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May 16, 1989 - MORGUE results from major code modification to the program EDINP [Pawley (1980). J. Appl. Cryst. 13, 630-. 633] to allow the introduction of ...
C O M P U T E R PROGRAMS

SALUNKE, D. M., KHAN, M. I., SUROLIA, A. & VIJAYAN, M. (1982). J. Mol. Biol. 154, 177-178. SALUNKE, D. M., SWAMY, M. J., KHAN, M. I., MANDE, S. C., SUROLIA, A. & VIJAYAN, M. (1985). J. Biol. Chem. 260, 13576-13579.

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VINAY KUMAR, KANNAN, K. K. & CHIDAMBARAM, R. (1989). Curt. ScL 58, 344-348. WLODAWER, A., NACHMAN, J., GILLILAND, G. L., GALLAGHER, W. & WOODWARD, C. (1987). J. Mol. Biol. 198, 469-480.

J. Appl. Cryst. (1989). 22, 629-633 MORGUE,

a neutron powder diffraction

profile refinement program with control-file facility t o

include structural and rigid-body thermal-motion constraints. By P. G. BYROM, S. E.

HOFFMANN* and B. W. LUCAS,t Department of Physics, University of Queensland, St Lucia, Brisbane, Queensland 4067, Australia

(Received 16 May 1989; accepted 19 July 1989)

Constraints

Abstract A neutron powder profile refinement program, MORGUE, has been written to facilitate the (possible) inclusion of both structural and rigid-body thermal-motion constraints. MORGUE results from major code modification to the program EDINP [Pawley (1980). J. Appl. Cryst. 13, 630633] to allow the introduction of constraint conditions from an input parameter file in most practical situations. This replaces the previous need to write constraint-specific subroutines for each structural and thermal-motion model refined, with the consequent repeated requirement for some recompilation and linkage of the modular parts to form the new executable program. The code is written in (VAX/VMS) Fortran77 and the program has been run on a VAX 11/750 computer. Examples of its use are included.

Introduction The technique introduced by Rietveld (1969) to refine crystal structures from neutron powder diffraction profiles is widely used. Rietveld's program allowed the application of some simple structural constraints, but the shortcomings of incorporating some physically useful constraints prompted Pawley (1980) to write a new computer program, EDINP. Generally, structure-specific constraint subroutines were written for each case considered and initially only isotropic temperature factors (Pawley, Mackenzie & Dietrich, 1977) were employed, although later rigid-body translational and librational tensors (T and L) were introduced (Baharie & Pawley, 1982). With the present program, MORGUE, standard packages of subroutines have been written for incorporation in the main program to allow structural and rigid-body thermalmotion constraints to be incorporated, while still allowing user-written constraints, if required. *Present address: Department of Physics, University of Toronto, Canada. t Author to whom correspondence and enquiries for copies of MORGUE (version for VAX 11/750) and user's manual (51 pages) may be addressed. 0021-8898/89/060629-05503.00

( a ) Structural There are several reasons why it may be desired to investigate a refinement where a group of atoms is considered to form a regular-shape unit by appropriately constraining structural parameters. A solid may be composed of molecules or atom groups which have some internal symmetry when in the free state. Distortion of this molecular or atom-group symmetry due to forces in the crystal lattice may be investigated using constrained refinement. First the molecule or atom group is considered as a regular-shape unit with the undistorted free-state symmetry, and only its orientation or size are allowed to vary in the refinement. The final R factor of this constrained refinement indicates the validity of the molecular-symmetry model when explaining the observed data. Then an unconstrained refinement that allows the atoms of the group to move independently in the lattice may or may not show significant improvement over the symmetry model. Consideration of the relative merits of the two models, and therefore a judgement on the amount of molecular distortion, can be made using a statistical significance test (e.g. Hamilton, 1965) on the R factors resulting from each model. The identical-molecule constraint can be used to investigate whether molecular groups of the same type situated on different lattice sites are distorted sufficiently to have individual identities, or whether they remain in effect identical when located within the crystal. In the constrained refinement, all supposedly identical groups are generated from the same set of internal molecular coordinates, and only individual orientations are allowed to vary until convergence is achieved. Again, a statistical significance test (Hamilton, 1965) can be made with an unconstrained refinement, where individual molecules are allowed to assume independent shapes. A set of constraints on the parameters may also be used just as an aid to the refinement process, by keeping the parameters away from physically unrealistic values and directing them closer to the minimum of the residual in parameter space. © 1989 International Union of Crystallography

