Helge B. Larsen

Angle calculations for a six-circle κ diffractometer

By parametrizing the conic surfaces spanned by the reciprocal-lattice vector under the action of the rotation axes, a new procedure for angle calculations for a κ diffractometer is presented. It is applied to obtain angle settings in various modes for a newly developed six-circle diffractometer.

Aspects of nonviral gene therapy: Correlation of molecular parameters with lipoplex structure and transfection efficacy in pyridinium-based cationic lipids

This study seeks correlations between the molecular structures of cationic and neutral lipids, the lipid phase behavior of the mixed-lipid lipoplexes they form with plasmid DNA, and the transfection efficacy of the lipoplexes. Synthetic cationic pyridinium lipids were co-formulated (1:1) with the cationic lipid 1,2-dimyristoyl-sn-glycero-3-ethylphosphocholine (EPC), and these lipids were co-formulated (3:2) with the neutral lipids 1,2-dioleoyl-sn-glycero-3-phosphatidylethanolamine (DOPE) or cholesterol. All lipoplex formulations exhibited plasmid DNA binding and a level of protection from DNase I degradation. Composition-dependent transfection (beta-galactosidase and GFP) and cytotoxicity was observed in Chinese hamster ovarian-K1 cells. The most active formulations containing the pyridinium lipids were less cytotoxic but of comparable activity to a Lipofectamine 2000™ control. Molecular structure parameters and partition coefficients were calculated for all lipids using fragment additive methods. The derived shape parameter values correctly correlated with observed hexagonal lipid phase behavior of lipoplexes as derived from small-angle X-ray scattering experiments. A transfection index applicable to hexagonal phase lipoplexes derived from calculated parameters of the lipid mixture (partition coefficient, shape parameter, lipoplex packing) produced a direct correlation with transfection efficiency.

Three-Beam Diffraction in Finite Perfect Crystals. I. Exploring Laue–Laue and Bragg–Laue Scattering Using a Series-Expansion Approach for the Solution of the Takagi–Taupin Equations

Using the boundary-value Green-function technique, analytical expressions in the form of finite series expansions are obtained for the relative change in the integrated power of the primary reflection due to the gradual excitation of a secondary reciprocal-lattice point on the Ewald sphere. Solutions are found for both a Laue-Laue and a Bragg-Laue case in finite shaped crystals confined by the scattering vectors. When the crystal sizes do not exceed the Pendell6sung length of the involved reflections, the 7z profiles exhibit the same qualitative features in the two cases. The solutions do however indicate a strong dependence on the outer crystal dimensions - which add a geometrical aspect to the interpretation of the Aufhellung and Umweganregung concepts.

Three-Beam Diffraction in Finite Perfect Crystals. II. Influence of Absorption, Resonant Scattering and Polarization

By using the boundary-value Green-function technique, effects of absorption, resonant scattering and polarization are incorporated in the solution of the Takagi–Taupin equations for three-beam diffraction in finite perfect crystals. It is shown how such features may influence the dynamical interactions. The potential of three-beam interference acting as a phase-sensitive probe for resonant scattering is demonstrated. Depending on the applied model used for the calculations of the corrections to the atomic scattering factor, profile asymmetry reversal is theoretically predicted to occur near the photoelectric threshold in a finite germanium crystal. Significant distortions of the three-beam profiles are found for polarized incident radiation, especially for reflection triplets having an invariant phase sum near 90°.

Primary Extinction in Cylinders and Spheres

By transforming the Takagi equations into a representation using angular coordinates, it is in principle possible to obtain analytical expressions for the coefficients in a series expansion for the primary extinction factor in perfect crystals with a circular diffraction plane. In practice, it has been possible to obtain the first five terms in the expansion. This involves establishing recurrence relations for the families of Bragg and Laue boundary-value Green functions combined with integrations over the entrance and exit surfaces. The calculations, which cover the whole range of values for the scattering angle, theta oh, are performed using the mathematical software systems Mathematica and Maple.

Absorption and Weighted Path Lengths in Cylinders and Spheres

By using the boundary-value Green-function technique for the Takagi equations, it is possible to calculate the normal absorption factor and weighted path length in cylinders and spheres as double integrals in angular coordinates of well defined functions. The results are easy to implement for numerical computations. Exact analytical expressions for both crystal geometries are found in the limits of the Bragg angle theta oh-->0 degree and theta oh-->90 degrees.

Approximate solution of the Takagi-Taupin equations for a semi-infinite crystal in the three-beam Laue-Laue case.

An analytical approximate solution of the Takagi-Taupin equations for a symmetrical three-beam Laue-Laue case in a perfect non-absorbing semi-infinite crystal slab has been obtained. The expression, a second-order expansion, is valid for situations where the effective crystal thickness does not exceed half the actual extinction length and it is shown to be in perfect agreement with the full numerical solution of the fundamental equations.

Existence of two crystal structures of the complex α-D-glucose . NaCl . H2O (2 :1:1) verified by three-beam diffraction experiments

Triplet phases from three-beam interference measurements have been used to resolve a case of apparent structural ambiguity. 13 crystals, all cut from one large single crystal of the complex α-d-glucose · NaCl · H2O (2:1:1) were subjected to physical measurements of triplet phases, which involved studies of a set of model-sensitive triplets being particularly sensitive to the differences in structure between the two models. From 8 to 43 triplets were examined for each crystal specimen. The estimated phases have been compared with the corresponding quantities calculated for the refined structure models. A statistical analysis of the results provides highly significant evidence that both structure models are present, but do not coexist in the same crystal. One possible explanation for this apparent anomaly is that a phase transition may be induced by the mechanical stress applied during cutting of the hard and nearly perfect crystals. Triplet phases for structure verification and discrimination between similar structure models, as demonstrated in the present work, appears to be a novel and potentially powerful application of three-beam interference measurements.

Three-Beam Diffraction in Finite Imperfect Crystals. An Analysis of Coherent Wavefield Interactions Using Statistical Dynamical Theory

By applying the concepts of statistical dynamical theory and the boundary-value Green-function technique, an analytical expression in the form of a series expansion has been obtained for the coherent contribution to the integrated power in a finite crystal geometry. The solution suggests that three-beam interference is likely to cause observable perturbations also in crystals with a high degree of imperfection. Owing to a first-order dependence on the invariant triplet phase sum, profile reversal may occur in cases where this sum is close to 90°. The result may serve as an experimental check on statistical dynamical parameters.

Experimental study on the synthesis and characterization of aplite rock-based geopolymers

This paper presents a new method for geopolymer synthesis of ground aplite rock. The resulting geopolymers were easy to manufacture and exhibited promising mechanical properties. Compressive strength testing, X-ray diffraction, and scanning electron microscope analyzes were performed. The results indicated that in manufacturing, the aplite-based geopolymers, potassium-containing systems gave noticeable improvements in comparison with sodium-containing systems. Rheological behavior of the geopolymeric slurry showed non-Newtonian behavior. The Bingham and Herschel–Bulkley models were selected to simulate the viscosities of the slurries. The Bingham model fitted to the measured data with an average deviation of 1.65 (lbf/100 ft2) while the Herschel–Bulkley model showed large deviations from the experimental data.