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Ch412 notes ch 24 solid state 2010
- 1. 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. 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. 3 F-centers NaCl Na1+xCl green/yellow epr “free e- ” NaCl NaKxCl green/yellow same KCl K1+xCl violet KCl KNaxCl violet Δ Δ Δ Δ Na Na K K
- 5. 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. 6 Extended defects Shear planes in WO3-x
- 9. 9 Ionic Conduction Concentration gradients: Fick’s Law Microscopic view: Correlation of defects with mechanism
- 10. 10 Ionic Conduction Macroscopic view: Measure σionic = Σ σi (Di, qi, ci) i i = all significant charge carriers D = diffusion coefficient (related to mobility) q = ion charge c = ion concentration Arrhenius behavior: σ = σo exp (-Ea/RT) ln σ vs 1/T is linear with slope = −Ea/R
- 11. 11 AgI β-AgI wurtzite (AaBb)n ↓ ∆, 146 °C α-AgI bcc I array with Ag+ statistically distributed in CN=3,4 sites σ~ 1Ω-1 cm-1 , Ea ~0.05 eV when α-AgI melts at 550 °C, the σAg+ decreases!
- 12. 12 Ag2HgI4 and RbAg4I5 Close packed I− lattice with 3/8 Td sites occupied order/disorder transition at 50 °C (break in σ data) RbAg4I5 is single phase from RT to 500 °C ~ bcc I array σ ~ 0.25 Scm-1 ; Ea~0.07eV VTF behavior - lattice activation contributes to conduction mechanism, so Arrhenius plot is curved
- 13. 13 Calcium-stabilized zirconia CaxZr1−xO2−x□x □ = O2− ion vacancy Fluorite structure (8,4) (AabBbcCca)n σ (O2− ) ~10−4 at 500°C
- 14. 14 Solid oxide fuel cell / sensor Concentration cell gas sample 2O2− → O2 + 4e− Air 4e− + O2 → 2O2− O2 sensor in auto exhaust E α log pO2 (sample) / pO2 (air) 2H2 + 202− → 2H2O + 4e− 4e− + O 2 → 202− 160 torr
- 15. 15 Na-β’’-alumina σ (Na+ ) ~10 Scm-1 at 300 °C
- 16. 16 D for some ion conductors
- 17. 17 1st row TM MOx compounds
- 18. 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+
- 20. 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 α µ2 α N(N+2) N = # unpaired spins Χ = magnetic susceptibility = µ F / H d µ = magnetic moment F = sample formula wt H = applied magnetic field D = sample density
- 21. 21 Magnetism ex: Fe3+ in aq solution or Fe(NO3)3 isolated mag. moments alignment is only induced by applied field, H
- 22. 22 Ferromagnetism all mag. moments (e− spins) spontaneously oriented in parallel direction (↑↑↑↑↑) often due to direct M-M interactions (d –d orbital overlaps) ex: α-Fe bcc ↑ along [100] Fe is d6 s2 N (obs) = 2.2 Ni fcc ↑ along [111] Ni is d8 s2 Tc = Curie temperature = temp for magnetic order (ferromagnetic / disorder (paramagnetic) transition measure of strength of interaction between spins α-Fe Tc = 760 °C (note that Fe bcc → fcc phase transition is 906°C)
- 23. 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. 24 Magnetic ordering in FeO TN ≈ 200 K 4.2 K 293 K
- 25. 25 Curie plots
- 26. 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. 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. 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 λ= occupancy factor (fraction of B cations in Td sites) λ range is λ = 0 (normal) to 0.5 (full inverse)
- 29. 29 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 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. 30 Magnetism in spinels γ - Fe2O3 inverse defect spinel, used in disk storage ~5 µm 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. 31 ReO3
- 32. 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. 33 Perovskites ABX3 CN A = 12 B = 6 X = 2 common for oxides and fluorides (ex NaFeF3)
- 35. 35 YBa2Cu3O7
- 37. 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
- 39. 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 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 = dσ P = polarization, σ = mechanical stress
- 40. 40 Piezoelectrics Piezoelectrics: ex: quartz crystal, BaTiO3 PbZrxTi1−xO3 (PZT) actuators, x~0.5 highest d positioning - apply E induce σ Qz transducers (pressure measurement) use σ from sensed pressure to produce E signal
- 42. 42 MX2
- 43. 43 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
- 46. 46 TaS2 intercalation Intercalate ion = [Fe6S8(P(C2H5)3)6]2+
- 47. 47 DOS diagrams for MS2 a1’ e’ e” t2g eg
- 48. Peierl’s distortion Peierl’s distortion: polyacetylene K2Pt(CN)4Br0.3 3H2O (KCP) Charge density waves: TaS2 48
- 49. 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. 50 LiCoO2
- 51. 51 Electrode and cell potentials http://www.mpoweruk.com/performance.htm
- 52. 52 Li+ battery chemistry Cathode LiCoO2 ↔ Li1-xCoO2 + xLi+ + xe- Anode 6C + Li+ + e- ↔ C6Li Electrolyte Organic solvent with LiPF6
- 57. Oregon State University 57 Pillared structures http://www.cem.msu.edu/~pinnweb/research-na.htm
- 58. 58 Ag(bipy)NO3
- 60. 60 Graphite Intercalation Graphite reduction at 0.1-0.5 V vs Li+ /Li Theoretical capacity: Li metal > 1000 mAh/g C6Li 370 Expands about 10% along z Li+ occupies hexagon centers of non-adjacent hexagons
- 61. 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: obs Pink: calc Unexpected anion orientation - long axis to sheets T