ID31 is a versatile instrument and can be exploited for a wide range of powder diffraction measurements including:
 

• Structural studies: the solving and refining of crystal structures, exploration of the structure of glasses, and atomic pair distribution function (PDF) analysis;
• Dynamic and In-situ studies: observation of structures or materials evolving with temperature, time, voltage, etc. during phase changes, solid-state chemistry, electrochemistry, etc.;
• Anomalous scattering: distinguishing between neighbouring elements in a material. We can access the K or L edge (sometimes both) for all elements above Ti in the Periodic Table;
• High throughput studies: involving many samples, synthesised with different compositions, or under varied preparation conditions, etc. A sample-changing robot allows automated screening of up to 50 capillaries in succession;
• Quantitative analysis: owing to the high angular resolution, diffraction patterns from complex mixtures with many contributing phases can be analysed; moreover, with the excellent statistical quality and low background, the detection of phases present in very low proportions is possible;
• Microstructure: detailed analysis of peak shapes yields information about the microstructure of a material. Since the instrumental contribution is small, the observed peak shapes are dominated by sample effects;
• Residual strain: Measurements of residual strain, either by the traditional sin2theta technique, or by mapping peak positions from within the bulk and surface of a sample, defining a gauge volume with slits and the angular acceptance of the analyser crystal;
• Grazing incidence and reflectivity: measurements from thin films and surfaces.

Structural studies

The combination of narrow peaks, accurate peak positions and intensities is essential for crystallographic studies using powder diffraction, which are necessary when a single crystal of a material is unavailable. The effective 2theta resolution of a diffractometer equipped with an analyser crystal, (delta_theta/theta), is only weakly dependent on the wavelength (improving marginally at longer wavelengths) so that the wavelength chosen for an experiment is determined primarily by questions of absorption and unit cell size. Thus powder patterns for structural studies are usually measured on ID31 using X-rays in the range 0.3 – 1.5 Å, (40 – 8 keV) depending on the nature of the sample. Inorganic specimens containing metals or heavy elements, a large part of the work on ID31, are measured in the range 0.3 – 0.4 Å with capillary diameters adopted to keep µr < 1.5, when a simple correction for absorption is possible. Organics and materials containing light elements are frequently measured at 0.8 Å in a 1-mm-diameter capillary, and proteins, because of the very large unit cells, at 1.25 – 1.5 Å, to move the peaks to diffraction angles away from the beam stop and the low-angle background air scatter from the main beam.

There have been numerous crystallographic studies using ID31. An example of note is the recent study of the perovskite oxide SmVO₃ [1] as a function of temperature. The very high resolution (at short wavelength) allows subtle changes in the diffraction profile to be observed, figure 1, and the coexistence of two phases at low temperature to be ascertained (one orthorhombic, the other monoclinic, angle = 90.019(4)º), representing different electronic orbital ordering schemes, as supported by the refined V–O bond lengths. The phase coexistence is triggered by an antiferromagnetic ordering of the vanadium spins near 130 K, below an initial orbital ordering near 200 K. The phase coexistence is the result of the intermediate ionic size of samarium coupled to exchange striction at the vanadium spin ordering. [external users]

The crystal structure of the organic molecule 9-ethylbicyclo[3.3.1]nona-9-ol was solved using direct methods from ID31 data [2]. The diffraction pattern measured originally on BM16 could be indexed and the space group determined (Pbca), but with four independent molecules in the unit cell (48 non-hydrogen atoms) and a cell volume near 8000 ų, no solution for the structure could be found, despite excellent looking powder data extending below 1 Šin d spacing. On ID31 data measured at five temperatures were combined to define a set of intensities from which the structure could be solved by direct methods, exploiting the anisotropic thermal expansion of the unit cell. In this approach, the anisotropic lattice changes modify the degree of overlap between adjacent reflections. By fitting a single set of intensities to the multiple data sets, the number and the reliability of the individual peak intensities that can be extracted from the powder profiles are increased. For such an approach, high-resolution data are essential as the shifts in relative peak positions with temperature can be rather small and do not affect peak overlap significantly unless the peaks are inherently narrow. Anisotropic lattice changes have also been exploited in powder diffraction studies on proteins (see below), either by precipitating the protein at different pH values, and/or by exploiting radiation damage. [in-house]

