NONIUS CAD4/MACH3 User manual

Introduction
Direct control of beam conditioning devices
Geometry transformation and goniometer positioning
Related position commands
Special position commands
Wavelengths and orientation matrix parameter commands
Setang scan parameters

Introduction

The operate group is a set of commands providing the user with direct control of the goniometer and the devices associated with it. It also provides routines for converting between the various geometries used by the program and for examining and/or modifying the wavelength and orientation matrix.

Direct Control of Beam Conditioning Devices

Commands to control independent devices:

SO	Shutter Open; Open the X-ray shutter
SC	Shutter Close; Close the X-ray shutter
RA	Remove Attenuator
SA	Set Attenuator

The remaining commands in this section control the position of the aperture wheel in front of the detector.

The actual encoder positions of the different apertures in the wheel are specified in the list of goniometer constants.
 
 

SAP	Set the APerture. Set the variable horizontal aperture to the size specified by the operator. On the line following the SAP command, type the desired size in mm. The specified value is limited to the minimum and maximum values specified in the list of goniometer constants as kept in the GCONST file. This value normally lies between 1 and 6 mm. If no value at all is specified (a carriage return must still be typed to terminate the line), the 9 mm aperture is set.
SV	Set Vertical slit
SH	Set Horizontal slit
SU	Set Upper half-circle aperture
SL	Set Lower half-circle aperture
SP	Set Positive skew slit
SN	Set Negative skew slit

Geometry transformation and goniometer positioning

The diffraction position of a reflection, or more generally any position, can be represented in several geometries. The geometries used in the CAD4 program are called the geometry set. They are represented by a single letter each. The geometry set is listed below, along with its corresponding parameters and relationships. See the Kappa geometry description (To be added).

Geometry set:
 
 

H	Index (h,k,l) A position in reciprocal space based upon reciprocal grid vectors a*, b*, c*. Index values may be, and often are, non-integer. Transformations from H to C and C to H use the orientation matrix R.
C	Coordinates of reciprocal-space vector in goniometer X,Y,Z-system (C1, C2, C3). A position in reciprocal space based upon orthogonal unit length coordinates with dimensions of Angstrom-1. C1 is directed towards the source along the primary beam, C2 lies in the horizontal plane towards positive theta and is perpendicular to C1, and C3 is perpendicular to the horizontal plane and is directed upwards. Transformations from C to B and from B to C use the wavelength value LAM1(Kalpha(1) wavelength). If the transformation from C to B cannot be made, the message 'Theta impossible' will be printed.
B	BISECTING (THETA, PHIB, CHIB) in degrees. This position will have the lowest possible CHIE value and a positive THETA value. The bisecting geometry.
E	EULERIAN (THETA, PHIE, OME, CHIE) in degrees. A position in the Eulerian geometry. Eulerian settings may differ from bisecting settings in that there may be a rotation around the scattering vector by an angle of PSI degrees. In the bisecting position PSI is defined to be zero and OME is equal to THETA. In the transformation from E to K and from K to E the goniometer constants CON1, CON2 and CON3 are used. If the transformation from E to K is impossible because the absolute value of CHIE>100 degrees the message 'CHIE TOO HIGH' will be printed.
K	KAPPA (THETA, PHIK, OMK, KAPPA) in degrees. A position in the Kappa geometry.
M	MEASURE Measure the current goniometer position in encoder format. The goniometer may be controlled manually.
P	POSITION Position the goniometer to the current encoder values.
.	DOT Not a geometry, the dot is a pointer to the result of the last geometry transformation. Used only as the first character of a command, it causes the program to use the values produced by the last transformation as starting values. The result to which the dot is pointing may be examined with '.O'.

Format of geometry transformation and positioning commands:

Geometry and position commands consist of two characters. The first character is the starting geometry, the second character is the final geometry. When a geometry command is entered, the program responds by prompting for input values in the starting geometry, performs the transformation and prints the result in the final geometry.

The following combinations of characters are available commands:

HH	HC	HB	HE	HK	HP
CH	CC	CB	CE	CK	CP
BH	BC	BB	BE	BK	BP
EH	EC	EB	EE	EK	EP
KH	KC	KB	KE	KK	KP
MH	MC	MB	ME	MK	MP
.H	.C	.B	.E	.K	.P

Input prompts which should be expected:

H K L Psi?	Index values and Psi
H K L?	Index values
C1 C2 C3?	Scattering Vector
T P C?	Bisecting (THETA, PHIB, CHIB)
T P O C?	Eulerian (THETA, PHIE, OME, CHIE)
T P O K?	Kappa (THETA, PHIK, OMK, KAPPA)

*** Exceptions ***

- Identity commands, e.g. HH, are for input only.

