Anomalous Behavior of Solid Helium Under Inhomogeneous Conditions B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy.

Anomalous Behavior of Solid Anomalous Behavior of Solid Helium Under Inhomogeneous Helium Under Inhomogeneous

Conditions Conditions

B. Verkin Institute for Low Temperature Physicsand Engineering of the National Academy of

Sciences of Ukraine, Kharkov

E.Rudavskii

OutlineOutline Observation of a disordered (glassy) Observation of a disordered (glassy)

phase in solid phase in solid 44He in the supersolidity He in the supersolidity regionregion

Anomalous fast mass transfer in solid Anomalous fast mass transfer in solid 33He-He-44He mixturesHe mixtures

Formation of liquid droplets during Formation of liquid droplets during the BCC-HCP transition in solid heliumthe BCC-HCP transition in solid helium

Thermodynamic measurements in solid Thermodynamic measurements in solid 44HeHe

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

Specific Heat MeasurementsSpecific Heat Measurements

- 1952- F.J.Webb et al, T=0.6-1.4 K, V=18.3-20.6 cm1952- F.J.Webb et al, T=0.6-1.4 K, V=18.3-20.6 cm33/mole/mole;;- 1962- E.C.Heltems,C.A.Swenson,T=0.3-2 K, V=12,8-19.6 - 1962- E.C.Heltems,C.A.Swenson,T=0.3-2 K, V=12,8-19.6 cmcm33/mole;/mole;- 1964- J.P.Frank, - 1964- J.P.Frank, T=1.3-4 K, V=10,8-16.3cmT=1.3-4 K, V=10,8-16.3cm33/mole;/mole; - 1965- D.O.Edwards, R.C.Pandorf, - 1965- D.O.Edwards, R.C.Pandorf, T=0.1- 4 K, T=0.1- 4 K, V=16.9-20.9cmV=16.9-20.9cm33/mole/mole;;..- 1966- G.Alhers, - 1966- G.Alhers, T=1.38-2.7 K, V=13.73-15.1cmT=1.38-2.7 K, V=13.73-15.1cm33/mole;/mole;- 1970- W.R.Gardner et al, - 1970- W.R.Gardner et al, T=0.35-1.8 K, V=20.45-20.96cmT=0.35-1.8 K, V=20.45-20.96cm33/mole/mole;;- 1975- S.Castles, E.D.Adams, - 1975- S.Castles, E.D.Adams, T=0.025-TT=0.025-Tmeltmelt, V=19.4-20.5cm, V=19.4-20.5cm33/mole;/mole;- 2005- A.C.Clark, M.Chan, 2005- A.C.Clark, M.Chan, T=0.08-0.3 K, P=39-50 bar; T=0.08-0.3 K, P=39-50 bar; (This data was analyzed by A.Balatsky et al (2006)(This data was analyzed by A.Balatsky et al (2006) .Recent works (2007) – X.Lin, A.Clark, and M.H.W.Chan, T=0.04-0.5 K. - H.Maris and S.Balibar, (analysis of phonon contribution).

ResultsResults

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

Pressure measurementsPressure measurements

1990 - E.Adams, M.Meisel (Univ.Florida) T1990 - E.Adams, M.Meisel (Univ.Florida) Tminmin=1mK, P=26 bar.=1mK, P=26 bar.

1991 - P.van de Haar, C.van Woerkeus, M.Meisel, R.Jochemsen, G.Frossati (Univ.Leiden) T=1.5 – 1991 - P.van de Haar, C.van Woerkeus, M.Meisel, R.Jochemsen, G.Frossati (Univ.Leiden) T=1.5 – 120 mK, P=26 bar, melting curve120 mK, P=26 bar, melting curve

2006-2007 - I.Todoshchenko, H.Alles, J.Bueno, H.Junes, A.Parshin, V.Tsepelin (Helsinki Univ.) T= 2006-2007 - I.Todoshchenko, H.Alles, J.Bueno, H.Junes, A.Parshin, V.Tsepelin (Helsinki Univ.) T= 80-400 mK, melting curve80-400 mK, melting curve

No indication of anomalous behaviorNo indication of anomalous behavior

;

i

ii

V V

C

T

P

2007 - New experiment2007 - New experiment::

V.Grigor’ev, V.Maidanov, V.Rubanskii, S.Rubets, V.Grigor’ev, V.Maidanov, V.Rubanskii, S.Rubets, E.Rudavskii. A.Rybalko, Ye.Syrnikov, V.TikhiiE.Rudavskii. A.Rybalko, Ye.Syrnikov, V.Tikhii, , Verkin Verkin Institute Low Temp.Phys., KharkovInstitute Low Temp.Phys., Kharkov

