Heat transport measurements in diamond anvil cell Daniele

Heat transport measurements in diamond anvil cell Daniele Antonangeli Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie Sorbonne Université Muséum National d'Histoire Naturelle, UMR CNRS 7590, IRD MECMATPLA, March 17 -23 2019, Montgenèvre FRANCE D. Antonangeli

Outline Diamond anvil cells: working principle and P-T metrology Thermal conductivity and thermal diffusivity: measurements Thermal conductivity: microscopic approach MECMATPLA, March 17 -23 2019, Montgenèvre FRANCE D. Antonangeli

P-T range by laser-heated DAC Techniques other than x-ray diffraction MECMATPLA, March 17 -23 2019, Montgenèvre FRANCE Reminder: 100 GPa=1 Mbar after Hirose et al. , Annu. Rev. Earth Planet. Sci. , 2013 D. Antonangeli

High pressure generation Basic principle: P = F/S P = Pressure F = Force S = Surface So high pressure can be generated by: Large force Larger volume press Small surface Diamond anvil cell MECMATPLA, March 17 -23 2019, Montgenèvre FRANCE D. Antonangeli

Diamond anvil cell (DAC) Pressure gage Gasket Pressure transmitting medium Sample Diamonds - Very hard - Transparent over a very large spectral range (from far IR to hard X-rays) Pressure : 0 to 1000 GPa (ambient and low T); 0 to 400 GPa (high T) Temperature : 0 to 6000 K Duration: several days at ambient T, but few hours at HT (when not few minutes…) Large variety of synchrotron, x-fel and laboratory techniques MECMATPLA, March 17 -23 2019, Montgenèvre FRANCE D. Antonangeli

Pressure generation Membrane-driven DAC Screw-driven DAC 5 cm MECMATPLA, March 17 -23 2019, Montgenèvre FRANCE D. Antonangeli

Pressure metrology: fluorescence Diamond Gasket 20 mm Diamond Or P-V relation of standards by XRD MECMATPLA, March 17 -23 2019, Montgenèvre FRANCE D. Antonangeli

HP-HT DAC: resistive heating whole cell heating: T< 900 K furnaces around diamonds: T<1300 K (1600 K) MECMATPLA, March 17 -23 2019, Montgenèvre FRANCE D. Antonangeli

HP-HT DAC: laser heating thermal emission T wavelength IR laser (1000) 1300 <T< 4000 (6000) K MECMATPLA, March 17 -23 2019, Montgenèvre FRANCE D. Antonangeli

Thermal conduction (steady heat flow in an isotropic medium) heat flux J= - k ∇T (Fourier’s law) thermal conductivity thermal diffusivity ∂T(r, t)/∂t = D ∇2 T(r, t) (heat equation) k= D ρ CP MECMATPLA, March 17 -23 2019, Montgenèvre FRANCE D. Antonangeli

Flash method D =1. 38 L 2 / π2 t½ or D = 0. 48 L 2 / π2 tx k = D Q / V TM (κ = D ρC) C = Q / ρ V TM Parker et al. , J. Appl. Phys. 1961 MECMATPLA, March 17 -23 2019, Montgenèvre FRANCE D. Antonangeli

Thermal diffusivity in DAC thermal diffusivity from transient heating technique Mg. O, Na. Cl, KCl up to 32 GPa at 2600 K Gated CCD Pulse Sample (transparent, insulating) τ Heating Pulse (8 ns) T vs. t Ir (laser absorber) Beck et al. , Appl. Phys. Lett. 2007 MECMATPLA, March 17 -23 2019, Montgenèvre FRANCE D. Antonangeli

Thermal diffusivity in DAC thermal diffusivity from pulsed-heating thermoreflectance measurements Mg. Si. O 3 pv and ppv up to 144 GPa Extension at high T by resistive heating Na. Cl (pressure medium) Sample Reflectivity vs. t T vs. t τ Heating Pulse (2 ns) Pt (Laser absorber) MECMATPLA, March 17 -23 2019, Montgenèvre FRANCE Ohta et al. , EPSL 2012 D. Antonangeli

Thermal conductivity in DAC thermal diffusivity from pulsed-heating method Fe up to 130 GPa and 3000 K Streak Camera Pulse Thermal insulator Pressure transmitting medium τ Heating Pulse Double side IR laser Metallic sample Kônopková et al. , Nature 2016 MECMATPLA, March 17 -23 2019, Montgenèvre FRANCE D. Antonangeli

