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

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Extended defects

Shear planes in WO3-x

7

Non-stoichiometric oxides

Mo8O23

8

Non-stoichiometry

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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

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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-’’-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

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+

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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+ 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

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Magnetismex: 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 906C)

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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 don’t cancel

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Magnetic ordering in FeO

TN ≈ 200 K

4.2 K

293 K

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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

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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

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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

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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

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Two-zone transport

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MX2

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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

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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

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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

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LiCoO2

51

Electrode and cell potentials

http://www.mpoweruk.com/performance.htm

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Li+ battery chemistry

Cathode LiCoO2 Li1-xCoO2 + xLi+ + xe-

Anode6C + Li+ + e- C6Li

ElectrolyteOrganic solvent with LiPF6

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Insertion hosts

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Framework solids

55

Molecular sieves

56

Pillared clays

Oregon State University 57

Pillared structures

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

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Ag(bipy)NO3

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Fe(III)4[Fe(II)(CN)6]3

Prussian blue

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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