- Dot commands use the results of the last geometry transformation as their starting values.

- Measure commands use the current position of the goniometer as their starting values. Besides the wanted and measured aperture (SAP) is given.

- Position commands move the goniometer. There is no other output.

- When .O is used for the first time, i.e. the current position is yet unknown, output is the position of the aperture wheel Aptm.

Internal note:

The program maintains a table of values for each geometry. The program also maintains an index status flag which is used to determine when valid index information is present. This flag is checked by the LD (List Dump) command. The flag is updated as follows

Index status flag set :

if index input was given, e.g. HK if index was calculated, e.g. .H if LG command transfers to the geometry set a line from the CRYSTAL file with index status of H

if a transformation starts at a geometry other than H, e.g. BE if LG command transfers to the geometry set a line from the CRYSTAL file with index status of N

if commands start with a dot (except .H) if commands perform an implicit .K transformation, e.g. LD

Related position commands

These commands are used to calculate related positions in Kappa geometry. They do an implicit .B transformation to obtain their starting values, then print the result in the current or bisecting geometry. The results may be examined in other geometries by the dot commands, etc.

NH  Negative H, K, L.

Calculate and print, in the current geometry, the position for the Friedel reflection. The indices are negated but not printed.

Calculate and print, in the current geometry, the position of the reflection at the other Theta side, i.e. a physical rotation of the crystal and reflection geometry around the primary beam, Psi is kept constant.

A combination of NH and TN. Calculate and print, in the current geometry, the position of the Friedel reflection on the other Theta side.

Calculate and print the alternative position of the goniometer for exactly the same position of the crystal. The algorithm describing this is given in Chapter II. The CAD4 routines may select this mode to avoid certain collision positions calculated during data collection.

A combination of NN and AA.

A combination of TO, AA and a Psi rotation of 180 degrees.

CD0> HH<CR>
H K L? 4 0 0<CR>
CD0> NN<CR>
PSI? 0<CR>
Theta= -8.16 Phib= 90.00 Chib=-180.00
CD0> .E<CR>
Psi? 0<CR>
Theta= -8.16 Phie= -90.00 Ome= 171.84 Chie= 180.00
CD0> .H<CR>
Psi= 0.00
H=-4.00 K= 0.00 L= 0.00
CD0>

Special position commands

Separate positioning commands for moving the goniometer to the most commonly used positions.
 

ZERO	All axes zero
VIEW 0	Theta = 70.00	Phie = -8.9889	Ome = 102.61	Chie= -45
VIEW 1	Theta = 70.00	Phie = 45.0000	Ome = 180.00	Chie= 90
VIEW 2	Theta = 70.00	Phie = -8.9889	Ome = 12.61	Chie= -45
VIEW 3	Theta = 70.00	Phie = 45.0000	Ome = 180.00	Chie= 90

If THPOS (GCONST parameter) is less than 70 the Theta value will be THNEG (GCONST parameter) + 0.1 for VIEW 0 and VIEW 1 and THPOS - 0.1 for VIEW 2 and VIEW 3.

It is recommended to align the crystal in either the View 0 or the View 2 position, and to check this alignment with the View 1 or the View 3 position respectively.

POLA  Polaroid rotation photograph position

Theta=67.50 Phik=0.00 Omk=-150.00 Kappa=0.00

      *** WARNING ***

Never use the POLA positioning command when the Polaroid cassette is mounted.

DEMO

This program demonstrates the goniometer motions. To run this program call DEMO and verify the switch register to contain 0000. The program can be interrupted by setting SWITCH XXX1.

MICROR

This command facilitates indexing of the crystal faces. Viewing the crystal through the optional equatorial-plane microscope, a crystal boundary face must be manually positioned parallel to the Z-Y-plane, i.e. the scattering vector of that face points in the X-direction towards the X-ray source. The index of that particular surface can be found by typing the command MICROR and the dimension of the crystal in that direction can be read in the microscope.

Example:

CD0> MICROR<CR>
HM=-1.06 KM=-0.03  LM=0.04
CD0>

Since the crystal faces generally have low indices it will be evident that the face in the above example has 1,0,0 as the indices.

MICROS

This command enables the operator to position any scattering vector specified by H, K, L and PSI along the X-axis. The microscope can then be used to view the crystal.

Example:

CD0> MICROS<CR>
H, K, L? 0,1,1<CR>
Psi? 0<CR>
HM=0.00 KM=1.00 LM=1.00
CD0>

Wavelengths and orientation matrix parameter commands

Four commands enable the operator to supply or examine both the orientation matrix and the wavelengths:

RI : Orientation matrix Input
RO : Orientation matrix Output
WI : Wavelength Input
WO : Wavelength Output.

