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Each element ''H''<sub>''i'',''j''</sub> is a 3 × 3 matrix which holds the anisotropic information regarding the orientation of nodes ''i'',''j''. Each such sub matrix (or the "super element" of the Hessian) is defined as
: <math>H_{ij} = \begin{bmatrix} {\partial^2 V_{ij}\over\partial x_i \, \partial x_j} & {\partial^2 V_{ij}\over\partial x_i \, \partial y_j} & {\partial^2 V_{ij}\over\partial x_i \, \partial z_j} \\ {\partial^2 V_{ij}\over\partial y_i \, \partial x_j} & {\partial^2 V_{ij}\over\partial y_i \, \partial y_j} & {\partial^2 V_{ij}\over\partial y_i \, \partial z_j} \\ {\partial^2 V_{ij} \over\partial z_i \, \partial x_j} & {\partial^2 V_{ij}\over\partial z_i \, \partial y_j} & {\partial^2 V_{ij}\over\partial z_i \, \partial z_j}\end{bmatrix}. </math>
Using the definition of the potential, the Hessian can be expanded as
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