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# crystalstructure (1).ppt

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Crystal structure
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# crystalstructure (1).ppt

different types of crystals

different types of crystals

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### crystalstructure (1).ppt

1. 1. Why Study Solid State Physics?
2. 2. Ideal Crystal • An ideal crystal is a periodic array of structural units, such as atoms or molecules. • It can be constructed by the infinite repetition of these identical structural units in space. • Structure can be described in terms of a lattice, with a group of atoms attached to each lattice point. The group of atoms is the basis.
3. 3. Bravais Lattice • An infinite array of discrete points with an arrangement and orientation that appears exactly the same, from any of the points the array is viewed from. • A three dimensional Bravais lattice consists of all points with position vectors R that can be written as a linear combination of primitive vectors. The expansion coefficients must be integers.
4. 4. Crystal lattice: Proteins
5. 5. Crystal Structure
6. 6. Honeycomb: NOT Bravais
7. 7. Honeycomb net: Bravais lattice with two point basis
8. 8. Crystal structure: basis
9. 9. Translation Vector T
10. 10. Translation(a1,a2), Nontranslation Vectors(a1’’’,a2’’’)
11. 11. Primitive Unit Cell • A primitive cell or primitive unit cell is a volume of space that when translated through all the vectors in a Bravais lattice just fills all of space without either overlapping itself or leaving voids. • A primitive cell must contain precisely one lattice point.
12. 12. Fundamental Types of Lattices • Crystal lattices can be mapped into themselves by the lattice translations T and by various other symmetry operations. • A typical symmetry operation is that of rotation about an axis that passes through a lattice point. Allowed rotations of : 2 π, 2π/2, 2π/3,2π/4, 2π/6 • (Note: lattices do not have rotation axes for 1/5, 1/7 …) times 2π
13. 13. Five fold axis of symmetry cannot exist
14. 14. Two Dimensional Lattices • There is an unlimited number of possible lattices, since there is no restriction on the lengths of the lattice translation vectors or on the angle between them. An oblique lattice has arbitrary a1 and a2 and is invariant only under rotation of π and 2 π about any lattice point.
15. 15. Oblique lattice: invariant only under rotation of pi and 2 pi
16. 16. Two Dimensional Lattices
17. 17. Three Dimensional Lattice Types
18. 18. Wigner-Seitz Primitive Cell: Full symmetry of Bravais Lattice
19. 19. Conventional Cells
20. 20. Cubic space lattices
21. 21. Cubic lattices
22. 22. BCC Structure
23. 23. BCC Crystal
24. 24. BCC Lattice
25. 25. Primitive vectors BCC
26. 26. Elements with BCC Structure
27. 27. Summary: Bravais Lattices (Nets) in Two Dimensions
28. 28. Escher loved two dimensional structures too
29. 29. Summary: Fourteen Bravais Lattices in Three Dimensions
30. 30. Fourteen Bravais Lattices …
31. 31. FCC Structure
32. 32. FCC lattice
33. 33. Primitive Cell: FCC Lattice
34. 34. FCC: Conventional Cell With Basis • We can also view the FCC lattice in terms of a conventional unit cell with a four point basis. • Similarly, we can view the BCC lattice in terms of a conventional unit cell with a two point basis.
35. 35. Elements That Have FCC Structure
36. 36. Simple Hexagonal Bravais Lattice
37. 37. Primitive Cell: Hexagonal System
38. 38. HCP Crystal
39. 39. Hexagonal Close Packing
40. 40. HexagonalClosePacked HCP lattice is not a Bravais lattice, because orientation of the environment Of a point varies from layer to layer along the c-axis.
41. 41. HCP: Simple Hexagonal Bravais With Basis of Two Atoms Per Point
42. 42. Miller indices of lattice plane • The indices of a crystal plane (h,k,l) are defined to be a set of integers with no common factors, inversely proportional to the intercepts of the crystal plane along the crystal axes:
43. 43. Indices of Crystal Plane
44. 44. Indices of Planes: Cubic Crystal
45. 45. 001 Plane
46. 46. 110 Planes
47. 47. 111 Planes
48. 48. Simple Crystal Structures • There are several crystal structures of common interest: sodium chloride, cesium chloride, hexagonal close-packed, diamond and cubic zinc sulfide. • Each of these structures have many different realizations.
49. 49. NaCl Structure
50. 50. NaCl Basis
51. 51. NaCl Type Elements
52. 52. CsCl Structure
53. 53. CsCl Basis
54. 54. CsCl Basis
55. 55. CeCl Crystals
56. 56. Diamond Crystal Structure
57. 57. ZincBlende structure
58. 58. Symmetry planes
59. 59. The End: Chapter 1
60. 60. Bravais Lattice: Two Definitions The expansion coefficients n1, n2, n3 must be integers. The vectors a1,a2,a3 are primitive vectors and span the lattice.
61. 61. HCP Close Packing
62. 62. HCP Close Packing
63. 63. Close Packing 2
64. 64. Close Packing 3
65. 65. Close Packing 4
66. 66. Close Packing 5
67. 67. NaCl Basis
68. 68. Close Packing of Spheres