The main objective:The main objective:

Searching for glassy phase of Searching for glassy phase of 44He in the supersolidity He in the supersolidity regionregion through precise barometry in the crystals of through precise barometry in the crystals of various qualityvarious quality

);()()()( TPTPTPPTP otherphvaco

Mei-Gruneisen equationMei-Gruneisen equation::

Advantages:Advantages:-There is no contribution equivalent to that -There is no contribution equivalent to that of an empty calorimeterof an empty calorimeterHigh-precision pressure measurements in High-precision pressure measurements in solid 4He (~10solid 4He (~10-5-5 bar) bar)

The relation between pressure and specific heat:The relation between pressure and specific heat:

Experimental cellExperimental cell

Cell: Ø9mm, h=1.5mm. Thermal relaxation time 30 s at T=100mK .Accuracy of pressure measurements ~10-5 bar.

23 crystals; T= 40 mK- Tmelt; P=26-43 bar.

Experimental conditionsExperimental conditions

0,01 K

0,7 K

1 K

He4

He4

Pumping

N2

4,2 K

He4

ProcedureProcedure

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

Typical temperature dependence of Typical temperature dependence of pressurepressure

(High temperatures)(High temperatures)

0 2 4 6 8 10

0,0

0,1

0,2

0,3

Pvac

Pph

P-P

0,ba

r

T4,K4

1,190 1,41 1,57 1,68 T,K

Pexp

((Ye.Vekhov, V.Grigor’ev et al, 2007Ye.Vekhov, V.Grigor’ev et al, 2007))

P(T) – PP(T) – Po o = P= Pvacvac(T) + P(T) + Pphph(T)(T)PP00 is pressure at T=0 is pressure at T=0

Phonon contributionPhonon contribution::

;5

3)(

3

44

Dph

TR

VTP

);exp()31()()( 3

T

QR

VQ

T

Q

TTP VQ

VVvac

Vacancy contribution Vacancy contribution (J.Hetherington,1978(J.Hetherington,1978):):

The molar volume dependence of The molar volume dependence of vacancy activation energy and Debye vacancy activation energy and Debye

temperaturetemperature

14 16 18 20 22 24

20

30

40

50

60

70

10

20

30

b)

D,K

V, cm3/mol

a)

QV,K

Universal molar Universal molar volume dependence of volume dependence of QQvv and and

for for 44He, He, 33He-He-44He He mixtures and BCC mixtures and BCC 33He He at the constant values at the constant values of the Gruneisen of the Gruneisen parameters.parameters.

For For 33He-He-44He mixtures the He mixtures the valuesvalues

of Debye temperature wereof Debye temperature were

obtained for the first timeobtained for the first time

D

Typical temperature dependence of Typical temperature dependence of pressurepressure

(Low temperatures )(Low temperatures )

0,1 0,2 0,3 0,4 0,5

0,0000

0,0005

0,0010

0,0015

0,0020

0,0025

P-P

0,b

ar

T, K

Pexp

Pglass

Pph

At T<0.5 K:At T<0.5 K:

PPexpexp(T) – P(T) – P00= P= Pphph + + PPgg

PPphph = a = aphph T T44

PPgg = a = agg T T22

Finding the parameters Finding the parameters a agg and and aaphph

(P(Pexpexp – P – P00) / T) / T22 = =

= a= agg + a + aphphTT22;;

До отжига

For 23 samples studied: aFor 23 samples studied: ag g = (1.5 – 4)10= (1.5 – 4)10-3-3 bar/Kbar/K22

Annealing and RelaxationAnnealing and Relaxation

55 typical regimestypical regimes:: 1- an initial state;1- an initial state; 2- a large increase in T2- a large increase in T

and a small increase in P;and a small increase in P; 3 – a dramatic drop in 3 – a dramatic drop in

pressure;pressure; 4 – a slow relaxation of 4 – a slow relaxation of

pressure;pressure; 5 – a new equilibrium state: 5 – a new equilibrium state:

T returns to its initial value T returns to its initial value andand aa huge difference in huge difference in pressure (~2 bar).pressure (~2 bar).

