Upload
brenton-brackett
View
213
Download
0
Tags:
Embed Size (px)
Citation preview
Can a solid be superfluid?
Symposium on Quantum Phenomena and Devices
at Low Temperatures, 2008
Helsinki Univ. of Technology
Moses Chan - Penn State
Outline
• Introduction
• Torsional oscillator measurements.
• Origin of supersolidity :
zero point vacancies, grain boundaries
glassy regions or dislocations?
• Specific heat and dc flow experiments
• Conclusions
• 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 or nonclassical rotational inertia (NCRI) fraction.Its upper limit is estimated by different theorists to range from 10-6 to 0.4; Leggett: 10-4
Solid Helium
RI(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.
Leggett, “Can a solid be superfluid?” 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
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=0.9mm
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
Total mass loading = 3012ns
Measured decoupling, -o=41ns
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
0.0 0.1 0.2 0.3 0.4 0.5
-12
-10
-8
-6
-4
-2
0
2
4
Blocked annulus, gap 73 m Open annulus, gap 73 m
Per
iod
[ns]
Temperature [K]
Gap 73 m, NCRI = 16 %
Top View: Blocked
Top View: Open
solid inertia
Nonclassicalrotational inertia
Reversibly blocked annulusRittner & Reppy, Cornell
• Nonclassical rotational inertia results have been replicated in five other labs.
• The temperature dependence of NCRI is reproduced.
• However, the magnitude of NCRIF varies from 0.015% up to 16%.
• Simulations studies indicate NCRI is not possible in a ‘perfect’ crystal and that quantum zero point vacancies concentration is too low to account for the observations.
(this conclusion not universally accepted).• This leaves other defects, e.g. grain
boundaries, glassy regions and dislocations as possible origins or at least ‘enhancer’ for NCRI.
Grain boundaries
• It has been suggested that the observed NCRI are due to atomically thin superfluid (liquid) films along the grain boundaries, if true, NCRI should scales with total grain boundary area.
• Grain size of solid 4He inside Vycor glass is ~ 7nm and in bulk it is ~0.1 mm. This means the grain boundary surface differs by many orders of magnitude, but observed NCRI is about the same, ~1%.
• Nevertheless, most bulk solid samples grown by the blocked capillary method is polycrystalline. Does NCRI exists in a single crystal ?
Solid helium in Vycor glass
-*
[ns]
*=971,000ns
62bar
Total mass loading = 4260ns
Measured decoupling, -o=17ns
NCRI fraction, or NCRIF = 0.4%
(with tortuosity, 2% )
f0=1024Hz7nm
E. Kim & M.H.W. Chan, Nature 427, 225 (2004).
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
Solid 4He (1ppb 3He) grown under constant P/T from superfluid
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
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)
Solid 4He (1ppb 3He) grown under constant P/T from superfluid
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
Solid 4He (1ppb 3He) grown under constant P/T from superfluid
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
Solid 4He (1ppb 3He) grown under constant P/T from superfluid
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
Solid 4He (1ppb 3He) grown under constant P/T from superfluid
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
Solid 4He (1ppb 3He) grown under constant P/T from superfluid
Samples grown under constant P/T from superfluid collapse onto one curve for T > 40mK and share common onset temperature, TC ~ 80mK. Superfluid film flow along grain boundary cannot be the ‘origin’ of NCRI.
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
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
• Superfluid film along the grain boundaries cannot be the mechanism for NCRI.
• What is the most likely origin for the large variation in NCRI from cell to cell?
Dislocation lines density in solid 4He ranges from ~10 to 109 cm-2 , sensitive to how the solid is nucleated and grown. But how does dislocations enable or enhance NCRI?
• Two of the common types: edge & screw
In solid 4He
• Dislocation density, = ~5 <1010 cm-2
Dislocations
3He impurities at “high” T
•Network pinning at the nodes
•3He impurities are not ‘attached’ to the dislocation lines.
Increasing fraction of 3He atoms condense onto and stiffen dislocation network with
decreasing T
Iwasa et.al., J.Phys. Soc. Jpn. 46, 1119( 1979);
Paalanen, Bishop and Dail,PRL 46, 664(1981)
3He Effect ( bulk samples)
E. Kim, J. S. Xia, J. T. West, X. Lin, A. C Clark, and M. H. W. Chan, , PRL 100, 065301( 2008)
Onset of NCRI tracks the expected temp. of 3He condensation onto dislocation
Direct measurement of the Shear Modulus
James Day and John Beamish, Nature (London) 450, 853 (2007).
