Torsional oscillator and specific heat measurements on solid helium PITP-Outing Lodge workshop, July 22, 2007 Moses Chan - Penn State

Torsional oscillator and specific heat

measurements on solid helium

PITP-Outing Lodge workshop,

July 22, 2007

Moses Chan - Penn State

Outline

• Introduction

• Torsional oscillator measurements on solid samples grown under constant temperature /constant pressure condition.

• Thermal history studies

• Specific heat measurements

Superfluidity in liquid Superfluidity in liquid 44HeHe

Superfluid Superfluid

helium film helium film

can flow can flow upup

a walla wall

Superfluid Superfluid

FountainFountain

Solid

Superfluid (He II)

Normal Liquid (He I)

T=2.176K

• Lindemann Parameter the ratio of the root mean square of the displacement of

atoms to the interatomic distance (da)

A classical solid will melt if the Lindemann’s parameter exceeds the

critical value of ~0.1 .

• X-ray measurement of the Debye-Waller factor of solid helium at ~0.7K and near melting curve shows this ratio to be 0.262.

(Burns and Issacs, Phys. Rev. B 55, 5767(1997))

26.02

a

L d

u

Zero-point Energy

Inter-atomic potential

total energy

zero-point energy

• Theoretical ‘consensus’ in 1970s: Superfluidity in solid is not impossible!

- If solid 4He can be described by a Jastraw-type wavefunction

that is commonly used to describe liquid helium then crystalline order (with finite fraction of vacancies) and BEC can coexist.

G.V. Chester, Lectures in Theoretical Physics Vol XI-B(1969);

Phys. Rev. A 2, 256 (1970) J. Sarfatt, Phys. Lett. 30A, 300 (1969) L. Reatto, Phys. Rev. 183, 334 (1969)

- Andreev and Liftshitz assume the specific scenario of zero-point vacancies and other defects ( e.g. interstitial atoms) undergoing BEC and exhibit superfluidity.

Andreev & Liftshitz, Zh.Eksp.Teor.Fiz. 56, 205 (1969).

fs(T) is the supersolid fractionIts upper limit is estimated by different theorists to range from 10-6 to 0.4; Leggett: 10-4

Solid Helium

R

I(T)=Iclassical[1-fs(T)]

Quantum exchange of particles arranged in an annulus under rotation leads to a measured moment of inertia that is smaller than the classical value

The ideal method of detection of superfluidity is to subject solid to dc or ac rotation and look for evidence of nonclassical rotational inertia

A. J. Leggett, PRL 25, 1543 (1970)

Torsional Oscillator Technique is ideal for the detection of superfluidity

DriveDetection

3.5 cmTorsion rod

Torsion cell f0

f

Am p Quality Factor

Q= f0 / f ~106

Stability in the period is ~0.1 ns

Frequency resolution of 1 part in 107

Mass sensitivity of ~10-7 g

K

Io 2 f~ 1kHz

Torsional oscillator studies of superfluid films

I total= I cell+ I helium film,

Above Tc the adsorbed normal liquid film behaves as solid and oscillates with the cell. In the superfluid phase, helium film decouples from oscillation.Hence Itotal and drops.

Vycor

Berthold,Bishop, Reppy, PRL 39,348(1977)

Δ

K

Io 2

Blocked capillary (BC) method of growing solid samples

0.0 0.5 1.0 1.5 2.0 2.520

25

30

35

40

45

50

55

60

bcc

He I

hcp

Blocked Capillary (constant volume)

Pre

ssur

e [b

ar]

Temperature [K]

He II

heat drain

Be-Cu torsion rodand fill-line

solidblocks fill-line

gravity

Solid 4He at 62 bars in Vycor glass

Period shifted by 4260ns due to mass loading of solid helium

*=966,000ns

Supersolid response of helium in Vycor glassSupersolid response of helium in Vycor glass

• Period drops at 175mK appearance of NCRI

• size of period drop - ~17ns

*=971,000ns

Solid helium in Vycor glass

-

*[n

s]

*=971,000ns

62bar

Total mass loading = 4260ns

Measured decoupling, -o=17ns

NCRIF = 0.4%

(with tortuosity, 2% )

f0=1024Hz7nm

E. Kim & M.H.W. Chan, Nature 427, 225 (2004).

Solid helium in porous gold

E. Kim & M.H.W. Chan, JLTP 138, 859 (2005).

f0=359Hz

27bar



NCRIF = 0.8%

(with tortuosity, 1.2% )

