CHEM 3300 / Topic 6d: Solid-State - Ionic Conductivity

ION DIFFUSION

• What are the four key factors affecting ion diffusion? How does each factor affect diffusion?

• Energy barriers.

  • There is an amount of energy required to pop the mobile ion out of its place from the unit cell.

• Ion charges and ion sizes.

  • The more positively charged the ion…

    • The greater attraction with negatively charged ions, making it more difficult for the positively charged ion to be mobile.

    • The greater the repulsion between other positively charged ions, which would be giving the original positively charged ion a boost around the unit cell.

  • The more negatively charged the ion…

    • The greater attraction with positively charged ions, making it more difficult for the negatively charged ion to be mobile.

    • The greater the repulsion between other negatively charged ions, which would be giving the original negatively charged ion a boost around the unit cell.

  • If you had a small ion, then it would diffuse more efficiently due to how light and small it is to allow other ions to diffuse.

• Concentration of defects.

  • You need enough defects to allow the diffusion to occur, but you don’t want too many defects or else you because you would collapse the skeleton of the conductor - the lattice.

  • Defects also allow low-energy pathways instead of the energy penalty of popping out of favourable ion sites.

• Concentration of mobile ions.

  • You need enough mobile ions to move for practically useful conductivity, but you don’t want to many mobile ions because you would collapse the skeleton of the conductor - the lattice.

SOLID ELECTROLYTES

• What’s the difference between conduction and diffusion?

• What’s the difference between ionic conductivity vs. electronic conductivity?

• At what temperatures do ion conductors usually work at? Why so?

• What is a solid-state electrolyte? Why are solid electrolytes favoured over liquid-electrolyte?

• Why are solid cationic electrolytes more popular over solid anionic electrolytes? At what temperatures do solid anionic conductors need to work compared to cationic conductors? What anions are we then limited to?

• The difference is…

  • Conduction is “Can I get from point A to point B?”

  • Diffusion is “How fast can I get from point A to point B?”

• The difference is…

  • One conducts ions.

  • One conducts electrons.

• A lot of solid-state ion conductors efficiently work at 1000K, this is because ion mobility isn’t present at RT, as opposed to liquid-state and gas-state.

• Solid-state ionic conductor and electron-insulating materials are preferred over their liquid counterparts due to spillage.

• Solids exhibiting high anion mobility are rare compared to cationic conductors and generally show high conductivity at higher temperatures than cationic conductors because anions are larger than cations. We are then limited to fluorides and oxides because they fairly big negative charge and small size.

SOLID CATIONIC ELECTROLYTES

• What are the three key solid cationic electrolytes?

• How does each work?

• Silver tetraiodidomercurate(II) or Ag₂HgI₂.

  • Below 50ºC, it is an ordered crystal. Above 50ºC, the Ag and Hg ions are randomly distributed over the tetrahedral sites. The silver cations will then be able to be conducted for whatever application. The mercury cations will not be able to be conducted because of their size and mass.

• β-alumina.

  • Scattered Na⁺ and O^2- ions are squeezed between Al₂O₃ slabs. The O^2- ions are there to keep crystal’s lattices together via charge balance with Na⁺ ions that will be conducted for whatever application.

• Sodium super ionic conductor or NASICON.

  • Composed of PO₄ tetrahedra and ZrO₆ octahedra, its original compound is NaZr₂P₃O₁₂. Once you replace phosphorus atoms with silicon atoms, you get Na_1+xZr₂P_3-xSi_xO₁₂. Compared to the original compound, due to the replacement of some phosphate tetrahedra with silicate tetrahedra, the structure expands in size, and, along with it, expands the channels for Na⁺ cations to be conducted through, being able to go from one vacant site to another vacant site easier.

  • Silicon’s larger ionic radius and thus longer bonds with oxygen, creating a relatively bigger tetrahedron, stretching the structure and the channels within.

MORE ABOUT NASICON

• What are four other NASICON-like electrolytes that are being heavily investigated too? Discuss each on how they are structured.

• What makes NASICON and their relatives fast ion conductors, say, over β-alumina.

• The four other NASICON-like electrolytes are as followed:

  • Li₄GeO₄: Li conductor with Li vacancies and improved channels made by framework of germanium oxide and vanadium oxide octahedra via replacement of Li⁺ and Ge⁴⁺ with V⁵⁺, creating Li_4-x(Ge_1-xV_x)O_4.

  • La_0.6Li_0.2TiO₃: Li conductor with Li vacancies and channel framework due to lanthanum and titanium polyhedra.

  • Na₅YSi₄O₁₂: Na conductor with Na vacancies and channel framework due to silicate tetrahedra and yttrium oxide octahedra.

  • Li_6.4La₃Zr_1.4Ta_0.6O₁₂: Li conductor with Li vacancies and improved channels made by framework of zirconium oxide octahedra, tantalum oxide octahedra, and lanthanum oxide distorted cubes.

• With β-alumina, the sodium ions are bound to the slabs, as they are part of the spinel structure keeping the spinel structure intact. Because they are bound to something, they can’t be conducted as efficiently as NASICON (and similarly to silver ions in sodium tetraidodidomercurate(II)), wherein the cations are loosely bound to the structure, and are able to be conducted efficiently.

