
35.553 35.553 -0.0003
1.00 -0.00001
2 3 3
0 18.357 18.344
0.0126 1.00 0.00027
3 9 3
1 34.043 34.043
0.0001 1.00 0.00000
4 6 0 -3
20.922 20.916 0.0057
1.00 0.00012
5 4 4 -5
34.899 34.900 -0.0013
1.00 -0.00002
6 4 0
2 17.292 17.295 -0.0035
1.00 -0.00007
7 14 4 -2
52.132 52.134 -0.0012
1.00 -0.00002
8 0 -4 -5
34.760 34.760 0.0001
1.00 0.00000
9 10 2 1
34.654 34.652 0.0014
1.00 0.00003
10 4 4 -6
39.431 39.432 -0.0007
1.00 -0.00001
11 2 4 -5
34.186 34.186 -0.0007
1.00 -0.00001
12 8 -4 1
34.788 34.787 0.0013
1.00 0.00002
13 -3 3 6
35.566 35.565 0.0013
1.00 0.00002
14 8 4 0
33.334 33.336 -0.0018
1.00 -0.00003
15 -7 5 1
35.174 35.174 -0.0006
1.00 -0.00001
rank = 4
mean deviation = 0.00004
reciprocal
dimensions
previous-value
shift new-parameter sigma
degrees
A axis * 0.066488
0.000000 0.066488 0.000003
B axis * 0.118864
-0.000000 0.118864 0.000010
C axis * 0.113454
-0.000000 0.113454 0.000009
beta * 1.347317
0.000000 1.347317 0.000141
77.1956
end of cycle 3
sigmasquared = 1.701287E-09
final real parameters
parameter
sigma
A
axis = 15.4239
0.0025
B
axis = 8.4129
0.0007
C
axis = 9.0389
0.0015
alpha
= 90.0000
0.0000
beta
= 102.8045
0.0081
gamma
= 90.0000
0.0000
unit-cell volume = 1143.722
0.285
CD0>
Example 2 CELDIM dialogue:
CD0> CELDIM<CR>
Unit cell refinement with constraints
Cell-type, Extrapolation, Weight,Density:
2<CR>
3 LAST INPUTS
///<CR>
21 reflections
MONOCLINIC
27.7240
3.4898 7.2962
90.0000 94.2065
90.0000
rank = 4
mean deviation = 0.00009
end of cycle 1
sigmasquared = 7.433212E-09
rank = 4
mean deviation = 0.00009
end of cycle 2
sigmasquared = 6.148098E-09
refl h k l
theta-obs theta-cal diff
wt minimize
1 12 0 -5
16.171 16.173 -0.0016
1.00 -0.00008
2 10 0 -4
13.024 13.025 -0.0017
1.00 -0.00008
3 16 0 -2
12.749 12.747 0.0020
1.00 0.00010
4 16 0 -1
11.971 11.971 0.0008
1.00 0.00004
5 14 0 2
12.155 12.150 0.0047
1.00 0.00023
6 3 1
5 15.627 15.627
0.0002 1.00 0.00001
7 5 1
4 13.469 13.472 -0.0028
1.00 -0.00014
8 1 1
4 12.769 12.771 -0.0014
1.00 -0.00007
9 13 1 3
14.544 14.545 -0.0007 1.00
-0.00003
10 17 1 0
13.916 13.919 -0.0030
1.00 -0.00014
11 13 1 -3
13.680 13.681 -0.0010
1.00 -0.00005
12 9 1 -4
13.980 13.980 -0.0002
1.00 -0.00001
13 3 1 -4
12.755 12.751 0.0034
1.00 0.00017
14 2 2 -4
16.351 16.350 0.0007
1.00 0.00003
15 4 2 -2
13.273 13.273 0.0000
1.00 0.00000
16 10 2 -2
14.823 14.821 0.0020
1.00 0.00010
17 4 2 2
13.459 13.459 -0.0000
1.00 -0.00000
18 8 2 2
14.512 14.513 -0.0008
1.00 -0.00004
19 4 2 3
14.937 14.934 0.0025
1.00 0.00012
20 10 2 0
13.902 13.906 -0.0042
1.00 -0.00020
21 11 1 -3
12.738 12.734 0.0036
1.00 0.00018
rank = 4
mean deviation = 0.00009
reciprocal
dimensions
previous-value
shift new-parameter sigma
degrees
A axis * 0.036162
0.000000 0.036162 0.000004
B axis * 0.286547
0.000000 0.286547 0.000029
C axis * 0.137425
-0.000000 0.137425 0.000013
beta * 1.497606
-0.000000 1.497606 0.000145
85.8065
end of cycle 3
sigmasquared = 6.148098E-09
final real parameters
parameter
sigma
A
axis = 27.7275
0.0051
B
axis = 3.4898
0.0004
C
axis = 7.2962
0.0013
alpha
= 90.0000
0.0000
beta
= 94.1935
0.0083
gamma
= 90.0000
0.0000
unit-cell volume = 704.122
0.192
CD0>
The matrix transformation routine 'TRANS' can operate in three modes, depending on the response to the question 'M,R or C? [C]'.
1. M - Transformation on the basis of a user specified transformation matrix.
2. R - Automatic transformation from an unreduced cell to a reduced cell (according to section 9.3 from The International Tables for X-ray Crystallography, Vol. A, 737 (1983)).
3. C - Automatic search of transformations for determining the conventional cell from a reduced cell (according to Table 9.3.1 from The International Tables for X-ray Crystallography, Vol. A, 742 (1983)).
*** Mode 1 --Manual transformation--
The question 'M,R or C? [C]' must be answered with M<CR>. This answer enables the operator to make a transformation of the cell. The new cell is determined from three operator specified direct cell vectors (u, v, w).
The program prompts 'U1 V W?' The operator must supply the three direct cell indices that define the new a-axis. The program prompts 'U2 V W?' Requesting the direct cell indices for the new b-axis. The program prompts 'U3 V W?'. Requesting the direct cell indices for the new c-axis. The new orientation matrix is calculated and printed.
Hereafter the question 'Save, repeat with Current or try again with Old. S, C or O? [O]' is printed. It enables the operator to Save the current matrix, to Continue with another TRANS cycle based upon the current matrix, or try another TRANS cycle on the Old matrix which still resides in the CRYSTAL file.
The program then asks 'Reind?'. If the operator responds with Y, the list of reflections is re-indexed to fit the new orientation matrix. Least-squares refinement (LS) and print out (RO) are executed as in INDEX. If the operator responds with N, the list of reflections is decoupled from the orientation matrix by changing the index status code to N for all reflections.The orientation matrix is printed as in INDEX.
Example 1 TRANS dialogue M(anual)-mode:
CD0> TRANS<CR>
M,R OR C? M<CR>
U1 V W? 0 1 0<CR>
U2 V W? 0 0 1<CR>
U3 V W? 1 0 0<CR>
Orientation matrix:
R11 = -0.078629 R12 = 0.088265 R13 = -0.056314
R21 = -0.057325 R22 = 0.021468 R23 = 0.115974
R31 = 0.132402 R32 = 0.135664 R33 = 0.019698
S11 = 42.7414 S22 = 43.2802 S33 =
58.8117
S32 = -0.1296 S31 = -0.7976 S21 = -15.6939
A = 6.5377 B =
6.5788 C = 7.6689
Alp = 90.1472 Bet = 90.9115 Gam =
111.4010 Vol =307.0447
Reciprocal axes:
A* = 0.1643 B* = 0.1633
C* = 0.1304
Alp*= 89.4846 Bet*= 88.9633 Gam*=
68.5938
Save, repeat with Current ortry again with Old. S,C,O?
