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X-ray birefringence imaging

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Science  30 May 2014:
Vol. 344, Issue 6187, pp. 1013-1016
DOI: 10.1126/science.1253537

A close-up view of carbon-bromide bonds

Polarizing filters are widely used in optical microscopy to highlight a range of material properties that cause optical path boundaries or birefringence in a material. Palmer et al. (see the Perspective by Lidin) developed an analog method for x-ray microscopy using linearly polarized x-ray beams and an area detector inside a synchrotron. The technique revealed the orientation of the C-Br bonds within crystalline materials.

Science, this issue p. 1013; see also p. 969

Abstract

The polarizing optical microscope has been used since the 19th century to study the structural anisotropy of materials, based on the phenomenon of optical birefringence. In contrast, the phenomenon of x-ray birefringence has been demonstrated only recently and has been shown to be a sensitive probe of the orientational properties of individual molecules and/or bonds in anisotropic solids. Here, we report a technique—x-ray birefringence imaging (XBI)—that enables spatially resolved mapping of x-ray birefringence of materials, representing the x-ray analog of the polarizing optical microscope. Our results demonstrate the utility and potential of XBI as a sensitive technique for imaging the local orientational properties of anisotropic materials, including characterization of changes in molecular orientational ordering associated with solid-state phase transitions and identification of the size, spatial distribution, and temperature dependence of domain structures.

Since its invention in the 19th century, the polarizing optical microscope has found ubiquitous applications in mineralogy (1), crystallography (2, 3), materials science (4, 5), and biology (6, 7) to investigate the structural properties of birefringent materials. From liquid crystals (8) to collagen fibers in tendons (9) and cartilage (10), and from amyloid plaques (11) to butterfly wings (12) and spider silk (13), the polarizing optical microscope has been used to establish the relationship between the structural anisotropy of materials and their function. In the phenomenon of birefringence, the refractive index of an anisotropic material depends on the orientation of the material with respect to the direction of linearly polarized incident radiation. When such a material is viewed in a polarizing optical microscope in crossed-polarizer configuration, the intensity of light transmitted through the polarization analyzer depends on the orientation of the optic axis or axes of the material relative to the direction of polarization of the incident light. By measuring the intensity of transmitted light as a function of the orientation of the material, information on the orientation of the optic axis or axes can be established. Furthermore, if the material comprises orientationally distinct domains, the spatial distribution and orientational relationships between the domains may be revealed.

Although x-ray and optical birefringence share several common characteristics, optical birefringence relates to the anisotropy of the material as a whole (for example, for a crystalline material it depends on the overall symmetry of the crystal structure), whereas x-ray birefringence (XB), when studied at an x-ray energy close to the absorption edge of a specific type of atom in the material, depends on the local anisotropy in the vicinity of the selected type of atom. Thus, XB depends on the orientational properties of the bonding environment of the x-ray–absorbing atom. As a consequence, the “optic axis” in the case of XB is not necessarily related to a crystallographic “optic axis,” and measurement of XB has the potential to yield structural information on the local orientational properties of individual molecules and/or bonds (14).

Previous studies of XB (1518) used a narrowly focused x-ray beam and did not provide spatially resolved mapping of the material. We propose an experimental setup (Fig. 1A) that allows XB measurements to be carried out in a spatially resolved imaging mode, using a large-area linearly polarized x-ray beam [with dimensions 0.8 mm (vertical) by 4.0 mm (horizontal)] incident on the sample (19). The intensity of the wide x-ray beam emerging from the polarization analyzer is recorded by using an area detector, mapping the XB of the material in a spatially resolved manner, with resolution of the order of 10 μm (20). In the present work, the exposure time to record each XB image was 1 s.

Fig. 1 Experimental setup and structures of materials.

