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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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STRUCTURES

OF

SOLIDS

PRESENTATION FOR CHILDRENS CLUB

16/4/2005

S. Chandravathanam


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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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Na+

Cl-

Ionic solids

Covalent Solids

Molecular Solids

Metallic solids

STRUCTURES OF CRYSTALLINE SOLID TYPES


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QUARTZ

DIAMOND

GRAPHITE


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• • •

• • •

• • •

=

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.


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a

a

a

ONE DIMENTIONAL LATTICE

ONE DIMENTIONAL UNIT CELL

UNIT CELL : Building block, repeats in a regular way



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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




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THREE DIMENTIONAL UNIT CELLS / UNIT CELL SHAPES

1

7

2

3

4

5

6


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LATTICE TYPES

Primitive ( P )

Body Centered ( I )

Face Centered ( F )

C-Centered (C )


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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

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



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SINGLE LAYER PACKING

SQUARE PACKING

CLOSE PACKING

Close-packing-HEXAGONAL coordination of each sphere




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Cubic close packing

Hexagonal 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

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


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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


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Primitive cubic

Body centered cubic

Face centered cubic

Coordination number

12

6

8


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ALLOTROPES

Existence of same element in different crystal structures.

eg. Carbon

Buckminsterfullerene

Diamond

Graphite


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TETRAHEDRAL HOLES

OCTAHEDRAL HOLES

TYPE OF HOLES IN CLOSE PACKING




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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.


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Radius of the positive ion

Radius ratio =

Radius of the negative ion

Hole Occupation - RADIUS RATIO RULE



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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


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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


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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)


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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)


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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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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


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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


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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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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


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COMPARISON OF CdI2 AND NiAs


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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.




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    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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    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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    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


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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


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