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Important Structure Types
1 5/23/2013 L.Viciu| ACII| Imprtant structure types
A. Structures derived from cubic close packed 1. NaCl- rock salt 2. CaF2 – fluorite/Na2O- antifluorite 3. diamond 4. ZnS- blende B. Structures derived from hexagonal close packed 1. NiAs – nickel arsenide 2. ZnS – wurtzite 3. CdI2 – cadmium iodide 4. CdCl2 – cadmium chloride
C. Non close packed structures 1. CsCl – cesium chloride 2. MoS2 - molybdenite D. Metal oxide structures 1. TiO2- rutile 2. ReO3 – rhenium trioxide 3. CaTiO3 – perovskite 4. MgAlO4 - Spinel
2 5/23/2013 L.Viciu| ACII| Imprtant structure types
• Td sites in the f.c.c . arrangement of anions •8 Td sites in total •Location: on the body diagonals – two on each body diagonal at ¼ of the distance from each end.
T • Oh sites in f.c.c. arrangement of anions (fcc unit cell) •4 Oh sites in total • location:
O
41124
1)(
)(
centreedge
Voids in f.c.c. structure
3 5/23/2013 L.Viciu| ACII| Imprtant structure types
A-1. Rock salt: NaCl (halite), Sp. Group, Fm-3m
Cl- form the c.c.p. array
Na+ fills all the Oh holes while the Td holes are empty
Na+: 8x1/8+6x ½= 4
Cl-: 12x ¼ +1=4
95.0
81.1
Na
Cl
r
r
4 NaCl per unit cell
Edge shared Oh
Ionic structure
4
dcoordinateOhNa
r
r
Cl
Na
52.0
Red balls are Cl-
Purple balls are Na+
5/23/2013 L.Viciu| ACII| Imprtant structure types
Compounds with NaCl-rock salt structure
• Halides: LiX, NaX, KX, RbX, AgX –except AgI
• Oxides: MgO, CaO, SrO, BaO, TiO, MnO, FeO, CoO
• Chalcogenides: MgS, CaS, MnS, MgSe, CaSe, CaTe,
At room temperature, they are electrical insulators and transparent in the visible spectral region.
At elevated temperatures, they could become ionic conductors, with the major contribution to charge transport from positive ion vacancy motion.
5 5/23/2013 L.Viciu| ACII| Imprtant structure types
A-2. CaF2-fluorite/Na2O antiflorite (Fm-3m)
I. Ca2+ ions form the c.c.p. array
F- fills all Td voids (Oh voids are empty)
Ca2+: 8 x 1/8 + 6 x ½ = 4
F-: 8 x 1=8
II. F- ions form a simple cubic array
Ca2+ – in the ½ of the cubic sites
F-: 8 x 1/8 +12 x ¼ + 6x ½ +1= 8
Ca2+: 4 x 1 = 4
4 CaF2 in the unit cell C.N.: Ca-8(cubic): F-4(Td)
In the Anti-Fluorite (Na2O) structure, Cation and Anion positions are reversed!
Ionic compound
6
Edge shared FCa4 Td
Corner shared CaF8 cubes
5/23/2013 L.Viciu| ACII| Imprtant structure types
• Fluorite: Halides: SrF2, SrCl2, BaF2, BaCl2, CdF2, HgF2
Oxides: PbO2, CeO2, PrO2,ThO2
Compounds with CaF2 (fluorite) and Na2O (antifluorite) structure:
7 5/23/2013 L.Viciu| ACII| Imprtant structure types
Compounds with fluorite structure are ionic conductors: the charge is carried by anions The fluorite structure favors anion motion because the anions have less charge and are closer together than the cations
• Antifluorite: Oxides: Li2O, Na2O, K2O, Rb2O Chalcogenides: Li2S, Li2Se, Na2S, Na2Se, Na2Te, K2S, K2Se, K2Te
ZrO2 stabilized with CaO or Y2O3: conduction through O2-
8
Batteries = energy conversion + energy storage Solid oxide fuel cells = energy conversion
http://www.gepower.com/research/seca/sofc_research.htm
Fluorite type compounds: Fast Ionic Conductors
High mobility of anion vacancies gives rise to fast ionic (anionic) conduction in fluorite type structure.
A-3. Diamond Structure Covalent structure: the directionality of the covalent bonds dictates
the crystal structure.
