Modified van der Pauw method based on formulas solvable by the Banach fixed point method

We propose a modification of the standard van der Pauw method for determining the resistivity and Hall coefficient of flat thin samples of arbitrary shape. Considering a different choice of resistance measurements we derive a new formula which can be numerically solved (with respect to sheet resistance) by the Banach fixed point method for any values of experimental data. The convergence is especially fast in the case of almost symmetric van der Pauw configurations (e.g., clover shaped samples).Comment: 8 page

Highly processable bulk metallic glass-forming alloys in the Pt–Co–Ni–Cu–P system

Highly processable bulk metallic glass alloys in the Pt–Co–Ni–Cu–P system were discovered. The alloys show low liquidus temperature below 900 K, excellent processability with low critical cooling rate reflecting in maximum casting thicknesses in quartz tubes of up to 20 mm, and a large supercooled liquid region. The Pt57.5Cu14.7Ni5.3P22.5 composition has a liquidus temperature of 795 K, a glass transition temperature of 508 K with a supercooled liquid region of 98 K. For medical and jewelry applications a Ni-free alloy, Pt60Cu16Co2P22 was discovered with a liquidus temperature of 881 K, a glass transition temperature of 506 K, and a supercooled liquid region of 63 K. Glass formation was observed in a wider composition range. Vickers hardness of these alloys is in the 400 Hv range. The alloys can be processed in the supercooled liquid region in air without any measurable oxidation. In this region, a large processing window is available in which the material does not embrittle. Embrittlement in these alloys is correlated with crystallization. It can be avoided as long as substantial crystallization does not take place during isothermal processing in the supercooled liquid region. Also, liquid processing can be performed in air when flux with B2O3

New coherent states and a new proof of the Scott correction

We introduce new coherent states and use them to prove semi-classical estimates for Schr\"odinger operators with regular potentials. This can be further applied to the Thomas-Fermi potential yielding a new proof of the Scott correction for molecules. This is the short version of a paper by the authors archived at math-ph/0208044.Comment: A misprint in definition of new coherent states corrected. To appear in Proceedings of the UAB 2002 Int'l Conference on Differential Equations and Mathematics Physic

History dependent crystallization of Zr41Ti14Cu12Ni10Be23 melts

The crystallization of Zr41Ti14Cu12Ni10Be23 (Vit 1) melts during constant heating is investigated. (Vit 1) melts are cooled with different rates into the amorphous state and the crystallization temperature upon subsequent heating is studied. In addition, Vit 1 melts are cooled using a constant rate to different temperatures and subsequently heated from this temperature with a constant rate. We investigate the influence of the temperature to which the melt was cooled on the crystallization temperature measured upon heating. In both cases the onset temperature of crystallization shows strong history dependence. This can be explained by an accumulating process during cooling and heating. An attempt is made to consider this process in a simple model by steady state nucleation and subsequent growth of the nuclei which results in different crystallization kinetics during cooling or heating. Calculations show qualitative agreement with the experimental results. However, calculated and experimental results differ quantitatively. This difference can be explained by a decomposition process leading to a nonsteady nucleation rate which continuously increases with decreasing temperature

Some Observations on the Performance of the Most Recent Exchange-Correlation Functionals for the Large and Chemically Diverse GMTKN55 Benchmark

Benchmarks that span a broad swath of chemical space, such as GMTKN55, are very useful for assessing progress in the quest for more universal DFT functionals. We find that the WTMAD2 metrics for a great number of functionals show a clear "Jacob's Ladder hierarchy"; that the "combinatorial" development strategy of Head-Gordon and coworkers generates "best on rung" performers; that the quality of the nonlocal dispersion correction becomes more important as functionals become more accurate for nondispersion properties; that fitting against small, unrepresentative benchmark sets leads to underperforming functionals; and that {\omega}B97M(2) is currently the best DFT functional of any kind, but that revDSD-D4 functionals are able to reach similar performance using fewer parameters, and that revDOD-D4 in addition permits reduced-scaling algorithms. If one seeks a range-separated hybrid (RSH) GGA that also performs well for optical excitation energies, CAM-QTP-01 may be a viable option. The D4 dispersion model, with its partial charge dependence, appears to be clearly superior to D3BJ and even possibly NL. Should one require a double hybrid without dispersion model, noDispSD-SCAN is a viable option. Performance for the MOBH35 transition metal benchmark is different: the best double hybrids are competitive but not superior to {\omega}B97M-V, which offers the best performance compromise for mixed main group-transition metal problems.Comment: 5 pages (ICCMSE-2019 conference proceedings), AIP Conference Proceedings, in pres