Titanium production in a plasma reactor: A feasibility investigation

The feasibility of producing titanium metal from titanium tetrachloride in a thermal plasma under equilibrium and adiabatic expansion conditions has been theoretically investigated. Free energy minimization and adiabatic expansion calculations to simulate a nozzle expansion were used to study the practicality of production. The crucial requirements for the production of titanium powder from TiCl₄ and H₂ appear to be rapid quenching of the plasma gas at high temperature (e.g., 3700 K) and appropriate reactant concentrations. Quenching of tire plasma gas and production of titanium powder can be achieved by adiabatic expansion through a nozzle. Preliminary experimental data indicate that titanium powder of approximately 5 nm in size can be produced in an argon plasma rising a nozzle expansion approach.     

第一性原理计算钛酸铅A位掺杂对其负热膨胀性的影响

近年来,实验发现钛酸铅基材料具有负热膨胀性,且其热膨胀程度会受到掺杂元素的影响. 目前所研究的A位掺杂体系中,仅Cd原子掺杂能使钛酸铅负热膨胀性增强. 所以研究A位掺杂钛酸铅,比较Cd原子与其他原子在掺杂钛酸铅时化学键的异同,有助于深刻理解钛酸铅负热膨胀的本质. 本文利用第一性原理,分别优化了Sr、Ba、Cd掺杂钛酸铅的晶格常数,计算了它们的态密度和电荷密度. 结果表明Cd―O键的共价性强于Pb―O键,而Ba―O键和Sr―O键几乎呈离子性,Ba/Sr对Pb的替代削弱了化合物的共价性,降低了自发极化强度. 与实验测量的热膨胀系数对比可以发现,A位原子与氧原子之间的共价性增强,化合物负热膨胀程度升高;若A位原子与氧原子之间的共价性削弱,负热膨胀程度降低. 可见A位原子与氧原子之间的共价性影响了钛酸铅基化合物负热膨胀性.     

Synthesis, Structures, and Thermal Expansion of the La2W2−xMoxO9 Series

The La₂W_2−xMo_xO₉ series has been synthesized by the ceramic method. An alternative synthesis using microwave radiation is also reported. La₂W₂O₉ has two polymorphs and the low-temperature phase (α) transforms to the high-temperature form (β) at 1077°C. The influence of the W/Mo substitution in this phase transition has been investigated by DTA. The β structure for x≥0.7 compositions can be prepared as single phase at any cooling rate. The β phase for 0.3≤x≤0.7 compounds can be prepared as single phase by quenching, whereas a mixture of α and β phases is obtained by slow cooling. The W/Mo ratio in both coexisting phases is different with the β-phase having a higher Mo content. The x=0.1 and 0.2 compounds have been prepared as mixtures of phases. The room temperature structure of β-La₂W_1.7Mo_0.3O₉ has been analyzed by the Rietveld method in P2₁3 space group. The final R-factors were R_WP=9.0% and R_F=5.6% with a structure similar to that of β-La₂Mo₂O₉. Finally, the thermal expansion of both types of structures has been determined from a thermodiffractometric study. The thermal expansion coefficients were 2.9×10⁻⁶ and 9.7×10⁻⁶°C⁻¹ for α-La₂W₂O₉ and β-La₂W_1.2Mo_0.8O₉, respectively.     

Low-temperature heat capacity of dysprosium diboride

A novel microcalorimeter based on a miniature liquid-in-glass thermometer is described. Heat is transduced into an optical, rather than electrical, signal, facilitating a future array format. The instrument performs batch analysis (drop mixing) with a 2 μL sample volume. Energy changes of 4 μJ produced by a dilution of sulfuric acid are resolvable. The effect of evaporation, and measures taken to limit it, are discussed.     

Thermal properties of rare earth dodecaborides

We have measured heat capacity and thermal expansion of rare earth dodecaborides REB₁₂ (RE=Y, Tb-Tm, Lu). YB₁₂ and LuB₁₂ are diamagnetics whereas the other dodecaborides are ordered antiferromagnetically. The amplitude of the heat capacity discontinuity at the Néel temperature and the shape of the heat capacity variation in the critical region for all these antiferromagnetics are characteristics for amplitude-modulated magnetic structures. In the ordered state TbB₁₂ reveals two first-order phase transitions, most likely due to magnetic structure changes. The heat capacity of ErB₁₂ just below the Néel point shows an anomaly of unclear origin. From the Schottky contribution to the heat capacity we have determined crystal field parameters. They are completely different than that is estimated from Point Charge Model.     