Crystal structures can also be solved from powders by incorporating known structural-chemical information into the procedure. Thus molecular structures can be solved by using a global minimisation procedure (e.g. simulated annealing) to position molecules or fragments in the unit cell, varying position, orientation and torsion angles, as appropriate. Such methods are now quite standard for powder crystallographers, and laboratory data is often adequate, provided the angular resolution is good enough to determine the unit cell and space group accurately. Chemical information about zeolite-framework co-ordination was also used in the FOCUS method to solve the structure of the complex zeolite TNU-9, figure 2, [3] from ID31 data, in conjunction with electron diffraction for indexing and space group determination, (C2/m, a = 28.2219 Å, b = 20.0123 Å, c = 19.4926 Å, ß = 92.33º) and very high quality HRTEM images that yielded starting phases for 258 reflections. The structure has a total of 76 atoms (of which 24 are framework Si). [External users]

Another example is the solution of the enormous metal-organic-framework material MIL-100, with a cubic unit cell of length 72.906 Å and a unit cell volume of 387,516 ų [4], via a computational scheme for predicting how the structure could be built up by the chemical combination of smaller subunits. Comparison of the calculated intensities with those observed on ID31 showed which of the predicted structures was correct. The even bigger (a = 88.869 Å, V = 701860.3 ų) MIL-101 [5] was solved following a similar procedure. [external users/collaboration]

Recently it has become apparent that the high resolution powder diffraction data can be used to refine the structures of small proteins (like lysozyme) by the Rietveld method when combined with extensive stereochemical restraints [6]. The in-house team of I. Margiolaki and J. Wright (now at ID11) has pushed powder protein diffraction to new frontiers, using ID31 data. Recently (in collaboration with N. Pinotsis and Matthias Wilmanns at EMBL Hamburg) the previously unknown structure of the SH3 domain of ponsin (comprising 67 amino acids, space group P2₁2₁2₁, V = 64879 ų) was solved by molecular replacement from a model protein molecule with only a 40% correspondence between the amino-acid residues [7]. Intensities were extracted by fitting to four data sets exploiting anisotropic differences in unit cell parameters induced by precipitating two batches of sample, and by radiation damage. Reflections with a reasonable signal-to-noise ratio were extracted up to a d spacing resolution of about 2.4 Å. In the final stages of the reconstruction of the electron density, 36 water molecules could be found in the structure via Fourier and total OMIT maps. A subsequent single-crystal experiment (a crystal having finally been grown) confirmed the accuracy of the powder determination. [In-house/collaboration; more information in here]

For materials that are not good crystalline powders a method that is proving increasingly important is the calculation of the atomic pair distribution function (PDF). This technique can be applied to structures that lack the translational periodicity of a crystal, and thus used to investigate poorly-crystalline or disordered materials. The method has recently been comprehensively reviewed [8]. A key requirement is that data should be measured to high values of Q, (ie. 4 pi sin(theta)/lambda), ideally beyond 30 Å^-1, to give high real-space resolution. Thus the measurements need to be made with short-wavelength radiation. The atomic PDF is a measure of the number of atoms in a spherical shell of radius r about a reference atom. Peaks represent the characteristic distances between pairs of atoms in the structure. Two methods of measuring the X-ray data for a PDF analysis are favoured. The first uses a high-resolution instrument like ID31 with analyser crystals and a wavelength of around 0.3 – 0.4 Å, scanning to beyond 90º 2theta, and recording the weakly-scattering high-angle data repeatedly to improve the statistical quality. Data collection takes a number of hours, but the analyser crystals help in the suppression of the background due to Compton scattering, fluorescence, etc. An alternative approach uses a very short wavelength of ≈0.1 Å and an area detector to record the full diffraction pattern in a single shot. The angular resolution of the pattern is lower, and the background is less effectively suppressed, however hours of data collection are reduced to just minutes which is obviously an advantage if following a system evolving during the course of the experiment. A comparison of the two methods (image plate at APS and scanning at ID31) with a series of icosahedral alloys [9] suggested that they give similar results, but with the ID31 measurements yielding somewhat clearer information in the high-r region. [External users/collaboration]

