Ge 101. Introduction to Geology and Geochemistry Lecture 2 Crystal Structure of Minerals.
Lecture 2: Crystal Structure
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Transcript of Lecture 2: Crystal Structure
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Lecture 2: Crystal Structure
PHYS 430/603 materialLaszlo Takacs
UMBC Department of Physics
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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.
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The elementary vectors of translation, i.e. the unit vectors of our coordinate system
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Find the unit cell
Maurits Cornelis Escher
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Unit cell and symmetries
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Crystal - glass
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The fourteen Bravais lattices
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Unit cells of the fcc structure
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Interstitial sites in fcc structure
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The hcp structure and its unit cell
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Interstitial sites in hcp structure
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Interstitial sites in bcc structure
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CsCl (B2) structure
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Packing based on hexagonal structure: AlB2 and WC