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

Types of structures adopted by solids CONTENTS Types of solids Types of structures adopted by solids

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

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)

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

QUARTZ DIAMOND GRAPHITE

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.

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

TWO DIMENTIONAL LATTICE

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

EXAMPLE OF TWO DIMENTIONAL UNIT CELL

TWO DIMENTIONAL UNIT CELL POSSIBILITIES OF NaCl

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

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

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

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

CLOSE-PACKING OF SPHERES

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

TWO LAYERS PACKING

THREE LAYERS PACKING

Hexagonal close packing Cubic close packing

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

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

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

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

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

TYPE OF HOLES IN CLOSE PACKING TETRAHEDRAL HOLES OCTAHEDRAL HOLES

LOCATION OF OCTAHEDRAL HOLES IN CLOSE PACKING

LOCATION OF TETRAHEDRAL HOLES IN CLOSE PACKING

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.

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

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 6 6 8 8 6 3 8 4 6 2 NaCl CsCl Rutile(TiO2) Fluorite (CaF2) ReO3

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

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

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)

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)

COMPARISON OF WURTZITE AND ZINC BLENDE

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+

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

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

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

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

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

COMPARISON OF CdI2 AND NiAs

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

HOLE FILLING IN CCP

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

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)

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

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

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

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