Triplet-phase measurements using a 2D detector
Figure 1. Reference-beam diffraction in Bragg-inclined geometry, where two sets of diffraction patterns (black and grey)interfere and generate a phase-sensitive diffraction image on an area detector.
Unlike ordinary two-beam diffraction experiments performed for intensity measurements, three-beam experiments are also sensitive to the phase difference (triplet phase) of the three structure factors involved. Already during the late 1940s, a suitable experiment based on Renninger
Ψ-scans was proposed. In the mid-1970s, the first three-beam interference profiles were observed, and since the end of the 1980s, one practical application has been the determination of the absolute structure of low Z
≤ 8) compounds. From the beginning of the 1990s, three-beam interference effects have been observed from crystals of small proteins, whose structures can in principle be solved by this method.
Figure 2. Reference-beam diffraction profiles of a Friedel pair on lysozyme, (a) H
= (324), G
= (230), and (b) H
= (324), G
= (230), recorded in inverse reference-beam measurements.
Up to that time, nearly all experiments were based on the Renninger
Ψ-scan technique, which requires the alignment of a primary reciprocal lattice vector H
with its diffraction position and an accurate rotation about H
to excite a second reflection G
. During such a three-beam experiment, two wavefields are propagated in the direction kH
of the first reflection H
. These are the direct wave due to H
and the twice-scattered Umweg
wave due to G
, which is rescattered by H
. This leads to characteristic intensity changes in the kH
direction that depend on the phase difference between the two wavefields ΔΦtot
+ ΔΦ(Ψ) with the triplet phase Φ3
and the resonance phase shift ΔΦ(Ψ) of the G
reflection as it passes through the Ewald sphere. The advantage of this procedure is the possibility to optimize experimental conditions for each three-beam case individually, resulting in a quite small phase error (approx. 20°). However, the method is slow compared with an intensity data collection using area detectors because only one triplet phase at a time can be determined.To tackle this problem, Shen et al.
propose an experimental procedure ['Triplet-phase measurements using reference-beam X-ray diffraction', Acta Cryst.
(2000), 268-279] that enables the use of a 2D detector (either an image plate or a CCD). This technique should speed up the measurement of triplet phases considerably. Hereby, a strong reflection G
aligned to a rotation axis φ is rocked through its diffraction position stepwise by a second rotation (say θ) perpendicular to the φ axis (Fig. 1). For each step in θ an oscillation image about φ over the same angular range is recorded. The intensity of each reflection Hi
recorded on the detector results now again from the interference of the direct wave due to Hi
and a twice-scattered Umweg
wave due to G
as explained above. The series of intensities recorded for each reflection Hi
as a function of the rocking angle θ of the strong reflection G
contains in principle the same information as a standard Ψ-scan interference profile. However, using a 2D detector a large number (≥1300) of interferences can be measured in a short time in one series. The intensity changes due to the three-beam interaction are in the range of ±2% for a crystal of tetragonal lysozyme (Fig. 2). In the example shown, the almost symmetric increase and decrease due to the constructive and destructive interference, respectively, of a three-beam interference with a triplet phase close to ±90° is clearly visible. Because the wavefield of the strong reflection can be considered as a sort of reference wave that interferes via the reciprocal lattice vectors Hi
with all directly excited reflections Hi
, the authors named this technique 'reference-beam X-ray diffraction'. The geometry and wavelength cannot be optimized for many three-beam cases simultaneously; therefore, the phase information obtained is less accurate compared with the standard Ψ-scan technique, for example because of overlap of neighbouring three-beam interference profiles. The authors report a mean triplet-phase error of 54° after rejection of about 60% of the measurements by suitable criteria derived from the fit of the experimental intensity profiles. However, the significantly larger number of phases that can be determined in a given time might easily counterbalance this larger phase error. The authors report further that this method can also be applied to quasicrystals. In a second contribution ['Enantiomorph determination using inverse reference-beam diffraction images', Acta Cryst.
(2000), 264–267], the same authors were able to show that the statistical significance achieved is sufficient for the determination of the absolute structure.
An important topic in this context - the utilization of the measured triplet phases in a structure solution procedure - is discussed in a third communication ['Shake-and-Bake applications using simulated reference-beam data for crambin', Acta Cryst. A56 (2000), 280–283]. Direct-methods programs like Shake-and-Bake that combine reciprocal space methods with realspace peak-picking techniques have already demonstrated several times that they are able to solve even the structure of small proteins ab initio if high-resolution intensity data (approx. 1.2 Å and better) are available. Additional experimental phase information might help these programs to also work with intensity data of significantly poorer resolution. The proposed reference-beam technique provides for a single series of images triplet phases that all contain one reflection G and phase information from an almost two-dimensional slab in reciprocal space. In this contribution, the authors used simulated data for the small protein crambin to investigate the important question of how many phases or series of reference-beam phase sets at what accuracy are needed to boost direct methods significantly. They discovered that they could find a set of reasonably good trial phases for all resolutions (3 Å and better) of the available intensity data provided one series of triplet invariants is available by the method discussed above with a phase error of less than 40°. This phase error is less than what seems to be available by the experiment but reasonably close for promising further developments. If more than one series of reference-beam phases are available, slightly higher phase errors can be tolerated, almost matching today's experimental achievements.
Thus the future of experimental phase determination would be very promising if the crystals could be persuaded to always crystallize with a mosaicity low enough for three-beam interference experiments.
Edgar Weckert, HASYLAB at DESY, Germany