1. The University of Tennessee Resonant Ultrasound Spectroscopy at The University of Tennessee Veerle Keppens Department of Materials Science and Engineering The University of Tennessee Work supported by The National Science Foundation

2. The University of Tennessee Collaborators: Raphaël Hermann, Zhiying Zhang U. Tennessee Takeshi Egami Brian Sales, David Mandrus, ORNL Bryan Chakoumakos, Hans Christen Michael McGuireU. Mississippi George NolasU. South Florida Peter Thalmeier, Ivica ZerecMPI, Dresden (Germany) Gary Long, Fernande Grandjean U. Missouri, Rolla / U. Liège (Belgium)

3. The University of Tennessee Shape, Dimensions, Mass, Resonant Frequencies Elastic Constants forward problem inverse problem Resonant Ultrasound Spectroscopy (RUS) Figure of merit: F=  w i (f i -g i ) 2

4. advantages of RUS: all elastic constants can be obtained in one measurement small samples (mm 3 ) The University of Tennessee

5. Sales et al., PRB 63, 245113 (2001) How does rattling reduce the thermal conductivity? PART 1: RUS on “rattling solids”

6. study (skutterudites and) clathrates using thermal conductivity (2-300 K) specific heat (2-300 K) neutron scattering (10-300 K) ultrasonic attenuation (0.3-10 K) resonant ultrasound spectroscopy (2-300 K) Mössbauer spectroscopy (0.03-30 K) rf absorption (5-30 K) The University of Tennessee

7. Sales et al., PRB 56, 15081 (1997) Filled Skutterudites RM 4 X 12 skutterudites

8. The University of Tennessee Keppens et al., Nature 395, 876 (1998) Model calculation La 0.75 Fe 3 CoSb 12 La-filled = unfilled + TLS (  =50 K) + TLS (  =200K)

9. The University of Tennessee clathrates XE 20 XE 24 Ge- Clathrates: X 8 Ga 12 Ge 30 X=Ba, Sr, Eu Sales et al., PRB 63, 245113 (2001) Eu Sr Ba Atomic Displacement Parameters

10. The University of Tennessee Sales et al., PRB 63, 245113 (2001) Cohn et al., PRL 82, 779 (1999) thermal conductivity

11. The University of Tennessee ultrasonic absorption Sr 8 Ga 16 Ge 30 Keppens et al., Phil. Mag. Lett. 80, 807 (2000)

12. d  V   : asymmetry  0 : energy-overlap broad and uniformly maybe not so broad in distributed in glasses crystalline environment??? The University of Tennessee Sr 8 Ga 16 Ge 30 tunneling model for glasses P.W. Anderson et al., Phil. Mag. Lett. 25, 1 (1971) W. A. Phillips, Rep. Prog. Phys. 20, 1657 (1987 )

13. Ba 8 Ga 16 Ge 30 The University of Tennessee Sr 8 Ga 16 Ge 30 Eu 8 Ga 16 Ge 30 elastic moduli

14. The University of Tennessee 2-level system with  =25K Eu 8 Ga 16 Ge 30

15. The University of Tennessee Ba 8 Ga 16 Ge 30 Sr 8 Ga 16 Ge 30 nuclear density plots

16. The University of Tennessee Eu 8 Ga 16 Ge 30

17. The University of Tennessee Four-well potential: V( ,  ) = ― [1+cos(4  )] + ― + ― K  2 1 2 22 V1V1 V0V0 22 formation of four-level systems 22  22 ~

18. The University of Tennessee Agreement with elastic moduli, specific heat and nuclear density plots Zerec I., Keppens V., McGuire M. A., Mandrus D., Sales B. C., and Thalmeier P., Phys. Rev. Lett. 92, 185502 (2004). Eu 8 Ga 16 Ge 30

19. The University of Tennessee mImI I=5/2 I=7/2 |m I | 21.6 keV  -ray 1/2 3/2 5/2 1/2 3/2 5/2 7/2 5/2 7/2 -7/2 -5/2 Isomer shift Hyperfine field Quadrupole interaction Bare s-electron E.F.G. ≠ 0Magnetism Nucleus densityE.F.G. = 0 151 Eu Mössbauer

20. The University of Tennessee

21. Symmetric double well:  E= e -  with  ~ m  a 2 /h hh  m = mass Eu  = 25 K - 30K a = 0.275 Å tunneling frequency of 165-450 MHz The University of Tennessee

22. RF absorption measurements

23. The University of Tennessee Attenuation relative to 35 K (dB) Frequency (MHz) 10 100 1000 0.6 0.4 0.2 0 22 K 15 K 5K

24. The University of Tennessee Conclusions Type I Ge-clathrates are fascinating materials nuclear density maps, elastic moduli, Mössbauer and rf absorption provide strong evidence for tunneling of Eu-atoms in Eu 8 Ga 16 Ge 30 at a frequency of 450 ± 50 MHz between 4 equivalent sites separated by 0.55 Å exceptionally clear example of the tunneling of a large concentration of heavy atoms in a solid.

25. PART 2: RUS on bulk metallic glasses Discovered by Pol Duwez in 1960. Commercialization of ribbons (~50 μm thick) by Allied Chemical, 1973. Development of bulk metallic glasses in 1990’s. Amorphous steel, Fe-based BMG by C. T. Liu, ORNL The University of Tennessee

26. P. W. Anderson, Science 267, 1615 (1995). Glasses and the glass transition

27. The University of Tennessee Fragility defined by Angell ( Science 267, 1924 (1995)) Many metallic glass systems are fragile liquids. The fragility of glass-forming liquids

28. The University of Tennessee Fragility and Poisson’s ratio  Large Poisson’s ratio; low G/B ratio  High  high m, which means fragile liquid. V. Novikov and A. Solokov, Nature 431, 961 (2004)

29. Zr-based BMGs: Shear and Bulk Modulus The University of Tennessee

30. Zr-based BMGs: Poisson’ s Ratio The University of Tennessee

31. Ca-based BMGs

32. The University of Tennessee Ca-based BMGs: Poisson’ s Ratio

33. The University of Tennessee Ca-based BMGs: Specific heat and 1/Q

34. The University of Tennessee A new theory…

35. The University of Tennessee Conclusions Work in progress…. Use high -T RUS probe at NCPA to study BMGs near T g