S<CR>
Reind? Y<CR>
(output depends on switch register setting; here SR=0000)
Reciprocal axis matrix
Direct axis matrix
-0.078629 0.088265 -0.056314 -4.701029 -2.879577
3.514226
-0.057325 0.021468 0.115974 5.061413
1.813768 3.791114
0.132402 0.135664 0.019698 -3.260625
6.863546 1.035289
Niggli-values
Sigma direct axis matrix
42.7414 43.2802 58.8117
0.004523 0.006068 0.006887
-0.1296 -0.7976 -15.6939 0.013277
0.017813 0.020214
0.018683 0.025066 0.028445
Cell parameters
Sigma cell parameters
6.5377 6.5788
7.6689 0.0056 0.0163 0.0241
90.1472 90.9115 111.4010
0.2270 0.1800 0.1708
-0.002569 -0.015908 -0.364890 0.003961 0.003141
0.002776
Volume= 307.0447
3.7942
Index-Status: HHHHHHKKKKKKKKKKKKKKKKKKK
CD0>
Example 2 TRANS dialogue M(anual)-mode:
Niggli-values
Sigma direct axis matrix
142.1768 142.3919 142.8692
0.003645 0.003553 0.002703
42.7112 42.8070
42.7240 0.002735 0.002665
0.002028
0.004590 0.004473 0.003403
Cell parameters
Sigma cell parameters
11.9238 11.9328
11.9528 0.0033
0.0026 0.0042
72.5752 72.5212
72.5260 0.0232
0.0264 0.0197
0.299454 0.300352 0.300272
0.000387 0.000440 0.000328
Volume= 1505.8270
0.7981
Index-Status: HHHHHHHHHHHHHHHH/////////
CD0> Trans<CR>
M, R or C? M<CR>
U1 V W? 1 -1 0<CR>
U2 V W? -1 0 1<CR>
U3 V W? -1 -1 -1<CR>
Orientation matrix:
R11= 0.026944 R12= -0.017084 R13= 0.032102
R21= -0.014778 R22= -0.071245 R23=-0.015048
R31= 0.075757 R32= 0.036131 R33=-0.014325
S11= 199.1206 S22= 199.4321 S33= 683.9222
S32= -0.6796 S31= 0.1193 S21= -99.3569
A = 14.1110 B = 14.1220 C =
26.1519
Alp = 90.1054 Bet = 89.9815 Gam =119.9067 Vol=
4517.4805
RECIPROCAL AXES:
A*= 0.0818 B*=
0.0817 C*= 0.0382
Alp*= 89.8890 Bet*= 89.9607 Gam*= 60.0933
Save, repeat with Current or try againwith Old. S, C or O? [O]
S<CR>
Reind? Y<CR>
(output depends on switch register setting)
*** Mode 2 --Reduced cell transformation--
The question 'M,R or C?' must be answered with R. The 'user supplied' unit-cell is normalized, i.e. a<b<c and the inter-axial angles are either acute (cell type I) or obtuse (cell type II).
Note: The unit-cell produced by the automatic indexing routine INDEX (Mode 1) is already in reduced form.
The user must also supply an acceptance parameter. This parameter is used by the program to distinguish between acute and obtuse cell types; a value of 0 is the default for the R transformation.
The elements of the Niggli matrix are used to perform tests on the main and special conditions layed out in the International Tables section 9.3 Vol.A.
The orientation matrix is recalculated and printed together with the metrical tensor and the cell dimensions in direct and reciprocal space. Then the decision for retaining the old matrix can be made. For further information is referred to the description of Mode 1.
Example TRANS dialogue
R(educed-cell)-mode:
CD0> TRANS<CR>
M, R or C? [C] R<CR>
Acceptance parameter(0:+500)? [ 0.] <CR>
Orientation matrix:
R11= -0.088265 R12= 0.078629 R13= 0.056314
R21= -0.021468 R22= 0.057325 R23= -0.115974
R31= -0.135664 R32= -0.132404 R33= -0.019698
S11= 43.2802 S22= 42.7414 S33=
58.8117
S32= -0.7976 S31= -0.1296 S21= -15.6939
A = 6.5788 B =
6.5377 C = 7.6689
Alp= 90.9115 Bet= 90.1472 Gam=
111.4010 Vol= 307.0447
Reciprocal axes:
A* = 0.1633 B* = 0.1643
C*= 0.1304
Alp*= 88.9633 Bet*= 89.4846 Gam*= 68.5938
Save, repeat with Current or try again with Old. S, C or O? [O]
S<CR>
CD0>
*** Mode 3 --Conventional cell transformation-- The question 'M, R or
C? [O]'
must be answered with C. The program tries to find out which conventional
representation of the cell can be used instead of the current reduced cell.
The user must also supply an acceptance parameter. This parameter is used by the program to distinguish between acute and obtuse cell types; a value of 10 is the default for the C transformation.
The elements of the Niggli matrix are used to perform test on the conditions specified in the International Tables Vol. A (Table 9.3.1).
A figure of merit FOM, is defined as:
FOM = max[abs((Y-A)/max(Y,A))] for lengths FOM = max([abs(A.B - U.W)]/abs(U)*abs(W)) for angles
E.g. for condition a.a = b.b, FOM = abs[(a**2-b**2)/max(a,b)]
For each table entry the largest FOM-value is stored. The program performs tests on all 44 entries. The results are sorted on the smallest FOM-value. All FOM values below 0.1 are printed including the first one above the value of 0.1; on each line the table entry number, the FOM-value, the lattice symmetry, the Bravais lattice type (POS or NEG) and the reduction type. The result with the highest symmetry is probably the right solution.
The operator is then asked to enter a 'Transformation-number?'. Any integer value ranging from 0 to 44 may be entered. Entering 0 causes the identity operation to be performed.
The orientation matrix is recalculated and printed together with the metrical tensor and the cell dimensions in direct and reciprocal space. Then the decision for retaining the old matrix can be made. For further information is referred to the description of Mode 1.
Example 1 TRANS dialogue
C(onventional-cell)-mode:
Niggli-values
Sigma direct axis matrix
142.1768 142.3919 142.8692
0.003645 0.003553 0.002703
42.7112 42.8070
42.7240 0.002735 0.002665
0.002028
0.004590 0.004473 0.003403
Cell parameters
Sigma cell parameters
11.9238 11.9328
11.9528 0.0033
0.0026 0.0042
72.5752 72.5212
72.5260 0.0232
0.0264 0.0197
0.299454 0.300352 0.300272
0.000387 0.000440 0.000328
Volume= 1505.8270
0.7981
Index-Status:HHHHHHHHHHHHHHHH/////////
CD0> TRANS<CR>
M, R or C? [C] C<CR>
Acceptance parameter (0:+500)? [10.]: <CR>
Nr FOM
Lattice Bravais Type
31 0.000000
TRICLINIC P OBTUSE
10 0.001511
MONOCLINIC C OBTUSE
20 0.003341
MONOCLINIC C OBTUSE
2 0.004847
RHOMBOHEDRAL HINP OBTUSE
28 0.198435
MONOCLINIC C OBTUSE
Transformation-number? 2<CR>
Orientation matrix:
R11= 0.026944 R12= -0.017084 R13= 0.032102
R21= -0.014778 R22= -0.071245 R23= -0.015048
R31= 0.075757 R32= 0.036131 R33= -0.014325
S11= 199.1205 S22= 199.4321 S33= 683.9219
S32= -0.6796 S31= 0.1193 S21= -99.3569
A = 14.1110 B = 14.1220 C =
26.1519
Alp = 90.1054 Bet = 89.9815 Gam =119.9067 Vol=
4517.4795
Reciprocal axes:
A*= 0.0818 B*=
0.0817 C*= 0.0382
