Sub-pixel high-resolution imaging of high-energy x-rays inspired by sub-wavelength optical imaging.

We have developed and demonstrated an image super-resolution method-XR-UNLOC: X-Ray UNsupervised particle LOCalization-for hard x-rays measured with fast-frame-rate detectors that is an adaptation of the principle of photo-activated localization microscopy (PALM) and stochastic optical reconstruction microscopy (STORM), which enabled biological fluorescence imaging at sub-optical-wavelength scales. We demonstrate the approach on experimental coherent Bragg diffraction data measured with 52 keV x-rays from a nanocrystalline sample. From this sample, we resolve the fine fringe detail of a high-energy x-ray Bragg coherent diffraction pattern to an upsampling factor of 16 of the native pixel pitch of 30 µm of a charge-integrating fastCCD detector. This was accomplished by analysis of individual photon locations in a series of "nearly-dark" instances of the diffraction pattern that each contain only a handful of photons. Central to our approach was the adaptation of the UNLOC photon fitting routine for PALM/STORM to the hard x-ray regime to handle much smaller point spread functions, which required a different statistical test for photon detection and for sub-pixel localization. A comparison to a photon-localization strategy used in the x-ray community ("droplet analysis") showed that XR-UNLOC provides significant improvement in super-resolution. We also developed a metric by which to estimate the limit of reliable upsampling with XR-UNLOC under a given set of experimental conditions in terms of the signal-to-noise ratio of a photon detection event and the size of the point spread function for guiding future x-ray experiments in many disciplines where detector pixelation limits must be overcome.

Bioapatite in shark centra studied by wide-angle and by small-angle X-ray scattering.

Members of subclass Elasmobranchii possess cartilage skeletons; the centra of many species are mineralized with a bioapatite, but virtually nothing is known about the mineral's organization. This study employed high-energy, small-angle X-ray scattering (SAXS) and wide-angle X-ray scattering (WAXS, i.e. X-ray diffraction) to investigate the bioapatite crystallography within blocks cut from centra of four species (two carcharhiniform families, one lamniform family and 1-ID of the Advanced Photon Source). All species' crystallographic quantities closely matched and indicated a bioapatite closely related to that in bone. The centra's lattice parameters a and c were somewhat smaller and somewhat larger, respectively, than in bone. Nanocrystallite sizes (WAXS peak widths) in shark centra were larger than typical of bone, and little microstrain was observed. Compared with bone, shark centra exhibited SAXS D-period peaks with larger D magnitudes, and D-period arcs with narrower azimuthal widths. The shark mineral phase, therefore, is closely related to that in bone but does possess real differences which probably affect mechanical property and which are worth further study.

Elastic heterogeneity in metallic glasses.

When a stress is applied on a metallic glass it deforms following Hook's law. Therefore it may appear obvious that a metallic glass deforms elastically. Using x-ray diffraction and anisotropic pair-density function analysis we show that only about 3/4 in volume fraction of metallic glasses deforms elastically, whereas the rest of the volume is anelastic and in the experimental time scale deform without resistance. We suggest that this anelastic portion represents residual liquidity in the glassy state. Many theories, such as the free-volume theory, assume the density of defects in the glassy state to be of the order of 1%, but this result shows that it is as much as a quarter.

Achieving large uniform tensile ductility in nanocrystalline metals.

Synchrotron x-ray diffraction and high-resolution electron microscopy revealed the origin of different strain hardening behaviors (and dissimilar tensile ductility) in nanocrystalline Ni and nanocrystalline Co. Planar defect accumulations and texture evolution were observed in Co but not in Ni, suggesting that interfacial defects are an effective passage to promote strain hardening in truly nanograins. Twinning becomes less significant in Co when grain sizes reduce to below ~15 nm. This study offers insights into achieving excellent mechanical properties in nanocrystalline materials.

Combined computed tomography and position-resolved X-ray diffraction of an intact Roman-era Egyptian portrait mummy.