A recent study [10] of ZrW₂O₈, investigated the amorphous phase that can be recovered after its high-pressure amorphization transition above 1.5 GPa. Reverse Monte Carlo modelling of neutron and ID31 data shows that the large increase in density on pressurising is accommodated within the structure by increased bonding between the WO₄ tetrahedra. This increases the tungsten coordination; postulated changes to the ZrO₆ octahedral environment are not required. This densified crystal based model, which contains significant local disorder within a distorted periodic structure, was also in keeping with data measured in situ at high pressure. [External users/collaboration]

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Dynamic / In-situ measurements 

One of the major general strengths of powder diffraction is the ability to carry out measurements under a wide range of environmental conditions. Dynamic measurements have included the exploration of phase diagrams with temperature, the kinetics of in-situ chemical reactions such as dehydration of samples on heating or hydrothermal synthesis, the kinetics of physical changes such as the growth of nanoparticles by high-temperature annealing, and following the changes in the crystalline components in electrochemical cells with charging and discharging, etc..

Microstructural studies

A potential lightweight hydrogen-storage system involves hydrogen cycling between lithium nitride Li₃N, lithium imide Li₂NH, and lithium amide LiNH₂ via two reversible steps, formally written as

(1) Li₃N + H₂ <=> Li₂NH + LiH

(2) Li₂NH + H₂ <=> LiNH₂ + LiH.

The reverse of step (2), the release of 6.5 weight percent of hydrogen from the amide to the imide, is viewed as a two-stage process

2 LiNH₂ -> Li₂NH + NH₃

LiH + NH₃ -> LiNH₂ + H₂.

Three samples that had undergone various cycles of hydrogen adsorption and desorption ex situ were examined on ID31 [11]. As well as a complex mixture of phases identified in sample SI, including the unexpected new phase Li_1.15NH_1.85 (composition from the refined Li stoichiometry), some remarkable peak shapes were apparent in samples SII and SIII, e.g. figure 3, implying complex microstructural behaviour. The broad Bragg peaks of the dominant cubic Li-N-H phase are highly structured and follow a strain-broadening dependence on diffraction angle, indicative of a pronounced variation in stoichiometry. Detailed modelling of the pattern using TOPAS allowed the range of non-stoichiometry to be evaluated. The variation in stoichiometry of the cubic phase was modelled by 11 uniformly varying phases Li_1+xnNH_2-xn, where x_n = x_low + 0.1n(x_high - x_low); n = 0 – 10. A linear variation in lattice constant was also assumed; a_n = a_high + 0.1n(a_low - a_high). The refined parameters were the lower and upper bounds of the lattice parameter (a_low and a_high) and the stoichiometry, (x_low and x_high), and the scale factor associated with each phase. Refined stoichiometries range from Li_1.08NH_1.92 to Li_1.65NH_1.35 with a weighted average of Li_1.52NH_1.48 for SII and from Li_1.18NH_1.82 to Li_1.70NH_1.30 with a weighted average of Li_1.58NH_1.42 for SIII.

Apart from illustrating what a truly powerful program TOPAS is in the right hands, and just how much information you can extract from high quality high resolution powder diffraction data, after further consideration of the results the experimenters were able to propose a mechanism for hydrogen storage and release.

