1. Lecture 10 (10/16/2006) Crystallography Part 3: Crystallographic Axes Numerical Notation of Crystal Faces and Atomic Planes – Miller Indices

2. Point Groups of Crystal Systems

3. Crystallographic Axes

4. Isometric Crystal System
Axes equal length, 90º
Aligned with A4 (432, 43m, 4/m32/m)
or with A2 (23, 2/m3)

5. Hexagonal Crystal System
1 long or short axis (c), 90º to 3 axes of equal length (a1, a2, a3), 120º to each other
c aligned with A6 or A3; a1, a2, a3 are aligned parallel to A2 or m planes or arbitrary (3, 3, 6, 6)

6. Tetragonal Crystal System
1 long or short axis (c), two axes of equal length (a1, a2); all axes 90º to each other
c aligned with A4; a1 and a2 are aligned parallel to A2 or m planes or arbitrary (4, 4)

7. Orthorhombic Crystal System
three axes of unequal length (a, b, c); all axes 90º to each other
axes aligned parallel to A2; for mm2, c aligned parallel with A2, a & b normal to m planes

8. Monoclinic Crystal System
three axes of unequal length (a, b, c); β ≠ 90º, α=γ= 90º,
b axis is parallel to A2 (2, 2/m) or normal to mirror (m); a and c axes normal to b and normal to crystal faces or edges

9. Triclinic Crystal System
three axes of unequal length (a, b, c); α ≠ β ≠ γ ≠ 90º
a, b, & c axes normal to crystal faces or edges

10. Numerical Notation for Crystal Planes and Faces
relative values, not absolute distances
units defined by largest face cutting all three axes – Unit Face
Unit
Face

11. Crystal Face Intercepts
UNIT
FACE
2/3c
1/3c 1b 2b 3b
or 1a, 1b, 1/3c
or 3a, 3b, 1c

12. Miller Indices Invert intercept values and clear fractions
Law of Rational Indices –
common faces have simple
whole numbers for Miller Indices
Negative
Indices

13. Crystal Face Intercepts
UNIT
FACE
2/3c
1/3c 1b 2b 3b
Miller Indices
(1/1,1/1,1/1) = 111
(1/2,1/2,3/2) = 113
(1/1,1/1,3/1) = 113
(1/3,1/3,1/1) = 113
or 1a, 1b, 1/3c
or 3a, 3b, 1c

14. Miller Indices in Hexagonal System

15. Crystal Zone and Zone Axis

16. Next Lecture Crystal Symmetry (Continued) Crystal Forms Twinning
Read: Chapter 5, p
Read: Chapter 6, p for Lab
No Lecture Next Week