Thermal conductivity in DAC thermal conductivity from electrical resistivity measurements Wiedemann-Franz relation Fe up to 157 GPa and 4500 K kel = L 0 T/ρ with L 0=2. 44 x 10 -8 W m-1 K-1 Ohta et al. , Nature 2016 MECMATPLA, March 17 -23 2019, Montgenèvre FRANCE D. Antonangeli

But… 1) Kônopková et al. , Nature 2016 k (Fe @ 136 GPa and 3800 K) = 33 +/-7 W m-1 K-1 2) Ohta et al. , Nature 2016 ρ (Fe @ 140 GPa and 3750 K) = 40 +/-8 μΩcm k= 226 +/-50 W m-1 K-1 Some consequences of the Earth’s core 1) Moderate heat transport by conduction, easy to generate convection (QCMB>>Qcond) core slowly cooling, old inner core (as old as 4. 2 Ga), no requirement of geodynamo before inner core formation (light-element driven convection) 2) Large QCMB needed to sustain whole outer core convection, core rapidly cooling by conduction, young inner core (<0. 7 Ga), early magnetic field not by thermal convection (core too hot), but by magnesium/Si. O 2 exsolution MECMATPLA, March 17 -23 2019, Montgenèvre FRANCE D. Antonangeli

Microscopic approach to thermal conductivity from insulating systems Lattice contribution to thermal conductivity from Boltzmann transport equation phonon energies life time Direct experimental measurements of fundamental quantities entering the Boltzmann transport equation Experimental validation of theoretical approach MECMATPLA, March 17 -23 2019, Montgenèvre FRANCE D. Antonangeli

Interatomic potentials and lattice dynamics Harmonic approximation - Phonon dispersion curves (elasticity and sound velocity) - Specific heat harmonic potential Failures non-harmonic potential - Phonon width (inverse of life time) Thermal conductivity Thermal expansion P-T dependence of elastic moduli Anharmonic approach: phonon-phonon scattering But also: scattering with defects, impurities, grain boundaries, isotopic disorder… MECMATPLA, March 17 -23 2019, Montgenèvre FRANCE D. Antonangeli

Inelastic x-ray scattering (IXS) Ein, kin, in photon E, Q Eo ut , pho ton ko ut , out • Energy transfer E = Eout – Ein (E<< Ein) • Momentum transfer Q = kout – kin = 2 k sin ( /2) (kout kin k) Directional analysis of the scattered photons Energy analysis of the scattered photons MECMATPLA, March 17 -23 2019, Montgenèvre FRANCE Q E dΩ No coupling D. Antonangeli

Phonons at high temperature Temperature induced softening and broadening Anharmonic effects MECMATPLA, March 17 -23 2019, Montgenèvre FRANCE D. Antonangeli

Experiments vs. calculations: case of Mg. O at HT Exp (300 K) Exp (873 K) O Exp (1223 K) DFT (300 K) DFT (873 K) DFT (1223 K) Fei He, Ph. D thesis MECMATPLA, March 17 -23 2019, Montgenèvre FRANCE D. Antonangeli

Temperature dependence of thermal conductivity MECMATPLA, March 17 -23 2019, Montgenèvre FRANCE D. Antonangeli

References w Parker W. J. et al. , Flash method of determining thermal diffusivity, heat capacity, and thermal conductivity. J. Appl. Phys. 32, 1679 (1961). w Beck P. et al. , Measurement of thermal diffusivity at high pressure using a transient heating technique. Appl. Phys. Lett. 91, 181914 (2007). w Ohta K. et al. , Lattice thermal conductivity of Mg. Si. O 3 perovskite and postperovskite at the core–mantle boundary. Earth Planet. Sci. Lett. 349, 109 (2012). w Kônopková Z. et al. , Direct measurement of thermal conductivity in solid iron at planetary core conditions. . Nature 534, 99 (2016) w Ohta K. et al. , Experimental determination of the electrical resistivity of iron at Earth’s core conditions. Nature 534, 95 (2016). MECMATPLA, March 17 -23 2019, Montgenèvre FRANCE D. Antonangeli

Thanks for your attention Questions? Now or later this week (I will be around…) MECMATPLA, March 17 -23 2019, Montgenèvre FRANCE D. Antonangeli