The orientation matrix:

The orientation matrix R contains the magnitudes and directions of the three reciprocal unit cell vectors a*, b*, c*, of the crystal mounted on the goniometer in a right handed orthogonal system x, y, z. All goniometer axes are assumed to be in the zero position. The origin is at the crystal center (intersection of OMK and KAPPA). For a detailed explanation is referred to Chapter II.

The orientation matrix R is equivalent to:
 
 

R(1,1)	R(1,2)	R(1,3)		a*x	b*x	c*x
R(2,1)	R(2,2)	R(2,3)	=	a*y	b*y	c*y
R(3,1)	R(3,2)	R(3,3)		a*z	b*z	c*z

RI : Orientation matrix input

RI enables the operator to specify the orientation matrix.

The program will prompt R11 2 3?
The operator must supply R(1,1), R(1,2) and R(1,3).
The program next prompts R21 2 3?
The operator must supply R(2,1), R(2,2) and R(2,3).
The program then prompts R31 2 3?
The operator must supply R(3,1), R(3,2) and R(3,3).

The program then calculates the determinant DET of R and the direct matrix D = R-1
If DET = 0; the message "Singular" is printed and the program returns to command mode (CD0>). If DET non-equal 0; R, DET and D are stored in the crystal file.

Note:
When a new matrix is specified by this procedure, the information present in the CRYSTAL file is invalid. Normally, the orientation matrix is derived from the data present in the CRYSTAL file by least-squares calculation.

RO  : Orientation matrix Output.

RO enables the operator to examine the orientation matrix and also the unit-cell information.

Note:
The unit-cell information may not be valid if the orientation matrix was not determined by the
least-squares calculation.

Examples:

CD0> RI<CR>
R11 2 3? -0.00013,.09964,-.05633<CR>
R21 2 3? -0.00015,0.07948,0.07061<CR>
R31 2 3? 0.13071,.00019,.00003<CR>
CD0>

CD0> RO<CR>
Orientation matrix:
R11=-0.000130 R12= 0.099640 R13=-0.056330
R21=-0.000150 R22= 0.079480 R23= 0.070610
R31= 0.130710 R32= 0.000190 R33= 0.000030

S11= 58.5304 S22= 61.5565 S33= 122.5564
S32= 0.0048 S31= -0.0047 S21= 0.0001

A = 7.6505 B = 7.8458 C = 11.0710
Alp= 89.9968 Bet= 90.0032 Gam= 89.9999 Vol=664.5282

Reciprocal axes:
A* = 0.1307 B* = 0.1275 C* = 0.0903
Alp*= 90.0032 Bet*= 89.9968 Gam*= 90.0001
CD0>

The S-values are elements of the NIGGLI matrix:
 

S11=a.a	S22=b.b	S33=c.c
S32=b.c	S31=a.c	S21=a.b

A, B and C are the dimensions of the unit-cell in Angstroms. Alp, Bet and Gam are the unit-cell angles in
degrees. Vol is the volume of the unit-cell in cubic Angstroms. A negative volume indicates that the three
base vectors compose a left handed system.

The wavelengths

WI Wavelengths input.

WI enables the operator to specify the wavelengths of the radiation source being used and the factor of the attenuator.
The program will prompt 'Symbol?'
The operator must supply the chemical symbol. If he does not want to use any of the standard wavelengths from Table VIII.1 he should specify N and continue giving the wavelengths required.
The program will prompt 'Filter-Factor?'
The operator must supply the Filter-Factor of the attenuator which is currently in use. To determine this value see CAD4 Operate group: Geometry transformation.
After that the monochromator setting should be given:
Monochromator setup:
-1 = antiparallel
0 = none
1 = parallel
2 = perpendicular :'
If there is no monochromator enter 0, if there is a monochromator give the right value (see also Starting & Stopping the CAD4) and the program will prompt:
'Monochromator angle (2 theta):'
For graphite this angle is 12.2 degrees for Mo Kalpha radiation, 26.6 degrees for Cu Kalpha radiation and 9.6 degrees for Ag Kalpha radiation.
Finally the program will prompt: 'Wavelength (alpha1/alpha2) ratio: [2]'
Normally this ratio is 2. By the diffraction through the monochromator this ratio can be changed, but the difference will not be very significant.
When changing type of radiation, do not forget to adapt the filter-factor, the physically used beta-filter and the attenuation filter. Do not forget to adapt the parameters for the scintillation counter HV, WD and LL.

Table VIII.1 Summary of wavelengths selectable by chemical symbol.
 

