Electrical Conduction in Ceramic Materials 1 Ref: Barsoum, Fundamentals of Ceramics, Ch7, McGraw-Hill, 2000

Transcription

1 MME 467 Ceramics for Advanced Applications Lecture 19 Electrical Conduction in Ceramic Materials 1 Ref: Barsoum, Fundamentals of Ceramics, Ch7, McGraw-Hill, 2000 Prof. A. K. M. B. Rashid Department of MME, BUET, Dhaka Topics to discuss... v Fundamentals and definitions relating conductivity v Ionic conductivity v Fast ion conductor 1

2 Fundamentals and Definitions Historically ceramics are used as ideal insulating materials for their good electrical insulating properties and chemical and thermal stability Example: power line, resistors Today, besides the above-mentioned applications, ceramics are used in many other fileds: u Electrode x Photoelectrode v Catalytes y Varistor w Fuel cell z Sensor Here comes the term Electronic Ceramics Electrical Conductivity The response of ceramics to the application of a constant electric field and the nature and magnitude of the steady-state current is identified by a material property, called electrical conductivity. Mathematically, the ratio of the current to the applied electric field is called conductivity, σ. Current Carrier Metals : Free electrons Semiconductors : Electrons and electron-holes Ceramics : Electrons and/or ions Mixed conduction does occur and this conduction is represented as: σ = σ elec + σ ionic 2

3 The range of electronic/electrical conductivity of ceramics varies over 24 orders of magnitude ( s/cm). metallic (RnO 2, TiO 2, LaCaO 3, SrTiO 3 ) semiconducting (V 2 O 3 -P 2 O 3, TiO 2-x ) insulating (ZnO, Al 2 O 3 ) Ionic conductivity of ceramics varies from fast ion conductor (β-al 2 O 3, ZnO.Y 2 O 3 ) solid electrolyte (LaF 3, NaCl) insulator (SiO 2 ) 4 th type of electronic ceramic conductor: superconductor Æ significant loss of resistivity below a critical temperature T c. Characteristics of Metals, Semiconductors and Insulators in terms of Energy Band Energy n=10 22 n=10 10 n=1 n = carrier density, cm Unoccupied conduction band partially occupied Occupied valence band Electronic: metal semiconductor insulator Ionic: fast ion solid insulator conductor electrolyte relative occupancy of valence and conduction bands relative occupancy of ionic sublattice 3

4 Some Definitions Electric current density, j electrical charge transported through a unit area in unit time j = n (ze) v n = carrier density or, no. of charged particle (mobile carrier) per unit volume ze = charge per particle v = drift velocity under an applied electric field, E Electrical conductivity, σ proportionality constant between j and E σ = j E = n (ze) v E Ω -1 cm -1 or S/cm The drift velocity is directly proportional to the locally acting electrical field strength, and their ratio is defined as the mobility, µ (i.e., velocity per unit field) µ = v E cm -1 V -1 s -1 σ = n (ze) v E σ = n (ze) µ Absolute mobility, B drift velocity per unit of applied force F (the virtual force which acts on a diffusing carrier) B = v F = v (ze)e σ = n (ze) 2 B µ = (ze)b 4

5 Conductivity in Terms of Experimentally Measurement Parameters V = ir R = Lρ /A ρ = 1/σ σ = 1 L R A V = Applied voltage, V i = Resulting current, A R = Electrical resistance of material, Ω conductivity in terms of material parameters σ = n(ze)µ L = Length of material, cm ρ = Specific resistance or resistivity of material, Ω cm A = Area of material, cm 2 Factors Affecting Conductivity σ = n (ze) µ n = carrier density µ = mobility of carrier 1. Temperature 2. Doping 3. Surrounding atmosphere : But in order to understand the reason behind v the phenomenal range of conductivity, and v why some ceramics are ionic conductors while others are electronic conductors It is necessary to relate the macroscopically measurable parameter σ with more fundamental microscopic parameters, such as carrier mobility and concentrations. 5

6 Ionic Conductivity Carrier of electrical charge charged ionic defects vacancy, interstitials moves under the influence of an electric field based on random ion hopping Ionic ceramics exhibit this behaviour assuming that empty sites or vacancy are always available i.e., [V] = 1. For an ion to move through the lattice, it must have sufficient thermal energy to pass over the energy barrier activation energy for ion motion Energy u or, ΔH m a = Fa No field E applied E applied Distance 6

7 Forward jump rate f + = θ e - u + 2 θ = probability of a site is available for a jump Backward jump rate f = θ e - u - 2 The net jump rate f = f + f - u = 2 θ e sinh 2 f = f + f - u = 2 θ e sinh 2 For typical values of E, a, and T (ze)e a << and sinh [ ] terms becomes very small. sinh 2 2 Then, the net jump rate f = θ e u 7

8 Total net flux naf = na 2 (ze)e - u / θ e n = carrier concentration af = drift velocity Electric current density j = n(ze)v = n(ze)af j = na 2 (ze) 2 E e θ - u / Ionic conductivity j σ = E = na 2 (ze) 2 e θ - u / σ = n(ze) 2 D σ n = c ion (vacancy mechanism) n = c int (interstitial mechanism) Nernst-Einstein (N-E) Relation Ionic diffusivity D σ = a 2 θ e -u / [V] = 1 D = A [V] a 2 θ e -ΔH m /RT 8

9 D σ Low T Extrinsic depends only on D 0 σ 0 = conductivity of pure material depends on D 0 and vacancy site High T Intrinsic 1/T Temperature dependence of diffusivity Fast Ion Conductors (FICs) Many ceramic compound shows exceptionally high ionic conduction, similar to those of molten salts (σ 10-2 s/cm). These are known as fast ion conductors (sometimes also referred to as solid electrolytes) Major structural features of FICs: u Framework a highly ordered, immobile sublattice which provides continuous open channels for ion transport v Mobile carrier sublattice a randomly distributed carrier over an excess number of equioptional sites 9

10 Other important fast ion conduction parameters: u High ionic conductivity (σ > 10-2 S/cm) well below the melting point v Low activation energies (Q ev) w Low pre-exponentials (σ S/cm.K) 3 groups of FICs: EXTRINSIC INTRINSIC structurally disorder solid highly defective solids u Silver ion conductor halides and chalcogenides of Ag and Cu metal atoms are disordered over several alternate sites example: α-agi v Alkali metal conductor nonstoichiometric aluminate example: β-al 2 O 3 i.e. Na 2 O.11Al 2 O 3 w Oxygen ion conductor oxides with fluorite structure, doped with lower valence cation oxides to create large oxygen vacancy example: CaO-ZrO 2, Y 2 O 3 -ZrO 2 10

11 Spinel block Spinel block Spinel block Na ions Conduction planes ( a ) Structure of Na-β-Al ( b) 2 O 3 (Na 2 O.11Al 2 O 3 ) x CaO C a " ZrO Zr + V O + O O 2 For every 1 mol of CaO added to ZrO 2, 1 mol of oxygen vacancy is created!! Effect of doping on ionic conductivity σ FIC ( ) β 1 β = const [ ] exp % ΔH * ( m ' & ) * β = n mob /n 0 11

12 To summarise: Ionic conduction creation and motion of atomic defects, notably vacancy and interstitial (E d and E m ) Addition of impurities results in a marked enhancement of carrier Next Class Lecture 20 Electrical Conduction in Ceramic Materials 2 12