1

STRUCTURES

OF

SOLIDS

S. ChandravathanamPRESENTATION FOR CHILDRENS CLUB

16/4/2005

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CONTENTS

Types of solids

Types of structures adopted by solids

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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

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Crystal Type

Particles Interparticle Forces

Physical Behaviour Examples

Atomic

Molecular

Metallic

Ionic

Network

Atoms

Molecules

Atoms

Positive and negative ions

Atoms

Dispersion

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

• Poor thermal and electrical conductors

Group 8A

Ne to Rn

O2, P4, H2O, Sucrose

Na, Cu, Fe

NaCl, CaF2, MgO

SiO2(Quartz)

C (Diamond)

TYPES OF CRYSTALLINE SOLIDS

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Molecular Solids Covalent Solids Ionic solids

Metallic solids

Na+

Cl-

STRUCTURES OF CRYSTALLINE SOLID TYPES

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DIAMOND QUARTZ

GRAPHITE

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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.

+

Space Lattice + Basis = Crystal Structure

=

• • •

• • •

• • •

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ONE DIMENTIONAL LATTICE

ONE DIMENTIONAL UNIT CELL

a

a

UNIT CELL : Building block, repeats in a regular way

a

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TWO DIMENTIONAL LATTICE

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a

ba b, 90°

a b, = 90°

a

b

a = b, = 90°

a

a

a b, = 90°

a

b

a = b, =120°

a

a

TWO DIMENTIONAL UNIT CELL TYPES

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EXAMPLE OF TWO DIMENTIONAL UNIT CELL

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TWO DIMENTIONAL UNIT CELL POSSIBILITIES OF NaCl

Na+

Cl-

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THREE DIMENTIONAL UNIT CELLS / UNIT CELL SHAPES

1

2

3

4

5

6

7

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Primitive ( P ) Body Centered ( I )

Face Centered ( F ) C-Centered (C )

LATTICE TYPES

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BRAVAIS LATTICES

7 UNIT CELL TYPES + 4

LATTICE TYPES = 14

BRAVAIS LATTICES

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COUNTING ATOMS IN THE THREE DIMENTIONAL UNIT CELL

Vertex(corner) atom shared by 8 cells 1/8 atom per cell

Edge atom shared by 4 cells 1/4 atom per cell

Face atom shared by 2 cells 1/2 atom per cell

Body unique to 1 cell 1 atom per cell

Atoms in different positions in a cell are shared by differing numbers of unit cells

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CLOSE-PACKING OF SPHERES

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Close-packing-HEXAGONAL coordination of each sphere

SINGLE LAYER PACKING

SQUARE PACKING CLOSE PACKING

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TWO LAYERS PACKING

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THREE LAYERS PACKING

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22

Hexagonal close packing Cubic close packing

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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

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NON-CLOSE-PACKED STRUCTURES

68% of space is occupied

Coordination number = 8

a) Body centered cubic ( BCC )

b) Primitive cubic ( P)

52% of space is occupiedCoordination number = 6

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6

ABCABC…12Cubic close packed

ABABAB…12Hexagonal close packed

ABABAB…8Body-centered Cubic

AAAAA…Primitive Cubic

Stacking pattern

Coordination number

Structure

Non-close packing

Close packing

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8 12Coordination

number 6

Primitive cubic Body centered cubic Face centered cubic

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ALLOTROPES

Existence of same element in different crystal structures.

eg. Carbon

Diamond Graphite Buckminsterfullerene

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TETRAHEDRAL HOLES

OCTAHEDRAL HOLES

TYPE OF HOLES IN CLOSE PACKING

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LOCATION OF OCTAHEDRAL HOLES IN CLOSE PACKING

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LOCATION OF TETRAHEDRAL HOLES IN CLOSE PACKING

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Ionic structures may be derived from the

occupation of holes by oppositely charged

ions (interstitial sites) in the close-packed

arrangements of ions.

IONIC CRYSTAL STRUCTURES

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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

Hole Occupation - RADIUS RATIO RULE

Radius of the positive ion

Radius ratio =

Radius of the negative ion

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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

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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

STRUCTURE TYPE - AX

CLOSE PACKED STRUCTURES

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• 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

b) SPHALERITE OR ZINC BLEND (ZnS) STRUCTURE

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• 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)

c) NICKEL ARSENIDE (NiAs)

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• 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)

d) WURTZITE ( ZnS )

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COMPARISON OF WURTZITE AND ZINC BLENDE

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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

+

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• 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)

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• 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)

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ALTERNATE REPRESENTATION OF FLUORITE STRUCTURE

Anti–Flourite structure (or Na2O structure) – positions of

cations and anions are reversed related to Fluorite structure

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RUTILE STRUCTURE, TiO2

• HCP of O2- ( distorted hcp or Tetragonal)

• Ti4+ in half of octahedral holes

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• HCP of Iodide with Cd in Octahedral holes of alternate layers

• CCP analogue of CdI2 is CdCl2

STRUCTURE TYPE - AX2

NON-CLOSE PACKED STRUCTURE

LAYER STRUCTURE ( eg. Cadmium iodide ( CdI2 ))

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COMPARISON OF CdI2 AND NiAs

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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

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HOLE FILLING IN CCP

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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 Not known

AX3 One third octahedral YCl3 BiI3

SUMMARY OF IONIC CRYSTAL STRUCTURE TYPES

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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 CCP Structure Adoption

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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

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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

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• 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)

PEROVSKITE

• Examples: NaNbO3 , BaTiO3 ,

CaZrO3 , YAlO3 , KMgF3

• Many undergo small distortions: e.g. BaTiO3 is ferroelectric

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SPINEL STRUCTURE

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