C- hybridized sp3
½ of the C form the c.c.p. array
½ of C fills ½ of the Td voids (Oh voids
are empty)
C: 8 x 1/8+6 x ½ = 4
C: 4 x 1 = 4
C.N.: 4
The most stable covalent structure
9 5/23/2013 L.Viciu| ACII| Imprtant structure types
0,1
0,1 ½
½
¼
¼
¾
¾
Properties of diamond
•High pressure allotrope of C (graphite diamond @80kbars)
•Insulator (Eg = 5.4 eV) and transparent; color in diamonds originates
from impurities
i.e. colored diamond:
• good thermal conductivity
i.e. used in semiconductors industry to prevent them from
overheating (thermal sink)
• high refractive index and high optical dispersion(shine) 10 5/23/2013 L.Viciu| ACII| Imprtant structure types
Lattice constant (Å)
Melting
Point (ºC)
Conductor? Eg(eV)
Carbon -diamond
3.56 3550 Insulator 5.4
Silicon 5.43 1410 Semiconductor 1.1
Germanium 5.66 940 Semiconductor 0.7
-Tin 6.49 230 Zero gap semiconductor
0
Group 4 of elements: Si, Ge and -Sn
radius
Compounds with diamond like structure
Eg is inverse proportional with the bond lengths
Longer bonds are weaker and the electrons are easily liberated small band gaps
-Tin is the largest in the group weakest bonds (larger unit cell)
All have the cubic structures (space group: Fd-3m)
11 5/23/2013 L.Viciu| ACII| Imprtant structure types
Changing the motif in diamond structure
5/23/2013 L.Viciu| ACII| Imprtant structure types 12
diamond Zinc Blende
A-4. ZnS- Zinc Blende (Sphalerite) Similar with diamond structure
Layers of ZnS4 Td stacked
..ABCABC..
The crystal may be thought of as two interpenetrating fcc lattices, one for sulfur the other for zinc, with their origins displaced by one quarter of a body diagonal.
13
•S2- form the c.c.p. array
•Zn2+ fills ½ of the Td voids (Oh voids are empty)
•S: 8 x 1/8+6 x ½ = 4
•Zn: 4 x 1 = 4
•C.N.: 4
Red spheres – S2- Green spheres – Zn2+
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Corner shared ZnS4 Td
A
• CuF, CuCl, -CuBr, -CuI, -AgI
• -MnS red, -MnSe, BeS, , ZnS,
• -SiC, BN, BP
• III-V compounds: GaP, GaAs, GaSb, InP, InAs, InSb
Compounds with Zinc Blende- type structure
Note: Crystals containing tetrahedral groups are often piezoelectric (a Td symmetry doesn’t have an inversion center).
14
Unstressed ZnS4 Td Stressed ZnS4 Td
i.e. Zinc blende is piezoelectric
5/23/2013 L.Viciu| ACII| Imprtant structure types
This small cation structure is found for small metallic elements, which tend to form strong sp3 covalent bonds.
Most semiconductors of commercial importance are isomorphous with diamond and zinc blende
Structure – electronic properties relations important for evaluating:
Band gap
Mobility
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16
Band Gap (Eg)
Band gap generally increases with ionicity
Eg increases with increasing the
electronegativity difference between
constituent ions.
kTEge /~ -conductivity -mobility Eg-Band gap T- temperature K-Boltzman constant
5/23/2013 L.Viciu| ACII| Imprtant structure types
Band gap increases with ionicity
Covalent semiconductors have narrow Eg
Generally, band gap and transparency are interconnected
kTEge /~
Ele
ctro
ne
gati
vity
dif
fere
nce
Mobility () for rock salt and zinc blende type materials
2. Mobility as the electronegativity difference btw ions (polarization effect
of mobile electrons or holes on the surrounding atoms) 17
In materials free of defects, the mobility is determined by the effective mass interaction with lattice vibration
Compounds with ionic bonding have low electron mobility
L.Viciu| ACII| Imprtant structure types
1. Mobility as the molecular weight
(heavy mass gives low scattering)
5/23/2013
GaAs
ZnS (Zinc Blende) Structure
4 Ga atoms at (0,0,0)+ FCC translations
4 As atoms at (¼,¼,¼)+FCC translations
Bonding: covalent, partially ionic
Silicon
Diamond Cubic Structure
4 atoms at (0,0,0)+ FCC translations
4 atoms at (¼,¼,¼)+FCC translations
Bonding: covalent
Typical Semiconductors
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19
Properties GaAs Si Crystal structure zinc blende diamond
Lattice constant 5.6532 5.43095
Band gap (eV) at 300 K 1.424 (direct) 1.12 (indirect)
Mobility (cm2/V.s) 8500 1500
Intrinsic carrier conc. (cm-3) 1.79x106 1.45x1010
Difficulty in growing stoichiometric GaAs crystals due to the loss of arsenic
evaporation (>600ᵒ); also the crystals are very brittle
crystal perfection and purity in silicon has reached levels never achieved with any
other synthetic materials.