Hawara Portrait Mummy 4, a Roman-era Egyptian portrait mummy, was studied with computed tomography (CT) and with CT-guided synchrotron X-ray diffraction mapping. These are the first X-ray diffraction results obtained non-invasively from objects within a mummy. The CT data showed human remains of a 5-year-old child, consistent with the female (but not the age) depicted on the portrait. Physical trauma was not evident in the skeleton. Diffraction at two different mummy-to-detector separations allowed volumetric mapping of features including wires and inclusions within the wrappings and the skull and femora. The largest uncertainty in origin determination was approximately 1.5 mm along the X-ray beam direction, and diffraction- and CT-determined positions matched. Diffraction showed that the wires were a modern dual-phase steel and showed that the 7 × 5 × 3 mm inclusion ventral of the abdomen was calcite. Tracing the 00.2 and 00.4 carbonated apatite (bone's crystalline phase) reflections back to their origins produced cross-sectional maps of the skull and of femora; these maps agreed with transverse CT slices within approximately 1 mm. Coupling CT and position-resolved X-ray diffraction, therefore, offers considerable promise for non-invasive studies of mummies.

High energy X-ray scattering tomography applied to bone.

High energy synchrotron X-ray scattering was developed for reconstruction of specimen cross-sections. The technique was applied to a model specimen of cortical bone containing a capillary tube of silicon, and reconstructions were produced with either full diffraction rings or texture-related subsets of a given ring. The carbonated apatite (cAp) 00.2 and 22.2 reconstructions and the Si 311 reconstructions agreed with absorption-based reconstructions from the measured X-ray transmissivity recorded during diffraction pattern acquisition and from reconstructions produced subsequently of the same specimen using a commercial microCT (microComputed Tomography) scanner.

Sparse recovery of undersampled intensity patterns for coherent diffraction imaging at high X-ray energies.

Coherent X-ray photons with energies higher than 50 keV offer new possibilities for imaging nanoscale lattice distortions in bulk crystalline materials using Bragg peak phase retrieval methods. However, the compression of reciprocal space at high energies typically results in poorly resolved fringes on an area detector, rendering the diffraction data unsuitable for the three-dimensional reconstruction of compact crystals. To address this problem, we propose a method by which to recover fine fringe detail in the scattered intensity. This recovery is achieved in two steps: multiple undersampled measurements are made by in-plane sub-pixel motion of the area detector, then this data set is passed to a sparsity-based numerical solver that recovers fringe detail suitable for standard Bragg coherent diffraction imaging (BCDI) reconstruction methods of compact single crystals. The key insight of this paper is that sparsity in a BCDI data set can be enforced by recognising that the signal in the detector, though poorly resolved, is band-limited. This requires fewer in-plane detector translations for complete signal recovery, while adhering to information theory limits. We use simulated BCDI data sets to demonstrate the approach, outline our sparse recovery strategy, and comment on future opportunities.

Time-resolved x-ray diffraction techniques for bulk polycrystalline materials under dynamic loading.

We have developed two techniques for time-resolved x-ray diffraction from bulk polycrystalline materials during dynamic loading. In the first technique, we synchronize a fast detector with loading of samples at strain rates of ~10(3)-10(4) s(-1) in a compression Kolsky bar (split Hopkinson pressure bar) apparatus to obtain in situ diffraction patterns with exposures as short as 70 ns. This approach employs moderate x-ray energies (10-20 keV) and is well suited to weakly absorbing materials such as magnesium alloys. The second technique is useful for more strongly absorbing materials, and uses high-energy x-rays (86 keV) and a fast shutter synchronized with the Kolsky bar to produce short (~40 µs) pulses timed with the arrival of the strain pulse at the specimen, recording the diffraction pattern on a large-format amorphous silicon detector. For both techniques we present sample data demonstrating the ability of these techniques to characterize elastic strains and polycrystalline texture as a function of time during high-rate deformation.

Variability in the nanoscale deformation of hydroxyapatite during compressive loading in bovine bone.

