CH 24. Solids
• Defects
– Non-stoichiometry, Ionic Conductivity
• Cooperative Phenomenon
– Magnetism, Piezoelectricity, Superconductivity
• Topochemical Reactions
– Intercalation chemistry
Defect types
Shottky (vacancy)
Frenkel
Substitution
(interstitial)
NaCl
TiO
AgCl
Shottky vacancy
10-12 M at 130 °C (1 / 1014 units)
Shottky vacancy
≈10 M at 25 °C (1 / 10 units)
Frenkel interstitial Ag+
2
F-centers
Δ
NaCl
 Na1+xCl
green/yellow epr “free e-”
Na
NaCl
Δ
 NaKxCl
green/yellow same
K
Δ
KCl
KCl

K1+xCl
violet

KNaxCl
violet
K
Δ
Na
3
Defect concentrations
4
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
5
Extended defects
Shear planes in WO3-x
6
Non-stoichiometric oxides
Mo8O23
7
Non-stoichiometry
8
Ionic Conduction
Microscopic view:
Correlation of defects with mechanism
Concentration gradients: Fick’s Law
9
Ionic Conduction
Macroscopic view:
Measure ionic =  i (Di, qi, ci)
i
i =
D=
q =
c =
all significant charge carriers
diffusion coefficient (related to mobility)
ion charge
ion concentration
Arrhenius behavior:  = o exp (-Ea/RT)
ln  vs 1/T is linear with slope = Ea/R
10
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!
11
Ag2HgI4 and RbAg4I5
RbAg4I5 is single phase from
RT to 500 C ~ bcc I array
 ~ 0.25 Scm-1; Ea~0.07eV
Close packed I lattice with 3/8 Td sites occupied
order/disorder transition at 50 C (break in  data)
VTF behavior - lattice activation contributes to conduction mechanism,
so Arrhenius plot is curved
12
Calcium-stabilized zirconia
CaxZr1xO2x□x
□ = O2 ion vacancy
Fluorite structure
(8,4) (AabBbcCca)n  (O2) ~104 at 500°C
13
Solid oxide fuel cell / sensor
Concentration cell
gas sample
Air
2O2  O2 + 4e
4e + O2  2O2
O2 sensor in auto exhaust
E  log pO2 (sample) / pO2 (air)
160 torr
2H2 + 202  2H2O + 4e
4e + O 2  202
14
Na-’’-alumina
 (Na+) ~10 Scm-1 at 300 C
15
D for some ion conductors
16
1st row TM MOx compounds
17
FeO1.04-1.17
3Fe2+
O2

