The University of Tennessee Resonant Ultrasound Spectroscopy at The University of Tennessee Veerle...

The University of Tennessee

Resonant Ultrasound Spectroscopy at The University of Tennessee

Veerle Keppens

Department of Materials Science and Engineering


Work supported by The National Science Foundation


Collaborators:

Raphaël Hermann, Zhiying Zhang U. Tennessee

Takeshi Egami

Brian Sales, David Mandrus, ORNL

Bryan Chakoumakos, Hans Christen

Michael McGuire U. Mississippi

George Nolas U. South Florida

Peter Thalmeier, Ivica Zerec MPI, Dresden (Germany)

Gary Long, Fernande Grandjean U. Missouri, Rolla / U. Liège (Belgium)


Shape, Dimensions, Mass,

Resonant Frequencies

Elastic Constants

forward problem

inverse problem

Resonant Ultrasound Spectroscopy (RUS)

Figure of merit: F=wi(fi-gi)2

advantages of RUS: all elastic constants can be obtained in one measurement

small samples (mm3)


1.0x106 1.1x106 1.1x106 1.1x106 1.2x106

0.0

0.5

1.0

1.5

2.0

2.5

Am

plitu

de (

V)

Frequency (Hz)


Sales et al., PRB 63, 245113 (2001)

How does rattling reduce the thermal conductivity?

0 50 100 150 200 250 3000

1

2

3

4

5

Ba8Ga

16Ge

30

Sr8Ga

16Ge

30

Eu8Ga

16Ge

30

Latti

ce(W

/m-K

)

Temperature (K)

PART 1: RUS on “rattling solids”

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)



0 50 100 150 200 250 3000.00

0.05

0.10

0.15

0.20

0.25

0.30

CeFe4Sb

12

Latt

ice(W

/cm

-K)

Temperature (K)

CoSb3

0 50 100 150 200 250 3000.000

0.005

0.010

0.015

0.020

0.025

Ato

mic

Dis

pla

cem

en

t p

ara

me

ter

U (

A2 )

Temperature (K)

La

Sb

Fe, Co

Sales et al., PRB 56, 15081 (1997)

Filled Skutterudites RM4X12

skutterudites


Keppens et al., Nature 395, 876 (1998)

0 5 10 15 20-0.5

0.0

0.5

1.0

1.5

2.0

80 K

170 K

LaFe4Sb

12 -CeFe

4Sb

12

La v

ibra

tiona

l DO

S (

arb.

uni

ts)

E (meV)

0 50 100 150 200 250 300

0.555

0.560

0.565

0.570

0.575

0.580

Temperature (K)

c 44 (1

011

N m

-2 )

Model calculation

La0.75Fe3CoSb12

La-filled = unfilled + TLS (=50 K)

+ TLS (=200K)


clathrates

XE20XE24

Ge- Clathrates: X8Ga12Ge30

X=Ba, Sr, Eu

Sales et al., PRB 63, 245113 (2001)

0 50 100 150 200 250 3000.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

Ato

mic

Dis

plac

emen

t P

aram

eter

U (

A2 )

Temperature (K)

Eu

Sr

Ba

Atomic Displacement Parameters


Sales et al., PRB 63, 245113 (2001)

0 50 100 150 200 250 3000

1

2

3

4

5

Ba8Ga

16Ge

30

Sr8Ga

16Ge

30

Eu8Ga

16Ge

30

Latti

ce(W

/m-K

)

Temperature (K)0.1 1 10 100

1E-4

1E-3

0.01

0.1

1

Sr8Ga

16Ge

30

a-SiO2

Latti

ce (

W/m

-K)

Temperature (K)

Cohn et al., PRL 82, 779 (1999)

thermal conductivity


0.1 1 101E-3

0.01

0.1

US

Abs

orpt

ion

(dB

/cm

)

Temperature (K)

250 MHz 155 MHz

0.1 1 100.01

0.1

1

10

a-GeO2

US

Atte

nu

atio

n (

dB

/cm

)

Temperature (K)

115 MHz 85 MHz

ultrasonic absorption

Sr8Ga16Ge30

Keppens et al., Phil. Mag. Lett. 80, 807 (2000)

d

V

: asymmetry

0: energy-overlap

broad and uniformly maybe not so broad indistributed in glasses crystalline environment???


1 101E-3

0.01

0.1

1

250 MHz 155 MHz fit

US

Att

enua

tion

(dB

/cm

)

Temperature (K)

Sr8Ga16Ge30

tunneling model for glassesP.W. Anderson et al., Phil. Mag. Lett. 25, 1 (1971)W. A. Phillips, Rep. Prog. Phys. 20, 1657 (1987)

Ba8Ga16Ge30

0 50 100 150 200 250 3000.470

0.475

0.480

0.485

0.490

0.495

c 44(1

011

N/m

2 )

Temperature (K)


0 50 100 150 200 250 3000.370

0.372

0.374

0.376

0.378

0.380

0.382

0.384

c 44 (

10

11 N

/m2 )

Temperature (K)

Sr8Ga16Ge30

0 50 100 150 200 250 300

0.356

0.357

0.358

0.359

0.360

0.361

0.362

0.363

c 44 (

10

11 N

/m2 )