(A) Experimental setup for XBI. The incident x-ray beam propagates along the z axis and is linearly polarized along the x axis. The tunnel axis (c axis; long-needle axis of crystal morphology) of the crystal was maintained in the plane (x-y plane) perpendicular to the incident x-ray propagation direction (z axis). The crystal orientation was altered by variation of angles χ and ϕ, where χ refers to rotation of the c axis of the crystal around the laboratory z axis and ϕ refers to rotation of the crystal around its c axis. (B) Structure of 1-BA/thiourea viewed perpendicular to the thiourea host tunnel (horizontal); the C–Br bonds of all 1-BA guest molecules are parallel to the tunnel axis (c axis), which is also parallel to the long-needle axis of the crystal morphology. (C) Structural changes associated with the phase transition in BrCH/thiourea (with H atoms omitted for clarity). (Left) Rhombohedral high-temperature phase viewed along the thiourea host tunnels (the isotropically disordered BrCH guests are not shown). (Middle and Right) Monoclinic low-temperature phase (110 K) viewed along the host tunnels (middle) and perpendicular to the tunnel (right); the C–Br bonds of all BrCH guests form an angle ψ ≈ 52.5° with respect to the tunnel axis (vertical at right). (D) Definition of angles ψ and ω specifying the orientation of the C–Br bond relative to the unit cell axes of the thiourea host structure in the low-temperature phase (shown superimposed on a schematic of the crystal morphology).

To demonstrate the XB imaging (XBI) technique, we focused on materials containing brominated organic molecules, using incident linearly polarized x-rays from a synchrotron source [beamline B16 at the Diamond Light Source (21)], with energy corresponding to the Br K-edge. In this case (15, 16, 2224), XB depends on the orientation of C–Br bonds relative to the incident polarized x-ray beam. To demonstrate the sensitivity and utility of XBI for spatially resolved mapping, our first experiment focused on a model material in which all C–Br bonds are parallel to each other—specifically, the thiourea inclusion compound containing 1-bromoadamantane (1-BA) guest molecules (Fig. 1B) (25). The orientation of the crystal relative to the linearly polarized incident x-ray beam is specified by the crystal orientation angles χ and ϕ defined in Fig. 1A.

XB images for a single crystal of 1-BA/thiourea as a function of χ (with ϕ fixed) are provided in Fig. 2 and movie S1. Each image shows a spatially resolved map of the transmitted x-ray intensity (brightness scales proportionally with intensity) for a specific orientation of the crystal. In Fig. 2, the intensity varies markedly as a function of χ, with maximum brightness at χ ≈ 45° and minimum brightness at χ ≈ 90° (26). Maximum intensity arises when the orientation of the C–Br bonds is at ~45° with respect to the direction of linear polarization of the incident x-ray beam. For each crystal orientation, the transmitted intensity is uniform across the entire crystal, indicating that the crystal comprises a single orientational domain. The observed dependence of intensity on χ is directly analogous to the behavior of a uniaxial crystal in the polarizing optical microscope. XB images recorded for 1-BA/thiourea as a function of ϕ (with χ fixed at 40°, close to the maximum transmitted intensity in Fig. 2) are provided in fig. S1 and movie S2. Because the orientational properties of the C–Br bonds are not altered by rotation around the bond axis, no appreciable change in transmitted intensity is observed as a function of ϕ.

Fig. 2 XB images for a model material with uni-directional alignment of C–Br bonds.

XBI data recorded at 280 K for a single crystal of 1-BA/thiourea as a function of χ (with ϕ fixed). The images represent spatially resolved maps of transmitted x-ray intensity across the crystal. Relative brightness in the images scales with x-ray intensity. The variation of normalized transmitted intensity (ItN) as a function of χ is shown in the plot at left, using data from all images recorded in the experiment (with χ varied in steps of 2°). To construct this plot, transmitted intensity It was measured by integrating the intensity across a region of the image with dimensions 62.5 μm by 192 μm at the center of the crystal and was scaled to give a normalized value in the range 0 ≤ ItN ≤ 1.

To assess the potential to exploit XBI to probe changes in molecular orientational distributions as a function of temperature, XBI experiments were carried out on a single crystal of the thiourea inclusion compound containing bromocyclohexane (BrCH) guest molecules (Fig. 1, C and D). This material is known (27) to undergo a phase transition at 233 K from a high-temperature phase in which the orientational distribution of the BrCH guest molecules is essentially isotropic (as a result of rapid molecular motion) to a low-temperature phase in which the BrCH molecules become orientationally ordered (specifically, with the C–Br bonds of all BrCH molecules oriented at ψ ≈ 52.5° and ω ≈ 3.5° with respect to the thiourea host structure, as defined in Fig. 1D).

