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Lectures co-financed by the European Union in scope of the European Social Fund

Ionic Conductors: Characterisation of Defect Structure Lectures 7-8 Fast ion conduction in solids I crystalline materials Dr. I. Abrahams Queen Mary University of London. Lectures co-financed by the European Union in scope of the European Social Fund. Introduction to Solid Electrolytes.

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Lectures co-financed by the European Union in scope of the European Social Fund

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  1. Ionic Conductors: Characterisation of Defect Structure Lectures 7-8Fast ion conduction in solids Icrystalline materialsDr. I. AbrahamsQueen Mary University of London Lectures co-financed by the European Union in scope of the European Social Fund

  2. Introduction to Solid Electrolytes Solids that show high electrical conductivity wholly or mainly due to the conduction of ions, are collectively known as solid electrolytes, fast ion conductors or superionic conductors. These materials can be crystalline or amorphous, organic or inorganic. They are a very important class of materials particularly in battery and fuel cell technology. Liquid electrolytes like 1 M KCl have conductivities in the range of 1  10–1 S cm–1. Solid electrolytes such as Na--alumina, have similar conductivities in the solid state. We shall examine both crystalline and amorphous solid electrolytes. Lectures co-financed by the European Union in scope of the European Social Fund

  3. All ionic solids conduct due to the motion of defects, e.g. in NaCl the Schottky defect is present and conductivity ()  10–12 S cm–1. If NaCl is dissolved in water (0.1 M), the conductivity rises because the Na+ ions are more mobile. 0.1M NaCl,   10–2 S cm–1 In solid electrolytes the conductivities are equally high. Na--alumina,   10–1 S cm–1 at 300 C Lectures co-financed by the European Union in scope of the European Social Fund

  4. Mobile sublattice can be cationic or anionic Compound Mobile ion Conductivity LISICON Li+ 10-1 S cm-1 @ ca. 500C Na -alumina Na+ 10-2 S cm-1 @ ca. 25C RbAg4I5Ag+ 10-1 S cm-1 @ ca. 25C Hydr.-Ce1-xYxO3-x/2 H+ 10-1 S cm-1 @ ca. 400C PbSnF4F 10-2 S cm-1 @ ca. 390C Zr1-xYxO2-x/2 O2 10-1 S cm-1 @ ca. 1000C Lectures co-financed by the European Union in scope of the European Social Fund

  5. Requirements for Fast Ionic Conduction in Solids There are two basic requirements for fast ion conduction in solids. (1) Partial occupancy of sites by mobile ions. Number of sites >> Number of ions (2) Sites must be connected by continuous pathways of suitable energy. Pathways should have low activation energy. Bottleneck size  ion size. Specific conductivity () of a material is given by: Where, ni is the number of charge carriers of type i,ei is the charge (the electronic charge for electrons and monovalent ions) and i is the mobility. Lectures co-financed by the European Union in scope of the European Social Fund

  6. Ways of increasing charge carrier concentration n In NaCl for example, the charge carrier is the Na+ vacancy. The concentration of these vacancies is very low at room temperature, therefore n is small and  is low. If we can introduce additional vacancies or interstitials into a system we can increase n and therefore increase . When NaCl is heated, thermodynamics dictates that the number of Schottky vacancies increases. This is known as the intrinsicvacancy concentration. However only at very high temperatures is the intrinsic vacancy concentration and ion mobility high enough for NaCl to show high conductivity:   10–12 S cm–1 at 25 C   10–3 S cm–1 at 800 C Lectures co-financed by the European Union in scope of the European Social Fund

  7. We can increase the number of vacancies by adding an aliovalent impurity such as Mn2+. This can be achieved through solid solution formation with MnCl2. Na1-2xMnxCl 2NaNa0  MnNa + VNa These vacancies are described as extrinsic. For all but the highest temperatures, the number of extrinsic Na+ vacancies is = x and is very much larger than the intrinsic vacancy concentration. Thus at most temperatures the conductivity is dominated by extrinsic vacancies. Lectures co-financed by the European Union in scope of the European Social Fund

  8. Doping with aliovalent ions through solid solution formation can be used to generate vacancies or interstitial ions. Doping with supervalent cations Cation Vacancies e.g. 3Li+ Al3+ in Li4-3xAlxSiO4 Anion Interstitials e.g. Ca2+ Y3+ + F– in Ca1-xYxF2+x Doping with subvalent cations Cation Interstitials e.g. P5+ Si4+ + Na+ in Na1+xZr2P3-xSixO12 Anion Vacancies e.g. 2Zr4+ + O2– 2Y3+ in Zr1-2xY2xO2-x Lectures co-financed by the European Union in scope of the European Social Fund

