1 / 62

Unit cell/ packing efficiency

Unit cell/ packing efficiency. Given 8 spheres to stack, how would you do it?. Simple cubic structure. Coordination Polyhedra. Consider coordination of anions about a central cation. Halite. Na. Cl. Cl. Cl. Cl. Coordination Polyhedra. Na. Could do the opposite, but conventionally

Rita
Download Presentation

Unit cell/ packing efficiency

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Unit cell/ packing efficiency

  2. Given 8 spheres to stack, how would you do it? • Simple cubic structure

  3. Coordination Polyhedra • Consider coordination of anions about a central cation Halite Na Cl Cl Cl Cl

  4. Coordination Polyhedra Na • Could do the opposite, but conventionally choose the cation • Can predict the coordination by considering the radius ratio: RC/RA Cations are generally smaller than anions so begin with maximum ratio = 1.0 Na Na Cl Na

  5. Coordination Polyhedra Radius Ratio: RC/RA = 1.0 (commonly native elements) • Equal sized spheres • “Closest Packed” • Hexagonal array: • 6 nearest neighbors in the plane • Note dimples in which next layer atoms will settle • Two dimple types: • Type 1 point NE • Type 2 point SW • They are equivalent since you could rotate the whole structure 60o and exchange them 2 1

  6. Closest Packing • Add next layer (red) • Red atoms can only settle in one dimple type • Both types are identical and red atoms could settle in either • Once first red atom settles in, can only fill other dimples of that type • In this case filled all type 2 dimples 1

  7. Closest Packing • Third layer ?? • Third layer dimples are now different! • Call layer 1 A sites • Layer 2 = B sites (no matter which choice of dimples is occupied) • Layer 3 can now occupy A-type site (directly above yellow atoms) or C-type site (above voids in both A and B layers)

  8. Closest Packing • Third layer: • If occupy A-type site the layer ordering becomes A-B-A-B and creates a hexagonalclosest packedstructure(HCP) • Coordination number (nearest or touching neighbors) = 12 • 6 coplanar • 3 above the plane • 3 below the plane

  9. Closest Packing • Third layer: • If occupy A-type site the layer ordering becomes A-B-A-B and creates a hexagonalclosest packedstructure(HCP)

  10. Closest Packing • Third layer: • If occupy A-type site the layer ordering becomes A-B-A-B and creates a hexagonalclosest packedstructure(HCP)

  11. Closest Packing • Third layer: • If occupy A-type site the layer ordering becomes A-B-A-B and creates a hexagonalclosest packedstructure(HCP)

  12. Closest Packing • Third layer: • If occupy A-type site the layer ordering becomes A-B-A-B and creates a hexagonalclosest packedstructure(HCP) • Note top layer atoms are directly above bottom layer atoms

  13. Closest Packing • Third layer: • Unit cell

  14. Closest Packing • Third layer: • Unit cell

  15. Closest Packing • Third layer: • Unit cell

  16. Closest Packing • Third layer: • View from top shows hexagonal unit cell

  17. Closest Packing • Third layer: • View from top shows hexagonal unit cell • Mg is HCP

  18. Closest Packing • Alternatively we could place the third layer in the C-type site (above voids in both A and B layers)

  19. Closest Packing • Third layer: • If occupy C-type site the layer ordering is A-B-C-A-B-C and creates a cubicclosest packedstructure(CCP) • Blue layer atoms are now in a unique position above voids between atoms in layers A and B

  20. Closest Packing • Third layer: • If occupy C-type site the layer ordering is A-B-C-A-B-C and creates a cubicclosest packedstructure(CCP) • Blue layer atoms are now in a unique position above voids between atoms in layers A and B

  21. Closest Packing • Third layer: • If occupy C-type site the layer ordering is A-B-C-A-B-C and creates a cubicclosest packedstructure(CCP) • Blue layer atoms are now in a unique position above voids between atoms in layers A and B

  22. Closest Packing • Third layer: • If occupy C-type site the layer ordering is A-B-C-A-B-C and creates a cubicclosest packedstructure(CCP) • Blue layer atoms are now in a unique position above voids between atoms in layers A and B

  23. Closest Packing • Third layer: • If occupy C-type site the layer ordering is A-B-C-A-B-C and creates a cubicclosest packedstructure(CCP) • Blue layer atoms are now in a unique position above voids between atoms in layers A and B

  24. Closest Packing • View from the same side shows the face-centered cubic unit cell that results. • The atoms are slightly shrunken to aid in visualizing the structure A-layer C-layer B-layer A-layer

  25. Closest Packing • Rotating toward a top view

  26. Closest Packing • Rotating toward a top view

  27. Closest Packing • You are looking at a top yellow layer A with a blue layer C below, then a red layer B and a yellow layer A again at the bottom

  28. Closest Packing • CCP is same as face centered cubic • Al is CCP

  29. What happens when RC/RA decreases? • The center cation becomes too small for the site (as if a hard-sphere atom model began to rattle in the site) and it drops to the next lower coordination number (next smaller site). • It will do this even if it is slightly too large for the next lower site. • It is as though it is better to fit a slightly large cation into a smaller site than to have one rattle about in a site that is too large.