490nm

Bulk solid helium in annulus

Torsion cell with helium in annulus

Mg disk

Filling line

Solid helium in annular channel

Al shell

Channel OD=10mm

Width=0.63mm

DriveDetection

3.5 cmTorsion rod

Torsion cell

E. Kim & M.H.W. Chan, Science 305, 1941 (2004)

f0=912Hz

Bulk solid helium in annulus

51bar



NCRIF = 1.4%

loading mass total

NCRIF

Total mass loading=3012ns at 51 bars

ρS/ρ |v|max

Non-Classical Rotational Inertia Fraction

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

NC

RIF

Temperature [K]

Open Annulus: 51bar, 4m/s

Blocked Annulus: 36bar, 3m/s

• Superfluids exhibit potential (irrotational) flow– For our exact dimensions, NCRIF in the blocked cell shou

ld be about 1% that of the annulus*

*E. Mueller, private communication.

Irrotational Flow

| |e

mv

i

S

Solid 4He at various pressures show similar temperature dependence, but the measured supersolid fraction shows

scatter with no obvious pressure dependenceN

CR

IF

NC

RIF

NC

RIF

NC

RIF

Pressure dependence of supersolid fraction

Blue data points were obtained by seeding the solid helium samples from the bottom of the annulus.N

CR

IF

What are the causes ofthe scatter in NCRIF?

Large number of experimental parameters.

1. Pressure

2. Oscillation speed.

3. 3He concentration ( Eunseong Kim)

4. Sample geometry/ crystal quality

5 . Frequency of measurement ( Kojima)

Strong and ‘universal’ velocity dependence in all annular samples

vC~ 10µm/s

=3.16µm/s for n=1

nRm

hv

nm

hdlv

s

s

2

ω

R

Vortices are important

3He Effect

E. Kim, J. S. Xia, J. T. West, X. Lin, and M. H. W. Chan, To be published.

Eunseong Kim

Data shifted vertically for easy comparison

3He Effect of solid 4He in Vycor

• Nonclassical rotational inertia results have been replicated in four labs.

• The temperature dependence of NCRI is reproduced.• However, the magnitude of NCRI varies from 0.03%

up to 20%(!!)• NCRI in cell with simple cylindrical geometry

appears to be smaller than that in annular geometry.• 20% NCRI was seen by Rittner and Reppy in solid

confined in a very narrow annulus of 0.15mm in width.

NCRI in open geometry appears to be smaller than in an annulus

25 35 45 55 65 75 85 95 105 115 125 1350.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016

0.018

0.020

NC

RIF

Pressure [bar]

Science [EK] PRL [EK] Open cell

Annealing effects

f0=185HzQuenched samples show large NCRI (~0.5%)Annealed samples show NCRI < 0.05%Velocities are between 9m/s and 45m/s

A.S. Rittner & J.D. Reppy, PRL 97, 165301 (2006).

• The variation in NCRI and the annealing effect seen by Rittner and Reppy suggest disorder in solid at least enhances NCRI.

• What kind of disorder? Vacancies and interstitials, dislocation lines and grain boundaries.

• It has been proposed that the observed effect is due to superfluid film flow along the grain boundaries.

0.0 0.5 1.0 1.5 2.0 2.520

25

30

35

40

45

50

55

60

bcc He I

hcp

Pre

ssur

e [b

ar]

Temperature [K]

He II

• High quality single crystals have been grown under constant temperature1 and pressure2

• Best crystals grownin zero temperaturelimit

Crystal Growth

1. O.W. Heybey & D.M. Lee, PRL 19, 106 (1967); S. Balibar, H. Alles & A. Ya Parshin, Rev. Mod. Phys. 77, 317 (2005).2. L.P. Mezhov-Deglin, Sov. Phys. JETP 22, 47 (1966); D.S. Greywall, PRA 3, 2106 (1971).

