Structure types and phase transformations in KMnCl3 and TlMnCl3

KMnCl₃ and TlMnCl₃ are known to crystallize in tetragonal and cubic perovskite structures, respectively. Room temperature X-ray diffraction data obtained in our laboratory proved that the perovskite structure of KmnCl₃ is orthorhombic. The space group is Pnma and Z = 4. Unit cell parameters are a = 7.08(1), b = 9.97(1), and c = 6.98(1) Å. Experimental data showed that the perovskite structures of KMnCl₃ and TlMnCl₃ are not stable, and that both materials transform slowly into another orthorhombic, nonperovskite KCdCl₃ structure with space group Pnma and Z = 4. Cell parameters of these structures are a = 8.769(7), b = 3.883(9), and c = 14.42(1) Å for KMnCl₃ and a = 8.926(8), b = 3.839(9), and c = 14.77(1) Å for TlMnCl₃. The nonperovskite structures of KMnCl₃ and TlMnCl₃ transform on heating to the perovskite structures and these phase transitions are not immediately reversed. No correlation could be found between the KCdCl₃ structure and water incorporation in the crystal lattice as has been previously suggested. An analysis of the factors that cause the K structure to be exhibited in chloride and to be absent in the fluoride compounds is also presented.     

On goodL p subspaces ofl p

Theorem. GivenK>1 and 1≦p<∞, there is λ>1 so that everyL _p,λ subspace ofl _p isK-isomorphic tol _p.     

Coordinating visualizations of polysemous action: values added for grounding proportion

We contribute to research on visualization as an epistemic learning tool by inquiring into the didactical potential of having students visualize one phenomenon in accord with two different partial meanings of the same concept. 22 Grade 4–6 students participated in a design study that investigated the emergence of proportional-equivalence notions from mediated perceptuomotor schemas. Working as individuals or pairs in tutorial clinical interviews, students solved non-symbolic interaction problems that utilized remote-sensing technology. Next, they used symbolic artifacts interpolated into the problem space as semiotic means to objectify in mathematical register a variety of both additive and multiplicative solution strategies. Finally, they reflected on tensions between these competing visualizations of the space. Micro-ethnographic analyses of episodes from three paradigmatic case studies suggest that students reconciled semiotic conflicts by generating heuristic logico-mathematical inferences that integrated competing meanings into cohesive conceptual networks. These inferences hinged on revisualizing additive elements multiplicatively. Implications are drawn for rethinking didactical design for proportions.     

The study of relations between loading history and yield surfaces in powder materials using discrete finite element simulations

Only a few studies in the literature have applied the finite-element method to analyse assemblies of meshed particles. These studies illustrated the relevance of this method for granular materials. Here, the compaction of ductile metal powders was studied through a numerical assembly of elastic–plastic and rate-independent spherical particles. The aim of this paper was to understand the evolution of yield surfaces with complex loading paths up to high relative density at the macroscopic scale and at the granular scale. Simulation results revealed that yield surfaces evolved with both isotropic and kinematic hardening mechanisms, depending on the compaction stage. An analysis of the sample microstructure was proposed, and a detailed study of contacts between particles revealed some of the mechanisms that led to the observed evolution of yield surfaces.     

Revisiting Bohr's semiclassical quantum theory

Bohr's atomic theory is widely viewed as remarkable, both for its accuracy in predicting the observed optical transitions of one-electron atoms and for its failure to fully correspond with current electronic structure theory. What is not generally appreciated is that Bohr's original semiclassical conception differed significantly from the Bohr-Sommerfeld theory and offers an alternative semiclassical approximation scheme with remarkable attributes. More specifically, Bohr's original method did not impose action quantization constraints but rather obtained these as predictions by simply matching photon and classical orbital frequencies. In other words, the hydrogen atom was treated entirely classically and orbital quantized emerged directly from the Planck-Einstein photon quantization condition, E = h nu. Here, we revisit this early history of quantum theory and demonstrate the application of Bohr's original strategy to the three quintessential quantum systems: an electron in a box, an electron in a ring, and a dipolar harmonic oscillator. The usual energy-level spectra, and optical selection rules, emerge by solving an algebraic (quadratic) equation, rather than a Bohr-Sommerfeld integral (or Schroedinger) equation. However, the new predictions include a frozen (zero-kinetic-energy) state which in some (but not all) cases lies below the usual zero-point energy. In addition to raising provocative questions concerning the origin of quantum-chemical phenomena, the results may prove to be of pedagogical value in introducing students to quantum mechanics.     

Detection of the site of phosphorylation in a peptide using Raman spectroscopy and partial least squares discriminant analysis

Normal (non-enhanced) Raman spectroscopy is used to determine the site of phosphorylation on a 13-residue peptide whose sequence derives from the cellular protein pp60(c-src) (protein tyrosine kinase). Raman spectra of serine, threonine and tyrosine amino acids and their phosphorylated derivatives are used to aid in the interpretation of peptide spectra. The purity of the synthetic peptides are confirmed by mass spectroscopy. Peptide Raman measurements are performed using the recently reported drop-coating deposition Raman (DCDR) method, followed by Savistky-Golay second derivative (SGSD) pre-processing and multivariate spectral classification using partial least squares (PLS) discriminant analysis. Leave-one-out training/testing results are displayed using a PLS psuedo-probability score plot and shown to facilitate error-free spectral determination of the site of phosphorylation.     

A note on monotone bases

In a finite-dimensional Banach space with a monotone basis, the range of a norm-1 projection has a monotone basis.     

Potentials and isometric embeddings inL 1

lp/3 does not embed isometrically inL ₁, forp>2. The question whenl _r ⁿ embeds isometrically inL _pis completely answered.     

Communication: Length scale dependent oil-water energy fluctuations

Interfacial fluctuations in the cohesive (van der Waals) interaction energy of spherical oil-drops with water provide evidence of a length scale dependent transition from linear to non-linear response behavior. For sub-nanometer oil-drop sizes, energy fluctuations are found to be independent of the van der Waals coupling strength, while nanometer (and larger) size oil drops experience highly non-linear energy fluctuations. The latter behavior is linked to enhanced hydrophobic density fluctuations and the emergence of entropic contributions to oil-water cohesive interaction free energies.     

Porosity dependence of electron percolation in nanoporous TiO2 layers

The electron diffusion coefficient at varying porosity has been determined in a series of nanostructured TiO(2) films of different initial thicknesses. The porosity was changed by applying different pressures prior to sintering, thereby modifying the internal morphology of the films though not their chemical and surface conditions. A systematic increase of the effective diffusion coefficient was observed as the porosity was decreased, indicating the improvement of the internal connectivity of the network of nanoparticles. The experimental results have been rationalized using percolation theory. First of all, applying a power law dependence, the diffusion coefficient as a function of porosity from different films collapsed in a single master curve. In addition, application of the models of effective medium approximation (EMA) allows us to compare the experimental results with previous data from Monte Carlo simulation. The different data show a similar dependence in agreement with the EMA predictions, indicating that the geometrical effect of electron transport due to variation of porous morphology in TiO(2) nanoparticulate networks is well described by the percolation concept.