High-energy synchrotron X-ray diffraction is used to study in situ elastic strains in hydroxyapatite (HAP) for bovine femur cortical bone subjected to uniaxial compressive loading. Load-unload tests at room temperature (27°C) and body temperature (37°C) show that the load transfer to the stiff nanosized HAP platelets from the surrounding compliant protein matrix does not vary significantly (p<0.05) with temperature. This emphasizes that the stiffness of bone is controlled by the stiffness of the HAP phase, which remains unaffected by this change in temperature. Both the extent of hysteresis and the residual value of internal strains developed in HAP during load-unload cycling from 0 to -100 MPa increase significantly (p<0.05) with the number of loading cycles, indicative of strain energy dissipation and accumulation of permanent deformation. Monotonic loading tests, conducted at body temperature to determine the spatial variation of properties within the femur, illustrate that the HAP phase carries lower strain (and thus stresses) at the anterio-medial aspect of the femur than at the anterio-lateral aspect. This is correlated to higher HAP volume fractions in the former location (p<0.05). The Young's modulus of the bone is also found to correlate with the HAP volume fraction and porosity (p<0.05). Finally, samples with a primarily plexiform microstructure are found to be stiffer than those with a primarily Haversian microstructure (p<0.05).

Variability in the elastic properties of bovine dentin at multiple length scales.

Various methods are used to investigate the variability in elastic properties across a population of deciduous bovine incisor root dentin samples spanning different animals, incisor types, and locations within teeth. First, measurements of elastic strains by high-energy synchrotron X-ray scattering during compressive loading of dentin specimens provided the effective modulus--the ratio of applied stress to elastic phase strain--for the two main phases of dentin (hydroxyapatite crystals and mineralized collagen fibrils), shedding light on load transfer operating at the nanoscale between collagen and mineral phases. Second, Young's moduli were measured at the macroscale by ultrasonic time-of-flight measurements. Third, thermogravimetry quantified the volume fractions of hydroxyapatite, protein and water at the macroscale. Finally, micro-Computed Tomography determined spatial variations of the mineral at the sub-millimeter scale. Statistical comparison of the above properties reveals: (i) no significant differences for dentin samples taken from different animals or different incisor types but (ii) significant differences for samples taken from the cervical or apical root sections as well as from different locations between buccal and lingual edges.

Evolution of load transfer between hydroxyapatite and collagen during creep deformation of bone.

While the matrix/reinforcement load-transfer occurring at the micro- and nanoscale in nonbiological composites subjected to creep deformation is well understood, this topic has been little studied in biological composites such as bone. Here, for the first time in bone, the mechanisms of time-dependent load transfer occurring at the nanoscale between the collagen phase and the hydroxyapatite (HAP) platelets are studied. Bovine cortical bone samples are subjected to synchrotron X-ray diffraction to measure in situ the evolution of elastic strains in the crystalline HAP phase and the evolution of viscoelastic strains accumulating in the mineralized collagen fibrils under creep conditions at body temperature. For a constant compressive stress, both types of strains increase linearly with time. This suggests that bone, as it deforms macroscopically, is behaving as a traditional composite, shedding load from the more compliant, viscoelastic collagen matrix to the reinforcing elastic HAP platelets. This behavior is modeled by finite-element simulation carried out at the fibrillar level.

Internal strain gradients quantified in bone under load using high-energy X-ray scattering.

High-energy synchrotron X-ray scattering (>60 keV) allows noninvasive quantification of internal strains within bone. In this proof-of-principle study, wide angle X-ray scattering maps internal strain vs position in cortical bone (murine tibia, bovine femur) under compression, specifically using the response of the mineral phase of carbonated hydroxyapatite. The technique relies on the response of the carbonated hydroxyapatite unit cells and their Debye cones (from nanocrystals correctly oriented for diffraction) to applied stress. Unstressed, the Debye cones produce circular rings on the two-dimensional X-ray detector while applied stress deforms the rings to ellipses centered on the transmitted beam. Ring ellipticity is then converted to strain via standard methods. Strain is measured repeatedly, at each specimen location for each applied stress. Experimental strains from wide angle X-ray scattering and an attached strain gage show bending of the rat tibia and agree qualitatively with results of a simplified finite element model. At their greatest, the apatite-derived strains approach 2500 µÎµ on one side of the tibia and are near zero on the other. Strains maps around a hole in the femoral bone block demonstrate the effect of the stress concentrator as loading increased and agree qualitatively with the finite element model. Experimentally, residual strains of approximately 2000 µÎµ are present initially, and strain rises to approximately 4500 µÎµ at 95 MPa applied stress (about 1000 µÎµ above the strain in the surrounding material). The experimental data suggest uneven loading which is reproduced qualitatively with finite element modeling.

