$($Explain step$-$by $-$step$)$

In a F$.$C$.$C$.$ crystal, a dislocation with $b=\frac{1}{2}\left[\begin{array}{cc}1& 0\end{array}\right]$ is invisible when imaged using a certain

diffraction vector, $g.$ If this dislocation splits into two partials $\frac{1}{6}\left[\begin{array}{cc}1z& 1\end{array}\right]+\frac{1}{6}\left[\begin{array}{ccc}2& 1& 1\end{array}\right]$ on either

side of a stacking fault on $(111),$ described by a fault vector $R=\frac{1}{3}[111],$ which of the

following are possible.

a$)$ Both partials and fault visible.

b$)$ Both partials and fault invisible.

c$)$ One partial and fault visible.

d$)$ One partial and fault invisible.

e$)$ Both partials visible, fault invisible.

f$)$ Both partials invisible, fault visible.

You need consider the $4$ lowest order reflections only.

You may assume that for partial dislocations $g*b=+-\frac{1}{3}$ produces invisibility and $g*b=+\frac{2}{3}$

produces visibility. For $g*b=-\frac{2}{3},$ dislocations are visible but only at small deviations from

the exact Bragg condition.