Robert M. Suter

X-ray structure determination of fully hydrated L alpha phase dipalmitoylphosphatidylcholine bilayers

Bilayer form factors obtained from x-ray scattering data taken with high instrumental resolution are reported for multilamellar vesicles of L alpha phase lipid bilayers of dipalmitoylphosphatidylcholine at 50 degrees C under varying osmotic pressure. Artifacts in the magnitudes of the form factors due to liquid crystalline fluctuations have been eliminated by using modified Caillé theory. The Caillé fluctuation parameter eta 1 increases systematically with increasing lamellar D spacing and this explains why some higher order peaks are unobservable for the larger D spacings. The corrected form factors fall on one smooth continuous transform F(q); this shows that the bilayer does not change shape as D decreases from 67.2 A (fully hydrated) to 60.9 A. The distance between headgroup peaks is obtained from Fourier reconstruction of samples with four orders of diffraction and from electron density models that use 38 independent form factors. By combining these results with previous gel phase results, area AF per lipid molecule and other structural quantities are obtained for the fluid L alpha phase. Comparison with results that we derived from previous neutron diffraction data is excellent, and we conclude from diffraction studies that AF = 62.9 +/- 1.3 A2, which is in excellent agreement with a previous estimate from NMR data.

Three-dimensional maps of grain boundaries and the stress state of individual grains in polycrystals and powders

A fast and non-destructive method for generating three-dimensional maps of the grain boundaries in undeformed polycrystals is presented. The method relies on tracking of micro-focused high-energy X-rays. It is verified by comparing an electron microscopy map of the orientations on the 2.5 × 2.5 mm surface of an aluminium polycrystal with tracking data produced at the 3DXRD microscope at the European Synchrotron Radiation Facility. The average difference in grain boundary position between the two techniques is 26 µm, comparable with the spatial resolution of the 3DXRD microscope. As another extension of the tracking concept, algorithms for determining the stress state of the individual grains are derived. As a case study, 3DXRD results are presented for the tensile deformation of a copper specimen. The strain tensor for one embedded grain is determined as a function of load. The accuracy on the strain is Δ∊ ≃ 10−4.

Measurement of chain tilt angle in fully hydrated bilayers of gel phase lecithins

The tilt angle theta tilt of the hydrocarbon chains has been determined for fully hydrated gel phase of a series of saturated lecithins. Oriented samples were prepared on glass substrates and hydrated with supersaturated water vapor. Evidence for full hydration was the same intensity pattern of the low angle lamellar peaks and the same lamellar repeat D as unoriented multilamellar vesicles. Tilting the sample permitted observation of all the wide angle arcs necessary to verify the theoretical diffraction pattern corresponding to tilting of the chains towards nearest neighbors. The length of the scattering unit corresponds to two hydrocarbon chains, requiring each bilayer to scatter coherently rather than each monolayer. For DPPC, theta tilt was determined to be 32.0 +/- 0.5 degrees at 19 degrees C, slightly larger than previous direct determinations and considerably smaller than the value required by recent gravimetric measurements. This new value allows more accurate determinations of a variety of structural parameters, such as area per lipid molecule, A = 47.2 +/- 0.5 A2, and number of water molecules of hydration, nw = 11.8 +/- 0.7. As the chain length n of the lipids was increased from 16 to 20 carbons, the parameters A and nw remained constant, suggesting that the headgroup packing is at its excluded volume limit for this range. However, theta tilt increased by 3 degrees and the chain area Ac decreased by 0.5 A2. This behavior is explained in terms of a competition between a bulk free energy term and a finite or end effect term.

Structure of the fully hydrated gel phase of dipalmitoylphosphatidylcholine.

X-ray diffraction intensities for lamellar repeats, h = 1 to 7, and wide-angle x-ray scattering were measured for the gel phase of fully hydrated dipalmitoylphosphatidylcholine. A hybrid model, which represents the electron density along the lamellar repeat direction as a continuous function composed of constant strips and superimposed Gaussians, is defined. The data were used to determine the best parameters in hybrid models and also in the older strip models. The most successful results were obtained when the density of the methylene region was constrained to the value obtained from the wide-angle scattering. Further analysis utilized the lipid volume obtained from absolute specific volume measurements. Together with the fundamental relations derived in the previous paper, the electron density modeling yielded the headgroup volume (340 +/- 10 A3) and the methylene volume (25.3 +/- 0.2A3). The results were in agreement whether the hybrid model or the strip model was used and whether our data or the data of Torbet and Wilkins were used. Additional structural results, such as the area (45.9 +/- 2.0 A2) and the number of waters of hydration per lipid (10.6 +/- 2.0), required one additional piece of information, which we took to be the tilt angle theta, which is 30 +/- 3 degrees from other experiments in the literature. Absolute electron density profiles, which clearly indicate two features in the headgroup region, are presented. The analysis yielded an accurate value of F(0), which contributes to the continuous scattering transform F(X), which is also given.

