Simple and Complex Defects Nalini Vajeeston Department of Chemistry, University of Oslo FERMiO, Gaustadalleen 21 NO-0349 Oslo, Norway

 Introduction  Kröger -Vink notations  Proton defects in oxides  Simple defect materials ● Acceptor doped-LaNbO 4 ● Phosphates and pyrophosphates  Complex defect materials ● Ba 2 In 2 O 5 ● Mayenite (Ca 12 Al 14 O 33 ) ● Ba 3 La(PO 4 ) 3  Summary Outline

Introduction Deviations from the ideal structures are present at any temperature and occur naturally in all crystalline compounds. These deviations or imperfections are called defects. Defects in stoichiometric compounds (crystal composition is unchanged) Schottky and Frenkel defects. Defect Structure A complete description of the point and electronic defects in a compound and their concentrations as a function of the partial pressures of the constituents and the temperature is termed the defect structure of the compound. Defects Defects in non-stoichiometric compounds (formed by introducing dopants or impurities) (composition is changed) Cation vacancies, interstitial anions, oxygen vacancies and electronic holes.

Kroger-Vink notations for simple defects Defect TypeNotationDefect TypeNotation Non-metal vacancy at non- metal site vXvX Impurity non-metal (Y) at non-metal site YXYX Metal vacancies at metal site vMvM Impurity metal (A) at metal site AMAM Neutral vacanciesvXMvXXvXMvXX Non-metal vacancies with positive effective charge* v X Metal vacancies with negative effective charge* v/Mv/M Interstitial metalMiMi Interstitial non-metalXiXi Intertitial metal with positive effective charge* M i Interstitial non-metal with negative effective charge* X/iX/i Free positive holeh Free electrone/e/ Substitutional hydroxideOH O * The effective charge is the charge that the defect has with respect to the normal crystal lattice.

The total effective charge is the same before and after the formation of the defects. (The net charge on the left and right hand sides of a reaction equation must be the same). Electroneutrality Defect reactions Mass balance The defect reaction must balance with respect to the mass. Vacancies, which only represent empty sites, have zero mass and do not count. Electronic defects are not considered to count in the mass balance. Ratios of regular lattice sites The ratio(s) of the number of regular cation and anion lattice sites in a crystalline compound is constant. No sites are created in the formation of electronic defects.

Hydrogen defects in metal oxides When a metal oxide is equilibrated in gas mixtures with hydrogen containing gases, e.g. H 2 O, hydrogen will dissolve in the metal oxide. The extent of the dissolution of hydrogen will depend on the defect structure of the oxide and the ambient oxygen and hydrogen activities. The dissolution of protons from water vapour may in these terms be written The concentration of protons in metal oxides is dependent on the partial pressures of both the ambient oxygen and water vapour as well as the concentration of electronic defects. Defect equilibrium:

Effect of water vapour on oxygen-deficient M 2 O 3 Undoped, oxygen-deficient oxide: The predominant defects  electrons and oxygen vacancies Electroneutrality condition in dry environments In wet environments: The predominant defects: protons Electroneutrality condition: Brouwer plot of effects of water vapour on defect concentrations in oxygen deficient M 2 O 3-d P O2 = constant; P H2O = varied Proton concentration is propotional to

Effect of water vapour on acceptor-doped M 2 O 3 Hydration reaction: Equilibrium constant: Electroneutrality: Concentration of protons: Brouwer plot of the effect of water vapour (at constant oxygen pressure) on defect concentrations in acceptor-doped, oxygen deficient M 2 O 3. Oxygen vacancies and protons compensate the acceptor doping.

Proton defects in Phosphates (Sr-doped LaPO 4 ) Substitution of divalent metals for rare earth metals leads to condensation of orthophosphate ions, i.e. formation of pyrophosphate ions as oxygen deficits. Protons dissolve into phosphates forming hydrogen phosphate groups through the equilibrium between the condensed phosphate ions and water vapor in ambient atmosphere. The electroneutrality condition of an acceptor-doped phosphates with oxygen vacancies and protons Monoclinic monazite type structure

Proton defects in Pyrophosphates: Hydration reaction: Equilibrium constant: Electroneutrality: TiP 2 O 7 Cubic superstructure

Acceptor doped LaNbO 4 LaNbO 4 exists in two different polymorphs Low temperature phase  Monoclinic-Fergusonite-type structure High temperature phase  Tetragonal-Scheelite structure MonoclinicTetragonal

Condensation occurs when oxygen vacancy is formed in phosphate. Based on this, oxygen vacancy in phosphate can be expressed as Same condensation can occur in LaNbO 4. Oxygen vacancy in LaNbO4 can be written as. more complicated than phosphate. The condensed coordination polyhedra of Nb 3 O 11 found by theoretical calculation. LaNbO 4 may have a tendency to dissolve ptotons by interacting with ambient water vapor: Electroneutrality condition:

Ba 2 In 2 O 5 (or BaInO 2.5 ) Ba 2 In 2 O 5 is an oxygen deficient perovskite ordered into the brownmillerite-structure at low temperatures. Around 930 °C it disorders into the perovskite. The oxygen vacancy conductivity jumps two orders of magnitude. The disordered phase has 5 oxide ions and 1 oxide ion vacancy sharing the same perovskite site. what is the compensating negative effective charge? Defects: Perovskite Brownmillerite-structure ●The disordering can be seen as a anion-Frenkel-disorder (the formation of oxide ion vacancies and interstitials) ● Acceptor New nomenclature