5/23/2013 L.Viciu| ACII| Imprtant structure types
• Why semiconductors have diamond or ZnS –blende structure?
20 5/23/2013 L.Viciu| ACII| Imprtant structure types
• Why semiconductors have diamond or ZnS –blende structure?
Due to the covalent character of its bonding interaction
(the lattice is always composed of those elements with the smallest difference in electronegativity).
21 5/23/2013 L.Viciu| ACII| Imprtant structure types
Structural Changing
• Pressure –coordination rule: “with increasing pressure an increase of the coordination number takes place”
• Pressure-distance paradox: “when the coordination number increases according to the previous rule, the interatomic distances also increases”
22
Graphite : C.N.= 3; dC-C = 1.415Å; =2.26g/cm3
Diamond: C.N. = 4 dC-C = 1.54Å; = 3.51g/cm3
typeNaClCdSeCdSInAstypeblendeZinc
DiamondGraphite
pressure
pressure
,,:
5/23/2013 L.Viciu| ACII| Imprtant structure types
U. Müller-Inorganic Structural Chemistry
• Td sites in the f.c.c . arrangement of anions •8 Td sites in total •Location: on the body diagonals – two on each body diagonal at ¼ of the distance from each end.
T • Oh sites in f.c.c. arrangement of anions (fcc unit cell) •4 Oh sites in total • location:
O
41124
1)(
)(
centreedge
Voids in f.c.c. structure
23 5/23/2013 L.Viciu| ACII| Imprtant structure types
24
all Td
½ Td
ZnS CaF2
all Oh
NaCl
all Td and all Oh
Li3Bi
c.c.p.
Filling voids in c.c.p. structures
5/23/2013 L.Viciu| ACII| Imprtant structure types
½ Td
5/23/2013 L.Viciu| ACII| Imprtant structure types 25
Fig. 128/pag203 “Relationships among the structures of CaF2, PbO, PtS, ZnS, HgI2, SiS2, and α-ZnCl2. In the top row all tetrahedral interstices (= centers of the octants of the cube) are occupied. Every arrow designates a step in which the number of =occupied tetrahedral interstices is halved; this includes a doubling of the unit cells in the bottom row. Light hatching = metal atoms, dark hatching = non-metal atoms. The atoms given first in the formulas form the cubic closest-packing”
Ulrich Müller: “Inorganic structural chemistry”
all Td sites filled
½ of the Td sites filled
¼ of the Td sites filled
A. Structures derived from cubic close packed 1. NaCl- rock salt 2. CaF2 – fluorite/Na2O- antifluorite 3. diamond 4. ZnS- blende
B. Structures derived from hexagonal close packed 1. ZnS – wurtzite 2. NiAs – nickel arsenide 3. CdI2 – cadmium iodide
C. Non close packed structures 1. CsCl – cesium chloride 2. MoS2 - molybdenite
D. Metal oxide structures 1. TiO2- rutile 2. ReO3 – rhenium trioxide 3. CaTiO3 – perovskite 4. MgAlO4 - Spinel 26
5/23/2013 L.Viciu| ACII| Imprtant structure types
Voids in h.c.p. structure
Td void
The voids are identical to the ones found in FCC
Octahedral voids occur in 1 orientation, tetrahedral voids occur in 2 orientations 27
The spacing of the close packed layers: d = √8r/√3 = 1.633r c=2x1.633r=2x1.633xa/2=1.633a c/a=1.633 A
B
A
(0,0,5/8), (⅔,⅓,7/8)
(⅔, ⅓,1/8),
(0,0,3/8)
Oh void (1/3, 2/3, ¼)
(1/3, 2/3, 3/4)
A
B
)2
1,
3
1,
3
2(
5/23/2013 L.Viciu| ACII| Imprtant structure types
B-1. Wurtzite (ZnS) (P63mc)
•Layers of ZnS4 Td stacked ..ABAB… •Alternate layers are rotated by 180ᵒ about c axis relative to each other.