Constant T/P growth fromsuperfluid (1ppb 3He) Heat in

Heat outQ ~ 500,000

Tony Clark and Josh West

BC samples can also be grown

Heat outQ ~ 500,000

NCRI in solid helium (1ppb 3He)

Samples grown carefully from superfluid collapse onto one curve for T > 40mK and share common onset temperature, TC ~ 80mK

NCRIF ~ 0.3%

0.00 0.05 0.10 0.15 0.20

0.0

0.1

0.2

0.3

0.4

NC

RIF

[%

]

Temperature [K]

TF = 1.38K


Samples grown carefully from superfluid collapse onto \ one curve for T > 40mK and share common onset temperature, TC ~ 80mK

NCRIF ~ 0.3%

0.00 0.05 0.10 0.15 0.20

0.0

0.1

0.2

0.3

0.4

NC

RIF

[%

]

Temperature [K]

TF = 1.38K

TF = 1.18K (CP)



NCRIF ~ 0.3%

0.00 0.05 0.10 0.15 0.20

0.0

0.1

0.2

0.3

0.4

NC

RIF

[%

]

Temperature [K]

TF = 1.38K

TF = 1.18K (CP)

TF = 1.14K



NCRIF ~ 0.3%

0.00 0.05 0.10 0.15 0.20

0.0

0.1

0.2

0.3

0.4

NC

RIF

[%

]

Temperature [K]

TF = 1.24K

TF = 1.38K

TF = 1.18K (CP)

TF = 1.14K



NCRIF ~ 0.3%

0.00 0.05 0.10 0.15 0.20

0.0

0.1

0.2

0.3

0.4

NC

RIF

[%

]

Temperature [K]

TF = 1.24K

TF = 1.38K

TF = 1.18K (CP)

TF = 1.14K

TF = 1.32K



NCRIF ~ 0.3%

0.00 0.05 0.10 0.15 0.20

0.0

0.1

0.2

0.3

0.4

NC

RIF

[%

]

Temperature [K]

TF = 1.24K

TF = 1.38K

TF = 1.18K (CP)

TF = 1.14K

TF = 1.32K

TF = 1.30K

TF = 1.15K

TF = 1.14K



NCRIF ~ 0.3%

0.02 0.05 0.1 0.25

0.0

0.1

0.2

0.3

0.4

NC

RIF

[%

]

Temperature [K]

TF = 1.24K

TF = 1.38K

TF = 1.18K (CP)

TF = 1.14K

TF = 1.32K

TF = 1.30K

TF = 1.15K

TF = 1.14K

Comparison of BeCu & AgCu cells-For a particular cell, NCRIF in BC samples > NCRIF in CT/CP samples-TO also higher in BC samples-Order of magnitude difference in NCRIF between two cells

0.00 0.05 0.10 0.15 0.20 0.25 0.30

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.00 0.05 0.10 0.15 0.20 0.25 0.30

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

BC T

F = 1.88 K

TF = 2.20 K

CP T

F = 1.39 K

TF = 1.37 K

Temperature [K]

300 ppb

(b) AgCu

NC

RIF

[%

]

BC T

F = 2.17 K

TF = 1.80 K

TF = 1.75 K

CT or CP, , ,, , ,,

1.14 K < TF < 1.40 K

1 ppb

(a) BeCu BC

TF = 1.63 K

CT T

F = 1.46 K

300 ppb

NCRIF increases upon annealingTF =2.2K (45.5bar)

1st anneal: 5hr at 1.75K

2nd anneal: ~20min above 1.5K

Annealing in AgCu cell (300ppb)

0.0 0.1 0.2 0.3

0.00

0.05

0.10

0.15

0.20 10 m/s Const. Amp (2nd anneal) 10 m/s Const. Amp (1st anneal) 10 m/s Const. Amp (original)

NC

RIF

[%

]

TMC

[K]

-Annealing BC samples usually decreases large NCRIF’s

-CT sample unchanged

-Need to be very close

to TF for high pressure

samples

-Most dramatic change

occurs in (likely

polycrystalline)

sample at low pressure

Annealing in BeCu cell (1ppb)

0 5 10 15 20 25 30 35 400.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

NC

RIF

[%

]

Cumulative Anneal Time [h]

Annealing of CT sample

0.00 0.05 0.10 0.15 0.20 0.25

0.000

0.001

0.002

0.003

0.004 25.7 bar

N

CR

IF

Temperature [K]

Melting temperature = 1.38K

0.00 0.05 0.10 0.15 0.20 0.25

0.000

0.001

0.002

0.003

0.004 25.7 bar 2 hr Anneal

N

CR

IF

Temperature [K]

Melting temperature = 1.38K2 hour anneal at 1.28K


0.00 0.05 0.10 0.15 0.20 0.25

0.000

0.001

0.002

0.003

0.004 25.7 bar 2 hr Anneal 37 hr Anneal

N

CR

IF

Temperature [K]