Shear Modulus mirrors NCRI
James Day and John Beamish, Nature (London) 450, 853 (2007).
• The increase in shear modulus and the onset of NCRI at low T must be related, but how?
• An increase in shear modulus of solid 4He in TO can result an increase in its resonant freq., ie. the same sign as the observed NCRI. But simulation studies shows the magnitude of the ‘Beamish’ effect is typically orders of magnitudes smaller than that observed in most TOs.
• The ‘Beamish’ effect or shear modulus stiffening cannot explain the blocked annulus experiments.
• It has been suggested (Anderson) that the onset of supersolidity stiffens the shear modulus.
• Simulations show the dislocation lines are ‘superfluid’ and it has been suggested that the onset of NCRI requires a ‘rigid’ dislocation network.
• What about the superglass model?
• Since glass has no crystalline order, it is thought superfluidity is more likely to occur.
• If this is the case there should be thermodynamic signatures ( e.g. thermal hysteresis, and linear specific heat)
Heat capacity
Is there a thermodynamic signature of the transition?
There is no specific heat information on solid 4He below 200 mK. The heat capacity of metal container swamps the contribution of solid 4He
Heat Capacity measurements in a Silicon cell
Si
Al
Glass Capillary
Stycast 2850
Heater
Thermometer
• Reasons for Si:
Low heat capacity:
High thermal conductivity:
Helium Volume= 0.926cc
1.5 cm
0.1mm ID
Heat capacity of solid 4He is more than 10 times largerthan the Si cell over the entire temp. range
AC Calorimetry
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]
Specific heat of commercially pure 4He (0.3ppm 3He)
0.03 0.05 0.1 0.50.01
0.1
1
10
A*T3
0.3ppm 33bar solid 4He
C [m
J m
ol-1 K
-1]
T [K]
Constant volume technique.20 hours to finish solidification.
No long time constant.
No hysteresis
No annealing effect
No thermal cycle effect
log C vs. log T
Specific heat of solid 4He (0.3ppm & 1ppb)
0.03 0.04 0.1 0.2 0.3 0.4
0.01
0.1
1
10 0.3 ppm 1 ppb
C
n [m
J m
ol-1 K
-1]
T [K]
log C vs. log T
C/T vs. T2
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 [m
J m
ol-1 K
-2]
T 2 [K2]
0.3 ppm
0.00
0.00 0.02 0.040
1
2
3
4
0.2
0.14
Data above 140 mK extrapolate to zero
0.00 0.02 0.040
1
2
3
4
0.2
1ppb
0.14
0.0 0.1 0.2
0.000
0.004
0.008
0.012
(P-P
0)/T
2 [bar
/K2 ]
T2 [K2]
freshly grown sample anneal sample 0.3ppm from HC
‘Linear T’ term from Pressure measurements ?
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~T P~Tn+1n+1
PHYSICAL REVIEW B 76, 224524 2007V. N. Grigor'ev et al
Specific heat with Debye phonon term subtracted
0.00 0.05 0.10 0.15 0.20-10
-5
0
5
10
15
20
25
1 ppb 0.3 ppm
T [K]
C [
J m
ol-1
K-1]
T3 subtracted
~20 J mol−1 K−1
~2.5×10-6 kB per 4He atom
0.00 0.05 0.10 0.15 0.20 0.25-30
-20
-10
0
10
20
30
40
50
Cp
ea
k [J
mo
l-1 K
-1]
T [K]
2008 BC 2007 BC 2008 CP
Solid sample grown under constant pressure condition has the smallest peak.
0.00 0.05 0.10 0.15 0.20 0.25-30
-20
-10
0
10
20
30
40
50
Cpe
ak [
J m
ol-1 K
-1]
T [K]
1ppb 20081ppb 2007 0.3ppm 2007
T3 subtracted
Higher resolution in 2008 sample cell
0.00 0.05 0.10 0.15 0.20 0.25-30
-20
-10
0
10
20
30
40
50
Cpe
ak [
J m
ol-1 K
-1]
T [K]
New 1ppb 33bar solid
T3 subtracted
0.02 0.06 0.2 0.4
0.01
0.1
1
A*T3
New 1ppb 33bar solid
C [m
J m
ol-1
K-1
]
T [K]
Minimum Temperature 25mK
New preliminary result with a more sensitive thermometer. Disadvantage of Si?
