Corners of self-conjugate (s,s + 1)-cores and (s‾,s+1‾)-cores

In this paper, we describe a result on self-conjugate $(s,s+1)$-core partitions with the fixed number of corners. We also define shifted corners of a distinct partition and find formulas for the number of $(\stackrel{￣}{s},\stackrel{￣}{s+1})$-core partitions and the number of $(s,s+1)$-core shifted Young diagrams with the fixed number of shifted corners.     

Measured and Predicted Solubility Phase Diagrams of Quaternary Systems LiBr-NaBr-MgBr2-H2O and LiBr-KBr-MgBr2-H2O at 298.15 K

The stable phase equilibria of quaternary systems LiBr-NaBr-MgBr₂-H₂O and LiBr-KBr-MgBr₂-H₂O at 298.15 K were studied by both experimental measurement(isothermal solution saturation method) and theoretical prediction(Pitzer model). The solubilities of the saturated solution have been determined experimentally and two stable phase diagrams and relevant water diagrams of the two quaternary systems were obtained. Results show that quaternary system LiBr-NaBr-MgBr₂-H₂O is hydrate II type as NaBr and NaBr·2H₂O coexistence. Its phase diagram consists of only one invariant point, four univariant curves, and five crystallization fields. The quaternary system LiBr-KBr-MgBr₂-H₂O is a complex type as the double salt KBr·MgBr₂·6H₂O formed. In addition to this double salt, the three single salts LiBr·2H₂O, KBr and MgBr₂·6H₂O also crystallize. In this paper, the solubilities of phase equilibria in above quaternary systems were also calculated by the Pitzer's electrolyte solution model. All the needed parameters can be obtained from the literature or be fitted by experimental data. On the Basis of the experimental and calculated results, the phase diagram of the quaternary system was plotted for comparison. It shows that the calculation results are consistent with the experimental ones.     

Phase transition in the one-dimensional pair-hopping model with unusual one-electron hopping

By modifying the conventional one-electron hopping behavior, we study effects of an occupation-dependent hopping on the ground state of the half-filled one-dimensional pair-hopping model. At weak coupling, the use of bosonization and renormalization-group analysis techniques helps to derive the phase diagram. Such unusual hopping is shown to drive a spin-gap transition and to introduce a new region where the triplet superconducting instability dominates for positively small pair-hopping interaction.     

单斜氧化锆表面水合和脱水的动态模拟

常用的氧化物负载金属催化剂通常在水相中制备，且在使用前常常需要经过煅烧. 因此，氧化物载体表面的水合和脱水过程对于负载型金属催化剂的真实建模至关重要. 通过第一性原理分子动力学模拟，本文考察了温和温度下无水单斜氧化锆(111)表面在显式溶剂水中的演化. 在模拟过程中，所有的双重配位桥位氧位点很快被溶剂水质子化，形成酸性羟基(HO_L)，并在锆原子上留下碱性羟基(HO^*). 这些碱性羟基(HO^*)可以与表面未解离的吸附水分子(H₂O^*$)进行活跃的质子交换，进而在表面自由扩散. 在273 K到373 K的温度范围下，第一性原理分子动力学水相模拟可以得到一种较为确定的、有代表性的平衡水合单斜氧化锆(111)表面，其表面锆原子上覆盖度(θ)为0.75. 随后，为了模拟低于800 K的温和煅烧温度下的表面脱水过程，本文使用密度泛函理论计算了表面水分子的逐步脱附自由能. 通过获得表面的脱水相图，总结了不同煅烧温度下有代表性的、部分水合的单斜氧化锆(111)表面(0.25≤θ<0.75). 这些水合单斜氧化锆(111)表面具有重要的理论意义，可以方便快捷地被应用于氧化锆催化剂及氧化锆负载金属催化剂的真实建模与模拟.     

Thermochemical investigation of Zr doping in LiNi8/12Co2/12Mn2/12O2 based on phase equilibria simulation

The doping behavior of Zr in LiNi_8/12Co_2/12Mn_2/12O₂ (LNCM) is investigated by a simulation of the phase equilibria for the Li-(M^*,Zr)-O system (M^* = Ni, Co, Mn) based on first-principles calculations followed by a thermochemical post-analysis of the resultant phase diagrams. The results indicate that the stable state at the synthetically stoichiometric composition of LNCM with Zr is a mixture of undoped LNCM with a Li₂ZrO₃ secondary phase; doping of Zr in the LNCM crystal is not thermodynamically favored. The energies of various states comprising LNCM supercells with defects, secondary phases, and Zr doping are examined, and the equilibrium doping concentration of Zr is calculated by considering the entire LNCM:Zr crystal as a statistical combination of these states. The doping concentration of Zr in the LNCM crystal is calculated to be very low, which enables balanced control between doping and coating, as recently reported through experimentation. The dopability of Zr is expected to increase with the depletion of O₂ supply during the heating of a system with a precisely controlled Li to M^* ratio, but this behavior is affected by the formation of defects, especially by M^* substitution for Li.