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Absolute specific heat measurements of a microgram Pb crystal using ac nanocalorimetry
Stockholm University, Faculty of Science, Department of Physics. (Experimental Condensed Matter Physics)
Stockholm University, Faculty of Science, Department of Physics. (Experimental Condensed Matter Physics)
2012 (English)In: Journal of Physics, Conference Series, ISSN 1742-6588, E-ISSN 1742-6596, Vol. 400, no 022120Article in journal (Refereed) Published
Abstract [en]

Heat capacity measurements using the ac steady state method are often considered difficult to provide absolute accuracy. By adjusting the working frequency to maintain a constant phase and using the phase information to obtain the heat capacity, we have found that it is possible to achieve good absolute accuracy. Here we present a thermodynamic study of a ~2.6 μg Pb superconducting crystal to demonstrate the newly opened capabilities. The sample is measured using a differential membrane-based calorimeter. The custom-made calorimetric cell is a pile of thin film Ti heater, insulation layer and Ge1-xAux thermometer fabricated in the center of two Si3N4 membranes. It has a background heat capacity < 100 nJ/K at 300 K, decreasing to 9 pJ/K at 1 K. The sample is characterized at temperatures down to 0.5 K. The zero field transition at Tc = 7.21 K has a width ≈20 mK and displays no upturn in C. From the heat capacity jump at Tc and the extrapolated Sommerfeld term we find ΔC/γTc = 2.68. The latent heat curve obtained from the zero field heat capacity measurement, and the deviations of the thermodynamic critical field from the empirical expression Hc = Hc(0)[1-(T/Tc)2] are discussed. Both analyses give results in good agreement with literature.

Place, publisher, year, edition, pages
2012. Vol. 400, no 022120
National Category
Condensed Matter Physics
Research subject
Physics
Identifiers
URN: urn:nbn:se:su:diva-64542DOI: 10.1088/1742-6596/400/2/022120ISI: 000314977100208OAI: oai:DiVA.org:su-64542DiVA: diva2:458118
Conference
26TH INTERNATIONAL CONFERENCE ON LOW TEMPERATURE PHYSICS (LT26), PTS 1-5Beijing, PEOPLES R CHINA, AUG 10-17, 2011
Available from: 2011-11-21 Created: 2011-11-21 Last updated: 2017-12-08Bibliographically approved
In thesis
1. Membrane-based nanocalorimetry for low temperature studies with high resolution and absolute accuracy
Open this publication in new window or tab >>Membrane-based nanocalorimetry for low temperature studies with high resolution and absolute accuracy
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

A differential, membrane-based nanocalorimeter has been designed and constructed for thermal studies of mesoscopic samples at low temperatures. The calorimeter is intended for sample masses from mg to sub-μg and a broad temperature range from above room temperature down to the sub-K region. It allows concurrent use of ac steady state and relaxation methods. Effort was spent to achieve good absolute accuracy to enable investigations of the electronic contribution to the heat capacity of superconductors. The calorimeter consists of a pair of cells, each of which is a stack of heaters and thermometer in the center of a silicon nitride membrane, in total giving a background heat capacity less than 100 nJ/K at 300 K, decreasing to 10 pJ/K at 1 K. The device has several distinctive features: i) The resistive thermometer, made of a GeAu alloy, displays a high sensitivity, dlnR/dlnT ≈ −1 over the entire temperature range. ii) The sample is placed in direct contact with the thermometer, which is allowed to self-heat. The thermometer can thus be operated at high dc current to increase the resolution. iii) Data are acquired with a set of eight synchronized lock-in amplifiers measuring dc, 1st and 2nd harmonic signals of heaters and thermometer. iv) Absolute accuracy is achieved via a novel variable-frequency fixed-phase technique in which the measurement frequency is automatically adjusted during ac-calorimetry measurements to account for the temperature variation of the sample specific heat and the device thermal conductance. The properties of the empty cell and the effect of the thermal link between sample and cell were analytically studied. Practical expressions for describing the frequency dependence of heat capacity, thermal conductance, and temperature oscillation amplitude of the system were formulated. Comparisons with measurements and numerical simulations show excellent agreement. Calibration procedures are simple, but care should be taken to minimize thermal radiation effects. The experimental setup is operated with self-regulation of heater powers and thermometer bias, including compensation to zero the differential dc signal. As a result its high resolution and compact format, the calorimeter is well suited for studies of phase transitions and phase diagrams as well as electronic specific heat. The performance of the device is demonstrated by a study of the superconducting state of a small lead crystal.