Alp*= 89.8890 Bet*= 89.9607 Gam*= 60.0933
Save, repeat with Current or try again with Old. S, C or O? S<CR>
Reind Y<CR>
(output depends on switch register setting)
Example 2 TRANS dialogue
C(onventional-cell)-mode:
Niggli-values
Sigma direct axis matrix
12.1790 53.2339
195.1944 0.000227 0.000154 0.000200
-7.4215 -6.0835
0.0058 0.000375 0.000255 0.000330
0.000671 0.000456 0.000590
Cell parameters
Sigma cell parameters
3.4898 7.2962
13.9712 0.0002 0.0003
0.0006
94.1752 97.1676
89.9870 0.0035 0.0042
0.0038
-0.072806 -0.124772 0.000227
0.000061 0.000073 0.000067
Volume= 352.0106
0.1325
Index-Status: HHHHHHHHHHHHHHHHHHHHH////
CD0> TRANS<CR>
M, R OR C? C<CR>
Acceptance parameter (0:+500)? [ 10.]:<CR>
Nr FOM
Lattice Bravais Type
37 0.000227
MONOCLINIC C ACUTE
44 0.000455
TRICLINIC P ACUTE
33 0.072806
MONOCLINIC P ACUTE
36 0.072806
ORTHORHOMBIC C ACUTE
32 0.124772
ORTHORHOMBIC P ACUTE
Transformation-number? 37<CR>
Orientation matrix:
R11= 0.032293 R12= -0.012739 R13= 0.070421
R21= 0.016147 R22= -0.012248 R23=-0.117999
R31= 0.002125 R32= 0.286000 R33=-0.001949
S11= 768.6224 S22= 12.1790 S33= 53.2339
S32= 0.0058 S31= -14.8373 S21= 0.0120
A = 27.7240 B = 3.4898
C = 7.2962
Alp = 89.9870 Bet = 94.2065 Gam = 89.9929 Vol=
704.0211
Reciprocal axes:
A*= 0.0362 B*=
0.2865 C*= 0.1374
Alp*= 90.0136 Bet*= 85.7935 Gam*= 90.0081
Save, repeat with Current or try again with Old. S, C or O? [O]
S<CR>
Reind? Y<CR>
Nr S H K
L Dev-Ang dTh
dPh dCh 0.0036167
1 H 12.001 0.000 -5.000
0.0083 0.001 0.005 -0.007 0.0001195
2 H 10.000 -0.000 -4.000 0.0029
0.001 0.002 0.002 0.0000567
3 H 16.001 0.000 -2.001
0.0095 -0.002 -0.008 -0.005 0.0001284
4 H 16.000 0.000 -1.000
0.0008 0.000 0.001 -0.000 0.0000145
5 H 14.003 0.000 2.000
0.0064 -0.002 -0.004 -0.005 0.0001265
6 H 3.000 1.000 5.000
0.0073 -0.001 0.001 -0.007 0.0001037
7 H 4.999 1.000 4.000
0.0076 0.003 0.001 0.008 0.0001494
8 H 0.999 1.000 4.000
0.0036 0.000 0.004 -0.001 0.0000448
9 H 12.998 1.000 3.000
0.0033 0.002 0.003 0.001 0.0000922
10 H 16.995 1.000 0.000
0.0038 0.004 0.004 0.001 0.0001908
11 H 13.001 1.000 -2.999 0.0077
0.001 0.008 0.004 0.0001008
12 H 9.001 1.000 -4.000
0.0046 0.000 0.003 0.003 0.0000569
13 H 2.999 1.000 -4.001
0.0102 -0.003 -0.005 0.009 0.0001640
14 H 1.999 2.000 -4.000
0.0031 0.001 -0.004 -0.001 0.0000645
15 H 3.999 2.000 -2.000
0.0046 0.001 -0.007 0.003 0.0000590
16 H 10.000 2.000 -2.000 0.0089
-0.002 0.007 -0.008 0.0001447
17 H 4.000 2.000 2.000
0.0080 -0.001 -0.005 -0.008 0.0001064
18 H 8.001 2.000 2.000
0.0041 -0.000 -0.006 0.003 0.0000507
19 H 4.005 2.000 3.001
0.0113 -0.004 -0.018 0.003 0.0002342
20 H 9.998 1.999 0.000
0.0042 0.004 0.006 0.003 0.0001906
21 H 11.002 1.000 -3.001 0.0073
-0.004 -0.006 -0.005 0.0001934
Reciprocal axis matrix
Direct axis matrix
0.032293 -0.012739 0.070421
23.775896 14.161738 1.665560
0.016147 -0.012248 -0.117999
-0.154360 -0.149664 3.483217
0.002125 0.286000 -0.001949
3.269563 -6.521197 -0.133642
Niggli-values
Sigma direct axis matrix
768.6222 12.1790
53.2339 0.001472 0.001000 0.001294
0.0058 -14.8373
0.0120 0.000227 0.000154 0.000200
0.000375 0.000255 0.000330
Cell parameters
Sigma cell parameters
27.7240 3.4898
7.2962 0.0014 0.0002
0.0003
89.9870 94.2065
89.9929 0.0038 0.0036
0.0044
0.000227 -0.073351 0.000124
0.000067 0.000064 0.000076
Volume= 704.0209
0.1448
Index-Status: HHHHHHHHHHHHHHHHHHHHH////
CD0>
Example 3 TRANS dialogue
C(onventional-cell)-mode:
Niggli-values
Sigma direct axis matrix
70.7877 77.1639
81.6915 0.000588 0.000490 0.000548
-15.4502 0.0052
-35.3932 0.000301 0.000251 0.000281
0.000565 0.000471 0.000527
Cell parameters
Sigma cell parameters
8.4135 8.7843
9.0383 0.0005 0.0003
0.0005
101.2213 89.9961 118.6128
0.0038 0.0050 0.0040
-0.194598 0.000069 -0.478888
0.000065 0.000087 0.000062
Volume= 571.8345
0.1430
Index-Status: HHHHHHHHHHHHHHH//////////
CD0> TRANS<CR>
M, R or C? [C] C<CR>
Acceptance parameter (0:+500)? [ 10.]:<CR>
Nr FOM
Lattice Bravais Type
39 0.000069
MONOCLINIC C ACUTE
44 0.000137
TRICLINIC P ACUTE
12 0.194598
HEXAGONAL P POS ACUTE
Transformation-number? 39<CR>
Orientation matrix:
R11= -0.025377 R12= -0.065544 R13=-0.091662
R21= -0.028238 R22= -0.072283 R23= 0.063526
R31= -0.054587 R32= 0.067867 R33=-0.020880
S11= 237.8706 S22= 70.7878 S33=81.6914
S32= 0.0052 S31= -30.8952 S21= 0.0013
A = 15.4231 B = 8.4135
C = 9.0383
Alp = 89.9961 Bet = 102.8049 Gam =89.9994 Vol=
1143.6691
RECIPROCAL AXES:
A*= 0.0665 B*=
0.1189 C*= 0.1135
Alp*= 90.0042 Bet*= 77.1951 Gam*=90.0015
Save, repeat with Current or try again
with Old. S, C or O? [O]
Example 4 TRANS dialogue
C(onventional-cell)-mode:
Niggli-values
Sigma direct axis matrix
145.2480 145.5687 213.0837
0.005965 0.006254 0.011807
-0.1150 -0.0945
-0.0018 0.002429 0.002546 0.004807
0.004990 0.005232 0.009877
Cell parameters
Sigma cell parameters
12.0519 12.0652
14.5974 0.0065 0.0029
0.0092
90.0374 90.0308
90.0007 0.0317 0.0564
0.0364
-0.000653 -0.000537 -0.000012 0.000553
0.000984 0.000634
Volume= 2122.5806
1.3743
Index-Status: HHHHHHHHHHHHHHHHHH/HHH///
CD0> TRANS<CR>
M, R or C? [C] C<CR>
Acceptance parameter (0:+500)? [ 10.]:<CR>
Nr FOM
Lattice Bravais Type
44 0.000000
TRICLINIC P ACUTE
35 0.000537
MONOCLINIC P ACUTE
32 0.000653
ORTHORHOMBIC P ACUTE
33 0.000653
MONOCLINIC P ACUTE
34 0.000653
MONOCLINIC P ACUTE
31 0.001306
TRICLINIC P OBTUSE
10 0.002203
MONOCLINIC C OBTUSE
11 0.002203
TETRAGONAL P POSACUTE
13 0.002203
ORTHORHOMBIC C ACUTE
14 0.002203
MONOCLINIC C ACUTE
20 0.316847
MONOCLINIC C OBTUSE
Transformation-number? 11<CR>
Orientation matrix:
R11= -0.057791 R12= -0.048845 R13=-0.028099
R21= -0.056669 R22= 0.059630 R23= 0.008656
R31= 0.018267 R32= 0.030463 R33=-0.061875
S11= 145.2480 S22= 145.5687 S33=213.0837
S32= -0.1150 S31= -0.0945 S21=-0.0018
A = 12.0519 B = 12.0652 C =
14.5974
Alp = 90.0374 Bet = 90.0308 Gam =90.0007 Vol=
2122.5801
RECIPROCAL AXES:
A*= 0.0830 B*= 0.0829
C*= 0.0685
Alp*= 89.9626 Bet*= 89.9692 Gam*=89.9993
Save, repeat with Current or try again with Old. S, C or O? [O]
S<CR>
Reind Y<CR>
Procedure for matrix determination
INDEX produces a unit-cell, a corresponding orientation matrix and it assigns indices to the reflections in the reflection list.
