L. Maosa, A. Planes, E. Vives M.Barrio, J.L. Tamarit D. Gonzlez, E. - PowerPoint PPT Presentation

Lluís Mañosa. Departament ECM. Facultat de Física. Universitat de Barcelona. lluis@ecm.ub.es

L. Mañosa, A. Planes, E. Vives M.Barrio, J.L. Tamarit D. González, E. Stern Univ. Polit. Catalunya. Univ. Barcelona. Catalonia. Catalonia. I. Titov, M. Acet Univ. Duisburg X. Moya, N. Mathur Germany. Univ. Cambridge U.K. D. Soto Parra CIMAV, Chihuahua Mexico. A. Battacharyya, S. Majumdar Indian Assoc. Cultivation Science Kolkata, India. R. Romero IFIMAT, Tandil. Argentina

Modern society relies on the possibility of cooling below ambient

How to cool ? Hot sink q 2 K q 1 Cold sink

How to cool ? Hot sink q 2 K Work Rudolf Emmanuel Clausius (1822-1888) q 1 Cold sink NOT FOR FREE !!!! Henri Poincaré (1854-1912)

The simplest cycle: The Carnot Cycle  T = T 2 – T 1 S |q 1 |= T 1  S |q 2 |= T 2  S T Refrigerant capacity    R S T Need: Materials with large changes in entropy and temperature

Undergraduate Thermodynamics Generalized displacement Generalized field Caloric effects Large caloric effects when is large

Isothermal entropy change S  Y   S ( T,Y =0)  S   ΔS   dY  iso    S iso Y T 0  Y   T S S ( T,Y )    ΔT   dY  adi   C Y T 0 T Δ S iso = S f – S i < 0 T f = T i Y

Adiabatic temperature change S  Y   S  S ( T,Y =0)  ΔS    dY  iso   Y T 0  Y   T S      ΔT dY S ( T,Y )  T adi  adi   C Y T 0 Δ T adi = T f – T i < 0 S f = S i Y

Caloric effect Conventional caloric effect    x   In general   S iso <0 when  Y > 0   0    T Inverse CE H S(Y ≠ 0 )  Δ S iso > 0 S(Y =0 ) S(H =0 ) S(Y =0 ) Sample heats up when applying field adiabatically S S Δ T ad < 0 S(H ≠0 ) S(Y ≠ 0 ) ≠0 ) But..... Δ T ad > 0 Δ T ad > 0    x Δ S iso < 0 Δ S iso < 0    S iso > 0 when  Y > 0   0    T MCE H  T T Sample cools down when applying field adiabatically Inverse caloric effect

Computation of caloric effects Calorimetric (adiabatic, relaxational, ac,..) From Maxwell relation: measurement of C under field Isothermal measurements x vs Y Direct methods: adiabatic measurement of temperature Other methods: pulsed fields, Clausius-Clapeyron, etc …

Undergraduate Thermodynamics Generalized displacement Generalized field Caloric effects Large caloric effects when is large

Measurements of entropy changes at a first order phase transition: DSC Calorimetry under constant temperature ( T ): sweeping field ( Y ) -1 ) dQ/dY -1 kg -  S (J K Y T (K) DSC Calorimetry under constant field ( Y ): sweeping temperature ( T ) S 800 -1 ) dQ/dT 600 -1 kg dQ/dT (mW/K) 400 -  S (J K T 200 T 0 0 T 285 290 295 300 305 T (K) T(K) T

Hall probe Thermobatteries Sample Pt-100 thermometer 16 mm 1 Cu block 2 Sensors (thermobatteries) 3 Sample 4 Reference 5 Carbon-glass resistor ( T ) Calorimeters under magnetic field. Marcos et al., Rev. Sci.Ints., 74, 4768 (2003)

S crew Calorimeter under Metallic O-ring hydrostatic pressure. O-ring Capillary Cells BaTiO 3 Cu E Calorimeters under electric field.

A FEW EXPERIMENTAL RESULTS Magneto caloric effect: Ni-Mn-Sn; Ni-Mn-In T. Krenke et al. Nature Mater. 4 (2005) 450 Barocaloric effect: Ni-Mn-In, La-Fe-Co-Si L. Mañosa et al. Nature Mater. 9 (2010) 478. L. Mañosa et al. Nature Comm. 2(2011) 595. Elastocaloric effect: Cu-Zn-Al E. Bonnot et al. Phys. Rev. Lett. 100 (2008) 125901. Electrocaloric effect: BaTiO 3

Magnetic shape memory alloys Martensitic transition (a) (b) (Fm3m) Heusler X 2 YZ Change in symmetry + Change in magnetization + Change in volume + Change in strain

Magnetocaloric effect Ni-Mn-X (X=Sn,In,Sb,Ga) Ni-Mn-Sn T. Krenke et al. Nature Mater. 4 (2005) 450 Magnetocaloric effect is inverse: entropy increases on applying field

Magnetocaloric effect Ni-Mn-X (X=Sn,In,Sb,Ga) T. Krenke et al. Nature Mater. 4 (2005) 450 L. Mañosa et al., Adv. Mater. 21 (2009) 3725.