Oh sites
2Fe3+ + □ (cation vacancy)
Td sites
Oh sites
Aggregate to form
extended defect
CoO1.0 – 1.01
NiO1.0 – 1.001
harder to oxidize to M3+
LixNi1-x/2O
CuO1.00 only
x ~ 0.01
add Li+, Ni2+  Ni3+
TiOx  MnOx can also have x > 1,
but also x < 1 (anion vacancies)
18
TiOx electronic structure
19
Magnetism
diamagnetism – only e pairs, weak repulsion of magnetic field (H)
X is small and negative
ex: SiO2, CaO
Χ = magnetic susceptibility =  F / H d
 = magnetic moment
F = sample formula wt
H = applied magnetic field
D = sample density
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
20
Magnetism
ex: Fe3+ in aq solution or Fe(NO3)3 isolated mag. moments
alignment is only induced by applied field, H
21
Ferromagnetism
all mag. moments (e spins) spontaneously oriented in parallel
direction ()
often due to direct M-M interactions (d –d orbital overlaps)
ex: -Fe
Ni
bcc
 along [100] Fe is d6s2 N (obs) = 2.2
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 906C)
22
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
23
Magnetic
ordering
in FeO
293 K
TN ≈ 200 K
4.2 K
24
Curie plots
25
Hysteresis / domain structure
Weiss domains
Hard vs. soft
For magnetic data storage (floppies/hard
drives/tapes)
Ex: hard – hard/floppy disks
want high residual M but small coercive force
soft – record heads
26
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
27
Spinels
= occupancy factor (fraction of B cations in Td sites)
 range is  = 0 (normal) to 0.5 (full inverse)
A
B
Mg2+ Mn2+
Fe2+
Co2+
Ni2+
Cu2+
Zn2+
d10
d0
d5
d6
d7
d8
d9
Al3+
d0
0
0
0
0
0.38
0
Cr3+
d3
0
0
0
0
0
0
Mn3+
d4
0
Fe3+
d5
0.45
Co3+
d6
0
0
0.1
0.5
0.5
0.5
0
0.5
0
0
28
Magnetism in spinels
ZnFe2O4
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
λ =0.5 (inverse spinel)
NiFe2O4
Fe[NiFe]O4
Oh sites
d8
(N = 2)
½ Fe(III) Oh sites
d5
(N = 5) 
½ Fe(III)
d5
(N = 5) 
Ni(II)
Td sites
µ = √2(2+1)µb = 2.5µb
ferrimagnet TN = 585 C (strong coupling between Oh and Td sites)
29
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 
30
ReO3
31
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
32
Perovskites
ABX3
CN A = 12 B = 6 X = 2
common for oxides and fluorides (ex NaFeF3)
33
Ruddlesden-Popper phases
Ca4Mn3O10
K2NiF4
Sr3Fe2O7
34
YBa2Cu3O7
35
Tl2Ba3Ca2Cu3O10
36
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
37
BaTiO3
Dielectric
constant vs temp
38
Ferro/piezoelectrics
CaTiO3 is not ferroelectric, the smaller Ca2+ ion reduces Oh site and Ti4+ is
not small enough to displace off center
BaxSr1x 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
39
Piezoelectrics
Piezoelectrics: ex: quartz crystal, BaTiO3
PbZrxTi1xO3 (PZT) actuators, x~0.5 highest d
positioning - apply E induce 
Qz transducers (pressure measurement)
use  from sensed pressure to produce E signal
40
Two-zone transport
41
MX2
42
Layered structures
MO2 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
43
Electrochemical intercalation
44
Intercalation compounds
45
TaS2 intercalation
Intercalate ion = [Fe6S8(P(C2H5)3)6]2+
46
DOS diagrams for MS2
eg
e”
e’
t2g
a1’
47
Peierl’s distortion
Peierl’s distortion: polyacetylene
K2Pt(CN)4Br0.3 3H2O
(KCP)
Charge density waves: TaS2
48
Charge density waves
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
49
LiCoO2
50
Electrode and cell potentials
http://www.mpoweruk.com/performance.htm
51
Li+ battery chemistry
Cathode
LiCoO2  Li1-xCoO2 + xLi+ + xeAnode
6C + Li+ + e-  C6Li
Electrolyte
Organic solvent with LiPF6
52
Insertion hosts
53
Framework solids
54
Molecular sieves
55
Pillared clays
56
Pillared structures
http://www.cem.msu.edu/~pinnweb/research-na.htm
Oregon State University
57
Ag(bipy)NO3
58
Fe(III)4[Fe(II)(CN)6]3
Prussian blue
59
Graphite Intercalation
Expands about
10% along z
Li+ occupies hexagon centers of
non-adjacent hexagons
Graphite reduction at 0.1-0.5 V vs Li+/Li
Theoretical capacity:
Li metal
> 1000 mAh/g
C6Li
370
60
Structures: borate chelate GIC’s
1.13
CxB(O2C2(CF3)4)2
Stage 1
0.85 nm
1.12
CxB(O2C2O(CF3)2)2
Blue: obs
Pink: calc
Stage 2
0.78 nm
T
Unexpected anion orientation - long axis
to sheets
61