An incommensurate modulated structure is the - Methods of ：非公度调制结构的方法.pptVIP

* * * What’s a modulated structure ? Muti-dimensional direct methods of solving modulated structures Incommesurate modulation in Bi-based supercondutors from electron crystallography What’s a Modulated Structure ? t T T = 0 (mod t) or MOD (T, t) = 0 Commensurate modulation T superstructures T T T 1 0 (mod t) or MOD (T, t) 1 0 Incommensurate modulation T incommensurate structures T T a* b* q Schematic diffraction pattern of an incommensurate modulated structure Conclusion In the reciprocal space: The diffraction pattern of an incommen-surate modulated crystal is the projection of a 4- or higher-dimensional weighted lattice In the direct space: An incommensurate modulated structure is the “hypersection” of a 4- or higher-dimensional periodic structure cut with the 3-dimensional physical space Representation of one-dimensionally modulated incommensurate structures Lattice vectors in real- and reciprocal- space Structure-factor formula Modulated atoms situated at their average positions Modified Sayre Equations in multi-dimensional space Strategy of solving incommensurate modulated structures i) Derive phases of main reflections ii) Derive phases of satellite reflections iii) Calculate the multi-dimensional Fourier map iv) Cut the resulting Fourier map with the 3-D ‘hyperplane’ (3-D physical space) v) Parameters of the modulation functions are measured directly on the multi-dimensional Fourier map using using Electron Crystallographic Study of Bi-based Superconductors using Multi-dimensional Direct Methods Why Electrons ? 1. Electrons are better for studying minute and imperfect crystalline samples 2. Electron microscopes are the only instrument that can produce simultaneously EM’s and ED’s for the same crystalline sample at atomic resolution 3. Electrons are better for revealing light atoms in the presence of heavy atoms Scattering of X-rays and Electrons by Different Elements Relat