Dr. JoAnn (Jodi) Crandall University of Maryland Baltimore County (UMBC) crandall@umbc
Lecture 2: Crystal Structure PHYS 430/603 material Laszlo Takacs UMBC Department of Physics.
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Transcript of Lecture 2: Crystal Structure PHYS 430/603 material Laszlo Takacs UMBC Department of Physics.
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