The effect of The effect of 33He He impurity impurity

on supersolidon supersolid

E. KimE. Kim,,

Korea Advanced Institute of Science and Korea Advanced Institute of Science and TechnologyTechnology

J. T. West, X. Lin, and M. H. W. ChanJ. T. West, X. Lin, and M. H. W. Chan

Penn State UniversityPenn State University

J. S. XiaJ. S. Xia

University of FloridaUniversity of Florida

NCRI Low 3He concentration mixtures in

Vycor glass The effect of 3He in open cylindrical

geometry

ideal for detection of superfluid mass

K

Io 2Be-Cu

Torsion rod

Torsion cellcontaining helium

Drive Detection

I : rotational inertia of torsion cellK: torsion constant of the torsion Rod

Change of rotational inertia, I, can be detected by increase (or decrease) of the resonant oscillation period, o.

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

We find evidence of superflow in bulk solid 4He and solid 4He in Vycor glass with pore diameter of 7nm and in porous gold with pore diameter of 490 nm.

Non-classical rotational inertia Non-classical rotational inertia has been reproduced by has been reproduced by Reppy group - Annealing Effect & Disorder effect (47%

NCRIF)

Shirahama group - NCRI and weak annealing effect

Kubota group - Solid helium under rotation

Kojima group - Frequency dependence & hysteresis

Non-Classical Rotational Inertia Excess Heat Capacity Anomaly (Xi and

Chan) Ultrasound Anomaly (Goodkind) Pressure driven DC Flow: No flow Annealing Effect & confining effect 2nd sound measurement ? No anomaly in Pm Superfluid flow in grain boundaries Shear modulus at low temperatures

Recent Experiments Recent Experiments … and … and more questions more questions to the nature to the nature of supersolidof supersolid

Role of Defects?Role of Defects?

What kind of defect is responsible for the various NCRI values?

What we can learn from 3He impurity effect?

-

*[ns

]

*=971,000ns

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

Data shifted vertically for easy comparison

44He solid diluted with a low He solid diluted with a low concentration of concentration of 33HeHe

Effect of Effect of 33He impuritiesHe impuritiesSup

ers

olid

fra

ctio

n [

%]

‘‘Bulk’ Bulk’ 44He solid diluted with He solid diluted with a low concentration of a low concentration of 33He (85ppm) at 60 barHe (85ppm) at 60 bar

Low f0

Annular cellOpen Cylinder

TO1Open

cylinder TO2

Confining dimension

0.5cm 0.7cm 1 cm

A/V (cm2/cc) 5.6 5.9 7.2

Resonant Frequency

156Hz 783Hz 1298Hz

Covered X3 concentration

1ppb-47ppb47ppb - 30ppm

1ppb-100ppb

Three torsional Three torsional oscillatorsoscillators

The effect of The effect of 33He impurityHe impurity

Resonant frequency=156Hz

Tc~85mK

Supersolid fraction at 51 bars=10/11000 ~ 0.1%

3.25cm

Channel width=0.5cm (ID=1.27cm OD=1.77cm)

3.0cm

47ppb 47ppb 33He in solid He in solid 44He at He at 55bars55bars

Tc~105mK , Supersolid fraction 2.3ns/1100ns~0.2%

Resonant frequency:783Hz, Q~1x106

Open cylinder (no annular channel)

Torsion cell

0.76cm

Tc~105mK , Supersolid fraction 2.3ns/1100ns~0.2%

Resonant frequency:783Hz, Q~1x106

Open cylinder (no annular channel)

Tc~140mK and Supersolid fraction 3.5ns/1110~0.3%

Tc~140mK and Supersolid fraction 4ns/1110~0.36%

150ppb 150ppb 33He in solid He in solid 44HeHeResonant frequency:783Hz, Q~1x106

Open cylinder (no annular channel)

Tc~ 150mK and Supersolid fraction ~0.36%

Supersolid fraction is smaller than that observed in annular channel.

Tc~ 150mKSupersolid fraction ~0.3%

Supersolid fraction is smaller than that observed in annular channel.

Annular cell Vs. Open cellAnnular cell Vs. Open cell

Even though supersolid fraction is sensitive to the geometry and thermal history,

The effect of 3He on the onset temperature is robust.

Even though supersolid fraction is sensitive to the geometry and thermal history,

The effect of 3He on the onset temperature is robust.

The effect of 3He on the onset temperature is robust.

Effect of 3He on supersolid transition

3.25cm

Channel width=0.5cm (ID=1.27cm OD=1.77cm)

3.0cm

Tc is too low?or

Supersolid fraction is too small?

Isotopically-pure Isotopically-pure 44He?He?

