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STRUCTURES OF SOLIDS

STRUCTURES OF SOLIDS. PRESENTATION FOR CHILDRENS CLUB 16/4/2005. S. Chandravathanam. CONTENTS Types of solids Types of structures adopted by solids. SOLIDS can be divided into two catagories. Crystalline Amorphous. Crystalline has long range order.

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STRUCTURES OF SOLIDS

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  1. STRUCTURES OF SOLIDS PRESENTATION FOR CHILDRENS CLUB 16/4/2005 S. Chandravathanam

  2. CONTENTS • Types of solids • Types of structures adopted by solids

  3. SOLIDS • can be divided into two catagories. • Crystalline • Amorphous Crystalline has long range order Amorphous materials have short range order Effect of Crystallinity on Physical properties - ex. Polyethylene

  4. TYPES OF CRYSTALLINE SOLIDS

  5. Na+ Cl- Ionic solids Covalent Solids Molecular Solids Metallic solids STRUCTURES OF CRYSTALLINE SOLID TYPES

  6. QUARTZ DIAMOND GRAPHITE

  7. • • • • • • • • • = Space Lattice + Basis = Crystal Structure CRYSTAL STRUCTURE Crystal structure is the periodic arrangement of atoms in the crystal. Association of each lattice point with a group of atoms(Basis or Motif). Lattice: Infinite array of points in space, in which each point has identical surroundings to all others. Space Lattice Arrangements of atoms = Lattice of points onto which the atoms are hung. + Elemental solids (Argon): Basis = single atom. Polyatomic Elements: Basis = two or four atoms. Complex organic compounds:Basis = thousands of atoms.

  8. a a a ONE DIMENTIONAL LATTICE ONE DIMENTIONAL UNIT CELL UNIT CELL : Building block, repeats in a regular way

  9. TWO DIMENTIONAL LATTICE

  10. b a  b,   90° a a a a  b,  = 90° a  b,  = 90° b b a = b,  =120° a = b,  = 90° a a a a TWO DIMENTIONAL UNIT CELL TYPES

  11. EXAMPLE OF TWO DIMENTIONAL UNIT CELL

  12. TWO DIMENTIONAL UNIT CELL POSSIBILITIES OF NaCl Na+ Cl-

  13. THREE DIMENTIONAL UNIT CELLS / UNIT CELL SHAPES 1 7 2 3 4 5 6

  14. LATTICE TYPES Primitive ( P ) Body Centered ( I ) Face Centered ( F ) C-Centered (C )

  15. BRAVAIS LATTICES 7 UNIT CELL TYPES + 4 LATTICE TYPES = 14 BRAVAIS LATTICES

  16. COUNTING ATOMS IN THE THREE DIMENTIONAL UNIT CELL Atoms in different positions in a cell are shared by differing numbers of unit cells • Vertex(corner) atom shared by 8 cellsÞ1/8 atom per cell • Edge atom shared by 4 cellsÞ1/4 atom per cell • Face atom shared by 2 cellsÞ1/2 atom per cell • Body unique to 1 cellÞ1 atom per cell

  17. CLOSE-PACKING OF SPHERES

  18. SINGLE LAYER PACKING SQUARE PACKING CLOSE PACKING Close-packing-HEXAGONAL coordination of each sphere

  19. TWO LAYERS PACKING

  20. THREE LAYERS PACKING

  21. Cubic close packing Hexagonal close packing

  22. Cubic close packing 4 atoms in the unit cell (0, 0, 0) (0, 1 /2, 1 /2) (1 /2, 0, 1 /2) (1 /2, 1 /2, 0) Hexagonal close packing 2 atoms in the unit cell (0, 0, 0) (2/3, 1 /3, 1 /2) 74% Space is occupied Coordination number = 12

  23. NON-CLOSE-PACKED STRUCTURES a) Body centered cubic ( BCC ) b) Primitive cubic ( P) 68% of space is occupied Coordination number = 8 52% of space is occupied Coordination number = 6

  24. Structure Coordination number Stacking pattern Primitive Cubic AAAAA… Non-close packing Body-centered Cubic 8 ABABAB… Hexagonal close packed 12 ABABAB… Close packing Cubic close packed 12 ABCABC… 6

  25. Primitive cubic Body centered cubic Face centered cubic Coordination number 12 6 8

  26. ALLOTROPES Existence of same element in different crystal structures. eg. Carbon Buckminsterfullerene Diamond Graphite

  27. TETRAHEDRAL HOLES OCTAHEDRAL HOLES TYPE OF HOLES IN CLOSE PACKING

  28. LOCATION OF OCTAHEDRAL HOLES IN CLOSE PACKING

  29. LOCATION OF TETRAHEDRAL HOLES IN CLOSE PACKING

  30. IONIC CRYSTAL STRUCTURES Ionic structures may be derived from the occupation of holes by oppositely charged ions (interstitial sites) in the close-packed arrangements of ions.

