Anomalous Behavior of Solid Helium Under Inhomogeneous Conditions

1
Anomalous Behavior of Solid Helium Under
Inhomogeneous Conditions
E.Rudavskii

• B. Verkin Institute for Low Temperature Physics
• and Engineering of the National Academy of
  Sciences of Ukraine, Kharkov

2
Outline

• Observation of a disordered (glassy) phase in
  solid 4He in the supersolidity region
• Anomalous fast mass transfer in solid 3He-4He
  mixtures
• Formation of liquid droplets during the BCC-HCP
  transition in solid helium

3
Thermodynamic measurements in solid 4He

• Two effects are expected - Anomaly associated
  with the transition (Lambda?)
• -
  Change in the temperature dependencies C(T), P(T)

• Specific Heat Measurements
• 1952- F.J.Webb et al, T0.6-1.4 K, V18.3-20.6
  cm3/mole
• - 1962- E.C.Heltems,C.A.Swenson,T0.3-2 K,
  V12,8-19.6 cm3/mole
• - 1964- J.P.Frank, T1.3-4 K, V10,8-16.3cm3/mole
  
• - 1965- D.O.Edwards, R.C.Pandorf, T0.1- 4 K,
  V16.9-20.9cm3/mole.
• - 1966- G.Alhers, T1.38-2.7 K,
  V13.73-15.1cm3/mole
• - 1970- W.R.Gardner et al, T0.35-1.8 K,
  V20.45-20.96cm3/mole
• - 1975- S.Castles, E.D.Adams, T0.025-Tmelt,
  V19.4-20.5cm3/mole
• 2005- A.C.Clark, M.Chan, T0.08-0.3 K, P39-50
  bar
• (This data was analyzed by A.Balatsky
  et al (2006) .
• Recent works (2007) X.Lin, A.Clark, and
  M.H.W.Chan, T0.04-0.5 K.
• - H.Maris and S.Balibar,
  (analysis of phonon contribution).

Results - A broad specific heat peak was
observed near 75 mK - No reliable indication of
linear contribution to heat capacity
4

• Pressure measurements
• 1990 - E.Adams, M.Meisel (Univ.Florida)
  Tmin1mK, P26 bar.
• 1991 - P.van de Haar, C.van Woerkeus, M.Meisel,
  R.Jochemsen, G.Frossati (Univ.Leiden) T1.5
  120 mK, P26 bar, melting curve
• 2006-2007 - I.Todoshchenko, H.Alles, J.Bueno,
  H.Junes, A.Parshin, V.Tsepelin (Helsinki Univ.)
  T 80-400 mK, melting curve
• No indication of anomalous behavior

5
2007 - New experiment V.Grigorev, V.Maidanov,
V.Rubanskii, S.Rubets, E.Rudavskii. A.Rybalko,
Ye.Syrnikov, V.Tikhii, Verkin Institute Low
Temp.Phys., Kharkov The main objective Searching
for glassy phase of 4He in the supersolidity
region through precise barometry in the crystals
of various quality
Advantages -There is no contribution equivalent
to that of an empty calorimeter High-precision
pressure measurements in solid 4He (10-5 bar)
The relation between pressure and specific heat
Mei-Gruneisen equation
6
Experimental cell
Cell Ø9mm, h1.5mm. Thermal relaxation time 30
s at T100mK . Accuracy of pressure measurements
10-5 bar. 23 crystals T 40 mK- Tmelt
P26-43 bar.
7
Experimental conditions

• Procedure
• - Crystallization of the sample (capillary
  blocking technique)
• - Fast cooling at a maximum possible rate down to
  1 K
• - Step-like cooling to temperatures below 100 mK
• - Isothermal ageing for several hours at a
  minimum temperature
• - Heating the sample in a step-like manner
• - Annealing the sample near the melting point
• - Repeating the above procedure

8
Typical temperature dependence of pressure(High
temperatures)

• (Ye.Vekhov, V.Grigorev et al, 2007)
• P(T) Po Pvac(T) Pph(T)
• P0 is pressure at T0
• Phonon contribution

Vacancy contribution (J.Hetherington,1978)
9
The molar volume dependence of vacancy activation
energy and Debye temperature

• Universal molar volume dependence of Qv and
• for 4He, 3He-4He mixtures and BCC 3He at the
  constant values of the Gruneisen parameters.
• For 3He-4He mixtures the values
• of Debye temperature were
• obtained for the first time

10
Typical temperature dependence of pressure(Low
temperatures )

• At Tlt0.5 K
• Pexp(T) P0 Pph Pg
• Pph aph T4
• Pg ag T2

11
Finding the parameters ag and aph
?? ??????

• (Pexp P0) / T2
• ag aphT2

For 23 samples studied ag (1.5 4)10-3
bar/K2
12
Annealing and Relaxation

• 5 typical regimes
• 1- an initial state
• 2- a large increase in T
• and a small increase in P
• 3 a dramatic drop in pressure
• 4 a slow relaxation of pressure
• 5 a new equilibrium state T returns to its
  initial value and a huge difference in pressure
  (2 bar).

