STRUCTURES

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STRUCTURES OF SOLIDS
S. Chandravathanam
PRESENTATION 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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TYPES OF CRYSTALLINE SOLIDS
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STRUCTURES OF CRYSTALLINE SOLID TYPES
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QUARTZ
DIAMOND
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.
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ONE DIMENTIONAL LATTICE
ONE DIMENTIONAL UNIT CELL
UNIT CELL Building block, repeats in a regular
way
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TWO DIMENTIONAL LATTICE
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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
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 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

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CLOSE-PACKING OF SPHERES
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SINGLE LAYER PACKING
SQUARE PACKING
CLOSE PACKING
Close-packing-HEXAGONAL coordination of each
sphere
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TWO LAYERS PACKING
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THREE LAYERS 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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6
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ALLOTROPES Existence of same element in
different crystal structures. eg. Carbon
Buckminsterfullerene
Diamond
Graphite
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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 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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Hole Occupation - RADIUS RATIO RULE
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IONIC CRYSTAL TYPES
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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 66 (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 44 (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 44 (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 88 (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
AntiFlourite 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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• 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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HOLE FILLING IN CCP
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SUMMARY OF IONIC CRYSTAL STRUCTURE TYPES
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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