Melting temperature = 1.38KAdditional 37 hours near 1.35K


Again

Annealing of BC sample

0.00 0.05 0.10 0.15 0.20 0.25 0.301.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

0.00 0.05 0.10 0.15 0.20 0.25 0.30

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Q-1 [

x 1

06 ]

Temperature [K]

Empty Cell

NC

RIF

[%

]

PF = 30.0 bar (BC)

Anneals: duration - T 65 min - 1.41 K 45 min - 1.585 K

PF = 25.8 bar (CT)

NCRIF, Q -1, and TO converge on that of the CT sample


0.00 0.05 0.10 0.15 0.20 0.25 0.301.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

0.00 0.05 0.10 0.15 0.20 0.25 0.30

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Q-1

[ x

106 ]

Temperature [K]

Empty Cell

NC

RIF

[%

]

PF = 30.0 bar (BC)

Anneals: duration - T 65 min - 1.41 K 45 min - 1.585 K 180 min - 1.605 K 290 min - 1.615 K 930 min - >1.5 K

PF = 25.8 bar (CT)

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

0.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

NC

RIF

Temperature [K]

0.04 0.08 0.12 0.16 0.20 0.24

0.0

0.1

0.2

0.3

0.4

NC

RIF

[%

]

Temperature [K]

TF = 1.24K

TF = 1.38K

TF = 1.18K (CP)

TF = 1.14K

TF = 1.32K

TF = 1.30K

TF = 1.15K

TF = 1.14K

BC - annealed

Reproducible results (1ppb)8 CT samples & 1 annealed BC sample collapse onto a single curve above 40mK

High temperature tail of NCRITransition broadened in BC samples (probably “polycrystalline”) and by 3He impurities

0.02 0.06 0.10 0.14 0.18 0.22 0.26

0.00.10.20.30.40.50.60.70.80.91.0 BC

300 ppb [1] 300 ppb 1 ppb

CT or CP, , 300 ppb, , ,, , ,, 1 ppb

Temperature [K]

Nor

mal

ized

NC

RIF

• Grain boundaries surely cannot be the sole mechanism.

• What then is the cause for variation in NCRI from cell to cell?

• Dislocation lines with density that ranges from 105 cm-2 to 1010 cm-2 and in particular how the interaction of vortices and 3He with dislocation lines are important.

Annealing lowers NCRIF, TO, and Q -1 peak


0.00 0.05 0.10 0.15 0.20 0.25 0.301.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

0.00 0.05 0.10 0.15 0.20 0.25 0.30

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Q-1 [

x 1

06 ]

Temperature [K]

Empty Cell

NC

RIF

[%

]

PF = 30.0 bar (BC)

Anneals: duration - T 65 min - 1.41 K

PF = 25.8 bar (CT)

Anderson’s vortex liquid modelJust a few details:

-”Free” vortices (relative to time scale of oscillator = resonant period) can respond to motion of oscillator and screen supercurrents, reducing measured NCRIF

-NCRI related to susceptibility of vortices: NCRIF largest when they are “pinned”

-3He may attach to vortices and slow them down (higher TO)

-Dissipation peak: vortex rate of motion ~ oscillator frequency (higher frequency, higher TO)

P.W. Anderson, Nature Phys. 3, 160 (2007).

Frequency dependence-TO increases with frequency-Low temperature NCRIF unchanged

Aoki, Graves & Kojima, PRL 99, 015301 (2007).

~150mK ~220mK

Critical velocity…vortices?

Velocity dependence

vC~ 10µm/s

=3.16µm/s for n=1

nRm

hv

nm

hdlv

s

s

2

ω

R

1 2.5 5 7.510 25 50 75100 2500.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

Nor

mal

ized

NC

RIF

Maximum Rim Velocity [m/s]

136 bar 108 bar 54 bar 30 bar 28 bar

E. Kim & M.H.W. Chan, PRL 97, 115302 (2006).

Critical velocity in single crystals of 1ppb purity?