This study was part of an extensive program to find new hydride materials [e.g. 12], exploiting the high-throughput capabilities of ID31. The users will come with as many as 200 samples to be measured over a couple of days on ID31. In-situ adsorption and desorption experiments are also performed. [External users]

Organisms can control the, morphology, orientation, and size of crystalline blocks in biogenic crystals (e.g. shells) by means of organic molecules involved in the biomineralization process, though how they do this is unclear. One hypothesis is that the organic macromolecules adhere to specific planes and impede crystal growth in the perpendicular direction. Calcite prisms separated from two seashells were investigated on ID31 [13] and annealed for 30 min. at temperatures ranging between 50°C and 600°C. Geological calcite was used as a control. Structural parameters were extracted with high precision (about 10 ppm) by Rietveld refinement. These reveal anisotropic lattice distortions in biogenic samples compared to the geological counterpart.

An intriguing result was the observation of a marked broadening of diffraction peaks of biogenic crystals annealed at temperatures above 200°C, figure 4, and a correlation of this broadening with a substantial relaxation of the anisotropic lattice distortions. Fitting a Voigt function provided estimates of the size of coherently scattered crystal blocks and averaged microstrain fluctuations. The broadening indicates a sharp drop in crystallite size and an increase in strain, which is interpreted as arising from the degradation of the structure-directing organic molecules. Changes in the microstructure correlate with the anisotropic lattice distortions, from which is was postulated that anisotropy of crystallite size and lattice distortions can be explained by assuming that during biomineralisation, organic macromolecules enter the calcite lattice oriented parallel to the (012) crystallographic plane. At the same time, the carboxylate groups of glutamic and aspartic residues replace those of calcium carbonate, producing maximum strain along the [001] direction. Understanding of the molecular mechanisms of such processes is a key issue towards fabrication of advanced materials via a biomimetic approach. [External users/collaboration]

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Residual strain   

Residual strain in engineered components can be investigated using the traditional sin²ψ technique, whereby the position of a diffraction peak is monitored in reflection geometry at different sample orientations (ψ). Alternatively, with the availability of X-rays up to 60 keV on ID31, a gauge volume in the sample can be defined by means of the incident and diffracted beams, figure 5. A map of residual strain is built up by translating the sample parallel and perpendicular to the beam and measuring the 2theta position of a peak for the different sample positions. High spatial resolution is available by working with narrow beams, though the gauge volume is lengthened by the low values of 2theta that arise from the use of hard X-rays.

Figure 5: Configuration for strain mapping using hard X-rays; the gauge volume has the cross section of a lozenge and is defined by the intersection of the incident and diffracted beams.

There are several advantages in using synchrotron X-rays and a high-resolution powder diffractometer equipped with an analyser crystal,

i) The intrinsically narrow peak widths give enhanced sensitivity to shifts in peak positions;

ii) The peak widths are independent of ψ, unlike traditional Bragg-Brentano geometry, where loss of parafocusing leads to peak broadening;

iii) The wavelength tunability gives versatility. Soft X-rays can be selected for surface sensitivity. The depth of penetration can be varied by changing wavelength, even exploiting absorption edges if appropriate. Hard X-rays (lambda ≤ 0.3 Å) allow transmission measurements and strain mapping.

iv) The use of an analyser crystal leads to accurate measurements free from the effects of surface shape or roughness, and confers immunity to aberrations that lead to undesired shifts in peak positions with conventional instruments, e.g. resulting from movement of the sample from the diffractometer axis, or surface effects when the gauge volume is only partially immersed in the sample. Thus components with complex shapes are readily investigated.

One of the most systematic studies conducted on ID31 in the field of residual stress characterisation was performed by E.M van der Aa [14, 16]. The study concerned the residual stresses generated by welding of thin steel plates and the resulting distortion, and methods to reduce them both, via the use of a trailing heat sink a short distance behind the welding heat source, a process called Dynamically Controlled Low Stress No Distortion (DC-LSND) welding. The aim was to assess the efficiency of this process on the residual stress state compared to conventional welding, and subsequently to characterise the influence of the process parameters of DC-LSND on the residual stresses. Since the welded samples were distorted in a complex manner, the analyser crystal optics of ID31 were critical to ensure the elimination of geometrically induced pseudo strains. Another aspect that lends ID31 well to such a study is the stability of the incident beam, ensured through temperature control and mechanical feedback on the monochromator crystals. Without such systems, possible drifts would need to be corrected for or lead to spurious strains if unaccounted for. The results revealed that the reduction in the distortion of welding plates produced with DC-LSND is driven by the decrease of both the longitudinal and transverse residual stress states compared to the conventional welding technique (without cooling).