630

C O M P U T E R PROGRAMS

( b ) Rigid-body thermal motion The T L / T L X / T L S constraints on thermal-motion parameters (Schomaker & Trueblood, 1968) treat a molecular unit as a genuine rigid body with regard to its thermal vibrations. Internal modes are disregarded, and the molecule is assumed to vibrate about an equilibrium position and librate about axes as would a rigid solid. The validity of these approximations can be tested by comparing R factors from both constrained and unconstrained refinements run on powder data of sufficient quality. The anisotropic thermal-motion matrix B of each atom in a unit is composed of thermal average displacement products, and here each instantaneous displacement is due to both translational and librational contributions from the rigid-molecule motion. In the full TLS model (see Willis & Pryor, 1975) B=T+RLRr

+SrRr +RS

where T = (uu T)

is the translation matrix

L = (00 r)

is the libration matrix

S = (Ou r)

is the screw matrix

and u, 0 are instantaneous translations and angular displacements of the rigid molecule, respectively, while () denotes thermal average. The components of 0 are the angles of rocking about the molecular axes. The antisymmetric matrix is

Ol

-- r 2

R

-- r 3

0

r, 0

r 2

-- r 1

where r is the position of the atom from the molecular centre. Changes in the choice of molecular origin will be absorbed into T and S, while L depends only on the choice of orthogonal lattice axes. However, if the molecule occupies a site of sufficient symmetry, S may vanish completely and Cruickshank's (1956) TL model is valid. Site symmetry imposes symmetry constraints on B, T, L and S elements. The diagonal elements of S are not independent; S~ + $22 + $33 is a constant, set arbitrarily to zero. So S ~ - $33 and $22-St~ are used as independent variables. Pawley's (1963) TLX model approximates the effect of screw motion by referring L to an origin whose position can be varied in the least-squares refinement along with T and L. Here r displacements are measured from the position x°+ 12, where t2 is the shift of the TLX 'centre of libration' away from the molecular centre x °.

Program details The Rietveld profile refinement program used as the starting point was E D I N P (Pawley, 1980), itself developed from ORFLS (Busing, Martin & Levy, 1962). Modifications were made to almost all sections of the code. Provision was made for assigning both isotropic and anisotropic thermal-motion parameters to the one atom, a feature useful in allowing

some account of internal motion in a rigid-body analysis. The unit-weight scheme of EDINP, Wx = 1, was extended to allow also choice of an alternative wx = 1/y °bs. The output format was extensively modified and improved. E D I N P required the user to create special subroutines for the application of constraints; the new program has standard package subroutines to allow the application of structural and rigid-body thermal-motion constraints, as well as frequently needed linear constraints such as those required by symmetry.

( a ) Constraint subroutines Subroutines were written to allow application of the required constraints and an outline of their respective functions is given below. C O N F I X applies the constraints necessary to fix positional and thermal-motion parameters of atoms at special positions. It may also be used to ensure that parameters for different atoms, not equal due to symmetry, be treated equivalently. C O N S T R applies user-written constraints on non-rigidbody parameters. C O N P S N parameters describing the coordinates of atoms in the molecule or atom group are functionally linked so that the internal relative positions can retain their symmetric structure. C O N T H M applies TL, TLX or TLS model constraints on thermal parameters (Schomaker & Trueblood, 1968) to treat a molecular unit as a genuine rigid body with regard to its thermal vibrations. Internal modes are disregarded, and the molecule is assumed to vibrate about an equilibrium position and librate about axes as would a rigid unit. C O N B O N D applies bond-length and interbond-angle constraints to molecules which have a central atom, i.e. an atom linked to all other atoms in the molecule. C O N T H E R M F I X applies symmetry constraints to the constrained thermal-motion matrices T, L and S, and the possible restriction of the molecular centre to a special position. This subroutine is similar to that of CONFIX, except that it applies constraints to the parameters used in the rigid-body subroutines CONPSN, C O N T H M and

C ON B ON D. C O N S Y M applies user-written constraints to structural and rigid-body thermal-motion parameters.

