The measurement C = ΔQ ΔT 62
How to measure Cp? Principle : apply P, read T and time adiabatic : isolated sample and pt by pt C = quasi-adiabatic, continuous heating P = C dt/dt ΔQ ΔT relaxation : heat pulse, thermal link to T bath large relaxation, dual slope,... P modulation : alternative heating at ω T ac = K + jc! 63
very demanding T measurements!! DC/C 10-3 T = 9.104785 DT/T 10-3 and TIME calibrations of thermometers is a nightmare!! and fitting procedure heat capacity C (a.u.) 25 20 15 Texte 10 superconducting transition of Nb!T c = 50 mk, 10 pts in transition C = 18.78 (dt/dt) 5 T = 9.105 0 0 2 4 6 8 10 12 T (K) 64
Thermodynamic thermometers 65
Thermometers What is a good thermometer? primary / secondary accuracy resolution/sensitivity reproducibility easy to use time response 66
Thermometers actually used in low temperature laboratory!"#$%&'(&)*+,)&$%-&)'"'&+&). '()*+#,-*#./+0$($+.+0## 1232# 4.#156# 751# *<;+0=('A<=.)',#B)C+A#;()'.*# 89+#57## 9+#:-;(0#;0+**<0+# =-0>('#?#@+#0+*)*.(0*# 0/(A)<$DE0('#0+*)*.(0*# 4.#0+*)*.(0*#!""#&%!#$%!"#$%!""#$%!#%!"#%!""#% 67
ADIABATIC P (Watts) 1 0!E B1%-C-4 heat pulse and isolated sample Excellent precision and accuracy 5.4 C =!E/DT λ transition in space shuttle 5.2 but 5 T (Kelvin) 4.8 4.6 4.4!T method point by point (tenuous) 4.2 4 how to cool the sample? 3.8-20 0 20 40 60 80 100 120 time (s) limited to large samples (parasitic non-adiabaticity) 68
' Apparatus used for calorimetric measurements in the adiabatic demagnetization range Superconducting switch SUPER- ANOM ETERS TO.DIFFUSION PUMP STEEL WIRES PRESSURE gvapor ~ THERMOMETFR ~SOLENOID CO~PE~ ROD Prof. N.E.Phillips University of California BERKELEY "RADIATION ((I[ TRAP ELFCTRICAL LEADS COPPER- WIRES w i FIXED PIVOT MECHANICAL HEAT SWITCH HELIUM DEWAR N IT BOG E N D E WAR COPPER TUSE Mechanical heat switch SOLENOID METAL SPECIMEN Sample LUCITE TUBE NET IC c. GNET POLE CES ~ e 3 INCHES ~ t ~ 4 SECONDARY PR I MAR Y COILS COILS 69
' Apparatus used for calorimetric measurements in the adiabatic demagnetization range SUPER- ANOM ETERS TO.DIFFUSION PUMP STEEL WIRES PRESSURE gvapor ~ THERMOMETFR ~SOLENOID CO~PE~ ROD Prof. N.E.Phillips University of California BERKELEY "RADIATION ((I[ TRAP ELFCTRICAL LEADS COPPER- WIRES SOLENOID w i FIXED PIVOT MECHANICAL HEAT SWITCH HELIUM DEWAR N IT BOG E N D E WAR COPPER TUSE METAL SPECIMEN 100mK-40K accuracy a few % LUCITE TUBE NET IC ΔC/C a few 10-3 3 INCHES ~ e ~ t c. ~ 4 SECONDARY GNET POLE CES PR I MAR Y COILS COILS 100mg-1g Heavy Fermion 69
QUASI-ADIABATIC Prof. A. Junod University of Geneva 1 heat pulse continuous heating and still isolated sample P (Watts) 0 P = Cste <> 0 5.2 P = C dt/dt 5 T (Kelvin) 4.8 4.6 4.4 4.2 dt / dt 4 3.8-20 0 20 40 60 80 100 120 time (s) 70
QUASI-ADIABATIC Prof. A. Junod University of Geneva heat pulse continuous heating 1 and still isolated sample P (Watts) 0 P = Cste <> 0 Double radiation shields 5.2 5 4.8 P = C dt/dt but still P parasitic a few 10-7 W with T (Kelvin) 4.6 4.4 4.2 4 dt / dt ΔT measured via Cr-Cn thermocouples and nanovoltmeter 3.8-20 0 20 40 60 80 100 120 time (s) 70
