Advanced Vitreous State - Physical Properties of Glass Lecture 25: Charge Conduction Properties of Glass: Ionic Conduction in Glass - Part 1 Relationship to Glass Structure and Composition p Steve W. Martin Department of Materials Science & Engineering Iowa State University Ames, IA swmartin@iastate.edu
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 man composition st dies of ranges make them ideal for many composition studies of the ionic conductivity � Low melting temperatures often make them compatible g p p with many industrial processing techniques such as sputtering and evaporation to produce thin film electrolytes electrolytes swmartin@iastate.edu Ionic Conduction in Glass – Part 1 2
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 f NBO = NBOs/(NBOs + BOs) NBO /(NBO + BO ) � = 2x/(x + 2(1-x)) = 2x/(2-x) f BO = 1- f NBO � Q 4 Q 3 Q 4 Q 3 swmartin@iastate.edu Ionic Conduction in Glass – Part 1 3
“Q i ” Units in Alkali Silicate Glasses Q 3 Q 4 Q 2 O Si Na + Q 0 Q 1 swmartin@iastate.edu Ionic Conduction in Glass – Part 1 4
Alkali Ions are “weakly” bound � “Frame work” cations, Si +4 , and anions, O = � Covalently bonded to the network “Large” bond strength 100+ kcal/mole 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 bond T b k th i k i i b d � And move from one alkali cation site to another � Thermally activated ionic conduction � Thermally activated ionic conduction…. swmartin@iastate.edu Ionic Conduction in Glass – Part 1 5
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
Molecular Dynamics Simulation of Ionic Conduction � Go to Movie….. swmartin@iastate.edu Ionic Conduction in Glass – Part 1 7
Relation of glass structure to ionic conduction BO BO - - + NBO NBO + BO +1/r n nergy Δ E act = ΔΕ s + Δ E c Δ E S En Δ E s = Strain Energy Δ E c = Coulomb Energy Δ E C -e 2 /r r r swmartin@iastate.edu Ionic Conduction in Glass – Part 1 8
Cation Conduction – “Rattle and Jump” BO BO - - NBO NBO + BO +1/r n MD Simulations gy Energ y Δ E S Δ E Δ E C -e 2 /r x r r swmartin@iastate.edu Ionic Conduction in Glass – Part 1 9
Theory of Ionic Conduction in Glass: Simple Models � σ = 1/ ρ ≡ neZ μ � n is the number density � eZ is the charge, +1 most of 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 ? � 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
Theory of Ionic Conduction in Glass: Simple Models λ ze E 2 → → λ ze E E Δ − E act 2 2 λ λ + + + + |E| λ /2 + + + + + swmartin@iastate.edu Ionic Conduction in Glass – Part 1 11
Theory of Ionic Conduction in Glass: Simple Models ⎡ Δ − λ ⎤ / 2 E ze E + υ = υ − act ⎢ ⎥ ( ) exp T 0 ⎣ ⎣ RT RT ⎦ ⎦ ⎡ Δ + λ ⎤ / 2 E ze E υ − = υ − act ⎢ ⎢ ⎥ ⎥ ( ) exp T 0 ⎣ ⎣ ⎦ ⎦ RT RT + − υ = υ − υ ( ) ( ) T T net ⎛ ⎛ ⎞ ⎞ ⎡ ⎡ λ ⎤ ⎤ ⎡− ⎡ λ ⎤ ⎤ Δ ⎡ ⎤ ze E ze E E act ⎜ ⎟ υ = υ − − exp exp ⎢ ⎥ exp ⎢ ⎥ ⎢ ⎥ ⎜ ⎟ 0 net ⎣ ⎦ 2 2 ⎣ ⎦ ⎣ ⎦ RT RT RT ⎝ ⎠ ⎛ ⎞ λ υ λ Δ Δ ⎡ ⎤ ⎡ ⎤ ze E ze E E E ⎜ ⎟ υ = υ − − 0 act act 2 exp sinh ~ exp ⎢ ⎥ ⎢ ⎥ ⎜ ⎟ 0 net ⎣ ⎦ ⎣ ⎦ ⎝ ⎝ 2 ⎠ ⎠ RT RT RT RT swmartin@iastate.edu Ionic Conduction in Glass – Part 1 12
