Thermal analysis heat capacity 590B F18 Sergey L. Bud ko
Heat capacity C p = (dq/dt) p = T( S/ T) p Q heat, S - entropy C v = (dq/dt) v = T( S/ T) v C p C v = TVβ 2 /k T β volume thermal expansion, k T isothermal volume compressibility For solids C p ~ C v Usually we measure C p
relaxation (QD PPMS) Heat capacity HOW?
Heat capacity HOW? relaxation (QD PPMS) simple P 0 0 power of the heater sample + platform T of the bath thermal conductance of wires solution: exponent with t = C total /K w
Heat capacity HOW? relaxation (QD PPMS) addenda more realistic fit with two exponents
relaxation (QD PPMS) Heat capacity HOW? Addenda - simple model Sample simple model
relaxation (QD PPMS) Heat capacity HOW? Sample 2-tau model
relaxation (QD PPMS) Heat capacity HOW? - Good for flat relatively thin samples with reasonable thermal conductivity - Liquids: need thin-walled sealed container made out of material with high thermal conductivity and low heat capacity. personally did not try (yet?) - Powders: - press a pellet (if has structural integrity); - mix with some metallic powder and press a pellet; - seal powder in aluminum DSC container (can be used for airsensitive powder samples as well, if assembled in a glove box) Remember addenda!
relaxation (QD PPMS) Heat capacity HOW? calibrated heater and thermometer sophisticated temperature control and fitting software need to measure addenda (platform + grease) every time need to calibrate heater and thermometer in magnetic field need to shape your sample vertical 3 He platform may oscillate in magnetic field remember about torque assembly is fragile measurements take long time not good for 1 st order phase transitions
Heat capacity HOW? ac modulation τ 1 sample to bath; τ 2 response time of the sample if τ 2 << 1/w << τ 1
ac modulation Heat capacity HOW?
Heat capacity HOW? ac modulation after Andreas Rydh
Heat capacity HOW? ac modulation Commercial chips with membrane (this is a commercial thermal conductivity gauge)
Heat capacity HOW? ac modulation Commercial chips with membrane you are invited to play with it
Heat capacity HOW? ac modulation differential cell after Andreas Rydh
Heat capacity HOW? ac modulation differential cell need to have (at least primitive) thin film technology and lithography after Andreas Rydh
Heat capacity HOW? ac modulation fast scalable, good for small sample accurate (relative measurements) easy to put on rotator can use e.g. in pressure cells hard to get absolute values
Heat capacity HOW? ac modulation under pressure
Heat capacity HOW? ac modulation under pressure Bridgman cell -heater and thermometer are at ambient pressure for DAC laser heating with thermocouple as sensor
Heat capacity HOW? ac modulation under pressure
Heat capacity HOW? ac modulation under pressure need to choose frequency
after Andreas Rydh
Heat capacity WHY? * Useful knowledge for useful (structural) materials how easy to cool down
Heat capacity WHY? * To learn something about electrons and phonons T -> 0: C p = γt + βt 3 (no magnetism) γ ~ N(0)(1 + λ) - electronic density of states λ - measure of e-e (and e-ph) interactions, m*/m 0 = (1 + λ) γ > 400 mj/mol K 2 heavy fermions an enormous, separate research field that entertains number of us Θ D = (1944/β) 1/3 - Debye temperature (use right units) tells you something about stiffness of the lattice, helps to understand BCS superconductors [T c ~ Θ D exp(-1/n(0)v)]
Heat capacity WHY?
Lattice heat capacity Debye and Einstein Einstein single frequency Debye elastic continuum (T << Θ D ) (T >> Θ D )
Lattice heat capacity Debye and Einstein Debye Einstein One can also use realistic phonon DOS and calculate C p Einstein Debye Blackman realistic
Lattice heat capacity Einstein mode Peak associated with the Einstein mode @ ~ Q E /20
Heat capacity WHY? To learn something about magnons Ferro (ferri) magnets isotropic anisotropic Antiferromagnets isotropic anisotropic And need to remember contributions from electrons and phonons: C p = γt + βt 3
Heat capacity WHY? To learn something about superconductors C s ~ exp(-1.76t c /T) BCS
Heat capacity WHY? To learn something about superconductors Strong coupling RMP 62, 1027 (1990)
Heat capacity WHY? To learn something about superconductors BCS value (3.53) phenomenological (1970s) α-model: 2Δ 0 /k B T c fitting parameter; temperature dependence of SC gap BCS; can calculate thermodynamic properties.
Heat capacity WHY? To learn something about superconductors MgB 2 Two-gap superconductor
Heat capacity WHY? To learn something about superconductors MgB 2 Two-gap superconductor
Heat capacity WHY? To learn something about superconductors four gaps
Heat capacity WHY? To learn something about superconductors BCS superconductors with paramagnetic impurities BCS PM impurities La-Gd jump in specific heat
Heat capacity WHY? To learn something about superconductors Kondo effect in SC jump in specific heat
Heat capacity WHY? To learn something about superconductors Iron-arsenides ΔC p ~ T c 3 Smart person might be able to make sense out of this
Heat capacity WHY? To learn something about phase transitions below superconducting T c T N T WFM? T c
Heat capacity Bulk, thermodynamic property In case of not so single phase samples results: -do not suffer from M&M effect in case of superconductors -do not suffer from impurity SC or FM signal in magnetization (although for FM need to remember about entropy)
Resistance SC normal normal bulk, superconducting shell V I Will get R=0 below T c of the shell
Low field ZFC susceptibility SC normal normal bulk, superconducting shell Will get complete flux expulsion below T c of the shell
Heat capacity SC normal normal bulk, superconducting shell Will get complete jump of C p at T c of the shell proportional to the fraction of the SC phase, e.g. very small
Heat capacity WHY? To learn something about crystal electric field (Schottky anomaly) maximum:
Heat capacity WHY? To learn something about spin glasses Scaling hypothesis
Heat capacity WHY? To learn something about spin glasses 1/T T max ~ 1.5 T f
Heat capacity WHY? To learn something about magnetic transitions HoNi 2 B 2 C Also can play entropy game and evaluate degeneracy of the ground state ΔS m = R ln N
Heat capacity beware of fool s gold low temperature C = AT in insulators
Heat capacity beware of fool s gold low temperature C = AT in insulators glasses - distribution of two level systems
Heat capacity beware of fool s gold fake heavy fermions (apparently large Sommerfeld coefficient): - (really) low temperature magnetic ordering - low temperature spin glass behavior One measurement technique, whatever sophisticated, is not enough
Reading: Quantum Design Manual and refs therein E.S.R. Gopal, Specific heats at low temperatures. A.Tari, Specific heat of matter at low temperatures. T.H.K. Barron and G.K. White, Heat capacity and thermal expansion at low temperatures. Review of Scientific Instruments search on heat capacity