8 out of 10 cells leaks under high pressure
4 hours to solidify a sample.
Comparison with the Helsinki melting curve measurement.
• No anomaly in melting curve after correction for instrumental effect.
• Discrepancy we don’t understand
0.0000 0.0005 0.0010 0.0015 0.0020-80
-70
-60
-50
-40
-30
-20
-10
0
10
Pre
ssur
e D
evia
tion
[b
ar]
T 4 [K4]
From 0.3ppm [PSU 2007] Pressure [HUT]
dP
dT
S S
V V
SC
TdT
V Vliq so l
liq so l
liqn
liq so l
Todoschenko et al., PRL 97, 165302 (2006); JETP Lett. 85, 555 (2007).
Constant pressure 1ppb 2008
Constant volume 1ppb 2008
dc ( superfluid-like ) flow?
• Greywall and Beamish carried out experiments by increasing pressure on one end of a solid ( bulk or in Vycor glass) sample. No evidence of flow.
• Balibar and collaborators saw flow in liquid-solid coexistence samples. The observed phenomenon is likely a consequence of liquid film flow through the ‘crack’ in the solid.
DC superflow reported by ‘pushing’ on super
fluid in contact with solid : ‘UMass Sandwich’ (R.B. Hallock)
31 2
R, reservoirs
V, Vycor
S, sample
C1 C2
Conclusions• NCRI or superfluid like behavior seen in solid 4He in 7
labs.• Shear modulus increases at low temperature, the
temperature dependence of the increases mimics that of NCRI
• It is possible that either (1) NCRI ‘requires’ a rigid dislocation network, or (2) onset of NCRI stiffens the solid lattice.
• No evidence of linear T term in specific heat, but a peak near NCRI onset is seen, size of peak is smaller for a ‘higher’ quality sample.
• Preliminary dc superfluid flow through solid helium reported.
Xi, Tony, Eunseong, Josh
• 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
Solid 4He at 62 bars in Vycor glass
Period shifted by 4260ns due to mass loading of solid helium
*=966,000ns
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
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
Supersolid response of helium in Vycor glassSupersolid response of helium in Vycor glass• Period drops at 175mK appearance of non-classical rotational inertia (NCRI)
• size of period drop - ~17ns
*=971,000ns
-
*[ns
]
*=971,000ns
3He impurity effect in Vycor
Solid helium in porous gold
E. Kim & M.H.W. Chan, JLTP 138, 859 (2005).
f0=359Hz
27bar
Total mass loading = 1625ns
Measured decoupling, -o=13ns
NCRIF = 0.8%
(with tortuosity, 1.2% )
490nm
0.03 0.04 0.1 0.2 0.3 0.4
0.01
0.1
1
10
30 ppm 10 ppm 0.3 ppm 1 ppb
Cn
[mJ
mol
-1 K
-1]
T [K]
Specific heat with the temperature independent
constant term subtracted
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.
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
0.00 0.02 0.04 0.06
0
1
2
3
4
5
6
70
30 ppm 10 ppm 0.3 ppm 1 ppb
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
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
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).
Results: pure 4He (0.3ppm & 1ppb)
Ln C vs. Ln T
What is the deviation?
0.03 0.04 0.1 0.2 0.3 0.4
0.01
0.1
1
10 0.3 ppm 1 ppb
Cn
[mJ
mol
-1 K
-1]
T [K]
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.
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
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
0.00 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)
BC samples can also be grown
Heat outQ ~ 500,000
Granato-Lucke applied to 4He
• Dislocations pinned by network, 3He, jogs?• Typical LN in pure 4He crystals ~ 5m
0.03 0.04 0.1 0.2 0.3 0.4
0.01
0.1
1
10 0.3 ppm 1 ppb
Cn
[mJ
mol
-1 K
-1]
T [K]
Ln C vs. Ln T
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
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?
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?
Thermal history of 1ppb samples
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 ( inside Vycor)
Frequency dependence-TO increases with frequency-Low temperature NCRIF unchanged
Aoki, Graves & Kojima, PRL 99, 015301 (2007).
~150mK ~220mK