THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what...
-
Upload
lucy-mckinney -
Category
Documents
-
view
216 -
download
3
Transcript of THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what...
![Page 1: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/1.jpg)
THE “MOST IMPORTANT”CRYSTAL STRUCTURES
![Page 2: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/2.jpg)
NOTE!!Much of the discussion & many figures in what follows was again constructed from lectures posted on the web by Prof. Beşire GÖNÜL in Turkey. She has done an excellent job of covering many details of crystallography & she illustrates her topics with many very nice pictures of lattice structures. Her lectures on this are posted Here: http://www1.gantep.edu.tr/~bgonul/dersnotlari/.Her homepage is Here: http://www1.gantep.edu.tr/~bgonul/.
NOTE!!Much of the discussion & many figures in what follows was again constructed from lectures posted on the web by Prof. Beşire GÖNÜL in Turkey. She has done an excellent job of covering many details of crystallography & she illustrates her topics with many very nice pictures of lattice structures. Her lectures on this are posted Here: http://www1.gantep.edu.tr/~bgonul/dersnotlari/.Her homepage is Here: http://www1.gantep.edu.tr/~bgonul/.
THE “MOST IMPORTANT”CRYSTAL STRUCTURES
![Page 3: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/3.jpg)
3
THE “MOST IMPORTANT” CRYSTAL STRUCTURES
• Sodium Chloride Structure Na+Cl-
• Cesium Chloride Structure Cs+Cl-
• Hexagonal Closed-Packed Structure
• Diamond Structure
• Zinc Blende
![Page 4: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/4.jpg)
1 – Sodium Chloride Structure• Sodium chloride also
crystallizes in a cubic lattice, but with a different unit cell.
• The sodium chloride structure consists of equal numbers of sodium & chlorine ions placed at alternate points of a simple cubic lattice.
• Each ion has six of the other kind of ions as its nearest neighbors.
![Page 5: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/5.jpg)
NaCl Structure
![Page 6: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/6.jpg)
![Page 7: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/7.jpg)
• This structure can also be considered as a face-centered-cubic Bravais lattice with a basis consisting of a sodium ion at 0 and a chlorine ion at the center of the conventional cell, at position
• LiF, NaBr, KCl, LiI, have this structure.
• The lattice constants are of the order of 4-7 Angstroms.
)(2/
zyxa
![Page 8: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/8.jpg)
• Take the NaCl unit cell & remove all “red” Cl ions, leaving only the “blue” Na. Comparing this with the FCC unit cell, it is found to be that they are identical. So, the Na ions are on a FCC sublattice.
NaCl Structure
![Page 9: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/9.jpg)
NaCl Type Crystals
![Page 10: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/10.jpg)
2 - CsCl Structure
![Page 11: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/11.jpg)
• Cesium Chloride, CsCl, crystallizes in a cubic lattice. The unit cell may be depicted as shown.(Cs+ is teal, Cl- is gold)
• Cesium Chloride consists of equal numbers of Cs and Cl ions, placed at the points of a body-centered cubic lattice so that each ion has eight of the other kind as its nearest neighbors.
2 - CsCl Structure
![Page 12: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/12.jpg)
• The translational symmetry of this structure is that of the simple cubic Bravais lattice, and is described as a simple cubic lattice with a basis consisting of a Cs ion at the origin 0 and a Cl ion at the cube center
• CsBr & CsI crystallize in this structure.The lattice constants are of the order of 4 angstroms.
)(2/
zyxa
CsCl Structure
![Page 13: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/13.jpg)
8 cells
CsCl Structure
![Page 14: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/14.jpg)
CsCl Crystals
![Page 15: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/15.jpg)
The Ancient “Periodic Table”
![Page 16: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/16.jpg)
4 - Diamond Structure• The Diamond Lattice consists of 2
interpenetrating FCC Lattices.• There are 8 atoms in the unit cell. Each atom bonds
covalently to 4 others equally spaced about a given atom.• The Coordination Number = 4.• The diamond lattice is not a Bravais lattice.C, Si, Ge & Sn crystallize in the Diamond structure.
![Page 17: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/17.jpg)
Diamond LatticeThe Cubic Unit Cell
Diamond Lattice
![Page 18: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/18.jpg)
• The Zincblende Structure has equal numbers of zinc and sulfur ions distributed on a diamond lattice, so that
Each has 4 of the opposite kind as nearest-neighbors.
• This structure is an example of a lattice with a basis, both because of the geometrical position of the atoms & because two types of atoms occur.
• Some compounds with this structure are:
AgI, GaAs, GaSb, InAs, ....
5 – Zinc Blende or ZnS Structure
![Page 19: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/19.jpg)
5 – Zinc Blende or ZnS Structure
![Page 20: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/20.jpg)
Zincblende (ZnS) Lattice
Zincblende LatticeThe Cubic Unit Cell
![Page 21: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/21.jpg)
Diamond & Zincblende StructuresA brief discussion of both of these structures & a comparison.
• These two are technologically important structuresbecause many common semiconductors have
Diamond or Zincblende Crystal Structures • They obviously share the same geometry.• In both structures, the atoms are all tetrahedrally
coordinated. That is, atom has 4 nearest-neighbors. • In both structures, the basis set consists of 2 atoms.
