lec3.pdf

BITS Pilani Hyderabad Campus

CRYSTAL STRUCTURE

Meenakshi Viswanathan

BITS Pilani, Hyderabad Campus

Classification of Crystal Lattice

SYMMETRY

Inversion – All Bravais lattices are inversion

symmetric

Reflection

Rotation – only 2, 3, 4 & 6 fold rotations are

possible

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Possible 2-D Lattice types

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SYMMETRY IN CRYSTALS

One of the beautiful qualities of solids is that they are often crystals of extraordinary regularity and shape. There are also other regular patterns one sees often, e.g., tile on a floor. Below are three figures of typical tile patterns. Imagine that each pattern extends to infinity in all directions. Describe any symmetry that you see in each of the patterns. For example, the pattern on the top left is the same if it is rotated by 180 degrees. Thus it is symmetric under 180 degree rotations. Are there other rotations that leave the pattern the same? Are there reflections that leave the pattern the same, i.e., if a mirror were placed vertically on the floor in a certain orientation, would the pattern look the same in the mirror?

BITS Pilani, Hyderabad Campus

BITS Pilani, Hyderabad Campus

BITS Pilani, Hyderabad Campus

BITS Pilani, Hyderabad Campus

Tetragonal Bravais Lattice

BITS Pilani, Hyderabad Campus

Orthorhombic Bravais Lattice

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Simple Hexagonal Bravais Lattice

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HCP Structure

BITS Pilani, Hyderabad Campus

BITS Pilani, Hyderabad Campus

BITS Pilani, Hyderabad Campus

Diamond Lattice

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NaCl

BITS Pilani, Hyderabad Campus

BITS Pilani, Hyderabad Campus

BITS Pilani, Hyderabad Campus

BITS Pilani, Hyderabad Campus