  9. General Equations for Defect Formation in Cation Substitutional Solid Solutions Cation Vacancies: An+ substituted by Bm+ where (m > n) mAA0  BA(m - n) + (m - n)VA  Anion Interstitials: An+ substituted by Bm+ and interstitial anion Zk- where (m > n) AA0 BA(m - n) + [(m - n)/k]Zik Cation Interstitials: An+ substituted by Bm+ and interstitial cation Ck+ where (m < n) AA0 BA(n - m)  + [(n - m)/k]Cik Anion Vacancies: An+ substituted by Bm+ where (m < n) vacancy introduced on Zk- AA0 + [(m - n)/k]ZZ0  BA(m - n)  + [(m - n)/k]VZk Lectures co-financed by the European Union in scope of the European Social Fund

  10. Ionic Mobility  Increasing  results in an increase in . Ionic conduction mechanism rely on ions squeezing past ions of opposite charge. These are known as bottle necks. Consider ionic conduction in NaCl. In order for the Na+ ion to enter the interstitial tetrahedral site, it must first squeeze through the bottleneck formed by the three Cl– ions. Lectures co-financed by the European Union in scope of the European Social Fund

  11. The size of the bottleneck is small. Similarly the size of the interstitial site is small. The resulting energy profile might look something like: In order to lower the migration energy and hence increase mobility it helps if the mobile ion is small and the stationary ion is polarisable. Lectures co-financed by the European Union in scope of the European Social Fund

  12. Factors affecting Em. (1) Bottleneck size Should be ion size (2) Rigid framework should be polarisable (3) Charge on mobile ions Highly charge ions are less mobile (they become trapped). Lectures co-financed by the European Union in scope of the European Social Fund

  13. Ionic mobility  is related to the ionic self-diffusion coefficient D (Einstein relationship): (1) where q is the is the charge, k is the Boltzman constant and T is the absolute temperature. The value of D can be obtained through consideration of random walk theory. (2) where z is number of equivalent sites in the 3D lattice, a0 is the distance between equivalent sites, c is the fraction of occupied sites, f is a correlation factor representing the deviation from randomness of atomic jumps (ca. 0.65 in a simple cubic system). 0 is the phonon frequency for the specific lattice and Gm is the free energy of migration. Lectures co-financed by the European Union in scope of the European Social Fund

  14. where: We can define a term  as: The mobility  can therefore be defined as: (3) Which can be abbreviated to: Lectures co-financed by the European Union in scope of the European Social Fund

  15. Ionic conductivity can be defined as: (1) The value of n is the product of N and c where N is the number of equivalent partially occupied sites per unit volume. Therefore: (2) Which can be expressed as an Arrhenius type form: Where Ea is the activation energy for conductivity Lectures co-financed by the European Union in scope of the European Social Fund

  16. Taking logs and plotting gives an Arrhenius plot of conductivity, the slope of which gives the activation energy. Lectures co-financed by the European Union in scope of the European Social Fund

  17. Ionic Conduction Mechanisms in Solids Ionic conduction in solids arises through ions hopping from one site to a vacant site in the crystal lattice. Three basic types of mechanisms: (1) Vacancy mechanism Where an ion hops onto an intrinsic or extrinsic vacancy (2) Interstitial mechanism Where an interstitial ions hops onto a neighbouring vacant interstitial site. (3) Interstitialcy mechanism Where an interstitial ion pushes a neighbouring ion in a normal lattice site into an interstitial vacancy and then takes its place on the normal lattice site (cooperative motion). Lectures co-financed by the European Union in scope of the European Social Fund

  18. Lectures co-financed by the European Union in scope of the European Social Fund

  19. Mechanism of Proton Conductivity The mechanism of proton conduction in solids have been the subject of some debate. One of the most accepted theories is the Grothuss mechanism. Grothuss (1806) This involves protons moving through the solid via a hydrogen bond network. Lectures co-financed by the European Union in scope of the European Social Fund

  20. Applications of Solid Electrolytes (1) Portable electric power sources for electric vehicle, mobile phones, digital watches, calculators, heart pacemakers etc. (2) Fuel cells (electric vehicles and space programme). (3) Gas sensors (emission control) (4) Electrolysers (gas separation) (5) Electrochromic displays Lectures co-financed by the European Union in scope of the European Social Fund

  21. e.g. The Sodium-Sulfur Cell Batteries can be primary (used once then disposed of) or secondary (rechargeable). Conventional secondary batteries use solid electrodes and liquid electrolytes (e.g. lead-acid car battery). The sodium-sulfur cell has a solid electrolyte and liquid electrodes. Lectures co-financed by the European Union in scope of the European Social Fund

