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 References of "Honecker, Dirk 50035792"      in Complete repository Arts & humanities   Archaeology   Art & art history   Classical & oriental studies   History   Languages & linguistics   Literature   Performing arts   Philosophy & ethics   Religion & theology   Multidisciplinary, general & others Business & economic sciences   Accounting & auditing   Production, distribution & supply chain management   Finance   General management & organizational theory   Human resources management   Management information systems   Marketing   Strategy & innovation   Quantitative methods in economics & management   General economics & history of economic thought   International economics   Macroeconomics & monetary economics   Microeconomics   Economic systems & public economics   Social economics   Special economic topics (health, labor, transportation…)   Multidisciplinary, general & others Engineering, computing & technology   Aerospace & aeronautics engineering   Architecture   Chemical engineering   Civil engineering   Computer science   Electrical & electronics engineering   Energy   Geological, petroleum & mining engineering   Materials science & engineering   Mechanical engineering   Multidisciplinary, general & others Human health sciences   Alternative medicine   Anesthesia & intensive care   Cardiovascular & respiratory systems   Dentistry & oral medicine   Dermatology   Endocrinology, metabolism & nutrition   Forensic medicine   Gastroenterology & hepatology   General & internal medicine   Geriatrics   Hematology   Immunology & infectious disease   Laboratory medicine & medical technology   Neurology   Oncology   Ophthalmology   Orthopedics, rehabilitation & sports medicine   Otolaryngology   Pediatrics   Pharmacy, pharmacology & toxicology   Psychiatry   Public health, health care sciences & services   Radiology, nuclear medicine & imaging   Reproductive medicine (gynecology, andrology, obstetrics)   Rheumatology   Surgery   Urology & nephrology   Multidisciplinary, general & others Law, criminology & political science   Civil law   Criminal law & procedure   Criminology   Economic & commercial law   European & international law   Judicial law   Metalaw, Roman law, history of law & comparative law   Political science, public administration & international relations   Public law   Social law   Tax law   Multidisciplinary, general & others Life sciences   Agriculture & agronomy   Anatomy (cytology, histology, embryology...) & physiology   Animal production & animal husbandry   Aquatic sciences & oceanology   Biochemistry, biophysics & molecular biology   Biotechnology   Entomology & pest control   Environmental sciences & ecology   Food science   Genetics & genetic processes   Microbiology   Phytobiology (plant sciences, forestry, mycology...)   Veterinary medicine & animal health   Zoology   Multidisciplinary, general & others Physical, chemical, mathematical & earth Sciences   Chemistry   Earth sciences & physical geography   Mathematics   Physics   Space science, astronomy & astrophysics   Multidisciplinary, general & others Social & behavioral sciences, psychology   Animal psychology, ethology & psychobiology   Anthropology   Communication & mass media   Education & instruction   Human geography & demography   Library & information sciences   Neurosciences & behavior   Regional & inter-regional studies   Social work & social policy   Sociology & social sciences   Social, industrial & organizational psychology   Theoretical & cognitive psychology   Treatment & clinical psychology   Multidisciplinary, general & others     Showing results 1 to 20 of 43 1 2 3     Magnetic structure factor of correlated moments in small-angle neutron scatteringHonecker, Dirk ; Fernández Barquín, Luis; Bender, Philipp Florian in Physical Review. B, Condensed Matter and Materials Physics (2020), 101(13), 134401The interplay between structural and magnetic properties of nanostructured magnetic materials allows one to realize unconventional magnetic effects, which results in a demand for experimental techniques ... [more ▼]The interplay between structural and magnetic properties of nanostructured magnetic materials allows one to realize unconventional magnetic effects, which results in a demand for experimental techniques to determine the magnetization profile with nanoscale resolution. Magnetic small-angle neutron scattering (SANS) probes both the chemical and magnetic nanostructure and is thus a powerful technique, e.g., for the characterization of magnetic nanoparticles. Here, we show that the conventionally used particle-matrix approach to describe SANS of magnetic particle assemblies, however, leads to a flawed