( b) Input-output data files The input data files are: INDATA.DAT which contains the initial values of the instrumental, structural and thermal-motion parameters, as well as the control parameters for the program operation and includes selection (if any) of the available constraint subroutine options. I N S C A N . D A T contains the experimentally observed scan profile data, (possibly) the background-corrected scan data, and a list of Bragg-peak Miller indices and multiplicities. The output data files are: LSTOUT.DAT which contains the program's major output, including parameter values and associated shifts and standard deviations, as well as residuals. NEWDAT.DAT contains updated values of the parameters in INDATA.DAT to facilitate further refinement cycles, if required.

COMPUTER PROGRAMS O U T S C N . D A T contains the background-corrected scan and a list of Bragg-peak Miller indices and multiplicities generated by the program. O U T R E F . D A T contains a list of reflections with positions, halfwidths and scaled calculated structure factors. The program is usually run interactively, and during the refinement process R-factor values after each cycle and warning messages (if appropriate) are displayed on the monitor screen. Applications (i) ND4NO3 (phase IV) at 298 K The preliminary refinement with M O RG U E (without constraints) confirmed the previously reported structure from neutron powder data (Lucas, Ahtee & Hewat, 1979), using the Hewat-modified Rietveld computer program (Rietveld, 1969; Hewat, 1973). The results are compared in Tables 1 and 2. The ND4 group was then constrained to a regular tetrahedral shape, and the oxygen atoms of the planar N O 3 group were constrained to lie on the corners of an equilateral triangle. The only variable parameters were the N - D and N - O bond lengths. Full TLS rigid-body thermal-motion constraints were also applied. A large correlation was found to exist between the S~2 and $21 elements of the NO3 group, necessitating their constraint to equality. The results are shown in Table 1. The elements of the T, L and S matrices are shown in Table 3, and the r.m.s, amplitudes of the translational and librational motion are shown in Table 4. To investigate the acceptability of the constrained model, Hamilton's (1965) test was applied to the residuals. Pawley (1980) has suggested that to compensate for the correlation between neighbouring points in the scan, the total scan angle should be divided by the average FWHM, to give a reasonable estimate for the number of independent observations to be used in the test. Hamilton's test was applied with this caveat. The number of variable parameters in the unconstrained model is 39, the number of observed points in the scan is 1917 (the effective number of independent observations is 197), and Rwp = 8"05%. For the constrained model, the number of parameters is 28, and Rwp = 9.20%. Thus RcorffRunc= 1"14 while R~la58,o.oo 5 = 1-09 indicates that the constrained model may be rejected at the 0.5% confidence level.

631

Table 1. Atomic parameters of N D 4 N O 3 (IV) at 298 K

determined by neutron powder profile refinement Three sets of values are shown in (vertical sequential) order for: (1) Rietveld refinement (Lucas et aL, 1979); (2) M O R G U E refinement without constraints; (3) M O R G U E refinement with ideal tetrahedral ND4 and equilateral triangle NO 3 group and rigid-body TLS constraints. E.s.d.'s are in parentheses; parameters without e.s.d.'s were fixed in refinement and those not given are zero, due to symmetry requirements. Rwp factors are for the weighted sum of scan points. Temperature factor = exp { - ( f i l t h 2 + fl22 k2 + fl3312 -4-2fl12hk

x 0-75

Y 0"25

0-25

D(2)

0.6110(41 0.6115(51 0.6135 0-75

N(2)

0.25

0(1)

0.25

0.25

o.4338 (4)

0.25

N(I) D(I)

0(2)

N(I)

0'0990(5) 0"0993 (6) 0-1055 0-25

0.4339 (4) 0.4354

/3t~ 0-017 (1) 0.017 (11

/~22 0.027 (!) 0"027 (I) 0-035 0'058 (1) 0.057 (I) 0-057 0-069 (1) 0'068 (1) 0'068 0'018 1) 0.018 1) 0"018 0.029 i ) 0.031 l) 0'030 0-050 1 ) 0.050 ( 1) 0.047

0.020 D(I)

D(2)

N(2) O(l)

0(2)

0'004(2)

o-o43 (2) 0.044 0.039(1) 0-038 (11 0.037 0.017 (1) 0.018 (1) o-o18 o.o14 (1) o.o15 (I) o.o16 0-024(I) 0"024 ( 1)

