diff --git a/docs/Equations.md b/docs/Equations.md index 45ad22e..66e6925 100644 --- a/docs/Equations.md +++ b/docs/Equations.md @@ -2,10 +2,6 @@ The Debye scattering equation is used to calculate scattering intensities from atomic structures considering the position of each atom in the structure: -\begin{equation}\label{eq:Debye} -I(Q) = \sum_{\nu=1}^{N} \sum_{\mu=1}^{N} b_{\nu} b_{\mu} \frac{\sin(Qr_{\nu\mu})}{Qr_{\nu\mu}} -\end{equation} - $$ I(Q) = \sum_{\nu=1}^{N} \sum_{\mu=1}^{N} b_{\nu} b_{\mu} \frac{\sin(Qr_{\nu\mu})}{Qr_{\nu\mu}} $$ @@ -14,12 +10,19 @@ In this equation $Q$ is the momentum transfer of the scattered radiation, $N$ is # S(Q) -XX +$$ +S(Q) = \frac{I_{\text{coh}}(Q) + \langle f(Q) \rangle^2 - \langle f(Q)^2 \rangle}{N \langle f(Q) \rangle^2} - 1 +$$ # F(Q) -XX +$$ +F(Q) = Q \left( S(Q) \right) +$$ + # G(r) -XX \ No newline at end of file +$$ +G(r) = \frac{2}{\pi} \int_{Q_{\text{min}}}^{Q_{\text{max}}} F(Q) \sin(Qr) \, dQ +$$