Ternary rare-earth alumo-silicides—single-crystal growth from Al flux, structural and physical properties

A number of rare-earth alumo-silicides (R-Al-Si) have been synthesized from the corresponding elements by high-temperature reactions, carried out in excess of aluminum to serve as a flux. Under these experimental conditions, large single crystals of all R-Al-Si ternary phases were readily produced. The crystal structures these ternaries adopt were studied by means of powder and single-crystal X-ray diffraction and were classified as follows: (1) the early rare-earths (R=La, Ce, Pr, Nd, Sm, Gd) yield RAl_xSi_2−x, x∼1, non-stoichiometric ternary derivatives of the body-centered α-ThSi₂-type; (2) the late rare-earths (R=Tb, Dy, Ho, Er, Tm) form stoichiometric R₂Al₃Si₂ compounds that crystallize in the C-centered monoclinic Y₂Al₃Si₂-type; (3) the divalent Eu and Yb produce EuAl₂Si₂ and YbAl₂Si₂ with the trigonal CaAl₂Si₂-type, whereas the last lanthanide element, Lu, forms LuAlSi with C-centered orthorhombic YAlGe-type. These structural trends are reviewed, and the evolution of the basic physical properties such as magnetism, heat capacity and electrical resistivity when moving across the series is described in detail.     

On the Motion of Substance in a Channel of a Network: Extended Model and New Classes of Probability Distributions

We discuss the motion of substance in a channel containing nodes of a network. Each node of the channel can exchange substance with: (i) neighboring nodes of the channel, (ii) network nodes which do not belong to the channel, and (iii) environment of the network. The new point in this study is that we assume possibility for exchange of substance among flows of substance between nodes of the channel and: (i) nodes that belong to the network but do not belong to the channel and (ii) environment of the network. This leads to an extension of the model of motion of substance and the extended model contains previous models as particular cases. We use a discrete-time model of motion of substance and consider a stationary regime of motion of substance in a channel containing a finite number of nodes. As results of the study, we obtain a class of probability distributions connected to the amount of substance in nodes of the channel. We prove that the obtained class of distributions contains all truncated discrete probability distributions of discrete random variable ω which can take values 0,1,⋯,N. Theory for the case of a channel containing infinite number of nodes is presented in Appendix A. The continuous version of the discussed discrete probability distributions is described in Appendix B. The discussed extended model and obtained results can be used for the study of phenomena that can be modeled by flows in networks: motion of resources, traffic flows, motion of migrants, etc.     

Simple Equations Method (SEsM): Algorithm,Connection with Hirota Method,Inverse Scattering Transform Method,and Several Other Methods

The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM. In more detail, we show that the Hirota method is connected to a particular case of SEsM for a specific form of the function from Step 2 of SEsM and for simple equations of the kinds of differential equations for exponential functions. We illustrate this particular case of SEsM by obtaining the three- soliton solution of the Korteweg-de Vries equation, two-soliton solution of the nonlinear Schrödinger equation, and the soliton solution of the Ishimori equation for the spin dynamics of ferromagnetic materials. Then we show that a particular case of SEsM can be used in order to reproduce the methodology of the inverse scattering transform method for the case of the Burgers equation and Korteweg-de Vries equation. This particular case is connected to use of a specific case of Step 2 of SEsM. This step is connected to: (i) representation of the solution of the solved nonlinear partial differential equation as expansion as power series containing powers of a “small” parameter ϵ; (ii) solving the differential equations arising from this representation by means of Fourier series, and (iii) transition from the obtained solution for small values of ϵ to solution for arbitrary finite values of ϵ. Finally, we show that the much-used homogeneous balance method, extended homogeneous balance method, auxiliary equation method, Jacobi elliptic function expansion method, F-expansion method, modified simple equation method, trial function method and first integral method are connected to particular cases of SEsM.     

Formation and stabilization of Pd(III) in presence of the porphyrinato-type ligand bilirubin

Formation of transient Pd(III) species was established in the course of PdCL₄ ²⁻-bilirubin (BR) reaction in basic-water medium. Using the EPR method the formation of an octahedral low-spin PdL.2H₂O complex was proved exhibiting an anisotropic 2-component EPR spectrum (g₁=2.007 and g_u=1.998) and effective magnetic moment μ_eff = 1.7 BM.     

Study of mercury surface diffusion on tantalum with and without an electric field by means of a field emission microscope

The surface diffusion of mercury atoms on tantalum substrate with and without high electric field was studied by means of a field emission microscope (Müller's). The activation energy during surface migration Q_m of mercury atoms with and without an electric field F on tantalum substrate depending on the thickness of the adsorbate was measured. It is shown that the electron density distribution at coverage θ < 0.65 with adsorbate is due to a dipole momentum P. At θ > 0.65 the slope of the curves of Q^F_m = ?(θ) is explained with the appearance of the effect of polarization. The energy of desorption Q_d as a function of the thickness of the adsorbed layer in the temperature range 100–300 K was measured also.     

Entropy enhancement and black hole microstates

We show that the entropy of fluctuating two-charge supertubes placed in three-charge scaling microstate solutions depends on their "effective" charges, which in strong magnetic fields can be much larger than their charges. This leads to a much larger entropy than one naively would expect. Since fluctuating supertubes source smooth geometries in certain duality frames, we propose that such an entropy enhancement mechanism might lead to a black-hole-like entropy coming entirely from configurations that are smooth and horizonless in the regime of parameters where the classical black hole exists.     

Zintl phase variations through cation selection. Synthesis and structure of A21Cd4Pn18 (A = Eu, Sr, Ba; Pn = Sb, Bi)

Four new Zintl compounds, Ba21Cd4Sb18, Ba21Cd4Bi18, Sr21Cd4Bi18, and Eu21Cd4Bi18, have been synthesized and structurally characterized. Despite the similarity in their chemical formulas and regardless of their identical electronic requirements, the structures of the Ba compounds and the Sr and Eu compounds are subtly different. Due to the cations, a cleavage of a selected pnicogen-cadmium bond occurs and the structures adapt to a novel packing of the resultant heteronuclear anions.