Chemical symbol	Alpha(1) wavelength	Alpha(2) wavelength
Ag	0.5594075	0.563798
Co	1.7889650	1.792850
Cr	2.2897000	2.293606
Cu	1.5405620	1.544390
Fe	1.9360420	1.939980
Mo	0.7093000	0.713590
W	0.2090100	0.213828

The values from Table VIII.1 will be used or those specified explicitely by the user. These values will be stored in the crystal file. It should be noted that using the command WI involves an automatic correction of the setang parameters SWOMB and DIAFRB. SWOMB is recalculated using (LAM2-LAM1)/LAM2 and the subsequent conversion to degrees. The value of DIAFRB is calculated by (LAM2-LAM1)*173./LAM2, 173. being the value of RADIUS from the GCONST file.

WO Wavelengths output.

WO enables the operator to examine the wavelengths and monochromator setting currently in use.

CD0>wo<CR>
Lam1= 0.70930 Lam2= 0.71359 Filf= 15.000
!molybdenum radiation!
Monochromator perpendicular; Mon. angle = 12.2000;
Alpha1/alpha2 ratio = 2.00
CD0>wo<CR>
Lam1= 1.54056 Lam2= 1.54439 Filf= 16.300     !copper radiation
                                             !No monochromator
CD0>wi<CR>
Symbol?mo<CR>                                !molybdenum radiation!
Filter-Factor?/<CR>
Monochromator setup:
      -1 = antiparallel
       0 = none
       1 = parallel
       2 = perpendicular : 2<CR>
Monochromator angle (2 theta): 12.2<CR>
Wavelength (alpha1/alpha2) ratio: [2]<CR>
CD0>WI<CR>
Symbol?MO<CR>                                !molybdenum radiation!
Filter-Factor? 18.200<CR>
CD0>WO<CR>
Lam1= 0.70930 Lam2= 0.71359 Filf= 18.200
CD0>WI<CR>
Symbol?N<CR>                                 !when using non-standard wavelengths!
Lam1 Lam2? 0.70926,0.70926<CR>
Filter-Factor? 18.400<CR>
CD0>WO<CR>
Lam1= 0.70926 Lam2= 0.70926 Filf= 18.400
CD0>

Setang scan parameters

The command SETPAR enables the operator to examine the scan parameters currently stored and also provides the possibility to change some or all of these values. The program will print the values stored for

the omega scan angle (SWOMA + SWOMB*tan(THETA)),
the aperture (DIAFRA + DIAFRB*tan(THETA)),

the scan ratio, the quality factor and the "Poisson" distribution fraction. The program asks whether the values stored are satisfactory. Any old value can be retained by entering a slash(/). In those cases that the optimum scan ratio has been determined DIAFRB can be set equal 0.

Fixing the omega scan angle at the specified value SWOMA can be achieved by entering SWOMA as a negative value. A quality factor of 1 adjusts the omega scan speed to obtain a net intensity of about 400 counts. More accurate results can be obtained with a higher quality factor at the cost of time. E.g. a quality factor of 2.0 corresponds with a net intensity 800 counts. A high value for PFRACT requests a high peak to background ratio. This implies that the current reflections are omitted if the nett peak intensity is less than (A*BG + B*BG**1/2 + C)*PFRACT. This expression estimates a minimum nett intensity from the empirical peak-shape constants A,B and C, the average background of the scan and the user supplied Poisson fraction(PFRACT). The three constants A, B and C have values 0.79, 4.36 and 2.67 respectively.
Example:

CD0>SETPAR<CR>
  Swoma Swomb Diafra Diafrb Scanr Qfact Pfract
  0.60 0.35 1.50 1.00 6. 1.00 1.00
0.8 / 1.7 1.1/ / /<CR> !slashes are used to retain current figures!
CD0>
 
 

Default values derived from the molydenum wavelengths, are stored for all setang parameters if a new CRYSTAL file is created at start-up of the system. When a new CRYSTAL file is created using the GCONST option under the CAD4 monitor the SETPAR values are copied from the crystal file which was connected before.

Table VIII.2 Examples of SETPAR parameters
 
 

	SWOMA	SWOMB	DIAFRA	DIAFRB	SCANR	QFACT	PFRACT
Mo-radiation default	0.80	0.35	2.40	1.05	6.	1.00	1.00
Cu-radiation default	0.80	0.15	2.40	0.43	6.	1.00	1.00
MO-sharp/strong refl.	0.45	0.35	1.90	1.05	6.	0.60	2.50
CU-broad/weak refl.	1.20	0.15	3.00	0.43	6.	2.00	0.70

The table given above (VIII.2) is intended to indicate in which sense the SETPAR parameters may be varied under different circumstances.

When will SETPAR values be used? Only when using SEARCH,after locating a reflection during PHIK-Scan, and when using SETANG for omega/2-theta and no valid scan information is available. Changing the scan information status code from S to * voids the information and forces SETANG to use the SETPAR values.