三维自由边界耦合软模

The 3-Dimension Free Boundary Coupling Soft Modes

将二维有限品格动力学方法推广到三维。讨论投影算符方法在大自由度有限体系问题中的应用。经群论方法化简后用数字计算解出了计及8体相互作用的N×N′×N″单原子立方晶格振动模和简谐频率。给出晶格边界具有O_h,D_(4h)和D_(2h)对称时的空间型相关表和不同空间型中简谐解的个数。相应于二维情况下出现的一个全对称型自由边界耦合软模,推广到三维后发现存在3个类似的软模。从模矢量图看出,Eg型自由边界耦合软模相应于钛酸钡铁电相变时出现的声学软模。

The projection operator method can be used for directly solving the vibrating modes and spectrum of a finite lattice.For degenerate modes,an effective char-acter is defined.The species correlation of modes in a cubic crystal is givenusing the projection operator method.The problem for a N×N′×N″ cubic latticeis solved up to 6×6×6 in nearest-neighour approximation accounting 3-body in-teraction,and the free boundary coupling soft modes are resulted.When covanle-nt characteristics of a crystal strengthens,the lowest soft mode A_1g-1 leads the smaller crystallite and becomes easier to melt or sublimate;and other doublet soft modes Eg-17 and Eg-19 are related to the acoustic soft mode presenting in the ferroelectric transition of barium titanate.The A_1g-1,Eg-17 and Eg-19 mode vector patterns are presented.