INDEX executes in a number of steps, of which the essence is briefly described here. Only the reflections in the list of which the index status is unequal 'N' are used. First the question: 'Enter Axis limit in Angstrom' should be explained. From the supplied value the shortest reciprocal vector can be deduced. Normally the default value (depending on lambda) is good enough. With smaller values the chance on parallel vectors is larger. A collection of vectors (V) in x, y, z co-ordinates is composed, containing i. the scattering vectors (Ri) calculated from the CRYSTAL file (< 25) and ii. the sum and difference vectors Ri+j of each combination of two scattering vectors (< 600). From (V) three vectors are selected using the following criterions:
R1 = shortest vector from (V) R2 = shortest vector from (V), which is most perpendicular to R1 R3 = shortest vector from (V), which is most perpendicular to the plane through R1 and R2.
Sorting of these vectors is effected by maximization of the empirical
expressions: [sin (angle(V,R1))]**4/(V) [sin (angle(V,R1))]**4*[sin
(angle(V,R2))]**4/(V)
Too small vectors Ri+j, viz. < (R)/25, are omitted. R1, R2 and R3 compose the columns of a preliminary orientation matrix R(3,3). The volume (V1) included by the vectors R1, R2 and R3 is compared with the volume (V2) of the rectangular block defined by R1, R2 and R3.
Preliminary indices are calculated using:
xi hi R(3,3)* yi = ki zi li
The indices calculated by this method for the reflections in the list are most likely fractional. In a kind of least-squares minimization procedure, the common multiplication factor M, which should be an integer, 1<M<25, is determined. All indices are multiplied by M and rounded off to integers. The message 'Determinant=M' is printed. In the next cycle the program tries to find smaller base vectors using the vectors of R(3,3) as a starting set. If the preliminary matrix would be the correct one, each vector of (V) would be equal to niR1 + miR2 + piR3, where ni, mi and pi are integers. When the preliminary matrix is incorrect, however, there will be a residual vector. A series of two-dimensional comparisons are applied in this case. The quantity minimized is Vi-niRi, while Ri=R1, R2 and R3. When a residual vector is more suitable to serve as a base vector, this one replaces one of the base vectors of R(3,3). Here, minimization of the in-products of the vectors is used to achieve 'perpendicularity' of the base vectors. To avoid degeneration, a new base vector cannot be smaller than any of the old base vectors divided by 10. To eliminate degeneration, it is advisable to check the list of reflections, especially with respect to scan angles, speeds and intensities. Reflections which have been measured with an exceptionally large or small scan angle or speed or reflections which produce an exceptionally high or low intensity should be labelled with index status 'N'. Reflections which cannot be indexed should not be deleted. These reflection should be examined more careful to find out why they cannot be indexed. If more space would be required it is advised to create a new CRYSTAL file or make a copy of the crystal file before these reflections are deleted. At a later stage another attempt can be made to attribute indeces to these reflections. Then another attempt to obtain an orientation matrix may be made.
If the program continues, the new base vectors are refined by a least-squares procedure using the reflections in the list. Indices are calculated. When the value in the last column (the lenght of the difference vector between the real scattering vector and the one as calculated from the current R matrix) is greater than the value in the header of that column, the status of this reflection is changed to N and this reflection is omitted for further calculations. Finally, the new base vectors are further refined on basis of the reflections, with index status '*' or 'H', in the list. The unit-cell is normalized (such that a<b<c and alpha, beta and gamma are all <90 or >90 degrees) to meet the conditions for unit-cell translations, given in the International Tables for X-ray Crystallography. Indices are assigned to the reflections in the list. If SR=X2XX the index information is printed. Reflections labelled with index status 'N' do not get an index based on the present orientation matrix. Reciprocal axes, direct axes and Niggli matrices are printed. The reduced cell scalars, which are printed as the Niggli matrix (metric tensor) allow one to choose the most probable lattice type (see also International Tables for X-ray Crystallography, Vol. A, 734-744 (1983)).
The subroutine TRANS serves to conform the unit-cell found by INDEX to the international conventions. It also offers many other features (Cf. section E of this Chapter).
The subroutine LS only refines the orientation matrix using the indices and the setting angles from the CRYSTAL file, i.e. it only executes the last cycle of INDEX.
Other convenient routines, SCAN TH OTPLOT ANIVEC LEARN
General scanning routine, SCAN
SCAN enables the operator to make a one or two axis scan through the current goniometer position. An intensity profile of the area scanned and some results of the peak analysis are printed on the terminal.
The program prompts:
MM Motor selection: No motor, one motor or two motors may be specified. When two motors are specified the first is called the master and the second the slave. Motors are specified by two consecutive characters; they must not be separated by a space. If the second character is omitted, it is assumed to be N (no motor).
Motor identifiers: N no motor. May be omitted for the slave selection. T theta motor. The actual two-theta moves twice as fast and twice as far. P phi motor. O omega motor. K kappa motor.
SA N R? Scan parameter selection: The scan angle and scan speed apply to the master motor. Only relative speed can be specified for the slave motor.
Scan parameters:
SA Scan angle for the master motor in degrees. A positive number specifies a scan in the positive direction, a negative number specifies a scan in the negative direction. Both scans are symmetric about the starting position. The actual scan angle is rounded off to a multiple of 0.066 degrees to accomodate the 96 step scan profile.
(-)N Scan speed for the master motor. The actual scan speed for the master motor is 16.48/N degree/min. Use a minus sign to indicate that the attenuator should be set. Use zero(0) as input to maximize time.
R Speed ratio for the slave motor. Not required when no slave motor is selected. With a positive sign, the slave scans in the positive direction. With a negative sign the slave scans in the negative direction. R must be an integer, -6<R<+6. Slave scan speed = master scan speed * (R/6) degree/min.
Example SCAN dialogue (omega-theta):
CD0> SCAN<CR>
MM? OT<CR>
SA N R? 2 2 3<CR>
TOTAL = 1217. NET = 997. WIDTH = 0.557
PEAK = 0.0000 GRAV = -0.019
111
1112369460957554311
963623536535894136627865060497111355250111101020 1
O 2 1 T 3 30
CD0>
TOTAL = the total number of counts in the scan NET = the net number of counts is the PEAK (minus background) WIDTH = the peak width as a franction of the scan angle PEAK = the peak position offset as a fraction of the scan angle GRAV = the center of gravity offset as a fraction of the scan angle.
The offsets are calculated from the midpoint of the scan. The offset directions and the profile output are independent of the scan direction; the profile output presents the more negative side on the left.
Scan information is printed to the right of the profile, e.q.
1 0 2 1 T 3 30
1 INCR1, the direction (sign) and increment for the master motor. O The master motor. 2 Scan speed parameter for the master motor. A minus sign indicates that the attenuator was set. 1 INCR2, the direction (sign) and increment for the slave motor. T The slave motor. 3 Relative scan speed parameter for the slave motor. 30 ISCANW, the scan width parameter. The scan angle of the master motor may be calculated as:
SA = INCR1*ISCANW*0.066 For example in the above case SA=1.0*30*.066, i.e. SA=2.0 degrees which has indeed been specified.
Special SCAN modes:
N = 0 The scan speed is calculated such that the time for the scan is 600 seconds (ten minutes).
No motors Stationary 'Scan', the time of the scan, in seconds (<600)
can be specified directly. Use a minus sign in front of the time, to indicate
that the attenuator should be set. With SR=4XXX the stationary scan is
repeated. This option can be used to perform repetitive measurements.