Lattice strains and load partitioning in bovine trabecular bone.

Microdamage and failure mechanisms have been well characterized in bovine trabecular bone. However, little is known about how elastic strains develop in the apatite crystals of the trabecular struts and their relationship with different deformation mechanisms. In this study, wide-angle high-energy synchrotron X-ray diffraction has been used to determine bulk elastic strains under in situ compression. Dehydrated bone is compared to hydrated bone in terms of their response to load. During compression, load is initially borne by trabeculae aligned parallel to loading direction with non-parallel trabeculae deforming by bending. Ineffective load partitioning is noted in dehydrated bone whereas hydrated bone behaves like a plastically yielding foam.

Effect of high-energy X-ray doses on bone elastic properties and residual strains.

Bone X-ray irradiation occurs during medical treatments, sterilization of allografts, space travel and in vitro studies. High doses are known to affect the post-yield properties of bone, but their effect on the bone elastic properties is unclear. The effect of such doses on the mineral-organic interface has also not been adequately addressed. Here, the evolution of elastic properties and residual strains with increasing synchrotron X-ray dose (5-3880 kGy) is examined on bovine cortical bone. It is found that these doses affect neither the degree of nanometer-level load transfer between the hydroxyapatite (HAP) platelets and the collagen up to stresses of -60 MPa nor the microscopic modulus of collagen fibrils (both measured by synchrotron X-ray scattering during repeated in situ loading and unloading). However, the residual elastic strains in the HAP phase decrease markedly with increased irradiation, indicating damage at the HAP-collagen interface. The HAP residual strain also decreases after repeated loading/unloading cycles. These observations can be explained by temporary de-bonding at the HAP/collagen interface (thus reducing the residual strain), followed by rapid re-bonding (so that load transfer capability is not affected).

High energy X-ray scattering quantification of in situ-loading-related strain gradients spanning the dentinoenamel junction (DEJ) in bovine tooth specimens.

High energy X-ray scattering (80.7keV photons) at station 1-ID of the Advanced Photon Source quantified internal strains as a function of applied stress in mature bovine tooth. These strains were mapped from dentin through the dentinoenamel junction (DEJ) into enamel as a function of applied compressive stress in two small parallelepiped specimens. One specimen was loaded perpendicular to the DEJ and the second parallel to the DEJ. Internal strains in enamel and dentin increased and, as expected from the relative values of the Young's modulus, the observed strains were much higher in dentin than in enamel. Large strain gradients were observed across the DEJ, and the data suggest that the mantle dentin-DEJ-aprismatic enamel structure may shield the near-surface volume of the enamel from large strains. In the enamel, drops in internal strain for applied stresses above 40MPa also suggest that this structure had cracked.

Synchrotron X-ray diffraction study of load partitioning during elastic deformation of bovine dentin.

The elastic properties of dentin, a biological composite consisting of stiff hydroxyapatite (HAP) nano-platelets within a compliant collagen matrix, are determined by the volume fraction of these two phases and the load transfer between them. We have measured the elastic strains in situ within the HAP phase of bovine dentine by high energy X-ray diffraction for a series of static compressive stresses at ambient temperature. The apparent HAP elastic modulus (ratio of applied stress to elastic HAP strain) was found to be 18+/-2GPa. This value is significantly lower than the value of 44GPa predicted by the lower bound load transfer Voigt model, using HAP and collagen volume fractions determined by thermo-gravimetric analysis. This discrepancy is explained by (i) a reduction in the intrinsic Young's modulus of the nano-size HAP platelets due to the high fraction of interfacial volume and (ii) an increase in local stresses due to stress concentration around the dentin tubules.

Deformation crossover: from nano- to mesoscale.