XB images recorded for BrCH/thiourea at 298 K (Fig. 3A and movies S3 and S4) demonstrate that for the high-temperature phase, there is no variation in transmitted x-ray intensity as a function of crystal orientation, which is fully consistent with the isotropic orientational distribution of the C–Br bonds of the BrCH guest molecules in this phase. In contrast, under the same conditions in the polarizing optical microscope in crossed-polarizer configuration (Fig. 3B) a single crystal of BrCH/thiourea exhibits the classical behavior of a uniaxial crystal, with minimum transmitted intensity when the optic axis is parallel to the polarizer or analyzer and with maximum transmitted intensity when the optic axis is at 45° to these directions (for BrCH/thiourea, the optic axis is the c axis of the rhombohedral thiourea host structure, parallel to the long-needle axis of the crystal morphology in Fig. 3B). These results demonstrate the difference between optical and x-ray birefringence: The former depends on the overall crystal symmetry, whereas the latter depends on the local orientational properties in the vicinity of the x-ray–absorbing atom within the material (in the present case, the orientational distribution of the C–Br bonds).

Fig. 3 Comparison of XBI and polarizing optical microscopy.

(A) XB images and (B) polarizing optical microscope images recorded as a function of χ for single crystals of BrCH/thiourea in the high-temperature phase [(A) 298 K and (B) 293 K].

In the low-temperature phase of BrCH/thiourea, the XB behavior changes dramatically. At 20 K, for the crystal orientation (28) {χ = 10°, ϕ = 0°} (Fig. 4, top left, and fig. S2) it is evident that the crystal comprises orientationally distinct domains. Thus, a large parallelogram-shaped domain (with dimensions of a few hundred micrometers) dominates the central region of the crystal (bright region in the image), with two smaller domains (dark regions) at each end of the crystal. The domain boundaries between the major domain and the two minor domains are parallel to each other and intersect the c axis at an angle of ~136°, allowing the domain boundary to be assigned as the crystallographic (Embedded Image) plane. For crystal orientation {χ = 10°, ϕ = 180°}, the XB image (Fig. 4, top right, and movie S5) is essentially an “inverted” form of the image for {χ = 10°, ϕ = 0°}, as expected given that these crystal orientations correspond to the incident x-ray beam passing in opposite directions through the crystal.

Fig. 4 XB images for the orientationally ordered phase of BrCH/thiourea.

XBI data recorded at 20 K for a single crystal of BrCH/thiourea as a function of χ (with ϕ fixed at 0°). Maximum brightness (for the large central domain) arises when the C–Br bonds form an angle of ~45° with respect to the linearly polarized incident beam (achieved at χ ≈ 82°) and minimum brightness arises when the C–Br bonds form an angle of ~90° with respect to the linearly polarized incident beam (achieved at χ ≈ 38°).

XB images recorded as a function of χ (with ϕ fixed at 0°) for BrCH/thiourea in the low-temperature phase (at 20 K) are provided in Fig. 4, left, and movie S6. For ϕ = 0°, the C–Br bonds in the major domain are very nearly perpendicular to the direction of propagation of the incident x-ray beam (29). The transmitted intensity for the major domain varies markedly with χ, with maxima and minima in intensity separated by Δχ ≈ 45°. As shown in Fig. 4 and given that the C–Br bonds are known (27) to form an angle ψ ≈ 52.5° with respect to the tunnel (c axis) of the thiourea host structure in the low-temperature phase, the observed intensity maximum (at χ ≈ 82°) corresponds to the C–Br bonds forming an angle of ~45° with respect to the direction of polarization of the incident x-ray beam (horizontal). Correspondingly, minimum transmitted intensity (observed at χ ≈ 38° in Fig. 4) occurs when the C–Br bonds form an angle of ~90° with respect to the direction of polarization of the incident x-ray beam. Thus, the χ-dependence of the XB images shown (for ϕ = 0°) in Fig. 4 is analogous to the behavior of a uniaxial crystal in the polarizing optical microscope, with the direction of the C–Br bonds representing the “optic axis” in the case of the XBI data. XB images (fig. S3 and movie S7) recorded as a function of temperature indicate that there is no change in the size and spatial distribution of the domains with variation of temperature in the low-temperature phase (30).

