First-principles study on the geometric and electronic structures and phase transition of PbZr1-xTixO3 solid solutions

With first-principles virtual-crystal approximation calculations, we systematically investigate the geometric and elec- tronic structures as well as the phase transition of lead zirconate titanate (PbZr1-xTixO3 or PZT) as a function of Ti content for the whole range of 0 ≤ x Ti ≤ 1. It can be found that, with the increase of the Ti content, the PbZr1-xTixO3 solid solu- tions undergo a rhombohedral-to-tetragonal phase transition, which is consistent with the experimental results. In addition, we also show the evolution in geometric and electronic structures of rhombohedral and tetragonal PbZr1-x TixO3 with the increasing content of Ti.     

广义模糊子半环的广义模糊双(内)理想

给出了广义模糊子半环的广义模糊双(内)理想的概念.运用截集、模糊子集的和与积得到了广义模糊子半环的广义模糊双(内)理想的等价条件及性质,同时还得到了在半环的同态映射下同态像及同态原像的性质.当λ=0,μ=1时,得到一般意义下的模糊子半环的模糊双(内)理想的相应结果.