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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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slide1

STRUCTURES

OF

SOLIDS

PRESENTATION FOR CHILDRENS CLUB

16/4/2005

S. Chandravathanam

slide2

CONTENTS

    • Types of solids
    • Types of structures adopted by solids
slide3

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

slide5

Na+

Cl-

Ionic solids

Covalent Solids

Molecular Solids

Metallic solids

STRUCTURES OF CRYSTALLINE SOLID TYPES

slide6

QUARTZ

DIAMOND

GRAPHITE

slide7

• • •

• • •

• • •

=

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.

slide8

a

a

a

ONE DIMENTIONAL LATTICE

ONE DIMENTIONAL UNIT CELL

UNIT CELL : Building block, repeats in a regular way

slide10

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

slide14

LATTICE TYPES

Primitive ( P )

Body Centered ( I )

Face Centered ( F )

C-Centered (C )

slide15

BRAVAIS LATTICES

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

slide16

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
slide18

SINGLE LAYER PACKING

SQUARE PACKING

CLOSE PACKING

Close-packing-HEXAGONAL coordination of each sphere

slide22

Cubic close packing

Hexagonal close packing

slide23

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

slide24

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

slide25

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

slide26

Primitive cubic

Body centered cubic

Face centered cubic

Coordination number

12

6

8

slide28

ALLOTROPES

Existence of same element in different crystal structures.

eg. Carbon

Buckminsterfullerene

Diamond

Graphite

slide29

TETRAHEDRAL HOLES

OCTAHEDRAL HOLES

TYPE OF HOLES IN CLOSE PACKING

slide32

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.

slide33

Radius of the positive ion

Radius ratio =

Radius of the negative ion

Hole Occupation - RADIUS RATIO RULE

slide35

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
slide36

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
slide37

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)
slide38

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)
slide40

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+
slide41

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
slide42

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
slide43

ALTERNATE REPRESENTATION OF FLUORITE STRUCTURE

Anti–Flourite structure (or Na2O structure) – positions of cations and anions are reversed related to Fluorite structure

slide44

RUTILE STRUCTURE, TiO2

  • HCP of O2- ( distorted hcp or Tetragonal)
  • Ti4+ in half of octahedral holes
slide45

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
slide47

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.
slide50

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)
slide51

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
slide52

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
slide53

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
slide54

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
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