Patterns Laue diffraction

A diffraction pattern with diffraction spots belonging to both zero-order Laue zone and higher order Laue zones can be used to determine the three-dimensional unit-cell of the crystal. 

Fig. 8. A full white beam Laue diffraction pattern recorded from a crystal of glycogen phosphorylase b, and (P4(3)2(l)2 a = b = 128.8 A, c= 116.2 A) using a 0.2 mm diameter collimator the exposure time was 0.5 s...

Szebenyi, D. M. E., Bilderback, D. H., LeGrand, A., et al. 1992. Quantitative analysis of Laue diffraction pattern recorded with a 120 ps exposure from an X-ray undulator. J. Appl. Cryst. 25 414-23. 

We have used x-ray diffraction in our laboratory to probe transient structures of laser-excited liquids, small-molecule crystals and protein crystals. The diffraction patterns are recorded on a CCD detector that makes efficient use of most of the diffracted x-rays. Several experimental protocols have been developed Laue diffraction from proteins [6-8], small-molecule diffraction [9,10] and diffraction from liquids [2,11,12]. In proteins, the... 

You can see from Fig. 9.8 that a Laue diffraction pattern is much more complex than a diffraction pattern from monochromatic X rays. But modern software can index Laue patterns and thus allow accurate measurement of many diffraction intensities from a single brief pulse of X rays through a still crystal. If the crystal has high symmetry and is oriented properly, a full data set can in theory be collected in a single brief X-ray exposure. In practice, this approach usually does not provide sufficiently accurate intensities because the data lack the redundancy necessary for high accuracy. Multiple exposures at multiple orientations are the rule. 

Fig. 3. Dififraction patterns from a clean (100) face of a nickel crystal. 144 volts, or 1.02 A. The bright spots of this pattern are (711) Laue diffraction beams at their maximum intensity.

Fig. 5. Diffraction pattern, at 200 volts or 0.865 A., from oxygon atoms adsorbed upon the nickel surface in the arrangement of Fig. 7—called the 4-Structure. The two very bright spots are (820) Laue diffraction beams from the nickel lattice at their maximum intensity.

Fig. 6. Diffraction pattern, at 72 volts or 1.44 A., from the nickel surface covered by atoms of oxygen arranged in the 4-Structure (Fig. 7), the same surface which gave the pattern of Fig. 5. The single spot at the top is a (511) Laue diffraction beam from the nickel lattice.

Continuous, white Single crystal No Spots Laue diffraction pattern... 

MWPCs have been successfully used at LURE and Stanford for multiple wavelength anomalous dispersion phasing measurements (see chapter 9). An MWPC has also been used to record Laue diffraction patterns at VEPP-3 (Gaponov et al 1989a,b,c). 

Figure 5.27 Protein crystal (concanavalin-A) Laue diffraction pattern recorded on a CCD detector with direct detection. From Allinson et al (1989) with permission.

The original synchrotron Laue diffraction patterns from protein crystals recorded at Daresbury using a broad bandpass were conducted on this instrument with the monochromator removed (see Helliwell (1984)). Some preliminary multiwavelength experiments with a silicon double crystal monochromator (Si (111) triangle removed) were conducted. The growth of the Laue and MAD experiments has led to two further stations at Daresbury (SRS-3 and SRS-4). 

The station has been used to record Laue diffraction patterns of protein crystals on photographic film (Popov, pers. comm.). 

This uses a multipole wiggler and will have operational modes for focussed Laue diffraction work and monochromatic experiments. The small source sizes should allow an equivalently small focal spot from a grazing incidence mirror system. Exposure times in the microsecond range for a macromolecular crystal should be feasible. Depending on the current achieved in single bunch mode it may be possible, at least for smaller unit cell sizes, to record a Laue pattern from one of the single bunches with an intrinsic time resolution therefore of the bunch width. (Feasibility experiments of this kind have been conducted at CHESS but on an undulator (Szebenyi et al 1989).)... 

Figure 7.1 (a) Pea lectin synchrotron Laue diffraction pattern recorded on photographic film on station 9.6 of the SRS and then in (b) the corresponding predicted Laue pattern is shown followed by those parts of the pattern which are (c) energy overlap spots, (d) spatial overlap spots, (e) spots which are both energy and spatial overlaps and, finally, those that are (f) neither energy nor spatial overlaps. From Helliwell (1985) with the permission of Elsevier. See Table 7.1, note 5 for experimental conditions (crystal to film 95 mm)... 

Figure 7.3 The coordinate geometry of Laue diffraction. The RLP at (x,y,z) lies on the Ewald sphere of radius 1IX and causes a spot on the Laue diffraction pattern. From Helliwell et al (1989b) with the permission of IUCr.

It is reasonable to assume that K, g(6) and j(x) are known, to a very good approximation. Thus, the quantifying of Laue diffraction patterns... 