28
•S2- form the h.c.p. array (c/a=1.633)
•Zn2+ fills ½ of Td voids (T+ or T-)
•S: at (0,0,0) and (2/3, 1/3, ½)
•Zn-: at (2/3, 1/3, 1/8) and (0,0, 5/8)
•c/a = 1.636 (the ideal c/a=1.633)
A
B
S2--yellow spheres Zn2+-green spheres
A
5/23/2013 L.Viciu| ACII| Imprtant structure types
Zn neighbors in Wurtzite structure
5/23/2013 L.Viciu| ACII| Imprtant structure types 29
nearest neighbors: 4 S ions Next nearest neighbors: 12 Zn ions
1
(ex: the ion 1 has 6 Zn ions at distance a in the same plane with it and three Zn in the plane below and then three in the plane above it –the next cell)
S2--yellow spheres Zn2+-green spheres
Two unit cells of the Wurtzite structure
30
(1/3, 2/3, 3/8)
(1/3, 2/3 ,0)
(0,0,0)
(0,0, 5/8)
5/23/2013 L.Viciu| ACII| Imprtant structure types
31
•Zn-: 2 x ½ + 1=2 per cell at (1/3, 2/3 ,0) + h.c.p translation (2/3, 1/3, ½)
•S: 2 x 1 = 2 per unit cell at (1/3, 2/3, 3/8) + h.c.p translation (2/3, 1/3, 7/8)
•2 ZnS per unit cell
•C.N.: 4:4 (Td)
Different view of the Wurtzite structure
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• ZnO, ZnS, ZnSe, ZnTe
• BeO
• CdS, CdSe, MnS, MnSe
• AgI
• AlN, GaN, InN, TlN,
• SiC
Compounds with wurtzite type structure
32
The highlighted blue compounds are piezoelectrics
The symmetry of the wurtzite type structure allows for a distortion along the c axis distorted Td
5/23/2013 L.Viciu| ACII| Imprtant structure types
33
Zinc Blende vs. Wurtzite
Zn is Td coordinated corner
shared Td
…ABCABC…
Zn is Td coordinated corner shared Td but the
layers are rotated by 180ᵒ relative to each other
…ABAB…
•Different electrostatic interaction between an atom and its third neighbors
(…ABCABC… VS …ABAB…);
•Covalent compounds with tendency towards lattice instability as ionicity increases
A
B
A
5/23/2013 L.Viciu| ACII| Imprtant structure types
= 4.11g/cm3 = 3.98g/cm3
5/23/2013 L.Viciu| ACII| Imprtant structure types 34
Zn next nearest neighbors in zinc blende structure
5/23/2013 L.Viciu| ACII| Imprtant structure types 35
Zinc Blende vs. Wurtzite
36 5/23/2013 L.Viciu| ACII| Imprtant structure types
zinc blende wurtzite m.p. sublimes at t=1185C 1850C Eg 3.68eV 3.911eV
(A = constant in the lattice energy formula which
depends on the crystal geometry. It is the sum of a series of numbers representing the number of nearest neighbors and their relative distance from a given ion)
Wurtzite structure is more open
Wurtzite is more ionic than Zinc Blende: the lattice energy of wurtzite is larger than
that of zinc blende
i.e. Awurtzite = 1.641
Azinc blende = 1.638
Covalent compounds with tendency towards lattice instability as ionicity increases
37
B2. NiAs- Nickel Arsenide(P63/mmc)
• As form the h.c.p. array (c/a=1.391)
• Ni fills all Oh voids (all Td voids empty)
•2As at (0,0,0) and (1/3,2/3,1/2
•2Ni at (2/3,1/3,1/4) and (2/3,1/3,3/4)
•C.N.: Ni 6 (octahedral) : As 6 (trigonal prismatic)
•NiAs6 Oh share opposite faces chains of face sharing Oh along c •Chains of edge shared Oh in the ab plane
5, 7 and 8 are arsenic ions common to two Oh; 3 and 7 are arsenic ions common to two Oh
•Edge sharing AsNi6 trigonal prisms
5/23/2013 L.Viciu| ACII| Imprtant structure types
5/23/2013 38 L.Viciu| ACII| Imprtant structure types
I. Ni at the corners of the hexagonal cell. One As is in the center of a hexagonal prism
formed by six Ni atoms. The result is doubling of the repeat unit in
the c- direction. 2NiAs per unit cell (Z=2)
Hexagonal layers of nickel alternating with hexagonal layers of arsenic. Note: this is not a layered structure ; it is a tightly connected three dimensional array!