interpretation. As a remedy, we provide general expressions for the field-dependent two-dimensional magnetic SANS cross section of correlated moments. It is shown that for structurally disordered ensembles the magnetic structure factor is in general, and contrary to common assumptions, (i) anisotropic also in zero field and (ii) that even in saturation the magnetic structure factor deviates from the nuclear one. These theoretical predictions explain qualitatively the intriguing experimental, polarized SANS data of an ensemble of dipolar-coupled iron oxide nanoparticles. [less ▲]Detailed reference viewed: 85 (2 UL) Magnetic Guinier lawMichels, Andreas ; Malyeyev, Artem ; Titov, Ivan et alin IUCrJ (2020), 7Small-angle scattering of x-rays and neutrons is a routine method for the determination of nanoparticle sizes. The so-called Guinier law represents the low-q approximation for the small-angle scattering ... [more ▼]Small-angle scattering of x-rays and neutrons is a routine method for the determination of nanoparticle sizes. The so-called Guinier law represents the low-q approximation for the small-angle scattering curve from an assembly of particles. The Guinier law has originally been derived for nonmagnetic particle-matrix-type systems, and it is successfully employed for the estimation of particle sizes in various scientific domains (e.g., soft matter physics, biology, colloidal chemistry, materials science). An important prerequisite for it to apply is the presence of a discontinuous interface separating particles and matrix. Here, we introduce the Guinier law for the case of magnetic small-angle neutron scattering (SANS) and experimentally demonstrate its applicability for the example of nanocrystalline cobalt. It is well- known that the magnetic microstructure of nanocrystalline ferromagnets is highly nonuniform on the nanometer length scale and characterized by a spectrum of continuously varying long-wavelength magnetization fluctuations, i.e., these systems do not manifest sharp interfaces in their magnetization profile. The magnetic Guinier radius depends on the applied magnetic field, on the magnetic interactions (exchange, magnetostatics), and on the magnetic anisotropy-field radius, which characterizes the size over which the magnetic anisotropy field is coherently aligned into the same direction. In contrast to the nonmagnetic conventional Guinier law, the magnetic version can be applied to fully dense random-anisotropy-type ferromagnets. [less ▲]Detailed reference viewed: 34 (9 UL) Anisometric mesoscale nuclear and magnetic texture in sintered Nd-Fe-B magnetsTitov, Ivan ; Honecker, Dirk ; Mettus, Denis et alin Physical Review Materials (2020), 4Detailed reference viewed: 42 (7 UL) Probing the stability and magnetic properties of magnetosome chains in freeze-dried magnetotactic bacteriaBender, Philipp Florian ; Honecker, Dirk in Nanoscale Advances (2020)Detailed reference viewed: 29 (2 UL) Unraveling Nanostructured Spin Textures in Bulk MagnetsBender, Philipp Florian ; Leliaert, Jonathan; Bersweiler, Mathias et alin Small Science (2020), (n/a), One of the key challenges in magnetism remains the determination of the nanoscopic magnetization profile within the volume of thick samples, such as permanent ferromagnets. Thanks to the large penetration ... [more ▼]One of the key challenges in magnetism remains the determination of the nanoscopic magnetization profile within the volume of thick samples, such as permanent ferromagnets. Thanks to the large penetration depth of neutrons, magnetic small-angle neutron scattering (SANS) is a powerful technique to characterize bulk samples. The major challenge regarding magnetic SANS is accessing the real-space magnetization vector field from the reciprocal scattering data. In this letter, a fast iterative algorithm is introduced that allows one to extract the underlying two-dimensional magnetic correlation functions from the scattering patterns. This approach is used here to analyze the magnetic microstructure of Nanoperm, a nanocrystalline alloy which is widely used in power electronics due to its extraordinary soft magnetic properties. It can be shown that the computed correlation functions clearly reflect the projection of the three-dimensional magnetization vector field onto the detector plane, which demonstrates that the used methodology can be applied to probe directly spin-textures within bulk samples with nanometer-resolution. This article is protected by copyright. All rights reserved. [less ▲]Detailed reference viewed: 124 (12 UL) In situ magnetorheological SANS setup at Institut Laue-LangevinZákutná, Dominika; Graef, Kevin; Dresen, Dominique et alin Colloid and Polymer Science (2020)A magnetorheological