Theory of Ionic Conduction in Glass: Simple Models ⎛ λ ⎞ υ λ Δ Δ ⎡ ⎤ ⎡ ⎤ ze E ze E E E ⎜ ⎟ υ = υ − − 0 act act 2 exp p sinh ~ exp p ⎢ ⎢ ⎥ ⎥ ⎢ ⎢ ⎥ ⎥ ⎜ ⎜ ⎟ ⎟ 0 0 net net ⎣ ⎣ ⎦ ⎦ ⎣ ⎣ ⎦ ⎦ 2 RT ⎝ RT ⎠ RT RT υ λ Δ 2 ⎡ ⎤ ze E E = = υ υ × × λ λ = = − − 0 act exp exp velocity velocity ⎢ ⎢ ⎥ ⎥ net ⎣ ⎦ RT RT υ 0 λ Δ ⎡ ⎤ 2 ze E = = = = − / / exp exp act mobility mobility velocity velocity E E ⎢ ⎢ ⎥ ⎥ ⎣ ⎦ RT RT = × × conductivi ty mobility conductivi ty charge ( ) υ λ Δ σ Δ 2 ⎡ ⎤ ⎡ ⎤ 2 n ze E E σ = − ≡ − 0 0 act act exp exp (T) ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ RT RT T RT swmartin@iastate.edu Ionic Conduction in Glass – Part 1 13
Theory of Ionic Conduction in Glass: Simple Models σ Δ ⎡ ⎤ E Δ E act = ΔΕ s + Δ E c σ = − 0 act exp (T) ⎢ ⎥ ⎣ ⎣ ⎦ ⎦ Δ E s = Strain Energy T RT s Δ E c = Coulomb Energy σ Δ + Δ ⎡ ⎤ E E = − 0 C S exp ⎢ ⎥ ⎣ ⎣ ⎦ ⎦ T RT Δ ⎡ ⎤ E BO = − C ( ) exp n T n - ⎢ ⎥ - 0 ⎣ ⎣ ⎦ ⎦ RT + + NBO NBO NB NB + + μ Δ ⎡ ⎤ O E BO nergy μ = − = +1/r n 0 S ( ) exp T ⎢ ⎥ ⎣ ⎣ ⎦ ⎦ T RT En Δ E S ν 0 λ Δ ⎡ ⎤ 2 2 ( ) ze E − Δ E C S exp ⎢ ⎥ -e 2 /r ⎣ ⎣ ⎦ ⎦ RT RT r r swmartin@iastate.edu Ionic Conduction in Glass – Part 1 14
Arrhenius Ionic Conductivity in Glass 00 00 00 00 o C) o 160 140 120 100 0 800 0 600 400 0 200 0 Temperature ( 0 1 10 Glassy Crystalline α -AgI Tg Tm 0 10 10 RbAg I 4 5 -1 β -NaAl 11 O 17 2 9 10 . 8 A g O -1 - 4 3 2 0 . 4 5 ( m) A L g g Zr ZrO 2 -9%Y 2 O 3 I I σ dc ( Ω -cm ) ) i i - 2 2 O O 9 9 2 . 2 8 2 - P 8 -2 3 . 6 O A 10 0 g 50Ag 2 S-5GeS-45GeS 2 L L O 5 i - i 4 2 2 25Li 2 O-25A B S . 8 4 2 ( A O O g 7 I ) - - 2 1 8 4 1 C . 2 6 2 0 M l ( o 2 O L -3 6 10 i . C 9 3 GeS 2 l L L ) ) Al 2 O 3 -50SiO 2 i i - O 2 1 2 2 - . 9 5 ( S 25Li 2 O -75B 2 O L i i C O -4 l 10 ) - LiAlSiO 4 2 1 LiNbO 3 - 2 6 2 4 . 5 . 1 B B O 2 O 2 2 O 3 3 3 4 -5 5 3 3 10 -6 10 0 5 0.5 1 0 1.0 1 5 1.5 2 0 2.0 2 5 2.5 3 0 3.0 3.5 3 5 4 0 4.0 -1 ) 1000 / T (K swmartin@iastate.edu Ionic Conduction in Glass – Part 1 15
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 except glasses is still very low except for the highest temperatures swmartin@iastate.edu Ionic Conduction in Glass – Part 1 16
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 g � concentration of Li 2 O, the higher the conductivity Lower resistivity � Activation energy � decreases with Li 2 O content swmartin@iastate.ed u Ionic Conduction in Glass – Part 1 17
Composition Dependence of the Conductivity Li 2 O+ SiO 2 Binary lithium phosphate � Li 2 O+ B 2 O 3 glasses, Li 2 O + P 2 O 5 , are 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 O+ P O conductors d t Binary lithium silicate glasses, � Li 2 O + SiO 2 are slightly better conductors yet. d t t Li 2 O:SiO 2 Li 2 O:P 2 O 5 Li 2 O:B 2 O 3 swmartin@iastate.edu Ionic Conduction in Glass – Part 1 18
Salt doped phosphate glasses Halide doping strongly � increases the conductivity swmartin@iastate.edu Ionic Conduction in Glass – Part 1 19
Effect of Sulfur Substitution swmartin@iastate.edu Ionic Conduction in Glass – Part 1 20
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
Silver Phosphate Glasses swmartin@iastate.edu Ionic Conduction in Glass – Part 1 22
Other Silver sulfide doped glasses swmartin@iastate.edu Ionic Conduction in Glass – Part 1 23
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