Velocity dependence

ω

R

1 2.5 5 7.510 25 50 75100 2500.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

Nor

mal

ized

NC

RIF


136 bar 108 bar 54 bar 30 bar 28 bar

Thermal history of 1ppb samples

More systematic study on a sample grown under constant P

Reproducible warming/cooling scans in the low velocity limit, i.e. ~1m/s

0.00 0.02 0.04 0.06 0.08 0.10 0.12

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

0.0035 1.5m/s

NC

RIF

Temperature [K]



Velocity increased (to 20m/s) at low temperature NCRIF unchanged

0.00 0.02 0.04 0.06 0.08 0.10 0.12

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

0.0035 1.5m/s 15m/s

NC

RIF

Temperature [K]

1



Decay of NCRI above 30mKCooling from 40mK “freezes in” NCRIF

0.00 0.02 0.04 0.06 0.08 0.10 0.12

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

0.0035 1.5m/s 15m/s

NC

RIF

Temperature [K]

12

3



Decay appears faster at higher temperature (but depends on initial conditions)

0.00 0.02 0.04 0.06 0.08 0.10 0.12

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

0.0035 1.5m/s 15m/s

NC

RIF

Temperature [K]

12

3

4

5



Exponential decay at 60mK with time constant of 2 hoursNCRIF reversible when warming/cooling above 60mK at 20m/s

0.00 0.02 0.04 0.06 0.08 0.10 0.12

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

0.0035 1.5m/s 15m/s

NC

RIF

Temperature [K]

6

87

For T < 60mK, different decay above & below the low velocity field trace

NCRIF decay

6 8 10 12 14 16 18 200.00

0.05

0.10

0.15

0.20

0.25

40

45

50

55

60

65

0.10

0.15

0.20

0.25

0.30

30

35

40

45

50

55

Time [hr]

NC

RIF

[%]

3rd

B

(b)

Tem

pera

ture

[mK

]

FE

D

2ndA

C

G

HI

(a)

20 30 40 50 60 70 80 90 100 1100.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

A

CB

F

NC

RIF

[%]

Temperature [mK]

Sample 11-21 1st (2.0m/s) 2nd (20 m/s) 3rd (20m/s)

D

E I

G

H

Metastability also in BC samples, but high speed trace always below that of low speed

–Quick decay for large differences in metastable and stable NCRIF values–BC: TO is smallest at high speed, CT: TO is independent of speed

NCRIF decay

20 30 40 50 60 70 80 90 100 1100.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

NCR

IF [%

]

20 40 60 80 100 1200.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

NCR

IF [%

]

Temperature [K]

Different velocity dependence for samples grown at CT/CP and by BC

-No saturation in the (presumably) worst quality crystals-If there is a “critical velocity,” it is very low

1 5 10 50 100 500

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

NC

RIF

[%

]


B.C. [TM = 2.17 K]

Annealed B.C.

C.T. [TM = 1.2 K]

Data extracted from cooling scans!!

Onset of NCRI is ~80mK in single crystal samples–Same for all CT/CP samples–Same for some BC samples after considerable annealing –Same for all samples at large rim speed

Several parameters produce rounding of onset–Isotopic impurities–Finite measurement frequency–Polycrystallinity

NCRI response to rim speed consistent with vortex susceptibility–Vortices pinned below some T < 60mK

(vortex pinning critical temperature?)–Residual defects determine degree of vortex pinning

Conclusions

Heat capacity

Xi Lin and Anthony Clark

Is NCRI due to a glassy phase or glassy regions in solid helium?

Previous solid 4He heat capacity measurements below 1K

Year Low temperature limit

Swenson1 1962,1967 0.2K

Edwards2 1965 0.3K

Gardner3 1973 0.35K

Adams4 1975 0.13K

Hebral5 1980 0.1K

Clark6 2005 0.08K

1. E. C. Heltemes and C. A. Swenson, Phys. Rev. 128, 1512 (1962); H. H. Sample and C. A. Swenson, Phys. Rev. 158, 188 (1967).

2. D. O. Edwards and R. C. Pandorf, Phys. Rev. 140, A816 (1965).3. W. R. Gardner et al., Phys. Rev. A 7, 1029 (1973).4. S. H. Castles and E. D. Adams, J. Low Temp. Phys. 19, 397 (1975). 5. B. Hébral et al., Phonons in Condensed Matter, edited by H. J. Maris (Plenum, New York, 1980), pg. 169. 6. A. C. Clark and M. H. W. Chan, J. Low Temp. Phys. 138, 853 (2005).

They all observed T3 phonon contribution.

Their sample cells used in these experiments were all constructed with heavy wall metal or epoxy which contribute significantly to the heat capacity at low temperature.

