fix_orient_fcc.tex
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	\newcommand{\br}{\mathbf{r}}

	\documentclass[12pt]{article}

	\begin{document}

	\begin{equation}
	\xi_{i} = \sum_{j=1}^{12} \left\| \br_{j} - \br_{j}^{\rm I} \right\|
	\end{equation}

	\begin{equation}
	\xi_{\rm IJ} = \sum_{j=1}^{12} \left\| \br_{j}^{\rm J} - \br_{j}^{\rm I} \right\|
	\end{equation}

	\begin{eqnarray}
	\xi_{\rm low} &=& {\rm cutlo} \, \xi_{\rm IJ} \\
	\xi_{\rm high} &=& {\rm cuthi} \, \xi_{\rm IJ}
	\end{eqnarray}

	\begin{eqnarray}
	\omega_{i} &=& \frac{\pi}{2}
	\frac{\xi_{i} - \xi_{\rm low}}{\xi_{\rm high} - \xi_{\rm low}} \\
	\mbox{\hspace*{72pt}} \nonumber \\
	u_{i} &=& 0 \mbox{\hspace{84pt} for } \xi_{i} < \xi_{\rm low} \nonumber \\
	&=& {\rm dE}\,\frac{1 - \cos(2 \omega_{i})}{2}
	\mbox{\hspace{10pt} for } \xi_{\rm low} < \xi_{i} < \xi_{\rm high} \\
	&=& {\rm dE} \mbox{\hspace{80pt} for } \xi_{\rm high} < \xi_{i}
	\nonumber
	\end{eqnarray}
	\end{document}