Figure 6: Influence of active cooling (LSND) on residual stresses compared to conventional non-cooled (CONV) [14, 16].

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References:

[2] Solving larger molecular crystal structures from powder diffraction data by exploiting anisotropic thermal expansion. Brunelli M. Wright J.P. Vaughan G.B.M. Mora A.J. Fitch A.N. Angewandte Chemie International Edition 42, 2029–2032 (2003)
[3] Complex zeolite structure solved by combining powder diffraction and electron microscopy.Gramm F. Baerlocher C. McCusker L.B. Warrender S.J. Wright P.A. Han B. Hong S.B. Liu Z. Ohsuna T. Terasaki O. Nature 444, 79–81 (2006)
[4] A hybrid solid with giant pores prepared by a combination of targeted chemistry, simulation, and powder diffraction. Férey G. Serre C. Mellot-Draznieks C. Millange F. Surblé S. Dutour J. Margiolaki I. Angewandte Chemie International Edition 43, 6296–6301 (2004)
[5] A chromium terephthalate-based solid with unusually large pore volumes and surface area. Férey G. Mellot-Draznieks C. Serre C. Millange F. Dutour J. Surblé S. Margiolaki I. Science 309, 2040–2042 (2005)
[6] Combined Rietveld and stereochemical restraint refinement of a protein crystal structure. Von Dreele R.B. Journal of Applied Crystallography. 32, 1084–1089 (1999)
[7] Second SH3 domain of Ponsin solved from powder diffraction. Margiolaki I. Wright J.P. Wilmanns M. Fitch A.N. Pinotsis N. Journal of the American Chemical Society 129, 11865-11871 (2007)
[8] Beyond crystallography: the study of disorder, nanocrystallinity and crystallographically challenged materials with pair distribution functions. Kanatzidis M. Billinge S.J. Chemical Communications 749–760 (2004)
[9] PDF from X-ray powder diffraction for nanometer-scale atomic structure analysis of quasicrystalline alloys. Brühne S. Uhrig E. Luther K.D. Assmus W. Brunelli M. Masadeh A.S. Billinge S.J.L. Zeitschrift für Kristallographie 220, 962–967 (2005)
[10] Structural description of pressure-induced amorphization in ZrW₂O₈. Keen D.A. Goodwin A.L. Tucker M.G. Dove M.T. Evans J.S.O. Crichton W.A. Brunelli M. Physical Review Letters 98, 225501-1–225501-4 (2007)
[11]  A mechanism for non-stoichiometry in the lithium amide/lithium imide hydrogen storage reaction. David W.I.F. Jones M.O. Gregory D.H. Jewell C.M. Johnson S.R. Walton A. Edwards P.P. Journal of the American Chemical Society 129, 1594–1601 (2007)
[12] Synthesis and crystal structure of Li₄BH₄(NH₂)₃. Chater P.A. David W.I.F. Johnson S.R. Edwards P.P. Anderson P.A. Chemical Communications 2439-2441 (2006)
[13] The microstructure of biogenic calcite: A view by high-resolution synchrotron powder diffraction. Pokroy B. Fitch A.N. Zolotoyabko E. Advanced Materials 18, 2363–2368 (2006)
[14] Influence of a trailing heat sink on the welding residual stress distribution. van der Aa E.M. et al. ESRF experimental report MA46, (2006)
[15] Local cooling during welding: prediction and control of residual stresses and buckling distortion. van der Aa E.M. PhD Thesis, Department of Materials Science and Technology, Delft University of Technology (2007)

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