Torsional oscillatorf0= 1298Hz, Q~1x106

Total mass loading due to solid heliumHe-empty=3939ns

Shift in the period=1ns

Supersolid fraction~1ns/3939ns~0.025%

This work is done in the B/T facility of the high magnetic field lab. Dr. Xia (University of Florida) Torsion cell

1.0cm

Isotopically-pure* Isotopically-pure* 44He He (*X(*X33<1ppb)<1ppb)

1ppb Samples grown by CP or CT

NCRIF0 Be-Cu TO ( 0.3%) Ag TO (0.03%)

Isotopically-pure* Isotopically-pure* 44He He (*X(*X33<1ppb)<1ppb)

1ppb Samples grown by CP or CT

NCRIF0 Be-Cu TO ( 0.3%) Ag TO (0.03%)

Isotopically-pure* Isotopically-pure* 44He He (*X(*X33<1ppb)<1ppb)

No extra temperature dependence down to 1mK.

This work is done in the B/T facility of the high magnetic field lab. Dr. Xia (University of Florida)

Isotopically-pure* Isotopically-pure* 44He He (*X(*X33<1ppb)<1ppb)

No extra temperature dependence down to 1mK.

This work is done in the B/T facility of the high magnetic field lab. Dr. Xia (University of Florida)

The effect of 3He impurity

Tc~110mKSupersolid fraction ~0.11%

Effect of Effect of 33He He

Addition of 3He enhances Tc

NCRI marches up to highertemperature with increasing3He concentration.

Effect of Effect of 33He He

Addition of 3He enhances Tc

NCRI marches up to highertemperature with increasing3He concentration.

Temperature dependence Temperature dependence

Temperature dependence Temperature dependence

Effect of Effect of 33HeHe Phase separation ?

regular solution theory

1)-2ln(1/x

2x-1

k

ET

Bps

• Common defect in crystals dislocation line

• Ultrasound measurements: Dislocation density in poor crystals ~ 109 per cm2

(constant volume1) Dislocation density in good crystals ~ 105 - 107 per cm2

(constant pressure2 or temperature3 above ~ 0.5K) Dislocation density in best crystals ~ 0 to 100

(constant temperature4 growth below ~ 0.2K)

Dislocation Dislocation

1. S.H. Castles & E.D. Adams, JLTP 19, 397 (1975).2. I. Iwasa, K. Araki & H. Suzuki, J. Phys. Soc. Jap. 46, 1119 (1979).3. V.L. Tsymbalenko, Low Temp. Phys. 21, 129 (1995).4. J.P. Ruutu, P.J. Hakonen, A.V. Babkin, A.Ya. Parshin & G. Tvalashvili, JLTP 112, 117 (1998).

• Dislocations intersect on a characteristic length scale of LN

( if ~105 to107 cm-2)

LN20.19 LN~ 1 to 10m

• Dislocations can also be pinned by 3He impuritiesLC~ Distance between 3He atoms

DislocationDislocation

Lc LN

• Dislocation density, = 5 ~ 1010 cm-2

Solid helium grown by a constant volume method; =105 to 107 cm-2

Dislocation slip Dislocation slip

Influence of an increasing external stress is shown in the fig. For small stress dislocation is pinned down by the impurity particles(A).Then for small stress the loops starts to deflects. At the break-away stress a large increase of the dislocation strain appears.

Torsion cell

Torsional oscillator at 10 m/s: ~ 0.001 Pa

DriveDetection

Torsion rod

Torsion cell

2

Rv

In our torsional oscillator measurements , we gently oscillate a solid helium sample contained in a torsional cell. (stress applied < 0.1 dyne/cm~ 10-3Pa)

33He and dislocationHe and dislocation• Actual 3He concentration on dislocation line is thermally activated

x xW

T3 00

exp

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

L AW xW

TH e3 01 3

02 3 02

3

/ / exp

• Pinning length due to 3He impurity

33He-dislocations interactionHe-dislocations interactionLine was drawn by considering W0=0.75Kand average L3He pinning length~ 0.15m.

Average lengthLNetwork ~ 0.15 m for ~ 109cm-2 (CV)

Smaller lengthsare expected for larger dislocation densities

cross-over from network pinning to 3He pinning

L AW xW

TH e3 01 3

02 3 02

3

/ / exp

33He-dislocations interactionHe-dislocations interaction

Much smaller lengthsare expected in Vycor glass ( most of all dislocations are pinned)

L AW xW

TH e3 01 3

02 3 02

3

/ / exp

Why no difference in Vycor?

3.25cm

Channel width=0.5cm (ID=1.27cm OD=1.77cm)

3.0cm

Wall thickness of some cells very thick

It is highly unlikely that NCRI is due to stiffening

Stiffening of solid helium in the Stiffening of solid helium in the cell?cell?

Effect of Effect of 33HeHe

Tc or onset temperature and supersolid fraction of superflow show strong dependence on concentration of 3He.

SummarySummary Dramatic effect of 3He impurities on supersolid

4He. The addition of 3He impurity broadens transition and

enhances the onset temperature. Not solely due to 3He impurities Not 3He-4He phase separation of a solid mixture The effect may be related with dislocation

pinning by 3He. After dislocation motion pinned by 3He impurities supersolid

phase appears

Pinning of dislocation increases shear modulus of solid helium?