Dynamic heterogeneity of glassy ionics: Results from nuclear magnetic resonance and low-frequency spectral hole burning

Dynamic heterogeneity of glassy ionics: Results from nuclear magnetic resonance and low-frequency spectral hole burning Roland Böhmer Video Module 1: Introduction 1. Introduction 2. Ion dynamics studied by NMR 3. Nonresonant spectral hole burning in CKN 4. Conclusions Glass Lecture Series: prepared for and produced by the International Material Institute for New Functionality in Glass An NSF sponsored program material herein not for sale Available at www.lehigh.edu/imi Delivered at Lehigh University Dec. 7, 2006 Lehigh 07.12.2005

Univ. Dortmund Experimentelle Physik III Ag K. R. Jeffrey Guelph / Canada CKN R. Richert Arizona State Univ. DFG S. Berndt R. Küchler F. Qi C. Rier Graduiertenkolleg 298

Transport in solid electrolytes Li ion battery "fuel" cell separator Membranes with high ionic conductivities required

electrical conducitivty of solid electrolytes studied by 2D NMR! Haile et al., Nature 410, 910 (2001) "superionic" anhydrous fuel cell Insight into transport mechanisms?

applications sensors, fuel cells, rechargeable batteries,... requirements stable, light, solid, inexpensive, high ionic & low electronic conductivity, suitable operating temperature,... goal of group at Dortmund U new experimental methods for better understanding of transport mechanisms in solid ion conductors energy spatial coordinate

Principle of magnetic resonance B 0 element specific quantitative locally selective non-destructive experimentally versatile

Principle of magnetic resonance B 0 hω ω rapid modulation of splitting facilitates re-equlilibration spin-lattice relaxation time T 1 frequency perturbation Δω encoded by spatial coordinate imaging electronic environment chemical analysis distances and angles structural elucidation orientation fiber texture testing element specific quantitative locally selective non-destructive experimentally versatile

Motional processes detection of NMR frequencies and their time evolution NMR frequency encoded by spatial coordinate chemical environment orientation... diffusion, flow exchange, translation reorientational motion Translation ω 2 ω 1 Rotation B 0 t p t m t p S 2 (t p,t m ) = exp[it p ω(0)] exp[ it p ω(t m )] 1 2 S(q,t) exp[iqr(0)] exp[ iqr(t)] t p t m evolution time mixing time correlation of ω at 2, 3, 4... points in time

Echo height measures the fraction of ions which did NOT hop during t m Direct determination of correlation time on which an ion hops energy Scattering vector q, i.e. spatial sensitivity is determined by the inverse mean jump length t p jump length τ hop t m t p conductivity pathway S 2 (t m ) (arb. units) 1.0 0.5 0.0 exp[ (t m /τ hop )] β here: τ hop ~ 0.2 s 10-5 10-3 10-1 10 1 mixing time t m (s)

This lecture continues on a 2 nd module - Video Module 2 : Ion Dynamics by NMR (Part 2)

Dynamic heterogeneity of glassy ionics: Results from nuclear magnetic resonance and low-frequency spectral hole burning Roland Böhmer Video Module 2: Ion Dynamics by NMR Glass Lecture Series: prepared for and produced by the International Material Institute for New Functionality in Glass An NSF sponsored program material herein not for sale Available at www.lehigh.edu/imi Delivered at Lehigh University Dec. 7, 2006 Lehigh 07.12.2005

1. Introduction Ion conductors Nuclear magnetic resonance 2. Ion dynamics studied by NMR Li hopping in alumino silicates Heterogeneity in silver borate glasses 3. Nonresonant spectral hole burning Material and method Experiments on Ca-K-NO 3 glass 4. Conclusions

Lithium aluminosilicates Mesocrystalline texture (Schott, Mainz) Zerodur x = 0.52 70% 62 nm Zerodur M x = 0.44 50% 45 nm crystalline phases α < 0 crystalline model systems x = [Al]/[Si] β-spodumene LiAlSi 2 O 6 0.5 β-eucryptite LiAlSiO 4 1 glass phase α > 0

Lithium aluminosilicates Mesocrystalline texture (Schott, Mainz) Zerodur x = 0.52 70% 62 nm Zerodur M x = 0.44 50% 45 nm precision optics, ceramic cooking ware crystalline model systems x = [Al]/[Si] β-spodumene LiAlSi 2 O 6 0.5 β-eucryptite LiAlSiO 4 1

