Advanced Vitreous State - Physical Properties of Glass

Transcription

1 Advanced Vitreous State - Physical Properties of Glass Lecture 25: Charge Conduction Properties of Glass: Steve W. Martin Ionic Conduction in Glass - Part 1 Relationship to Glass Structure and Composition Department of Materials Science & Engineering Iowa State University Ames, IA swmartin@iastate.edu

2 Ionic Conduction in glass Glasses can be systematically doped to increase conductivity From near insulating values to those that rival ionic liquids Strong glass forming character over wide compositions ranges make them ideal for many composition studies of the ionic conductivity Low melting temperatures often make them compatible with many industrial processing techniques such as sputtering and evaporation to produce thin film electrolytes Ionic Conduction in Glass Part 1 2

3 Formation of Non-Bridging Oxygens Modifier M 2 O or MO creates two NBOs per M 2 O or MO added xna 2 O (1-x)SiO 2 creates 2x NBOs f NBO = NBOs/(NBOs BOs) f BO = 1- f NBO = 2x/(x 2(1-x)) = 2x/(2-x) Q 4 Q 4 Q 3 Q 3 swmartin@iastate.edu Ionic Conduction in Glass Part 1 3

4 Q i Units in Alkali Silicate Glasses Q 4 Q 3 Q 2 O Q Na 0 Q 1 Si swmartin@iastate.edu Ionic Conduction in Glass Part 1 4

5 Alkali Ions are weakly bound Frame work cations, Si 4, and anions, O = Covalently bonded to the network Large bond strength, 100 kcal/mole Modifying cations, M, and anions F - Ionically bonded to the network Small bond strength, < 50 kcal/mole Alkali cations can be thermally activated To break their weak ionic i bond And move from one alkali cation site to another Thermally activated ionic conduction. swmartin@iastate.edu Ionic Conduction in Glass Part 1 5

6 Relation of glass structure to ionic conduction xna 2 O (1-x)SiO 2 Glass in 2-D E swmartin@iastate.edu Ionic Conduction in Glass Part 1 6

7 Molecular Dynamics Simulation of Ionic Conduction Go to Movie.. Ionic Conduction in Glass Part 1 7

8 Relation of glass structure to ionic conduction - NBO BO - NBO En nergy 1/r n ΔE S ΔE C -e 2 /r BO ΔE act = ΔΕ s ΔE c ΔE s = Strain Energy ΔE c = Coulomb Energy r r swmartin@iastate.edu Ionic Conduction in Glass Part 1 8

9 Cation Conduction Rattle and Jump - NBO BO - NBO Energ gy 1/r n ΔE S BO y MD Simulations ΔE C -e 2 /r x r r swmartin@iastate.edu Ionic Conduction in Glass Part 1 9

10 Theory of Ionic Conduction in Glass: Simple Models σ = 1/ρ nezμ n is the number density ez is the charge, 1 most of the time μ is the mobility What are the units of n? #/cm 3 What are the units of μ? (cm/sec)/v = cm/v-sec What are the units of σ? (Ω cm) -1 S/cm swmartin@iastate.edu Ionic Conduction in Glass Part 1 10

11 Theory of Ionic Conduction in Glass: Simple Models λze E 2 E λzee ΔE act 2 E λ/2 λ swmartin@iastate.edu Ionic Conduction in Glass Part 1 11

12 Theory of Ionic Conduction in Glass: Simple Models υ υ ΔE T ) = υ exp ( 0 ( T ) 0 λze E act / 2 RT ΔE = λze E υ exp RT υnet = υ ( T ) υ ( T ) υ υ net net act / 2 ΔE = act λze E υ0 exp exp RT 2RT ΔE λze E act = 2υ 0 exp sinh RT 2RT λze E exp 2RT ~ υ0λze E RT exp ΔE RT act swmartin@iastate.edu Ionic Conduction in Glass Part 1 12

13 Theory of Ionic Conduction in Glass: Simple Models ΔE λze E υ ze E act 0λ υ = net 2υ 0 exp sinh ~ RT 2RT RT 2 υ0λ ze E ΔEact velocity = υ = RT net λ exp RT 2 υ ze ΔEact 0 λ mobility = velocity / E = exp RT RT conductivity = mobility conductivity charge σ(t) = 2 nυ λ RT ( ze) 2 0 σ ΔEact 0 exp RT T exp ΔE RT exp act ΔE RT act swmartin@iastate.edu Ionic Conduction in Glass Part 1 13