SOLID ANIONIC ELECTROLYTES

• With fluorides and oxides, what specific ionic structure is usually used for solid anionic electrolytes? What is the mechanism by which the anions move?

• Would electronic conductivity rule in a solid anionic electrolyte?

• Explain how would one improve anion mobility and their reasoning behind it.

• Explain the most common way to produce solid anionic electrolytes.

• Fluorite-structure-based compounds are usually used as solid anionic electrolytes. Anions hop from normal to interstitial to vacancy.

• Anionic conductivity rules and is faster than electronic conductivity because the anions are big and blocking the way of electrons getting through.

• To improve anion mobility, vacancies are introduced via doping simple oxides and simple fluorides. Because once doped, there may be introduction to charge imbalance or size difference of ions, and the disturbed lattice may have to create vacancies. To dope, we just need to use cations of similar oxidation state to the oxidation state of the original cationic partner of the fluoride or oxide anions. We need to have an oxidation state that ensures a noble gas configuration to ensure no electronic conductivity and allow ionic conductivity only.

• The most common way to do this is to use simple oxide zirconium oxide ZrO_2, which is a fluorite structure at a high temperature but not a fluorite structure at a low temperature (for higher-level reasons we won’t be getting into). We stabilize the high-temperature fluorite structure by doping via replacement of Zr⁴⁺ ions with similarly sized Ca²⁺ and Y³⁺ ions. If we use Y³⁺, we get a compound called Yttrium-stabilized zirconia (YSZ) Y_xZr_1−xO_2−x/2.

SOFC

How does a typical solid oxide fuel cell (SOFC) work?

• All we need is a supply of fuel (H₂) and oxidizer (O₂).

• ANODE: 2H₂ + 2O^{2- _→} 2H₂O + 4e^-

  • H₂ must combine with O^2- to produce H₂O and electrons. Its production of electrons makes this electrode an anode - negatively charged.

  • Ni-YSZ is used as an anode.

    • Ni adsorbs incoming H₂ from inlet, keeping them available for oxidation by O^2- to form water.

    • Ni conducts electrons from reaction to the interconnect (electrical conductivity)

    • YSZ conducts oxide anions from the electrolyte to form water. (ionic conductivity).

• CATHODE: O₂ + 4e^- → 2O^2-

  • O₂ must combine with e^- to produce oxide anions. Its non-production of electrons makes this electrode a cathode - positively charged.

  • La_1-xSr_xFeO_3-y is used as a cathode, which is a perovskite-structured compound with disordered La,Sr on the A-site, Feⁿ⁺ on the B-site.

    • La,Sr disorders creates oxide anion vacancies which allow for increased anion mobility from anode to electrolyte.

    • Sr dopant changes the oxidation state of Feⁿ⁺, ultimately increasing oxidation state and removing electrons from Sr dopant changes the oxidation state of Feⁿ⁺. By doing this, you increase the electronic conductivity by putting an electron from Feⁿ⁺ band into the Sr dopant band. Electrons are kept in dopant band, never to return to Feⁿ⁺. We are now left with a lesser filled Feⁿ⁺ band that can conduct electrons better.

    • Feⁿ⁺, on that note, conducts electrons from interconnect (electrical conductivity).

• ELECTROLYTE:

  • YSZ is used as an electrolyte, conducting oxide anions from cathode to anode to repeat the cycle.

MORE ABOUT SOFC

• On your typical SOFC, what’s the special ability of ferrum or cobalt or any other ferrum-like atom in any SOFC-cathode-perovskite-like cathode in regards to electrical conductivity?

• In the SOFC cathode La_1-xSr_xFeO_3-y or La_1-xSr_xCoO_3-y, what is y equal to?

• The oxidation state of an ion affects whether its electrons are localized or delocalized.

  • Fe³⁺ has a high charge and fewer electrons in its d-orbitals (only 5 electrons), which tends to pull the remaining electrons closer to the nucleus, making them more tightly bound. This makes the electrons less free to move around.

  • Fe²⁺, in contrast, has more electrons (6 in its d-orbitals), and the additional electron allows for greater electron mobility. The electrons are less tightly bound and can move more freely, contributing to better conductivity.

  • Fe³⁺ has fewer electrons and is less likely to donate electrons to oxygen because its electrons are more localized and tightly bound.

  • Fe²⁺, with more delocalized electrons, is more mobile and ready to participate in electron transfer, making it better for facilitating the oxygen reduction reaction at the cathode.

• If B cation (Feⁿ⁺ or Coⁿ⁺) is only +3, then y = x/2. If B cation can switch between +3 and +, then y > x/2.

IONIC CONDUCTIVITY VS. ELECTRONIC CONDUCTIVITY

• How would one achieve electrical conductivity over ionic conductivity?

• How would one achieve ionic conductivity over electronic conductivity?

• Advantage of ionic conductivity over electronic conductivity and vice versa?

• Electronic conductivity can be achieved over ionic conductivity by using metals. Metals are electronic conductors using light energy and are ion-insulating because there are no ions to begin with. Our material is made of metal atoms, not metal ions.

• Ionic conductivity can be achieved over electronic conductivity by using materials that do not conduct electrons due to a full valence band and large energy gap and is made of vacancies that can conduct ions.

• The advantages of either conductivity depends on the application used, e.g. SOFCs.