sample environment is presented that allows for in situ magnetic field and shear flow during small-angle neutron scattering (SANS) measurements and is now available at the Institut ... [more ▼]A magnetorheological sample environment is presented that allows for in situ magnetic field and shear flow during small-angle neutron scattering (SANS) measurements and is now available at the Institut Laue-Langevin (ILL). The setup allows performing simultaneous magnetorheological measurements together with the investigation of structural and magnetic changes on the nanometer length scale underlying the rheological response of ferrofluids. We describe the setup consisting of a commercial rheometer and a custom-made set of Helmholtz coils and show exemplarily data on the field and shear flow alignment of a dispersion of hematite nanospindles in water. [less ▲]Detailed reference viewed: 58 (0 UL) The benefits of a Bayesian analysis for the characterization of magnetic nanoparticlesBersweiler, Mathias ; Rubio, Helena Gavilan; Honecker, Dirk et alin Nanotechnology (2020), 31(43), 435704Magnetic nanoparticles offer a unique potential for various biomedical applications, but prior to commercial usage a standardized characterization of their structural and magnetic properties is required ... [more ▼]Magnetic nanoparticles offer a unique potential for various biomedical applications, but prior to commercial usage a standardized characterization of their structural and magnetic properties is required. For a thorough characterization, the combination of conventional magnetometry and advanced scattering techniques has shown great potential. In the present work, we characterize a powder sample of high-quality iron oxide nanoparticles that are surrounded with a homogeneous thick silica shell by DC magnetometry and magnetic small-angle neutron scattering (SANS). To retrieve the particle parameters such as their size distribution and saturation magnetization from the data, we apply standard model fits of individual data sets as well as global fits of multiple curves, including a combination of the magnetometry and SANS measurements. We show that by combining a standard least-squares fit with a subsequent Bayesian approach for the data refinement, the probability distributions of the model parameters and their cross correlations can be readily extracted, which enables a direct visual feedback regarding the quality of the fit. This prevents an overfitting of data in case of highly correlated parameters and renders the Bayesian method as an ideal component for a standardized data analysis of magnetic nanoparticle samples. [less ▲]Detailed reference viewed: 86 (7 UL) Field Dependence of Magnetic Disorder in NanoparticlesZákutná, Dominika; Nižňanský, Daniel; Barnsley, Lester C. et alin Physical Review X (2020), 10The performance characteristics of magnetic nanoparticles toward application, e.g., in medicine and imaging or as sensors, are directly determined by their magnetization relaxation and total magnetic ... [more ▼]The performance characteristics of magnetic nanoparticles toward application, e.g., in medicine and imaging or as sensors, are directly determined by their magnetization relaxation and total magnetic moment. In the commonly assumed picture, nanoparticles have a constant overall magnetic moment originating from the magnetization of the single-domain particle core surrounded by a surface region hosting spin disorder. In contrast, this work demonstrates the significant increase of the magnetic moment of ferrite nanoparticles with an applied magnetic field. At low magnetic field, the homogeneously magnetized particle core initially coincides in size with the structurally coherent grain of 12.8(2) nm diameter, indicating a strong coupling between magnetic and structural disorder. Applied magnetic fields gradually polarize the uncorrelated, disordered surface spins, resulting in a magnetic volume more than 20% larger than the structurally coherent core. The intraparticle magnetic disorder energy increases sharply toward the defect-rich surface as established by the field dependence of the magnetization distribution. In consequence, these findings illustrate how the nanoparticle magnetization overcomes structural surface disorder. This new concept of intraparticle magnetization is deployable to other magnetic nanoparticle systems, where the in-depth knowledge of spin disorder and associated magnetic anisotropies are decisive for a rational nanomaterials design. [less ▲]Detailed reference viewed: 420 (3 UL) Sub-millisecond time-resolved small-angle neutron scattering measurements at NISTGlinka, Charles; Bleuel, Markus; Tsai, Peter et alin Journal of Applied