  30. The next smaller crystal site is: • Body-Centered Cubic (BCC) with cation (red) in the center of a cube • All cations need to be the same element for BCC • Coordination number is now 8 (corners of cube)

  31. A central cation will remain in VIII coordination with decreasing RC/RA until it again reaches the limiting situation in which all atoms mutually touch. • Then a hard-sphere cation would “rattle” in the position, and it would shift to the next lower coordination (next smaller site). • What is the RC/RA of that limiting condition?? Set = 1 arbitrary since will deal with ratios Diagonal length then = 2

  32. A central cation will remain in VIII coordination with decreasing RC/RA until it again reaches the limiting situation in which all atoms mutually touch. • Then a hard-sphere cation would “rattle” in the position, and it would shift to the next lower coordination (next smaller site). • What is the RC/RA of that limiting condition?? Rotate

  33. A central cation will remain in VIII coordination with decreasing RC/RA until it again reaches the limiting situation in which all atoms mutually touch. • Then a hard-sphere cation would “rattle” in the position, and it would shift to the next lower coordination (next smaller site). • What is the RC/RA of that limiting condition?? Rotate

  34. A central cation will remain in VIII coordination with decreasing RC/RA until it again reaches the limiting situation in which all atoms mutually touch. • Then a hard-sphere cation would “rattle” in the position, and it would shift to the next lower coordination (next smaller site). • What is the RC/RA of that limiting condition?? Rotate

  35. A central cation will remain in VIII coordination with decreasing RC/RA until it again reaches the limiting situation in which all atoms mutually touch. • Then a hard-sphere cation would “rattle” in the position, and it would shift to the next lower coordination (next smaller site). • What is the RC/RA of that limiting condition?? Rotate

  36. A central cation will remain in VIII coordination with decreasing RC/RA until it again reaches the limiting situation in which all atoms mutually touch. • Then a hard-sphere cation would “rattle” in the position, and it would shift to the next lower coordination (next smaller site). • What is the RC/RA of that limiting condition?? Rotate

  37. A central cation will remain in VIII coordination with decreasing RC/RA until it again reaches the limiting situation in which all atoms mutually touch. • Then a hard-sphere cation would “rattle” in the position, and it would shift to the next lower coordination (next smaller site). • What is the RC/RA of that limiting condition?? Rotate

  38. A central cation will remain in VIII coordination with decreasing RC/RA until it again reaches the limiting situation in which all atoms mutually touch. • Fe, Na will form in body centered cubic

  39. CCP coordination = 12 HCP coordination = 12 Body centered coordination = 8 Rc/Ra = 1.0 Rc/Ra = 1.0 Rc/Ra = 0.732 - 1.0 The limits for VIII coordination are thus between 1.0 (when it would by CCP or HCP) and 0.732

  40. As RC/RA continues to decrease below the 0.732 the cation will move to the next lower coordination: VI, or octahedral. The cation is in the center of an octahedron of closest-packed oxygen atoms

  41. As RC/RA continues to decrease below the 0.732 the cation will move to the next lower coordination: VI, or octahedral. The cation is in the center of an octahedron of closest-packed oxygen atoms

  42. As RC/RA continues to decrease below the 0.732 the cation will move to the next lower coordination: VI, or octahedral. The cation is in the center of an octahedron of closest-packed oxygen atoms

  43. As RC/RA continues to decrease below the 0.732 the cation will move to the next lower coordination: VI, or octahedral. The cation is in the center of an octahedron of closest-packed oxygen atoms

  44. As RC/RA continues to decrease below the 0.732 the cation will move to the next lower coordination: VI, or octahedral. The cation is in the center of an octahedron of closest-packed oxygen atoms

  45. As RC/RA continues to decrease below the 0.414 the cation will move to the next lower coordination: IV, or tetrahedral. The cation is in the center of an tetrahedron of closest-packed oxygen atoms

  46. As RC/RA continues to decrease below the 0.414 the cation will move to the next lower coordination: IV, or tetrahedral. The cation is in the center of an tetrahedron of closest-packed oxygen atoms

  47. As RC/RA continues to decrease below the 0.414 the cation will move to the next lower coordination: IV, or tetrahedral. The cation is in the center of an tetrahedron of closest-packed oxygen atoms

  48. As RC/RA continues to decrease below the 0.414 the cation will move to the next lower coordination: IV, or tetrahedral. The cation is in the center of an tetrahedron of closest-packed oxygen atoms

  49. As RC/RA continues to decrease below the 0.414 the cation will move to the next lower coordination: IV, or tetrahedral. The cation is in the center of an tetrahedron of closest-packed oxygen atoms

  50. As RC/RA continues to decrease below the 0.414 the cation will move to the next lower coordination: IV, or tetrahedral. The cation is in the center of an tetrahedron of closest-packed oxygen atoms

More Related