Electromigration of Sn-9wt.%Zn Solder

The morphological evolution of Sn-9wt.%Zn solder under electromigration at a current density of about 10⁵ A/cm² was examined. Sn extrusion was observed, suggesting that Sn is the dominant moving species under electromigration. In contrast, Zn appeared to be immobile. It was also found that the microstructure of the solder had a significant effect on the electromigration behavior. For the solder with fine Zn precipitates, the surface morphology of the solder was almost unchanged except for the formation of Sn extrusion sites at␣the anode side after electromigration. However, for the solder with coarse Zn precipitates, more Sn extrusion sites were observed, and they were located not only at the anode side but also within the solder. Coarse Zn precipitates appeared to block Sn migration, thus Sn migration was intercepted in front of the Zn precipitates. The Sn atoms accumulated there, which led to its extrusion. The blocking effect was found to depend strongly on the size and orientation of the Zn precipitates.     

Bifurcation indicator based on meshless and asymptotic numerical methods for nonlinear poisson problems

We propose in this work new algorithms associating asymptotic numerical method and meshless discretization (MFS‐MPS: Method of fundamental solutions‐Method of particular solutions) to compute branch solutions of nonlinear Poisson problems. To detect singular points on these branches, geometrical indicator, Padé approximants, and analytical bifurcation indicator are proposed. Numerical applications show the robustness and the effectiveness of the proposed algorithms. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 978–993, 2014     

Characterizing the Phragmén‐Lindelöf condition for evolution on algebraic curves

For an algebraic curve V in ${\mathbb C}^k \times {\mathbb C}^n$ it is investigated when it satisfies the Phragmén‐Lindelöf condition PL(ω) of evolution in certain classes of ultradifferentiable functions. Necessary as well as sufficient conditions are obtained which lead to a complete characterization for curves in ${\mathbb C}\times {\mathbb C}^n$. Some examples illustrate how these results can be applied. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Riemann‐Hilbert problem and matrix discrete Painlevé II systems

Matrix Szeg? biorthogonal polynomials for quasi‐definite matrices of Hölder continuous weights are studied. A Riemann‐Hilbert problem is uniquely solved in terms of the matrix Szeg? polynomials and its Cauchy transforms. The Riemann‐Hilbert problem is given as an appropriate framework for the discussion of the Szeg? matrix and the associated Szeg? recursion relations for the matrix orthogonal polynomials and its Cauchy transforms. Pearson‐type differential systems characterizing the matrix of weights are studied. These are linear systems of ordinary differential equations that are required to have trivial monodromy. Linear ordinary differential equations for the matrix Szeg? polynomials and its Cauchy transforms are derived. It is shown how these Pearson systems lead to nonlinear difference equations for the Verblunsky matrices and two examples, of Fuchsian and non‐Fuchsian type, are considered. For both cases, a new matrix version of the discrete Painlevé II equation for the Verblunsky matrices is found. Reductions of these matrix discrete Painlevé II systems presenting locality are discussed.     

Crystal structure,Hirshfeld surface analysis,Thermal study and Conduction mechanism of [(C4H9)4P]3Bi2Cl9 compound

A novel tris (tetrabutylphosphonium) nonachlorodibismuthate (III) compound has been synthesized and characterized by a single‐crystal X‐ray diffraction, calorimetric, IR spectroscopy and electrical measurements. X‐ray diffraction analysis at room temperature reveals that the title compound belongs to the monoclinic system with P2₁/c space group. The unit cell dimensions are: a = 19.201(6) Å, b = 16.743 (5) Å, c = 22.396 (8) Å, β = 98.96 (2)° and Z = 4. The crystal structure was solved down to R equal to 0.035 for 5597 independent reflections. The crystal package is provided by electrostatic interactions and hydrogen bonds (C‐H ^…. Cl). Intermolecular interactions present in the grown single crystal were analyzed by Hirshfeld surface and 2‐dimensional fingerprint plot. The differential scanning calorimetry reveals one order–disorder phase transition at 400 ± 5 K.The electrical conductivity were carried out in the frequency range 200 Hz–1 MHz at various temperatures 343–413 K using impedance spectroscopy technique. The obtained results were analyzed by fitting the experimental data to an equivalent circuit model. The temperature dependence of alternating and direct current conductivities confirms the observed phase transition in the calorimetric study; they were described in terms of Arrhenius relation. AC conductivity measurements reveal that the conduction depends on both frequency and temperature, this agrees well with Correlated Barrier Hopping model in phase I and II.     

A significant enhancement in thermoelectric power factor of In2Te3 thin films by Se doping and Te composition tuning

Thermoelectric power factor of a material significantly relies on its electrical conductivity, thermal conductivity, and Seebeck coefficient. Herein, an attempt has been made to enhance the thermoelectric power factor of In₂Te₃ thin films by tuning their Te composition and via Se doping. The optimum Se-doping concentration and Te composition enhanced the power factor of pristine In₂Te₃ films by 14 and 7.4 times, respectively. The modified chemical composition, structural characteristics, and surface morphological features of In₂Te₃ films are observed to be pivotal in improving their thermoelectric power factor. Overall, this study offers a facile approach to control the thermoelectric power factor of In₂Te₃ thin films which is significant for their futuristic applications.