Electrical conduction in ceramics

Transcription

1 Laurea Magistrale in Scienza dei Materiali Materiali Inorganici Funzionali Electrical conduction in ceramics Prof. Antonella Glisenti - Dip. Scienze Chimiche - Università degli Studi di Padova

2 Conductivity in oxides Defects Defects and doping Defects and oxygen Defects in fluorite-type oxides Conductivity in MO 2 -type oxides

3 Bibliography 1. P. J. van der Put: The inorganic chemistry of materials How to make things out of elements Plenum Press N.Q. Minh, T. Takahashi: Science and technology of ceramic fuel cells Elsevier 1995

4 I siti difettuali sono responsabili del trasporto di materia e di carica: 1 Salto di uno ione da una posizione interstiziale ad un altra 2 Salto di uno ione da una posizione reticolare ad una interstiziale accompagnato dalla migrazione di un altro ione interstiziale nella vacanza formatasi 3 Salto di uno ione da una posizione reticolare ad una vacanza adiacente. Il trasporto degli ioni avviene se: 1) la particella ha un difetto disponibile situato nei siti adiacenti 2) la particella ha energia sufficiente per attraversare la barriera di potenziale che si oppone alla sua migrazione.

5 Defects The properties of ceramics or crystalline solids depends on the material lattice defects. Stoichiometry Stoichiometric defects: crystal composition is unchanged Non-stoichiometric defects: crystal composition changes Size and Shape Point defects: interstitials or vacancies Line defects: dislocations Plane defects: the whole layer in a crystal structure is defective Electrical conduction in ceramics or crystalline solids depends on point defects.

6 Types of defects in solids

7 Defects and Kröger-Vink notation Vacancies: V; in NiO: V Ni and V O Interstitials: subscript i; In AgBr: Ag i Electrons or electron holes in the VB or CB: e, h Dopants: Y 3+ ions in ZrO 2 : Y Zr Ti 4+ in CeO 2 : Ti x Ce Defect concentrations are not independent of each other: Electroneutrality Mass balance Site balance Intrinsic defect concentrations: < 10-4 ppm for an oxide with bandgap > 4 ev (impurity concentration: ppm) n Q exp ( H f /RT) k = exp ( G f /RT)

8 Frenkel-type defects (1926): interstitials and vacancies Frenkel defects move in the crystal N = total number of ions; N i = total number of interstitials; k = Boltzmann constant, T = temperature, E F = formation energy of the Frenkel defects) the radii of ions of the crystal differ considerably high van der Waals energy and dielectric constant Schottky-type defects (1935): cation/anion vacancies N = total number of ion pairs; N i = total number of Schottky defects; k = Boltzmann constant, T = temperature, E S = formation energy of the Schottky defects) Small differences between the radii of the cations and anions Poor polarizability Small van der Waals energy and dielectric constant

9 Extrinsic defect concentration: doped MO Doping depends on solubility (phase diagrams) MgO doped with Li 2 O Mg 2+ replaced by Li + MgO doped with Sc 2 O 3 Mg 2+ replaced by Sc 3+ Li 2 O = 2 Li Mg + O x O + V O > Li > Oxygen vacancies Sc 2 O 3 = 2 Sc Mg + 3 O x O + V Mg > Sc > Mg vacancies Doping with aliovalent species affects the concentration of the defects that are formed thermally in the intrinsic equilibrium The equilibrium constants: K s and K F (if one defect is added by doping its partner in the equilibrium decreases)

10 Phase diagram of a ZrO 2 -CaO system

11 Gas equilibria Schottky type Adsorpion ½ O 2 (g) = O x O + 2 h + V M K a = [h ] 2 [V M ]p -1/2 (O2) > Oxygen partial pressure > p-type conductivity Desorption O x O = ½ O 2 (g) + 2 e + V O K d = [e ] 2 [V O]p (O2) 1/2 Oxides that prefer to desorb oxygen may more easily accomodate electron than holes (n-type semiconductors) and become less conducting with increasing oxygen partial pressure

12 Gas equilibria Frenkel type Adsorpion ½ O 2 (g) = O i + 2 h K a = [h ]2 [O i ]p (O2) -1/2 > Oxygen partial pressure > p-type conductivity Desorption M x M + Ox O = ½ O 2 (g) + 2 e + M i K d = [e ] 2 [M i]p (O2) 1/2 > metal-rich n-type semiconductors

13 Calculated equilibrium defect diagrams for a binary oxide MO with Schottky defect pairs K i «K S Oxides with a wide bandgap: the oxide is a pure ionic conductor under an oxygen pressure at the middle region K i» K S Oxides with a narrow bandgap: the oxide is a semiconductor at all oxygen pressures (low oxygen pressures = n-type, high oxygen pressure = p- type)

14 TM oxides that can reach higher oxidation states (MnO, FeO, CoO, NiO) Oxygen uptake MO 1+x (x > 1) to become p-type semiconductors Li 2 O in NiO: Aliovalent doping: Li 2 O 2 Li Ni + O x O + V O Vacancies may react with oxygen ½ O 2 (g) + V O O x O + 2 h Li 2 O + ½ O 2 (g) 2 Li Ni + 2 O x O + 2 h Cr 2 O 3 in NiO: n-type conductivity Exceeding oxygen may be lost: Cr 2 O 3 2 Cr Ni + 3 O x O + V Ni Cr 2 O 3 2 Cr Ni + 2 O x O + 2 e + ½ O 2 (g)

