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Mineralogy

Mineralogy. Carleton College Winter 2003. Lattice and its properties. Lattice: An imaginary 3-D framework, that can be referenced to a network of regularly spaced points each of which represents the position of a motif. Lattice and its properties. line lattice plane lattice space lattice

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Mineralogy

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  1. Mineralogy Carleton College Winter 2003

  2. Lattice and its properties • Lattice: An imaginary 3-D framework, that can be referenced to a network of regularly spaced points each of which represents the position of a motif.

  3. Lattice and its properties • line lattice • plane lattice • space lattice • unit cell • primitive and non-primitive cells

  4. Lattice and its properties • I can generate a lattice line from a lattice point by translating my lattice point with a vector (a)

  5. Lattice and its properties • I can generate a lattice line from a lattice point by translating my lattice point with a vector (a)

  6. Lattice and its properties • I can generate a lattice line from a lattice point by translating my lattice point with a vector (a)

  7. Lattice and its properties • I can generate a lattice line from a lattice point by translating my lattice point with a vector (a)

  8. Lattice and its properties • Plane lattice: by introducing another vector b, that is not in the same direction as a, I can produce a plane lattice

  9. Lattice and its properties • Space lattice, by introducing another vector c, which is not in the same plane as a and b, I can generate a space lattice

  10. Unit Cell • The smallest representative unit of structure which when repeated in 3-D gives the whole crystal.

  11. Structure: • Nearly all minerals are crystalline solids composed of atoms or ions held in an orderly, 3-D array by inter atomic forces. Such array of atoms are called crystal structure and are characterized by periodic duplication of any grouping of atoms along any line through the structure. • In other wards the ordered arrangement of atoms or group of atoms within crystalline substance.

  12. Unit Cell • How to choose a Unit cell from plane lattice?

  13. Choice of a Unit Cell

  14. Choice of a Unit Cell • Look at this pattern, it is produced by simple translations. • There are several possible choices for the Unit Cell.

  15. Choice of a Unit Cell

  16. Choice of a Unit Cell

  17. Choice of a Unit Cell

  18. Choice of a Unit Cell • A lattice point occurs where the corners of four cells meet, and therefore, 1/4 point per corner lies in a give cell (1/4 * 4=1)

  19. Choice of a Unit Cell • Unit Cells that include one lattice point, such as A, and B are called primitive Cells. • Unit Cell C is Non-primitive.

  20. Choice of a Unit Cell • Many different cells containing a single lattice point may be chosen.

  21. Choice of a Unit Cell • How do you chose the Unit Cell? • To keep the translations short • To provide as highly specialized a lattice geometry as possible • To have the cell shape comparable with the shape of the crystal

  22. Symmetry of a Lattice: • Lets see what symmetry exist in a lattice for a moment and we will come back to Unit Cell

  23. Elements of symmetry operations: • Symmetry operations: Movements performed on an object such that when completed, the object looks the same as when you started. • These include:

  24. Elements of symmetry: • Translation • Reflection • Rotation • Inversion • Roto-inversion • Roto-reflection • Glide • screw axis

  25. Elements of symmetry: • What elements of repetition exist? • Translation

  26. Elements of symmetry: • What elements of repetition exist? • Reflection/Mirror • Mirror plane: plane passed through object such that the images on opposite sides of the plane are mirror images of one another

  27. Elements of symmetry: • What elements of repetition exist? • Reflection

  28. Elements of symmetry: • What elements of repetition exist? • Rotation • Rotation Axis - An axis through the object, around which the object is rotated such that the original "motif" (or appearance) is repeated a specific number of times during 360 degrees

  29. Elements of symmetry: • What elements of repetition exist? • Rotation

  30. Elements of symmetry: • What elements of repetition exist? • Rotation of 90 degrees will give me..

  31. Elements of symmetry: • What elements of repetition exist? • Rotation of 90 degrees will give me..

  32. Elements of symmetry: • What elements of repetition exist? • Rotation of 90 degrees will give me..

  33. Elements of symmetry: • What elements of repetition exist? • Rotation of 90 degrees will give me..

  34. Elements of symmetry: • What elements of repetition exist? • Rotation of 90 degrees will give me..

  35. Elements of symmetry: • What elements of repetition exist? • Here is a different unit cell

  36. Elements of symmetry: • What elements of repetition exist? • Here is a different unit cell

  37. Elements of symmetry: • What elements of repetition exist? • Rotation of 60 degrees gives me another motif

  38. Elements of symmetry: • What elements of repetition exist? • Rotation • 1 axis 360 degrees • 2 axes 180 degrees • 3 axes 120 degrees • 4 axes 90 degrees • 6 axes 60 degrees

  39. Elements of symmetry: • What elements of repetition exist? • Inversion

  40. Elements of symmetry: • What elements of repetition exist? • Roto-inversion • first a rotation, then an inversion of 180 degrees

  41. Elements of symmetry: • What elements of repetition exist? • Roto-reflection

  42. Elements of symmetry: • What elements of repetition exist? • Glide

  43. Elements of symmetry: • What elements of repetition exist? • Glide

  44. Elements of symmetry: • What elements of repetition exist? • Glide

  45. Elements of symmetry: • What elements of repetition exist? • Glide

  46. Elements of symmetry: • What elements of repetition exist? • Glide

  47. Elements of symmetry: • What elements of repetition exist? • Glide

  48. Elements of symmetry: • What elements of repetition exist? • Glide

  49. Elements of symmetry: • What elements of repetition exist? • screw axis • This include translation and rotation together

  50. Screw Axis

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