Three-dimensional GaN-Ga2O3 core shell structure revealed by x-ray diffraction microscopy

In combination of direct phase retrieval of coherent x-ray diffraction patterns with a novel tomographic reconstruction algorithm, we, for the first time, carried out quantitative 3D imaging of a heat-treated GaN particle with each voxel corresponding to 17 x 17 x 17 nm3. We observed the platelet structure of GaN and the formation of small islands on the surface of the platelets, and successfully captured the internal GaN-Ga2O3 core shell structure in three dimensions. This work opens the door for nondestructive and quantitative imaging of 3D morphology and 3D internal structure of a wide range of materials at the nanometer scale resolution that are amorphous or possess only short-range atomic organization.     

Carbon-13 NMR spectra of hydroxylated bile acid stereoisomers

Carbon-13 NMR signals were assigned for the complete set of the 26 theoretically possible isomers of methyl 5β-cholanates having one to three hydroxy groups at positions C-3, C-7 and/or C-12 in the nucleus. Substituent effects on the ¹³C NMR shielding data serving to characterize the position and configuration of the hydroxy groups are discussed.     

Novikov homology,jump loci and Massey products

Let X be a finite CW complex, and ρ: π ₁(X) → GL(l, ?) a representation. Any cohomology class α ∈ H ¹(X, ?) gives rise to a deformation γ _t of ρ defined by γ _t (g) = ρ(g) exp(t〈α, g〉). We show that the cohomology of X with local coefficients γ _gen corresponding to the generic point of the curve γ is computable from a spectral sequence starting from H*(X, ρ). We compute the differentials of the spectral sequence in terms of the Massey products and show that the spectral sequence degenerates in case when X is a Kähler manifold and ρ is semi-simple. If α ∈ H ¹(X, ?) one associates to the triple (X, ρ, α) the twisted Novikov homology (a module over the Novikov ring). We show that the twisted Novikov Betti numbers equal the Betti numbers of X with coefficients in the local system γ _gen. We investigate the dependence of these numbers on α and prove that they are constant in the complement to a finite number of proper vector subspaces in H ¹(X, ?).     

Simulation and Experimental Study of Wavefront Measurement Accuracy of the Pencil-Beam Method

Ultra-bright and high-coherence X-rays are now being used in synchrotron radiation facilities and X-ray free electron laser facilities. X-ray focusing techniques are essential to take full advantage of these excellent X-ray light sources. To meet the strong demand, high-quality X-ray focusing optics have been developed owing to the advancement of ultraprecision machining and measurement. State-of-the-art refractive lenses [1 C.G. Schroer, Applied Physics Letters 87, 124103 (2005).[Crossref], [Web of Science ®] , [Google Scholar]], zone plates [2 T. Chen, Optics Express 19, 19919 (2011).[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]], and Laue lenses [3 H. Yan, Optics Express 19, 15069 (2011).[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]] can be used to achieve X-ray focusing to a spot a few tens of nanometers.     

Nanoscale imaging of mineral crystals inside biological composite materials using X-ray diffraction microscopy

We for the first time applied x-ray diffraction microscopy to the imaging of mineral crystals inside biological composite materials--intramuscular fish bone--at the nanometer scale resolution. We identified mineral crystals in collagen fibrils at different stages of mineralization. Based on the experimental results and biomineralization analyses, we suggested a dynamic model to account for the nucleation and growth of mineral crystals in the collagen matrix. The results obtained from this study not only further our understanding of the complex structure of bone, but also demonstrate that x-ray diffraction microscopy will become an important tool to study biological materials.     

Enantioselective, biocatalytic reduction of 3-substituted cyclopentenones: application to the asymmetric synthesis of an hNK-1 receptor antagonist

A convergent and enantioselective route to the hNK-1 receptor antagonist (1) is described, which sets all six stereogenic centers with high diastereoselectivity and delivers 1 in only 11 steps and 23% overall yield. The process was enabled by the development of the enantioselective enzymatic reduction of 3-functionalized cyclopentenones and stereospecific Pd-catalyzed etherification coupling of fragments 6 and 7.     

A highly stereoselective synthesis of optically active trisubstituted 1,2-ethylenediamines: the first example of grignard addition to N-diphenylphosphinoyl ketimines derived from amino acids

The efficient synthesis of optically active trisubstituted 1,2-ethylenediamines is described. Addition of aryl and/or alkyl Grignard reagents to alpha-amino N-diphenylphosphinoyl ketimines derived from alpha-amino acids was demonstrated to afford the desired trisubstituted 1,2-ethylenediamines in good yields and with high diastereoselectivities. Subsequent removal of the diphenyphosphinoyl group from the adduct was smoothly accomplished in reasonable yield without racemization under newly developed reductive conditions.     

Advancement of Hard X-ray Nano-focusing Ellipsoidal Mirror at SPring-8

Ellipsoidal mirror optics can produce a smaller, two-dimensional focus with diffraction-limited properties than is possible when using mirror optics in Kirkpatrick–Baez (K–B) geometry [1 P. Kirkpatrick and A.V. Baez, Journal of the Optical Society of America 38, 766–773 (1948).[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]]. This is because ellipsoidal focusing mirrors can be designed such that they have a larger numerical aperture in the sagittal focusing direction as compared to that in the meridional focusing direction. Although ellipsoidal focusing mirrors have this crucial advantage over K–B optics, K–B optics are widely utilized as micro-/nano-focusing devices [2 H. Mimura, Nature Physics 6, 122–125 (2010).[Crossref], [Web of Science ®] , [Google Scholar]–8 H. Mimura, Nature Communications 5, 3539 (2014).[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]] in synchrotron radiation facilities and X-ray free electron laser facilities [9 P. Emma, Nature Photonics 4, 641–647 (2010).[Crossref], [Web of Science ®] , [Google Scholar], 10 T. Ishikawa, Nature Photonics 6, 540–544 (2012).[Crossref], [Web of Science ®] , [Google Scholar]]. Figure 1 shows a schematic of focusing mirror optics; Figure 1(a) shows the ellipsoidal mirror and Figure 1(b) the K–B mirror arrangement. In K–B geometry, two mirrors with a one-dimensionally curved surface, such as an elliptical cylinder, are orthogonally arranged in tandem to reflect and focus light independently in a direction perpendicular to each other under grazing-incidence conditions. Ellipsoidal focusing mirrors, which can generate a two-dimensional focusing beam by a single reflection, have a highly sloped surface with a two-dimensional aspherical shape, when compared to elliptical-cylinder mirrors that are used for line-focusing in K–B geometry. In addition, surface shapes of nano-focusing mirrors must be fabricated with nanometer-level accuracy. Therefore, fabrication of ellipsoidal nano-focusing mirrors is extremely difficult. There are no reports on ellipsoidal nano-focusing mirrors in the hard X-ray region with superior performances to provide diffraction-limited beams.     

Bar complex, configuration spaces and finite type invariants for braids

We show that the bar complex of the configuration space of ordered distinct points in the complex plane is acyclic. The 0-dimensional cohomology of this bar complex is identified with the space of finite type invariants for braids. We construct a universal holonomy homomorphism from the braid group to the space of horizontal chord diagrams over Q, which provides finite type invariants for braids with values in Q.