Example SCAN dialogue (no motors):
CD0> SCAN<CR>
MM? N<CR>
TIME? 30<CR>
TOTAL = 85 INT = 2.83
CD0>
TOTAL : the number of counts in the 'scan' INT : the intensity in counts/second (TOTAL/TIME).
Calculating h,k,l limits and number of reflections, TH
A routine to calculate the maximum range of indices to be used in the data collection zigzag routine. It also calculates the number of reciprocal cell volumes, within the given specified theta range.
Operation:
The program prompts 'T1 2?' The operator must supply the minimum and maximum theta angles (in degrees) of the shell to be calculated. The program calculates and prints the maximum possible indices and the number of reciprocal cell volumes, that lie within the given theta range. This last number is an approximation of the number of possible (although not necessarily observable) reflections in the entire Ewald sphere within the theta range specified.
Example:
CD0> TH<CR>
T1 2? 10 11<CR>
HMAX = 4 KMAX = 4 LMAX = 5 TOTAL =
106.80
CD0>
In ZIGZAG (see data collection description) these values may be specified as:
HMIN = -4 HMAX = 4 KMIN = -4 KMAX = 4 LMIN = -5 LMAX = 5
This specification allows the data collection program to measure every reflection in this Theta range. This is often not necessary, due to crystallographic symmetry. For a monoclinic space group such as, for example P21/c with the b-axis the unique axis, a unique set of reflections in a single quadrant may be collected by specifying the indices in the following way,
HMIN = -4 HMAX = 4 KMIN = 0 KMAX = 4 LMIN = 0 LMAX = 5 HST = 0 KST = 0 LST = 0 and chosing the sequence HKL or HLK.
Omega - theta profile plot, OTPLOT
OTPLOT produces an omega/theta plot of reflections out of the reflection list. The reflection(s) must be centered first (SETANG, DETTH or SET4). When the LCH code is N, the reflection is not used.
Each output line is the result of a theta scan (stationary crystal) with the vertical slit (SV) at various offsets from the centered position. The theta scan width is calculated in such a way that the scan follows the reflection profile, and as a result no time is wasted in measuring backgrounds. The intensity is scaled automatically. The output will show 10 levels of intensity; the lowest level is 2.5 counts and there is a constant ratio between the levels. For normal measurements an N will be placed above the plot, if the attenuation filter had been used an F appears . INTINT gives the sum of the real intensities along a line of the plot.
Note that dtheta does not refer to a movement along a central lattice line (i.e. the radiation streak), but only to a displacement of the counter by theta motor rotation. In reciprocal space this movement follows a line making an angle theta with the streak. In OTPLOT this angle is fixed; this makes an OTPLOT picture similar to a Weissenberg reflection. This representation is chosen for easy determination of the scan-area; see below.
The omega/theta plot OTPLOT can easily be understood by considering hypothetical situations in which each time one reflection component is the only important contributor and the others are negligible:
1) Mosaicity, on its own, produces a vertical line in the domega direction, i.e. the omega scan direction, with ratio dtheta:domega = 0:1. The intensity distribution is determined by the mosaic spread of the crystal. With anisotropic mosaicity and/or fragmentation this distribution is psi dependent, an effect explored and used in ANIVEC and VECHOR respectively.
2) Wavelength dispersion results in a diagonal along the omega/2theta scan direction, with dtheta:domega = 1:1. The intensity reveals the reflected source spectrum (filtered and discriminated), possibly on top of lower and/or higher order streaks.
3) The horizontal primary beam divergence and intensity variations are seen along the source scan direction, with dtheta:domega = 1:2.
4) Crystal shape and absorption effects are geometrically predictable but rather complicated to describe; they result in extra domega and dtheta variations of the reflection spot. Sometimes the crystal shape is the predominant factor for the reflection shape, as may be seen on Weissenberg photographs from needle or plate-like crystals. One should bear in mind that beam size and/or crystal size and shape are generally chosen less carefully on Weissenberg cameras than on a single crystal diffractometer. Effects on the third dimension of the reflection, i.e. the z-direction, are not shown directly in OTPLOT because the vertical slit dimension integrates these out in OTPLOT; it gives a kind of projection of the reflection volume.
If the distributions due to mosaicity, dispersion and source size were block shaped and the crystal very small, an OTPLOT would look like a hexagon, with three pairs of parallel edges, originating from the three effects; in practice, however, with (multiple) peaked distributions and streaks, the general effect is best described as blurring the picture.
OTPLOT can be used to establish the DATCOL scan parameters: a scan area covers a parallelogram with one pair of edges always parallel to the dtheta axis (aperture width can be read on the dtheta scale) and the other pair parallel to the scan direction given by dtheta:domega (The projection of these edges on the domega scale gives the scan angle).
The centre of the parallelogram lies at the OTPLOT centre. (a special scan area is the full area of OTPLOT itself: it corresponds to an omega scan over the full domega range with aperture equal to the full dtheta range. the profile is read in the column INTINT as a function of domega.) The parameters SCANR, DOMA, APTA and APTB can be obtained from OTPLOTs at various thetas; DOMB is fixed by the wavelength dispersion and may be taken equal to SWOMB as calculated by WI.
One should choose a parallelogram (or rectangle) that encompasses the desired reflection area as close as possible, but with allowances for variations between reflections (accuracy of angles, crystal shape, etc.). remember that DATCOL itself adds background regions at both ends.
The integrated intensity over such a scan area in OTPLOT is proportional, not equal, to the intensity of a scan with the area parameters, because of different exposure time, effect of slit width in OTPLOT and overlap or space between OTPLOT lines (i.e. theta scans).
Note that in DATCOL the scan direction is confined to dtheta:domega = n/6, with n = 0,1,2,3,4,5,6 (n = SCANR).
OTPLOT uses the values from SETPAR.
Example OTPLOT dialogue:
CD0> OTPLOT<CR>
Omega - Theta plot
Nr: 3 HKL: -3. 5. -4. Theta,Phib,Chib: 39.79 81.85 33.99 PSI: 0.
Level 1 =
2.5 Level 6=
48.5
Level 2 =
4.5 Level 7=
87.8
Level 3 =
8.2 Level 8= 158.8
Level 4 =
14.8 Level 9= 287.2
Level 5 =
26.8 Level 10= 519.6
Analysis of anisotropic mosaic crystals, ANIVEC
Introduction
Anisotropic mosaicity or even fragmentation of a crystal (leading to HKLand PSI-dependent broadened and/or split profiles) often can be described as the result of small rotations of crystal fragments about (mainly) one direction, which direction is symbolized by a vector A. This vector A is found by analyzing the effect of the (supposed) rotation upon reflection profiles. The vector A can be used in data collection (in PSI mode VECHOR) to calculate a PSI that minimizes the effect of anisotropy upon the profiles and hence upon the scan parameters. To find the vector A a dataset must be collected of at least 2 (preferably more) reflections in PSI-mode AZIMUT.
example of relevant input (DATCIN) to obtain data for determination of the vector A
SCAN = 2 0 5.9 0 0 (large omega scan with large aperture) (use large vertical slit too, if necessary) INT = 3 0.02 12 1 1 (see above) (NPIPRE = 12 for a reasonable speed, (MAXTIME = 1 to suppress final scans.) PSI = AZIMUT 36 0.00 10.00 / / / MODE = SEPHKL
For each reflection the best Psi is determined by the program ANIVEC; this Psi (called: Psi(obs)) is the one at which the reflection is narrowest and the least split up. The result of the combination of the Psi(obs) is the vector A, i.e. the anisotropy vector or torsion axis.
Example ANIVEC dialogue (SR=5200)
CD0> ANIVEC<CR>
Number of observations was: 4
indices (current) psi(obs)
psi(calc)
-0.0 4.0
6.0 -74.51 -74.21
2.0 4.0
6.0 31.31 31.98
-0.0 5.0
-6.0 -74.31 -69.21
1.0 4.0
7.0 -22.44 -23.73
Ani-Vector: 0.314489 -0.844407 0.433674,
indices: -4.59 1.00
2.63
Copy into Dvect? Y<CR>
CD0>
Vector A is expressed as an indexed reflection as well, because it often is and it is connected with the crystal and not with the (arbitrary) setting. The indices of this reflection are normalized in such a way that one or more of these is either 0 or 1; when it coincides with a real HKL this is easily seen. When there is no good correspondence between Psi(obs) and Psi(calc) (with more than two independent reflections!), the A model does not apply and there must be some other reason for the profile splitting; maybe there is more than one important torsion or one is dealing with twinning, which generally cannot be described as a rotation of crystal fragments over a small angle.