Forward modeling method for microstructure reconstruction using x-ray diffraction microscopy: Single-crystal verification

We describe and illustrate a forward modeling method for quantitatively reconstructing the geometry and orientation of microstructural features inside of bulk samples from high-energy x-ray diffraction microscopy data. Data sets comprise charge-coupled device images of Bragg diffracted beams originating from individual grains in a thin planar section of sample. Our analysis approach first reduces the raw images to a binary data set in which peaks have been thresholded at a fraction of their height after noise reduction processing. We then use a computer simulation of the measurement and the sample microstructure to generate calculated diffraction patterns over the same range of sample orientations used in the experiment. The crystallographic orientation at each of an array of area elements in the sample space is adjusted to optimize overlap between experimental and simulated scattering. In the present verification exercise, data are collected at the Advanced Photon Source beamline 1-ID using microfocused ...

Small-angle x-ray scattering from lipid bilayers is well described by modified Caille theory but not by paracrystalline theory.

X-ray scattering data at high instrumental resolution are reported for multilamellar vesicles of L alpha phase lipid bilayers of 1,2-dipalmitoyl-sn-glycero-3-phosphatidylcholine at 50 degrees C under varying osmotic pressure. The data are fitted to two theories that account for noncrystalline disorder, paracrystalline theory (PT) and modified Caillé theory (MCT). The MCT provides good fits to the data, much better than the PT fits. The particularly important characteristic of MCT is the long power law tails in the scattering. PT fits (as well as ordinary integration with no attempt to account for the noncrystalline disorder) increasingly underestimate this scattering intensity as the order h increases, thereby underestimating the form factors used to obtain electron density profiles.

Adaptive reconstruction method for three-dimensional orientation imaging

An adaptive orientation reconstruction algorithm is developed for near-field high-energy X-ray diffraction microscopy. When combined with a spatially adaptive extension the algorithm results in a factor of 10–1000 speed-up over the existing forward modeling reconstruction method while preserving most of the spatial and orientation resolution characteristics. Tests of the reconstruction code based on simulated structures and real data on a complex microstructure are presented. Simulated structures include intra-granular orientation gradients and noisy detector images. It is shown that resolution in both real space and orientation space degrades gracefully as complexity and detector noise increase.

Three-dimensional plastic response in polycrystalline copper via near-field high-energy X-ray diffraction microscopy

The evolution of the crystallographic orientation field in a polycrystalline sample of copper is mapped in three dimensions as tensile strain is applied. Using forward-modeling analysis of high-energy X-ray diffraction microscopy data collected at the Advanced Photon Source, the ability to track intragranular orientation variations is demonstrated on an ∼2 µm length scale with ∼0.1° orientation precision. Lattice rotations within grains are tracked between states with ∼1° precision. Detailed analysis is presented for a sample cross section before and after ∼6% strain. The voxel-based (0.625 µm triangular mesh) reconstructed structure is used to calculate kernel-averaged misorientation maps, which exhibit complex patterns. Simulated scattering from the reconstructed orientation field is shown to reproduce complex scattering patterns generated by the defected microstructure. Spatial variation of a goodness-of-fit or confidence metric associated with the optimized orientation field indicates regions of relatively high or low orientational disorder. An alignment procedure is used to match sample cross sections in the different strain states. The data and analysis methods point toward the ability to perform detailed comparisons between polycrystal plasticity computational model predictions and experimental observations of macroscopic volumes of material.

Kinetics of subgel formation in DPPC: X-ray diffraction proves nucleation-growth hypothesis

Wide-angle and low-angle X-ray diffraction data were obtained during the time course of the gel to subgel phase transformation in fully hydrated DPPC. When the system was kept close to equilibrium by following a T-jump protocol, the X-ray data unequivocally demonstrate the coexistence of growing subgel and shrinking gel domains. When the system was supercooled and held further from equilibrium as in previous studies, the kinetic behavior was more complicated. These data prove that the basic mechanism for the gel to subgel phase transformation is one of nucleation of subgel domains followed by growth of the domains.

A rotational and axial motion system load frame insert for in situ high energy x-ray studies

High energy x-ray characterization methods hold great potential for gaining insight into the behavior of materials and providing comparison datasets for the validation and development of mesoscale modeling tools. A suite of techniques have been developed by the x-ray community for characterizing the 3D structure and micromechanical state of polycrystalline materials; however, combining these techniques with in situ mechanical testing under well characterized and controlled boundary conditions has been challenging due to experimental design requirements, which demand new high-precision hardware as well as access to high-energy x-ray beamlines. We describe the design and performance of a load frame insert with a rotational and axial motion system that has been developed to meet these requirements. An example dataset from a deforming titanium alloy demonstrates the new capability.