  22. Electrolyte = Na--alumina Electrodes = molten sodium (anode) molten sulfur (cathode) The cell operates at around 300 C. But the reactions are exothermic and once heated can be self sustaining if adequately insulated. Anode: At the interface between the molten sodium and the electrolyte Na is ionised to Na+. Na+ migrates through the electrolyte e– passes into the external circuit. Na  Na+ + e– Lectures co-financed by the European Union in scope of the European Social Fund

  23. Cathode: Molten sulfur is reduced to the sulfide ion, where it can form sodium sulfide with the Na+ ions entering from the electrolyte. S + 2e– S2– The reactions are reversed on charging. The overall cell reaction may be written as 2Na + 5S  Na2S5 2.08 V The cell voltage varies from 2.08 to 1.8 V depending on the state of charge and is very similar to that of the lead acid cell. The main advantage is that it is much lighter. Lectures co-financed by the European Union in scope of the European Social Fund

  24. The Oxygen Concentration Sensor The oxygen concentration sensor utilises an oxide ion conducting solid electrolytes such as calcium stabilised zirconia. Zr1-xCaxO2-x The cell consists of a solid electrolyte tube coated with porous electrodes on its inner and outer surfaces. There are different oxygen pressures inside and outside the tube. Lectures co-financed by the European Union in scope of the European Social Fund

  25. If PO2’’ > PO2’ oxygen ionises on the inner electrode (which becomes the cathode). O2 2O· 2O· + 2e– O2– The O2–migrates through the solid electrolyte to the outside chamber where it is oxidised (anode). O2– O· + 2e– 2O·  O2 At equilibrium, the EMF of the cell (E) is given by the Nernst equation. Therefore if we keep PO2’ constant we can obtain PO2’’ by measuring E and hence obtain the oxygen concentration. Lectures co-financed by the European Union in scope of the European Social Fund

  26. Similar cells used as fuel cells, for example using air in the inner chamber and H2 in outer. Inner chamber reaction O2 2O· 2O· + 2e– O2– Outer chamber reaction O2– O· + 2e– O·+ H2 H2O Therefore uses H2 and air or O2 as fuels and produces water. Very clean and efficient (ca. 90%). Lectures co-financed by the European Union in scope of the European Social Fund

  27. Important Structures adopted by Solid Electrolytes The structures adopted by solid electrolytes are often massively defective. They are all characterised by pathways for ionic conduction. Here we will examine a few of the important structural types. Apatites: A10 (MO4)6X2 (A = alkaline earth, rare earth, Pb; M = Si, Ge, P, V; X = O, OH, halides) The apatites are an important group of structures, particularly in biomaterials where minerals such as hydroxylapatite Ca10(PO4)6(OH)2 form the main component of bone mineral. Their structure consists of a framework of isolated MO4 tetrahedra, which corner share with A atom polyhedra to give a hexagonal channel structure with channels running parallel to the c-axis. Lectures co-financed by the European Union in scope of the European Social Fund

  28. e.g. La8Y2Ge6O27. Recent Neutron and modelling studies have confirmed a mechanism involving the GeO4 tetrahedra. Conduction can also occur via this mechanism between channels. The mechanism of conductivity has been the subject of debate. Emma Kendrick, Alodia Orera and Peter R. Slater J. Mater. Chem., 2009, 19, 7955-7958 Lectures co-financed by the European Union in scope of the European Social Fund

  29. Na--alumina: Na--alumina is a Na+ ion conductor. It is formed as a solid solution between Al2O3 and Na2O. The general formula is: Na1+2xAl11O17+x (note that there is some argument as to the true solid solution formula). In the stoichiometric end member, NaAl11O17,  is low However in the solid solutions  = 10–3 S cm–1 at 25 C  = 10–1 S cm–1 at 300 C Structure consists of thick layers of alumina (Al2O3) separated by oxygen deficient layers in which the Na+ ions reside. Lectures co-financed by the European Union in scope of the European Social Fund

  30. The Na+ ions are mobile within the oxygen deficient layer but cannot penetrate the thick alumina layers. Hence Na+ conduction is 2-D. Lectures co-financed by the European Union in scope of the European Social Fund

  31. NASICON: Na3Zr2PSi2O12 NASICON is an important sodium ion conductor that is commercially used in batteries. The structure consists of corner sharing ZrO6 octahedra and P/SiO4 tetrahedra. This results in 3 dimensional tunnels in which the Na+ ions reside. Similar structure adopted by fast lithium ion conductors such as Al doped Li1+xTi2-xAlx(PO4)3 (LATP) NASICON based battery Ceramatec http://www.iitg.ernet.in/physics/fac/padmakumarp/nasicon.htm Lectures co-financed by the European Union in scope of the European Social Fund

