Vibrational Dynamics Studies by Nuclear Resonant Inelastic X-Ray Scattering

Nuclear resonant inelastic X-ray scattering of synchrotron radiation is being applied to ever widening areas ranging from geophysics to biophysics and materials science. Since its first demonstration in 1995 using the ⁵⁷Fe resonance, the technique has now been applied to materials containing ⁸³Kr, ¹⁵¹Eu, ¹¹⁹Sn, and ¹⁶¹Dy isotopes. The energy resolution has been reduced to under a millielectronvolt. This, in turn, has enabled new types of measurements like Debye velocity of sound, as well as the study of origins of non-Debye behavior in presence of other low-energy excitations. The effect of atomic disorder on phonon density of states has been studied in detail. The flux increase due to the improved X-ray sources, crystal monochromators, and time-resolved detectors has been exploited for reducing sample sizes to nano-gram levels, or using samples with dilute resonant nuclei like myoglobin, or even monolayers. Incorporation of micro-focusing optics to the existing experimental setup enables experiments under high pressure using diamond-anvil cells. In this article, we will review these developments. This revised version was published online in August 2006 with corrections to the Cover Date.     

Amorphous Fe–Mg alloy thin films: magnetic properties and atomic vibrational dynamics

Amorphous (a-) Fe _x Mg_1?x alloys are interesting materials for the investigation of non-Debye-like low-energy vibrational excitations. We have prepared a-Fe _x Mg_1?x alloy thin films (0.3 ≤ × ≤0.7) by vapour quenching. The amorphous state was confirmed by conversion electron Mössbauer spectroscopy between 4.2–300 K, and the x- and temperature-dependence of the isomer shift and hyperfine magnetic field was measured. For x= 0.6 and 0.7, magnetic ordering occurs below ~150 K. The atomic vibrational density of states, g(E), was determined by nuclear resonant inelastic scattering, providing clear evidence for the non-Debye-like low-energy vibrational excitations.     

Time‐integrated energy domain measurements with synchrotron radiation

A new time integrated method for the study of resonant nuclear scattering of synchrotron radiation in the forward direction or in Bragg directions is introduced. This method gives in principle similar information as the well known time differential method. A brief comparison of both methods is presented. The idea is to excite coherently the nuclei incorporated in two absorbers, one moving with respect to the other. The fields radiated by the nuclei from both absorbers interfere and each time the nuclear energy in one absorber matches, by Doppler modulation, the nuclear energy of the other, an extremum in the time integrated intensity is observed. The results of the first experiments at the Advanced Photon Source at the Argonne National Laboratory will be presented. This revised version was published online in August 2006 with corrections to the Cover Date.     

Nuclear forward scattering vs. conventional Mössbauer studies of atomically tailored Eu-based materials

With the decrease in size of devices, rapid characterization of nano-devices is an inevitable necessity. It is shown that Mössbauer spectroscopy using synchrotron radiation from the advanced photon source provides such a tool of investigation. Results are presented and compared for conventional Mössbauer and Nuclear Forward Scattering for ¹⁵¹Eu-doped magnesium sulfide as an example, especially at low concentrations.     

Reversible $$G^k$$ G k -codes with applications to DNA codes

Designs, Codes and Cryptography - In this paper, we give a matrix construction method for designing DNA codes that come from group matrix rings. We show that with our construction one can obtain...     

Direct determination of the complete set of iron normal modes in a porphyrin-imidazole model for carbonmonoxy-heme proteins: [Fe(TPP)(CO)(1-MeIm)

