xrd report

adv_lab.bib

@@ -1,3 +1,11 @@
+@online{MACNIST,
+  author={Hubbell, J.H. and Seltzer, S.M.},
+  title={Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients from 1 KeV to 20 MeV for Elements Z=1 to 92 and 48 Additional substances of Dosimetric Interest},
+  publisher={NIST},
+  year={1996},
+  url={http://www.nist.gov/pml/data/xraycoef/index.cfm}
+  }
+
 @online{fundcrystal,
   author = {Cook, Joseph},
    }
@@ -9,6 +17,20 @@ howpublished = {\url{www.panalytical.com/Xray-diffraction-software/HighScore/Spe
 year = {2016}
 }
 
+@online{naclwiki,
+  title="Sodium Chloride",
+  month=apr,
+  year={2017},
+  url={https://en.wikipedia.org/wiki/Sodium_chloride}
+}
+
+@online{carbonwiki,
+  title="Carbon",
+  month=apr,
+  year={2017},
+  url={https://en.wikipedia.org/wiki/Carbon}
+}
+
 @ONLINE{empyrean,
 title = {PANalytical - Empyrean},
 month = apr,
@@ -23,8 +45,6 @@ year = {2017},
 url = {http://www.panalytical.com/XCelerator/Specifications.htm}
 }
 
-
-
 @techreport{advlabxrd,
   author = {Burns, Clem},
   title = {X-ray Diffraction},
@@ -35,7 +55,6 @@ url = {http://www.panalytical.com/XCelerator/Specifications.htm}
   type = {Lab Guide}
 }
 
-
 @MISC{xraytubephoto,
   author = {},
   title = {X-ray Tube},
@@ -50,6 +69,18 @@ url = {http://www.panalytical.com/XCelerator/Specifications.htm}
 
 
 
+@article{10.1021/ja01631a014,
+  author = {Wallace, W.E. and Barrett, W.T.},
+  title = {Studies of NaCl-KCl Solid solutions.},
+  journal = {Journal of the American Chemical Society},
+  volume = {76},
+  pages = {366-369},
+  year = {1954},
+  doi = {10.1021/ja01631a014}
+}
+
+
+
 
 
 @misc{Xraybinary,

xrd/report/report.tex

@@ -103,26 +103,63 @@ Western Michigan University's new X-ray Diffractometer is used to probe four mat
 
         The modern approach to analyzing materials by Bragg diffraction is to interpret the output as the reciprocal space representation of the lattice positions. An inverse Fourier transform then gives the positions that make the lattice. The HighScore Plus software, associated with the Empyrean XRD, is used to perform these operations. \cite{highscore} It computes a spacing constant in angstroms, which can be interpretted as the cubic lattice constant, and other quantities.
 
+        A crystal powder sample will have random orientations across all possible rotations in 3 dimensions; we call this powder diffraction. In a cubic crystal the Miller indices ($h k l$) describe the orientation of the planes, thereby predicting a periodic lattice points along the z-axis that will produce constructive interference. While the lattice constant does not change, each orientation may result in a different diffraction spacing, so a powder diffraction will result in a diffraction pattern where signals are observed at many angles. The lattice constant can be computed in each case.
 
+        \subsection{Structure of Samples}
+        \label{subsec:nacl}
+
+        The structure of some samples tested here are known. Sodium-Chloride is a face-centered cubic lattice with lattice constant $a = 564.02 pm$. \cite{naclwiki} The allowed miller indices for a FCC lattice are given in Table~\ref{tab:cubicstructure}, with the computed diffraction spacing. 
 
 
 
 \section{Computational Details}
     \label{sec:compdets}
-    The phase of the X-rays are not known, so the program determines the phase by fitting predicted profiles. A background is determined using the minimum 2nd derivative method with ``bending factor'' = 5, ``granularity'' = 20, and using smoothed input data. Peaks are located with ``minimum significant'' = 10.00, ``minimum tip width'' = 0.01, ``maximum tip width'' = 1.00, and ``peak base width'' = 2.00. The program was able to identify the copper Bragg diffraction pattern, which was very prominent, seen in Figure~\ref{fig:cudiff}.
+    The phase of the X-rays are not known, so the program determines the phase by fitting predicted profiles. A background is determined using the minimum 2nd derivative method with ``bending factor'' = 5, ``granularity'' = 20, and using smoothed input data. Peaks are located with ``minimum significant'' = 10.00, ``minimum tip width'' = 0.01, ``maximum tip width'' = 1.00, and ``peak base width'' = 2.00. The program was able to identify the copper Bragg diffraction pattern, which was prominent, seen in Figure~\ref{fig:cudiff}.
+
+
+    \subsection{Penetration Depth}
+    	\label{subsec:pendepth}
+
+    	The penetration depth is computed for each material. The defining formula
+
+    	\begin{equation}
+    		I_L = I_0 \times e^{-(\frac{\mu}{\rho}\rho L)}
+    	\end{equation}
+    
+    	is valid for symmetric (gonio) scans. \cite{highscore} The HighScore Plus software is able to compute these values, reported in Table~\ref{tab:pendepth}. Computing the penetration depth relies on mass attentuation coefficient, the specific gravity of the material, and a packing number. The powder packing ratio for NaCl is estimated at 0.7 and for any amorphous samples 0.6. NaCl's density is reported as 2.165 g/cm$^3$ \cite{naclwiki}, and for the amorphous samples the amorphous carbon density 2.0 g/cm$^3$. \cite{carbonwiki}. Penetration is computed for an incidence angle 90\degree, which gives maximum penetration. The mass attenuation coefficients are taken from the NIST Hubbell and Seltzer database, and are 73.7 cm$^2$/g for NaCl and 4.3 cm$^2$/g for amorphous carbon. \cite{MACNIST}
+
+    	for NaCl: penetration depth  206.156 $\mu m$ ; 111.692 1/cm linear abs. coeff
+
+    	for Carbon: 4462.403 $\mu m$; 8924.806 1/cm
+
+    	383 8872
+
+    	\cite{10.1021/ja01631a014}
+
+
+
 
 
     \begin{figure}
         \centering
-        \includegraphics[width=4in]{}
+        %\includegraphics[width=4in]{}
+        \caption{[A] HighScore Plus identified the characteristic NaCl diffraction pattern from Cu K-$\alpha$ and K-$\beta$ emission, and this is used to fit the phase and in turn determine the lattice constant. [B] The detector measurements (red) strongly correlate to the computed diffraction lines (blue).}
     \end{figure}
 
 
 
+
+
+
+
+
+
+
 %─────────────    
 \section{Results}
     \label{sec:results}
 
+    The observed diffraction pattern from NaCl is presented in Figure~\ref{fig:nacldiffraction}. The HighScore software 
 
 %─────────────
 \section{Conclusion}