(ii) KIO3 (phase I) at 523 K

The crystal structure determination of phase I KIO3 at 523 K from neutron powder diffraction profile analysis has been reported previously (Byrom & Lucas, 1987). As the iodine and oxygen atoms form bonded groups, the possibility arises of essentially rigid-body thermal motion of the IO3 groups; MOR GUE was employed to investigate this possibility. The initial values for the parameters used in refinement were derived from the refined values produced by the Hewat-modified Rietveld program and the results are shown in Tables 5 and 6. The elements of the translation T, libration L and translation-libration S matrices produced from the refinement are shown in Table 7. The off-diagonal elements of the T and L matrices are nearly zero, indicating that the principal axes of T and L almost coincide with the orthogonal-lattice axes. The r.m.s, amplitude of the translational motion is 0.152 (11/~, and the r.m.s, amplitude of libration is 7.7 (2) °.

0.025

~33 0'026 (2) 0"026 (2) 0"013 0"078 (2) 0'075 (2) 0-067 0'093 (2) 0"089(2) 0'076 0"012 (1) 0.015 (1) 0.016 0-017 (2) 0'012(21 0'016 0"029 (11 0.031 (l) 0"025

+ 2fit 3hi + 2flz3kl)}.

z

Rwr (%)

-0'0834 (4) -0'0833 (5) -00845 - 0 ' 1932 (6) -0"1937 (6) -0'i973 0.0244 (6) 0.0240 (6) 0.0283 0"5059 (4) 0-5067 (4) 0"5078 0.7613 (6) 0"7613 (6) 0-7578 0.3857 (5) 0'3849 (5) 0'3827

7.3 8.0 9.2

~23

/~31

-0'033 ( 1) -0.031 (1) -0.036 0"038 ( 1) 0'038(1) 0-046

0"012 (I) 0.012 (1) 0.010

Table 2. Bond lengtks (,~) and interbond angles (o) for N D a N O 3 (IV) at 298 K determined by neutron powder profile refinement Two sets of values are shown in (vertical) order for: ( 1 ) M O R G U E refinement without constraints; (2) M O R G U E refinement with ideal tetrahedral ND4 and equilateral triangle NO 3 group and rigid-body TLS constraints. N-D(I)

0.965 (3)

0.963 N-O(I)

(2)

N-D(2)

=

1.257 (4) i . 2 3 3 (2)

N-O(2) =

0.976(3)

D(I)-N-D(2) I)(2)-N-D(2) D(I)-N-D(I)

107.8(11 i 14-3 (4) i11.4(3)

0.963 (2)

D-N-D

109.47

1.217(3)

O(I)-N-O(2) O(2)-N-O(2)

119.6(I) 120.9 (2)

i-233 (2)

O-N-O

~20.0

632

C O M P U T E R PROGRAMS

Table 3. The T, L and S matrices of ND4NO 3 (IV) at 298 K Elements of T are in A 2, L in (rad) 2 and S in A rad. E.s.d.'s are in parentheses and those elements not shown are zero due to symmetry requirements. Group ND4 r. 1"22 7"33 0.034 (1)

0.053 (1)

0.016 (2)

Lt I 0"126 (4)

L22 0"107 (4)

L33 0"004 (6)

Si2 -0.009 (2)

S2I -0.006 (2)

Tll 0.030(1)

7"22 0.027(1)

NO3

LIt St2 -0.007 ( I )

Two sets of values are shown in (vertical) order for: (1) MORGUE refinement without constraints; (2) MORGUE with rigid-body motion thermal constraints. 1.777 (4) 1-776(2)

S21 -0.007 ( 1)

7",,

r22

T33

Table 4. ND4NO3 (IV) at 298 K: the r.m.s, amplitudes of

Ttl L22 Lit

LI L33 Lll

the translational (l~) and librational motion (°) about axes a, b, c, respectively, of the ND4 and N O 3 groups

S23

S31

St2

0"0042 (10)

823

$23

0.184 (4), 0-173 (2), 20.4 (3), 0.5 (5.8),

0.230 (3), 0.163 (3), 18-7 (4), 5"8 (2),

0.127 (7); 0' 138 (2) 3.8 (2.5); 12.3 (3)