Temperature (K)

Eu8Ga16Ge30

elastic moduli


0 50 100 150 200 250 300

0.356

0.357

0.358

0.359

0.360

0.361

0.362

0.363

c 44 (

1011

N/m

2 )

Temperature (K)

2-level system with =25K

Eu8Ga16Ge30


Ba8Ga16Ge30 Sr8Ga16Ge30

nuclear density plots


Eu8Ga16Ge30


Four-well potential: V(, ) = ― [1+cos(4)] + ― + ― K21

22

V1V0

2

formation of four-level systems

2

2

~ ~


Agreement with elastic moduli, specific heat and nuclear density plotsZerec I., Keppens V., McGuire M. A., Mandrus D., Sales B. C., and Thalmeier P., Phys. Rev. Lett. 92, 185502 (2004).

Eu8Ga16Ge30


mI

I=5/2

I=7/2

|mI| 21.6 keV

-ray

1/23/25/2

1/23/25/27/2

5/2

7/2

-7/2

-5/2

Isomer shift Hyperfine field Quadrupole interaction

Bare s-electron E.F.G. ≠ 0 MagnetismNucleus density E.F.G. = 0

151Eu Mössbauer

0

50

100

150

200

250

300

350

400

-0.5 0 0.5

V(x

) (K

)

Eu position (Å)

Symmetric double well: E= e-with ~ ma2/h h

m = mass Eu = 25 K - 30Ka = 0.275 Å

tunneling frequency of 165-450 MHz



RF absorption measurements


Att

enua

tion

rela

tive

to 3

5 K

(dB

)

Frequency (MHz)

10 100 1000

0.6

0.4

0.2

0

22 K15 K 5K


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 Eu8Ga16Ge30 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.

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



P. W. Anderson, Science 267, 1615 (1995).

Glasses and the glass transition


• Fragility defined by Angell (Science 267, 1924 (1995))

• Many metallic glass systems are fragile liquids.

gTTg TT

m

log

The fragility of glass-forming liquids


12

213

B

G

1221

13.191229

G

Bm

Fragility and Poisson’s ratio

Large Poisson’s ratio; low G/B ratio

High high m, which means fragile liquid.

z

x

V. Novikov and A. Solokov,

Nature 431, 961 (2004)

Zr-based BMGs: Shear and Bulk Modulus

0 50 100 150 200 250 300 350 400

32.5

33.0

33.5

34.0

34.5

35.0

35.5

Zr50

Cu40

Al10

Zr50

Cu37

Al10

Pd3

Zr50

Cu35

Al10

Pd5

Zr50

Cu33

Al10

Pd7

Sh

ea

r M

od

ulu

s, G

(G

Pa

)

Temperature (K)

0 50 100 150 200 250 300 350 40090

95

100

105

110

115

120

Zr50

Cu40

Al10

Zr50

Cu37

Al10

Pd3

Zr50

Cu35

Al10

Pd5 Zr

50Cu

33Al

10Pd

7

Bu

lk m

od

ulu

s (G

Pa

)

Temperature (K)


Zr-based BMGs: Poisson’ s Ratio

0 100 200 300 400

0.35

0.36

0.37

0.38

Zr50

Cu40

Al10

Zr50

Cu35

Al10

Pd5

Zr50

Cu37

Al10

Pd3 Zr

50Cu

33Al

10Pd

7

Po

isso

n r

atio

Temperature (K)



Ca-based BMGs

0 100 200 300 400

10

11

12

13

14

Ca50

Mg20

Cu30

Ca55

Mg18

Zn11

Cu16

Ca65

Mg15

Zn20c 44

, She

ar M

odul

us, G

(G

Pa)

Temperature (K)

0 100 200 300 400

20

22

24

26

28

30

32

Bul

k M

odul

us, K

(G

Pa)

Temperature (K)

Ca50

Mg20

Cu30

Ca55

Mg18

Zn11

Cu16

Ca65

Mg15

Zn20


Ca-based BMGs: Poisson’ s Ratio

0 100 200 300 400

0.295

0.300

0.305

0.310

0.315

Ca50

Mg20

Cu30

Ca55

Mg18

Zn11

Cu16

Ca65

Mg15

Zn20

Poi

sson

Rat

io

Temperature (K)


300 320 340 360 380 40025

26

27

28

29

30

31

32

Ca50

Mg20

Cu30

Ca55

Mg18

Zn11

Cu16

Ca65

Mg15

Zn20

Hea

t Cap

acity

(J/

mol

/K)

Temperature (K)

0 100 200 300 400

0.000

0.005

0.010

0.015

0.020

0.025 Line 14 for Ca

50Mg

20Cu

30

Line 13 for Ca55

Mg18

Zn11

Cu16

Line 30 for Ca65

Mg15

Zn20

1/Q

Temperature (K)

Ca-based BMGs: Specific heat and 1/Q


A new theory…

)21(2

)1(3

2 2,

v

Tvv

g

K

K

VBkT


Conclusions

• Work in progress….

• Use high -T RUS probe at NCPA to study BMGs near Tg

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