The main principle behind detection schemes for Laue diffraction patterns is the use of a hybrid arrangement to provide the necessary range of options, namely a large aperture plus on-line facility, for film and CCD, respectively. 

Figure 10.7 Diffraction from small crystal volumes. This example is an SR Laue diffraction pattern from a (20 tm)3 ciystal of gramicidin. From Hedman et al (1985) with permission.

The diffraction spots are expected where transmitted and diffracted electron beams Intersect with the detector. The basis for diffraction pattern geometry analysis, thus. Is the crystal reciprocal lattice and the Laue diffraction condition, or the equivalent Bragg s law, for diffraction ... 

OrientExpress V3.3 freeware was used to index the Laue diffraction patterns. We developed a special algorithm to measure the sample-detector distance (d) and to determine the coordinates of the projection of the sample position in the recording plane of the CCD detector. The algorithm implies the analysis of two Laue diffraction patterns detected at two different distances dpi at the same angular position of the sample. A Pearson VII two-variable function was used to approximate the profiles of the Bragg reflections. 

Fig. 1 a shows a section of a Laue diffraction pattern of a LSGMO ciystal detected at room-temperature with a ciystal-detector distance of < 58 mm after the 4 thermal cycle. The Laue pattern shows multiplets splitting into 4 reflections, each one generated by Bragg reflections from its corresponding orientation state. The symbols TOl, T02, T03 and T04 (Fig. la) indicate different ferroelastic orientation states and corresponding reflections. 

Figure 1. Sections of Laue diffraction patterns of LSGMO detected at 300 K (a) and 753 K (b) (d=58 mmQ=87°, =15°). Reflections are indexed according to the best solution determinedfor each of the four domain states.

Laue diffraction patterns show that heating the sample to the trigonal phase causes the multiplets to split into 4 reflections too. The symbols TRl, TR2, TR3 and TR4 (Fig. lb) indicate the corresponding orientation state respectively. All Laue diffraction patterns were separately indexed using the reflections of each of 4 domain states. Positions of reflections (up to 30 in total) were used to refine the orientation matrix and sample-detector distance for the trigonal and orthorhombic phase. 

Our identification of the twin walls was based on the setting of one selected domain, referred to as "reference" domain. Using the transformation matrices given in Table 1 we determine the orientation matrices of all allowed domain states according to equation (1). We take for example the domain TRl as a "reference", i.e. Di, and perform the calculations with respect to its orientation matrix. With the orientation matrices determined in this way we calculate the positions of the Bragg reflections of all domain states in the Laue diffraction pattern. 

Fig. 2a shows a section of the Laue diffraction pattern obtained at a sample-detector distance of 358 mm. Additionally to the Bragg reflections from four TR domains, the calculated positions of reflections from allowed domain states in this phase are plotted as round spots. As seen in Fig. 2 the reflection positions caused by twinning due to the planes (Oil) and (121) coincide with the position of the 2 / 7 reflection of the domains TR2 and TR3. 

Figure 2. Enlarged section of the Laue diffraction pattern observed at 358 mm and 753 K (tp=S, Additionally to experimental Bragg reflections of four TR domains,...

A "chevron-like" twin structure is also observed in the orthorhombic phase. Figure 4 shows a section of the Laue diffraction pattern observed at room temperature. Besides Bragg reflections of four TO domains, the reflection positions calculated with respect to the orientation state T03 from all allowed domain states in the orthorhombic phase are shown. As seen in Fig. 4 reflection positions due to twiiming by (101) and (121) planes regarding T03 coincide with positions of the 1,2,1 and 2,0,0 reflections from domain states TOl and T02 correspondingly. 

Figure 4. Section of a Laue diffraction pattern measured at RT and crystal-detector distance of358 mm (

Figure 6. Sections of Laue diffraction patterns of a LSGMO crystal observed at 300 K before (a) and after (b) the F and before (c) and (d) after the 3 heating cycle (d=358 mm, (p=8(f.

Fig. 6 shows Laue diffraction patterns detected for a multiplet before and after heating the crystal above the trigonal transition point for the first and third time. After the first heating cycle (see Fig. 6b) the crystal maintains the initial orientation states (Fig. 6a), however the intensities of the reflections corresponding to the four orientation states indicate a change of individual state volumes because the ratio of the intensities changed considerably after the first thermal treatment. Fig. 6 also shows Laue diffraction patterns determined after the 3 thermal cycle, which are practically identical to the Laue diffraction pattern observed after the initial heating cycle. Reflection... 

Reversibility of orientation and configuration of twin walls was also observed in the high temperature rhombohedral phase as indicated by identical Laue diffraction patterns, detected above the ferroelastic phase transition point. Fig. 7 shows that the position, shape and intensity of reflections of four domains remain unchanged after the first heating and further thermal treatment. 

Figure 7. Laue diffraction patterns of LSGMO observed in the trigonal phase at the f (a)...

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