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THE COLLECTION OF SINGLE-CRYSTAL DIFFRACTION DATA WITH AREA DETECTORS
U. Arndt
To cite this version:
U. Arndt. THE COLLECTION OF SINGLE-CRYSTAL DIFFRACTION DATA WITH AREA DE- TECTORS. Journal de Physique Colloques, 1986, 47 (C5), pp.C5-1-C5-6. �10.1051/jphyscol:1986501�.
�jpa-00225818�
Colloque C5, suppli5ment a u no 8, Tome 47, aoat 1986
THE COLLECTION OF SINGLE-CRYSTAL DIFFRACTION DATA WITH AREA DETECTORS
U. W. ARNDT
M.R.C. Laboratory of Molecular Biology, Hills Road, GB-Cambridge C B 2 2QH, Great-Britain
Resume
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L'emploi de dktecteurs bi-dimensionnels demande une reevaluation corrplhte des procedes de mesure : un diffractomhtre B d&tecteur 2-D n'est ni une camera B rotation oh le film serait remplace par un detecteur electronique, ni un diffractomstre B quatre cercles equip6 d'un dbtecteur 2-D au lieu du detecteur uni-dimensionnel. Les nouveaux instruments doivent Ctre relies B des mini-ordinateurs relativement puissants ~ossedant une grande memoire pour le stockage des donn6es et des programmes. Ces ordinateurs offrent de nouvelles possibilit6s pour l'optimisation de la strategic de la collection des donnees.De telles dispositions permettent des mesures trss rapides; elles permettent aussi une precision superieure par comparaison aux methodes classiques, parce qu'elles rendent possible une calibration exacte du detecteur et une correc- tion totale des mesures. Ces possibilites representent un pari formidable pour le programmeur afin d'arriver B produire un evsemble de programmes d'une versatilite, d'une fiabilite et d'une facilite d'utilisation suffisantes pour encourager une large communaute scientifique B se servir de ces instruments nouveaux.
Abstract
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The use of area detector methods requires a complete re-thinking of optimum procedures of data collection: Area detector diffractometers have to be interfaced to relatively powerful mini-computers with very large amounts of program and data storage space which present new opportunities of optimising data collection strategies. In addition to making possible very fastdata-collection, they permit a higher accuracy to be achieved than is possible with other methods, because they allow very elaborate and complete calibration and correction of the measurements. Software packages of great flexibility, reliability and user-friendliness are required to encourage the wide-spread use of the new instruments by a large user community.
1. Introduction
The collection of single-crystal intensity data with an area detector diffractometer is basically quite diff ereni from that with either a single-counter dif f ractometer or with a screenless rotation camera. In principle, the new method can give more accurate results faster and more conveniently than the older methods, but this is possible only if the fundamental differences are clearly recognised and if the diffractometer is under the control of a software package which is necessarily large and complex. Proposals to use area detectors for single-crystal diffractometry have a long history [ 1 , 2 , 3 , 4 , 5 ] However, it is no accident that these methods are only maturing now at a time when affordable minicomputers have achieved a power in excess of that of the main-frame computers of the period when development of the detectors started.
In reciprocal space every diffraction spot has a three-dimensional intensity distribution, which can be sampled on a three-dimensional grid only with an area detector. In a rotating-crystal photographic method the intensity distribution is projected on to a plane and in point-counter diffractometry it is projected on to a line; consequently area-detector diffractometry permits a much more elaborate three-dimensional profile analysis than do the other methods. Such an analysis can result in a considerable gain in signal-to-background ratio with a consequent gain
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1986501
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in precision. A knowledge of the spread function of the detector coupled with profile analysis also increases the effective spatial resolution of the detector.
The increased speed of area detector methods in which many reflexions are measured simultaneously is obvious, at least for thickly populated reciprocal lattices, but perhaps not quite as obvious as it was before the development of high-intensity synchrotron radiation sources. We have now reached a situation in which the speed of data collection is limited by that of the data processing rather than by the photon flux.
2. Effect of Detector on Data collection Strategy
The choice of recording method, whether on photographic film, by single counter or by area detector, affects a11 aspects of the design of the goniometer as well as the actual data collection strategy.
2.1 Collimation
In rotation photography the angular range through which the crystal is rotated during the exposure is always much larger than the reflecting range of any one reflexion and there is no advantage in making this reflecting range as small as possible, except for the purpose of reducing the proportion of partially recorded reflexions. The primary beam can, therefore, have an appreciable cross-fire, preferably convergence, in the plane containing the crystal rotation axis; in the plane orthogonal to the rotation axis the beam should be as parallel as possible so as not to make off-equatorial reflexions too wide.
With electronic area detectors the signal-to-background ratio is maximised if the angular profiles of the reflexions are as narrow as possible. On a single counter diffractometer all reflexions are measured in the equatorial plane and the beam should be parallel in this plane; cross-fire in the plane containing the rotation axis has little effect on the reflexion width and should be large in the interests of increasing diffracted intensity. On an area-detector diffractometer most reflexions are measured off the equator and the beam should be parallel in both planes. It should be noted that profile-f itting for very narrow reflexions is possible only with a goniometer of very high shaft-setting precision.
