Post on 12-Sep-2018
21/09/2011 CryoCourse Chichiliane
Experimental set-ups in 3He and 4He probes
81
I:,'.%+'&#-$(/'#>",(J. Kacmarcik, Z. Pribulova, et al. , SAS, Kosice
21/09/2011 CryoCourse Chichiliane
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 ...
21/09/2011 CryoCourse Chichiliane
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!#
21/09/2011 CryoCourse Chichiliane
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
21/09/2011 CryoCourse Chichiliane
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
21/09/2011 CryoCourse Chichiliane
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
21/09/2011 CryoCourse Chichiliane
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)
21/09/2011 CryoCourse Chichiliane
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)
21/09/2011 CryoCourse Chichiliane
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!
21/09/2011 CryoCourse Chichiliane
addenda contribution
90
C
Pac Tac
Tbase
K cadd+
Tac =P
Ktanh(L/l) + jC!
}addenda
especially important in pressure cellwhere Cadd is large
21/09/2011 CryoCourse Chichiliane
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
21/09/2011 CryoCourse Chichiliane
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
21/09/2011 CryoCourse Chichiliane
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
21/09/2011 CryoCourse Chichiliane
AC-Calorimetry in Capacitor-Bank-Driven Pulsed Fields
94
coll: Y. Kohama and M. Jaime, Los Alamos National LaboratoryZ"$/'1(+-5&'43(['$1/(-#(NBON(
Long pulsed magnet�
Short & Mid pulsed magnet�
21/09/2011 CryoCourse Chichiliane
AC microcalorimetry in pulsed field :
An external time constant 1ms : - adaptation of thermal link K
An internal time constant 100 μs : ) - choice of fast enough thermometer) ) - sample mounting (glue)) ) - heater in good thermal contact) )Keeping a good signal/noise ratio with such a bandwidth !!!!
95
Challenges to build a calorimeter :
21/09/2011 CryoCourse Chichiliane
Some thermodynamics : magneto-caloric effect and Cp (H)
96
9*+'(#F'.+*16&-+%3/(J(+-5&'#*>3-$*.%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�
21/09/2011 CryoCourse Chichiliane
Sample holder
97
9-+,$'(F*$1'.(
Heater (P)�
Thermal link�
Bath�
T (Kelvin)
21/09/2011 CryoCourse Chichiliane
frequency tests
98
7.'D"'&36(#'/#/J(
T AC!f
(a.u.)
Sr3Cr2O8
4K
C=1.1 10-8 J/K
21/09/2011 CryoCourse Chichiliane
tests in zero field
99
<'/#(%&(V'.*(['$1((3.6/#-$(*0(#.%-&5"$-.(-&40'.*+-5&'#(2C7'8E*!^?K(
!
400 Hz
2.5 K/s !!!!
C (a
.u.)
21/09/2011 CryoCourse Chichiliane
tests in moderate pulsed fields
100
<'/#/(%&(,"$/'1(['$1(
21/09/2011 CryoCourse Chichiliane
Thank you