Ba 2 In 2 O 5 (or BaInO 2.5 )- new nomenclature Disordered Ba 2 In 2 O 5  oxide ions and vacancies on the oxide ion sublattice. The perfect oxide ion site is statistically occupied 5/6 with an oxide ion and 1/6 with a vacancy  Each oxide ion occupying the site to a degree of 5/6 has a formal charge -2 the site statistically has a charge of -2 · 5/6 = -5/3 Real charge of oxide ion = -2 Real charge of vacancy = 0 Its effective charge = ‑ 2 ‑ ( ‑ 5/3) = -1/3. Effective charge = 0-(-5/3) = +5/3. The oxide ion is denoted in the expanded Kröger-Vink nomenclature as Electroneutrality condition Site occupancy sum interms of mole fraction and Oxide ion vacancy 

Defect chemical reactions with Ba 2 In 2 O 5 Electroneutrality: Equilibrium coefficient: Electrons  minority defects Equilibrium coefficient: Solve this with respect to the concentration of electrons and obtain Reduction and oxidation The corresponding oxidation reaction is sum of the reduction and oxidation reactions yields the intrinsic ionisation of electrons or

Hydration reaction: Hydration reaction for disordered Ba 2 In 2 O 5 : Equilibrium coefficient: Hydroxide defects < two native defects are dominating and constant, The concentration of hydroxide defects takes on a dependency. To increase the water vapour partial pressure,the hydroxide defects become dominating, Electroneutrality  The 6 oxygen sites are disorderly filled with 4 oxide ions and 2 hydroxide ions overall formula Ba 2 In 2 O 4 (OH) 2, or BaInO 2 (OH).

Zr Doping The electroneutrality becomes At 50 % substitution  one oxygen vacancy and eleven oxide ions out of twelve positions; Ba 4 In 2 Zr 2 O 11. At high doping levels, it gets the same whether one considers it to be Zr-doped Ba 2 In 2 O 5 or In-doped BaZrO 3.

Mayenite, Ca 12 Al 14 O 33 Unit cell  (Ca 24 Al 28 O 64 ) 4+ · 2O 2- lattice framework with 12 nano-cages extra-framework oxide ions are randomly distributed in the nano-cages and can be replaced by F -,Cl -,OH - and H - ions. Each nano-cage contains two crystallographic positions for the oxide ion. It is reasonable to assume that only one oxide ion can be fitted in a cage at any time, and that the energy barrier between the two positions is small enough that the oxide ion is effectively delocalized over the two positions at elevated temperatures. In this way, each oxide ion occupies one out of 6 available cages. J. Medvedeva

Effective charge of O 2- : (-2) – (-1/3) = -5/3 Effective charge of cage: (0) – (-1/3) = +1/3 Effective charge of OH - : -1 – (-1/3) = -2/3 The real charge of the species minus the real charge of the perfect reference lattice The defect situation in mayenite can be described as one with an inherently deficient sublattice (the oxide ions in the extra-framework nanocages). The site is denoted as 1/6 occupancy of oxide ions as the perfect state, consequently with a charge of -2/6 = -1/3.

The electroneutrality in the pure, dry material then reads Mayenite has a strong tendency to become hydrated by replacing the oxide ions with hydroxide ions. Hydration reaction:Equilibrium constant:

The new electroneutrality: Site limitation: The site sum of 6 enforces concentrations to refer to fractions of one formula unit mayenite Ca 12 Al 14 O 33, or molar fraction of the same The concentration of hydroxide ions as a function of water vapour partial pressure and temperature:

Ba 3 La(PO 4 ) 3 Eulytite structure The four cations (three divalent Ba 2+ and one trivalent La 3+ ) disorderly occupies the same site. The site is statistically occupied by (3·2 + 1·3)/4 = 9/4 = 2¼ positive charges. New nomenclature: Site: or or Ba 2+ or La 3+ ion would be denoted  or Systems with disordered occupancy by several cccupants

The electroneutrality reads An abbreviation for the complex site expression can be useful in such cases. Thus, defining allows to denote Ba 2+  La 3+  Acceptor doping with an excess of Ba2+ to dissolve protons, in phosphates represented as hydrogen phosphate defects on phosphate sites, The new electroneutrality reading

Assume the compound is perfectly stoichiometric, we consider a minor concentration of additional defects formed by oxidation. (oxygen interstitials and electron holes) Since the two defects of disordered Ba 2+ and La 3+ are dominating in numbers, the holes end up as minor defects with the familiar dependency they attain when ionic defects rule.

Summary ● The new extension of the Kröger-Vink nomenclature, and defects present in the disordered Ba 2 In 2 O 5 have been discussed. ● Defect structures of Mayenite (Ca 12 Al 14 O 33 ) and Ba 3 La(PO 4 ) 3 are derived. ● Proton defects in oxides, phosphates and pyrophosphates are explained. ● Defect chemistry of acceptor doped-LaNbO4 was discussed.

References ● A Kröger-Vink-compatible notation for defects in inherently defective sublattices Truls Norby - to be submitted. ● High temperature hydration and conductivity of mayenite, Ca 12 Al 14 O 33 Ragnar Strandbakke, Camilla Kongshaug, Reidar Haugsrud, Truls Norby - to be submitted. ● Local condensation of oxygen vacancies in t-LaNbO 4 from first principle calculations Akihide Kuwabara,*, Reidar Haugsrud, Svein Stølen,Truls Norby –submitted. ● Defects and transport in crystalline solids Per Kofstad and Truls Norby ● High-temperature protonic conduction in TiP 2 O 7 and Al-doped TiP 2 O 7 Nalini Vajeeston*, Reidar Haugsrud, Helmer Fjellvåg, Truls Norby - to be submitted. ● High-temperature protonic conduction in acceptor doped-LaPO 4 K. Amezawa, S. Kjelstrup, T. Norby, and Y. Ito, Electrochem. Soc. 145 (1999) 3313.