Note: when all PSI profiles are split up in the same way and do not show much variation, you may be looking at primary beam discontinuities. This might be observed with a very small crystal of high quality.
Lit: Duisenberg, A.J.M. (1983). Acta Cryst. A39, 211-216
Learnt profile analysis, LEARN
Introduction
With the classic BPB method the net integrated intensity is obtained by subtracting the left and right Background measurements from the Peak region. The CAD4 stores the left background in IDUMP[1] to IDUMP[16] (=L), the peak region in IDUMP[17] to IDUMP[80] (=T) and the right background in IDUMP[81] to IDUMP[96] (=R).
I = T - 2 * (L + R), (1) and sigma(I) is given by:
sigma(I) = sqrt(T + 4 * (L + R)) (2)
Formulae (1) and (2) assume a linearly (sloping) background and Poisson statistics for the individual, independent IDUMPs. If we assume relations between the IDUMPs, a profile, we may obtain the net intensity with a lower sigma. (One procedure that would not work is smoothing the observations by filtering out high frequency Fourier terms from the transformed profile. The only term containing the integrated intensity is F(0); the other integrals vanish, so there only is a cosmetic effect upon the profile and none upon sigma.)
Principle
The CAD4 profile method consists of three parts:
1) Profile learning. Here the standard alpha1 profile at theta = 0 is calculated from a number of selected reflections. The learning process is executed before data-collection; there is no automatic updating of this profile during DATCOL, but the process may be used as often and with as many reflections as desired. It may be useful even when no profile method is intented to examine crystal quality (mosaicity) and instrument properties (beam characteristics). 2) Preparation of the expected histogram. This is done for each reflection in DATCOL (under certain conditions; details below). The histogram consists of 64 numbers: IDUMP[17] to IDUMP[80] (stored in an auxiliary array CDUMP), representing the net expected profile shape for the reflection under investigation, built up from the standard profile itself (for alpha1) and a standard profile half as high (for alpha2) shifted over the a1-a2 dispersion distance: DOMB * tan(THETA).
3) Least squares fit of the parameters K, A and B, using the 96 observed IDUMPs and the 64 expected CDUMPs: A and B for the (supposed) linear sloping background and K for the ratio between the integrals (sums) over CDUMP and the net IDUMP:
IDUMP[i] = K * CDUMP[i] + A * i + B, (3)
with i = 1..96; CDUMP[i] = 0 for i<17 and for i>80. A residue and a sigma are calculated and both the results of the BPB method and the profile method are put out.
Description
The assumptions is made that all reflections are described by formula (3), i.e. by superposition of a standard alpha1 profile, a similar alpha2 profile half as high, and a linearly (sloping) background. The angular separation between the alpha1 and alpha2 profile maxima is given by DOMB * tan(THETA). If we denote the net IDUMP[i] values by T[i] and the alpha1 profile values by P[i] we have:
T[i] = P[i] + 0.5 * P[i-d], (4)
where d is the alpha2-alpha1 distance in dumps. (Generally d will be a non-integer; an interpolation formula for P[i-d] is used.) T is obtained by subtracting the linear sloping background calculated from IDUMP[1..16] (=L) and IDUMP[81..96] (=R), as follows:
T[i] = IDUMP[i] - BGA * i - BGB (5a) with: BGA = (L/16 - R/16) / 80 (5b) and: BGB = L/16 - 8.5 * BGA (5c)
It can be verified easily that the P[i] for the pure alpha1 are obtained from T by:
P[i] = T[i]-1/2*T[i-d]+1/4*T[i-2*d]-1/8*T[i-3 *d]+1/16*T[i-4*d]..., (6)
with i = 17..80.
The series is terminated when i-n*d < 16, because T[i] is supposed to be zero for i<16 (and for i>80). This divides T into two exactly similar parts with intensity ratio 2:1. Because T is affected by (Poisson) noise, P obtained from one reflection T will be noisy too; therefore the analyzing process has to be repeated (using reflections of about the same intensity) and the individual results cumulated to cancel this random noise.
There may be a small angular offset in T and so in P; the center of gravity of P is calculated:
Center = sum(i * P[i])/sum(P[i]), i = 17..80 (7)
and P shifted accordingly before adding it to the previous profiles. Moreover, each P is brought to the 'standard width at theta = 0' ; because the 96 IDUMPs represent a different angular width at different thetas, because of the dispersion term and from the fact that the scan angle must be set to an integer number of motor increments. Further P is left as it is: no folding, no smoothing. In the ideal case (small, spherical, non-absorbing, single crystal, isotropic mosaicity) the standard alpha1 profile after 20 to 30 reflections represents the sum (convolution) of beam divergence (apparent source size), crystal dimension and mosaic spread for the current experiment as if an ideal monochromator were used.
The expected histogram
The histogram consists of the expected values for IDUMP[17..80] under the assumption of formulas (3) and (4). It is stored in CDUMP:
CDUMP[i] = P[i'] + 0.5 * P[i'-d], (8)
where d represents the a1-a2 distance and the primes indicate that there may be a shift between the true and the expected positions of the profile, which is calculated by determining the center of gravity of the net profile, as described under the learning process. If the reflection is too weak to determine an accurate center it is assumed to be in the center, for a zero reflection this does not matter at all. (It is strongly recommended to do an orientation check on every reflection (unless it is to weak), for data collection on a good crystal that has been carefully centered. This can be affected by giving DEV-ANG (Chapter XI, section B.3) a negative value).
Histogram fitting
The fitting process (if called for at all) is not activated if: 1) SIGMA < SIGMA(final): desired accuracy reached with BPB. 2) reflection 'TOO STRONG'. 3) attenuation filter set. 4) intensity monitoring reflection is measured.
In other cases a least squares calculation on equations (3) is carried out:
with i from 1..96.
This gives K, from which the desired net intensity FITINT is found:
FITINT = S[1,3] * K / NPI (12)
(FITINT (and FITSIG, (13c)) are reduced to the value for NPI = 1). A and B describe the linear background. They are used to reconstruct BPB data, which are put out as well. No weights are used as the fitting is applied only to rather weak reflections, where the weights for the dumps would not differ very much anyway. Sigma is calculated by the propagation of errors, assuming negligeable errors in the expected profile CDUMP and Poisson statistics for each IDUMP[i].
First the CN[i] terms are calculated:
CN[i] = invS[1,3]+i*invS[1,2]+CDUMP[i]*invS[1, 1] (13a)
( invS = inv([S]), the inverse of [S] ).
Then a sum s':
s'= sum(CN[i]*CN[i]*IDUMP[i]), (13b)
with i from 1..96, CDUMP[i] = 0 for i<17 or i>80, and finally sigma(fit):
FITSIG = sqrt(s')/detS * S[1,3] / NPI, (13c)
with detS = the determinant of [S].
The measure of fit between expected and true net profile is expressed as a residue RES, calculated via res':
res' = sum(square(IDUMP[i]-K*CDUMP[i]-A*i-B)/ IDUMP[i]), (14a)
i from 1..96.
RES = sqrt(res'/N). (14b)
N is the number of terms in res' with positive IDUMP[i]; terms with IDUMP[i] = 0 are skipped.
Operation instructions
The learning process uses only reflections centered with SETANG. When LCA status equals A, first the SETANG procedure is done. Too weak reflections and reflections found to be badly centered are not used either.
The DATCIN parameters DOMA,DOMB,APTA,APTB and TYPE are used, so make sure these are the values intended for DATCOL (see Data collection input). Learning is activated by the command LEARN. The operator answers the question 'NEW or CONT(inue)?' with N for a new crystal or new learning process, and with C if the learnt profile sofar has to be updated with new reflections. DATCOL profile fitting is activated if the DATCIN parameter SIGMA in INT is negative. The learnt profile of the current CRYST file is used.
