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.