Observation of Mass Flux through

1
Observation of Mass Flux through Solid 4He off
the Melting Curve. M.W. Ray and R.B.
Hallock Laboratory for Low Temperature
Physics, Department of Physics, University of
Massachusetts, Amherst, MA, USA
Supported by the National Science Foundation,
the CRDF and Research trust funds from the
University of Massachusetts Amherst.
2

• Observation of Mass Flux through
• Solid 4He off the Melting Curve.
• Outline
• A few Reminders
• Experiment Concept and Design
• Growing Solids
• Mass Flux through the Solid
• Interpretations
• Conclusion

3
Following the work by John Goodkinds group,
considerable renewed interest in solid 4He was
stimulated by Kim and Chan.
Observed period shift was interpreted as the
observation of NCRI some mass does not couple
to the motion of the oscillator.
J. Low Temp. Phys. 109, 409 (1977) Nature
427, 225 (2004) Science 305, 1941 (2004)
4
Is it possible to cause solid helium to flow?
The basic conceptual design of the experiments by
Greywall (1977) and by Day and Beamish
(2005,6)
B
A
Squeeze the solid directly (off the melting
curve) E.g., increase the pressure in A and see
no change in B. ? no flow, i.e. no more than
10-3 nm/sec) (assuming 1 of the entire sample
was superfluid.)
Greywall Phys. Rev. B 16, 1291 (1977)
Beamish group Phys. Rev. Lett. 95, 035301
(2005) Phys. Rev. Lett. 96, 105304 (2006)
5
Greywall, Phys. Rev. B 16 1291 (1977)
6
Images and data set provided, thanks to John
Beamish Day and Beamish, PRL 96, 105304 (2006)
7
Recent work by Rittner et al. in a narrow
annular slit (designed to be very rigid) shows
no flow for low frequency AC drives with f
0.002 Hz. 20 mK lt T lt 400 mK 27 bar lt P lt 40
bar Why do oscillators show apparent mass
motion? They suggest that apparent supersolidity
might be a finite frequency effect (oscillators
100 to 1 kHz), or might have an analog in
superconductivity. Flow limit consistent with
the Beamish lab flow limit. Differs from our
zero-frequency results.
Rittner, Choi, Mueller and Reppy
arXiv0904.2640
8
Some other (melting curve) flow experiments
Flow observed at a variety of temperatures on the
melting curve interpreted as due to liquid
channels.
Earlier work Bonfait et al., J. Phys (Paris)
50, 1997 (1989) no flow seen Sasaki, et al.
Science 313, 1098 (2006) Phys. Rev. Lett. 99,
205302 (2007)
9
Grains may also meet in the absence of walls to
form liquid channels.
From Sasaki, et al. Phys. Rev. Lett. 99, 205302
(2007)
10
Our Conceptual Design Do not squeeze the
lattice, but, apply a chemical potential
difference by applying pressure to superfluid
helium in contact with the solid.
8
11
Our Conceptual Design Do not squeeze the
lattice, but, apply a chemical potential
difference by applying pressure to superfluid
helium in contact with the solid.
One needs a liquid-solid interface and so this
can generally only be done on the melting
curve, where liquid and solid coexist.
12
Our Conceptual Design Do not squeeze the
lattice, but, apply a chemical potential
difference by applying pressure to superfluid
helium in contact with the solid.
One needs a liquid-solid interface and so this
can generally only be done on the melting
curve, where liquid an solid coexist. But, we
wish to work off the melting curve.
13
Note helium in a porous material remains liquid
to a higher pressure than it does in bulk.
For example Vycor
Beamish et al., Phys. Rev. Lett. 50, 425 (1983)
Adams et al., J. Low Temp. Phys. 66, 85
(1987) Lie-zaho et al., Phys. Rev. B 33, 106
(1986).
14
We utilize this fact and create a symmetric
sandwich
Liquid Helium in Vycor
Solid Helium
Capillary to add, subtract helium
Bulk Liquid Helium
15
We utilize this fact and create a sandwich
Liquid Helium in Vycor
Solid Helium
?T
?T
Capillary to add, subtract helium
Bulk Liquid Helium
We must apply a temperature gradient across
the Vycor sections for the solid to be off the
melting curve.
