Updated Equations.md

docs/Equations.md

@@ -1,28 +1,32 @@
-# I(Q)
+# The scattering intensity - $I(Q)$
 
 The Debye scattering equation is used to calculate scattering intensities from atomic structures considering the position of each atom in the structure:
 
 $$
-I(Q) = \sum_{\nu=1}^{N} \sum_{\mu=1}^{N} b_{\nu} b_{\mu} \frac{\sin(Qr_{\nu\mu})}{Qr_{\nu\mu}}
+I(Q) = \sum_{\nu=1}^{N} \sum_{\mu=1}^{N} b_{\nu}(Q) b_{\mu}(Q) \frac{\sin(Qr_{\nu\mu})}{Qr_{\nu\mu}}
 $$
 
 In this equation $Q$ is the momentum transfer of the scattered radiation, $N$ is the number of atoms in the structure, and $r_{\nu\mu}$ is the distance between atoms $\nu$ and $\mu$. For X-ray radiation, the atomic form factor, $b$, depends strongly on $Q$ and is usually denoted as $f(Q)$, but for neutrons, $b$ is independent of $Q$ and referred to as the scattering length. 
 
-# S(Q)
+# The Total Scattering Structure Function - $S(Q)$
 
+The Total Scattering Structure Functionm, $S(Q)$, is calculated as:
 $$
-S(Q) = \frac{I_{\text{coh}}(Q) + \langle f(Q) \rangle^2 - \langle f(Q)^2 \rangle}{N \langle f(Q) \rangle^2} - 1
+S(Q) = \frac{I_{\text{coh}}(Q) + \langle b(Q) \rangle^2 - \langle b(Q)^2 \rangle}{N \langle b(Q) \rangle^2} - 1
 $$
+Where $I_{coh}$ is the scattering intensity as we only simulate the coherent scattering signal.
 
-# F(Q)
+# The Reduced Total Scattering Function - $F(Q)$
 
+The Reduced Total Scattering Function, $F(Q)$, is calculated as:
 $$
 F(Q) = Q \left( S(Q) \right)
 $$
 
+# The Reduced Atomic Pair Distribution Function - $G(r)$
 
-# G(r)
-
+The Reduced Atomic Pair Distribution Function, $G(r)$, is calculated as:
 $$
-G(r) = \frac{2}{\pi} \int_{Q_{\text{min}}}^{Q_{\text{max}}} F(Q) \sin(Qr) \, dQ
+G(r) = \frac{2}{\pi} \int_{Q_{\text{min}}}^{Q_{\text{max}}} F(Q) \sin(Qr) \dQ
 $$
+Where $Q_{min}$ and $Q_{max}$ is the minimum and maximum Q-values of the data.