As demonstrated above, XBI enables spatially resolved mapping of the orientational properties of specific types of molecule and/or bond in materials, offering particular opportunities in cases for which the application of x-ray diffraction techniques may not be feasible (such as partially ordered materials, multiply twinned crystals, or other materials with complex domain structures). Although demonstrated here for the study of single-crystal samples, there is no requirement for crystallinity because XB is sensitive specifically to local molecular orientations; thus, XBI may be applied to any material (including liquids or amorphous solids) with an anisotropic distribution of molecular orientations. The results reported for BrCH/thiourea in the low-temperature phase highlight the potential to exploit XBI for spatially resolved analysis of orientationally distinct domains. Knowledge of domain structures (in particular, aspects such as domain sizes, the orientational relationships between domains, and the nature of domain boundaries) can be critical for controlling the performance of electronic, optical, and magnetic devices (31, 32) and the mechanical properties of biomaterials (33).

Because XBI is a full-field imaging technique (34), with the entire image recorded simultaneously, the measurement of XB images is fast (exposure time of 1 s for each image shown here), leading to the potential to study dynamic processes (such as the propagation of domain boundaries during phase transitions). The time to record a single image in XBI could be reduced to ~1 ms for a storage ring undulator source (rather than the bending-magnet source used here) and by using a faster x-ray detector than that used in the present study, and could even be reduced to less than 100 fs by using a single pulse from an x-ray free-electron laser, creating a new opportunity for imaging ultra-fast molecular dynamics.

Supplementary Materials

www.sciencemag.org/content/344/6187/1013/suppl/DC1

Materials and Methods

Figs. S1 to S3

Movies S1 to S7

References and Notes

  1. For molecular solids, XB depends on the orientational properties of the molecule containing the x-ray–absorbing atom, and in particular depends on the bonding environment of this atom in the molecule. Here, we focus on XB studies at the Br K edge for materials containing brominated organic molecules. In this case, XB behavior can be rationalized simply on the basis of the orientational properties of the C–Br bonds (15, 16).
  2. Materials and methods are available as supplementary materials on Science Online.
  3. The spatial resolution of the XB images in the vertical direction (~13 μm) is limited by the resolution of the charge-coupled device–based detector, and the spatial resolution in the horizontal direction (~28 μm) is limited by the penetration of the beam into the polarization analyzer [Si(555) reflection]. The latter could be reduced to less than 1 μm by using high-quality crystals of heavier elements.
  4. For χ = 0°, the crystal c axis is horizontal (x-z plane), parallel to the linearly polarized incident x-ray beam.
  5. For BrCH/thiourea, the c axis is the tunnel axis of the thiourea host structure in both the high- and low-temperature phases. With respect to the hexagonal unit cell (ah, bh, ch) of the high-temperature phase, the crystal orientation {χ = 0°, ϕ = 0°} has the ch axis parallel to the laboratory x axis and a {100} plane perpendicular to the z axis. With respect to the monoclinic unit cell (am, bm, cm) of the low-temperature phase, in the crystal orientation {χ = 0°, ϕ = 0°} the cm axis is parallel to the laboratory x axis, the bm axis is parallel to the z axis, and the projection of the am axis on the plane perpendicular to the cm axis [denoted proj(am)] is perpendicular to the x-z plane.
  6. For ϕ = 0°, the bm axis of the crystal in the low-temperature phase is parallel to the laboratory z axis. Hence, because the angle ω (defined in Fig. 1D) is known (27) to be only ~3.5°, the C–Br bonds in the major domain are very nearly perpendicular to the direction of propagation of the incident x-ray beam.
  7. The changes of transmitted x-ray intensity as a function of temperature in this material have been rationalized previously (16) from XB studies using a focused x-ray beam.
  8. In contrast, other techniques (3539) for imaging materials that use incident x-ray radiation (such as scanning x-ray microscopy and x-ray topography) generally involve scanning a focused x-ray beam across the material (leading to the construction of a spatially resolved image through the analysis of the interaction of the beam with the material at each position of the beam). The time required to record a single image in XBI is clearly much faster than would be the case with a scanning probe. One consequence is that the overall radiation dose received by the sample should be lower in the case of XBI, suggesting that XBI may be advantageous in studying materials that are susceptible to radiation damage.
  9. Acknowledgments: We are grateful to Diamond Light Source for the award of beam-time for experiments on beamline B16. We thank the Engineering and Physical Sciences Research Council (studentships to B.A.P. and G.R.E.-G.) and Cardiff University for financial support.

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