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Why Study Solid State Physics?

Why Study Solid State Physics?. 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.

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Why Study Solid State Physics?

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  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. Honeycomb net: Bravais lattice with two point basis

  8. Crystal structure: basis

  9. Translation Vector T

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

  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. 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. Summary: Bravais Lattices (Nets) in Two Dimensions

  28. Escher loved two dimensional structures too

  29. Summary: Fourteen Bravais Lattices in Three Dimensions

  30. Fourteen Bravais Lattices …

  31. FCC Structure

  32. FCC lattice

  33. Primitive Cell: FCC Lattice

  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. Elements That Have FCC Structure

  36. Simple Hexagonal Bravais Lattice

  37. Primitive Cell: Hexagonal System

  38. HCP Crystal

  39. Hexagonal Close Packing

  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. HCP: Simple Hexagonal Bravais With Basis of Two Atoms Per Point

  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. Indices of Crystal Plane

  44. Indices of Planes: Cubic Crystal

  45. 001 Plane

  46. 110 Planes

  47. 111 Planes

  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. NaCl Structure

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