Phonon dispersion relation

Phonon dispersion relation

Yanming Wang, Saad Bhamla and Wei Cai

May, 2012

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Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V({r_i}) = V({R_i})+\frac{1}{2}\sum_{i,j}U_i^T\cdot \left[ \frac{\partial^2V}{\partial r_i\partial r_j} \right]\cdot U_j}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left[ {\begin{array}{ccc} \frac{\partial^2V}{\partial x_i\partial x_j} & \frac{\partial^2V}{\partial x_i\partial y_j} & \frac{\partial^2V}{\partial x_i\partial z_j} \\ \frac{\partial^2V}{\partial y_i\partial x_j} & \frac{\partial^2V}{\partial y_i\partial y_j} & \frac{\partial^2V}{\partial y_i\partial z_j} \\ \frac{\partial^2V}{\partial z_i\partial x_j} & \frac{\partial^2V}{\partial z_i\partial y_j} & \frac{\partial^2V}{\partial z_i\partial z_j} \\ \end{array}} \right] }