7 Li ion conductor β-spodumene Spin-lattice relaxation indirect information on fast motion T-dependent time scale and non-exponentiality of ion hopping 10 2 LiAlSi 2 O 6 1.0 T 1-1 (s -1 ) 10 1 10 0 10-1 crystal 39 MHz 46 MHz 0 2 4 6 8 10 12 T -1 (10-3 K -1 ) S 2 (t m ) (arb. units) 0.5 β-spodumene crystal 365 K 315 K rate maxima for ωτ ~ 0.61 0.0 10-4 10-2 10 0 10 2 mixing time t m (s)

10-1 Motion of Li + in crystalline and in glassy environments distribution g(e) glass crystal hopping barrier E hopping time τ (s) 10-2 10-3 10-4 β-spodumene spodumene glass crystal phases 10-5 400 500 600 temperature T(K) glass phase Qi, Rier, Böhmer, Franke, Heitjans, Phys. Rev. B 72, 104301 (2005)

Conductivity of glassy ionics Angell, Chem. Rev. 90, 523 (1990) glass former sodium trisilicate silver iodo borate glass calcium potassium nitrate T g 738 K 610 K 333 K scaled T g /T Ag: 1.0 I: 1.8 B: 0.5 O: 0.9 Å Howells et al., JP-CM 11, 9275 (1999) large decoupling and T ~ T g are prerequisites for battery application

high temperatures NMR-line shape of AgI-glasses narrow Lorentzian motional narrowing low temperatures broad Gaussian intermediate temperatures? hopping rate τ? Kawamura et al., Solid State Ionics 154-155, 183 (2002)

Line shape of ( 109 AgI) x -(Ag 2 O-B 2 O 3 ) 1 x superposition of sub-spectra -30-20 -10 0 10 20 30 Frequenz [khz] 148 K 170 K 195 K 231 K broadening due to distribution of isotropic chemical shifts intensity (arb. units) 1.0 0.5 0.0-20 0 20 frequency ν (khz) hint: slow and fast Ag + ions could coexist Berndt, Jeffrey, Küchler, Böhmer, Solid State Nucl. Magn. Reson. 27, 122 (2005)

Heterogeneity of ion conductors (AgI) 0.6 -(Ag 2 O-B 2 O 3 ) 0.4 spatial heterogeneity! Ag: 1.0 I: 1.8 B: 0.5 O: 0.9 Å Howells et al., JP-CM 11, 9275 (1999)

Nature of the non-exponential relaxation? homogeneous heterogeneous Richert JNCS 172, 209 (1994) dynamic heterogeneity? amplitude macroscopic response line shape modification identical in both modification cases

Nature of the non-exponential relaxation homogeneous heterogeneous experimentally distinguishable via sub-ensemble selection multi-dimensional NMR single-molecule detection nonresonant hole burning optical probe spectroscopy computer simulation amplitude Makroskopische Antwort line shape modification in beiden Fällen modification gleich

resonance frequencies: 1 Η: 43 MHz/Tesla 109 Ag: 2 MHz/Tesla!! Interdisziplinäres Zentrum für magnetische Resonanz (IZMR) Universität Dortmund problem: Ag: very low sensitivity solution: availability of very high magnetic fields 14 Tesla

four-time NMR t p t, t filter jump correlation function t p Filter F 2 measure for the probability that no jump occured during t filter Filter t req t G 4 jump correlation function of the selected subensemble extensively used for polymers and supercooled organic liquids: Schmidt-Rohr, Spiess, Phys. Rev. Lett. 66, 3020 (1991) Böhmer, Diezemann, Hinze, Rössler, Prog. NMR Spectrosc. 39, 191 (2001) Ag-phosphates: Vogel, Brinkmann, Eckert, Heuer, PRB 69, 094302 (2004)

(AgI) 0.5 -(Ag 2 O-B 2 O 3 ) 0.5 stimulated echo (arb. units) 1,0 0,8 0,6 0,4 0,2 0,0 F 2 G 4 10-4 10-3 10-2 10-1 10 0 10 1 mixing time t m (s) t filter = 7 ms t p = 100 μs T = 208 K successful low-pass filtering confirms dynamic heterogeneity in AgI-borate glasses effective distributions slow τ 4 > τ 2 β 4 > β 2 low-pass filter log (rate) fast