0,01 0,1 1 100

500

1000

1500

2000

T, m

K

t, hour

1 2 3 4

a

b

5

41

42

43

44

P,

bar

Metastable liquid/glass drops,Metastable liquid/glass drops,traped in ‘pockets’ during fast traped in ‘pockets’ during fast crystallization.crystallization.Amount of liquid necessary to Amount of liquid necessary to explain the effect is ~5%explain the effect is ~5%

Annealing influenceAnnealing influence

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35

0,000

0,002

0,004

0,006

0,008

0,010

0,012

(P-P

0)/T

2 , bar

/K2

T2, К2

before

after annealing

Before annealingBefore annealing

aagg= 2.7 mbar/K= 2.7 mbar/K22

After annealingAfter annealing

aagg < 0.1 mbar/K < 0.1 mbar/K22

The glassy contribution to the pressure can be The glassy contribution to the pressure can be eliminated in well-annealed crystalseliminated in well-annealed crystals

Conclusion 1Conclusion 1

The TThe T2 2 contribution to the pressure is contribution to the pressure is observed in the supersolid region. It observed in the supersolid region. It can be attributed to formation of the can be attributed to formation of the glassy phase.glassy phase.

In well-annealed crystals the glassy In well-annealed crystals the glassy contribution can be eliminated.contribution can be eliminated.

A dramatic pressure decrease (~ 2 A dramatic pressure decrease (~ 2 bar) is observed under annealingbar) is observed under annealing

Solid Solid 33He-He-44He mixtures: observation of He mixtures: observation of anomalously fast mass transportanomalously fast mass transport

Systems under investigationSystems under investigation

Dilute Mixtures of Dilute Mixtures of 33He inHe in

44HeHe

Coherent band Coherent band

motion of impurities motion of impurities (quantum diffusion),(quantum diffusion),

Andreev-Lifshits model.Andreev-Lifshits model.

After separation: After separation:

Matrix – Matrix – 44He (HCP),He (HCP),

Inclusions – Inclusions – 33He (BCC).He (BCC).

Concentrated Concentrated MixturesMixtures

Localization of the Localization of the impurities impurities (Yu.Kagan, (Yu.Kagan, L.Maksimov,1983):L.Maksimov,1983):

δε > Δ; (δε ~ xδε > Δ; (δε ~ x4/34/3).).

At x>xAt x>xc c ~10% ~10% 33He: He: should be no mass should be no mass transfertransfer

Dilute Mixtures of Dilute Mixtures of 44He in He in 33HeHe

Incoherent tunnel motionIncoherent tunnel motion

(random distribution of 3He (random distribution of 3He nuclear spins).nuclear spins).

After separation:After separation:

Matrix – Matrix – 33He (BCC),He (BCC),

Inclusions – Inclusions – 44He (HCP).He (HCP).

Adjacent Problem: What can cause the Adjacent Problem: What can cause the 33He He impurities?impurities?

Measurements of the pressure variation Measurements of the pressure variation during phase transitionduring phase transition

1 – Phase separation:1 – Phase separation:

P(t)= (PP(t)= (Pf f –P–Pii) exp (-t/) exp (-t/))

2 – homogenization:2 – homogenization:- very fast process;very fast process;- P(t) depends on TP(t) depends on Tff-T-Tii..

)1(4.0 xxVE (W.Mullin,1968). At V=const: ;MVEV

EP PaxP ,106

xx00 =2,05 % =2,05 %33He; VHe; Vmm= 20,27cm= 20,27cm33/mole./mole.

Giant asymmetry of separation and homogenizationGiant asymmetry of separation and homogenization

Time variation of pressure for different Time variation of pressure for different TTff-T-Tii

a)a) TTii=103 mK; T=103 mK; Tff=110mK.=110mK.

effeff= 1200s.= 1200s.

b)b) TTii=103 mk; T=103 mk; Tff=150mK.=150mK.

effeff= 850s.= 850s.

c)c) TTii=103mK; T=103mK; Tff=570mK.=570mK.

effeff= 150s.= 150s.

Suggestion:Suggestion:Such fast mass transport Such fast mass transport might be provided by might be provided by nondiffusive ballistic processnondiffusive ballistic process

The rate of homogenization does not depend on initial The rate of homogenization does not depend on initial concentration xconcentration x00

XX00=2.6% =2.6% 33HeHe

XX00=34.2% =34.2% 33HeHe

XX00=87.1% =87.1% 33HeHe

V.Grigorev, V.Maidanov, V.Grigorev, V.Maidanov, A.Penzev,A.Penzev,S.Rubets, E.Rudavskii, S.Rubets, E.Rudavskii, A.Rybalko, LTP, 2005.A.Rybalko, LTP, 2005.

-The character of all The character of all curves is the samecurves is the same sep sep / / homhom > 300 > 300

-The fast homogenization The fast homogenization can not be explained by can not be explained by ballistic processballistic process

--Very fast mass transport is observed Very fast mass transport is observed under transition from phase separated to under transition from phase separated to homogeneous state of solid 3He-4He homogeneous state of solid 3He-4He mixtures.mixtures.- - Probably we a dealing with a new Probably we a dealing with a new unknown mechanism of mass transfer.unknown mechanism of mass transfer.What is the nature of the mechanism?What is the nature of the mechanism?