Metastable liquid/glass drops, traped in
pockets during fast crystallization. Amount of
liquid necessary to explain the effect is 5
13
Annealing influence
Before annealing ag 2.7 mbar/K2 After
annealing ag lt 0.1 mbar/K2
The glassy contribution to the pressure can be
eliminated in well-annealed crystals
14
Conclusion 1

• The T2 contribution to the pressure is observed
  in the supersolid region. It can be attributed to
  formation of the glassy phase.
• In well-annealed crystals the glassy contribution
  can be eliminated.
• A dramatic pressure decrease ( 2 bar) is
  observed under annealing

15
Solid 3He-4He mixtures observation of
anomalously fast mass transport
Adjacent Problem What can cause the 3He
impurities?

• Systems under investigation

• Dilute Mixtures of 3He in 4He
• Coherent band
• motion of impurities (quantum diffusion),
• Andreev-Lifshits model.
• After separation
• Matrix 4He (HCP),
• Inclusions 3He (BCC).

• Concentrated Mixtures
• Localization of the impurities (Yu.Kagan,
  L.Maksimov,1983)
• de gt ? (de x4/3).
• At xgtxc 10 3He should be no mass transfer

• Dilute Mixtures of 4He in 3He
• Incoherent tunnel motion
• (random distribution of 3He nuclear spins).
• After separation
• Matrix 3He (BCC),
• Inclusions 4He (HCP).

16
Measurements of the pressure variation during
phase transition
(W.Mullin,1968). At Vconst
Giant asymmetry of separation and homogenization
x0 2,05 3He Vm 20,27cm3/mole.

• 1 Phase separation
• ?P(t) (Pf Pi) exp (-t/?)
• 2 homogenization
• very fast process
• P(t) depends on Tf-Ti.

17
Time variation of pressure for different Tf-Ti

• Ti103 mK Tf110mK.
• ? eff 1200s.
• Ti103 mk Tf150mK.
• ? eff 850s.
• Ti103mK Tf570mK.
• ? eff 150s.

Suggestion Such fast mass transport might be
provided by nondiffusive ballistic process
18
The rate of homogenization does not depend on
initial concentration x0

• V.Grigorev, V.Maidanov, A.Penzev,
• S.Rubets, E.Rudavskii, A.Rybalko, LTP, 2005.
• The character of all curves is the same
• ?sep / ? hom gt 300
• The fast homogenization can not be explained by
  ballistic process

X02.6 3He
X034.2 3He
X087.1 3He
19
Conclusion 2
-Very fast mass transport is observed under
transition from phase separated to homogeneous
state of solid 3He-4He mixtures.
- Probably we a dealing with a new unknown
mechanism of mass transfer. What is the nature of
the mechanism?
- In concentrated 3He-4He mixtures, theory
predicts that diffusion is depressed due to
localization of impurities but experiments show
intense mass transfer.
20
What happens in solid helium at the interface
region?
BCC-HCP transition in solid helium
- Two strongly different crystalline
structures - The ease of formation of defects
in the interface region
NMR experiment
A.Polev, N.Mikhin, E.Rudavskii, JLTP, 2002. The
aim identification of diffusion processes in
each of the coexisting phases. Method pulsed
NMR technique (spin echo)
f3.6MHz probe pulses 90o- ?
-180o. Experimental conditions x 1.05 3He
T 1.3
1.9 K
21
Spin-echo decay
The Carr-Pursell method the echo amplitude h at
the distance 2?h/h0
0.3ms
The diffusion echo decay was identified for
coexisting phases BCC and HCP.
?10ms
25ms
An additional diffusion process is clearly
defined at small ?. The corresponding D'x depends
on ? (bounded diffusion).
52ms
The bounded diffusion
The fitting parameters a(20.5)10-3 cm

Dx(42)10-4cm2/s.
22
The diffusion coefficients for each of the
coexisting phases
Along the BCC-HCP phase equilibrium line
Along the melting curve
New phase
New Phase
BCC
BCC
HCP
HCP
23
Pressure measurements during the HCP-BCC
transition(N.Mikhin, E.Rudavskii, Ye.Vekhov,
JLTP, 2007)
Well-annealed crystal
Non-annealed crystal
The pressure drops by 0.2at (p.2?3) (
Crystallization of liquid droplets formed
during the HCP-BCC transition)
Monotonic exponential time dependence of pressure
at each heating step
24
Conclusion 3

• ? An additional diffusion process with very high
  diffusion coefficient Dx is observed during the
  BCC-HCP transition. The diffusion is spatially
  restricted.
• ? In non-annealed crystals a sharp pressure drop
  is observed during the HCP-BCC transition.
• ? We suggest that liquid droplets appear on the
  HCP-BCC interface

25
Summary

• New effects have been observed in solid helium
  which may be of relevance to the supersolid
  problem
• T2 contribution to the pressure in non-annealed
  helium crystals.
• Very fast mass transfer during transition of
  phase-separated 3He-4He mixtures into homogeneous
  state.
• Anomaly in kinetics of the BCC-HCP transition
  attested that liquid droplets are formed