The command LCL (chapter IX) is used to check the status of the profile indicator of the reflections.
Output rules
If profile fitting is active during DATCOL a second output line is written with learnt profile information about the current reflection. This line is not written if:
. fitting not active (SIGMA greater equals zero) . attenuation filter was set . sigma(final) reached already . intensity control reflection
The terminal output line has the Fortran format: FORMAT(6X'DGRAV='F6.3,A1,'PROFIT
RES:'F5.2,I6,I7,I6,F10.1,1X,F6.1)
Example LEARN data collection OUTPUT
line to the terminal:
DGRAV=-0.012 PROFIT RES: 1.03 40.6 2.5
-0.012: center of gravity 1.03: measure of fit (residue) 40.6: net intensity from fit, FITINT 2.5: sigma from fit, FITSIG
DGRAV= 0.000* means: gravity set to zero because the reflection is too weak to calculate the center.
A record number 19 is written to the
data file with Fortran format: FORMAT (I6,F8.1,F6.1,F5.2,F8.1,F6.1)
Example LEARN data collection OUTPUT
line to the data file:
19 17 37.8 2.9 1.03 40.6 2.5
19 : recordnumber
17 : NREFL
37.8 : NETTI/NPI
2.9 : SIGMI/NPI
1.03 : FIT
40.6 : FITI/NPI
2.5 : FITSIG/NPI
Note: Optimizing experimental conditions should certainly not be replaced by sophisticated manipulation of poor data.
Literature: Clegg, W. (1981). Acta Cryst. A37,22-28 Diamond, R. (1969).
Acta Cryst. A25,
43-55
Example LCL dialogue:
CD0> lcl<CR>
Type= 6., Doma= 0.80, Domb= 0.15, Apta=2.40, Aptb= 0.30
:
:
:
:
:
:
:=
:=
:=
:=
:==
:=====
:=============
:============================
:==============================================
:Alpha1 profile learned from 5.reflections =============
:Picture-width= 0.800; Maximum= 4121.====================
:===================================================
:=============================
:==========
:===
:===
:===
:==
:==
:==
:
:
:
:
:
:
QLLLLL**K**************** OK?
y<CR>
CD0>
In each scan 96 intensity dumps are collected. In the profile output these are compressed to 48 steps. Each step is presented vertically, the bottom line representing the units place, the next higher line representing the tens place, etc.
The average intensity per step is calculated and then subtracted from each dump. This may be visualized as a new baseline through the profile, with one-half the intensity below the baseline and one-half above. This line normally cuts the profile at two or more points. In the example given below, these points are P and Q. The number of dumps included in PQ is denoted as K. The peak width, WIDTH, is defined as K/96. The peak position, PEAK, is the offset of the midpoint of PQ from the center of the scan as a fraction of the scan angle.
Fig. X.4 Peak analysis procedure
In other words, when the midpoint of PQ lies n dumps from the center of the scan PEAK = n/96. The back ground level (BG) is calculated from the 96-K dumps on both sides of PQ. The center of gravity of the peak, GRAV, is the fractional offset of the gravity center of the peak, based upon real intensity, above BG, from the center of the scan. Thus GRAV = m/96. This procedure is described in Fig. X.4.
When another peak cuts the profile, the width will include both peaks only if the area of the second peak above the baseline is greater than the area below the baseline seperating the two peaks. In this case the peak position and center of gravity will represent the combined peaks. The same procedure is followed for more than two peaks. Secondary peaks not meeting these criteria will be ignored in these peak statistics.
The parameters TOTAL, NET, WIDTH, PEAK, GRAV, RATIO, INT and EDGE are available to the program. RATIO is the peak to background ratio. (RATIO=SNETTI/(BG*K)). EDGE is used to specify that a peak is not totally included in the scan, i.e. P or Q lies outside the scan.
The scan range is adjusted to that it is a multiple of 96 encoder steps. Every 2.5*NPI msec the master encoder position will be changed by the amount specified by INCR1. This will be repeated (ISCANW*96) times, i.e.,
Scan range = INCR1*ISCANW*96 encoder steps Scan angle = INCR1*ISCANW*96*360/(128*4096) degrees Scan time = NPI1*ISCANW*96*2.5 msec
The slave motor will be changed by INCR2 every (NPI2/6) times the master motor is changed.
Slave scan range = INCR2*ISCANW*96*(NPI2/6) encoder steps Slave scan angle = INCR2*ISCANW*96*(NPI2/6)*360/(128*4096 ) degrees
The total elapsed time of the scan is not affected by the slave scan.
Routines related to special hardware
Makes axial oscillation photograph to evaluate symmetry properties.
AXIAL is a routine which essentially coincides a specified axis with the Z-axis of the goniometer. This implies the omega axis to be the oscillation axis. The central omega value of the oscillation is determined by the program to avoid collision during the oscillation motion. This routine requires a special piece of hardware, namely a support (part no. 0538.460) attached to the goniometer base. The polaroid cassette is mounted symmetrically with respect to the primary beam. Oscillation angles between zero and ninety degrees are allowed. The maximum oscillation time is 3600. seconds.
***WARNING***
Do not mount the cassette before you are asked to
do so.
Operation:
The program prompts 'CASSETTE DOWN'. If so answer Y<CR>. The program prompts 'H K L1?'. The operator must specify a h,k,l. The program prompts 'H K L2?'. The operator must specify another h,k,l. Typically 0,0,1 and 0,1,0 should be entered to rotate around the a-axis. Table X.1 gives pairs of suitable h,k,l's for each of the more common direct-lattice directions.
Table X.1 Relation between h,k,l pairs for AXIAL and rotation axes
| Real space axis | h,k,l1 | h,k,l2 |
| a | 0,1,0 | 0,0,1 |
| b | 1,0,0 | 0,0,1 |
| c | 1,0,0 | 0,1,0 |
| a+b | 0,0,1 | -1,1,0 |
| a+c | 0,1,0 | -1,0,1 |
| b+c | 1,0,0 | 0,-1,1 |
| a+b+c | -1,0,1 | -1,1,0 |
The program prompts 'SA, TIME?'. The operator must specify the scan angle in degrees and the scan time in seconds. Allowable values range from 0 to 90 degrees for SA and from 0 to 3600 seconds for TIME. After entering the time the goniometer positions to axis along Z.
The program prompts 'CASSETTE UP?' Verify whether the cassette is UP indeed before you continue by typing 'Y'. After this answer the oscillation starts.
When ready the program prompts 'CASSETTE DOWN?'. The operator must put the cassette down and respond to the question. This finalizes the dialogue and the CAD4 monitor response appears.
Example AXIAL dialogue:
CD0> AXIAL<CR>
CASSETTE DOWN? Y<CR>
H K L1? 0,0,1<CR>
H K L2? 0,1,0<CR>
SA TIME? 90,600<CR> positions
goniometer
CASSETTE UP? Y<CR>
starts oscillation
CASSETTE DOWN? Y<CR> ends session
CD0>
A special utility program for searching reflections when using a high pressure cell is called NIMBUS. NIMBUS serves to search for a user specified reflection using: - known cell parameters - known and optimized setting angles for one indexed reflection
Prerequisites are: - the first entry in the list must contain optimized setting angles for a reflection of known indices (hkl1) - a valid reciprocal axes matrix without orientation components must be stored in the CRYSTAL file - the indices of a second strong reflection (hkl2) must be known.
Description
The routine NIMBUS looks for reflections on the cone and puts the approximate setting angles in list. The reflections found are not indexed nor are the settings optimized. Starting angles for each scan and profile output are conditional to SR=X4XX (See Optional Terminal output).
NIMBUS calculates the angle between the scattering vectors of hkl1 and hkl2. This angle is printed by the program. NIMBUS asks the operator to specify the number of scans. Any integer number between 8 and 24 is allowed; the default value is 12. The program follows the nimbus to be searched by an omega/kappa scan. A higher value for the number of scans allows the program to follow the nimbus more closely. One reflection can be stored for each scan. It simply overwrites any information stored in list entries 2 to 25. NIMBUS will be able to locate upto 24 reflections.