Is there a linear T term?• T3 only : Edwards, Hébral• T3+T7 : Gardner• T3+T :

Year Density

[cc mol-1]

Linear slope

[J mol-1K-2]

T limit

[K]

Note

Swenson1 1962 14.50

16.74

20.64

21.04

3.3*10-3

7.1*10-3

8.8*10-3

5.0*10-3

0.2 12 4He samples. A tendency of higher linear term at higher molar volumes. In agreement with J. P. Franck.

Franck2 1964 14.88

16.30

0.8*10-3

2.5*10-3

1.3 Annealing samples cut down the linear term by 30%. Temperature range is 1.3 to 4K

Swenson3 1967 12.23 0.2*10-3 0.3 No effects due to annealing or cooling sample down slowly

Adams4 1975 19.43

20.59

0.9*10-3

2.5*10-3

0.13 Anneal the sample for about two hours

1. E. C. Heltemes and C. A. Swenson, Phys. Rev. 128, 1512 (1962).2. J. P. Franck, Phys. Lett. 11, 208 (1964).3. H. H. Sample and C. A. Swenson, Phys. Rev. 158, 188 (1967).4. S. H. Castles and E. D. Adams, J. Low Temp. Phys. 19, 397 (1975).

Linear term, on top of phonon term for the whole temperature range

Later study on heat capacity of solid 3He doesn’t observe the same excess linear heat capacity. (Greywall, PRB, 15,2604,1977)

AdamsFrank

3He

3He

3He

3He

Results from Edwards and Hebral

0 1 2 3 425

30

35

40

45

50

55

20. 93 cc/ mol 19. 68 cc/ mol 19. 18 cc/ mol 18. 22 cc/ mol 17. 87 cc/ mol 16. 90 cc/ mol

de

g. K

]

T [K]

0 1 2 3 425

30

35

40

45

50

55

20. 93 cc/ mol 19. 68 cc/ mol 19. 18 cc/ mol 18. 22 cc/ mol 17. 87 cc/ mol 16. 90 cc/ mol

de

g. K

]

T [K]

The background problem

0.01 0.1 11E-5

1E-4

1E-3

0.01

0.1

C [J

K-1

]

T [K]

solid 4He empty cell background

Edwards Hebral

34

v θ

T

5

π12C

baKN

Effect of changing 1% of the empty cell

A. C. Clark and M. H. W. Chan, J. Low Temp. Phys. 138, 853 (2005).

Clark and Chan, 2005 Aluminum cell

Our experimentThe Silicon cell

Si

Al

Glass Capillary

Stycast 2850

Heater

Thermometer

• Reasons for Si:

Low heat capacity:

High thermal conductivity:

Helium Volume= 0.926cc

At 0.1K Si Cu He

Specific Heat [J mol-1 K-1] 4x10-9 7x10-5 7x10-5

Thermal conductivity [W cm-1 K-1] 10-4* 4x10-2 4x10-3

* Using the value of quartz

0.6”

4 mil ID

AC Calorimetry 1,2

1. Paul F. Sullivan, G. Seidel, Phys Rev. 173, 679 (1968).2. Yaakov Kraftmakher, Physics Reports, 356 (2002) 1-117.

221

0 )(cos tQQ 2

1

3

211

2, 2

int2

220

s

b

ssac C

QtLT

ac

ac

T

QC

C

QT

2

2

Internal time constant << 1/ω

External time constant >> 1/ω

Kb

Sample

Thermal Bath

Thermometer

KΘ

Heater

Kh

0.01 0.1 11

10

100

1000

C [J

/K]

f [Hz]

0.03 0.05 0.1 0.51E-7

1E-6

1E-5

1E-4

1E-3 Background

0.3ppm Solid 4He

C [J

K-1

]

Temperature [K]

Glass capillary Cell Cu-Ni capillary Cell

Results: pure 4He (0.3ppm)

Temperature scale based on3He melting curve

Minimum temperature 40mK

0.03 0.05 0.1 0.25 0.5

0.1

1

10

100

1000

30 ppm 10 ppm 0.3 ppm 1 ppb Empty Cell

He

at

Ca

pa

city

, C

[J

K-1

]

Temperature, T [K]

Results: 4He at different 3He concentrations in glass capillary cell

No long time constant.

No hysteresis

No change due to annealing

No thermal cycle effect

Constant volume technique

Is there a linear T term?

