Crystals and Symmetry. Why Is Symmetry Important? Identification of Materials Prediction of Atomic Structure Relation to Physical Properties –Optical. - ppt download

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Repeating Atoms in a Mineral
Identification of Materials Prediction of Atomic Structure Relation to Physical Properties –Optical –Mechanical –Electrical and Magnetic.
Unit Cells All repeating patterns can be described in terms of repeating boxes
The problem in Crystallography is to reason from the outward shape to the unit cell
Which Shape Makes Each Stack
Some shapes that result from stacking cubes
Symmetry – the rules behind the shapes
Single Objects Can Have Any Rotational Symmetry Whatsoever
Rotational Symmetry May or May Not be Combined With Mirror Symmetry
The symmetries possible around a point are called point groups
Objects plus operations  New Objects Closure: New Objects are part of the Set –Objects: Points on a Star –Operation: Rotation by 72 Degrees Point Group: One Point Always Fixed.
What Kinds of Symmetry Can Repeating Patterns Have
Symmetry in Repeating Patterns 2 Cos 360/n = Integer = -2, -1, 0, 1, 2 Cos 360/n = -1, -1/2, 0, ½, 1 360/n = 180, 120, 90, 60, 360 Therefore n = 2, 3, 4, 6, or 1 Crystals can only have 1, 2, 3, 4 or 6-Fold Symmetry
No. The Stars Have 5- Fold Symmetry, But Not the Overall Pattern
Symmetry Can’t Be Combined Arbitrarily
Translation p p p p p p p p p p p p p pq pq pq pq pq pd pd pd pd pd p p p p p p p p p p p p p b b b b b b b b b b b b b pd pd pd pd pd pd pd pd pd pd bq bq bq bq bq bq bq bq bq bq pd bq pd bq pd bq pd bq pd bq pd bq pd bq p b p b p b p b p b p b p b
Space Symmetry Rotation + Translation = Space Group Rotation Reflection Translation Glide (Translate, then Reflect) Screw Axis (3d: Translate, then Rotate) Inversion (3d) Roto-Inversion (3d: Rotate, then Invert)
There are 17 possible repeating patterns in a plane. These are called the 17 Plane Space Groups
Triclinic, Monoclinic and Orthorhombic Plane Patterns