Magnetocaloric effect Ni-Mn-X (X=Sn,In,Sb,Ga) Ni-Mn-In Inverse magnetocaloric: Sample cools on applying Magnetic field. X. Moya et al. Phys. Rev. B 75 (2007) 184412

Barocaloric effect Ni-Mn-In L. Mañosa et al Nature Mater. 9 (2010) 478

Barocaloric effect Ni-Mn-In CONVENTIONAL INVERSE L. Mañosa et al Nature Mater. 9 (2010) 478

La-Fe-Si NaZn 13 structure ( Fm-3c) No change in symmetry + Change in magnetization + Change in volume

Barocaloric effect Magnetocaloric effect L. Mañosa et al Nature Commun. 2 (2011) 595

Barocaloric effect INVERSE Magnetocaloric effect CONVENTIONAL L. Mañosa et al Nature Commun. 2 (2011) 595

Inverse caloric effect Sample warms up on releasing pressure. Conventional caloric effect Sample cools down on removing field. L. Mañosa et al Nature Commun. 2 (2011) 595

Shape memory alloys (the classic ones) Martensitic transition (a) (b) (Fm3m) Heusler X 2 YZ Change in symmetry + NO Change in volume + Change in strain

Elastocaloric effect Cu 0.6813 Zn 0.1574 Al 0.1613          S     E. Bonnot et al.        S 0 d d            Phys. Rev. Lett 100 (2008) 125901 T  0 0 T

Elastocaloric effect 1.4 1.2  =105MPa 1.0  =110MPa -  S (J/K.mol) Δ S max = Δ S t = -1.2 J/mol K  =115MPa 0.8  =120MPa = - 20 J/kg K  =125MPa 0.6  =130MPa  =135MPa 0.4  =140MPa  =143MPa 0.2 0.0 296 298 300 302 304 306 308 310 T (K) Clausius-Clapeyron calorimetry M f M s M f  1 dQ  d     S dT 1 . 3 J / molK       t S V 1 . 2 J / molK T dT t dT M s

Elastocaloric effect Adiabatic temperature change E. Vives et al. Appl. Phys. Lett. 98 (2011) 011902

BaTiO 3 Pm3m P4/mmm Change in symmetry + Change in volume + Change in polarization

Electrocaloric effect Sweeping temperature 0 2 -1 ) -1 E = 0 kV cm -1 ) -1 kg -1 kg dQ/dT (J K -1000 S (J K -1 E = 3 kV cm -1 E = 0 kV cm 0 -2000 -1 E = 3 kV cm 394 396 398 400 394 396 398 400 T (K) T (K) 2 T - C phase transition (cooling) -1 E = 2 kV cm -1 E = 3 kV cm -1 ) -1 kg BaTiO 3 Cu 1 -  S (J K E 0 394 396 398 400 T (K)

Electrocaloric effect Sweeping electric field Field-induced transition -1 E = 4 kV cm 0.0000 2 -1 ) -0.0002 -1 kg calorimetric signal -0.0004 -  S (J K 1 -0.0006 T= 397.28 K -0.0008 0 -0.0010 0 100 200 300 400 500 394 396 398 400 T (K) Electric Field (kV/m) BaTiO 3 Cu E

Electrocaloric effect Indirect method: P ( T , E ) P ( E ) different T (cooling) P ( T ) different E 385 K 20 20 405 K 10 -2 ) -2 ) P (  C cm P (  C cm 0 10 -10 -1 E = 0 kV cm -1 E = 4 kV cm -20 0 380 400 420 -20 -10 0 10 20 T (K) -1 ) E (kV cm -1 E = 4 kV cm -1 ) 2 -1 kg ECE -  S (J K 0 380 400 420 T (K)

Electrocaloric effect Direct Indirect 3 -1 -1 E = 3 kV cm E = 4 kV cm -1 E = 4 kV cm T sweep E sweep -1 ) -1 ) 2 2 -1 kg -1 kg -  S (J K -  S (J K 1 0 0 394 396 398 400 380 400 420 T (K) T (K)

Electrocaloric effect 1.0 409 K 404 K 0.5 E off E off T (K) 0 E on E on -0.5 -1.0 0 100 200 0 100 200 t (s) t (s) 1.0 -1 E = 8 kV cm E on E off  T (K) 0.5 0 395 400 405 410 415 420 T (K)

Δ S = Δ S mag + Δ S str + Δ S el S low T < S high T Y= 0  Y Y  Y= 0 X X CONVENTIONAL CALORIC EFFECT T T INVERSE CALORIC EFFECT S S |  S t | |  S t | T T  S  S T |  S t | |  S t | T

Caloric effect latent heat of the transition Entropy increases  S > 0 Low entropy phase High entropy phase Field applied Pressure released Stress released Field removed Pressure applied Stress applied Low (high) High (low) magnetization magnetization Low volume Large volume Entropy decreases Large strain Low strain  S < 0

Materials with structural transitions + LARGE changes in extensive properties (Cross-response to external stimuli) GIANT caloric effects Eco-friendly refrigeration Energy Harvesting

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