KJM-MENA 3120 Inorganic Chemistry II Materials and Applications Solid-State Electrochemistry

1. KJM-MENA 3120 Inorganic Chemistry II Materials and Applications Solid-State Electrochemistry Fundamentals, Fuel Cells, Batteries Week 1 Electrochemistry Fundamentals Defectchemistry Diffusion and conductivity Electrochemicalcells Truls Norby Week 1 Introduction and Fundamentals Week 2 Solid oxidefuelcells Week 3 Batteries Themes and applications not covered: Membranes, oxidation/corrosion, metallurgy, photoelectrochemistry…

2. Redox Chemistry and Electrochemistry • Redoxreaction • Electrochemicalreaction

4. In order to understand, analyse, and affect the conductivity in crystalline solids, we need to understand defect concentrations Defect chemistry

5. Briefhistoryofdefects • Earlychemistryhadnoconceptof stoichiometry or structure. • The findingthat compounds generallycontained elements in ratiosofsmallintegernumberswas a greatbreakthrough! H2O CO2 NaCl CaCl2 NiO • Understandingthatexternalgeometryoftenreflectedatomicstructure. • Perfectnessruled. Variable composition (non-stoichiometry) wasout. • However, variable composition in some intermetallic compounds became indisputable and in the end forcedre-acceptanceofnon-stoichiometry. • But real understandingofdefectchemistryof compounds mainlycameabout from the 1930s and onwards, attributable to Frenkel, Schottky, Wagner, Kröger…, manyofthemphysicists, and almost all German! Frenkel Schottky Wagner

6. Notice the distortions of the lattice around defects The size of the defect may be taken to be bigger than the point defect itself Defects in an elemental solid (e.g. Si or Ni metal) Adapted from A. Almar-Næss: Metalliske materialer, Tapir, Oslo, 1991.

7. Defects in an ionic solid compoundExample: Cation and anion vacancies in NiODefects in ioniccompoundsarecharged

8. We will now start to consider defects as chemical entities We need a notation for defects. Many notations have been in use. In modern defect chemistry, we use Kröger-Vink notation (after Kröger and Vink). It describes any entity in a structure; defects and “perfects”. The notation tells us Whatthe entity is, as the main symbol (A) Chemical symbol or v (for vacancy) Wherethe entity is, as subscript (S) Chemical symbol of the normal occupant of the site or i for interstitial (normally empty) position Its charge, real or effective, as superscript (C) +, -, or 0 for real charges or ., /, or x for effective positive, negative, or no charge Note: The use of effective charge is preferred and one of the key points in defect chemistry. We will learn what it is in the following slides Point defects nomenclature: Kröger-Vink notation

9. The effective charge is defined as the charge an entity in a site has relative to (i.e. minus) the charge the same site would have had in the ideal structure. Example: An oxide ion O2- in an interstitial site (i) Real charge of defect: -2 Real charge of interstitial (empty) site in ideal structure: 0 Effective charge: -2 – 0 = -2 Effective charge

10. Example: An oxide ion vacancy Real charge of defect (vacancy = nothing): 0 Real charge of oxide ion O2- in ideal structure: -2 Effective charge: 0 – (-2) = +2 Example: A zirconium ion vacancy, e.g. in ZrO2 Real charge of defect: 0 Real charge of zirconium ion Zr4+ in ideal structure: +4 Effective charge: 0 – 4 = -4 Effective charge – more examples

11. Dopants and impurities Y3+ substituting Zr4+ in ZrO2 Li+ substituting Ni2+ in NiO Li+ interstitials in e.g. NiO Electronic defects Defect electrons in conduction band Electron holes in valence band Kröger-Vink notation – more examples

12. Cations, e.g. Mg2+ on normal Mg2+ sites in MgO Anions, e.g. O2- on normal site in any oxide Empty interstitial site Kröger-Vink notation – also for elements of the ideal structure (constituents)

13. Silicon atom in silicon Boron atom (acceptor) in Si Boron in Si ionised to B- Phosphorous atom (donor) in Si Phosphorous in Si ionised to P+ Kröger-Vink notation of dopants in elemental semiconductors, e.g. Si

14. Protonic defects • Hydrogen ions, protons H+ , are naked nuclei, so small that they can not escape entrapment inside the electron cloud of other atoms or ions • In oxidic environments, they will thus always be bonded to oxide ions –O-H • They can not substitute other cations • In oxides, they will be defects that are interstitial, but the interstitial position is not a normal one; it is inside an oxide ion. • With this understanding, the notation of interstitial proton and substitutional hydroxide ion are equivalent.

15. Electroneutrality • One of the key points in defect chemistry is the ability to express electroneutrality in terms of the few defects and their effective charges and to skip the real charges of all the normal structural elements •  positive charges =  negative charges can be replaced by •  positive effective charges =  negative effective charges •  positive effective charges -  negative effective charges = 0

16. The number of charges is counted over a volume element, and so we use the concentration of the defect species s multiplied with the number of charges z per defect Example, oxide MO with oxygen vacancies, acceptor dopants, and defect electrons: If electrons dominate over acceptors, we can simplify: Note: These are not chemical reactions, they are mathematical relations and must be read as that. For instance, in the above: Are there two vacancies for each electron or vice versa? Electroneutrality

17. Defectchemicalreactionequations • Defectchemicalreactionequationrules: • Conservemass • Conserve charge • Conservethestructure (ratio of sites)

18. Electronic defects

19. Intrinsic electronic ionisation Three equivalent reaction equations: Consider charges, electrons and sites: Simpler; skip sites: Simplest; skip valence band electrons:

20. Valence defects – localised electrons and holes Example: Fe2O3

21. Doping of semiconductors • In covalently bonded semiconductors, the valence electrons will strive to satisfy the octet rule for each atom. • As example, we add P or B to Si. • Si has 4 valence electrons and forms 4 covalent bonds. • Phosphorous P has 5 valence electrons. When dissolved in the Si structure it thus easily donates its extra electron to the conduction band in order to become isoeletronic with Si. • Boron B has 3 valence electrons. When dissolved in the Si structure it thus easily accepts the lacking electron from the valence band in order to become isoeletronic with Si.