In situ synchrotron and neutron diffraction were used to study deformation mechanisms in Ni over a broad range of grain sizes. The experimental data show that unlike in coarse-grained metals, where the deformation is dominated by dislocation slip, plastic deformation in nanocrystalline Ni is mediated by grain-boundary activities, as evidenced by the lack of intergranular strain and texture development. For ultrafine-grained Ni, although dislocation slip is an active deformation mechanism, deformation twinning also plays an important role, whose propensity increases with the grain size.

Elastic strains in antler trabecular bone determined by synchrotron X-ray diffraction.

The microstructure and associated mechanical properties of antler trabecular bone have been studied using a variety of techniques. The local trabeculae properties, as well as the three-dimensional architecture were characterized using nanoindentation and X-ray microtomography, respectively. An elastic modulus of 10.9+/-1.1 GPa is reported for dry bone, compared with 5.4+/-0.9 GPa for fully hydrated bone. Trabeculae thickness and separation were found to be comparable to those of bovine trabecular bone. Uniaxial compression conducted in situ during X-ray microtomography showed that antler can undergo significant architectural rearrangement, dominated by trabeculae bending and buckling, due to its low mineral content. High-energy synchrotron X-ray diffraction was used to measure elastic strains in the apatite crystals of the trabeculae, also under in situ uniaxial compression. During elastic loading, strain was found to be accommodated largely by trabeculae aligned parallel to the loading direction. Prior to the macroscopic yield point, internal strains increased as trabeculae deformed by bending, and load was also found to be redistributed to trabeculae aligned non-parallel to the loading direction. Significant bending of trabecular walls resulted in tensile strains developing in trabeculae aligned along the loading direction.

Micromechanical response of mineral and collagen phases in bone.

We report the first simultaneous quantification of Young's modulus in the separate material phases of bone: collagen and carbonated hydroxyapatite. High-energy X-ray scattering and in situ loading revealed macroscopic, mineral, and collagen Young's moduli (90% confidence limit) for a canine fibula equaled 24.7(0.2) GPa, 38.2(0.5) GPa {for 00.4 and 43.6(1.4) GPa for 22.2}, and 18(1.2) GPa, respectively. The mineral contained compressive residual stresses on the order of -60 to -80 MPa before loading and had a stress enhancement (ratio of internal to applied stress) between 2.0 and 2.3. The diffraction peak width increased with increasing applied stress, mainly along the bone's longitudinal direction, and peak widths returned to pre-deformation values when load was removed. In a second fibula section from the same animal, the mineral's internal stress changed from -50 MPa (22.2 reflection) to -75 MPa (00.4) just after removal from formalin to -10 MPa after eight hours immersion in phosphate-buffered saline; the corresponding change in collagen D-spacing DeltaD/D equaled 4.2x10(-3).

High-energy X-ray optics with silicon saw-tooth refractive lenses.

Silicon saw-tooth refractive lenses have been in successful use for vertical focusing and collimation of high-energy X-rays (50-100 keV) at the 1-ID undulator beamline of the Advanced Photon Source. In addition to presenting an effectively parabolic thickness profile, as required for aberration-free refractive optics, these devices allow high transmission and continuous tunability in photon energy and focal length. Furthermore, the use of a single-crystal material (i.e. Si) minimizes small-angle scattering background. The focusing performance of such saw-tooth lenses, used in conjunction with the 1-ID beamline's bent double-Laue monochromator, is presented for both short ( approximately 1:0.02) and long ( approximately 1:0.6) focal-length geometries, giving line-foci in the 2 microm-25 microm width range with 81 keV X-rays. In addition, a compound focusing scheme was tested whereby the radiation intercepted by a distant short-focal-length lens is increased by having it receive a collimated beam from a nearer (upstream) lens. The collimation capabilities of Si saw-tooth lenses are also exploited to deliver enhanced throughput of a subsequently placed small-angular-acceptance high-energy-resolution post-monochromator in the 50-80 keV range. The successful use of such lenses in all these configurations establishes an important detail, that the pre-monochromator, despite being comprised of vertically reflecting bent Laue geometry crystals, can be brilliance-preserving to a very high degree.