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Crystalline Structures

Crystalline Structures. Edward A. Mottel Integrated, First-Year Curriculum in Science, Engineering and Mathematics. Crystalline Solid State. Study of the arrangement of atoms/ions in metallic and ionic crystals. Enables the calculation of the size of atoms/ions.

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Crystalline Structures

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  1. Crystalline Structures Edward A. Mottel Integrated, First-Year Curriculum in Science, Engineering and Mathematics

  2. Crystalline Solid State • Study of the arrangement of atoms/ions in metallic and ionic crystals. • Enables the calculation of the size of atoms/ions. • Allows the "environment" (the number of atoms/ions and the types of atoms/ions) surrounding each atom/ion to be studied.

  3. Physical PropertiesRelated to Solid Structure • Density • Luster • Hardness • Electrical Properties • Melting Point • Magnetic Properties

  4. Distinctions Between Solid Structures • Crystalline versus Amorphous Solids • Crystal Structure versus Crystal Morphology • Equivalent Sphere versus Ionic Structures

  5. b a c a b g Triclinic a ¹ b ¹ c a ¹ b ¹ g¹ 90° Unit Cells Simple Cubic a = b = c a = b = g = 90°

  6. Crystal Structure Definitions • Unit cell • cell dimensions • unit cell length (a, b, c) • cell angles (a, b, g)

  7. Crystal Structure Definitions • Cell relationships • edge • face-diagonal • body-diagonal • cell volume

  8. Crystal Structure Definitions • Cell relationships • edge • face-diagonal • body-diagonal • cell volume

  9. Crystal Structure Definitions • Cell relationships • edge • face-diagonal • body-diagonal • cell volume If the cell edge is a, how long is the face diagonal? If the cell edge is a, how long is the body diagonal?

  10. Crystal Structure Definitions • Cell relationships • edge • face-diagonal • body-diagonal • cell volume

  11. The Unit CellCrystal Structure Definitions • Begin working on page J-4 of laboratory manual • Refer to page J-1 for definitions • Unit Cell

  12. Solid State Model Kit • Obtain one kit for every 3-4 people. • Sit in a circle so that everyone can see the models as they are being built. • Refer to pg. 5 of the Model Kit Manual (in the box) for instructions • how to select the plastic base to use. • which holes of the base to use. • how to build the models. • how to take them apart.

  13. Equivalent Sphere StructuresCrystal Structure Definitions • Start at page J-5 of laboratory manual; work through page J-10 • Refer to page J-1 for definitions • Net atoms per unit cell • Percentage void space (packing efficiency) • Coordination Number (CN)

  14. Questions to ConsiderWhen Studying Solid State Structures • How do the atoms touch? • What is the length of the edge of the unit cell in terms of the atomic radii? • How many net atoms are there per unit cell? • What is the percentage void space in the structure? • Build the primitive (simple) unit cell (pg. 9, 102) • Build the small cube, then the large cube • Answer questions on page J-5 of lab manual

  15. Solid State Model KitModels to Build • Primitive (simple) unit cell (pg. 9, 102) • Build the small cube, then the large cube • Page J-5 of lab manual • Body-Centered Cubic (bcc) pg 18, J-6 • Face-Centered Cubic (fcc) pg 27, J-7 • Cubic Closest Pack (ccp) pg 26, J-8 • Shaded area and hollow numbers • Hexagonal Closest Pack (hcp) pg 24, 99, J-8

  16. Simple (Primitive) Cubic • 1) 6 • 2) 2r • 3) 2Ö2 r • 4) 2Ö3 r • 5) 1 net atom per unit cell • 6) 47.6%

  17. Body-Centered Cubic • 1) 8 • 2) 8 • 3) 4r • 4) 4r/Ö3 • 5) 2 net atoms per unit cell • 6) 31.9%

  18. 1) 12 2) 4r 3) 2Ö2 r 4) 4 net atoms per unit cell 5) 25.9% Face-Centered Cubic

  19. Equivalent Sphere Summary Along which dimensions of a cube do the atoms touch Structure Length simple (primitive) cubic edge 2 r body-centered cubic body-diagonal 4 r face-centered cubic face-diagonal 4 r

  20. Diamond • Hardest naturally occurring material • Strong because • strong covalent bonds • 3-dimensional strength • Same structure is formed by • silicon and germanium • Similar structure formed by several semiconducting materials • GaAs, GaP

  21. Diamond Structure Atoms occur at the corners of the unit cell

  22. Diamond Structure Atoms occur at the face centers of the unit cell

  23. Diamond Structure Atoms occur at four positions within the unit cell The four positions are at the centers of alternate smaller cubes

  24. Diamond Structure Atoms occur at four positions within the unit cell The four positions are at the centers of alternate smaller cubes

  25. Diamond Structure Atoms occur at the corners of the unit cell Atoms occur at four positions within the unit cell The four positions are at the centers of alternate smaller cubes Atoms occur at the face centers of the unit cell How many net carbon atoms are there per unit cell?

  26. Diamond Structure How long is the body-diagonal in terms of r? Some atoms touch along the body-diagonal The density of diamond is 3.51 g·cm3. What is the radius of a carbon atom?

  27. Graphite Structure

  28. 1 7 7 How many spheres can fit into the following square (2-D)

  29. How many spheres can fit into the following square (2-D) 49

  30. How many spheres can fit into the following square (2-D) 52 + 8/2 Hexagonal packing is efficient.

  31. C Electrical resistance B A Temperature Experiment JJ: Solid State IIElectrical Resistance metal metal semiconductor semiconductor superconductor superconductor Based on your observations, which type of material corresponds to which line?

  32. Experiment JJ: Solid State IIStructure • Sodium nitrate crystal formation • Bobby Pin heat treatment • Copper wire work hardening

  33. Solid State Model KitModels to Build • Cubic Closest Pack (ccp) pg 26, J-8 • Shaded area and hollow numbers • Hexagonal Closest Pack (hcp) pg 24, 99, J-8 • Hole Calculation, Radius Ratio and Coordination Number pg 93, J-11 • How is r/R calculated?

  34. Cesium ChlorideTwo Different Kinds of Ions One type of ion occurs at the corners of a cube The other ion occurs at the center of the cell

  35. Sodium ChlorideA Different Structure with Two Kinds of Ions One type of ion occurs at The other ion occurs at the corners of a cube the center of the each edge the centers of a each face the center of the cell

  36. Questions to ConsiderWhen Studying Solid State Structures • How do the ions touch? • What is the length of the edge of the unit cell in terms of the ionic radii? • How many net ions are there per unit cell? • What is the percentage void space in the structure?

  37. Ionic Structures • Cesium Chloride (CsCl) pg 96 • Answer questions on page J-12 of lab manual • Rock Salt (NaCl) pg 33, 31 • Answer questions on page J-13 of lab manual

  38. i) 8, 8, 0 ii) 8, 8, 0 iii) cubic hole iv) 2r+ + 2r- v) 1 cation vi) 1 anion vii) 5.50/Ö3 = 3.18 Å viii) 32.0 Å3 ix) 30.3% Cesium Chloride Structure

  39. i) 6, 6, 0 ii) 6, 6, 0 iii) octahedral hole iv) 2r+ + 2r- v) 4 cations vi) 4 anions vii) 125 Å3 viii) 38.0% Rock Salt Structure

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