0.00 0.05 0.10 0.15 0.200

2

4

6

8

10

12

14

16

T [K]

0.450.380.310.22

Cn

/T [

mJ

mo

l-1 K

-2]

T 2 [K2]

30 ppm 10 ppm 0.3 ppm 1 ppb

0.00

0.00 0.02 0.040

1

2

3

4

5

6

0.2

0.3ppm

1ppb

0.14

For 0.3ppm, T>0.14K T3 relation only

Comparison with Castle & Adams

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.200

10

20

C/T

[mJ

mol

-1K

- 2]

T2 [K2]

0.3ppm solid 4He linear fit for 0.3ppm

0.370.25 0.320.1 T [K]

0.45

Adams 19.43cc/mole

Pressure measurement

Freshly grown sample

Annealed sample (19.83cc/mole)

v

V

C

T

P

)(

— — Grüneisen constantGrüneisen constant

ρρ — molar volume — molar volume

CCVV~T~Tnn

P~TP~Tn+1n+1

0.00 0.05 0.10 0.15 0.200

6

12

18

0.450.380.310.22

C/T

[mJ*

mol

-1K

-2]

T2 [K2]

0.3ppm linear fit Ukraine after anneal Ukraine before anneal

0.00T [K]

V.N.Grigorev, V.A.Maidanov, V.Yu.Rubanskii, S.P.Rubets, E.Ya.Rudavskii, A.S.Rybalko, Ye.V.Syrnikov, V.A.Tikhii

cond-mat/0702133

0.00 0.05 0.10 0.15 0.200

2

4

6

8

10

12

14

16

T [K]

0.450.380.310.22

Cn

/T [

mJ

mo

l-1 K

-2]

T 2 [K2]


0.00

0.00 0.02 0.040

1

2

3

4

5

6

0.2

0.3ppm

1ppb

0.14

For 0.3ppm, T>0.14K T3 relation only

0.00 0.02 0.04 0.06

0

1

2

3

4

5

6

70


0.390.34

Cn [

mJ

mo

l-1 K

-1]

T 3 [K3]

0.27T [K]

0.000 0.002 0.004

0.0

0.1

0.2

0.3

0.4

0.5

0.16

0.13

C vs T3

Constant contribution from 3He impurity

10ppm sample

0.7+/-0.2 kB per 3He

30ppm sample

1.7+/-0.3 kB per 3He

NMR measurement of spin (3He) diffusion:

A. R. Allen, M. G. Richards & J. Schratter J. Low Temp. Phys. 47, 289 (1982).

M. G. Richards, J. Pope & A. Widom, Phys. Rev. Lett. 29, 708 (1972).

NMR measurement of spin diffusion

V. N. Grigor'ev, B. N. Esel'son, V. A. Mikheev, V. A. Slusarev, M. A. Strzhemechny, Yu. E. Shulman JLTP 13 65 (1973).

The constant specific heat of ~1 kB per 3He atom is most likely related to the 3He impuriton wave.

Note however 3He concentrations and temperature range in heat capacity measurement are lower than NMR measurements.

.

0.03 0.04 0.1 0.2 0.3 0.4

0.01

0.1

1

10


Cn

[mJ

mol

-1 K

-1]

T [K]

Specific heat with the temperature independent

constant term subtracted

0.00 0.05 0.10 0.15 0.20 0.25

-30

-20

-10

0

10

20

30 10 ppm 0.3 ppm 1 ppb

Cpe

ak [J

mo

l-1 K

-1]

T [K]

0.00 0.05 0.10 0.15 0.20

0

20

40

60

80

Specific heat peak is found when T3 term subtracted The peak is independent of 3He concentration

Peak height: 20 μJ mol-1 K-1

(2.5 x 10-6 kB per 4He atom)

Excess entropy: 28 μ J mol-1 K-1

(3.5 x 10-6 kB per 4He atom)

Is the peak related to phase separation?

0.0 0.1 0.2-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Cpe

ak m

J m

ol-1

K-1

Temperature [K]

0.3ppm from present experiment 760ppm phase seperation peak warming 760ppm phase seperation peak cooling

Hysteresis seen in phase separation in 1000ppm and 760ppm samples.

We do not observe hysteresis in the present experiment.

Hebral at al. PRL 46, 42 (1981).


Latent heat due to phase separation3He (ppm)

Measured Latent heat (uJ/cc)

Calculated Latent heat due to phase separation (uJ/cc)

Pobell 9000 3300 4000

Pobell 4500 1400 1800

Hebral 1000 5 450

Clark 760 5 350

PSU 10 0.06 5

PSU 0.3 0.06 0.2

PSU 1E-3 0.06 0.0009

R.Schrenk,O.Friz,Y.Fujii,E.Syskakis, F. Pobell, JLTP 84, 133 (1991).