1/4
3/4
0, 1/2
As
Ni
Ni
Ni
As
As
1/2
1/4, 3/4
0,1
NiAs – alternative views
I. II.
II. As’s form the hexagonal close packed sub-lattice, which is interpenetrated by a primitive hexagonal sublattice of the metal (Ni) atoms.
Compounds with NiAs type structure
39
The NiAs structure is a common structure in metallic compounds of
(a) transition metals with (b) heavy p-block elements (As, Sb, Bi, S, Se).
•Intermetallic compounds: NiSb, NiSn, FeSb, PtSn, MnAs, MnBi, PtBi •Transition metals chalcogenides: NiS, NiSe, NiTe, FeS, FeSe, FeTe, CoS, CoSe, CoTe, CrSe, CrTe, MnTe
5/23/2013 L.Viciu| ACII| Imprtant structure types
c/a < 1.633 due to metallic bonding on c direction
Overlap of 3d orbitals gives rise to metallic bonding.
Bond distance, dNi-Ni, in NiAs is 2.55Å
Typical dNi-Ni is the the range 2.7-2.9 Å
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Change at the Fermi surface with change in the bond distance change in c/a ratio as changing the electron count.
Most NiAs type materials are metallic.
A.West: page 249
NiAs vs. NaCl
A
A
B
B
5/23/2013 41 L.Viciu| ACII| Imprtant structure types
A
B
C
A
Both structures have all the octahedral voids filled
AB compounds: appreciable metallic bond adopt NiAs structure type appreciable ionic bond adopt NaCl structure type
B3: CdI2: Cadmium Iodide (P-3m1)
42
• I form the h.c.p. array
• Cd2+ fills ½ of Oh voids
• Hexagonal lattice
•1CdI2 in the unit cell
I-
Cd2+
A
B
A
B
• one Cd at (0,0,0);
• Two I:
(2/3,1/3,1/4); (1/3,2/3,3/4)
C.N.: Cd - 6 (Octahedral) : I - 3 (base pyramid) 5/23/2013 L.Viciu| ACII| Imprtant structure types
43
Alternative views
C.N.: Cd 6 (Octahedral) I 3 (base pyramid)
6:3 Cd ion in the highlighted sulfur unit cell
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¾
0,1
¼
Compounds with CdI2 structure
44
•Iodides of moderately polarizing cations; bromides and chlorides of strongly polarizing 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
5/23/2013 L.Viciu| ACII| Imprtant structure types
van der Waals attraction between neighboring iodine layers
The structure is stabilized by highly covalent interactions and large, polarizable
anions
Anisotropic properties due to the layered structure
NiAs vs. CdI2
45
CdI2 view on the c axis (top view)
NiAs view on c axis (top view)
5/23/2013 L.Viciu| ACII| Imprtant structure types
Ni
As
As
Ni
Ni
Ni Ni Ni
Ni Ni Ni
Ni Ni Ni
Cd
I
I
Cd
Cd Cd
Cd Cd
Cd Cd
¼
¾ 0, ½ , 1
¼
¾ 0, 1
CdI2 vs. CdCl2 (R-3m)
46
•2D hexagonal structures with different stacking in the 3rd direction •Layers made of CdX6 octahedra •Between layers only van der Waals interactions
A
B
C
A
B
C
A
B
A
B
A
B
A
B
5/23/2013 L.Viciu| ACII| Imprtant structure types
Cubic close packed anions hexagonal close packed anions
Compounds with CdCl2 structure
47
•Chlorides of moderately polarizing cations e.g. MgCl2, MnCl2 •Di-sulfides of quadrivalent cations e.g. TaS2, NbS2 •Cs2O has the anti-cadmium chloride structure
5/23/2013 L.Viciu| ACII| Imprtant structure types
Hexagonal structure with c.c.p. anion arrangement therefore not
h.c.p. derived!