2.2 Comparison with Photographic Methods
The aim in the development of photographic methods has been to maximise the number of identifiable non-overlapping reflexions recorded on any one film. The need to identify or to index the spots led to the development of the various layer-line-screen methods; the need to maximise the number of spots so as to ease microdensitometry led first to the abandonment of the layer-line screen in the small-angle rotation and precession techniques. [61, then to the modified Weissenberg method of Sakabe [7] and, finally, to the re-introduction of white radiation methods [8], [ 9 ] . The need to maximise the number of spots in a given exposure is in direct conflict with the requirements of optimum signal-to-background requirements: the total background recorded on a film depends on the total volume of reciprocal space illuminated and, therefore, ultimately on the total number of reciprocal lattice points contained in that volume, that is on the number of diffraction spots recorded'on the film.
The strategy of data-collection is strongly influenced by the response characteristics of the three types of detector which influence its mode of use for single-crystal data collection:
2.2.1. The absolute response depends critically on development and it cannot be assumed that two separate films which have had identical exposures will have identical blackening. Since there is no easy way of calibrating the absolute response it is always necessary to scale the results from separate films from common reflexions. Because this scaling is necessary in any case no particular precautions are necessary to ensure that the crystal volume which is illuminated in two exposures of the same data set is identical, provided that this illuminated volume remains reasonably constant during a given exposure. Consequently it is customary in rotation photography to employ a primary beam which is smaller than the sample;
constant in time and whose spatial variations can be calibrated; accordingly, they are capable of making absolute measurements. With area-detector diffractomers, as with single-counter diffractometers it is, therefore, more usual to bathe the entire sample in the beam so that the whole of it is illuminated during the entire data-collection run.
2.2.2. During the microdensitometry of a film the quantity which is actually measured is the amount of light transmitted through the film and this is a logarithmic function of the optical density of the blackened film. Evaluation of the intensity of a diffraction spot requires the area integration of the density and it is, therefore; necessary to sample the film on a very fine grid and with a very fine sampling light beam in order to avoid errors. The response of area detectors is a linear function of the incident X-ray intensity and so the diffraction pattern can be sampled much more coarsely. Thus a relatively small number of pixels is often sufficient for an area detector and the volume of the uncontracted raw data set is smaller than in photographic measurements.
3. Data Collection Strategy
In all sinele-counter diffractometer methods onlv the regions of reci~rocal
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m a c e in the immediate vicinity of reciprocal lattice points are surveyed. (This is why single-counter methods will always remain the most efficient for small unit cells and long-wavelength radiation when reciprocal space is thinly populated with lattice points). Data collection can therefore, begin only when the unit cell and the orientation of the crystal relative to the goniometer have been determined so that the coordinates of all reflexions can be computed.A complete data-set collected with an area detector covers the whole of reciprocal space up to the resolution limit. It contains within itself all the information necessary to determine the orientation matrix and the unit cell parameters. In principle, therefore, it is possible to collect and store the complete set and to process it later, the only necessary task before data collection being to centre the sample in the beam. This will probably be the preferred procedure when cheap very-large-scale storage devices such as laser disks become available. At this point exchange of programs between different laboratories and different instruments will become easy and will only require a common file structure.
At present the storage of an uncontracted data .set is not practicable. The area detectors of today have a resolution of about 512 x 512 pixels and measurements must be made at least every 0.05' over a total equivalent crystal rotation range of about ZOO0 (the crystal may be rotated about more than one goniometer axis, either Bequentially or simultaneously). The intensity, or the photon count, must be represented by a two-byte number for an adequate dynamic range if no background subtraction is carried out before storage. The total data volume, therefore, is 2 Gigabytes.
At the opposite extreme would be a method of data collection in which the orientation and unit cell dimensions are determined at the outset and in which the coordinates of all reflexions are determined in real time as the crystal rotates, the orientation matrix being refined and up-dated as the measurements proceed.
Complete data processing would proceed during run-time, the output consisting only of a set of structure factors with their individual statistical weights. This method requires very fast prediction algorithms [10,11]; it suffers from the disadvantage that it is highly specific not only of the diffractometer and detector but also of the computer hardware.
The most promising procedure at present is an intermediate one: measurements are made in three-dimensional 'boxes' around each reflexion large enough to obviate the need for real-time refinement but small enough to give a reduction in the raw data volume by a factor of about 20. Data reduction, including profile-fitting of the desired degree of sophistication, is carried out off-line.
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The method adopted determines the electronic hardware of the area-detector diffractometer; in some cases the hardware provided will influence the choice.
Rapid data transfer is required if complete images are to be dumped; this is best achieved with a double memory so that data can be read from one while the next frame, or angular slot, is being accumulated in the other. Real-time data contraction in which only the active parts of the pattern are read out requires an efficient hardware mask.
4. Location of the Detector
A pre-requisite for the prediction of the positions of diffraction spots is an accurate knowledge of the position of the origin of the coordinate system of the detector, of its precise distance from the crystal, of any departures from orthogonality to the goniometer axes and of the spatial distortions introduced by the detector. These quantities can be derived by means of standard calibration crystals giving a known diffraction pattern and with the help of shadow masks placed in front of the detector.
