Any two planes parallel to each other are equivalent and have identical indices Procedure is:

1. CRYSTALLOGRAPHIC PLANES Any two planes parallel to each other are equivalent and have identical indicesProcedure is: • If the plane passes through the selected origin, construct another parallel plane within the unit cell/ establish a new origin at the corner of another unit cell • The plane intersects/ parallels each of the 3 axes; determine the length of planar intercept for each axis in terms of a, b, &c. • Take reciprocals of these numbers. (if a plane parallels an axis, intercept is infinity & thus a zero index ) • Change to a set of smallest integers • Enclose within parentheses as (h k l)

2. Crystallographic Planes specified by MILLER INDICES STEPS: • One corner of Unit cell is Origin • The plane cuts X axis at a, Y axis at b, Z axis at c

3. Direction [1 1 1]& Plane (1 1 1) FOR CUBIC CRYSTALS ONLY Planes and Directions having same indices are perpendicular to oneanother

4. [1 2 3]

6. (0 1 1)

7. (1 1 1)

8. (1 3 0)

9. [1 1 0] [2 1 1]

10. Problem 1

11. Problem 2

12. Problem 3

13. Problem 4

14. Problem 5

15. Problem 6

16. Problem 7

17. Problem 8 a & b Sketch [0 0 0 1] and (0 0 0 1)

18. Problem 9

19. Problem 10

20. Problem 11

21. Problem 12

22. Problem 13

23. Problem 14

24. Problem 15