16
Pressure Gauge (room temp)
Fill Capillary
Reservoir
Thermometer
Heater
Vycor
Capacitance Pressure Gauge
12
Solid Helium
17
15 cm
18
Mixing Chamber
Fill Capillary
Copper Bus Bars
Reservoir
Vycor Rod (in SS tube)
Sample Cell
Capacitor
Copper Base Plate
19
1.91 cm
Vycor diameter 1.52 mm 0.76 mm
6.99 cm
Capacitor
0.635 cm
4.45 cm
Cell Cylindrical Bore
20
Typical Cross Section
21
We need to check the behavior of the Vycor to see
if the Vycor will influence any flow measurement.
22
We need to check the behavior of the Vycor to see
if the Vycor will influence any flow measurement.
Some thoughts (1) Proper fountain effect
indicates that there is an effective
superleak through the Vycor. (2) Solid samples
made under very similar conditions show
different flow rates, which implies that the
Vycor system is not the flow limitation. (3)
Vycor liquid flows are 10 to 50 times faster
than what is typically seen with solid in
the cell.
23
Growth curves for growth by blocked capillary.
24
Growth curves for growth by blocked capillary.
Growth curves for growth from superfluid.
25
Increase pressure to line 1 and line 2 grow
solid from the superfluid phase.
18
26
Increase pressure to line 1 and line 2 grow
solid from the superfluid phase.
27
Expanded view.
28
Another example.
29
Expanded view.
30
(No Transcript)
31
Temperature spikes and pressure shifts on and
very near to the melting curve. Temperature
transients 2 mK Pressure drops 50
mbar Liquid converting to solid?
Dislocations disappearing? Grain boundaries
disappearing?
32
Temperature spikes and pressure shifts on and
very near to the melting curve. Temperature
transients 2 mK Pressure drops 50
mbar Most likely due to small localized regions
of metastable liquid that convert to solid. The
typical size of one of these is about 0.2 of
the volume of the solid region of the cell.
33
(No Transcript)
34
Try to make mass move from side 1 to side 2.
35
Add helium to line 1 and see what happens at P2.
36
The first sample we studied that showed evidence
for flow
Ray and Hallock, Phys. Rev. Letters 100, 235301
(2008)
37
Quantitative detail (Sample A) full cross
section conducts
1 x 10-4 grams of 4He moved from line 1 to line
2 (in 20 hours, which is 1.4 x 10-9 g/sec) 4.5 x
10-4 grams of 4He joined the solid M/t ? ?
VXY mass moved from 1 to 2 in time t Assume
full cross section is available ? VXY 8 x
10-9 cm3 / sec ? V 2.5 x 10-8 cm / sec If V
100 µm/sec, then ? 2.5 x 10-6 If ? 1
then V 2.5 x 10-6 cm / sec 25 nm/sec
38
Quantitative detail (Sample A) full cross
section conducts
1 x 10-4 grams of 4He moved from line 1 to line
2 (in 20 hours, which is 1.4 x 10-9 g/sec) 4.5 x
10-4 grams of 4He joined the solid M/t ? ?
VXY mass moved from 1 to 2 in time t Assume
full cross section is available ? VXY 8 x
10-9 cm3 / sec ? V 2.5 x 10-8 cm / sec If V
100 µm/sec, then ? 2.5 x 10-6 If ? 1
then V 2.5 x 10-6 cm / sec 25
nm/sec (compare to few x 10-3 nm/sec)
39
Quantitative detail discrete structures
conduct
Either a line or a plane with one thickness, x
0.5 nm Then, ? VY 0.16 cm2 / sec If ? 1,
then VY 0.16 cm2/sec If V 200 cm/sec, then
Y 8 x 10-4 cm If structures are 0.5 nm x 0.5
nm, then we need 1.6 x 104 pipe-like
conduits. This would be a density 5.0 x 104
cm-2.
40
Quantitative detail discrete structures
conduct
Either a line or a plane with one thickness, x
0.5 nm Then, ? VY 0.16 cm2 / sec If ? 1,
then VY 0.16 cm2/sec If V 200 cm/sec, then
Y 8 x 10-4 cm If V 100 µm/sec, then Y 16
cm If structures are 0.5 nm x 0.5 nm, then we
need 1.6 x 104 ( 3.2 x 108) pipe-like
conduits. This would be a density 5.0 x 104
cm-2 ( 1.0 x 109 cm-2).