14 Theory of Ionic Conduction in Glass: Simple Models ΔE act = ΔΕ s ΔE c ΔE s = Strain Energy ΔE c = Coulomb Energy En nergy - NB O σ(t) = σ 0 T = σ 0 T exp exp ΔE C ΔE RT act ΔE RT BO ΔEC - n( T ) = n0 exp NBO RT 1/r n BO μ0 ΔES μ( T ) = exp = T RT ΔE S 2 2 ν ΔE 0 λ ( ze) ΔES C -e 2 /r exp RT RT r r S swmartin@iastate.edu Ionic Conduction in Glass Part 1 14

15 Arrhenius Ionic Conductivity in Glass o Temperature ( o C) 10 0 Crystalline Glassy Tm Tg α-agi RbAg 4 I Ag 2 O-40.4(AgI) P 2 O 5 β-naal 11 O 17 m) Ag 2 O-42.8(AgI) MoO 3 50Ag 2 S-5GeS-45GeS 2 35Li 2 O-30Li 2 SO 4-10(LiCl) SiO B 2 O 3 Li 4 B 7 O 12 Cl 26.9Li 2 O-9(LiCl) B 2 O 3 ZrO 2-9%Y 2 O 3 25Li 2 O-25Al 2 O 3-50SiO σdc (Ω-cm LiAlSiO Li 2 O -75B 2 O LiNbO 3 2 O / T (K -1 ) swmartin@iastate.edu Ionic Conduction in Glass Part 1 15

16 Binary Alkali Silicate Glasses Addition of Na 2 O Increases the ionic conductivity, decreases the electrical resistivity Increasing the temperature re increases the ionic conductivity, decreases the ionic resistivity Ionic conductivity of soda glasses is still very low except for the highest temperatures swmartin@iastate.edu Ionic Conduction in Glass Part 1 16

17 DC ion conductivity in glass xli 2 O (1-x)P 2 O 5 Creation of non- Bridging oxygens Mobile lithium ions The higher the concentration of Li 2 O, the higher the conductivity Lower resistivity Activation energy decreases with Li 2 O content swmartin@iastate.edu Ionic Conduction in Glass Part 1 17

18 Composition Dependence of the Conductivity Binary lithium phosphate glasses, Li 2 O P 2 O 5, are relative poor ion conductors Binary lithium borate glasses, Li 2 O B 2 O 3, are slightly better conductors Li 2 O SiO 2 Li 2 O B 2 O 3 d t Li 2 O P 2 O 5 Binary lithium silicate glasses, Li 2 O SiO 2 are slightly better conductors yet. Li Li 2 O:P 2 O 2 O:SiO 2 5 Li 2 O:B 2 O 3 swmartin@iastate.edu Ionic Conduction in Glass Part 1 18

19 Salt doped phosphate glasses Halide doping strongly increases the conductivity Ionic Conduction in Glass Part 1 19

20 Effect of Sulfur Substitution Ionic Conduction in Glass Part 1 20

21 Salt doped phosphate glasses LiI doped LiPO 3 show highest conductivity and lowest activation energy among the halides Crystallization at the end of the glass forming limit T = 298 K swmartin@iastate.edu Ionic Conduction in Glass Part 1 21

22 Silver Phosphate Glasses Ionic Conduction in Glass Part 1 22

23 Other Silver sulfide doped glasses Ionic Conduction in Glass Part 1 23

24 Mixed Glassformer Systems Phosphate and borate mixed glasses show non-linear Mixed Glassformer effect Conductivity and Activation Energies in 0.65Na 2 S 0.35[xB 2 S 3 (1-x)P 2 S 5 ] 5.0x10-5 Conductivity x σ at 25 o d.c. (S/cm) C 3.0x x x /mol) ΔE act (kj 0.0 Activation Energy Composition (x) 17 swmartin@iastate.edu Ionic Conduction in Glass Part 1 24

25 Short Range Order models of Conduction Energetics Anderson-Stuart Model Assignment of Coulombic and Strain energy terms ΔE C Assignment of Coulombic and Strain energy terms, ΔE C ΔE s Creation or Concentration versus Migration energy terms, ΔE C ΔE m Coulomb energy term, ΔE C attractive force between cation and anion cation and anion 2 ) ( 1 ) ( 2 / r r e Z Z C r r e Z Z e Z Z C a c struct a c a c struct = λ ε λ ε. ) ( ) ( 2 / 2. const e Z Z C E Lim r r r r a c struct t a c a c = Δ λ ε λ ε swmartin@iastate.edu Ionic Conduction in Glass Part ) ( const r r E Lim a c act Δ λ ε

26 Short Range Order models Strain energy term - ΔE s Work required to dilate the network so large cations can migrate 50 Cation size affect on Strain Energy 2 ΔE = πg( r r ) λ / S c d 2 ΔE s (kcal/m mole) Cation Radius (nm) G Shear modulus r c Cation radius r d Interstitial site radius λ Jump distance swmartin@iastate.edu Ionic Conduction in Glass Part 1 26

