Crystal Structure
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Transcript of Crystal Structure
Crystal Structures & Crystal GeometryCrystal Structures & Crystal Geometry
The Platonic SolidsThe Platonic Solids
http://home.teleport.com/~tpgettys/platonic.shtmlTetrahedronOctahedron
Icosahedron
20 faces and 12 verticesCube
Dodecahedron
Christian Huygens, 1690
Snow flakesSnow flakes
Bentley captured more than 5000 snowflakes during his lifetime, not
finding any two alike.
http://www.its.caltech.edu/~atomic/snowcrystals/http://www.its.caltech.edu/~atomic/snowcrystals/
Caltech work
What I expect you to know for this courseWhat I expect you to know for this course
Space LatticeSpace Lattice
Atomic arrangements in crystalline solids can be described with respect to a network of lines in three dimensions.
The intersections of the lines are called “lattice sites” (or lattice points). Each lattice site has the same environment in the same direction.
A particular arrangement of atoms in a crystal structure can be described by specifying the atom positions in a
repeating “unit cell”.
Lattice: regular patternLattice: regular pattern
BravaisBravais
14 BravaisLattices14 BravaisLattices
Why not pentagons???Why not pentagons???
Principal Metal Crystal StructuresPrincipal Metal Crystal Structures
There are three principle crystal structures for metals:–(a) Body-centered cubic (BCC)–(b) Face-centered cubic (FCC) –(c) Hexagonal close-packed (HCP)
Reallyimportant for
Thiscourse!!
Body-centered cubic (BCC)
BCCBCC
Face-centered cubic (FCC)
Geometry of the BCC StructureGeometry of the BCC Structure
FCCFCC
Geometry of the FCC StructureGeometry of the FCC Structure
Hexagonal close-packed (HCP)Hexagonal close-packed (HCP)
HCPHCP
Geometry of the HCP StructureGeometry of the HCP Structure
RelationshipsRelationships
Simple cube
a = 2 r
BCC FCC
Directions in a crystalDirections in a crystal
Directions in a crystalDirections in a crystal
Negative: use overbar
ExampleExample
FractionFraction
For cubic systemFor cubic system
<100> edge direction<110> face diagonal<111> body diagonal
Directions FCCDirections FCC
Directions BCCDirections BCC
Interstial spacesInterstial spaces
It depends on the r/R ratios, leading to different coordination numbers
4
Interstial spacesInterstial spaces
6
Interstial spaces -8Interstial spaces -8
Interstial spaces -12Interstial spaces -12
ExamplesExamples
NaCl (FCC, octahedral bonding)
Examples – SiO2Examples – SiO2
Some Materials have Different Crystal Structures at Different TemperaturesSome Materials have Different Crystal Structures at Different Temperatures
Many elements and compounds exist in more than one crystalline form under different conditions of temperature and pressure.
This phenomenon is called polymorphism or allotropy.
Last Century workLast Century work
The Nobel Prize in Physics 1914"for his discovery of the diffraction of
X-rays by crystals"
PaulingPauling
The Nobel Prize in Chemistry 1954"for his research into the nature of
the chemicalbond and its application to the
elucidation of thestructure of complex substances"
Penrose tilingPenrose tiling
The C60 or 'Buckball' belongs to a verysmall set of known molecules withicosahedral symmetry
The C60 or 'Buckball' belongs to a verysmall set of known molecules withicosahedral symmetry
Curl, Kroto, Smalleyreceived the Nobel
prize in Chemistry 1996.