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CH 24. Solids
• DefectsDefects– Non-stoichiometry, Ionic ConductivityNon-stoichiometry, Ionic Conductivity
• Cooperative PhenomenonCooperative Phenomenon– Magnetism, Piezoelectricity, SuperconductivityMagnetism, Piezoelectricity, Superconductivity
• Topochemical ReactionsTopochemical Reactions– Intercalation chemistryIntercalation chemistry
2
Defect types
Frenkel
(interstitial)
Shottky (vacancy) Substitution
NaCl Shottky vacancy 10-12 M at 130 °C (1 / 1014 units)TiO Shottky vacancy ≈10 M at 25 °C (1 / 10 units)AgCl Frenkel interstitial Ag+
3
F-centers
NaCl Na1+xCl green/yellow epr “free e-”
NaCl NaKxCl green/yellow same
KCl K1+xCl violet
KCl KNaxCl violetΔ
Δ
Δ
Δ
Na
Na
K
K
4
Defect concentrations
5
Intrinsic vs extrinsic defects
Intrinsic – thermodynamic effect, defects are favored by G min
Extrinisic – defects introduced by sample prep conditions, dopants, impurities (intentional or unintentional)
Examples:
n-doped Si (m) “n-doped Si”
Li2O in NiO LixNi(III)xNi(II)1-xO introduce Li+ to change electronic properties
6
Extended defects
Shear planes in WO3-x
7
Non-stoichiometric oxides
Mo8O23
8
Non-stoichiometry
9
Ionic Conduction
Concentration gradients: Fick’s Law
Microscopic view:Correlation of defects with mechanism
10
Ionic Conduction
Macroscopic view:
Measure ionic = i (Di, qi, ci)
i
i = all significant charge carriers
D = diffusion coefficient (related to mobility)
q = ion charge
c = ion concentration
Arrhenius behavior: = o exp (-Ea/RT)
ln vs 1/T is linear with slope = Ea/R
11
AgI
-AgI wurtzite (AaBb)n
, 146 C -AgI bcc I array with Ag+ statistically distributed in CN=3,4 sites
~ 1Ω-1cm-1 , Ea ~0.05 eV
when -AgI melts at 550 C, the Ag+ decreases!
12
Ag2HgI4 and RbAg4I5
Close packed I lattice with 3/8 Td sites occupied
order/disorder transition at 50 C (break in data)
RbAg4I5 is single phase from RT to 500 C ~ bcc I array
~ 0.25 Scm-1; Ea~0.07eV
VTF behavior - lattice activation contributes to conduction mechanism, so Arrhenius plot is curved
13
Calcium-stabilized zirconia
CaxZr1xO2x□x □ = O2 ion vacancy
Fluorite structure
(8,4) (AabBbcCca)n (O2) ~104 at 500°C
14
Solid oxide fuel cell / sensor
Concentration cell
gas sample 2O2 O2 + 4e
Air 4e + O2 2O2
O2 sensor in auto exhaust
E log pO2 (sample) / pO2 (air)
2H2 + 202 2H2O + 4e
4e + O 2 202
160 torr
15
Na-’’-alumina
(Na+) ~10 Scm-1 at 300 C
16
D for some ion conductors
17
1st row TM MOx compounds
18
FeO1.04-1.17
3Fe2+ 2Fe3+ + □ (cation vacancy)
Oh sites Td sites Oh sites
Aggregate to form
extended defect
CoO1.0 – 1.01
NiO1.0 – 1.001 harder to oxidize to M3+
CuO1.00 only
TiOx MnOx can also have x > 1,
but also x < 1 (anion vacancies)
O2
LixNi1-x/2O x ~ 0.01
add Li+, Ni2+ Ni3+
19
TiOx electronic structure
20
Magnetism
