Specific heat under pressure

Transcription

1 Specific heat under pressure Physics 590 B Elena Gati T DC T AC ~ 1/C temperature T Bath time 11/16/2018 Specific heat under pressure 1

2 Last lectures. relevant pressure units and scales? How to generate pressure? How to determine pressure? 11/16/2018 Specific heat under pressure 2

3 Last lectures. relevant pressure units and scales? How to generate pressure? How to determine pressure? P (GPa) Helium gas Piston pressure cells (modified) Bridgman anvil cells Diamond anvil pressure cells hydrostaticity, sample space 11/16/2018 Specific heat under pressure 3

4 Today s lecture What properties can be measured under pressure? Technique (well established at ambient pressure) Technique suited? Challenges? Pressure cell (piston pressure cell, Diamond anvil cell ) Example case: Specific heat 11/16/2018 Specific heat under pressure 4

5 General: Techniques under pressure transport thermodynamic probes scattering local probes resistivity thermopower etc. magnetization, susceptibility specific heat thermal expansion X-ray Neutron Photons (Raman) msr NMR etc. etc. etc. 11/16/2018 Specific heat under pressure 5

6 General: Techniques under pressure transport thermodynamic probes scattering local probes resistivity thermopower etc. magnetization, susceptibility specific heat thermal expansion X-ray Neutron Photons (Raman) msr NMR etc. etc. etc. surface probes ARPES STM/STS etc. 11/16/2018 Specific heat under pressure 6

7 General: Techniques under pressure transport thermodynamic probes scattering local probes resistivity thermopower etc. magnetization, susceptibility specific heat thermal expansion X-ray Neutron Photons (Raman) msr NMR etc. etc. etc. surface probes ARPES STM/STS etc. 11/16/2018 Specific heat under pressure 7

8 Recap: Specific heat: What, why and how? What? Why? sensitive to electronic, magnetic and lattice degree of freedom Phase transitions! superconductors: gap structure magnets: entropy? crystal electric-field effects etc. pressure! 11/16/2018 Specific heat under pressure 8

9 Recap: Specific heat: What, why and how? How? Relaxation method Simplified model T S power P P 0 T B temperature T s time ~ exp(-t/ 1 ) P = 0 T B + T T B Thermal bath, T B l S sample C S, T S (t) 1 = C S /l S 11/16/2018 Specific heat under pressure 9

10 Recap: Specific heat: What, why and how? How? Relaxation method More realistic model T S power P T B T P temperature T s ~ exp(-t/ 2 ) ~ exp(-t/ 1 ) time 1- -model 2- -model Thermal bath, T B l P Platform C P, T P (t) l S sample C S, T S (t) 1 and 2 C S + consider addenda 11/16/2018 Specific heat under pressure 10

11 Specific heat: how else? AC calorimetry (Why else for pressure cell application will be discussed later) P. F. Sullivan and G. Seidel, Phys. Rev. 173, 679 (1968) voltage /2 U 0 -U 0 power temperature time P 0 0 T AC T AC ~ 1/C S 11/16/2018 Specific heat under pressure 11

12 Specific heat: how else? (Why else for pressure cell application will be discussed later) voltage AC calorimetry /2 U 0 -U 0 T AC : lock-in amplifier very good signal-to-noise ratio! power temperature time P 0 0 T AC T AC ~ 1/C S introduced by R. Prozorov in lecture on AC susceptibility 11/16/2018 Specific heat under pressure 12

13 Specific heat: how else? (Why else for pressure cell application will be discussed later) AC calorimetry voltage power temperature time /2 U 0 -U 0 P 0 0 T AC Good for measuring small specific heat ( = small samples) with high relative resolution T AC ~ 1/C S 11/16/2018 Specific heat under pressure 13

14 AC calorimetry: models Simplified model P = P 0 sin 2 ( t/2) time-dependent P(t) = C S dt S (t)/dt + l S [T S (t)-t B ] T DC T AC ~ 1/C Thermal bath, T B l S sample C S, T S (t) Solution: temperature T S (t) = T DC + T AC (t) T Bath time T DC = T B + P 0 /(2l S ) T AC = P 0 /(2l S ) * (1+ 2 S2 ) -1/2 * cos( t+f) S = C S /l S 11/16/2018 Specific heat under pressure 14

