Mendis Budhika G
Department of Physics, Durham University, South Road, Durham, DH1 3LE, United Kingdom.
Acta Crystallogr A Found Adv. 2025 Mar 1;81(Pt 2):113-123. doi: 10.1107/S2053273325000142. Epub 2025 Jan 30.
Bloch waves are often used in dynamical diffraction calculations, such as simulating electron diffraction intensities for crystal structure refinement. However, this approach relies on matrix diagonalization and is therefore computationally expensive for large unit cell crystals. Here Bloch wave theory is re-formulated using the physical optics concepts underpinning the multislice method. In particular, the multislice phase grating and propagator functions are expressed in matrix form using elements of the Bloch wave structure matrix. The specimen is divided into thin slices, and the evolution of the electron wavefunction through the specimen calculated using the Bloch phase grating and propagator matrices. By decoupling specimen scattering from free space propagation of the electron beam, many computationally demanding simulations, such as 4D STEM imaging modes, 3D ED precession and rotation electron diffraction, phonon and plasmon inelastic scattering, are considerably simplified. The computational cost scales as {\cal O}({N^2} ) per slice, compared with {\cal O}({N^3} ) for a standard Bloch wave calculation, where N is the number of diffracted beams. For perfect crystals the performance can at times be better than multislice, since only the important Bragg reflections in the otherwise sparse diffraction plane are calculated. The physical optics formulation of Bloch waves is therefore an important step towards more routine dynamical diffraction simulation of large data sets.
布洛赫波常用于动力学衍射计算，例如模拟用于晶体结构精修的电子衍射强度。然而，这种方法依赖于矩阵对角化，因此对于大晶胞晶体而言计算成本很高。在此，利用支撑多层法的物理光学概念对布洛赫波理论进行了重新表述。具体而言，多层相位光栅和传播函数使用布洛赫波结构矩阵的元素以矩阵形式表示。将样品分成薄片，并使用布洛赫相位光栅和传播矩阵计算电子波函数在样品中的演化。通过将样品散射与电子束在自由空间中的传播解耦，许多计算量很大的模拟，如4D STEM成像模式、3D ED进动和旋转电子衍射、声子和等离子体非弹性散射等，都得到了显著简化。计算成本按每片({\cal O}({N^2} ))缩放，而标准布洛赫波计算的成本为({\cal O}({N^3} ))，其中(N)是衍射束的数量。对于完美晶体，其性能有时可能优于多层法，因为只计算了原本稀疏衍射平面中重要的布拉格反射。因此，布洛赫波的物理光学表述是朝着对大数据集进行更常规的动力学衍射模拟迈出的重要一步。
