NONIUS CAD4/MACH3 User manual

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.

calculates maximum h,k,l-values approximates the number of reflections within operator specified theta limits.

performs successive omega scans on reflections in the CRYSTAL file and plots the results as an omega-theta plot.

calculates the direction vector in case of anisotropic mosaic splitting of the crystal.

performs a learnt profile analysis on reflections in the the CRYSTAL file.

sets up for axial oscillation photograph and conducts oscillation according to operator specifications.

locates and centers a particular reflection; usually when applying the high pressure cell.

performs texture analysis, using the texture device.

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.

Reflection centering

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

Introduction

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&nbs