CH 24. Solids

1
CH 24. Solids

• Defects
• Non-stoichiometry, Ionic Conductivity
• Cooperative Phenomenon
• Magnetism, Piezoelectricity, Superconductivity
• Topochemical Reactions
• Intercalation 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 ? Na1xCl green/yellow epr free
e- NaCl ? NaKxCl green/yellow same K
Cl ? K1xCl violet KCl ?
KNaxCl violet
Na
?
K
?
K
?
Na
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
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Extended defects
Shear planes in WO3-x
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Non-stoichiometric oxides
Mo8O23
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Non-stoichiometry
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Ionic Conduction
Microscopic view Correlation of defects with
mechanism
Concentration gradients Ficks Law
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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

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AgI

• ?-AgI wurtzite (AaBb)n
• ? ?, 146 ?C
• ?-AgI bcc I array with Ag statistically
  distributed in CN3,4 sites
• ? 1O-1cm-1 , Ea 0.05 eV
• when ?-AgI melts at 550 ?C, the ?Ag decreases!

12
Ag2HgI4 and RbAg4I5
RbAg4I5 is single phase from RT to 500 ?C bcc I
array ? 0.25 Scm-1 Ea0.07eV
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
13
Calcium-stabilized zirconia
CaxZr1?xO2?x?x ? O2? ion vacancy Fluorite
structure (8,4) (AabBbcCca)n ? (O2?) 10?4 at
500C
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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
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Na-b-alumina
? (Na) 10 Scm-1 at 300 ?C
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D for some ion conductors
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1st row TM MOx compounds
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FeO1.04-1.17
O2
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 gt
1, but also x lt 1 (anion vacancies)
LixNi1-x/2O x 0.01 add Li, Ni2 ? Ni3
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TiOx electronic structure
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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 T)
Curie-Weiss law C Curie constant C ? ?2 ?
N(N2) N
unpaired spins
? magnetic susceptibility ? F / H d ?
magnetic moment F sample formula wt H applied
magnetic field D sample density
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Magnetism
ex Fe3 in aq solution or Fe(NO3)3 isolated
mag. moments alignment is only induced by
applied field, H
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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 906?C)
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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 dont
cancel
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Magnetic ordering in FeO
293 K

• TN 200 K

4.2 K
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Curie plots
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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
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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 BABO4 A
in Oh sites, ½ B in Td sites, ½ B in Oh sites
Ex NiFe2O4 FeNiFeO4
Fe3O4 Fe(III)Fe(II)Fe(III)O4
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Spinels

• occupancy factor (fraction of B cations in Td
  sites)
• range is l 0 (normal) to 0.5 (full inverse)

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
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Magnetism in spinels
ZnFe2O4 Zn(II) Td sites d10 (NO) Fe(III) Oh
sites d5 (N 5) antiferromagnetic TN 10K
weak superexchange coupling between Oh sites in
spinel NiFe2O4 ? 0.5 (inverse
spinel) FeNiFeO4 Ni(II) Oh sites d8 (N
2) ½ Fe(III) Oh sites d5 (N 5) ? ½ Fe(III)
Td sites d5 (N 5) ? µ v2(21)µb 2.5µb
ferrimagnet TN 585 ?C (strong coupling
between Oh and Td sites)
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Magnetism in spinels

• - Fe2O3 inverse defect spinel, used in disk
  storage
• 5 ?m film deposited on plastic tape
• Fe(III)Fe1.67(III)?0.33O4
• Td Oh
• medium-hard ferrimagnet 1 Fe(III) Td d5
  N5 ?
• 1.67 Fe(III) Oh d5 N5 ?

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ReO3
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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.

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Perovskites
ABX3 CN A 12 B 6 X 2 common for oxides
and fluorides (ex NaFeF3)
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Ruddlesden-Popper phases
Ca4Mn3O10
K2NiF4
Sr3Fe2O7
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YBa2Cu3O7
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Tl2Ba3Ca2Cu3O10
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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 antiferro
electric ???? ferrielectric ???? one
difference dipole ordering is tied to
structural change
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BaTiO3

• Dielectric constant vs temp

39
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 e
occurs at a lower temp. Its used in dynamic RAM
(DRAM) capacitor elements e
Ex water 80 TiO2, MgTiO3 10100 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, s
mechanical stress
40
Piezoelectrics

• Piezoelectrics ex quartz crystal, BaTiO3
• PbZrxTi1?xO3 (PZT) actuators, x0.5 highest d
• positioning - apply E induce ?
• Qz transducers (pressure measurement)
• use ? from sensed pressure to produce E
  signal

41
Two-zone transport
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MX2
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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
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Electrochemical intercalation
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Intercalation compounds
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TaS2 intercalation

• Intercalate ion Fe6S8(P(C2H5)3)62

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DOS diagrams for MS2
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Peierls distortion

• Peierls distortion polyacetylene
•  
•  
•  
• K2Pt(CN)4Br0.3 3H2O (KCP)
•  
•  
•  
•  
•  
•  
•  
• Charge density waves TaS2

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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 (a00.33 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
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LiCoO2
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Electrode and cell potentials
http//www.mpoweruk.com/performance.htm
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Li battery chemistry
Cathode LiCoO2 ? Li1-xCoO2 xLi
xe- Anode 6C Li e- ?
C6Li Electrolyte Organic solvent with LiPF6
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Insertion hosts
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Framework solids
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Molecular sieves
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Pillared clays
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Pillared structures

• http//www.cem.msu.edu/pinnweb/research-na.htm

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Ag(bipy)NO3
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Fe(III)4Fe(II)(CN)63
Prussian blue
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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 gt 1000 mAh/g C6Li 370
61
Structures borate chelate GICs
Blue obs Pink calc
CxB(O2C2O(CF3)2)2
Stage 2