CH 24. Solids. Defects Non-stoichiometry, Ionic Conductivity. Cooperative Phenomenon Magnetism, Piezoelectricity, Superconductivity

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1 CH 24. Solids Defects Non-stoichiometry, Ionic Conductivity Cooperative Phenomenon Magnetism, Piezoelectricity, Superconductivity Topochemical Reactions Intercalation chemistry

2 Defect types Shottky (vacancy) Frenkel (interstitial) Substitution NaCl Shottky vacancy M at 130 C (1 / units) TiO Shottky vacancy 10 M at 25 C (1 / 10 units) AgCl Frenkel interstitial Ag + 2

3 F-centers Δ NaCl Na 1+x Cl green/yellow epr free e - Na Δ NaCl NaK x Cl green/yellow same K Δ KCl K 1+x Cl violet K Δ KCl KNa x Cl violet Na 3

4 Defect concentrations 4

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 Li 2 O in NiO Li x Ni(III) x Ni(II) 1-x O introduce Li + to change electronic properties 5

6 Extended defects Shear planes in WO 3-x 6

7 Non-stoichiometric oxides Mo 8 O 23 7

8 Non-stoichiometry 8

9 Ionic Conduction Microscopic view: Correlation of defects with mechanism Concentration gradients: Fick s Law 9

10 Ionic Conduction Macroscopic view: Measure σ ionic = Σ σ i (D i, q i, c i ) i i = all significant charge carriers D = diffusion coefficient (related to mobility) q = ion charge c = ion concentration Arrhenius behavior: σ = σ o exp (-E a /RT) ln σ vs 1/T is linear with slope = E a /R 10

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, E a ~0.05 ev when α-agi melts at 550 C, the σ Ag+ decreases! 11

12 Ag 2 HgI 4 and RbAg 4 I 5 RbAg 4 I 5 is single phase from RT to 500 C ~ bcc I array σ ~ 0.25 Scm -1 ; E a ~0.07eV Close packed I lattice with 3/8 Td sites occupied order/disorder transition at 50 C (break in σ data) VTF behavior - lattice activation contributes to conduction mechanism, so Arrhenius plot is curved 12

13 Calcium-stabilized zirconia Ca x Zr 1 x O 2 x x = O 2 ion vacancy Fluorite structure (8,4) (AabBbcCca) n σ (O 2 ) ~10 4 at 500 C 13

14 Solid oxide fuel cell / sensor Concentration cell gas sample Air 2O 2 O 2 + 4e 4e + O 2 2O 2 O 2 sensor in auto exhaust E α log po 2 (sample) / po 2 (air) 160 torr 2H H 2 O + 4e 4e + O

15 Na-β -alumina σ (Na + ) ~10 Scm -1 at 300 C 15

16 D for some ion conductors 16

17 1 st row TM MO x compounds 17

FeO 1.04-1.17 O 2 3Fe 2+ 2Fe 3+ + (cation vacancy) Oh sites Td sites Oh sites Aggregate to form extended defect CoO 1.0 1.

18 FeO O 2 3Fe 2+ 2Fe 3+ + (cation vacancy) Oh sites Td sites Oh sites Aggregate to form extended defect CoO NiO harder to oxidize to M 3+ CuO 1.00 only Li x Ni 1-x/2 O x ~ 0.01 add Li +, Ni 2+ Ni 3+ TiO x M n O x can also have x > 1, but also x < 1 (anion vacancies) 18

19 TiO x electronic structure 19

20 Magnetism diamagnetism only e pairs, weak repulsion of magnetic field (H) X is small and negative ex: SiO 2, CaO Χ = magnetic susceptibility = µ F / H d µ = 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 α µ 2 α N(N+2) N = # unpaired spins 20

21 Magnetism ex: Fe 3+ in aq solution or Fe(NO 3 ) 3 isolated mag. moments alignment is only induced by applied field, H 21

orbital overlaps) ex: α-fe bcc along [100] Fe is d 6 s 2 N (obs) = 2.

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 d 6 s 2 N (obs) = 2.2 Ni fcc along [111] Ni is d 8 s 2 T c = 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) 22

temp = temp for antiferromagnetic / paramagnetic transition NiO

23 Antiferromagnetism spins align antiparallel ( ) Usually due to superexchange coupling (M-L-M interaction) Ex: NiO T N = Neel temp = temp for antiferromagnetic / paramagnetic transition NiO T N = 250 C Ferrimagnetism spins antiparallel, but don t cancel 23

24 Magnetic ordering in FeO 293 K T N 200 K 4.2 K 24

25 Curie plots 25

26 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

27 Spinels Normal spinel AB 2 O 4 A(II) B(III) O 2 ccp array A in 1 / 8 Td sites B in ½ Oh sites Ex: MgAl 2 O 4 or ZnFe 2 O 4 Inverse spinel B[AB]O 4 A in Oh sites, ½ B in Td sites, ½ B in Oh sites Ex: NiFe 2 O 4 = Fe[NiFe]O 4 Fe 3 O 4 = Fe(III)[Fe(II)Fe(III)]O 4 27

28 Spinels λ= occupancy factor (fraction of B cations in Td sites) λ range is λ = 0 (normal) to 0.5 (full inverse) A Mg 2+ Mn 2+ Fe 2+ Co 2+ Ni 2+ Cu 2+ Zn 2+ B d 0 d 5 d 6 d 7 d 8 d 9 d 10 Al 3+ d Cr 3+ d Mn 3+ d Fe 3+ d Co 3+ d

