Oblique lattice

3. Oblique lattice • a ≠ b • a ≠ 90˚ • Symmetry 2

4. Rectangular lattice • a ≠ b a = 90˚ • Symmetry 2mm

5. Centered rectangular latticeDiamond lattice • a = b a ≠ 90˚ or 120˚ • Symmetry 2mm

6. Hexagonal lattice • a = b a = 120˚ • Symmetry 6mm

7. Square lattice • a = b a = 90˚ • Symmetry 4mm

9. Triclinic • General case: All side lengths different, all angles different

10. cubic • a = b = c • a = b = g = 90˚

11. tetragonal • a = b ≠ c • a = b = g = 90˚

12. Orthorhombic • a ≠ b ≠ c • a = b = g = 90˚

13. monoclinic • a ≠ b ≠ c • a = g = 90˚, b > 90˚

14. hexagonal • a = b ≠ c • a = b = 90˚, g = 120˚

15. Trigonal (rhombohedral) • a = b = c • 90˚ ≠ a = b = g < 120˚

16. Cube 4C3 R 1C3

17. Symmetry axes and planes of the cube C4 C3 C2

20. Arrangement of atoms in simple cubic Crystal in an arbitrarily chosen plane. Miller Indices characterize the plane independent of unit cell type.

24. Symmetry equivalent planes:{100}

25. l i k h (1010) h+k+i=0

26. Close Packing Either B or C are occupied by next layer, but not both.

27. Close-packed structures A C B A A B A unit cell unit cell

28. Deformability of metals

29. Ordered Alloys CuAu Cu3Au

30. Distribution of interstitial sites between two cp layers

31. Voids in hcp

32. Voids in ccp

33. Tetrahedral voids in ccp

34. 8 tetrahedral sites in fcc

36. Compounds with NaCl structure r+ / r- =0.414

37. Fluorite/Anti-Fluorite Structure • CCP: Ca2+ with F- in all Tetrahedral holes • 4CaF2 in unit cell • Ca2+ at (0,0,0); 2F- at (1/4,1/4,1/4) & (3/4,3/4,3/4) • Coordination: Ca2+ 8 (cubic) : F- 4 (tetrahedral)

38. In the related Anti-Fluorite structure (Na2O) Cation and Anion positions are reversed.

40. Zinc blende (sphalerite) Structure

41. Zinc blende (sphalerite) Structure • CCP: S2- with Zn2+ in half Tetrahedral holes (only T+ {or T-} filled) • Lattice: fcc • 4 ZnS in unit cell • Motif: S at (0,0,0); Zn at (1/4,1/4,1/4) • Coordination: 4:4 (tetrahedral) • Cation and anion sites are topologically identical. • AaBbCcAaBbCc

42. Zinc blende structure minimum r+/r- ratio • rZn2+/rS2- ~ 0.40  oct. Void too large forZn2+  Zn2+ more stable in tetr. Void.  coordination number 4 not 6.  C.N. determined by r+/r- ratio (Pauling’s 1st Rule). • Examples CuF, CuCl, g-CuBr, g-CuI, b-MnS, b-CdS, HgS, BN, BP, AlP, InP, InSb. • Compounds less ionic than corresponding AB cmpd with NaCl structure. Oxides don’t usually have this structure. r- + r- =1.414 a r+ + r- = 0.866 a  r+/r- = 0.225 • cations in contact with anions. • Anions contact each other.

43. ZnS Wurtzite

44. Wurtzite Structure • HCP: S2- with Zn2+ in half Tetrahedral holes (only T+ {or T-} filled) • Lattice: Hexagonal - P • a = b, • Motif: 2S at (0,0,0) & (2/3,1/3,1/2); 2Zn at (2/3,1/3,1/8) & (0,0,5/8) • 2ZnS in unit cell • Coordination: 4:4 (tetrahedral) • AaBbAaBb • Examples: CdS, MnS, AgI, AlN, BeO.

45. 1293 K Zinc blende → Wurtzite

46. Zinc blende vs. Wurtzite .

47. NiAs structure

48. Octahedral void in hcp

49. Octahedral voids in hcp

50. NiAs