Advanced Vitreous State - Physical Properties of Glass Lecture 26: Charge Conduction Properties of Glass: Ionic Conduction in Glass - Part 2 Activation Energies in Glass Steve W. Martin Department of Materials Science & Engineering Iowa State University A Ames, IA IA swmartin@iastate.edu
Binary Alkali Silicate Glasses � Addition of Na 2 O Increases the ionic conductivity, y, decreases the electrical resistivity � Increasing the temperature Increasing the temperat re increases the ionic conductivity, decreases the ionic resistivity � Ionic conductivity of soda glasses is still very low glasses is still very low except for the highest temperatures swmartin@iastate.edu Ionic Conduction in Glass – Part 2 2
DC ion conductivity in glass � xLi 2 O + (1-x)P 2 O 5 � Creation of non-Bridging � Creation of non Bridging oxygens � “Mobile” lithium ions � The higher the concentration of Li 2 O, the higher the conductivity higher the conductivity � Lower resistivity � Activation energy decreases with Li 2 O content swmartin@iastate.edu Ionic Conduction in Glass – Part 2 3
Composition Dependence of the Conductivity Li 2 O+ SiO 2 Binary lithium phosphate � 50 o C Li 2 O+ B 2 O 3 glasses, Li 2 O + P 2 O 5 , are T = 15 relative poor ion conductors l ti i d t Binary lithium borate glasses, � Li 2 O + B 2 O 3 , are slightly better Li 2 O+ P 2 O 5 Li 2 O+ P 2 O 5 conductors d t Binary lithium silicate glasses, � Li 2 O + SiO 2 are slightly better conductors yet. d t t Li 2 O:SiO Li 2 O:P 2 O 5 2 Li 2 O:B 2 O 3 swmartin@iastate.edu Ionic Conduction in Glass – Part 2 4
Salt doped phosphate glasses Halide doping strongly � increases the conductivity swmartin@iastate.edu Ionic Conduction in Glass – Part 2 5
Salt doped phosphate glasses Halide doping strongly � increases the conductivity swmartin@iastate.edu Ionic Conduction in Glass – Part 2 6
Effect of Sulfur Substitution – “Fast Ion Conductors” swmartin@iastate.edu Ionic Conduction in Glass – Part 2 7
Silver Phosphate Glasses swmartin@iastate.edu Ionic Conduction in Glass – Part 2 8
Other Silver sulfide doped glasses swmartin@iastate.edu Ionic Conduction in Glass – Part 2 9
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 2 10
Mixed Glassformer Systems Phosphate and borate mixed glasses show non-linear “Mixed Phosphate and borate mi ed glasses sho non linear “Mi ed � Glassformer” effect Conductivity and Activation Energies in 0.65Na 2 S + 0.35[xB 2 S 3 + (1-x)P 2 S 5 ] 0 65N S 0 35[ B S (1 )P S ] 23 -5 5.0x10 Conductivity 22 -5 4.0x10 21 o C -5 3.0x10 /mol) at 25 20 σ d.c. (S/cm) a Δ E act (kJ -5 2.0x10 19 -5 1.0x10 18 18 17 0.0 Activation Energy 0 0 0.0 0 2 0.2 0 4 0.4 0.6 0 6 0 8 0.8 1 0 1.0 Composition (x) swmartin@iastate.edu Ionic Conduction in Glass – Part 2 11
Composition Dependence of the Conductivity Li 2 O+ SiO 2 Binary lithium phosphate � 50 o C Li 2 O+ B 2 O 3 glasses, Li 2 O + P 2 O 5 , are T = 15 relative poor ion conductors l ti i d t Binary lithium borate glasses, � Li 2 O + B 2 O 3 , are slightly better Li 2 O+ P 2 O 5 Li 2 O+ P 2 O 5 conductors d t Binary lithium silicate glasses, � Li 2 O + SiO 2 are slightly better conductors yet. d t t Li 2 O:SiO Li 2 O:P 2 O 5 2 Li 2 O:B 2 O 3 swmartin@iastate.edu Ionic Conduction in Glass – Part 2 12
Ionic motion in glassy electrolytes xNa 2 O + (1-x)SiO 2 + Glass in 2-D + + + + |E| + MD Simulations + + y + + x - BO - + + NBO NBO ergy BO +1/r n = ΔΕ s + Δ E c Δ E act c act s Ene Δ E S Δ E s = Strain Energy Δ E C -e 2 /r Δ E c = Coulomb Energy r r S.W. Martin, C.A. Angell, JNCS, 1983 swmartin@iastate.edu 13 Ionic Conduction in Glass – Part 2
Mobility and number dependence of the conductivity σ − Δ ⎛ ⎞ E σ = μ = ⎜ ⎟ 0 act ( ) ( ) ( ) exp T n T eZ T c ⎝ ⎝ ⎠ ⎠ T T RT RT − Δ ⎛ ⎞ E = ⎜ ⎟ c ( ) o exp n T n ⎝ ⎝ RT ⎠ ⎠ RT μ − Δ ⎛ ⎞ E μ μ = ⎜ ⎜ ⎟ ⎟ 0 s ( ( ) ) exp p T ⎝ RT ⎝ ⎠ ⎠ T ( ( ) ⎞ ) ⎟ 0 μ − Δ Δ + Δ Δ ⎛ ⎛ ⎞ Z Z en E E E E σ = ⎜ 0 c c s ( ) exp T ⎝ ⎠ T RT Question: What are the magnitudes of Δ E S(M) and Δ E C ? Question: What are the magnitudes of Δ E and Δ E ? swmartin@iastate.edu Ionic Conduction in Glass – Part 2 14
