Resonant Ultrasound Spectroscopy at 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 The University of Tennessee

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

Resonant Ultrasound Spectroscopy (RUS) Shape, Dimensions, Mass, Elastic Constants forward problem inverse problem Resonant Frequencies Figure of merit: F=Swi(fi-gi)2 The University of Tennessee

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

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

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

skutterudites Filled Skutterudites RM 4 X 12 Sales et al. , PRB 56, 15081 (1997) The University of Tennessee

Model calculation La 0. 75 Fe 3 Co. Sb 12 La-filled = unfilled + TLS (D=50 K) + TLS (D=200 K) Keppens et al. , Nature 395, 876 (1998) The University of Tennessee

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

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

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

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

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

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

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

Eu 8 Ga 16 Ge 30 The University of Tennessee

V 0 V 1 1 Four-well potential: V(r, f) = ― [1+cos(4 f)] + ― Kr 2 2 r 2 formation of four-level systems 2 D 2 ~ D 3 2 D 1 The University of Tennessee

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

151 Eu Mössbauer Bare Nucleus s-electron density E. F. G. ≠ 0 Magnetism E. F. G. = 0 7/2 5/2 3/2 1/2 I=7/2 21. 6 ke. V -ray I=5/2 -7/2 m. I 5/2 |m. I| 5/2 3/2 1/2 Isomer shift 7/2 -5/2 Quadrupole interaction Hyperfine field The University of Tennessee

The University of Tennessee

hw -f Symmetric double well: DE= p e with f ~ mwa 2/h m = mass Eu w = 25 K - 30 K a = 0. 275 Å 400 350 V(x) (K) 300 tunneling frequency of 165 -450 MHz 250 200 150 100 50 0 -0. 5 0 0. 5 Eu position (Å) The University of Tennessee

RF absorption measurements The University of Tennessee

Attenuation relative to 35 K (d. B) 0. 6 22 K 15 K 5 K 0. 4 0. 2 0 10 1000 Frequency (MHz) 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. The University of Tennessee

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

Glasses and the glass transition P. W. Anderson, Science 267, 1615 (1995). The University of Tennessee

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

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

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

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

Ca-based BMGs The University of Tennessee

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

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

A new theory… The University of Tennessee

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