Download Lecture 2: Crystal Structure

Lecture 2: Crystal Structure
PHYS 430/603 material
Laszlo Takacs
UMBC Department of Physics
Unless we specify otherwise, “solid” means
“crystalline,” at least on the microscopic scale
• Short range structure reflects the nature of bonds, but the crystal
structure also has to conform to translational symmetry:
• If we shift the crystal by certain vectors of translation, T, every
atom moves into the position of an identical atom.
• The possible vectors of translation are linear combinations with
integer coefficients of three “primitive translational vectors”:
T = na + mb + pc
• The entire structure can be described by a “unit cell” defined as a
parallelepiped defined by a, b, c and its repeated translations by
a, b, c. There can be symmetries beyond translation.
• A smallest possible unit cell is the “primitive cell.”
• The points in a lattice are mathematical points, we get the crystal
structure by putting identical groups of atoms - the basis - on
each lattice point. In simple cases, the basis is a single atom.
The elementary vectors of translation, i.e. the
unit vectors of our coordinate system
Find the unit cell
Maurits Cornelis
Escher
Unit cell and symmetries
Crystal - glass
The fourteen
Bravais lattices
Unit cells of the fcc structure
Interstitial sites in fcc structure
The hcp
structure
and its
unit cell
Interstitial sites in hcp structure
Interstitial sites in bcc structure
CsCl (B2) structure
Packing based on hexagonal structure: AlB2 and WC