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

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

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

4. TYPES OF CRYSTALLINE SOLIDS
Crystal Type
Particles
Interparticle Forces
Physical Behaviour
Examples
Atomic
Molecular
Metallic
Ionic
Network
Atoms
Molecules
Positive and negative ions
Dispersion
Dipole-dipole
H-bonds
Metallic bond
Ion-ion attraction
Covalent
Soft
Very low mp
Poor thermal and electrical conductors
Fairly soft
Low to moderate mp
Poor thermal and electrical conductors
Soft to hard
Low to very high mp
Mellable and ductile
Excellent thermal and electrical conductors
Hard and brittle
High mp
Good thermal and electrical conductors in molten condition
Very hard
Very high mp
Group 8A
Ne to Rn
O2, P4, H2O, Sucrose
Na, Cu, Fe
NaCl, CaF2, MgO
SiO2(Quartz)
C (Diamond)

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

6. QUARTZ
DIAMOND
GRAPHITE

7. 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.
Space Lattice + Basis = Crystal Structure =
• • • +
Elemental solids (Argon): Basis = single atom.
Polyatomic Elements: Basis = two or four atoms.
Complex organic compounds: Basis = thousands of atoms.

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

9. TWO DIMENTIONAL LATTICE

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

11. EXAMPLE OF TWO DIMENTIONAL UNIT CELL

12. TWO DIMENTIONAL UNIT CELL POSSIBILITIES OF NaCl

13. THREE DIMENTIONAL UNIT CELLS / UNIT CELL SHAPES1 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 cells Þ 1/8 atom per cell
Edge atom shared by 4 cells Þ 1/4 atom per cell
Face atom shared by 2 cells Þ 1/2 atom per cell
Body unique to 1 cell Þ 1 atom per cell

17. CLOSE-PACKING OF SPHERES

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

19. TWO LAYERS PACKING

20. THREE LAYERS PACKING

22. Hexagonal close packing
Cubic close packing

23. 2 atoms in the unit cell (0, 0, 0) (2/3, 1 /3, 1 /2)
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

24. 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

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

26. Coordination number Primitive cubic Body centered cubic8 12
Coordination number 6
Primitive cubic
Body centered cubic
Face centered cubic

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

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

30. LOCATION OF OCTAHEDRAL HOLES IN CLOSE PACKING

31. LOCATION OF TETRAHEDRAL HOLES IN CLOSE PACKING

32. 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.

33. Holes in which positive ions pack
Hole Occupation - RADIUS RATIO RULE
Radius of the positive ion
Radius ratio =
Radius of the negative ion
Radius ratio
Coordinate number
Holes in which positive ions pack
0.225 – 0.414 4
Tetrahedral holes
0.414 – 0.732 6
Octahedral holes
0.732 – 1 8
Cubic holes

34. Ionic crystal type Co-ordination number A X Structure type
IONIC CRYSTAL TYPES
Ionic crystal type
Co-ordination number
A X
Structure type AX
AX2
AX3
NaCl
CsCl
Rutile(TiO2)
Fluorite (CaF2)
ReO3

35. CLOSE PACKED STRUCTURES
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

36. 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

37. 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)

38. 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)

39. COMPARISON OF WURTZITE AND ZINC BLENDE

40. NON – CLOSE PACKED STRUCTURES
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+

41. 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

42. 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

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

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

45. 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

46. COMPARISON OF CdI2 AND NiAs

47. 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.
Unknown HCP analogue of Fluorite
Fluorite

48. HOLE FILLING IN CCP

49. Type and fraction of sites occupied
SUMMARY OF IONIC CRYSTAL STRUCTURE TYPES
Formula
Type and fraction of sites occupied
CCP
HCP AX
All octahedral
Half tetrahedral (T+ or T-)
Rock salt (NaCl)
Zinc Blend (ZnS)
Nickel Arsenide (NiAs)
Wurtzite (ZnS)
AX2
All Tetrahedral
Half octahedral (ordered framework)
Half octahedral (Alternate layers full/ empty)
Fluorite (CaF2),
Anti-Fluorite (Na2O)
Anatase (TiO2)
Cadmium Chloride (CdCl2)
Not known
Rutile (TiO2)
Cadmium iodide (CdI2)
A3X
All octahedral & All Tetrahedral
Li3Bi
AX3
One third octahedral
YCl3
BiI3

50. 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)

51. Examples of HCP Structure Adoption
Nickel Arsenide ( NiAs ) – occupation of all octahedral holes
Transition metals with chalcogens, As, Sb, Bi e.g. Ti(S,Se,Te); Cr(S,Se,Te,Sb); Ni(S,Se,Te,As,Sb,Sn)
Cadmium Iodide ( CdI2 ) – occupation half octahedral (alternate) holes
Iodides of moderately polarising cations; bromides and chlorides of strongly polarising cations. e.g. PbI2, FeBr2, VCl2
Hydroxides of many divalent cations. e.g. (Mg,Ni)(OH)2
Di-chalcogenides of many quadrivalent cations . e.g. TiS2, ZrSe2, CoTe2
Cadmium Chloride CdCl2 (CCP equivalent of CdI2) – half octahedral holes
Chlorides of moderately polarising cations e.g. MgCl2, MnCl2
Di-sulfides of quadrivalent cations e.g. TaS2, NbS2 (CdI2 form as well)
Cs2O has the anti-cadmium chloride structure

52. PEROVSKITE STRUCTURE
Formula unit – ABO3
CCP of A atoms(bigger) at the corners
O atoms at the face centers
B atoms(smaller) at the body-center

53. PEROVSKITE Lattice: Primitive Cubic (idealised structure)
1 CaTiO3 per unit cell
A-Cell Motif: Ti at (0, 0, 0); Ca at (1/2, 1/2, 1/2); 3O at (1/2, 0, 0), (0, 1/2, 0), (0, 0, 1/2)
Ca 12-coordinate by O (cuboctahedral)
Ti 6-coordinate by O (octahedral)
O distorted octahedral (4xCa + 2xTi)
Examples: NaNbO3 , BaTiO3 , CaZrO3 , YAlO3 , KMgF3
Many undergo small distortions: e.g. BaTiO3 is ferroelectric

54. SPINEL STRUCTURE INVERSE SPINEL
Formula unit AB2O4 (combination of Rock Salt and Zinc Blend Structure)
Oxygen atoms form FCC
A2+ occupy tetrahedral holes
B3+ occupy octahedral holes
INVERSE SPINEL
A2+ ions and half of B3+ ions occupy octahedral holes
Other half of B3+ ions occupy tetrahedral holes
Formula unit is B(AB)O4