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The above is a direct outcome of one of the key underlying assumptions of ANM - that a given crystal structure is an energetic minimum and does not require energy minimization.
The force constant of the system can be described by the [[Hessian
: <math>\Eta = \begin{bmatrix} {H_{ii}} & {H_{ij}} \\ {H_{ji}} & {H_{jj}} \end{bmatrix}. </math>
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
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