Anisotropic properties due to the layered structure
5/23/2013 L.Viciu| ACII| Imprtant structure types 48
Filling voids in h.c.p. structures
h.c.p. array
½ Oh filled
all Oh filled
½ Td filled
all Td filled?
No!
CdI2
NiAs
ZnS
A. Structures derived from cubic close packed: 1. NaCl- rock salt 2. CaF2 – fluorite/Na2O- antifluorite 3. diamond 4. ZnS- blende
B. Structures derived from hexagonal close packed 1. NiAs – nickel arsenide 2. ZnS – wurtzite 3. CdI2 – cadmium iodide
C. Non close packed structures 1. CsCl – cesium chloride 2. MoS2 - molybdenite
D. Metal oxide structures 1. TiO2- rutile 2. ReO3 – rhenium trioxide 3. CaTiO3 – perovskite 4. MgAlO4 - Spinel 49 5/23/2013 L.Viciu| ACII| Imprtant structure types
50
C1: CsCl- Cesium Chloride (Pm-3m)
½
•Cl- ions form a primitive array Cubic lattice
• One Cl atom at (0,0,0);
•One Cs at (1/2,1/2,1/2)
•1CsCl unit in the cell
Adopted by chlorides, bromides and iodides of large cations: Cs+, Tl+, NH4+
Adopted by intermetallic compounds: CuZn, CuPd, TiX with X=Fe, Co, Ni; etc.
5/23/2013 L.Viciu| ACII| Imprtant structure types
•C.N.: Cs - 8 (cubic) : Cl - 8 (cubic)
C2: MoS2 – Molybdenite (P63/mmc)
51
Hexagonal layers of S are not close-packed in 3D Hexagonal lattice
•2Mo at (2/3,1/3,3/4) and (1/3,2/3,1/4)
• 4I at (2/3,1/3,1/8), (2/3,1/3,3/8), (1/3,2/3,5/8) & (1/3,2/3,7/8)
•2MoS2 in unit cell
•C.N.: Mo - 6 (Trigonal Prismatic) : S 3 (base pyramid) L.Viciu| ACII| Imprtant structure types
1/8, 3/8, ¾
¼ , 5/8, 7/8 Layers of edge shared MoS6 trigonal prisms
5/23/2013
MoS2 vs. CdI2
MoS2
A
B
A
B
A
B
CdI2
Staggered stacks of prisms Eclipsed stacks of octahedra
A
A
B
B
A
A
5/23/2013 52 L.Viciu| ACII| Imprtant structure types
5/23/2013 L.Viciu| ACII| Imprtant structure types 53
Compounds with MoS2 structure
Compounds of type: TX2
T = transition metal of group IVB, VB or VIB X= S, Se, Te
where
Anisotropic electronic properties due to the layered structure
Ion intercalation gives mixed valence materials with interesting physics
Li-intercalation in MoS2 changes the coordination of Mo from trigonal prismatic to Oh
MoS2, ZrS2, and HfS2 when intercalated with alkali metals become superconducting
A. Structures derived from cubic close packed 1. NaCl- rock salt 2. CaF2 – fluorite/Na2O- antifluorite 3. diamond 4. ZnS- blende
B. Structures derived from hexagonal close packed 1. NiAs – nickel arsenide 2. ZnS – wurtzite 3. CdI2 – cadmium iodide
C. Non close packed structures 1. CsCl – cesium chloride 2. MoS2 - molybdenite
D. Metal oxide structures 1. TiO2- rutile 2. ReO3 – rhenium trioxide 3. CaTiO3 – perovskite 4. MgAlO4 - Spinel 54 5/23/2013 L.Viciu| ACII| Imprtant structure types
D1: Rutile, TiO2(P42/mnm)
•O2- ions form a distorted h.c.p. array or a
tetragonal structure
•Ti4+ fills ½ of the Oh voids
• two Ti4+ ions at (0, 0, 0) and (1/2, 1 / 2, 1 /2)
• four O2- at ±(0.3, 0.3, 0) and (0.8, 0.2, 1 /2)
• 2TiO2 per unit cell (Ti2O4) 55
Chains of edge shared TiO6 Oh on
c direction
Edge-shared chains are linked by corners
Blue spheres Ti4+
Red spheres O2-
5/23/2013 L.Viciu| ACII| Imprtant structure types
½
½
½ 0,1
0,1 0, 1
C.N.: Ti - 6 (Oh) : O - 3 (trigonal planar)
Two unit cells on top of each other are shown
56
h.c.p.