  32. Fluorite based structures: The fluorite structure is an important host for ionic conduction of anions, such as O2- and F-. It is essentially made up of a ccp array of large cations with anions in the tetrahedral sites. http://electronicstructure.wikidot.com/predicting-the-ionic-conductivity-of-ysz-from-ab-initio-calc Lectures co-financed by the European Union in scope of the European Social Fund

  33. e.g. YSZ The cubic phase of zirconia can be stabilised through solid solution formation with a variety of oxides. Most commonly yttria stabilised zirconia Zr1-xYxO2-x is used commercially in fuel cells. YSZ shows a maximum in conductivity at around x = 0.10 The mechanism of conductivity has been widely studied and modelled using a variety of methods. Most studies agree that diffusion occurs via the edge shared between two neighbouring OZr4 tetrahedra. Lectures co-financed by the European Union in scope of the European Social Fund

  34. e.g. PbSnF4 Cordered ccp array of Pb and Sn resulting in a lyared tetragonal fluorite structure. In -PbSnF4, ¾ of the fluoride ions located in two crystallographic sites F2 and F3 corresponding to those in the ideal fluorite structure and the remaining fluoride ions located in an octahedral site F4 between the Sn and Pb layers. Ions located in the F4 site. The remaining tetrahedral site, F1 between adjacent Sn layers is vacant. Lectures co-financed by the European Union in scope of the European Social Fund

  35. The mechanism of conductivity was studied by NMR and neutron diffraction. Lectures co-financed by the European Union in scope of the European Social Fund

  36. Pyrochlores Pyrochlores are fluorite based phases that show cation ordering and have 1/8 of the anion sites vacant. e.g. Gd2-xCaxTi2O7-x/2 These materials show good ionic conductivity at around 1000C. Vacancies are introduced through subvalent substitution of Gd3+ https://web.chemistry.ohio-state.edu/~woodward/ch754/lect2003/solid_electro_lect27.pdf Lectures co-financed by the European Union in scope of the European Social Fund

  37. Brownmillerite In the brownmillerite structure 1/6 of the perovskite oxygen sites are vacant. These are ordered in layers giving a perovskite like octahedral layers separated by tetrahedral layers. e.g. Ba2In2O5 There is high oxide ion conductivity in the tetrahedral layers at ca. 10-1 S cm-1 at 800C Lectures co-financed by the European Union in scope of the European Social Fund

  38. Perovskite based structures: e.g. KCaF3 This is a classic perovskite structure that shows high fluoride ion conductivity at intermediate temperatures. Neutron diffraction studies using an anharmonic model for thermal vibration reveal details of the F- ion conduction pathway. Lectures co-financed by the European Union in scope of the European Social Fund

  39. Ruddlesden Popper Phases e.g. Lan+1NinO3n+1 Ruddlesden-Popper phases are tetragonal layered perovskite materials with a general formula of AO(ABO3)n . A typical Ruddlesden-Popper structure is made of alternating perovskite blocks, with the perovskite blocks increasing as the n value increases. n = 1 n = 2 n = 3 Lectures co-financed by the European Union in scope of the European Social Fund

  40. In La2NiO4+δ there are excess oxide ions located in interstitial sites. This gives high ionic conductivity up to a value of δ = 0.2. Doping also alows the improvement of ionic/electronic conductivity in these systems. Doping can be either for A site (La) or B site (Ni) cations. Successful doping occurs with Sr, Nd, and Sm on the A-site of the perovskite layer, and Cu, Fe, and Co in the B-site. Experimental results suggest that doping at the A-site of the RP phase have resulted in improvements in electronic conductivity of nickelate material, while on the B-site, it has improved ionic and decreased electronic conductivities respectively. e.g. La2Ni1-xCoxO4+δ and La4Ni3-xCoxO10±δ Lectures co-financed by the European Union in scope of the European Social Fund

  41. Aurivillius Structures: [Bi2O2][An-1BnO3n+1] (A = large cation, B = small cation) These are layered structures based on stacking of layers of [Bi2O2]n2n+ or equivalent lead oxide layers and perovskite like layers of metal octahedra such as [WO4]n2- (in Bi2WO6). The structure of Bi4V2O11 is that of an n = 1 Aurivillius phase with vacancies concentrated in the vanadate layer. [VO3.5V0.5]n2n- The BIMEVOXes are derived by substitution of V/Bi by a variety of cations and show exceptionally high conductivity at low and intermediate temperatures. e.g. Bi2V1-xCuxO5.5-3x/2 Lectures co-financed by the European Union in scope of the European Social Fund

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