structures of solids
DESCRIPTION
STRUKTUR OF SOLIDTRANSCRIPT
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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
DispersionDipole-dipoleH-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 8ANe 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°
aa
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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Hexagonal close packing Cubic close packing
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74% Space is occupied. Coordination number = 12
V. 1 atom = 4/3∏ r33
V. Unit cell = a3 = r3
Efficiency of packing = V. 4 atom : V. unit cell = V. 4 atom : V. cubic = 0,7405
CUBIC CLOSE PACKEDCUBIC CLOSE PACKED HEXAGONALCLOSE PACKED
V. 1 atom = 4/3∏ r33
V. Unit cell = 6.a.c = 6.(r.r√3).cEff. Of pack.= V. 6 atom : V. hexagonal = 0,7405
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NON-CLOSE-PACKED STRUCTURES
68% of space is occupiedCoordination number = 8
a) Body centered cubic ( BCC )
b) Primitive cubic ( P)
52% of space is occupiedCoordination number = 6
V. 1 atom = 4/3∏ r3V. Unit cell = a3 = r3Eff. Of pack. = V. 2 atom : V. cubic = 0,6802
V. 1 atom = 4/3∏ r3V. Unit cell = a3 = r3Eff. Of pack. = V. 1 atom : V. cubic = 0,5238
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D = mass per sel satuan / Volume sel satuan = massa molar x Z/ molar volum = FW x Z / (V x N)
V= volume sel satuanN= bilangan avogadroZ= jumlah atom dalam sel satuan D = ( FW x Z x1,66)/ V (0A) gram/cm3
CRYSTAL DENSITIES
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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
NaClCsCl
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 AdoptionNickel 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