network of corner sharing Oh in a h.c.p. array made of O2- ions with Ti4+ filling ½ of Oh sites in an alternant manner: one full then one empty
TiO2 (Rutil): tetragonal structure resulted from h.c.p. distortion
tetragonal
5/23/2013 L.Viciu| ACII| Imprtant structure types
TiO2 – is a 3 D structure!!!
distortion
Strong M-O bonds
CdI2 vs. TiO2
h.c.p. array of I- with Cd2+ in ½ Oh voids
The Oh voids in one layered empty
Layered structure
h.c.p. array of O2- with Ti4+ in ½ Oh voids
The Oh voids are alternating in a layer
3D structure 5/22/2013 57 L.Viciu| ACII| Imprtant structure types
Examples of TiO2 –type structure adoption
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Oxides: MO2 (e.g. Ti, Nb, Cr, Mo, Ge, Pb, Sn)
Fluorides: MF2 (e.g. Mn, Fe, Co, Ni, Cu, Zn, Pd)
TiO2-x anisotropic conductor (extensive overlap of the d-orbitals along c axis and no
orbital overlap on the perpendicular direction the conductivity in the ab plane is 3 order
of magnitude smaller than on the c axis)
5/22/2013 L.Viciu| ACII| Imprtant structure types
Rutile-type oxides with one or more d electrons often display remarkable electronic and magnetic properties.
One type of M-M bonds (2.96Å) (in Ti metal, Ti-Ti bond is 2.92Å)
Alternating short (2.51Å vs 2.725Å in Mo metal) and long M-M bonds
Ti4+ (d0)are equidistant
Mo4+ (d2)
TiO2
MoO2
5/22/2013 L.Viciu| ACII| Imprtant structure types 59
2 Ti t2g orbitals overlap with O p orbitals metal-oxygen π band 1 Ti t2g orbital (along the tetragonal c axis) forms nonbonding cation sublattice band (the conduction band, ) (a) empty (b) partially filled by the 2 e- of V (c) split into localized bonding and antibonding levels
Structure -properties relationship in the rutile compounds
TiO2-rutile VO2-rutile type VO2-monoclinic
Ti, d0 ion -insulator V, d1 ion -metal V, d1 ion in a distorted
structure-insulator
Brookite Anatase Rutile
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TiO2 polymorphs
C915 C750
Tetragonal *Eg = 1.78eV
Tetragonal *Eg=2.04eV
Orthorhombic *Eg = 2.20eV
* Calculated values
High refractive index; Excellent optical transmittance in the VIS and NIR region; High
dielectric constant;
All have been studied for their photocatalytic and photoelectrochemical applications. 5/22/2013 L.Viciu| ACII| Imprtant structure types
D2: Rhenium Trioxide, ReO3 (bronzes)(Pm-3m)
•Defective f.c.c. array : one oxygen site on the face
missing; Cubic lattice
• Re at (0, 0, 0);
•3O at (1/2, 0, 0), (0, 1/2, 0), (0, 0, 1/2)
•1ReO3 per unit cell
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Black spheres Re6+
Red spheres O2- Corner shared ReO6 Oh
5/22/2013 L.Viciu| ACII| Imprtant structure types
C.N.: Re - 6 (Oh) : O - 2 (linear)
0, ½ , 0
0,1
0,1
5/22/2013 L.Viciu| ACII| Imprtant structure types 62
Compounds with ReO3 structure
Oxides: WO3 , UO3, Fluorides: AlF3, ScF3 , FeF3 , CoF3, MoF3 Others: Sc(OH)3, TaO2F, Cu3N,
Re6+ is d1 system and metallic conductivity is expected Ion intercalation/substitution led to mixed oxidation state magnetic and electronic properties
Ex: WO3 is a band insulator with a band gap of 2.6 eV WO3-xFx – superconducts at 0.4K (x up to 0.45 Li doped WO3 is metallic Na doped WO3 shows superconductivity (NaxWO3 (0.2 < x < 0.4), 0.7 K < Tc < 3 K
ternary structures derived from this 3D octahedral network are among the most
important in oxide chemistry
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