Table 5. Atomic parameters of KIO3 (I) at 523 K determined

by neutron powder profile refinement Two sets of values are shown in (vertical) order for: (1) MORGUE refinement without constraints; (2) MORGUE with rigid-body motion thermal constraints. E.s.d.'s are in parentheses; parameters without e.s.d.'s were fixed in refinement and those not given are zero, due to symmetry requirements. Rwv factors are for the weighted sum of scan points. Temperature factor = exp { - (fit1 h2 + fl22 k2 + fl3312 + 2fl12hk + 2flt3hl + 2f123kl)}. x y z Rwp(% ) K I O

0"5115 (9) 0"5114 0"0 0"0 0"0570 (12) 0.0567

x 0"0 0"0 0"0263 (12) 0"0265

x

~11 0.047 (1) 0"047

~22 ,Bit

~33 flit

I

0.022 (1) 0"023

fill

fill

0

o. 105 (5)

0.090 (5)

0.021 (1)

0"105

0.091

0"020

/312 K

-0"002 (1)

14"0 14"0

0"0 0"0 -0"3912 (5) -0"3910

K

~13 fit2

/323 Bt2

Bt2

B12

-0.001 I O

-0.001 (1) -0.001 -0.003 (2)

-0.0o4

-0.002 (3)

o.ool

100.8 (3) 100.8 (2)

Elements of T are in ~2, L in (rad) 2 and S in/~ rad. E.s.d.'s are in parentheses and those elements not shown are zero due to symmetry requirements.

0.046(2)

0.0231 (4) Lit 0"0183 (9)

ND 4 NO 3 ND4 NO 3

O-I-O

Table 7. Elements of the T, L and S matrices for KIO3 (I) at 523 K

L33

0-010(1)

refinement

I-O

T33 0.019(1)

L22

0.OOO(2)

Table 6. Bond lengths ( ~ ) and interbond angles (°) for KIO3 (I) at 523 K determined by neutron powder profile

-0.009 (3)

-0.011

To decide whether the rigid-body model was appropriate to this structure, Hamilton's test (Hamilton, 1965) was intended to be employed. However, for the unconstrained refinement, Rwp (defined as in Rietveld's program) was

/'23 -0.0003 (7) L23 0"0010 (6)

$32

-0"0079 (12) $33 - $22 = Sii - S33 -- 0"0

r3,

T,2

T23 L31 L23

7"23 Ll2 L23

$13

S21

$32

$32

14-0%, with 22 variable parameters, the number of observed points in the scan was 1986 (the effective number of independent observations was 126); while, for the constrained refinement, Rwp was also 14.0%, with 20 variable parameters. As there are two fewer parameters in the rigidbody model, this model is preferred. Discussion

M O R G U E allows the convenient inclusion of both structural and rigid-body motion constraints by, in general, the simple change of parameter-control values in an input file read by the program during execution. Modification to the constraint conditions during a refinement procedure is thereby easily achieved. Choice between the rigid-body constraint model TL, the approximate TLX or the fullconstraint model TLS can be made and comparison between them (if appropriate) investigated. The program has been tested by application to neutron powder data for phase IV ND4NO3 and phase I KIO3 and comparison with the results under equivalent conditions (for the same data) obtained using the Hewat-modified Rietveld program confirmed the correct functioning of the new program. M O R G U E offers the potential to investigate conveniently physically and chemically interesting matters, such as the effect of lattice-site environment on atomicgroup or molecular shapes and distortions etc. Investigation of organic molecules, which "will become more frequent with the better-quality diffraction data now becoming available, will be greatly aided by the convenient specification of structural constraints. Further, some of the problems associated with the interpretation of powder data may be overcome by the inclusion of the previously known molecular shapes, thus allowing the refinement to focus on the position, size and orientation of the molecule. The approximation of rigid-body motion to that of the actual structural unit may also be investigated, although the inherent problem of obtaining meaningful information about

C O M P U T E R PROGRAMS thermal motion generally from neutron powder data is often present. Inclusion of additional features, such as optional choice of alternative peak-shape functions, is intended for future up-date versions of the program. The authors thank G. S. Pawley for his assistance in sending them a copy of his computer program, EDINP, and agreement to use the program code. The work was supported by an Australian Institute of Nuclear Science and Engineering (AINSE) research grant.

References BAHARIE, E. & PAWLEY, G. S. (1982). Acta Cryst. A38, 803-810. BUSING, W. R., MARTIN, K. O. & LEVY, H. A. (1962). ORFLS. Report ORNL-TM-305. Oak Ridge National Laboratory, Tennessee, USA.