Detailed Fe vibrational spectra have been obtained for the heme model complex [Fe(TPP)(CO)(1-MeIm)] using a new, highly selective and quantitative technique, Nuclear Resonance Vibrational Spectroscopy (NRVS). This spectroscopy measures the complete vibrational density of states for iron atoms, from which normal modes can be calculated via refinement of the force constants. These data and mode assignments can reveal previously undetected vibrations and are useful for validating predictions based on optical spectroscopies and density functional theory, for example. Vibrational modes of the iron porphyrin-imidazole compound [Fe(TPP)(CO)(1-MeIm)] have been determined by refining normal mode calculations to NRVS data obtained at an X-ray synchrotron source. Iron dynamics of this compound, which serves as a useful model for the active site in the six-coordinate heme protein, carbonmonoxy-myoglobin, are discussed in relation to recently determined dynamics of a five-coordinate deoxy-myoglobin model, [Fe(TPP)(2-MeHIm)]. For the first time in a six-coordinate heme system, the iron-imidazole stretch mode has been observed, at 226 cm(-)(1). The heme in-plane modes with large contributions from the nu(42), nu(49), nu(50), and nu(53) modes of the core porphyrin are identified. In general, the iron modes can be attributed to coupling with the porphyrin core, the CO ligand, the imidazole ring, and/or the phenyl rings. Other significant findings are the observation that the porphyrin ring peripheral substituents are strongly coupled to the iron doming mode and that the Fe-C-O tilting and bending modes are related by a negative interaction force constant.     

Anomalous NMR behavior of meso compounds with remote stereogenic centers on addition of chiral shift reagent or chiral solvating agent

A problem has arisen in using chiral shift reagents (CSR) and chiral solvating agents (CSA) to determine meso and racemic forms of diastereoisomers in which the stereogenic centers of the molecules are separated by achiral spacers. It is found that NMR signals of both meso and racemic forms of diastereoisomers may exhibit doubling on addition of CSR/CSA, which means that unequivocal assignments cannot be made without characterizing the effects for separate meso and racemic forms; this is particularly important for additions of CSR/CSA at relatively low concentrations, which always result in the splitting of some NMR signals of diastereoisomers. The phenomenon is demonstrated in the (31)P NMR spectra of meso and racemic forms of three spermine-bridged gem-disubstituted cyclotriphosphazatrienes, 1a-c, and compared with analogous achiral molecules, the per-substituted spermine-bridged cyclotriphosphazatrienes 2a-d. As expected, only one set of (31)P NMR signals was observed for the achiral compounds 2a-d, even on addition of CSA. Two sets of (31)P NMR ABX multiplets corresponding to meso and racemic diastereoisomers were observed for compounds 1a-c; on addition of CSA, the signals of at least one of the multiplets for each compound separated into more than the expected groups of three lines with an intensity distribution of 2:1:1. To understand this phenomenon, the meso and racemic forms of 1a and 1b and the meso form of 1c have been separated and characterized by X-ray crystallography. On addition of CSA to the racemic forms of 1a and 1b, the (31)P NMR spectrum shows the expected doubling of signals, but, unexpectedly, the same is observed for each of the meso forms of 1a-c. Analogous results using both CSA and CSR have been obtained for the meso and racemic forms of the diastereoisomeric piperazine-bridged macrocyclic-phosphazene compound, 3, whereas no effect was observed for the two meso forms of the doubly bridged macrocyclic-phosphazene compound 4. The phenomenon of doubling of the (31)P NMR signals of the meso form of singly bridged cyclotriphosphazatrienes, 1a-c and 3, is explained by consideration of the equilibrium in solution of independent complexation of a chiral ligand with molecules that have two chiral cyclophosphazene moieties separated by an achiral spacer group. The results show that the stereogenicity of such diastereoisomeric molecules in solution cannot be characterized unequivocally by NMR measurements on addition of either CSR or CSA.     

Faber polynomial coefficient estimates for a comprehensive subclass of analytic bi-univalent functions

In this work, considering a general subclass of analytic bi-univalent functions, we determine estimates for the general Taylor–Maclaurin coefficients of the functions in this class. For this purpose, we use the Faber polynomial expansions. In certain cases, our estimates improve some of those existing coefficient bounds.     

Synthesis and Spectroscopic Studies of N,N’-dialkyl Derivatives of Antisymmetrical 2H,5H-Dihydropyrrolo[3,4-c]pyrrole-1,4-diones

2,5-dihydropyrrolo[3,4-c]pyrrole-1,4-dione derivatives (DPP) are chemically stable, fluorescent molecules, known as High Performance Pigments. Preparation of the soluble derivatives of DPPs provides great advantage in designing the optic sensor for new and existing applications and overcoming aggregation problems in solid matrices. For this purpose, the synthesis of antisymmetric DPPs and the formation of new organic dyes through N,N’-dialkylation and their spectroscopic studies have been carried out both in solutions and in solid phase.