## Solution ### Q2. Sketch the [01̅1] Direction First, interpret the direction indices [01̅1]: - The first index () means no movement along the x-axis. - The second index (1̅) means move -1 unit along the y-axis (negative y-direction). - The third index (1) means move +1 unit along the z-axis (positive z-direction). To sketch [01̅1] on the cube, start from the origin (, , ). Since x=, there is no movement along x. Move -1 along the y-axis (towards negative y), and +1 along the z-axis (upwards). Draw a vector starting at the origin and ending at (, -1, 1), which is outside the conventional cube, so you can draw the direction as an arrow starting at the origin, going parallel to the edge opposite the y and z axes—heading down the back side (negative y) and up (positive z). **Final Answer:** The [01̅1] direction is a vector starting from the origin, with no movement along x, moving one unit in the negative y-direction, and one unit in the positive z-direction. Draw an arrow from the origin pointing diagonally, upward (z) and backward (negative y). --- ### Q3. Sketch the (122) Plane The Miller indices (hkl) = (1 2 2) indicate intercepts with the axes: - x-intercept at a/1 = a - y-intercept at a/2 - z-intercept at a/2 First, mark the intercepts on the axes: - On the x-axis, mark the point at a (the far right corner of the cube). - On the y-axis, mark the halfway point (a/2). - On the z-axis, mark the halfway point (a/2). Next, connect these three points to form a triangle. To complete the plane, find parallel points on the opposite faces of the cube and connect them to form a parallelogram that represents the (122) plane. **Final Answer:** The (122) plane cuts the x-axis at a, the y-axis at a/2, and the z-axis at a/2. Draw a triangle within the cube that passes through these three points, and then extend this pattern to show the full plane within the unit cell as a parallelogram by connecting equivalent points on opposite faces. --- #### Sketch Reference (Description): For [01̅1], draw a straight arrow from the origin towards the midpoint of the edge where y is negative and z is positive. For (122), draw a triangle connecting (a, , ), (, a/2, ), and (, , a/2), then repeat on the opposite side and shade or outline the parallelogram formed.