Experimental set-ups in He and He...

21/09/2011 CryoCourse Chichiliane

Experimental set-ups in 3He and 4He probes

81

I:,'.%+'&#-$(/'#>",(J. Kacmarcik, Z. Pribulova, et al. , SAS, Kosice


a little math

82

C

Pac Tac

Tbase

K

C dT/dt + K (T-Tb) = P(or C dT/dt + K (T-Tb(ω))=0)

Steady-state solution:T=Tb+Tdc+Tacexp(jωt)

Tdc = P0/KTac=P1/(K+jCω)

discussion of limitations later ...


different regimes

83

Tac 0

Tb+Tdc

t

T

Tb

! << 1/"ext = K/C

Tb+Tdc

t

T

Tb

1/"ext << ! << 1 /"int #

Tb+Tdc

t

T

Tb

1/"int<< !#

Tac = P0

K + j C!# Tac = P0

K +j C!#Tac 0

Tb+Tdc

t

T

Tb

! << 1/"ext = K/C

Tb+Tdc

t

T

Tb

1/"ext << ! << 1 /"int #

Tb+Tdc

t

T

Tb

1/"int<< !#

Tac = P0

K + j C!# Tac = P0

K +j C!#Tac 0

Tb+Tdc

t

T

Tb

! << 1/"ext = K/C

Tb+Tdc

t

T

Tb

1/"ext << ! << 1 /"int #

Tb+Tdc

t

T

Tb

1/"int<< !#

Tac = P0

K + j C!# Tac = P0

K +j C!#Tac 0

Tb+Tdc

t

T

Tb

! << 1/"ext = K/C

Tb+Tdc

t

T

Tb

1/"ext << ! << 1 /"int #

Tb+Tdc

t

T

Tb

1/"int<< !#

Tac = P0

K + j C!# Tac = P0

K +j C!#


ac-calorimetry: Higher sensitivity

Hc1 in MgB2

iradiated KKBO

pulsed magnetic field 62T, 100ms

high pressure, diamond anvil pressure cell 15GPa

thin films

quantization of phonons (O. Bourgeois, CNRS-grenoble)

84


Phase : qualitative test for hysteresis !!!

85

tan (ϕ) = - Cω/K and ΔC > 0 implies < 0

in liquid crystals (many phases nematic, smectic,...)

obervation in ac-calorimetry :

2nd order transition: Δϕ < 0

1st order transition: Δϕ > 0 in FACT hysteresis


anomaly in the phase at Tc is NEGATIVE

86

1.54

1.56

1.58

1.6

1.62

-0.2

-0.1

0

0.1

0.2

80 85 90 95 100

C T

(J

.mol

-1K-2

)�� (°)

Température (K)

/Y-Arg


anomalous behavior of phase at vortex melting due probably to hysteresis

87

0

3

6

9

12

82 83

Tac = 12 mK� = 1 Hz

T (K)

C(H

) - C

(0)

/ T (m

J.m

ol -1

K -2

)(

(

0

0.04

0.08��

(°)

Y-Arg H = 5 T

82 83

Tac = 2 mK � = 6 Hz

T (K)82 83

Tac = 2 mK � = 1 Hz

T (K)


You measure X and Y (K and C) !!

88

can be used to measure thermal conductivity at the same time

c +�

Pac Tac

Tbase

L

c@T

@t

= @

2T

@x

2 with boundary conditions

l2 = jc! = L2 K

jC!thermal length

Tac =P

Ktanh(L/l)


You measure X and Y (K and C) !!

89

can be used to measure thermal conductivity at the same time

c +�

Pac Tac

Tbase

L

Tac =P

Ktanh(L/l)

at low f, Cω/K<<1: Tac = P/K

at intermediate f, both K and Cω/K

at high f: thermal effusivitymod Tac =

PpKC!


addenda contribution

90

C

Pac Tac

Tbase

K cadd+

Tac =P

Ktanh(L/l) + jC!

