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The complex interplay of elastic and inelastic scattering amenable todifferent levels of approximation constitutes the major challenge for thecomputation and hence interpretation of TEM-based spectroscopical methods. Thetwo major approaches to calculate inelastic scattering cross sections of fastelectrons on crystals-Yoshioka-equations-based forward propagation and thereciprocal wave method-are founded in two conceptually differing schemes-anumerical forward integration of each inelastically scattered wave function,yielding the exit density matrix, and a computation of inelastic scatteringmatrix elements using elastically scattered initial and final states (doublechanneling). Here, we compare both approaches and show that the latter iscomputationally competitive to the former by exploiting analytical integrationschemes over multiple excited states. Moreover, we show how to include fullnonlocality of the inelastic scattering event, neglected in the forwardpropagation approaches, at no additional computing costs in the reciprocal wavemethod. Detailed simulations show in some cases significant errors due to thez-locality approximation and hence pitfalls in the interpretation ofspectroscopical TEM results.

Fully nonlocal inelastic scattering computations for spectroscopical transmission electron microscopy methods