QUASI-ADIABATIC Prof. A. Junod University of Geneva heat pulse continuous heating 1 and still isolated sample P (Watts) 0 P = Cste <> 0 10K-300K 5.2 P = C dt/dt 5 4.8 accuracy 1-5 % T (Kelvin) 4.6 4.4 dt / dt ΔC/C a few 10-3 4.2 4 3.8-20 0 20 40 60 80 100 120 time (s) 10mg-100g HTSC 70
QUASI-ADIABATIC in dilution range R. Calemczuk CEA-grenoble ΔT measured via Au:Fe thermocouples and SQUID!! SQUID + Chopper = 1-2 pa/(hz) 1/2 71
QUASI-ADIABATIC in dilution range R. Calemczuk CEA-grenoble p V 2 = p 4k B TR = 0.5 pv/ p Hz p I2 = p 4k B T/R = 10 pa/ p Hz p T 2 =2µK/ p Hz P parasitic = at 100 mk L S/T p I2 = 10 13 W 71
QUASI-ADIABATIC in dilution range R. Calemczuk CEA-grenoble 1-10% of 10mg Cu BUT!! no calibration of S (null detector) ΔT = 0 therefore thermometer in compensated area 71
RELAXATIONS Methods heat pulse or steplike, heat link to thermal bath at T b 1 P (Watts) 0 PPMS P 4.6 4.5 4.4! exp (-t k/c) T C T (Kelvin) 4.3 4.2 4.1 4 k T base 3.9 0 20 40 60 80 100 120 time (s) 72
PPMS Quantum Design : 4 He and 3 He 73
Set-up at ultra-low T (10mk-1K) J.P. Brison CEA-grenoble Ressort en CuBe Chauffage collé sur l'échantillon via une languette d'argent Thermalisation de la SiP par un fil d'or et une languette d'argent Plaquette support en Si Thermomètre de mesure : SiP Echantillon Fuite thermique : fil d'or soudé sur l'échantillon Pointe support en erasil 74
(Dis) Advantages, popular, reliable, and widely used at low T extended down to below 10mK (J.P. Brison) good accuracy (5%), but not excellent resolution mass down to a fraction of a mg relaxation time >= 1s Cp can vary by orders of magnitude between the interesting T-range, so does relaxation time Point by point, long and tenuous, 1pt at 100K=20mns 75
AuCrS 2 : antiferromagnetic + structural Courtesy: F. levy CNRS-grenoble 76
Options define internal and external time constants choose duration time vs τ int and τ ext fitting procedure : introduce constrains Large relaxations and local dt/dt (A. Demuer) faster, larger current,... Dual Slope method (dynamic, no calibration of κ) 77
Modulation (alternative) ac-power P (Watts) 1 0 P cos 2 (ωt/2) 4.5 4.4 T ac = P K+jC! T C 4.3 T (Kelvin) 4.2 4.1 4 T dc = P K k T base 3.9 0 20 40 60 80 100 120 time (s) 78
Characteristics lock-in detection, filters, noise rejection (true for all modulation technics) excellent resolution (typical 10-4 ), lesser accuracy but ΔC = a few 10-12 J/K 100 nanogram < m < a few milligram continuous: during H and/or T sweeps easy to extend a differential configuration extrem conditions: 45T-DC, pulsed 60T, 15Gpa, 10kHz 79
Schematic Lumière V ac V dc transformer at room T: a few 0.1 mk/(hz) 1/2 Ref. V ac diff Éch. transformer at 4K: a few 10 µk/(hz) 1/2 Transformateur + 100 Nanovoltmètre Squid detection: a few 0.1 µk/(hz) 1/2 Pré-amplificateur 100 + Détection synchrone 80