｝addenda

especially important in pressure cellwhere Cadd is large


Extreme conditions: resistive 30Tesla

91

9*+'(.'3'&#(.'/"$#/(%&(,&%341'(/",'.3*&1"3#*.J(7'89':;<'=>:?(",(#*(KL(<'/$-(8E=M(%&(NO)EP?(

(+*&*3.6/#-$(J(+�(QM(R5(-&1(0(S(=TUV(

6 8 10 12 14 167

8

9

10

11

12

CP/T

2 (mJ/

mol

K3 )

T (K)

H//ab

Ha(T) = 0

81216202428

6 8 10 12 14 167

8

9

10

11

12

T (K)

H//c

Ha(T) = 0

81216202428


Extreme conditions: pressure 15Gpa

92

E%3.*3-$*.%+'#.6(%&(W%-+*&1(B&H%$()'$$(8=Q(X,-?(

Pressure chamber

350 µm

Sample

Thermocouple!

Rubis!

Flattened wire!

Au

AuFe

Experimental principle

Laser!

Trigger at !!

Lock-In A.!

Optic fiber!

V " Tac = !P0

K + jC!

Chopper

0(�=MYUV


ideal tool to draw a phase diagramunder pressure

93

0

2

4

6

0

2

4

2 3 4 5 6 7 8 9 10

T(K)

(C/T

) eff (

unité

arb

itrai

re)

C/T

(J.mol -1.K

-2)

P = 0 kbar

21 kbar

11 kbar

5 kbar

3 kbar

0

2

4

6

8

10

12

0 20 40 60 80

T(K

)

P (kbar)

TN

TC

TL

AFM

FM

Expérience idéale pour établir rapidement un diagramme de phase

Détection des anomalies associées aux transitions de phase 0

2

4

6

0

2

4

2 3 4 5 6 7 8 9 10

T(K)

(C/T

) eff (

unité

arb

itrai

re)

C/T

(J.mol -1.K

-2)P = 0 kbar

21 kbar

11 kbar

5 kbar

3 kbar

0

2

4

6

8

10

12

0 20 40 60 80T

(K)

P (kbar)

TN

TC

TL

AFM

FM

Expérience idéale pour établir rapidement un diagramme de phase

Détection des anomalies associées aux transitions de phase

CeRu2Ge2


AC-Calorimetry in Capacitor-Bank-Driven Pulsed Fields

94

coll: Y. Kohama and M. Jaime, Los Alamos National LaboratoryZ"$/'1(+-5&'43(['$1/(-#(NBON(

Long pulsed magnet�

Short & Mid pulsed magnet�


AC microcalorimetry in pulsed field :

An external time constant 1ms : - adaptation of thermal link K

An internal time constant 100 μs : ) - choice of fast enough thermometer) ) - sample mounting (glue)) ) - heater in good thermal contact) )Keeping a good signal/noise ratio with such a bandwidth !!!!

95

Challenges to build a calorimeter :


Some thermodynamics : magneto-caloric effect and Cp (H)

96

9*+'(#F'.+*16&-+%3/(J(+-5&'#*>3-$*.%3(']'3#(-&1(),(8U?(

P = C dTdt + T

��S�H

�T

dHdt

dq = TdS = T�

�S�H

�T

dT + T�

�S�T

�H

dH

no heating

P = k (Tb –T)

MCE

ac heating

P = k (Tb –T) + Pac

Cp (H)

�TT /

��S�H

�T

dHdt

kTac = Pac

k+( �S�H )

TdHdt +jC�


Sample holder

97

9-+,$'(F*$1'.(

Heater (P)�

Thermal link�

Bath�

T (Kelvin)


frequency tests

98

7.'D"'&36(#'/#/J(

T AC!f

(a.u.)

Sr3Cr2O8

4K

C=1.1 10-8 J/K


tests in zero field

99

<'/#(%&(V'.*(['$1((3.6/#-$(*0(#.%-&5"$-.(-&40'.*+-5&'#(2C7'8E*!^?K(

!

400 Hz

2.5 K/s !!!!

C (a

.u.)


tests in moderate pulsed fields

100

<'/#/(%&(,"$/'1(['$1(


Thank you

Experimental set-ups in He and He...

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