Darwin-Howie-Whelan Equation for a Strained Crystal

Available identifiers

MaRDI QIDQ6674129

simuating TEM images by numerically solving the Darwin–Howie–Whelan equation describing the electron propagation

Defining Formula: $\begin{array}{cc}\frac{\mathrm{d}}{\mathrm{d}z}{\phi }_{𝐠}(z)& =2\mathrm{i}\pi (s_{𝐠}+\frac{\mathrm{d}}{\mathrm{d}z}(𝐠\cdot 𝐮(𝐫))){\phi }_{𝐠}(z)+\mathrm{i}\pi \sum _{𝐡\in {\Lambda }_m^{*}}{U}_{𝐠\mathbf{-}𝐡}{\phi }_{𝐡}(z)\\ s_g& =-\frac{g\cdot (2k_0+g)}{2n\cdot (k_0+g)}\end{array}$

$U_g$ symbol represents Electric Potential Fourier Coefficients

${\Lambda }_m^{*}$ symbol represents Reciprocal Lattice

${\psi }_g$ symbol represents Amplitude of Electron Wave

$g$ symbol represents Reciprocal Lattice Vectors

$k_0$ symbol represents Wave Vector of an Electron

$n$ symbol represents Unit Normal Vector

$s_g$ symbol represents Excitation Error

$u$ symbol represents Displacement of Atoms

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