In both structures, the primitive lattice Face Centered Cubic (FCC).
• In both the Diamond & the Zincblende lattice there are 2 atoms per fcc lattice point.
In Diamond: The 2 atoms are the same.In Zincblende: The 2 atoms are different.
![Page 22: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/22.jpg)
Diamond & Zincblende Lattices
Diamond LatticeThe Cubic Unit
Cell
Zincblende LatticeThe Cubic Unit Cell
Other views of the cubic unit cell
![Page 23: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/23.jpg)
A view of the tetrahedral coordination& the 2 atom basis
Zincblende & Diamond Lattices
Face Centered Cubic (FCC) lattices with a
2 atom basis
![Page 24: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/24.jpg)
The Wurtzite Structure• A structure related to the Zincblende Structure is the
Wurtzite Structure • Many semiconductors also have this lattice structure.• In this structure there is also
Tetrahedral Coordination• Each atom has 4 nearest-neighbors. The Basis set is 2 atoms.• Primitive lattice hexagonal close packed (hcp).
2 atoms per hcp lattice point. A Unit Cell looks like
![Page 25: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/25.jpg)
The Wurtzite Lattice
Wurtzite Lattice Hexagonal Close
Packed (HCP)Lattice + 2 atom basis
View of tetrahedralcoordination & the 2 atom basis.
![Page 26: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/26.jpg)
Diamond & Zincblende crystals• The primitive lattice is FCC. The FCC primitive
lattice is generated by r = n1a1 + n2a2 + n3a3. • The FCC primitive lattice vectors are:
a1 = (½)a(0,1,0), a2 = (½)a(1,0,1), a3 = (½)a(1,1,0)
NOTE: The ai’s are NOT mutually orthogonal!
Diamond: 2 identical atoms per FCC point
Zincblende: 2 different atoms per FCC point
Primitive FCC Lattice cubic unit cell
![Page 27: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/27.jpg)
Wurtzite Crystals• The primitive lattice is HCP. The
HCP primitive lattice is generated byr = n1a1 + n2a2 + n3a3.
• The hcp primitive lattice vectors are:
a1 = c(0,0,1)a2 = (½)a[(1,0,0) + (3)½(0,1,0)]a3 = (½)a[(-1,0,0) + (3)½(0,1,0)]
NOTE!These are NOT mutually orthogonal!
Wurtzite Crystals2 atoms per HCP point
Primitive HCPLattice: Hexagonal
Unit Cell
Primitive Lattice Points
![Page 28: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/28.jpg)
• Each of the unit cells of the 14 Bravais lattices has one or more types of symmetry properties, such as inversion, reflection or rotation,etc.
SYMMETRY
INVERSION REFLECTION ROTATION
ELEMENTS OF SYMMETRY
![Page 29: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/29.jpg)
Typical symmetry properties of a lattice.Some types of operations that can leave a lattice invariant.
Operation Element
Inversion Point
Reflection Plane
Rotation Axis
Rotoinversion Axes
![Page 30: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/30.jpg)
Inversion• A center of inversion: A point at the center of the molecule.
(x,y,z) --> (-x,-y,-z)• A center of inversion can only occur in a molecule. It is
not necessary to have an atom in the center (benzene, ethane). Tetrahedral, triangles, pentagons don't have centers of inversion symmetry. All Bravais lattices are inversion symmetric. Mo(CO)6
![Page 31: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/31.jpg)
• A plane in a cell such that, when a mirror reflection in this plane is performed, the cell remains invariant.
Rotational Invariance &Invariance on Reflection Through a Plane
Rotational Invarianceabout more than one axis
Invariance on Reflectionthrough a plane
![Page 32: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/32.jpg)
Examples
• A triclinic lattice has no reflection plane.• A monoclinic lattice has one plane midway
between and parallel to the bases, and so forth.
![Page 33: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/33.jpg)
• There are always a finite number of rotational symmetries for a lattice.
• A single molecule can have any degree of rotational symmetry, but an infinite periodic lattice – can not.
Rotational Symmetry
![Page 34: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/34.jpg)
• This is an axis such that, if the cell is rotated around it through some angles, the cell remains invariant.
• The axis is called n-fold if the angle of rotation is 2π/n.
90º
120° 180°
Rotational Symmetries
![Page 35: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/35.jpg)
Axes of Rotation
![Page 36: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/36.jpg)
Axes of Rotation
![Page 37: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/37.jpg)
This type of symmetry is not allowed because it can not be combined with translational periodicity!
5-Fold Symmetry
![Page 38: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/38.jpg)
90°
Examples• A Triclinic Lattice has no axis of rotation.• A Monoclinic Lattice has a 2-fold axis
(θ = [2π/2] = π) normal to the base.
![Page 39: THE “MOST IMPORTANT” CRYSTAL STRUCTURES. NOTE!! Much of the discussion & many figures in what follows was again constructed from lectures posted on the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649cdc5503460f949a745e/html5/thumbnails/39.jpg)
Examples