This lecture continues on a 3rd module - Video Module 3 : Nonresonant spectral hole burning

Dynamic heterogeneity of glassy ionics: Results from nuclear magnetic resonance and low-frequency spectral hole burning Roland Böhmer Video Module 3 : Nonresonant spectral hole burning Glass Lecture Series: prepared for and produced by the International Material Institute for New Functionality in Glass An NSF sponsored program material herein not for sale Available at www.lehigh.edu/imi Delivered at Lehigh University Dec. 7, 2006 Lehigh 07.12.2005

Non-exponential conductivity and structural relaxation 0.050 M" 306K 342K 361K CKN 393K 468K M = iωε 0 /σ 0.025 T g = 333 K 0.000-2 0 2 4 6 8 10 log 10 [ν(hz)] 2 Ca(NO 3 ) 2 3KNO 3 (CKN) NO 3 K + Ca 2+ cage Pimenov, Lunkenheimer, Rall, Kohlhaas, Loidl, Böhmer, Phys. Rev. E 54, 676 (1996)

Structural relaxation log 10 [τ(s)] -5-10 α 0 CKN -15 0 1 2 3 4 5 T T g 1000/T (K -1 ) large slope in Angell plot d(log τ/s) 10 fragility m = d(t g /T) T=T g 6 7 Böhmer, Ngai, Angell, Plazek, JCP 99, 4201 (1993)

Structural and decoupled relaxations log 10 [τ(s)] dynamic -5-10 0 CKN CRN σ T 1 heterogeneity? -15 0 1 2 3 4 5 T T g 1000/T (K -1 ) large slope in Angell plot d(log τ/s) 10 fragility m = d(t g /T) T=T + α Böhmer, Ngai, Angell, Plazek, JCP 99, 4201 (1993) g η NO 3 σ β α β σ η NO 3 6 7 T < T g thermally activated processes

Origin of non-exponentiality Nanoscopic heterogeneity in ionic conductors? heterogeneous cluster model: glass phase crystal phases glass ceramics, nanocrystals, ion conductors in general?? effective potential or correlation effects? homogeneous jump-relaxation-model: Coulomb interactions central ion at t 1 t 1 t 2 t 3 ionic pathway effectively time dependent rates W(t) time evolution exp[ t W(t)] exp[ (t/τ) β ] Funke, SSI 40, 200 (1990)

HOMOGENEOUS HETEROGENEOUS frequency domain χ" log (frequency) time domain

HOMOGENEOUS HETEROGENEOUS χ" log (frequency) mark a subensemble

amplitude modification HOMOGENEOUS HETEROGENEOUS χ" line shape modification log (frequency) Selection experiments then remove that subensemble 1. 2. spectral or spatial selection or excitation of sub-ensemble detection of sub-ensemble

Nonresonant hole burning supercooled liquids : Schiener, Loidl, Böhmer, Chamberlin, Science 274, 752 (1996)

Nonresonant hole burning supercooled liquids α: Schiener, Loidl, Böhmer, Chamberlin, Science 274, 752 (1996) β: Richert, EPL 54, 767 (2001) wing: Jeffrey, Richert, Duvvuri, JCP 119, 6150 (2003) relaxor ferroelectrics Kircher, Schiener, Böhmer, PRL 81, 4520 (1998) plastic crystal Wirsch, Kircher, Böhmer (1998, unpublished,*) magnetic (spin glasses) Chamberlin, PRL 83, 5134 (1999) ion conductor CKN Richert, Böhmer, PRL 83, 4337 (1999) solids quantum paraelectrics Kleemann et al., Ferroelectrics 261, 43 (2001) stochastic models Diezemann, EPL 53, 604 (2001) electrical circuit analog Richert, Physica A 322, 143 (2003) binary glass-formers Blochowicz, Rössler, JCP 122, 224511 (2005) mechanical (polymers) Shi, McKenna, PRL 94, 157801 (2005) *review Böhmer, Diezemann, in: Broadband Dielectric Spectroscopy edited by Kremer, Schönhals (Springer, 2002), p. 523-569