“Extreme” Models of the Activation Energy � Strong Electrolyte Model � All cations are dissociated from their “host” anion and are available for conduction available for conduction Like NaCl, HCl, NaOH, H 2 SO 4 dissolved in water � � Na + …. - O-Si ≡ � Δ E C is “small” and not strongly compositionally dependent � σ d.c. ~ Zen 0 μ 0 /T exp(- Δ E m /RT) � Migration energy dominates the d.c. conductivity Mi ti d i t th d d ti it swmartin@iastate.edu Ionic Conduction in Glass – Part 2 15
“Extreme” Models of the Activation Energy � Weak Electrolyte Model � Only a small fraction of the cations are dissociated Like HOAC, Acetic Acid, K a ~ 1.8 x 10 -5 10 5 Lik HOAC A ti A id K 1 8 � � Δ E m is “small” and not strongly compositionally dependent dependent � Most of the cations are bound with their charge compensating anion � σ d.c. ~ Ze μ 0 n 0 /T exp(- Δ E c /RT) / ( / ) � Creation energy dominates the d.c. conductivity swmartin@iastate.edu Ionic Conduction in Glass – Part 2 16
Strong and Weak Electrolyte models “Strong electrolyte” SE model � suggests all cations are equally available for conduction available for conduction. Each cation experiences an energy � barrier which governs the rate at which it hops “Weak electrolyte” WE model � suggests only those dissociated cations are available for conduction Dissociation creates mobile carriers Dissociation creates mobile carriers � available for conduction SE models suggests that Δ E C + Δ E s � both contribute, one could be larger or , g smaller than the other WE model suggests that Δ E c is the � dominant term S.W. Martin, C.A. Angell, JNCS, 1983 swmartin@iastate.edu Ionic Conduction in Glass – Part 2 17
Coulomb Energy Barrier � Anderson-Stuart Model � Assignment of Coulombic and Strain energy terms � Assignment of Coulombic and Strain energy terms � Δ E C + Δ E s � “Creation” or Concentration versus Migration energy terms, Δ E C + Δ E m � Coulomb energy term, Δ E C attractive force between cation and anion cation and anion ⎡ ⎤ ⎡ ⎤ − − 2 2 2 1 2 C Z Z e Z Z e C Z Z e ≈ − = − . . struct ⎢ c a c a ⎥ struct c a ⎢ ⎥ ε ε λ λ + + ε ε + + λ λ ⎣ ⎣ / / 2 2 ( ( ) ) ⎦ ⎦ ⎣ ⎣ ( ( ) ) ⎦ ⎦ r r r r r r r r ∞ ∞ c a c a 2 C Z Z e Δ Δ → → = struct . c a . . E E const const Lim Lim ε + act t ( ) r r λ → ∞ ∞ c a swmartin@iastate.edu Ionic Conduction in Glass – Part 2 18
Strain Energy Barrier � Strain energy term - Δ E s � “Work” required to “dilate the network so large cations can migrate i t Cation size affect on Strain Energy gy Δ E = π − λ 2 ( ) / 2 G r r 50 S c d 40 mole) Δ E s (kcal/m 30 30 G Shear modulus 20 r c Cation radius 10 r d Interstitial site radius d λ 0 Jump distance 0 0.04 0.08 0.12 0.16 0.2 Cation Radius (nm) swmartin@iastate.edu Ionic Conduction in Glass – Part 2 19
Cation Radius Dependence of Δ E c and Δ E m Δ E s Δ E Δ E c Δ E c ~ 1/r c 2 Δ E s ~ r c Δ E tot (A.U.) Δ E s , Δ E c dominated ominated Δ E s d Δ E c d 0.0 0.5 1.0 1.5 2.0 2.5 3.0 + Cs + (?) + + + H K Na Li o r cation ( Α ) ( ) swmartin@iastate.edu Ionic Conduction in Glass – Part 2 20
“Rational” Models of the Activation Energy Both activation energies are non-zero and contribute to the total � activation energy Anderson-Stuart 1 model calculation � ⎡ ⎤ β 2 1 2 Z Z e Δ = Δ = π − Δ = − 2 4 ( ) . struct c a ⎢ ⎥ E E r G r r E ε + λ s m d c d C ⎣ ( ) ⎦ r r ∞ c a Δ E s (calc) Δ E c (calc) Δ E act (calc) Δ E act 2 x Na 2 O + (1-x)SiO 2 11.8 11.7 66.9 78.6 68.1 19 2 19.2 10 9 10.9 62 3 62.3 73 2 73.2 63.7 63 7 29.7 10.0 56.1 66.1 59.7 Calculation shows that the Δ E c term is the larger of the two energy Calculation shows that the Δ E c term is the larger of the two energy � � barriers. Weak-Electrolyte behavior? � 1 Anderson, Stuart, J. Amer. Cer. Soc., 1954 2 SciGlass 5.5, Average of many glasses SciGlass 5.5, Average of many glasses swmartin@iastate.edu Ionic Conduction in Glass – Part 2 21
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