Crystallography (2020), 53(3), Instrumentation for time-resolved small-angle neutron scattering measurements with sub-millisecond time resolution, based on Gähler's TISANE (time-involved small-angle neutron experiments) concept, is in ... [more ▼]Instrumentation for time-resolved small-angle neutron scattering measurements with sub-millisecond time resolution, based on Gähler's TISANE (time-involved small-angle neutron experiments) concept, is in operation at NIST's Center for Neutron Research. This implementation of the technique includes novel electronics for synchronizing the neutron pulses from high-speed counter-rotating choppers with a periodic stimulus applied to a sample. Instrumentation details are described along with measurements demonstrating the utility of the technique for elucidating the reorientation dynamics of anisometric magnetic particles. [less ▲]Detailed reference viewed: 40 (4 UL) Experimental observation of third-order effect in magnetic small-angle neutron scatteringMetlov, Konstantin L.; Suzuki, Kiyonori; Honecker, Dirk et alin Physical Review. B, Condensed Matter and Materials Physics (2020), 101Detailed reference viewed: 36 (1 UL) Supraferromagnetic correlations in clusters of magnetic nanoflowersBender, Philipp Florian ; Honecker, Dirk ; Fernández Barquín, Luisin Applied Physics Letters (2019), 115Magnetic nanoflowers are densely packed aggregates of superferromagnetically coupled iron oxide nanocrystallites, which excel during magnetic hyperthermia experiments. Here, we investigate the nature of ... [more ▼]Magnetic nanoflowers are densely packed aggregates of superferromagnetically coupled iron oxide nanocrystallites, which excel during magnetic hyperthermia experiments. Here, we investigate the nature of the moment coupling within a powder of such nanoflowers using spin-resolved small-angle neutron scattering. Within the powder, the nanoparticles are agglomerated to clusters, and we can show that the moments of neighboring nanoflowers tend to align parallel to each other. Thus, the whole system resembles a hierarchical magnetic nanostructure consisting of three distinct levels, i.e., (i) the ferrimagnetic nanocrystallites as building blocks, (ii) the superferromagnetic nanoflowers, and (iii) the supraferromagnetic clusters of nanoflowers. We surmise that such a supraferromagnetic coupling explains the enhanced magnetic hyperthermia performance in the case of interacting nanoflowers. [less ▲]Detailed reference viewed: 94 (5 UL) Magnetic ordering of the martensite phase in Ni-Co-Mn-Sn-based ferromagnetic shape memory alloysSarkar, Sudip Kumar; Ahlawat, Sarita; Kaushik, S. D. et alin Journal of Physics: Condensed Matter (2019)The magnetic state of low temperature martensite phase in Co-substituted Ni-Mn-Sn-based ferromagnetic shape memory alloys (FSMAs) has been investigated, in view of numerous conflicting reports of ... [more ▼]The magnetic state of low temperature martensite phase in Co-substituted Ni-Mn-Sn-based ferromagnetic shape memory alloys (FSMAs) has been investigated, in view of numerous conflicting reports of occurrences of spin glass (SG), superparamagnetism (SPM) or long range anti- ferromagnetic (AF) ordering. Combination of dc magnetization, ac susceptibility and small angle neutron scattering (SANS) studies provide a clear evidence for AF order in martensitic phase of Ni45Co5Mn38Sn12 alloy and rule out SPM and SG orders. Identical studies on another alloy of close composition of Ni44Co6Mn40Sn10 point to presence of SG order in martensitic phase and absence of SPM behavior, contrary to earlier report. SANS results do show presence of nanometre-sized clusters but they are found to grow in size from 3 nm at 30 K to 11 nm at 300 K, and do not correlate with magnetism in these alloys.

[less ▲]Detailed reference viewed: 34 (1 UL) Small-angle neutron scattering (SANS) and spin-echo SANS measurements reveal the logarithmic fractal structure of the large-scale chromatin organization in HeLa nucleiIashina, Ekaterina G.; Filatov, Mikhail V.; Pantina, Rimma A. et alin Journal of Applied Crystallography (2019), 52(4), 844-853This paper reports on the two-scale fractal structure of chromatin organization in the nucleus of the HeLa cell. Two neutron scattering methods, small-angle neutron scattering (SANS) and spin-echo SANS ... [more ▼]This paper reports on the two-scale fractal structure of chromatin organization in the nucleus of the HeLa cell. Two neutron scattering methods, small-angle neutron scattering (SANS) and spin-echo SANS, are used to unambiguously identify the large-scale structure as being a logarithmic fractal with the correlation function $\gamma$( r) $\sim$ ln( r/$\xi$). The smaller-scale structural level is