15 AC calorimetry: models Simplified model P = P 0 sin 2 ( t/2) Solution frequency-dependent! T AC = P 0 /(2l S ) * (1+ 2 S2 ) -1/2 * cos( t+f) S = C S /l S Thermal bath, T B l S sample C S, T S (t) log T AC log T AC * log frequency log frequency If S >> 1: T AC,0 = P 0 /(2 C S ) 11/16/2018 Specific heat under pressure 15

16 AC calorimetry: models Simplified model P = P 0 sin 2 ( t/2) Solution frequency-dependent! T AC = P 0 /(2l S ) * (1+ 2 S2 ) -1/2 * cos( t+f) S = C S /l S Thermal bath, T B voltage l S sample C S, T S (t) /2 U 0 -U 0 log T AC log T AC * temperature power time P 0 0 T AC log frequency log frequency If S >> 1: T AC,0 = P 0 /(2 C S ) 11/16/2018 Specific heat under pressure 16 energy

17 AC calorimetry: models More realistic model 1 >> 2 T AC = P 0 /(2 C) * ( /( 2 12 )+const.) -1/2 bath l 1, 1 thermometer, C Q sample, C S heater, C H l 2, 2 C = C S + C H + C Q If 2 << 1 and 1 >> 1: T AC = P 0 /(2 C) P = P 0 sin 2 ( t/2) log(t AC ) log(t AC *frequency) opt log (frequency) log (frequency) 11/16/2018 Specific heat under pressure 17

18 AC calorimetry: models More realistic model 1 >> 2 T AC = P 0 /(2 C) * ( /( 2 12 )+const.) -1/2 bath l 1, 1 thermometer, C Q sample, C S heater, C H l 2, 2 C = C S + C H + C Q If 2 << 1 and 1 >> 1: T AC = P 0 /(2 C) P = P 0 sin 2 ( t/2) Need to choose measurement frequency, then T AC independent of l s! log(t AC ) log(t AC *frequency) opt log (frequency) log (frequency) 11/16/2018 Specific heat under pressure 18

19 Pressure cell: Which method? bath pressure medium pressure cell C addenda sample C S short relaxation time to bath (vs. typically weak links in ambientpressure experiments) small sample mass 11/16/2018 Specific heat under pressure 19

20 Pressure cell: Which method? bath pressure medium pressure cell C addenda relaxation method C addenda > C sample sample C S short relaxation time to bath (vs. typically weak links in ambientpressure experiments) small sample mass 11/16/2018 Specific heat under pressure 20

21 Pressure cell: Which method? bath pressure medium pressure cell C addenda relaxation method C addenda > C sample sample C S AC calorimetry short relaxation time to bath (vs. typically weak links in ambientpressure experiments) small sample mass Decoupling from pressure medium and cell by choice of measurement frequency Good for small C! 11/16/2018 Specific heat under pressure 21

22 Experimental realizations What thermometer? What heater? Thermal link between heater, thermometer and sample? 11/16/2018 Specific heat under pressure 22

23 Experimental realizations What thermometer? What heater? Thermal link between heater, thermometer and sample? Limitations set by: Pressure range (pressure cell dimensions) desired temperature range 11/16/2018 Specific heat under pressure 23

24 Experimental realizations: thermometer Small in change in T large change in measured quantity (typically voltage) 11/16/2018 Specific heat under pressure 24

25 Experimental realizations: thermometer Small in change in T large change in measured quantity (typically voltage) Chip resistance thermometers RuO 2 thermometers: large dr/dt at low temperatures low magnetic-field induced errors typical dimensions: 1 x 0.5 x 0.35 mm 3 (restricted to piston-pressure cells) R ( ) RuO 2 chip resistor T (K) 11/16/2018 Specific heat under pressure 25

26 Experimental realizations: thermometer Small in change in T large change in measured quantity (typically voltage) Chip resistance thermometers Cernox thermometers: large dr/dt in wide temperature ranges low thermal response time (1.5 ms at 4.2 K) typical dimensions: 1 x 0.75 x 0.2 mm 3 (restricted to piston-pressure cells) 11/16/2018 Specific heat under pressure 26