Abstract [sv]

En differentiell, membran-baserad nanocalorimeter har designats och tillverkats för termiska studier av mesoskopiska prover vid låg temperatur. Kalorimetern är avsedd för provmassor från mg till sub-μg och ett brett temperaturområde från över rumstemperatur till under 1 K. Den tillåter samtidig användning av både ac steady state och relaxations-metod. Fokus har lagts på att uppnå en god absolut noggrannhet för att möjliggöra studier av det elektroniska bidraget till värmekapaciteten hos supraledare. Kalorimetern består av två celler, var och en uppbyggd som en stack med värmeelement och termometer i mitten av ett kiselnitrid-membran, med en total bakgrundsvärmekapacitet på mindre än 100 nJ/K vid 300 K, minskande till 10 pJ/K vid 1 K. Kalorimetern har flera särdrag: i) Den resistiva termometern, gjord av en GeAu legering, visar en hög känslighet, dlnR/dlnT ≈ −1 över hela temperaturområdet. ii) Provet placeras i direkt kontakt med termometern, som tillåts att självvärma. Termometern kan alltså användas vid hög dc ström för att öka upplösningen. iii) Mätningarna genomförs med en uppsättning av åtta synkroniserade lock-in förstärkare, som mäter dc, grundfrekvens och 1:a övertonen hos värme-element och termometer. iv) Absolut noggrannhet uppnås genom en ny variabel-frekvens konstant-fas teknik där mätfrekvensen justeras automatiskt under ac-kalorimetrimätningar för att kompensera temperaturberoendet hos provets specifika värmekapacitet och kalorimetercellens värmeledningsförmåga. Egenskaperna hos den tomma cellen och inverkan av den termiska länken mellan prov och cell studerades analytiskt. Praktiska uttryck för att beskriva frekvens beroendet hos systemets värmekapacitet, värmeledningsförmåga, och temperaturoscillationer har formulerats. Jämförelser mellan mätningar och numeriska simuleringar visar mycket bra överensstämmelse. Kalibreringsförfarandet är enkelt, men försiktighet bör vidtas för att minimera värmestrålningseffekter. Experimentuppställningen drivs med självreglering av värmare och termometer, inklusive kompensation för att nollställa den differentiella dc signalen. Som en följd av dess höga upplösning och kompakta format är kalorimetern väl lämpad för studier av fasövergångar och fasdiagram såväl som det elektroniska specifika värmet. Kalorimeterns prestanda demonstreras genom en studie av det supraledande tillståndet hos en liten blykristall.

Place, publisher, year, edition, pages
Stockholm: Department of Physics, Stockholm University, 2011. 114 p.
Keyword
Nanocalorimetry, specific heat, membrane-based calorimeter, AC steady state, frequency dependence, thermal link conductance, thermal relaxation, GeAu thermometer, numerical simulations
National Category
Condensed Matter Physics
Research subject
Physics
Identifiers
urn:nbn:se:su:diva-64523 (URN)978-91-7447-400-8 (ISBN)
Public defence
2011-12-20, sal FA31, AlbaNova universitetscentrum, Roslagstullsbacken 21, Stockholm, 10:00 (English)
Supervisors
Note
At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 5: Accepted.Available from: 2011-11-28 Created: 2011-11-21 Last updated: 2011-12-14Bibliographically approved

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