15 TM oxides that can not reach higher oxidation states (Ta 2 O 5, CeO 2, ZnO) Oxygen desorption MO 1+x (x < 1) to become n-type semiconductors Li 2 O in ZnO: Aliovalent doping: Li 2 O 2 Li Zn + O x O + V O Vacancies may react with oxygen Li 2 O + ½ O 2 (g) + 2e 2 Li Zn + 2 O x O Li doping oxidizes ZnO and lowers its n-type conductivity by consuming the surplus electrons in the conduction band Cr 2 O 3 in ZnO: n-type conductivity Cr 2 O 3 2 Cr Zn + 2 O x O + 2e + ½ O 2(g) Doping ZnO with cromium oxide that has too many oxide ions for ZnO evolves gaseous oxygen that leaves electrons behind; n-type character of ZnO is increased

16 Defects in fluorite-type oxides The fluorite (CaF 2 ) structure is adopted by a number of oxides (MO 2 with M = large tetravalent cation), sulfides, hydrides, intermetallic compounds of AX 2 type Unit cell (=M 4 O 8 structure): each metal ion is surrounded by eight oxygen ions forming a body-centred cubic structure, and each oxygen ion is surrounded by four metal ions forming a tetrahedral arrangement. The minimum metal-ion radius/oxygen-ion radius is At RT ZrO 2 has not a fluorite structure (ionic radius ratio condition not satisfied); fluorite structure is observed at T > 2370 C or when stabilized by aliovalent doping (divalent or trivalent cations) Defects in doped zirconia with fluorite structure: 1) oxygen-ion vacancies with the metal ions being fixed at their lattice points 2) cation interstitials with oxygen ions being fixed at their lattice sites (Frenkel) 3) Schottky

17 Defect structure of doped MO 2 Incorporation of AO into MO 2 : Incorporation of oxygen from the environment into MO 2 : Equilibrium constant, K: Intrinsic Schottky equilibrium: Equilibrium constant, K S : Intrinsic electronic equilibrium: Equilibrium constant, K i : Electroneutrality condition:

18 Defect structure of doped MO 2 : low oxygen partial pressure region As the oxygen pressure decreases the concentration of oxygen-ion vacancy increases (to maintain K); this increase causes the metal vacancy concentration to decrease (to maintain K S ); thus: The concentration of oxygen-ion vacancy exceeds that of A M (fixed by the dopant level); n must increase to maintain the electroneutrality condition and p must decrease; electroneutrality reduces to: Oxygen partial pressure dependence of oxygen-ion vacancy: Oxygen partial pressure dependence of the metal vacancy concentration: Oxygen partial pressure dependence of the hole concentration:

19 Defect structure of doped MO 2 : intermediate oxygen partial pressure region Over the intermediate oxygen pressure range, the concentration of oxygen-ion vacancies is not dependent on oxygen partial pressure but fixed by the dopant level: As the oxygen partial pressure increases, the concentration of electrons decreases and that of the holes increases; on the other hand the metalion vacancy concentration is independent of oxygen partial pressure and determined solely the K S and the oxygen-ion vacancy concentration.

20 Defect structure of doped MO 2 : high oxygen partial pressure region Electroneutrality condition con be approximated as: Oxygen partial pressure dependence of the anion and cation vacancies: Electron concentration is given by: Electron concentration is constant in this oxygen partial pressure region.

21 Defect structure of doped MO 2 : very high oxygen partial pressure region The concentration of metal-ion vacancy becomes very large: Electroneutrality condition con be approximated as: Oxygen partial pressure dependence of defect concentration:

22 Defect structure of AO and B 2 O 3 doped MO 2 Variation of defect concentration as a function of oxygen partial pressure for a MO 2 -AO system Variation of defect concentration as a function of oxygen partial pressure for a MO 2 -B 2 O 3 system

23 Conductivities of oxygen ions, electrons, and electron holes The total electrical conductivity, σ, of a fluorite-type oxide is given as: µ = mobilities; i, n, p = ions, electrons, electron holes; the ionic conductivity due to the migration of cations of the dopants and the host is neglected because the mobilities of the cations have been shown by diffusivity measurements to be several order of magnitude lower than the mobility of oxygen-ion vacancy.

24 Conductivities of MO 2 -B 2 O 3 systems Since the mobility of oxygen-ion vacancy is generally much lower than that of electrons and electron holes, B 2 O 3 -doped MO 2 can only exhibit an appreciable ionic conductivity over a wide range oxygen partial pressures when the concentration of oxygen-ion vacancy is considerably larger than n and p. Conductivity is at the maximum when σ n = σ p Variation of electrical conductivity as a function of oxygen partial pressure for a MO 2 -B 2 O 3 system

25 Defect domains in Patterson type maps Electrolytic domain boundaries = oxygen partial pressure where σ i = 100σ p and σ i = 100 σ n Electronic, ionic, and electrolytic domains of a MO 2 -B 2 O 3 system

26 Defect association and clusters At low temperature oppositely charged oxygen-ion vacancies and dopant cations may associate to form randomly distributed pairs; the concentration of free oxygen-ion vacancy is determined by the association equilibriums: Break temperature = temperature for the break of the associated vacancy behaviour

27 Defect association and clusters 1. The formation of defect association and clusters and trapped vacancies causes the decrease of conductivity: trapped vacancies are not immobile but must overcome an energy barrier to move (dissociation or rearrangement of clusters), this barrier is higher than that present in systems having only single vacancies. Calculated break temperature between associated and free vacancies in CaO-doped CeO 2 for various association energies. Conductivity data of CaO-doped ThO 2 indicate the association of vacancies and does not show break temperature as ceria does: the association energies (1.16 to 1.42 ev or to kj/mol) of CaO/ThO 2 (dopant 1 to 7 mol%) are much higher than those (0.20 to 0.50 ev or 19.3 to 48.2 kj/mol) of CaO/CeO 2 2. At high defect concentration a random distribution of defects and defect pairs may be converted into an ordered two- or three-dimensional defect structure