Electron backscatter diffraction: Difference between revisions

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Where <math>C</math> is the crystal anisotropic stiffness tensor. These two equations are solved to re-calculate the refined elastic deviatoric strain (<math>\varepsilon_{kl}</math>), including the missing ninth (spherical) strain tensor. An alternative approach that considers the full <math>\beta</math> can be found in.<ref name=":17" />

<math>e_{ij}=\begin{pmatrix} {e_{11}} \\{e_{22}} \\{e_{33}}\\{2e_e_{12}+e_{21}}\\{2e_e_{13}+e_{31}}\\{2e_e_{23}+e_{32}} \\\end{pmatrix}, \qquad \begin{pmatrix} {k_{1}} \\{k_{2}} \\{k_{3}} \\\end{pmatrix}=\begin{pmatrix} {e_{11}-e_{33}} \\{e_{22}-e_{33}} \\{e_{12}C_{3312}+e_{13}C_{3313}+e_{23}C_{3323}} \\\end{pmatrix}</math>

<math>\varepsilon_{33}={k_1C_{1133}+k_2C{2233}+k_3\over C_{1133}+C_{2233}+C_{3333}},\qquad \therefore\varepsilon_{kl}=\begin{pmatrix} {k_1+\varepsilon_{33}} \\{k_2+\varepsilon_{33}} \\{\varepsilon_{33}}\\{2e_{12}}\\{2e_{13}}\\{2e_{23}} \\\end{pmatrix}</math>