  31. Radius of the positive ion Radius ratio = Radius of the negative ion Hole Occupation - RADIUS RATIO RULE

  32. IONIC CRYSTAL TYPES

  33. STRUCTURE TYPE - AX CLOSE PACKED STRUCTURES a)ROCK SALT STRUCTURE (NaCl) • CCP Cl- with Na+ in all Octahedral holes • Lattice: FCC • Motif: Cl at (0,0,0); Na at (1/2,0,0) • 4 NaCl in one unit cell • Coordination: 6:6 (octahedral) • Cation and anion sites are topologically identical

  34. b) SPHALERITE OR ZINC BLEND (ZnS) STRUCTURE • CCP S2- with Zn2+ in half Tetrahedral holes ( T+ {or T-} filled) • Lattice: FCC • 4 ZnS in one 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

  35. c) NICKEL ARSENIDE (NiAs) • HCP with Ni in all Octahedral holes • Lattice: Hexagonal - P • Motif: 2Ni at (0,0,0) & (0,0,1/2) 2As at (2/3,1/3,1/4) & (1/3,2/3,3/4) • 2 NiAs in unit cell • Coordination: Ni 6 (octahedral) : As 6 (trigonal prismatic)

  36. d) WURTZITE ( ZnS ) • HCP S2- with Zn2+ in half Tetrahedral holes ( T+ {or T-} filled ) • Lattice: Hexagonal - P • Motif: 2 S at (0,0,0) & (2/3,1/3,1/2); 2 Zn at (2/3,1/3,1/8) & (0,0,5/8) • 2 ZnS in unit cell • Coordination: 4:4 (tetrahedral)

  37. COMPARISON OF WURTZITE AND ZINC BLENDE

  38. STRUCTURE TYPE - AX NON – CLOSE PACKED STRUCTURES CUBIC-P (PRIMITIVE) ( eg.Cesium Chloride ( CsCl ) ) • Motif: Cl at (0,0,0); Cs at (1/2,1/2,1/2) • 1 CsCl in one unit cell • Coordination: 8:8 (cubic) • Adoption by chlorides, bromides and iodides of larger cations, • e.g. Cs+, Tl+, NH4+

  39. STRUCTURE TYPE - AX2 CLOSE PACKED STRUCTURE eg. FLUORITE (CaF2) • CCP Ca2+ with F- in all Tetrahedral holes • Lattice: fcc • Motif: Ca2+ at (0,0,0); 2F- at (1/4,1/4,1/4) & (3/4,3/4,3/4) • 4 CaF2 in one unit cell • Coordination: Ca2+ 8 (cubic) : F- 4 (tetrahedral) • In the related Anti-Fluorite structure Cation and Anion positions are reversed

  40. STRUCTURE TYPE - AX2 CLOSE PACKED STRUCTURE eg. FLUORITE (CaF2) • CCP Ca2+ with F- in all Tetrahedral holes • Lattice: fcc • Motif: Ca2+ at (0,0,0); 2F- at (1/4,1/4,1/4) & (3/4,3/4,3/4) • 4 CaF2 in one unit cell • Coordination: Ca2+ 8 (cubic) : F- 4 (tetrahedral) • In the related Anti-Fluorite structure Cation and Anion positions are reversed

  41. ALTERNATE REPRESENTATION OF FLUORITE STRUCTURE Anti–Flourite structure (or Na2O structure) – positions of cations and anions are reversed related to Fluorite structure

  42. RUTILE STRUCTURE, TiO2 • HCP of O2- ( distorted hcp or Tetragonal) • Ti4+ in half of octahedral holes

  43. STRUCTURE TYPE - AX2 NON-CLOSE PACKED STRUCTURE LAYER STRUCTURE( eg. Cadmium iodide ( CdI2 )) • HCP of Iodide with Cd in Octahedral holes of alternate layers • CCP analogue of CdI2 is CdCl2

  44. COMPARISON OF CdI2 AND NiAs

  45. Unknown HCP analogue of Fluorite Fluorite • HCP ANALOGUE OF FLOURITE (CaF2) ? • No structures of HCP are known with all Tetrahedral sites (T+ and T-) filled. (i.e. there is no HCP analogue of the Fluorite/Anti-Fluorite Structure). • The T+ and T- interstitial sites above and below a layer of close-packed spheres in HCP are too close to each other to tolerate the coulombic repulsion generated by filling with like-charged species.

  46. HOLE FILLING IN CCP

  47. SUMMARY OF IONIC CRYSTAL STRUCTURE TYPES

  48. Examples of CCP Structure Adoption • Rock salt(NaCl) – occupation of all octahedral holes • Very common (in ionics, covalents & intermetallics ) • Most alkali halides (CsCl, CsBr, CsI excepted) • Most oxides / chalcogenides of alkaline earths • Many nitrides, carbides, hydrides (e.g. ZrN, TiC, NaH) • Fluorite (CaF2) – occupation of all tetrahedral holes • Fluorides of large divalent cations, chlorides of Sr, Ba • Oxides of large quadrivalent cations (Zr, Hf, Ce, Th, U) • Anti-Fluorite (Na2O) – occupation of all tetrahedral holes • Oxides /chalcogenides of alkali metals • Zinc Blende/Sphalerite ( ZnS ) – occupation of half tetrahedral holes • Formed from Polarizing Cations (Cu+, Ag+, Cd2+, Ga3+...) and Polarizable Anions (I-, S2-, P3-, ...) • e.g. Cu(F,Cl,Br,I), AgI, Zn(S,Se,Te), Ga(P,As), Hg(S,Se,Te)

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