633

BYROM, P. G. & LUCAS, B. "W. (1987). Acta Cryst. C43, 1649-1651. CRUICKSHANK, D. W. J. (1956). Acta Cryst. 9, 754756. HAMILTON, W. C. (1965). Acta Cryst. 18, 502-510. HEWAT, A. W. (1973). UKAEA Research Group Report R-7350. Unpublished. LUCAS, B. W., AHTEE, M. & HEWAT, A. W. (1979). Acta Cryst. B35, 1038-1041. PAWLEY, G. S. (1963). Acta Cryst. 16, 1204-1208. PAWLEY, G. S. (1980). J. Appl. Cryst. 13, 630-633. PAWLEY, G. S., MACKENZIE, G. A. & DIETRICH, O. W. (1977). Acta Cryst. A33, 142-145. RIETVELD, H. M. (1969). J. Appl. Cryst. 2, 65-71. SCHOMAKER,V. & TRUEBLOOD, K. N. (1968). Acta Cryst. B24, 63-76. WILLIS, B. T. M. & PRYOR, A. W. (1975). Thermal Vibrations in Crystallography. Cambridge Univ. Press.

J. Appl. Cryst. (1989). 22, 633-639 C R Y S T - a system to display 3D images of crystal structure, symmetry operations and crystal forms. By TOSIO SAKURAI,Faculty of Education, Shinshu University, Nishinagano, Nagano 380, Japan, KIMIKO KOBAYASHI and TSUYOSHI HORIKI, The Institute of Physical and Chemical Research, Wako, Saitama 351-01, Japan, and MASAO FURUKAWA and KIMITOSHI NAITOU, F A C O M - H I T A C Ltd, Chiyoda, Tokyo 102, Japan (Received 15 February 1989; accepted 13 June 1989)

Abstract C R Y S T is a 3D computer graphics program to help the understanding of crystallographic procedures. The threedimensional image of a crystal structure is displayed, together with the arrangement of the symmetry elements in the unit cell. The symmetry-related atoms can be generated successively on a graphics screen by designating symmetry elements with a pen and tablet. Changes in morphology of a growing crystal may also be drawn by computer. Several applications of the system are described.

Introduction Nowadays, routine crystal structure analysis can be done automatically. On the other hand, important crystallographic knowledge is sometimes overlooked, A computer graphics system has been developed that helps one to understand the fundamental ideas of crystallography. The main part of the system, RSCG, is related to the space-group symmetry. The spatial distribution of symmetry elements is shown on the display. Symmetry-related molecules can be generated by designating the symmetry element on the display. Intermediate stages of crystal structure analysis can be displayed on the screen. The crystal habit can be generated by the program RSCH. These programs are useful for the teaching of crystallography as well as for research purposes. 0021-8898/89/060633-07503.00

Outline of the CRYST system The graphics device is a COMTEC DS301B coiour-graphics display with 3D raster scan, supplied by Daikin Industries Ltd. The DS301B has a 4.5 Mbyte segment buffer. The display is connected to the FACOM M-780 computer of the Institute of Physical and Chemical Research, through an RS232C interface (19 200 byte s-~). Input devices are a pen and tablet, a joystick, a function keyboard and an alphanumeric keyboard. The output devices are a CIR-320 colour image recorder, supplied by Nippon Avionics Co. Ltd, and an ED-320A(NTSC mode) for video output. The program is written in Fortran 77. The graphics part was written by the GRIP-II system developed by Daikin Industries Ltd. GRIP- I I consists of 450 graphics subroutine packages which can be called from Fortran 77 programs. An,outline of the system is shown ~n Fig. 1. The graphics data are stored in a layered form as shown in Fig. 2. Each element of the figure is stored as a PRIMITIVE. Balls and sticks are constructed from the elements and stored as SEGMENT. Figures for the symmetry elements are stored as CLASS. These are labeled by their own numbers. Firstly, PRIMITIVE data are transferred from the host computer and stored in the buffer. Graphics data stored in the buffer can easily be rotated, translated and clipped in nearly real time. The interaction between user and the program is accomplished by the selection of a command. Once PRIMITIVEs are stored in © 1989 International Union of Crystallography