29 Magnetism in spinels ZnFe 2 O 4 Zn(II) Td sites d 10 (N=O) Fe(III) Oh sites d 5 (N = 5) antiferromagnetic T N = 10K weak superexchange coupling between Oh sites in spinel NiFe 2 O 4 λ =0.5 (inverse spinel) Fe[NiFe]O 4 Ni(II) Oh sites d 8 (N = 2) ½ Fe(III) Oh sites d 5 (N = 5) ½ Fe(III) Td sites d 5 (N = 5) µ = 2(2+1)µ b = 2.5µ b ferrimagnet T N = 585 C (strong coupling between Oh and Td sites) 29

30 Magnetism in spinels γ - Fe 2 O 3 inverse defect spinel, used in disk storage ~5 µm film deposited on plastic tape Fe(III)[Fe 1.67 (III) ]O 4 Td Oh medium-hard ferrimagnet 1 Fe(III) Td d 5 N= Fe(III) Oh d 5 N=5 30

31 ReO 3 31

32 Perovskites (CaTiO 3 ) Simple perovskites have an ABX 3 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 BX 3 perovskite 32

33 Perovskites ABX 3 CN A = 12 B = 6 X = 2 common for oxides and fluorides (ex NaFeF 3 ) 33

34 Ruddlesden-Popper phases K 2 NiF 4 Sr 3 Fe 2 O 7 Ca 4 Mn 3 O 10 34

35 YBa 2 Cu 3 O 7 35

36 Tl 2 Ba 3 Ca 2 Cu 3 O 10 36

37 Ferroelectrics Ideal perovskite structure has cubic symmetry (centrosymmetric) But structures are often distorted to be non-centrosymmetric These can be ferroelectric In BaTiO 3, 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 T c (=120 C) the dipoles are randomly oriented, and structure is cubic (paraelectic) Below T c - 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

38 BaTiO 3 Dielectric constant vs temp 38

39 Ferro/piezoelectrics CaTiO 3 is not ferroelectric, the smaller Ca 2+ ion reduces Oh site and Ti 4+ is not small enough to displace off center Ba x Sr 1 x TiO 3 (BST) is ferroelectric with a lower T c, so the max in ε occurs at a lower temp. It s used in dynamic RAM (DRAM) capacitor elements Ex: water 80 TiO 2, MgTiO BST ferroelectrics piezoelectrics crystals polarize under applied mechanical stress and vice versa (applied E across crystal generates lattice strain) crystals must be noncentrosymmetric ε P = dσ P = polarization, σ = mechanical stress 39

40 Piezoelectrics Piezoelectrics: ex: quartz crystal, BaTiO 3 PbZr x Ti 1 x O 3 (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 40

41 Two-zone transport 41

42 MX 2 42

43 Layered structures MO 2 and MS 2 structures and intercalation Two basic structure types with different cation coordnation geometries 1. CdI 2 structure, cations in Oh sites, filling alternate layers (AcB) n 1T Polytypes, ex: (AcB CbA BaC) n 3R CdI 2, TiS 2, TaS 2, ZrS 2, Mg(OH) 2 (brucite) 2. MoS 2 structure, cations in trig prismatic sites (D 3h ), filling alternate layers MoS 2, NbS 2 (AbA BaB) n 2H (AbA CbC) n (Aba BcB CaC) n 43

44 Electrochemical intercalation 44

45 Intercalation compounds 45

46 TaS 2 intercalation Intercalate ion = [Fe 6 S 8 (P(C 2 H 5 ) 3 ) 6 ] 2+ 46

47 DOS diagrams for MS 2 e g e e t 2g a 1 47

48 Peierl s distortion Peierl s distortion: polyacetylene K 2 Pt(CN) 4 Br 0.3 3H 2 O (KCP) Charge density waves: TaS 2 48

Charge density waves To observe CDW typical tunnelling parameters of 2-3 na and 10-20 mv gap voltage were observed.

TaS2 (and TaSe2) exhibit an electronic phase transition from a normal into a condensed state which is called the Charge Density Wave (CDW) state.

49 Charge density waves To observe CDW typical tunnelling parameters of 2-3 na and 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. 49

50 LiCoO 2 50

51 Electrode and cell potentials 51

52 Li + battery chemistry Cathode LiCoO 2 Li 1-x CoO 2 + xli + + xe - Anode 6C + Li + + e - C 6 Li Electrolyte Organic solvent with LiPF 6 52

53 Insertion hosts 53

54 Framework solids 54

55 Molecular sieves 55

56 Pillared clays 56

57 Pillared structures Oregon State University 57

58 Ag(bipy)NO 3 58

59 Fe(III) 4 [Fe(II)(CN) 6 ] 3 Prussian blue 59

Graphite Intercalation Expands about 10% along z Graphite reduction at 0.1-0.

60 Graphite Intercalation Expands about 10% along z Graphite reduction at V vs Li + /Li Theoretical capacity: Li metal > 1000 mah/g C 6 Li 370 Li + occupies hexagon centers of non-adjacent hexagons 60

61 Structures: borate chelate GIC s C x B(O 2 C 2 (CF 3 ) 4 ) Stage nm C x B(O 2 C 2 O(CF 3 ) 2 ) 2 Blue: obs Pink: calc 1.12 Stage nm Unexpected anion orientation - long axis T to sheets 61

Metal Oxides. Types of metal oxides: 1. Metal monoxides (MO) such as TiO and NiO

Metal Oxides. Types of metal oxides: 1. Metal monoxides (MO) such as TiO and NiO Metal Oxides Metal oxides are the compounds of oxygen and metals: The study of metal oxides is central to solid state chemistry due to: stability ease of synthesis variable structure and composition Properties: