The Ternary System Nickel/Silicon/Titanium Revisited

The constitution of the ternary system Ni/Si/Ti is investigated over the entire composition range using X‐ray diffraction (XRD), energy dispersive X‐ray spectroscopy (EDS), differential thermal analysis (DTA), and metallography. The solid state phase equilibria are determined for 900 °C. Eight ternary phases are found to be stable. The crystal structures for the phases τ₁NiSiTi, τ₂Ni₄Si₇Ti₄, τ₃Ni₄₀Si₃₁Ti₁₃, τ₄Ni₁₇Si₇Ti₆, and τ₅Ni₃SiTi₂ are corroborated. For the remaining phases the compositions are determined as Ni₆Si₄₁Ti₅₃ (τ₆), Ni₁₆Si₄₂Ti₄₂(τ₇), and Ni₁₂Si₄₅Ti₄₃ (τ₈). The reaction scheme linking the solid state equilibria with the liquidus surface is amended to account for these newly observed phases. The discrepancies between previous experimental conclusions and modeling results are addressed. The liquidus surface is dominated by the primary crystallisation field of τ₁NiSiTi, the only congruently melting phase.     

The ternary system cerium-rhodium-silicon

Phase relations have been established in the ternary system Ce-Rh-Si for the isothermal section at 800 °C based on X-ray powder diffraction and EPMA on about 80 alloys, which were prepared by arc melting under argon or by powder reaction sintering. From the 25 ternary compounds observed at 800 °C 13 phases have been reported earlier. Based on XPD Rietveld refinements the crystal structures for 9 new ternary phases were assigned to known structure types. Structural chemistry of these compounds follows the characteristics already outlined for their prototype structures: τ₇—Ce₃RhSi₃, (Ba₃Al₂Ge₂-type), τ₈—Ce₂Rh_3−xSi_3+x (Ce₂Rh_1.35Ge_4.65-type), τ₁₀—Ce₃Rh_4−xSi_4+x (U₃Ni₄Si₄-type), τ₁₁—CeRh₆Si₄ (LiCo₆P₄-type), τ₁₃—Ce₆Rh₃₀Si_19.3 (U₆Co₃₀Si₁₉-type), τ₁₈—Ce₄Rh₄Si₃ (Sm₄Pd₄Si₃-type), τ₂₁—CeRh₂Si (CeIr₂Si-type), τ₂₂—Ce₂Rh_3+xSi_1−x (Y₂Rh₃Ge-type) and τ₂₄—Ce₈(Rh_1−xSi_x)₂₄Si (Ce₈Pd₂₄Sb-type). For τ₂₅—Ce₄(Rh_1−xSi_x)₁₂Si a novel bcc structure was proposed from Rietveld analysis. Detailed crystal structure data were derived for τ₃—CeRhSi₂ (CeNiSi₂-type) and τ₆—Ce₂Rh₃Si₅ (U₂Co₃Si₅-type) by X-ray single crystal experiments, confirming the structure types. The crystal structures of τ₄—Ce₂₂Rh₂₂Si₅₆, τ₅—Ce₂₀Rh₂₇Si₅₃ and τ₂₃—Ce_33.3Rh_58.2−55.2Si_8.5−11.5 are unknown. High temperature compounds with compositions Ce₁₀Rh₅₁Si₃₃ (U₁₀Co₅₁Si₃₃-type) and CeRhSi (LaIrSi-type) have been observed in as-cast alloys but these phases do not participate in the phase equilibria at 800 °C.     

Ternary systems Sr-{Ni,Cu}-Si: Phase equilibria and crystal structure of ternary phases

Phase relations were established in the Sr-poor part of the ternary systems Sr-Ni-Si (900 °C) and Sr-Cu-Si (800 °C) by light optical microscopy, electron probe microanalysis and X-ray diffraction on as cast and annealed alloys. Two new ternary compounds SrNiSi₃ (BaNiSn₃-type) and SrNi_9−xSi_4+x (own-type) were found in the Sr-Ni-Si system along with previously reported Sr(Ni_xSi_1−x)₂ (AlB₂-type). The crystal structure of SrNi_9−xSi_4+x (own-type, x=2.7, a=0.78998(3), c=1.1337(2) nm; space group P4/nbm) was determined from X-ray single crystal counter to be a low symmetry derivative of the cubic, parent NaZn₁₃-type. At higher Si-content X-ray Rietveld refinements reveal the formation of a vacant site (□) corresponding to a formula SrNi_5.5Si_6.5□_1.0. Phase equilibria in the Sr-Cu-Si system are characterized by the compounds SrCu_2−xSi_2+x (ThCr₂Si₂-type), Sr(Cu_xSi_1−x)₂ (AlB₂-type), SrCu_9−xSi_4+x (0≤x≤1.0; CeNi_8.5Si_4.5-type) and SrCu_13−xSi_x (4≤x≤1.8; NaZn₁₃-type). The latter two structure types appear within a continuous solid solution. Neither a type-I nor a type-IX clathrate compound was encountered in the Sr-{Cu,Ni}-Si systems.Structural details are furthermore given for about 14 new ternary compounds from related alloy systems with Ba.     

Crystal structure and physical properties of quaternary clathrates Ba8ZnxGe46−x−ySiy, Ba8(Zn,Cu)xGe46−x and Ba8(Zn,Pd)xGe46−x

Three series of vacancy-free quaternary clathrates of type I, Ba₈Zn_xGe_46−x−ySi_y, Ba₈(Zn,Cu)_xGe_46−x, and Ba₈(Zn,Pd)_xGe_46−x, have been prepared by reactions of elemental ingots in vacuum sealed quartz at 800 °C. In all cases cubic primitive symmetry (space group Pm3?n, a∼1.1 nm) was confirmed for the clathrate phase by X-ray powder diffraction and X-ray single crystal analyses. The lattice parameters show a linear increase with increase in Ge for Ba₈Zn_xGe_46−x−ySi_y. M atoms (Zn, Pd, Cu) preferably occupy the 6d site in random mixtures. No defects were observed for the 6d site. Site preference of Ge and Si in Ba₈Zn_xGe_46−x−ySi_y has been elucidated from X-ray refinement: Ge atoms linearly substitute Si in the 24k site whilst a significant deviation from linearity is observed for occupation of the 16i site. A connectivity scheme for the phase equilibria in the “Ba₈Ge₄₆” corner at 800 °C has been derived and a three-dimensional isothermal section at 800 °C is presented for the Ba-Pd-Zn-Ge system. Studies of transport properties carried out for Ba₈{Cu,Pd,Zn}_xGe_46−x and Ba₈Zn_xSi_yGe_46−x−y evidenced predominantly electrons as charge carriers and the closeness of the systems to a metal-to-insulator transition, fine-tuned by substitution and mechanical processing of starting material Ba₈Ge₄₃. A promising figure of merit, ZT ∼0.45 at 750 K, has been derived for Ba₈Zn_7.4Ge_19.8Si_18.8, where pricey germanium is exchanged by reasonably cheap silicon.     

Computing approximate Nash equilibria in general network revenue management games

Computing optimal capacity allocations in network revenue management is computationally hard. The problem of computing exact Nash equilibria in non-zero-sum games is computationally hard, too. We present a fast heuristic that, in case it cannot converge to an exact Nash equilibrium, computes an approximation to it in general network revenue management problems under competition. We also investigate the question whether it is worth taking competition into account when making (network) capacity allocation decisions. Computational results show that the payoffs in the approximate equilibria are very close to those in exact ones. Taking competition into account never leads to a lower revenue than ignoring competition, no matter what the competitor does. Since we apply linear continuous models, computation time is very short.     

On a New Class of Systems of Generalized Quasi-Variational Inequalities

We introduce new types of systems of generalized quasi-variational inequalities and we prove the existence of the solutions by using results of pair equilibrium existence for free abstract economies. We consider the fuzzy models and we also introduce the random free abstract economy and the random equilibrium pair. The existence of the solutions for the systems of quasi-variational inequalities comes as consequences of the existence of equilibrium pairs for the considered free abstract economies.     

Solubility of carbon dioxide in aqueous solution of 2-amino-2-methyl-1-propanol and piperazine

In this work, new experimental results of the vapour-liquid equilibrium (VLE) of CO₂ in aqueous 2-amino-2-methyl-1-propanol (AMP) and piperazine (PZ) have been presented in the temperature range of 298-328 K and PZ concentration range of 2-8 mass%, keeping the total amine concentration in the solution at 30 mass%. The partial pressures of CO₂ were in the range of 0.1-1450 kPa. A thermodynamic model was developed to correlate and predict the VLE of CO₂ in aqueous AMP + PZ. The electrolyte nonrandom two liquid (ENRTL) theory has been used to develop the VLE model for the quaternary system (CO₂ + AMP + PZ + H₂O) to describe the equilibrium behaviour of the solution. The experimental data from this work and data available in the literature were used to regress the ENRTL interaction parameters. The model predictions are in good agreement with the experimental data of CO₂ solubility in aqueous blends of this work as well as those reported in the literature. The current model can also predict speciation, heat of absorption, pH of the CO₂ loaded solution, and amine volatility.     

Liquid-crystal phase equilibria of Lennard-Jones chains

Liquid-crystal phase equilibria of Lennard-Jones chain fluids and the solubility of a Lennard-Jones gas in the coexisting phases are calculated from Monte Carlo simulations. Direct phase equilibria calculations are performed using an expanded formulation of the Gibbs ensemble. Monomer densities, order parameters, and equilibrium pressures are reported for the coexisting isotropic and nematic phases of: (1) linear Lennard-Jones chains, (2) a partially-flexible Lennard-Jones chain, and (3) a binary mixture of linear Lennard-Jones chains. The effect of chain length is determined by calculating the isotropic-nematic coexistence of linear Lennard-Jones chain fluids made of 8, 10, and 12 segments (8-, 10-, 12-mer). The effect of molecular flexibility on the isotropic-nematic equilibrium is studied for a Lennard-Jones 10-mer chain fluid with one freely-jointed segment at the end of the chain. An isotropic-nematic phase split and fractionation are reported for a binary mixture of linear 7-mer and 12-mer chains. Simulation results are compared with theoretical results as obtained from a recently developed analytical equation of state based on perturbation theory. Excellent agreement between theory and simulations is observed. The solubility of a monomer Lennard-Jones gas in the coexisting isotropic and nematic phases is estimated using the Widom test-particle insertion method. A linear relationship between solubility difference and density difference at isotropic-nematic coexistence is observed. It is shown that gas solubility is independent of the nematic ordering of the fluid, at constant temperature and density conditions.