If the program finds a reflection on the edge of a scan it generally finds the same reflection in a subsequent scan; scans overlap by means of the aperture. The program selects a horizontal aperture width of 5.9 mm. A SLIT of 4 or 6 mm vertically must be used. If a profile output indicates the presence of two or more peaks close to each other, the settings stored in the list are not necessarily the correct ones (Cf. the dump number as printed with each peak output). The intensity stored in the list is the one found by NIMBUS and thus not neccesarily an absolute measure for the intensity. The correct intensities will be found after centering the reflections using SETANG.
Procedure for preparing to use NIMBUS:
>LK 1-25
>BP one known reflection
by T=12.42, P=0, C=90, PSI=0
>SAP
9mm aperture
>SCAN omega, SA=10, N=1>>GRAV=2.8
>EK T=12.42, P=0, O=15.22,C=90
*)
>LD >>1
>SETANG
>RAMCEL A,B,C,AL,BE,GA,T any arbitrary H,K,L
and H,K,L and settings of EK as specified above
*)
>NIMBUS
Example NIMBUS:
CD0> NIMBUS<CR>
ENTER INDICES OF LIST REFLECTION NR.1 : ; only prompts
if unknown
0 0 4<CR>
ENTER INDICES OF REFLECTION TO SEARCH FOR :
3 5 5<CR>
ALPHA=22.55
; half-top angle of cone
ENTER NUMBER OF SEARCH SCANS(R8-24;D12) :
/<CR>
; use default=12
ENTER SPEED AND DISCRIMINATION-FACTOR :
12 1<CR>
; as with SEARCH
; output if SR=X4XX
additional output of TPOK(theta,phik,omk,kappa) and PSI for the beginning of the scan
NIMBUS SEARCH FOUND 7 REFLECTIONS IN 12 SCANS
CD0>
>SETANG to optimize settings
>INDEX depending on the total number of reflections
with or without cell-dimensions
>RAMCEL if all other attempts fail e.g. when only one additional
reflection has been found
Texture analysis, TEXIN TEXOUT TEXCOL
Introduction
The method of collecting pole-figure data depends on the sample type. The current version of the program supports only two types:
Type 0 Sample of a sheet-like structure, mounted on the texture-device so that the phi axis is perpendicular to the sheet. The data will be collected from the planes lying perpendicular to the normal direction. The relative intensity of diffraction from such planes would be represented at te center (pole) of a pole figure, this point being denoted by Nd. Phi-offset is defined as the Phi-angle value where, while Omega and Kappa are equal to zero, either Rd or Td is parallel to the X-ray beam.
The three orthogonal directions are: Nd Normal direction perpendicular to the plane of the sheet Rd Rolling direction in the plane of the sheet Td Transverse direction in the plane of the sheet and perpendicular to the rolling direction
Type 1 Sample of a laminar structure so that the sample surface makes equal angles with the Rd, Td and Nd. Phi-offset is defined as the Phi-angle value where, while Omega and Kappa are equal to zero, the line joining the ends of the Rd and Td axes is parallel to the X-ray beam.
The data-collection on texture samples happens with fixed detector position for each group of measuring points (pole-figure), so the detector angle value Theta is also a subject to the operator input.
The input routine TEXIN
Requests input from the operator for the data-collection of a figure and stores the given input in the CRYSTAL file. Up to 25 pole-figure data-collection specifications can be entered depending on the number of empty entries in the list. If the input is stored in the entry of the CRYSTAL file that entry is marked for texture data-collection (Angle-status 'T')
Example:
CD0> TEXIN<CR>
1 Type, Theta, Phi, Time? 0 23.45
24.56 10<CR>
2 Type, Theta, Phi, Time? 1 12.56
79.20 12<CR>
3 Type, Theta, Phi, Time? Q<CR>
Where: 1/2 is the first/next empty entry in the CRYSTAL file where the operator input will be stored. Type is one of the types described above (non-zero always will be interpreted as type 1) Theta is the detector angle value for the pole-figure measuring points Phi is the Phi-offset value which usually is determined as stated above Time is the wanted time in seconds to collect counts at each measuring point
The output routine TEXOUT
Prints a list of used values from entries in the CRYSTAL file marked for texture data-collection.
Example:
CD0> TEXOUT<CR>
From to: 1 2<CR>
1 Type 0, T 23.450, P 24.560, Time
10.00, * 0 0 0 N 0
2 Type 1, T 12.560, P 79.200, Time
12.00, * 0 0 0 N 0
CD0>
Where:
1 2 means print from 1 till 2 all entry information if the entry is
marked for texture data-collection
Type displays the type as entered by operator
T is Theta as entered by operator
P is Phi as entered by operator
Time is the Time as entered by the operator
* is the start-code position
Start-code normally has one of the following values:
'*' Data-collection must be started on this entry
'S' Data-collection is busy or ready (see Busy-code)
'D' If Theta value lies outside Theta-range
0 0 0 are three pointers used by the data-collection routine to remember the next measuring point
N is busy-code position If this position is an '*' and the start-code is not '*' data-collection was interrupted and this entry is busy for all other combinations the status depends on the start-code 0 The last number displays the number of already measured points for the pole-figure
The data collection routine TEXCOL
Opens the data-collection output-file, writes a record of type 41, writes
the CRYSTAL file information for all entries marked for texture according
to the blank record type and start measuring the next point of the pole-figure
which was interrupted or start measuring the first point of a new pole-figure.
The collected data is saved in the data- collection output-file with a
record of type 42. Untill all pole- figure specifications are handled.
Blank record type:
A2, I4, I3, I3, I3, 6A1, F6.2, F7.2,
F7.2, F7.2, I4, F4.2, I6, A2
L
C T P
O C N
T
i
o h h
m h r
i
s
d e i
e i e
m
t
e t
g f
e
n
a
a l
r
Listnr Number of the CRYSTAL file entry Code 1e character is Busy code ('*' if busy) 3e character is always 'T' for texture 6e character is Start code ('*' for start) Theta saved input value Phi saved input value Omega saved input value for Theta Chi 90.00 for sample-type 0 0.00 for sample-type 1 Nrefl Number of points already measured (if Code6 not equal '*') Time saved input value multiplied by 100
Record-type 41
A2, I2, 5A2, F10.7, F10.7, F10.6,
F9.6, F9.6, A2
R
T C C
F F F
t
e o o
l l i
y
x n n
a a l
p
t 1 2
m m f
e
1 2
Rtype '41' (record-type) Text '-TEXTURE-' Con1 constant to convert from Eulerian to Kappa geometry Con2 constant to convert from Eulerian to Kappa geometry Flam1 Lambda-alpha1 wavelength Flam2 Lambda-alpha2 wavelenght Filf Filter-Factor of the attenuator
Record-type 42
A2, I2, I6, I5, X, A1, F8.3, F9.3, F9.3, F8.3,
F9.0, I2, A2
R L
N B C T P
C T I
T
t i
r l o h h
h i n
y
y s
e a d e i
i m t
p
p t
f n e t
e e
e n
l k a
r
Rtype '42' (record-type) Listnr the CRYSTAL file entry with pole-figure specification Nrefl Measuring point number in pole-figure Code '*' Normal status-code 'X' if Chi too high 'D' if Detector angle out of range 'C' if arithmetic Collision 'S' if intensity is Strong (>100/2.5 msec) pile-up 'T' if intensity Too strong (>255/2.5 msec) loss of counts Theta Used detector angle during measurement Phi Used Phi angle in Eulerian geometry Chi Used Chi angle in Eulerian geometry Time Exact used time for this measuring point in seconds Int Total integrated intensity for this measuring point Type Sample type from input
Remarks: With LCH it is possible to change the busy-code from '*' to 'N' this means that if a measurement is interrupted and the busy code is modified. The measurement is set to ready! With LCS it is possible to change the Start-code to '*'. So an entry can be reset to start to remeasure the specified pole-figure.
Example TEXCOL dialogue:
CD0> TEXCOL<CR> ; no further input is required!!