Stability of a eutectic interface during directional solidification

Directional solidification of eutectic alloys shows different types of eutectic morphologies. These include lamellar, rod, oscillating and tilting modes. The growth of these morphologies occurs with a macroscopically planar interface. However, under certain conditions, the planar eutectic front becomes unstable and gives rise to a cellular or a dendritic structure. This instability leads to the cellular/dendritic structure of either a primary phase or a two-phase structure. The objective of this work is to develop a fundamental understanding of the instability of eutectic structure into cellular/dendritic structures of a single phase and of two-phases;Experimental studies have been carried out to examine the transition from a planar to two-phase cellular and dendritic structures in a ceramic system of Alumina-Zirconia (Al[subscript]2O[subscript]3-ZrO[subscript]2) and in a transparent organic system of carbon tetrabromide and hexachloroethane (CBr[subscript]4- C[subscript]2Cl[subscript]6). Several aspects of eutectic interface stability have been examined;Studies in the colony structures show that the planar eutectic temperature decreases as the velocity is increased. However, as the planar interface becomes unstable, the temperature of the two-phase cellular structure increases with velocity, goes through a maximum, and finally decreases as the cellular structure transforms into a two-phase dendritic structure. Careful experiments on both transparent as well as ceramic systems have shown deviations of the eutectic spacings in these colony structures from the planar interface model. Based on these results, a new model is proposed to explain the steady-state features of the colony growth;Experimental studies in the instability of eutectics into a single phase formation have shown that the interactions in the microstructures give rise to oscillations between the two stable morphologies around the threshold conditions. The effect of velocity on the oscillation has been examined quantitatively, and it was found that the oscillations decrease as the velocity is increased. A finite band of velocity was observed in which oscillating structures were found to exist. Furthermore, the composition of the alloy showed a large effect on the oscillation of the actual interface velocity which was found to increase as the alloy composition deviated further from the eutectic composition

Improved H_2 Storage in Zeolitic Imidazolate Frameworks Using Li^+, Na^+, and K^+ Dopants, with an Emphasis on Delivery H_2 Uptake

We use grand canonical Monte Carlo simulations with first principles based force fields to show that alkali metal (Li^+, Na^+, and K^+)-doped zeolitic imidazolate frameworks (ZIFs) lead to significant improvement of H_2 uptake at room temperature. For example, at 298 K and 100 bar, Li-ZIF-70 totally binds to 3.08 wt % H_2, Na-ZIF-70 to 2.19 wt % H_2, and K-ZIF-70 to 1.62 wt % H_2, much higher than 0.74 wt % H_2 for pristine ZIF-70. Thus, the dopant effect follows the order of Li-ZIF > Na-ZIF > K-ZIF, which correlates with the H_2 binding energies to the dopants. Moreover, the total H_2 uptake is higher at lower temperatures: 243 K > 273 K > 298 K. On the other hand, delivery H_2 uptake, which is the difference between the total adsorption at the charging pressure (say 100 bar) and the discharging pressure (say 5 bar), is the important factor for practical on-board hydrogen storage in vehicles. We show that delivery H_2 uptake leads to Na-ZIF-70 (1.37 wt %) > K-ZIF-70 (1.25 wt %) > Li-ZIF-70 (1.07 wt %) > ZIF-70 (0.68 wt %), which is different from the trend from the total and excess uptake. Moreover, the delivery uptake increases with increasing temperatures (i.e., 298 K > 273 K > 243 K)! To achieve high delivery H_2 uptake at room temperature, the large free volume of ZIFs is required. We find that higher H_2 binding energy needs not always lead to higher delivery H_2 uptake

Zeolitic Imidazolate Frameworks as H_2 Adsorbents: Ab Initio Based Grand Canonical Monte Carlo Simulation

We report the H_2 uptake behavior of 10 zeolitic−imidazolate frameworks (ZIFs), based on grand canonical Monte Carlo (GCMC) simulations. The force fields (FFs) describing the interactions between H_2 and ZIF in the GCMC were based on ab initio quantum mechanical (QM) calculations (MP2) aimed at correctly describing London dispersion (van der Waals attraction). Thus these predictions of H_2 uptake are based on first principles (non empirical) and hence applicable to new framework materials for which there is no empirical data. For each of these 10 ZIFs we report the total and excess H_2 adsorption isotherms up to 100 bar at both 77 and 300 K. We report the hydrogen adsorption sites in the ZIFs and the relationships between H_2 uptake amount, isosteric heat of adsorption (Q_(st)), surface area, and free volume. Our simulation shows that various ZIFs lead to a variety of H_2 adsorption behaviors in contrast to the metal−organic frameworks (MOFs). This is because ZIFs leads to greater diversity in the adsorption sites (depending on both organic linkers and zeolite topologies) than in MOFs. In particular, the ZIFs uptake larger amounts of H_2 at low pressure because of the high H_2 adsorption energy, and ZIFs have a variety of H_2 adsorption sites. For example, ZIF-11 has an initial Q_(st) value of ~15 kJ/mol, which is higher than observed for MOFs. Moreover, the preferential H_2 adsorption site in ZIFs is onto the organic linker, not nearby the metallic joint as is the case for MOFs

Choi matrices revisited, II

In this paper, we consider all possible variants of Choi matrices of linear maps, and show that they are determined by non-degenerate bilinear forms on the domain space. We will do this in the setting of finite dimensional vector spaces. In case of matrix algebras, we characterize all variants of Choi matrices which retain the usual correspondences between $k$-superpositivity and Schmidt number $\le k$ as well as $k$-positivity and $k$-block-positivity. We also compare de Pillis' definition [Pacific J. Math. 23 (1967), 129--137] and Choi's definition [Linear Alg. Appl. 10 (1975), 285--290], which arise from different bilinear forms.Comment: 17 page