41
Another Example Interpreted as Evidence for Flow
P1
P2
C1, C2
42
Quantitative detail (Sample AO) full cross
section conducts
3.5 x 10-5 grams of 4He moved from line 1 to
line 2 (in 250 minutes, which is 2.4 x 10-9
g/sec) 1.1 x 10-4 grams of 4He joined the
solid M/t ? ? VXY mass moved from 1 to 2 in
time t Assume full cross section is available
? VXY 1.3 x 10-8 cm3 / sec ? V 4.1 x 10-8 cm
/ sec If V 100 µm/sec, then ? 4.1 x
10-6 If ? 1 then V 4.1 x 10-6 cm / sec
41 nm/sec
43
Quantitative detail discrete structures
conduct
Either a line or a plane with one thickness, X
0.5 nm Then, ? VY 0.26 cm2 / sec If ? 1,
then VY 0.26 cm2/sec If V 200 cm/sec, then
Y 1.3 x 10-3 cm If structures are 0.5 nm x
0.5 nm, then we need 2.6 x 104 pipe-like
conduits. This would be a density 8.2 x 104
cm-2.
44
Quantitative detail discrete structures
conduct
Either a line or a plane with one thickness, X
0.5 nm Then, ? VY 0.26 cm2 / sec If ? 1,
then VY 0.26 cm2/sec If V 200 cm/sec, then
Y 1.3 x 10-3 cm If V 100 µm/sec, then Y 26
cm If structures are 0.5 nm x 0.5 nm, then we
need 2.6 x 104 ( 5.2 x 108) pipe-like
conduits. This would be a density 8.2 x 104
cm-2 ( 1.6 x 109 cm-2).
45
Another Interpreted as Evidence for Flow
P1
P2
C1
C2
Note Sometimes C1 and C2, like in this case,
show a gradient is present in the cell.
(A long-term rather stable gradient)
46
Another Interpreted as Evidence for Flow
P1
P2
C2
C2
C1
Note Other times, e.g. here, very little
gradient is present C1 C2. (And, imposition of
a finite P1 P2 does not create a gradient.)
47
An Example Interpreted as Long-term No Flow
28
48
Another Interpreted as Long-term No Flow
49
Summary of results for freshly grown samples
and samples that were not cycled thermally
50
What causes the behavior we see? Flow in Liquid
channels? Flow along dislocations, grain
boundaries? Some sort of plastic flow?
Something else? What is the relationship to
other work?
51
Flow in Liquid channels? Should remain up to 1.1
K at our pressures (presuming the liquid channel
does not anneal) Should be pressure
dependent. Should be present in fresh samples at
various temps. Flow along dislocations, grain
boundaries? May have a transition temperature
that depends on pressure or temperature, or both.
52
Look first at some sequential measurements.
53
So, some sequential measurements AR -
AV Create sample at 360 mK, 26.249 bar, push,
see flow Warm sample to 608 mK, 26.373 bar,
push, no flow Cool to 360 mK, 26.363 bar, push,
no flow At 360 mK, pull, see flow At 360 mK,
push, see flow.
Seq. AR - AV
360
608
54
New Sample Create at 400 mK and repeat cycle
with 800 mK instead of 600 mK yields the same
result.
55
New Sample Create at 400 mK and repeat cycle
with 800 mK instead of 600 mK yields the same
result. Maybe the warming damages the flow path.
So, create fresh samples at the higher
temperatures.
56
New Sample Create at 400 mK and repeat cycle
with 800 mK instead of 600 mK yields the same
result. Next, create fresh samples at 600 mK,
push, and observe no flow. Same result with
fresh samples Created at 800 mK, no flow.
57
New Sample Create at 400 mK and repeat cycle
with 800 mK instead of 600 mK yields the same
result. Next, create fresh samples at 600 mK,
push, and observe no flow. Same result with
fresh samples Created at 800 mK, no flow. Also,
at 600 mK, after push and no flow, also did a
pull (subtraction) with the result of no flow.
58
New Sample Create at 400 mK and repeat cycle
with 800 mK instead of 600 mK yields the same
result. Next, create fresh samples at 600 mK,
push, and observe no flow. Same result with
fresh samples Created at 800 mK.
If what we see were due to liquid channels, we
believe that they should be created at 600 mK
and at 800 mK and should conduct. We do not
see flow behavior for T gt 600 mK at any pressure
studied.
40
59
Doubtful we have annealing at 600 mK (No
evidence for pressure shifts of the sort seen
very close to the MC.) Perhaps something happens
between 400 mK And 600 mK.