diamagnetism – only e pairs, weak repulsion of magnetic field (H)
X is small and negative
ex: SiO2, CaO
paramagnetism – unpaired e with random orientation, strong attraction to H
X = C / (T+ Θ) Curie-Weiss law
C = Curie constant C 2 N(N+2)
N = # unpaired spins
Χ = magnetic susceptibility = F / H d
= magnetic momentF = sample formula wtH = applied magnetic fieldD = sample density
21
Magnetismex: Fe3+ in aq solution or Fe(NO3)3 isolated mag. moments
alignment is only induced by applied field, H
22
Ferromagnetism all mag. moments (e spins) spontaneously oriented in parallel direction ()
often due to direct M-M interactions (d –d orbital overlaps)
ex: -Fe bcc along [100] Fe is d6s2 N (obs) = 2.2
Ni fcc along [111] Ni is d8s2
Tc = Curie temperature = temp for magnetic order (ferromagnetic / disorder (paramagnetic) transition
measure of strength of interaction between spins
-Fe Tc = 760 C (note that Fe bcc fcc phase transition is 906C)
23
Antiferromagnetism
spins align antiparallel ()
Usually due to superexchange coupling
(M-L-M interaction)
Ex: NiO
TN = Neel temp = temp for antiferromagnetic / paramagnetic transition
NiO TN = 250 C
Ferrimagnetism – spins antiparallel, but don’t cancel
24
Magnetic ordering in FeO
TN ≈ 200 K
4.2 K
293 K
25
Curie plots
26
Hysteresis / domain structure
Weiss domains
Hard vs. soft
Ex: hard – hard/floppy disks
soft – record heads
For magnetic data storage (floppies/hard drives/tapes)
want high residual M but small coercive force
27
Spinels
Normal spinel
AB2O4 A(II) B(III)
O2 ccp array
A in 1/8 Td sites
B in ½ Oh sites
Ex: MgAl2O4 or ZnFe2O4
Inverse spinel
B[AB]O4
A in Oh sites, ½ B in Td sites, ½ B in Oh sites
Ex: NiFe2O4 = Fe[NiFe]O4
Fe3O4 = Fe(III)[Fe(II)Fe(III)]O4
28
Spinels
A Mg2+ Mn2+ Fe2+ Co2+ Ni2+ Cu2+ Zn2+
B d0 d5 d6 d7 d8 d9 d10
Al3+ d0 0 0 0 0 0.38 0
Cr3+ d3 0 0 0 0 0 0 0
Mn3+ d4 0 0
Fe3+ d5 0.45 0.1 0.5 0.5 0.5 0.5 0
Co3+ d6 0 0
occupancy factor (fraction of B cations in Td sites) range is = 0 (normal) to 0.5 (full inverse)
29
Magnetism in spinelsZnFe2O4
Zn(II) Td sites d10 (N=O)
Fe(III) Oh sites d5 (N = 5)
antiferromagnetic TN = 10K weak superexchange coupling
between Oh sites in spinel
NiFe2O4 λ =0.5 (inverse spinel)
Fe[NiFe]O4
Ni(II) Oh sites d8 (N = 2)
½ Fe(III) Oh sites d5 (N = 5)
½ Fe(III) Td sites d5 (N = 5) µ = √2(2+1)µb = 2.5µb
ferrimagnet TN = 585 C (strong coupling between Oh and Td sites)
30
Magnetism in spinels
- Fe2O3 inverse defect spinel, used in disk storage
~5 m film deposited on plastic tape
Fe(III)[Fe1.67(III)□0.33]O4
Td Oh
medium-hard ferrimagnet 1 Fe(III) Td d5 N=5
1.67 Fe(III) Oh d5 N=5
31
ReO3
32
Perovskites (CaTiO3)
Simple perovskites have an ABX3 stoichiometry. The A cation and X anions, taken together, comprise a close-packed array, with B cations filling 1/4 of the octahedral sites.