Nonresonant hole burning supercooled liquids α: Schiener, Loidl, Böhmer, Chamberlin, Science 274, 752 (1996) β: Richert, EPL 54, 767 (2001) wing: Jeffrey, Richert, Duvvuri, JCP 119, 6150 (2003) relaxor ferroelectrics Kircher, Schiener, Böhmer, PRL 81, 4520 (1998) plastic crystal Wirsch, Kircher, Böhmer (1998, unpublished) magnetic (spin glasses) Chamberlin, PRL 83, 5134 (1999) ion conductor CKN Richert, Böhmer, PRL 83, 4337 (1999) quantum paraelectrics Kleemann et al., Ferroelectrics 261, 43 (2001) stochastic models Diezemann, EPL 53, 604 (2001) electrical circuit analog Richert, Physica A 322, 143 (2003) binary glass-formers Blochowicz, Rössler, JCP 122, 224511 (2005) mechanical (polymers) Shi, McKenna, PRL 94, 157801 (2005) review Böhmer, Diezemann, in: Broadband Dielectric Spectroscopy edited by Kremer, Schönhals (Springer, 2002), p. 523-569

conventional SHB inhomogeneous line width nonresonant (NHB) pump wait probe absorption laser homogeneous line width applied field i ii iii iv time Φ*(t) Φ(t) + + + 0 + 0 phase cycle: ΔΦ(t) = Φ*(t) Φ(t) spectral hole photoproduct i 1 i i+1 frequency NMR (optical) spectroscopy vibrational bath

10 years ago: First results on a viscous liquid ε(t) Δε(t) 100 75 50 25 0 0.0 0.5 1.0 1.5 propylene carbonate T = 157 K 2.00 Hz 0.05 Hz 0.01 Hz Δ(t) -2-1 0 1 2 log 10 [t(s)] Δε(t) 78 77 1.00 1.05 76 high-frequency pump: short-time modifications low-frequency pump: long-time modifications selection of different sub-ensembles possible: dynamic heterogeneity Schiener, Loidl, Böhmer, Chamberlin, Science 274, 752 (1996)

high pump frequencies M(t) / M 1.0 0.5 0.0 CKN 300 K -2-1 1 log 10 [t(s)] low pump frequencies 0 0 ΔM(t) 10 3 1 2 3 4 10 Hz 1 Hz 0.56 Hz -2-1 0 1 log 10 [t(s)] ΔM(t) 10 3 1 2 3 4 1.8 mhz 18 mhz 100 mhz -2-1 0 1 log 10 [t(s)] frequency selectivity dynamic heterogeneity no frequency selectivity homogeneous for Ω C /2π < 0.1 Hz

CKN pump frequency dependence ΔM(t m ) 10 3 log 10 (Ω/s -1 ) 2 1 0-1 3 ΔM max (Ω) 2 1 ε''(ω) 1.5 1.0 0.5 ε''(ω) heterogeneous regime: hole depths dielectric loss frequency selective energy absorption log 10 (t m /s) 0 1.0 0.5 0.0-0.5 t max (Ω) τ ρ(t) 0.0 10 12 10 11 10 10 ρ(t) / Ω cm OBSERVATION: t C corresponds to transition from dc to ac resistivity ρ (or σ) 2 1 0-1 log 10 (t/s) ion needs t C ~ 1/Ω C to average over heterogeneity

heterogeneity length ξ? energy displacement ξ during t c τ hop jump length a conductivity pathway nonresonant hole burning spectroscopy at low frequencies dynamic and spatial heterogeneity in CKN ξ 2 = 6 D t C ξ2 = a 2 t C /τ hop D = a 2 /(6τ hop ) a hopping length mean separation of sites for mobile ions τ hop hopping time necessary to estimate ξ but not known for CKN requires direct measurement of τ hop in the slow domain!

Conclusions Structure dynamic relationship in crystalline and glassy lithium aluminosilicates High magnetic fields facilitate investigations of dynamic heterogenities in ion conductors also with less favorable nuclear probes (Ag) distribution log (rate) slow fast log (frequency) Nonresonant spectral hole burning is a useful tool for different classes of materials. Direct observation of transition from heterogeneous to homogeneous behavior in CKN