torsional oscillator and specific heat measurements on solid helium pitp-outing lodge workshop, july...
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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
Total mass loading = 1625ns
Measured decoupling, -o=13ns
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
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
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
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
TF = 1.18K (CP)
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
TF = 1.18K (CP)
TF = 1.14K
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 = 1.24K
TF = 1.38K
TF = 1.18K (CP)
TF = 1.14K
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 = 1.24K
TF = 1.38K
TF = 1.18K (CP)
TF = 1.14K
TF = 1.32K
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 = 1.24K
TF = 1.38K
TF = 1.18K (CP)
TF = 1.14K
TF = 1.32K
TF = 1.30K
TF = 1.15K
TF = 1.14K
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%
0.02 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
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 2 hr Anneal 37 hr Anneal
N
CR
IF
Temperature [K]
Melting temperature = 1.38KAdditional 37 hours near 1.35K
Annealing of CT sample
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
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
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
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
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
Maximum Rim Velocity [m/s]
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]
Thermal history of 1ppb samples
More systematic study on a sample grown under constant P
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
Thermal history of 1ppb samples
More systematic study on a sample grown under constant P
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
Thermal history of 1ppb samples
More systematic study on a sample grown under constant P
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
Thermal history of 1ppb samples
More systematic study on a sample grown under constant P
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
[%
]
Maximum Rim Velocity [m/s]
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]
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
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
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
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
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).
A. C. Clark and M. H. W. Chan, J. Low Temp. Phys. 138, 853 (2005).
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).
A. C. Clark and M. H. W. Chan, J. Low Temp. Phys. 138, 853 (2005).
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
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