27 Thermodynamic Models Glass is considered as a solvent into which salt is dissolved If dissolved salt dissociates strongly, then glass is considered a strong electrolyte If dissolved salt dissociate weakly, then glass is considered a weak electrolyte Coulomb energy term calculations suggest that the salts are only weakly dissociated, largest of the two energy terms Migration energy term is taken to be minor and weak function of composition Dissociation constant then determines the number of mobile cations available for conduction, dissociation limited conduction swmartin@iastate.edu Ionic Conduction in Glass Part 1 27

28 Weak Electrolyte model, Ravaine & Souquet 80 1/2M 2 O SiO 4/2 3/2 O-Si-O - M 3/2 O-Si-O - M (Unreacted) (Reacted tdbtudi but Undissociated) itd)(dissociated) K diss = a M a OM -/ a M2O ~ [M ][OM - ]/a = 2 M2O [M ] /a M2O [M ] ~ K diss 1/2 a M2O 1/2 n σ = zeμn = zeμk diss 1/2 a M2O 1/2 ~ C a M2O 1/2 log K diss ~ -Ne 2 RT/4πε ο ε (r r - ) As r, r - increase, K diss increases As ε increases, K diss increases swmartin@iastate.edu Ionic Conduction in Glass Part 1 28

29 Strong and Weak Electrolyte models Strong electrolyte model suggests all cations are equally available for conduction. Each cation experiences an energy barrier which governs the rate at which it hops Weak electrolyte model suggests only those dissociated cations are available for conduction Dissociation creates mobile carriers available for conduction SE models suggests that ΔE C ΔE s both contribute, one could be larger or smaller than the other WE model suggests that ΔE c is the dominant term swmartin@iastate.edu Ionic Conduction in Glass Part 1 29

30 Intermediate Range Order models Models recognize that ion conductivity requires ion motion over relatively long length scales Ions must be able to move from one side of the electrolyte to the other Long range connectivity of the SRO structures favorable to conduction must exist Deep traps along the way must be infrequent and not severe Rather, low energy conduction pathways are thought to exist which maximize connectivity and minimize energy barriers and traps Cluster pathway model of Greeves 85, for example Ionic Conduction in Glass Part 1 30

31 Intermediate Range Order models Cluster pathway model, Greeves et al 85 Ionic Conduction in Glass Part 1 31

32 AC versus DC ionic conductivity ωτ < 1 ωτ > 1 lo og 10 (σ a.c. ) K/T Energ gy y r x log 10 (f/hz) D.C. Conductivity Conductivity A.C. swmartin@iastate.edu Ionic Conduction in Glass Part 1 32

33 AC ionic conductivity in glass Connection to Far-IR vibrational modes, Angell 83 Ionic Conduction in Glass Part 1 33

34 Intermediate Range Order models Percolation Models - Johari et al. 87 At low dopant concentrations Cations are far separated Mobile species are diluted in a non-conducting host glass At intermediate concentrations Cations begin to approach proximity Preferential conduction paths form Sites percolate At high concentrations Cations are fully connected Conduction pathways are fully developed swmartin@iastate.edu Ionic Conduction in Glass Part 1 34

35 Conductivity percolation in AgI AgPO 3 swmartin@iastate.edu Ionic Conduction in Glass Part 1 35

36 RMC Modeling of AgI AgPO 3, Swenson et al. 98 Ionic Conduction in Glass Part 1 36

37 Intermediate Range Order models Microdomain models of conductivity Dopant salts such as AgI to oxide glasses, especially AgPO 3, are added to increase conductivity AgI is itself a FIC crystal above 150 o C Extrapolations of σ to xagi = 1 give ~ σ AgI (298K) The question then is: Does the AgI create microdomains of α-agi giving rise to the high conductivity? swmartin@iastate.edu Ionic Conduction in Glass Part 1 37

38 AgI Microdomain model Most well known of all glasses is xagi (1-x)AgPO 3 AgPO 3 is a long chain structure of -O-P(O)(OAg)-O repeat units Intermediate range structure is for these long chains to intertwine and as such frustrate crystallization Added AgI dissolves into this liquid without disrupting the structure of the phosphate chains Microdomain model then suggests that this dissolved AgI creates increasingly large clusters of α-agi between the phosphate chains swmartin@iastate.edu Ionic Conduction in Glass Part 1 38

39 AgI Microdomain model Ionic Conduction in Glass Part 1 39

40 Ionic Conduction in Glass Ohms law V=IR V = I ρ t/a = I ρ k ρ = 1/σ ρ(ωcm), σ(ωcm) -1 Calculate σ for I = 1 μa V = 1 V k = 1 mm/1 cm 2 A t swmartin@iastate.edu Ionic Conduction in Glass Part 1 40