A separate calibration may be necessary at each position at which the detector is used for data collection, since the origin and the spatial distortion may be affected, for example, by local variations of the magnetic field. The calibration procedures must, therefore, be rapid and under software control which allows them to be as automatic as possible.
5. Calibration of Detector Response
The area detector may display a spatial non-uniformity of response, it may have a number of blemishes which render measurements of reflexions falling on them invalid and its response may be non-linear with intensity. These characteristics must be determined by calibration, and again the calibration procedure should be automated.
It should be noted that such a calibration is not easy: it is difficult to derive a way of illuminating the whole area of the detector with an accurately uniform illumination and a pixel-by-pixel calibration with a finely collimated beam is very time-consuming. Linearity calibration ideally requires an X-ray beam intensity which is variable over three orders of magnitude and such a variation cannot be achieved by means of absorbers which.would completely alter the spectral composition of the beam in an unpredictable manner.
6. Orientation of the Crystal
In most methods the orientation matrix of the crystal relative to the goniometer axes must be known at least approximately before data collection can co-ence. The obvious way of determining this matrix is by some variation of the normal procedure used in the rotation method which involves the measurement of two stills or small-angle rotation patterns at two spindle settings separated by 90'. In principle, it is possible for the computer to conduct a search for reflexions in these two patterns, to find their centroids, to index the reflexions and to derive the orientation matrix. In practice, the poor signal-to-background ratio in most patterns makes such a search for completely unknown reflexions slow and the results inaccurate. Some intervention by the operator is thus desirable which leaves the finding and selection of the reflexions to him or her. Hardware must be provided to produce a display, together with a light-pen or a cursor under the control of the operator.
7. Data Collection
The way in which the reciprocal lattice is surveyed is determined by the spatial reso1u;ion of the detector- and of the collimation- geometry which together determine the maximum number of diffraction orders which can be measured parallel to the edges of the detector. Suppose a detector has 512 x 512 pixels and the minimum permissible distance between the centres of neighbouring reflexions is 5 pixels as determined by the size of the spots and the spread function of the detector; the maximum number of measurable orders is then 102, that is f 51 orders if the direct beam is aimed at
the centre of the detector or 0 to +I02 or 0 to -102 if the beam strikes the edge of the detector. Other parts of the reciprocal lattice can be surveyed by off-setting the 28- arm, if any, on which the detector is mounted. In the plane at
lattice can be brought into an equatorial belt by suitable movements of the Eulerian cradle or other device on which the crystal is mounted. Versatility is thus much reduced if the goniometer does not permit rotation about three axes, or if the detector position is fixed. Single-axis rotation of the crystal leaves a cusp in reciprocal space which must be filled in by limited rotation abaut a second axis after re-mounting the crystal; programmable rotation about several goniometer axes in principle, permits a crystal movement which explores the whole of reciprocal space. [121.
Algorithms must be found which determine the optimum procedure for a given diffractometer, unit cell dimensions and required resolution. These are complicated by the fact that collisions and shadowing of the pattern occur much more easily on an area-detector diffractometer than with a single-counter instrument.
8. Data Corrections
The measurements must be corrected for soatial nen-uniformity and non-linearity of the detector as well as for oblique incidence of the beam, except with spherical drift chamber detectors. Corrections must also be made for Lorentz and polarisation factors, specimen absorption and radiation damage. A complete software package will provide the necessary look-up tables or analytical derivation of the corrections and will provide automatic sequences for monitoring the state of the sample and for measuring its absorption.
9. Hardware Checks
An area detector diffractometer contains one or more mass memories, other special-purpose hardware and, often, several mini
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or micro-processors which communicate with one another. The software package should contain programs for exercising the hardware and for diagnosing possible faults.10. Data processing
All.the usual programs are needed for merging and analpsing data and for performing statistical assessments of the quality o f the data. Area-detector methods are, or should be, so efficient that they will often allow a complete data set to be collected on one specimen crystal; they, therefore, provide the possibility of calculating the statistical weight of each intensity measurement directly from the counting statistics.
11. User-friendliness
An area-detector diffraatometer installation is complex and expensive. It thus seems likely that each instrument will have to senve a larger user community than is normal for any one single-counter diffractometer; indeed, several area-detector diffractometers have already been set up as 'regional facilities' serving many users, [ 1 3 ] . It is thus of particular importance that the software package should be written with user-friendliness as a prime consideration and should contain prompt statements, skilfully chosen default parameters and 'help' files so that the diffractometer can be used by relatively unskilled operators.
12. Conclusions
The first three-circle diffractometers appeared in the middle nineteen fifties and recommendations on their use were oubldshed in 1957. 1141. - - - Ten years later it was possible to write a monograph on diffractometry [3] which contaGed no chapter on software and it was not until the ~ a r l y nineteen seventies that automatic diffractometers became conrmercially available which were complete hardware-software packages. It will take time before area-detector diffractometry becomes a turn-key operation but with the cooperation of many groups such as those represented at the nresent workshop the process will be a rapid one.
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