1. Why Study Solid State Physics?

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. 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. Crystal lattice: Proteins

5. Crystal Structure

6. Honeycomb: NOT Bravais

7. Crystal structure: basis

8. Translation Vector T

9. Translation(a1,a2), Nontranslation Vectors(a1’’’,a2’’’)

10. 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. 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. Five fold axis of symmetry cannot exist

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. Oblique lattice: invariant only under rotation of pi and 2 pi

16. Two Dimensional Lattices

17. Three Dimensional Lattice Types

18. Wigner-Seitz Primitive Cell: Full symmetry of Bravais Lattice

19. Conventional Cells

20. Cubic space lattices

21. Cubic lattices

22. BCC Structure

23. BCC Crystal

24. BCC Lattice

25. Primitive vectors BCC

26. Elements with BCC Structure

27. FCC Structure

28. FCC lattice

29. Primitive Cell: FCC Lattice

30. Elements That Have FCC Structure

31. HCP Crystal

32. Hexagonal Close Packed

33. HCP

34. Primitive Cell: Hexagonal System

35. Miller indices of lattice plan
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:

36. Indices of Crystal Plane

38. Indices of Planes: Cubic Crystal

39. 001 Plane ?

40. 110 Planes

41. 111 Planes

42. 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.

43. NaCl Structure

44. NaCl Basis

45. NaCl Type Elements

46. CsCl Structure

47. CeCl Basis

48. CeCl Basis

49. CeCl Crystals

50. ZincBlende structure

51. Diamond Crystal Structure

52. Symmetry planes

53. The End: Chapter 1

55. Bragg Diffraction

56. Periodic Table

57. Lanthanoids and Actinoids

58. 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.

59. HCP Close Packing

60. HCP Close Packing

61. NaCl Basis

62. lattice