60
Another sequential experiment AJ - AM Create
sample at 500 mK, push, observe flow Remain at
500 mK, push, see flow, but smaller Cool to 360
mK, push, see flow, but larger Warm to 500 mK,
push, see flow, but smaller.
Seq. AJ - AM
500
360
61
This suggests There is indeed temperature and
pressure dependence to the flow. In this
pressure regime, something may change between 500
mK and 600 mK. Passing 600 mK seems to change
things. We doubt that this is due to annealing.

Seq. AJ - AM
62
There is indeed temperature and pressure
dependence to the flow. In this pressure regime,
something changes between 500 mK and 600 mK.
Passing 600 mK changes things. We doubt that
this is due to annealing. A possiblity is that
we are seeing evidence for hysteretic behavior.
Seq. AJ - AM
44
63
Another sequential experiment BS - BU BS
Create sample at 400 mK, push, observe flow BT
Warm to 547 mK, push, see no flow BU Cool to
398 mK, push, see flow, much like BS

Seq. BS - BU
550
400
64
So, if we think in terms of a simple superfluid
phase diagram this picture may be too simple
No Flow
Flow
65
So, if we think in terms of the most
recent experiments we have done we are led to
think that maybe we have
No Flow
Hysteretic Region
Flow
No Flow
Flow
66
So, if we think in terms of the most
recent experiments we have done we are led to
think that maybe we have
No Flow
Hysteretic Region
No Flow
No Flow
Flow
67
So, if we think in terms of the most
recent experiments we have done we are led to
think that maybe we have
No Flow
AJ-AM
Hysteretic Region
Flow
Flow
Flow
Flow
68
So, if we think in terms of the most
recent experiments we have done we are led to
think that maybe we have
No Flow
AR-AS-AT
Hysteretic Region
No Flow
No Flow
Flow
Flow
69
So, if we think in terms of the most
recent experiments we have done we are led to
think that maybe we have
No Flow
AR-AS-AT AU-AV
Hysteretic Region
No Flow
Flow
No Flow
Flow
Flow
Flow
70
So, if we think in terms of the most
recent experiments we have done we are led to
think that maybe we have
No Flow
BS-BU-BT
Hysteretic Region
Flow
No Flow
Flow
Flow
71
So, if we think in terms of the most
recent experiments we have done we are led to
think that maybe we have
No Flow
Hysteretic Region
No Flow
No Flow
Flow
72
Flow in Liquid channels? Should remain above 1.1
K (presuming the liquid channel does not anneal
away). At the pressures we have studied, no long
term flow is ever seen above 600 mK, under any
conditions. Should be pressure dependent. Yes,
it is. Should be in samples at various temps.
No, T gt 600 mK May depend on the specific
sample. Yes, it does. Should remain after a
cycle in temperature (presuming the liquid
channel does not anneal away). Not if the cycle
exceeds roughly 550 mK.
73
Flow along dislocations, grain boundaries? May
have a temperature at which behavior changes
that depends on pressure. Yes, it does. Should
be pressure dependent. Yes, it is. May depend
on the specific sample. Yes, it does. Could be
hysteretic. Possible evidence for this.
74
Plastic flow? Would not likely result in a
linear change in P2 or C1, C2 as a function of
time. Probably not plastic flow. Related
phenomena Frost Heave. Would likely result in
a changing differential pressure to be recorded
on C1 and C2, which is not observed. Frost heave
is a small effect at low pressure and low
melting temperature such as we have. Probably
not frost heave.
Hiroi et al, Phys Rev. B 40, 6581 (1989)
75
Relationship to other work? We need to get
colder to establish this. (Frankly, we are
frustrated by our apparatus difficulties.) We
could be seeing early-stage behavior (note
that finite NCRI is seen above 200 mK). Some of
the behavior may be consistent with the lack of
good thermal contact between defects and the
lattice. We can attempt to check this by
imposing temperature steps during flows.
S. Soyler et al, in preparation
76
Conclusions We have seen clear evidence for
the flow of helium atoms though a cell that is
filled with solid 4He in the hcp region of the
phase diagram. Growth from superfluid or blocked
capillary shows qualitatively similar
behavior. We believe that there is evidence to
suggest that liquid channels of the sort
reported by Sasaki et al. may not be responsible
for the behavior that we see. Not yet proven as
present, hysteresis is consistent with the
observations. So is defect-lattice thermal
contact. Our experiments continue. Note Our
technique will work for pressures that allow
helium to remain liquid in a porous material.
77
Thank you.