ASSIGNMENT 1: CRYSTALLOGRAPHY MILLER INDICES Miller indices are important in mineralogy because they are universally used to describe and label crystal faces. A complete understanding of Miller indices can be quite complex. However, a basic understanding is necessary in order to use them to describe simple crystal morphology. Miller indices are the reciprocals of the intercept lengths made by faces cutting crystallographic axes. That is, for intercepts of, say, 1/3, 1 and on the a, b and c axis of a crystal, the Miller index is 263. However, in practice many simple crystals can be described by indexes involving only 0 and 1. The mineral shown below belongs to the cubic crystal system (it is essentially a cube with the corners cut off). This exercise is designed to derive the Miller indices for all of the faces shown.

(b)

(a)

Use these simple rules:

1. If a face (or its projection) cuts an axis, its Miller index for that axis is 1 2. If a face (or its projection) does not cut an axis, its index is 0 (it

intercepts the axis at and 1/ = 0) 3. + and indices are as shown: 4. An intercept of -1 is written (bar 1) +

+

+

Question 1: For the crystal shown on the previous page: Draw and label crystallographic axes on the crystal (look up notes on crystal systems)

1. Select face (a). How many axes does it cut? 3 (a, b and c) 2. What is its Miller index? 111 . 3. Select face (b) How many axes does it cut? ... 4. What is its Miller index? 5. Label all remaining faces with Miller indices

Question 2: Using a similar procedure to the above, draw crystallographic axes and label all of the faces shown on the crystals below. Write the crystal system below each crystal.

Question 3: In general, a face perpendicular to the c axis is labelled? . In general, a face cutting any two axes is labelled? (3 answers)

. In general, a face cutting all three axes is labelled?