\pagestyle{plain}\clearpage\centerline{\Huge  Question Sheet 1}

\begin{enumerate}
\item Draw an accurate 127~mm diameter stereogram of a cubic crystal centred on (001), showing all poles of the form $\{100\}$, $\{110\}$ and $\{111\}$.

A single crystal of copper deforms simultaneously on the slip planes (111) and $(1\overline 11)$. When dislocations on these planes intersect the free surface they leave the traces of the planes visible on the free surface.
\begin{figure}[!ht]
  \begin{center}
    \begin{minipage}[t]{0.22\linewidth}
\raisebox{-4cm}{\includegraphics[width=0.98\linewidth]{QA/trace.eps}} 
    \end{minipage}\hfill
    \begin{minipage}[t]{0.75\linewidth}
      \caption{ Traces on the free surface of a crystal due to slip on two planes. Indicate on your stereogram the traces of the two slip planes and of the plane parallel to the $(\overline{11}2)$ face of the crystal. By finding the intersection of the traces, mark on your stereogram the two directions of the slip planes on $(\overline{11}2)$. Use a Wulff net to determine the angle between these two directions and check by calculation.}  \label{fig:trace}
    \end{minipage}
  \end{center} \end{figure} 

\item In an hexagonal crystal the angle $(10\overline 10):(10\overline 1 1)$ is found to be $37.2^\circ$. Calculate the ratio $c/a$. What are the indices of the direction common to these faces, in both three and four index notation?

	Show that $(0001):(11\overline 22)=48.8^\circ$.  Draw an accurate 127~mm diameter stereogram centred on 0001 showing all the poles of the form $\{10\overline 10\}$,  $\{10\overline 11\}$, $\{11\overline 20\}$, and $\{11\overline 22\}$.

\item A tetragonal crystal  (point group 422, $a=1.03\,$nm, $c=0.69\,$nm) has faces of the forms $\{100\}$,  $\{110\}$, $\{101\}$ and $\{111\}$ as well as an unknown form $\{hkl\}$. One face $F$ of the latter form lies in the same zone as (101) and (110) with $F:(101)=42^\circ$ and $F:(110)=25^\circ$.

\begin{itemize}
\item Draw a sketch stereogram of the symmetry elements of the group 422 and the poles of the general form $\{hkl\}$.
\item Show that $(001):(101)=33.8^\circ$. Draw an accurate 127~mm diameter stereogram centred on 001, showing all the faces of the forms listed above. Locate the face $F$ and all its equivalents in the same form.
\item Verify that $F$ is (321).
\end{itemize}

\end{enumerate}

