Phase equilibria in the Tl2MoO4-Fe2(MoO4)3-Hf(MoO4)2 system and the crystal structure of ternary molybdate Tl(FeHf0.5)(MoO4)3

The subsolidus region of the ternary salt system Tl₂MoO₄-Fe₂(MoO₄)₃-Hf(MoO₄)₂ was studied by X-ray powder diffraction. New compounds Tl₅FeHf(MoO₄)₆ (5: 1: 2) and Tl(Fe,Hf_0.5)(MoO₄)₃ (1: 1: 1). were found to be formed in this system. Crystals of new ternary molybdate of the composition Tl(FeHf_0.5)(MoO₄)₃ were grown by spontaneous flux crystallization. Its composition and crystal structure were refined based on X-ray diffraction data. The mixed three-dimensional framework of the crystal structure is composed of Mo tetrahedra sharing O vertices with (Fe,Hf)O₆ octahedra. The thallium atoms occupy wide channels in the framework.     

Evolution of epitaxial titanium silicide nanocrystals as a function of growth method and annealing treatments

Titanium silicide grows on silicon in a form of discontinuous layers, which is the most serious obstacle to the formation of high-quality epilayers for VLSI applications. At the same time, nanometric dimensions of the epitaxial silicide islands attract interest as quantum nanostructures. However, for this purpose, nanocrystals in a self-assembled array have to be defect-free, and exhibit high shape and size uniformity. In this work titanium silicide was grown on Si(1 1 1) substrates by reactive deposition epitaxy and by solid-phase epitaxy. Since the reaction and phase-formation kinetics depend on the growth method, accordingly different lattice matching and facet energies may result in different morphological shapes of the nanocrystals. Nanocrystals from reaction in a solid-state could be characterized as highly non-uniform in both shape and size, and their evolution due to post-deposition anneals increased that non-uniformity even further. Relaxation of epitaxial mismatch strain by misfit dislocations could be inferred from a gradual reduction of the nanocrystal vertical aspect ratio and development of flat top facets out of the initially sharp conical crests, in accord with generalized Wulf-Kaishew theorem. On the other hand, the silicide nanocrystals formed by reactive deposition exhibited high uniformity and thermal stability. Significant strain relaxation, as could be judged by the nanocrystal flattening, took place only at temperatures in excess of 650 °C, followed by progressive nanocrystal coalescence. It thus could be inferred, that better titanium silicide nanocrystal arrays (in the sense of uniformity and stability) are more easily obtained by reactive deposition epitaxy than by solid-phase epitaxy. While terminal, stable C54-TiSi₂ phase, did eventually form in the epilayers in both methods, different evolution pathways were manifested by different respective morphologies and orientations even in this final state.     

Blue Light Emitting Defective Nanocrystals Composed of Earth‐Abundant Elements

Copper‐based ternary (I–III–VI) chalcogenide nanocrystals (NCs) are compositionally‐flexible semiconductors that do not contain lead (Pb) or cadmium (Cd). Cu‐In‐S NCs are the dominantly studied member of this important materials class and have been reported to contain optically‐active defect states. However, there are minimal reports of In‐free compositions that exhibit efficient photoluminescence (PL). Here, we report a novel solution‐phase synthesis of ≈4 nm defective nanocrystals (DNCs) composed of copper, aluminum, zinc, and sulfur with ≈20 % quantum yield and an attractive PL maximum of 450 nm. Extensive spectroscopic characterization suggests the presence of highly localized electronic states resulting in reasonably fast PL decays (≈1 ns), large vibrational energy spacing, small Stokes shift, and temperature‐independent PL linewidth and PL lifetime (between room temperature and ≈5 K). Furthermore, density functional theory (DFT) calculations suggest PL transitions arise from defects within a CuAl₅S₈ crystal lattice, which supports the experimental observation of highly‐localized states. The results reported here provide a new material with unique optoelectronic characteristics that is an important analog to well‐explored Cu‐In‐S NCs.     

The reflection from a semi-infinite crystal of point scatterers

The reflection from a semi-infinite crystal of point scatterers (Fermi pseudopotentials) is calculated exactly. The reflection is given as an infinite product of trigonometric functions. The arguments of these depend on the momenta and Bloch momenta that obey the conservation laws. No further information on the Bloch waves is needed.     

Functional holography analysis: simplifying the complexity of dynamical networks

We present a novel functional holography (FH) analysis devised to study the dynamics of task-performing dynamical networks. The latter term refers to networks composed of dynamical systems or elements, like gene networks or neural networks. The new approach is based on the realization that task-performing networks follow some underlying principles that are reflected in their activity. Therefore, the analysis is designed to decipher the existence of simple causal motives that are expected to be embedded in the observed complex activity of the networks under study. First we evaluate the matrix of similarities (correlations) between the activities of the network's components. We then perform collective normalization of the similarities (or affinity transformation) to construct a matrix of functional correlations. Using dimension reduction algorithms on the affinity matrix, the matrix is projected onto a principal three-dimensional space of the leading eigenvectors computed by the algorithm. To retrieve back information that is lost in the dimension reduction, we connect the nodes by colored lines that represent the level of the similarities to construct a holographic network in the principal space. Next we calculate the activity propagation in the network (temporal ordering) using different methods like temporal center of mass and cross correlations. The causal information is superimposed on the holographic network by coloring the nodes locations according to the temporal ordering of their activities. First, we illustrate the analysis for simple, artificially constructed examples. Then we demonstrate that by applying the FH analysis to modeled and real neural networks as well as recorded brain activity, hidden causal manifolds with simple yet characteristic geometrical and topological features are deciphered in the complex activity. The term "functional holography" is used to indicate that the goal of the analysis is to extract the maximum amount of functional information about the dynamical network as a whole unit.     

Quantum confinement and electronic properties of tapered silicon nanowires

Using ab initio calculations, structural tapering of silicon nanowires is shown to have a profound effect on their electronic properties. In particular, the electronic structure of small-diameter tapered silicon nanowires is found to have a strong axial dependence, with unoccupied eigenstates being substantially more sensitive to diameter. Moreover, the states corresponding to the highest occupied and the lowest unoccupied states are spatially separated along the wire axis by the tapering-induced charge transfer and a strong electrostatic potential gradient, due to an appreciable variation in quantum confinement strength with diameter.     

Uniqueness of volume-minimizing submanifolds calibrated by the first Pontryagin form

One way to understand the geometry of the real Grassmann manifold parameterizing oriented -dimensional subspaces of is to understand the volume-minimizing subvarieties in each homology class. Some of these subvarieties can be determined by using a calibration. In previous work, one of the authors calculated the set of -planes calibrated by the first Pontryagin form on for all , and identified a family of mutually congruent round -spheres which are consequently homologically volume-minimizing. In the present work, we associate to the family of calibrated planes a Pfaffian system on the symmetry group , an analysis of which yields a uniqueness result; namely, that any connected submanifold of calibrated by is contained in one of these -spheres. A similar result holds for -calibrated submanifolds of the quotient Grassmannian of non-oriented -planes.