Ryuji Nomura
H. Matsuda, A. Ochi, R. Isozaki, and Y. Okuda
Avalanche Crystallization of 4He in Aerogel
Tokyo Institute of Technology
By NASA
Aerogel: ~ 98% high porosity,
very transparent,
suitable for visualizing the dynamics in it.
98% model aerogel
By Haard
30 nm
3 nm
0. Introduction
No viscous effect in pores.
No release of latent heat.
New quantum phenomena may emerge
at very low temperatures.
Effect of quenched disorder, which induces
complex energy landscape, on the crystallization
can be revealed down to absolute 0 K.
We are interested in the dynamics of the first order phase transition in disordered media at very low temperatures.
Why 4He?
Variable volume cellPlow
Phigh
P (
atm
)
T (K)
superfluidnormal fluid
bcc
hcp
T (K)
superfluidnormal fluid
solid
bcc
hcp
aerogel
Crystallization at low temperatures can be investigated systematically.
①②
P (
bar
)
bulkaerogel
Bulk He crystal
Aerogel is in a thin glass tube and has a contact
with the bulk crystals on the upper surface.
10mm
8mm
1mm
open surface
Porosities: 96% made by Panasonic
98% made by Pollanen and Halperin
at Northwestern University
T (K)
superfluidnormal fluid
solid
1. Crystallization of 4He in aerogel by pressurization
①
P (
bar
)
170 mK 850 mK
Crystallization in 98% aerogel
(50 times faster replay) (100 times faster replay)
Avalanche at low
temperatures
Creep at high
temperatures
Transition in a growth mode
98%
■ creep
▲ coexist
● avalanche
Dynamical phase diagram
2.0x10-3
1.5
1.0
0.5
0.0
press
uriza
tion r
ate [
bar/
s]
1.20.80.40.0
T [K]T (K)
pre
ssu
riza
tio
n r
ate
(b
ar/
s)
Competition between thermal fluctuation and disorder
Nomura et al. PRL 101, 175703 (2008)
4He crystals are formed deep in the aerogel.
Outer bulk crystal has to be melted by the stress,
and enter the aerogel in the superfluid state.
Mass has to be transferred for the crystallization.
Avalanche (quantum?) Creep (thermal?)
t
P
t
P
a b c
d e f
a b c
d e f
Nucleation probability
The critical overpressure was
measured 50 times at constant
temperature.
Critical overpressure at which the first
crystal appeared.
Clear metastability:
not instability but nucleation
1.0
0.8
0.6
0.4
0.2
0.480.440.400.36
P[bar]
200mK1K
P1/2 P1/2
0 1000 100t (s)
P
(bar)
0 100
P1/2
0.48
0.46
0.44
0.42
0.40
P
1/2[b
ar]
1.21.00.80.60.40.2
T[K]
T < 600 mK
Quantum nucleation700 mK < T < 1 K
Thermal nucleation
T > 1 K dissipation effect
on thermal nucleation?
Avalanche: quantum nucleation Creep: thermal activation
mean critical overpressure in 98% aerogel
Avalanche Creep
Matsuda et al. PRE (2013)
Power law in the avalanche size distribution in 98% aerogel
1
2
4
6
810
2
4
6
8100
N
2 3 4 5 6 7 8 90.1
2 3 4 5
S (mm2)
200 mK 400 mK 575 mK
cS
SASN exp
= 3
Nomura et al., JPSJ 80, 123601 (2011).
Editors’ choice
Self-organized
criticality
(SOC) in
quantum growth
cS
SASN exp
Sc decrease as approaching the transition.
(due to dissipation?)
Looks like a crossover.
Avalanche Creep
8.03
2'
2.5
2.0
1.5
1.0
0.5
0.0
0.60.40.2
T (K)
0.5
0.4
0.3
0.2
0.1
0.0
Sc (m
m2)
2. Crystallization of 4He in aerogel on cooling
Due to “supersolidity”?
T (K)
superfluidnormal fluid
solid
②
P (
bar
)
Crystallization of 4He in 96% aerogel on cooling
100 times faster
b
c
a
def
completion
Crystallization of 4He in 96% aerogel on cooling
beginning
Mass supply from the surrounding bulk crystals
into aerogel is needed to grow crystal in aerogel,
even without pressurization.
28.4
28.0
27.6
27.2
P (
bar)
0.70.60.50.40.3
T (K)
Crystallization rate and Pressure of bulk crystals on cooling
Mass flowed from the surrounding
bulk crystals into aerogel.
1. What is the driving force for crystallization on cooling?
TSSP slsl
11
Equilibrium crystallization pressure is temperature independent
at low temperatures in 4He.
Usually neglected
2. How mass is transported in bulk 4He crystals?
May be related to the so called “supersolidity”.
But, occurrence of mass flows in 4He crystal was reported by
Hallock et al. (PRL 2008) by direct flow measurements.
Mass flow experiment
Original torsional oscillator experiment by Kim and Chan
(Nature 2004) was retracted.
Tflow = 630 mK
Superfluid components at a core of edge dislocation
Path integral Monte Carlo technique
Boninsegni et al., PRL 99, 035301 (2007)
This issue has not been is settled, yet.
Crystallization diagram in aerogel on cooling
TgrowTinitial
Pc
Tgrow < Tflow = 630 mK
by Hallock
Summary
Crystallization in aerogel is via creep at high T and via
avalanche at low T by pressurization.
Creep growth is thermal activation and avalanche growth is
macroscopic quantum tunneling from both crystallization rate
and nucleation probability measurements.
Avalanche size follows a power low: Self-organized
critical states in macroscopic quantum tunneling.
Crystallization on cooling was observed.
Tgrow was lower than Tflow.
Tgrow had a anomalous pressure dependence.
Tgrow had a anomalously wide distribution; large supercooling
in nucleation process.
This can be an observation of a new crystallization mode as
“supersolidity”-assisted crystallization in pores.