An ordered AA’BX3 perovskite
33
Perovskites
ABX3 CN A = 12 B = 6 X = 2
common for oxides and fluorides (ex NaFeF3)
34
Ruddlesden-Popper phases
K2NiF4
Sr3Fe2O7
Ca4Mn3O10
35
YBa2Cu3O7
36
Tl2Ba3Ca2Cu3O10
37
Ferroelectrics
Ideal perovskite structure has cubic symmetry (centrosymmetric)
But structures are often distorted to be non-centrosymmetric
These can be ferroelectric
In BaTiO3 , the Ti cation is a little smaller than the Oh site (Ti-O ~ 1.95Å), and is displaced ~0.1Å off site center towards an oxide ligand, forming a dipole
Above Tc (=120 C) the dipoles are randomly oriented, and structure is cubic (paraelectic)
Below Tc - all dipoles orient along the same direction (ferroelectric)
Note: ferroelectricity is named by analogy to ferromagnetism, but it is not common for Fe-containing materials
Also: antiferroelectric ferrielectric
one difference – dipole ordering is tied to structural change
38
BaTiO3
Dielectric constant vs temp
39
Ferro/piezoelectricsCaTiO3 is not ferroelectric, the smaller Ca2+ ion reduces Oh site and Ti4+ is not small enough to displace off center
BaxSr1x TiO3 (BST) is ferroelectric with a lower Tc, so the max in ε’ occurs at a lower temp. It’s used in dynamic RAM (DRAM) capacitor elements
ε’
Ex: water 80
TiO2, MgTiO3 10–100
BST ferroelectrics 4000-8000
piezoelectrics – crystals polarize under applied mechanical stress and vice versa (applied E across crystal generates lattice strain)
crystals must be noncentrosymmetric
P = d P = polarization, σ = mechanical stress
40
Piezoelectrics
Piezoelectrics: ex: quartz crystal, BaTiO3
PbZrxTi1xO3 (PZT) actuators, x~0.5 highest d
positioning - apply E induce
Qz transducers (pressure measurement)
use from sensed pressure to produce E signal
41
Two-zone transport
42
MX2
43
Layered structuresMO2 and MS2 structures and intercalation
Two basic structure types with different cation coordnation geometries
1. CdI2 structure, cations in Oh sites, filling alternate layers
(AcB)n 1T CdI2, TiS2, TaS2, ZrS2, Mg(OH)2 (brucite)
Polytypes, ex: (AcB CbA BaC)n 3R
2. MoS2 structure, cations in trig prismatic sites (D3h) , filling alternate layers
MoS2, NbS2
(AbA BaB)n 2H
(AbA CbC)n
(Aba BcB CaC)n
44
Electrochemical intercalation
45
Intercalation compounds
46
TaS2 intercalation
Intercalate ion = [Fe6S8(P(C2H5)3)6]2+
47
DOS diagrams for MS2
a1’
e’
e”
t2g
eg
Peierl’s distortionPeierl’s distortion: polyacetylene
K2Pt(CN)4Br0.3 3H2O (KCP)
Charge density waves: TaS2
48
Charge density waves
49
To observe CDW typical tunnelling parameters of 2-3 nA and 10-20 mV gap voltage were observed. The atomic lattice can be seen simul- taneously when the current is increased to higher values (30 - 40 nA).
TaS2 (and TaSe2) exhibit an electronic phase transition from a normal into a condensed state which is called the Charge Density Wave (CDW) state. The transition is caused by an electron-phonon coupling. STM images of TaS2 show a triangular atomic lattice (a0=0.33 nm) with a superimposed CDW lattice of about 3.5 a0. The CDW lattice is rotated 11° with respect to the atomic lattice.
http://www.nanosurf.com
50
LiCoO2
51
Electrode and cell potentials
http://www.mpoweruk.com/performance.htm
52
Li+ battery chemistry
Cathode LiCoO2 Li1-xCoO2 + xLi+ + xe-
Anode6C + Li+ + e- C6Li
ElectrolyteOrganic solvent with LiPF6
53
Insertion hosts
54
Framework solids
55
Molecular sieves
56
Pillared clays
Oregon State University 57
Pillared structures
http://www.cem.msu.edu/~pinnweb/research-na.htm
58
Ag(bipy)NO3
60
Graphite Intercalation
Graphite reduction at 0.1-0.5 V vs Li+/Li Theoretical capacity: Li metal > 1000 mAh/g C6Li 370
Expands about10% along z
Li+ occupies hexagon centers of non-adjacent hexagons
61
1.12
0.78 nm
CxB(O2C2O(CF3)2)2
Stage 2
1.13
0.85 nm
Stage 1
CxB(O2C2(CF3)4)2
Structures: borate chelate GIC’s
Blue: obsPink: calc
Unexpected anion orientation - long axis to sheets
T