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

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Presentation transcript:

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

Point Groups of Crystal Systems

Crystallographic Axes

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

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)

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)

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

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

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

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

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

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

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

Miller Indices in Hexagonal System

Crystal Zone and Zone Axis

Next Lecture Crystal Symmetry (Continued) Crystal Forms Twinning Read: Chapter 5, p. 201-213 Read: Chapter 6, p. 240-251 for Lab No Lecture Next Week