Hebral at al. PRL 46, 42 (1981).


Melting curve measurements from Helsinki

I. A. Todoshchenko,H. Alles, J. Bueno,H.J. Junes, A.Ya. Parshin & V.Tsepelin, Phys. Rev. Lett., 97, 165302 (2006). I. A. Todoshchenko, H. Alles, H. J. Junes, A. Ya. Parshin, & V. Tsepelin JETP 85, 555(2007)

Apparent anomaly has the origin of Be-Cu diaphragm.

PRLJETP

Compare with torsional oscillator

0.02 0.06 0.10 0.14 0.18

0.00.10.20.30.40.50.60.70.80.91.0

0

5

10

15

20

25

CT or CP, , ,, , ,, 1 ppb

Temperature [K]

N

orm

aliz

ed N

CR

IF

Xi, Tony, Eunseong, Josh


Velocity changes at low temperature lead to interesting behavior…

Protocol followed below: (1) cooling, (2) velocity increase, (3) warming, (4) cooling

0.00 0.05 0.10 0.15 0.20 0.25 0.30

0.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

29.5bar, 11m/s 29.5bar, 150m/s

NC

RIF

Temperature [K]

1

3

4

2

End

0.00 0.05 0.10 0.15 0.20 0.25-30

-20

-10

0

10

20

30 10 ppm 0.3 ppm 1 ppb

Cpe

ak [J

mo

l-1 K

-1]

T [K]

0.00 0.05 0.10 0.15 0.20

0

20

40

60

80

Specific heat with T3 term subtracted

Peak height: 20 μJ mol-1 K-1 (2.5 x 10-6 kB per 4He atom)

Excess entropy: 28 μ J mol-1 K-1 (3.5 x 10-6 kB per 4He atom)

1. Specific heat peak is independent of 3He concentrations.

2. Assuming 3D-xy universality class (same as the lambda transition in liquid 4He).

3. Use two-scale-factor universality hypothesis, ρs ~0.06%. 1ppb study of TO found this number lays between 0.03% and 0.3%.

Hysteresis in Pressure measurement of phase separation

A.N.Gan'shin, V.N.Grigor'ev, V.A.Maidanov, N.F.Omelaenko, A.A.Penzev, É.Ya.Rudavskii, A.S.Rybalko., Low Temp. Phys. 26, 869 (2000).

1E-6 1E-5 1E-4 1E-3 0.01

0.1

0.2

Standard theory model Ganshin warming Ganshin cooling

TP

S [

K]

X3

• Two of the common types: edge & screw

• Dislocation density, = ~5 <1010 cm-2

– 3-d network, LN ~ 1 to 10 m (~105 to 107)

[LN ~ 0.1 to 1 m (~109)]

Dislocations

• Dislocations intersect on a characteristic length scale of LN ~ 1 5m

• Dislocations can also be pinned by 3He impurities– Distance between 3He atoms (if uniformly distributed):

– 1ppb 1000a ~ 0.3m

– 0.3ppm 150a ~ 45nm

– 1% 5a ~ 15nm

Granato-Lucke applied to 4He

3He-dislocation interactionActual 3He concentration on dislocation line is thermally activated

x xW

T3 00

ex p

*Typical binding energy, W0 is 0.3K to 0.7K

3He-dislocations interaction

1 10 100 1000 10000 10000020

40

6080

100

200

400

600800

1000

2000

LC ~ L

N ~ 1m

Binding energy, W0 = 1K

TC [

mK

]

X3 [ppb]

open cell (PSU) open cell (UF) annular cel Vycor

Line considered as crossover from network pinning to 3He impurity pinning of dislocations (LNetwork ~ L3

He spacing)

Average lengthLNetwork ~ 1 to 10mFor ~ 105 to 106cm-2

Smaller lengths (< 1m) are expected for larger dislocation densities

L A W xW

TH e3 01 3

02 3 02

3

/ / ex p

Solid helium in Vycor glass

Weak pressure dependence…

from 40 to 65bar

Strong velocity dependence

-

*[ns

]

*=971,000ns

Question: If there is a transition between

the normal and supersolid phases,

where is the transition

temperature?

3He-4He mixtures

3He-4He mixtures

Documents

Torsional oscillator and specific heat measurements on solid helium PITP-Outing Lodge workshop, July 22, 2007 Moses Chan - Penn State