Schrödinger Equation Solutions for the Central Field Power Potential Energy I. V(r) = V 0(r/a 0)2ν−2, ν ≥ 1

The solution of a generalized non-relativistic Schrödinger equation with radial potential energy V(r)=V ₀(r/a ₀)^2–2 is presented. After reviewing the general properties of the radial ordinary differential equation, power series solutions are developed. The Green's function is constructed, its trace and the trace of its first iteration are calculated, and the ability of the traces to provide upper and lower bounds for the ground eigenvalue is examined. In addition, WKB-like solutions for the eigenvalues and eigenfunctions are derived. The approximation method yields valid eigenvalues for large quantum numbers (Rydberg states).     

Self-ordering process of phenanthrene polyesters observed by the simultaneous DSC-XRD method

Phase transition behavior of polyesters derived from 2,7-phenanthrene dicarbonic acid diethylester and alkanediols with even methylene carbon number was investigated by the simultaneous DSC-XRD method. The smectic A phase was observed on cooling from the molten state. The transition entropy from the isotropic state to the smectic A phase was about 9.0 J mol^-1 K^-1, which depended on the methylene carbon number. The linear expansion coefficients, based on the (001) spacing of the crystalline phase at room temperature, were 1.3·10^-4 K^-1 (crystalline phase), 5.7·10^-4 K^-1 (crystallization region), 1.7·10^-3 K^-1 (smectic A phase) during cooling, and 1.5·10^-4 K^-1 (crystalline phase), and 1.0·10^-3K^-1(melting region) on heating. This revised version was published online in July 2006 with corrections to the Cover Date.     

The methoxycarbonylcarbene insertion into 1,3-dithiolane and 1,3-oxathiolane rings

Treatment of substituted 1,3-dithiolanes and 1,3-oxathiolanes with methyl diazoacetate in the presence of Rh₂(OAc)₄ effects ring expansion to the corresponding substituted 1,4-dithiane-2-carboxylates and 1,4-oxathiane-3-carboxylates. The sulfur ylides initially generated in these reactions undergo Stevens rearrangement in competition with both [2,3]-C-C-sigmatropic rearrangement and intramolecular fragmentation. In the case of 2-styryl-substituted 1,3-oxathiolane and 1,3-dithiolane, ring expansion on one-, three- and four-carbons subsequently takes place.     

Construction of Spatiotemporal-Coupling Optimal Low-Dimensional Dynamical Systems for Compressible Navier-Stokes Equations; [可压缩 Navier-Stokes 方程的时空耦合优化低维动力系统建模方法]北大核心CSCD

For the low-dimensional dynamical system model to study dynamics properties of Navier-Stokes equations, it is very important that the attraction domain of the low-dimensional model is the same as that of Navier-Stokes equations. However, to date, there is no universal approach to ensure this purpose for general problems. Herein, it is found that any low-dimensional model based on spatial bases, such as proper orthogonal decomposition bases, optimal spatial bases, and other classical spatial bases, is not predictable, i.e., the error increases with the time evolution of the flow field. With the theoretical framework for building optimal dynamical systems and the new concept of spatiotemporal-coupling spectrum expansion, the low-dimensional model for compressible Navier-Stokes equations was constructed to approximate the numerical solution to large-eddy simulation equations, and the numerical results and novel time evolution of spatiotemporal-coupling bases were given. The entire field error is typically below 10−2%, and the average error at each grid point is below 10−8%. The spatiotemporal-coupling optimal low-dimensional dynamical systems can ensure that the attraction domain of the low-dimensional model is the same as that of Navier-Stokes equations. Therefore, characteristic dynamics properties of spatiotemporal-coupling optimal low-dimensional dynamical systems are the same as those of real flow. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Uniqueness and clustering properties of Gibbs states for classical and quantum unbounded spin systems

We consider quantum unbounded spin systems (lattice boson systems) in -dimensional lattice space Z. Under appropriate conditions on the interactions we prove that in a region of high temperatures the Gibbs state is unique, is translationally invariant, and has clustering properties. The main methods we use are the Wiener integral representation, the cluster expansions for zero boundary conditions and for general Gibbs state, and explicitly -dependent probability estimates. For one-dimensional systems we show the uniqueness of Gibbs states for any value of temperature by using the method of perturbed states. We also consider classical unbounded spin systems. We derive necessary estimates so that all of the results for the quantum systems hold for the classical systems by straightforward applications of the methods used in the quantum case.