Effects of Crystal Growth/Annealing

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Effects of Crystal Growth/Annealing on
Supersolidity of Helium 4
Motoshi Kondo Shun-ichi Takada Hitomi
Yoshimura Yoshiyuki Shibayama Keiya
Shirahama Keio University, Yokohama, Japan
Support Grand-in-Aid for Scientific Research on
Priority Area Physics of Superclean Materials
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Outline

• Effect of Crystal Growth Velocity
• 2. Effect of Crystal Annealing
• 3. Discussion Dislocations?
• 4. Bulk Porous Media Preliminary Result

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Torsional Oscillator and Pressure Cells
Thermometers on platform and cell
f 1496 Hz
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Confirmation of the Kim-Chan Experiment
M. Kondo et al. cond-mat/0607032, JLTP in press
Rim Velocity
Velocity-dependent Frequency (period) Shift
Dissipation Peak
Supersolid Fraction 1/3 1/10 of KC
2.97 MPa
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Phase Diagram
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Crystal Growth with Constant Velocity
Solidification Start
Conjecture
End
Growth Velocity 10 mm /sec
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Effect of Growth Velocity
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Growth-Velocity Dependence of NCRI
Velocity-Dependent NCRI
Velocity-Independent NCRI
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Quench Cooling
Quench
Time(sec )
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NCRI of Quench-Cooled Samples
T 70 mK
Quench Cooled
Quenched
Slowly Grown
Slowly Grown
Quenched sample shows large rs, but not
systematic.
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Phased Annealing for Single Samples
Quench
0.8K
1K
1.2K
1.4K
1.6K
CRI increases by annealing / NCRI decreases
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NCRI after Annealings at Various Temperatures
We repeated the annealing at 0.8, 1.0, ...., 1.6
K.
2.75 MPa
Annealing at Higher T Smaller Supersolid
Fraction But could not be eliminated.
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Effect of Annealing on NCRI and CRI
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Effect of Annealing on NCRI and CRI
Change in CRI
NCRI
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Pressure and NCRI
Change in Pressure (65 mK)
NCRI
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Annealing for Many Samples
Change in CRI
NCRI
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Growth and Annealing Result
Fragile?
Robust Supersolid Component 0.04
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Growth and Annealing Results

• NCRI increases as the growth velocity increases.
• VGrowth?0 Limit Finite NCRI (0.04 at 70 mK)
• Quenching can further increase NCRI,
• but up to 0.25.
• NCRI decreases little by little,
• by phased annealing above 0.8 K.
• 2. CRI increases by annealing above 1 K.
• 3. NCRI of 0.04 could not be eliminated
• 1. 1-Day annealing, 20 mK below Tm x 5 times
• 2. Annealing without torsional oscillation
• ?Robust Supersolid Component exists
• ? Consistent with single crystal result (Clark
  et al.)
• Velocity-Independent NCRI Robust NCRI

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Discussion Increase in CRI
Conjecture
Annealing
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Dislocations formed in Crystal Growth
Single Crystal Growth by Chochralsky Method
Dislocation Density (cm-2)
(T. Suzuki, in Lattice Defects (in Japanese),
edited by H. Suzuki (1978))
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Crystal Growth with Constant Velocity
Solidification Start
Conjecture
End
Growth Velocity 10 mm /sec
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Growth Velocity and Temperature Gradient
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Origin of Temperature Gradient
Latent Heat
Balance of Cooling Power and Latent Heat
(F.D.Rosi, RCA Review 19, 349 (1958) (Germanium))
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Dislocations formed in Crystal Growth
F. R. N. Nabarro, Theory of Crystal Dislocations
(1967)

1. Impingement of two lattices
2. Thermal stresses
3. Aggregation of vacancies
4. Segregation of impurities

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Dislocations formed by Thermal Stresses
Solid 4He has very large thermal expansion
coefficient. This causes large thermal stress
under temperature gradient.
thermal expansion coefficient (K-1)
Ge 6x10-6
Cu 2.5x10-5
hcp 4He (20.5cm3/mol, 1.65 K) 10-2
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Dislocations formed by Thermal Stress
Y. Hiki and F. Tsuruoka, Phys. Rev. B 27, 696
(1983)
Ultrasound study for hcp 4He grown at
constant pressures
Sudden temperature change DT 50 mK produces
dislocations of 109 cm-2 (diminished 1 hr)
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Speculation Edge/Screw Dislocations
Edge Dislocations
Screw Dislocations
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Annealing Effect Exceptional Behavior
Increase in NCRI Chan et al. Kubota et al.
Only once in about 40 annealings
Change in Dislocation Connectivity?
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Helium in Porous Media
Helium 4 in Vycor (Adams, Beamish, Brewer, Reppy)
S-S-S Junction
(alias U-Mass Sandwich)
Vycor chunk
Svistunov, Hallock Davis et al.
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Helium in Nanoporous Gelsil Glass
4He in porous Gelsil (25 A)
4He in Vycor (70 A)
(Yamamoto et al. PRL 93, 075302
(2004)) (Shirahama, JLTP 146, 485 (2007) )
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Torsional Oscillator
Bulk helium
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Ideas

• P gt 25 bar
• Search for NCRI in bulk solid (0.5 mm thick
  disk)
• 2. P gt 35 bar
• Search for NCRI of solid in 25 A nanopores
• 3. 25 lt P lt 35 bar
• Supersolid in contact with
• Superfluid Reservoir
• 4. Where is 3He impurity going?
• (Kojima, Ceperley, Huse)

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Preliminary Result
2.99 MPa
Solid Tonset
liquid Tc
Coexistence of bulk supersolid and nanopore
superfluid
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Preliminary Result Dissipation Peak
2.99 MPa
Velocity-Dependent Dissipation Supersolid
Signal
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Summary

• Effect of Crystal Growth
• NCRI is altered by the growth velocity
• or temperature gradient in the crystal growth.
• Velocity-Independent NCRI
• 2. Effect of Annealing
• NCRI decreases by annealing above 0.8 K.
• NCRI of 0.04 could not be eliminated.
• ?Robust NCRI
• 3. Supersolid-Superfluid Double Layer

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Frequency and Pressure
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Control of Crystal Growth Velocity
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Slow Cooling is equivalent to Annealing
Robust Supersolid Fraction
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Annealing Effect Pressure
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Annealing Effect
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Annealing Effect
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Superglass State?
Boninsegni, Prokofev Svistunov, PRL 96, 105301
(2006)
ODLRO exists in glassy solids
In a glass at low temperatures
C a T P b T2
T linear specific heat has been observed by Lin
et al. Note Mobile Dislocations can also
give T2 Term in Pressure (A. Granato, Phys.
Rev. 111, 740 (1958))
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Pressure T2 term indicates a glassy state?
T2 Term smaller than other data (Grigorev
et al., cond-mat/0702133)) decreased after
annealing
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Summary

• Attempt of rapid cooling
• produces large supersolid fraction
• 2. Substantial annealing effect
• depending on annealing temperature
• These results support the Disorder/Defect
  Scenarios.
• 3. Robust supersolid fraction (0.1)
• could not be eliminated by annealing
• 4. Pressure small T2 term decreases by
  annealing?

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Effect of Temperature Difference
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Attempts to Control Crystal Growth Velocity
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Annealing Effect Pressure
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