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Sodium Chloride Structure Na + Cl - Cesium Chloride Structure C s + Cl -

Sodium Chloride Structure Na + Cl - Cesium Chloride Structure C s + Cl - Hexagonal Closed-Packed Structure Diamond Structure Zinc Blende Structure. The “Most Important” Crystal Structures. 1. Sodium Chloride (NaCl) Structure.

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Sodium Chloride Structure Na + Cl - Cesium Chloride Structure C s + Cl -

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  1. Sodium Chloride Structure Na+Cl- Cesium Chloride Structure Cs+Cl- Hexagonal Closed-Packed Structure Diamond Structure Zinc Blende Structure The “Most Important” Crystal Structures 1

  2. Sodium Chloride (NaCl) Structure Sodium chloride crystallizes in a lattice with cubic symmetry. This 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.

  3. NaCl Structure

  4. LiF,NaBr,KCl,LiI,have this structure. • The lattice constants are of the order of 4-7 Angstroms. 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

  5. NaCl Structure Take the NaCl unit cell & remove all “red” Clions, 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.

  6. NaCl Type Crystals

  7. Cesium Chloride, CsCl, also crystallizes in a cubic lattice.  The unit cell may be depicted as shown. (Cs+  is teal, Cl- is gold) CsCl Structure • Cesium Chloride,CsCl, consists of equal numbers of Csand Clions, placed at the points of a body-centered cubic lattice so that each ion has eight of the other kind as its nearest neighbors. 

  8. CsCl Structure

  9. CsCl Structure • CsBr & CsI crystallize in this structure.The lattice constants are of the order of 4 angstroms. 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:

  10. CsCl Structure 8 cells

  11. CsCl Crystals

  12. Diamond Structure The Diamond Latticeconsists of 2 interpenetrating FCC Lattices. It is not a Bravais Lattice. There are 8 atoms in the unit cell. Each atom bonds covalently to 4 others equally spaced about a given atom..

  13. The Diamond Latticeconsists of 2 interpenetrating FCC Lattices. The Coordination Number = 4. The diamond lattice is not a Bravais lattice. C, Si, Ge & Sncrystallize in the Diamond structure.

  14. Diamond Lattice Diamond Lattice The Cubic Unit Cell

  15. The Zincblende Structurehas 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. Zinc Blende or ZnS Structure

  16. Zinc Blende or ZnS Structure • Some compounds with this structure are: • AgI,GaAs,GaSb,InAs, ....

  17. Zincblende (ZnS) Lattice Zincblende Lattice The Cubic Unit Cell

  18. Diamond & Zincblende Structures A brief discussion of both of these structures & a comparison. • These two are technologically important structures because 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 are2 atoms per fcc lattice point. In Diamond:The 2 atoms are the same. In Zincblende: The 2 atoms are different.

  19. Diamond & Zincblende Lattices Zincblende Lattice The Cubic Unit Cell Diamond Lattice The Cubic Unit Cell Other views of the cubic unit cell

  20. Zincblende & Diamond Lattices Face Centered Cubic (FCC) lattices with a 2 atom basis A view of the tetrahedral coordination & the 2 atom basis

  21. 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

  22. The Wurtzite Lattice View of tetrahedral coordination & the 2 atom basis. Wurtzite Lattice  Hexagonal Close Packed (HCP) Lattice + 2 atom basis

  23. 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:Theai’s are NOTmutually orthogonal! Diamond: 2 identical atoms per FCC point Zincblende: 2 different atoms per FCC point Primitive FCC Lattice cubic unit cell

  24. Primitive Lattice Points Wurtzite Crystals • The primitive lattice is HCP. The HCP primitive lattice is generated by r = 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! Theseare NOTmutually orthogonal! Wurtzite Crystals 2 atoms per HCP point Primitive HCP Lattice:Hexagonal Unit Cell

  25. 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. ELEMENTS OF SYMMETRY

  26. Typical symmetry properties of a lattice. Some types of operations that can leave a lattice invariant.

  27. 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

  28. Rotational Invariance & Invariance on Reflection Through a Plane A plane in a cell such that, when a mirror reflection in this plane is performed, the cell remains invariant. Invariance on Reflection through a plane Rotational Invariance about more than one axis

  29. Examples A triclinic lattice has no reflection plane. A monoclinic lattice has one plane midway between and parallel to the bases, and so forth.

  30. Rotational Symmetry • 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.

  31. 90º Rotational Symmetries 180° 120° • 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.

  32. Axes of Rotation

  33. Axes of Rotation

  34. 5-Fold Symmetry This type of symmetry is not allowed because it can not be combined with translational periodicity!

  35. 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. 90°

  36. Examples

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