27 Experimental realizations: thermometer Small in change in T large change in measured quantity (typically voltage) Thermocouples (remember from K. Dennis lecture ) Very small use in diamond-anvil cells low thermal mass Typically chromel AuFe Reference temperature? Firm contact often requires spot-welding Wire A T 1 voltage Wire B T 2 11/16/2018 Specific heat under pressure 27

28 Experimental realizations: heaters Constant heating power as a function of temperature Joule heating with R(T) ~ const. (choice depends on size limitations) manganin wire thin-film resistors strain gauges thermocouples Source: LakeShore 11/16/2018 Specific heat under pressure 28

29 Experimental realizations: heaters Constant heating power as a function of temperature Joule heating with R(T) ~ const. (choice depends on size limitations) manganin wire thin-film resistors strain gauges thermocouples future: BaZnGa? 11/16/2018 Specific heat under pressure 29

30 Experimental realizations: heaters Constant heating power as a function of temperature Joule heating with R(T) ~ const. (choice depends on size limitations) manganin wire thin-film resistors strain gauges thermocouples Diamond-anvil cell: laser heating Demuer et al., J. Low Temp. Phys. 120, 245 (2000) 11/16/2018 Specific heat under pressure 30

31 Photographs piston-pressure cell in Canfield s group H. Wilhelm, MPI CPfS Dresden Bridgman-type pressure cell 11/16/2018 Specific heat under pressure 31

32 change temperature Some data 1 st order T C typical frequencies: ~ 100 Hz (be careful: depends on T and p!; differs for every sample) Measure frequency dependence Determine optimal frequency 2 nd order T N Determine T AC at optimal frequency Bouquet et al., Sol. Stat. Commun. 113, 367 (2000) 11/16/2018 Specific heat under pressure 32

33 Some data new type of magnetic order Bouquet et al., Sol. Stat. Commun. 113, 367 (2000) 11/16/2018 Specific heat under pressure 33

34 Ongoing work in our own group BaFe 2 As 2 under pressure N. Ni et al., PRB 78, (08) C molar /T (J/mol/K 2 ) p 1 = 0 GPa p 2 = 0.73 GPa p 3 = 0.95 GPa p 4 = 1.31 GPa p 5 = 1.53 GPa p 6 = 1.87 GPa p 7 = 2.05 GPa C/T/(C/T) max T (K) T-T mag (K) J. Chu et al., PRB 79, (09) 11/16/2018 Specific heat under pressure 34

35 Summary What do I need to consider for measurements under pressure? 11/16/2018 Specific heat under pressure 35

36 Summary What do I need to consider for measurements under pressure? Is my technique suited? Is there another more suitable way to measure same quantity? specific heat: relaxation vs. AC calorimetry Can I fulfill limitations set by pressure cell dimensions? small in piston-pressure cell, very small in DAC specific heat: choice of heaters and thermometers Are there any technique-specific limitations? How do they influence my data interpretation? specific heat: strong coupling between sample and bath due to pressure medium; magnetization: additional background signal from cell; etc. 11/16/2018 Specific heat under pressure 36

37 Summary What do I need to consider for measurements under pressure? Is my technique suited? Is there another more suitable way to measure same quantity? specific heat: relaxation vs. AC calorimetry Can I fulfill limitations set by pressure cell dimensions? small in piston-pressure cell, very small in DAC specific heat: choice of heaters and thermometers Are there any technique-specific limitations? How do they influence my data interpretation? specific heat: strong coupling between sample and bath due to pressure medium; magnetization: additional background signal from cell; etc. If you can answer all questions satisfactorily, go ahead! Pressure is an essential tuning parameter in condensed matter physics! 11/16/2018 Specific heat under pressure 37

38 Sources and further reading Stewart, Rev. Sci. Instrum. 54, 1 (1983) Bachmann et al., Rev. Sci. Instrum. 43, 205 (1972) Sullivan and Seidel, Phys. Rev. 173, 679 (1968) Eichler and Gey, Rev. Sci. Instrum. 50, 1445 (1979) Baloga and Garland, Rev. Sci. Instrum. 48, 105 (1977) H. Wilhelm, AC calorimetry at high pressures and low temperatures, Advances in Solid State Physics, Springer (2003) and many more papers describing specifics of their individual setups 11/16/2018 Specific heat under pressure 38