22. Doping of Si with P (donor) or B (acceptor)

23. Point defects

24. Frenkel disorder in NiO Ni2+ O2-

25. Schottky disorder in NiO Ni2+ new structural unit O2- or, equivalently:

26. Oxygen deficiency “Normal” chemistry: The two electrons of the O2- ion are shown left behind Defect chemistry: More realistic picture, where the two electrons are delocalised on neighbouring cations

27. Oxygen deficiency The two electrons of the O2- ion are shown left behind The two electrons are loosely bonded since the nuclear charge of the former O2- ion is gone. They get a high energy close to the state of the reduced cations…the conduction band. The vacancy is a donor.

28. Ionisation of the oxygen vacancy donor Electrons excited to conduction band delocalised over entire crystal, mainly in orbitals of reduced cation

29. Oxygen deficiency – overall reaction

30. Defect reactions involving foreign elementsSubstituentsDopants

31. Foreign elements; some terminology • Foreign elements are often classified as • impurities – non-intentionally present • dopants – intentionally added in small amounts • substituents – intentionally substituted for a host component (we tend to call it all doping and dopants) • They may dissolve interstitially or substitutionally • Substitutionally dissolved foreign elements may be • homovalent – with the same valency as the host it replaces • heterovalent – with a different valency than the host it replaces. • Also called aliovalent • Heterovalent metals • Higher valent metals will sometimes be denoted Mh (h for higher valent). • Lower valent metals will sometimes be denoted Ml (l for lower valent).

32. Ni1-xO doped substitutionally with Li2O Li+ and Ni2+ are similar in size, so Li+ may substitute Ni2+. This will constitute acceptor-doping with effectively negative dopants. (This is utilised in Li-doped NiO for p-type conducting electrodes for fuel cells, batteries etc.) Ni1-xO contains nickel vacancies and electron holes. The doping may thus be compensated by consuming Ni vacancies or – better - by producing electron holes. This is an oxidation reaction and requires uptake of oxygen

33. ZrO2-y doped substitutionally with Y2O3 • Y3+ will form effectively negative defects when substituting Zr4+ and thus acts as an acceptor. It must be compensated by a positive defect. • ZrO2-y contains oxygen vacancies and electrons • The doping is thus most relevantly written in terms of forming oxygen vacancies:

34. ZrO2-y doped substitutionally with Y2O3 Note: Electrons donated from oxygen vacancy are accepted by Y dopants; no electronic defects in the bands.

35. Water as source of protons. Equivalent to other oxides as source of foreign elements. Example: Hydration of acceptor-doped MO2, whereby oxygen vacancies are annihilated, and protons dissolved as hydroxide ions. Hydration – dissolution of protons from H2O The acceptor dopants are already in, and are not visible in the hydration reaction in this case

36. Ternary and higher compounds • With ternary and higher compounds the site ratio conservation becomes a little more troublesome to handle, that’s all. • For instance, consider the perovskite CaTiO3. To form Schottky defects in this we need to form vacancies on both cation sites, in the proper ratio: • And to form e.g. metal deficiency we need to do something similar: • (But oxygen deficiency or excess would be just as simple as for binary oxides, since the two cations sites are not affected in this case …)

37. Doping of ternary compounds • The same rule applies: Write the doping as you imagine the synthesis is done: If you are doping by substituting one component, you have to remove some of the component it is replacing, and thus having some left of the other component to react with the dopant. • For instance, to make undoped LaScO3, you would probably react La2O3 and Sc2O3 and you could write this as: • Now, to dope it with Ca2+ substituting La3+ you would replace some La2O3 with CaO and let that CaO react with the available Sc2O3: • The latter is thus a proper doping reaction for doping CaO into LaScO3, replacing La2O3.

38. Defectstructure • Equilibriumcoefficients • Electroneutrality • Allowsdetermination of all defectconcentrations • For 2-3 defects: Analyticalsolutions • For 3 or more defects: Numericalsolutionsnecessary

39. Frenkel defects in NiO • Defectformation • Equilibriumcoefficient • Electroneutrality • Insert and solve:

40. Intrinsicsemicondutor • Intrinsicelectronicexitation • Equilibriumcoefficient • Electroneutrality, insert, solve:

41. Brouwer diagram Oxygendeficientoxide • Oxygenvacancyformation • Equilibriumcoefficient • Electroneutrality, insert, solve:

42. Defectstructurewith 3 defects; Y-substituted ZrO2-y • Total electroneutrality • Total solution; • Analytic or numerical or • Simple limiting Brouwer cases

43. LiFePO4 • Li deficiency

44. LiFePO4Brouwer diagram vsaLi

45. LiFePO4Brouwer diagram vs[D]

46. LiFePO4concentration and conductivity of holes vs 1/T

47. Computationalmethods in defectchemistry • Examplereaction • Energy calculation • Staticlatticeenergy or • Quantum mechanical (ab initio, DensityFunctionalTheory (DFT)) • Entropyestimate or calculation • Defectconcentration • Electroneutrality • Solve for Fermi levelμe and all concentrations at T, pi…

50. TransportDiffusion and ionicconductivity(Electronic conductivity)