shown to be a volume fractal with dimension D$F$ = 2.41. By definition, the volume fractal is self-similar at different scales, while the logarithmic fractal is hierarchically changed upon scaling. As a result, the logarithmic fractal is more compact than the volume fractal but still has a rather high surface area, which provides accessibility at all length scales. Apparently such bi-fractal chromatin organization is the result of an evolutionary process of optimizing the compactness and accessibility of gene packing. As they are in a water solution, the HeLa nuclei tend to agglomerate over time. The large-scale logarithmic fractal structure of chromatin provides the HeLa nucleus with the possibility of penetrating deeply into the adjacent nucleus during the agglomeration process. The interpenetration phenomenon of the HeLa nuclei shows that the chromatin-free space of one nucleus is not negligible but is as large as the volume occupied by chromatin itself. It is speculated that it is the logarithmic fractal architecture of chromatin that provides a comfortable compartment for this most important function of the cell. [less ▲]Detailed reference viewed: 45 (0 UL) Magnetic ordering of the martensite phase in Ni-Co-Mn-Sn-based ferromagnetic shape memory alloysSarkar, Sudip Kumar; Ahlawat, Sarita; Kaushik, Som Datta et alin Journal of Physics: Condensed Matter (2019)The magnetic state of low temperature martensite phase in Co-substituted Ni-Mn-Sn-based ferromagnetic shape memory alloys (FSMAs) has been investigated, in view of numerous conflicting reports of ... [more ▼]The magnetic state of low temperature martensite phase in Co-substituted Ni-Mn-Sn-based ferromagnetic shape memory alloys (FSMAs) has been investigated, in view of numerous conflicting reports of occurrences of spin glass (SG), superparamagnetism (SPM) or long range anti-ferromagnetic (AF) ordering. Combination of DC magnetization, AC susceptibility and small angle neutron scattering (SANS) studies provide a clear evidence for AF order in martensitic phase of Ni45Co5Mn38Sn12 alloy and rule out SPM and SG orders. Identical studies on another alloy of close composition of Ni44Co6Mn40Sn10 point to presence of SG order in martensitic phase and absence of SPM behavior, contrary to earlier report. SANS results do show presence of nanometre-sized clusters but they are found to grow in size from 3 nm at 30 K to 11 nm at 300 K, and do not correlate with magnetism in these alloys. [less ▲]Detailed reference viewed: 49 (2 UL) Coherent Magnetization Rotation of a Layered System Observed by Polarized Neutron Scattering under Grazing Incidence GeometryMaruyama, Ryuji; Bigault, Thierry; Saerbeck, Thomas et alin Crystals (2019), 9(8), 383The in-plane magnetic structure of a layered system composed of polycrystalline grains smaller than the ferromagnetic exchange length was studied to elucidate the mechanism controlling the magnetic ... [more ▼]The in-plane magnetic structure of a layered system composed of polycrystalline grains smaller than the ferromagnetic exchange length was studied to elucidate the mechanism controlling the magnetic properties considerably different from the bulk using polarized neutron scattering under grazing incidence geometry. The measured result, together with quantitative analysis based on the distorted wave Born approximation, showed that the in-plane length of the area with a uniform orientation of moments ranging from 0.5–1.1 μ m was not significantly varied during the process of demagnetization followed by remagnetization. The obtained behavior of moments is in good agreement with the two-dimensional random anisotropy model where coherent magnetization rotation is dominant. [less ▲]Detailed reference viewed: 40 (0 UL) Using the singular value decomposition to extract 2D correlation functions from scattering patternsBender, Philipp Florian ; Zákutná, Dominika; Disch, Sabrina et alin Acta Crystallographica. Section A, Foundations and Advances (2019), A75Detailed reference viewed: 57 (2 UL) Critical size limits for collinear and spin-spiral magnetism in $CoCr_2\mathrmO_4$Zákutná, D.; Alemayehu, A.; Vlček et alin Physical Review. B, Condensed Matter and Materials Physics (2019), 100The multiferroic behavior of CoCr2O4 results from the appearance of conical spin-spiral magnetic ordering, which induces electric polarization. The magnetic ground state has a complex size-dependent ... [more ▼]The multiferroic behavior of CoCr2O4 results from the appearance of conical spin-spiral magnetic ordering, which induces electric polarization. The magnetic ground state has a complex size-dependent behavior, which collapses when reaching a critical particle size. Here the magnetic phase stability of CoCr2O4 in the size range of 3.6–14.0 nm is presented in detail using the combination of neutron diffraction with XYZ polarization analysis and macroscopic magnetization measurements. We establish critical coherent domain sizes for the formation of the spin spiral and ferrimagnetic structure and reveal the evolution of the incommensurate spin spiral vector with particle size. We further confirm the presence of ferroelectric polarization in the spin spiral phase for nanocrystalline CoCr2O4. [less ▲]Detailed reference viewed: 71 (11 UL) Spin-wave stiffness of the Dzyaloshinskii-Moriya helimagnet compounds Fe1−xCoxSi studied by small-angle neutron scatteringGrigoriev; Pschenichnyi; Altynbaev et alin Physical Review. B, Condensed Matter (2019), 100The spin wave stiffness was measured by small-angle neutron scattering method in the Dzyaloshinskii-Moriya helimagnet compounds Fe1−xCoxSi with x=0.25,0.30,0.50. It has been shown that the spin wave ... [more ▼]The spin wave stiffness was measured by small-angle neutron scattering method in the Dzyaloshinskii-Moriya helimagnet compounds Fe1−xCoxSi with x=0.25,0.30,0.50. It has been shown that the spin wave dispersion in the fully polarized state is anisotropic due to Dzyaloshinskii-Moriya interaction. It is reflected in the neutron scattering pattern as two circles for neutrons obtaining and losing the magnon energy, respectively. The centers of the circles are shifted by the momentum transfer oriented along the applied magnetic field H and equal to the wave vector of the spiral ±ks. The radius of the circles is directly related to the stiffness of spin waves and depends on the magnetic field. We have found that the spin-wave stiffness A change weakly with temperature for each individual compound. On the other hand, the spin-wave stiffness A increases linearly with x in contrast to the x dependences of the critical temperature Tc and the low-temperature ordered moment. Experimentally obtained values of the stiffness A approve quantitative applicability of the Bak-Jensen model for the compounds under study. [less ▲]Detailed reference viewed: 40 (2 UL) Transverse and longitudinal spin-fluctuations in INVAR Fe0.65Ni0.35.Stewart, J. Ross; Giblin, Sean R.; Honecker, Dirk et alin Journal of physics. Condensed matter : an Institute of Physics journal (2019), 31(2), 025802The presence of spin-fluctuations deep within the ordered state of ferromagnetic [Formula: see text] alloy [Formula: see text] has long been suspected but seldom directly observed. Inhomogeneities of one ... [more ▼]The presence of spin-fluctuations deep within the ordered state of ferromagnetic [Formula: see text] alloy [Formula: see text] has long been suspected but seldom directly observed. Inhomogeneities of one type or another have been cited as important in stabilizing [Formula: see text] behaviour-either longitudinal spin-fluctuations associated with the [Formula: see text]-state (local environment) model or transverse magnetisation arising from non-collinear spin structures. In this study we employ small-angle neutron scattering with neutron polarization analysis to distinguish between the two possibilities. Surprisingly we in fact find evidence of dominant but uncorrelated longitudinal spin-fluctuations coexisting with transverse magnetisation which exists in short-range clusters of size ~[Formula: see text]. This finding supports recent first principles calculations of [Formula: see text] in which both longitudinal spin-fluctuations and magnetic short-range order are identified as important ingredients in reproducing the equilibrium [Formula: see text] lattice. [less ▲]Detailed reference viewed: 31 (3 UL) Phase-Transfer and Stabilization of Highly Monodisperse Ferrite Nanoparticles into Polar Solvents by Ligand Exchange Synthesis.Zakutna, Dominika; Honecker, Dirk ; Disch, Sabrinain Journal of nanoscience and nanotechnology (2019), 19(8), 5048-5051Cobalt ferrite nanoparticles with controlled particle size are transferred from nonpolar into polar solvent by exchange of the as-synthesized oleic acid ligand shell with polyacrylic acid (PAA). The ... [more ▼]Cobalt ferrite nanoparticles with controlled particle size are transferred from nonpolar into polar solvent by exchange of the as-synthesized oleic acid ligand shell with polyacrylic acid (PAA). The nanoparticles are highly monodisperse (sigmalog < 6%), and the ligand exchange synthesis has no measurable effect on particle size, shape, or size distribution. The stability of the aqueous particle dispersion without significant interparticle correlations as observed using small-angle X-ray scattering confirms the successful phase-transfer. [less ▲]Detailed reference viewed: 68 (1 UL) 1 2 3