- - In concentrated In concentrated 33He-He-44He mixtures, theory He mixtures, theory predicts that diffusion is depressed due to predicts that diffusion is depressed due to localization of impuritieslocalization of impurities but experiments but experiments showshow intense mass transfer.intense mass transfer.

Conclusion Conclusion 22

What happens in solid helium at the interface What happens in solid helium at the interface region?region?

1.3 1.4 1.5 1.6 1.7 1.8

26

28

30

32

Liquid He

BCC

Pre

ss

ure

, b

ar

Temperature, K

HCP

NMR experiment

- Two strongly different crystalline structures;

- The ease of formation of defects in the interface region;

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) f=3.6MHz; probe pulses 90o- -180o.

Experimental conditions: x= 1.05 %3He; T= 1.3 – 1.9 K;

BCC-HCP transition in solid BCC-HCP transition in solid heliumhelium

Spin-echo decaySpin-echo decay

)3

2exp( 322

ii

i DG

An additional diffusion process is clearly defined at small . The corresponding D'xdepends on (bounded diffusion).

=10ms

0.3ms

25ms

52ms

1966,....

13

2

2

4'

CottsMRandWayneCR

D

aB

AD

aD

xxx

The bounded diffusion

The fitting parameters: a=(2±0.5)10-3 cm;

Dx=(4±2)10-

4cm2/s.

The diffusion echo decay was identified for coexisting phases – BCC and HCP.

The Carr-Pursell method: the echo amplitude The Carr-Pursell method: the echo amplitude h h at the distance 2at the distance 2::

h/hh/h00 = =

The diffusion coefficients for each of the The diffusion coefficients for each of the coexisting phasescoexisting phases

Along the BCC-HCP phase equilibrium line

Along the melting curve

HCP

BCC

New phase

BCC

HCP

New Phase

Pressure measurements during the HCP-BCC Pressure measurements during the HCP-BCC transitiontransition

(N.Mikhin, E.Rudavskii, Ye.Vekhov, JLTP, 2007)(N.Mikhin, E.Rudavskii, Ye.Vekhov, JLTP, 2007)

1.59 1.62 1.65 1.6828.0

28.2

28.4

28.6

1.4 1.5 1.6 1.726

27

28

29

30 5

43

2

P,b

ar

T,K

1

Liquid He

BCC

HCP

1,56 1,60 1,64 1,68

27,8

28,0

28,2

28,4

1,4 1,5 1,6 1,7 1,826

27

28

29

30

5

4

3

2

1

P,b

ar

T,K

Liquid He

BCC

HCP

0 100 200 300 400 500 60028.0

28.1

28.2

28.3

1.62

1.64

1.66

1.68

P,b

ar

time,s

b)

a)

54

32

T,K

1

0 50 100 150 200 250 300 35028.0

28.2

28.4

28.6

1.62

1.64

1.66

1.68

1.70

P,b

ar

time,s

54

3

2

b)

T,K

a)

1

Well-annealed crystal Non-annealed crystal

Monotonic exponential time dependence of pressure at each heating step

The pressure drops by 0.2at (p.23)( Crystallization of liquid droplets formed during the HCP-BCC transition)

Conclusion 3Conclusion 3

An additional diffusion process with An additional diffusion process with very high diffusion coefficient Dvery high diffusion coefficient Dxx is is observed during the BCC-HCP observed during the BCC-HCP transition. The diffusion is spatially transition. The diffusion is spatially restricted. restricted.

In non-annealed crystals a sharp In non-annealed crystals a sharp pressure drop is observed during the pressure drop is observed during the HCP-BCC transition.HCP-BCC transition.

We suggest that liquid droplets We suggest that liquid droplets appear on the HCP-BCC interfaceappear on the HCP-BCC interface

SummarySummary

New effects have been observed in solid helium New effects have been observed in solid helium which may be of relevance to the supersolid which may be of relevance to the supersolid problem:problem:

TT22 contribution to the pressure in non- contribution to the pressure in non-annealed helium crystals.annealed helium crystals.

Very fast mass transfer during transition of Very fast mass transfer during transition of phase-separated phase-separated 33He-He-44He mixtures into He mixtures into homogeneous state.homogeneous state.

Anomaly in kinetics of the BCC-HCP transition Anomaly in kinetics of the BCC-HCP transition attested that liquid droplets are formed attested that liquid droplets are formed