Solid-State Diffusion and NMR

Transcription

1 Solid-State Diffusion and NMR P. Heitjans, S. Indris, M. Wilkening University of Hannover Germany Diffusion Fundamentals, Leipzig, 3 Sept. 005

2 Introduction Diffusivity in Solids as Compared to Liquids and Gases D / m s -1 time for 1 cm Gases s Liquids d Solids < > 30 a Interfaces/ < 10-9 > 1 d Surfaces RT < T m

3 Reason for Slow Diffusion in Solids: Formation of Defects is needed Activation Energy D ~ e -(E F +E M ) / k B T E F > 0 E F 0 for Solids for Liquids, Gases after Philibert: Diffusion et Transport de Matière dans les Solides (1985)

4 Overview: Defective Solids single crystalline amorphous nanocrystalline (see Talk: Chadwick)

5 Microscopic and Macroscopic Aspects of Diffusion elementary jumps macroscopic transport

6 Microscopic and Macroscopic Diffusion Quantities Jump rate τ -1 r 6 f = D T Tracer diffusivity Correlation factor f 1 Diff.mechanism (see Talk: Murch) τ s -1 at RT Temperature dep. E A (depends on time window)

7 Experimental Methods Microscopic Macroscopic NMR Relaxation / Lineshape Spin alignment echo Field gradient NMR Pulsed / Static β-radiation detected NMR Radioactive tracer Quasielastic neutron scattering Ion beam analysis AC conductivity DC conductivity

8 Ranges of Diffusivities and Correlation Times T D [m /s] macroscopic DC Tracer Diffusion Conductivity AC FG-NMR e.g. 71 numerous posters e.g. 67 microscopic SAE NMR Relaxation β-nmr e.g. 60, 68 QENS e.g. 16 MS e.g. 6 Solid Liquid τ [s] c P. Heitjans, S. Indris, J. Phys.: Condens. Matter 15 (003) R157

9 Overview NMR Spin-Lattice Relaxation, Spin-Spin Relaxation; Spin-Alignment Echo e.g. 7 Li in Li 0.7 TiS M. Wilkening, PhD thesis, University of Hannover, 005.

10 Motional Correlation Rates Li 0.7 TiS sub-hz...hz khz MHz... GHz Dynamics Nanosec Dekasec

11 Beta-NMR: Principle (1)

12 Beta-NMR: Principle ()

13 Beta-NMR: Setup

14 Beta-NMR: Operating Modes

15 Beta-NMR: Some Features and Implications (1) P ( 10%) independent of Boltzmann factor low B, high T accessible SLR measurements do not require rf fields B easily variable no skin effect: metallic samples/containers SLR time window: 0.01 τ < T 1 < 100 τ β β

16 Beta-NMR: Some Features and Implications () Concentration of probes extremely small (1:10 18 ) probes surrounded only by unlike nuclei no spin diffusion no SLR by distant paramagnetic impurities inequivalent sites: inhomogeneous SLR Complementary probes e.g. Q=0 for NMR Q 0 for β-nmr probe 19 F (100%) 0 F 107 Ag, 109 Ag (5%+48%) 108 Ag, 110 Ag

17 Multiple Time NMR: Spin-Alignment Echo (SAE)

18 Macroscopic Diffusion Measurem. in a Field Gradient SFG PFG = + 3 exp exp (0) / ) ( 1 1 T τ τ τ γ τ τ τ τ τ g D T T M M = + 3 exp exp (0) / ) ( T δ δ γ τ τ τ τ τ g D T T M M

19 Case Studies: Glassy and Crystalline Spodumene LiAlSi O 6 β-lialsi O 6 P4 3 1 a = b = Å c = Å 4 pairs of Li sites per unit cell (distance of neighbored paires: 4.5Å): only one site of each pair occupied (distance only 1.3Å) long-range and short-range jumps of Li ions?

20 7 Li Spin-Lattice Relaxation in Glassy and Crystalline Spodumene LiAlSi O 6 39 MHz high-t peak: long-range Li diffusion faster in the glass E A (glass) = 0.34eV E A (cryst.) = 0.50eV low-t peak: short-range (local) jumps F. Qi et al., Phys. Rev. B7 (005)

21 8 Li β-nmr Spin-Lattice Relaxation in Glassy and Crystalline Spodumene LiAlSi O 6 3 MHz low-t peak: localized Li motion between the pair sites in the crystal E A 50 mev From: Diffusion in Condensed Matter - Methods, Materials, Models, P. Heitjans, J. Kärger (Eds.), Springer, Berlin 005

22 Nanocrystalline Composites

23 7 Li NMR Lineshapes: (1-x)Li O:xB O 3 micro x = 0 micro x = 0.5 T = 433 K micro: one-component line nano x = 0 nano x = 0.5 nano: two-component line Frequency (khz) Frequency (khz) S. Indris et al., J. Non-Cryst. Solids (00) 555

24 7 Li-NMR Lineshapes: micro nano (1-x)Li O:xAl O 3 x=0.5 M. Wilkening et al., Phys. Chem. Chem. Phys. 5 (003) 5

25 7 Li-NMR Lineshape: nanocryst. (1-x)Li O:xAl O 3 Fraction of mobile Li + fast ions are located in the interfaces between ionic conductor and insulator conductivity increases with insulator content x possible route to design fast solid electrolytes

26 DC Conductivity: (1-x) Li O:xB O 3 x= K S. Indris et al., Phys. Rev. Lett. 87 (000) 889.

27 Percolation Model σ dc A f

28 7 Li Spin-Alignment Echo t m S (t p,t m ) sin( ωq( 0)t p)sin( ωq(t m )t p ) exp T1 Q Li 0.7 TiS 193 K, 155 MHz, 15 :s O t local Li + hopping M. Wilkening, PhD thesis, University of Hannover, 005.

29 Motional Correlation Rates Li 0.7 TiS sub-hz...hz khz MHz... GHz Dynamics Nanosec Dekasec

30 7 Li SFG and PFG NMR on Solid Lithium as Simple Test Case D T measured down to about m /s Comparison with T 1 : D T calculated from 8 Li SLR data assuming Monovacancy- Divacancy-Mechanism D. M. Fischer et al., Solid State NMR, 6 (004) 74

31 7 Li SFG NMR on Solid Lithium effective correlation factor f eff = D T r / 6τ D T = f 1V D 1V + f V D V f 1V = 0.77 f V = (Mehrer 1973) consistent with 1V-V mechanism

32 Conclusion NMR provides arsenal of techniques microscopic: macroscopic: T 1, T, T 1ρ, β-nmr, SAE SFG NMR, PFG NMR Used to measure jump rates ( s -1 ) and tracer diffusion coefficients ( m s -1 ) in metals, glasses, ceramics, nanocrystals, intercalation compounds, solid electrolytes... Comparison of microscopic and macroscopic diffusion parameters allows determination of diffusion mechanisms

33 Acknowledgement P. Duwe A. Bunde D.M. Fischer R. Böhmer W. Franke T. Dippel R. Goldstein W. Heink W. Küchler J. Kärger W. Puin J. Maier A. Schirmer H.E. Roman E. Schmidtke M. Ulrich DFG, BMBF, Land Niedersachsen