Pressure-inducedphase transitionsforsolid-statecooling: … · 2019-03-28 · Pressure-inducedphase...

Pressure-induced phasetransitions for solid-state cooling:

Barocaloric effect

Josep Lluís Tamarit · María del BarrioAraceli Aznar

Group of Characterization of Materials

XIII Jornada de Recerca

Pol Lloveras

Vapor compression refrigeration cycleNeeded everywhere

Buildings: Homes, offices

Data centers, web servers

TransportIndustry

Storage of food, medicines, vaccines, blood, artwork

- 1914: First domestic air-conditioning unit- 1930: First domestic fridge- 2010: 50 000 000 units sold in China in 2010- 2014: Cooling > 20% world-electricity consumption- Future: Growth > 30-fold from 2000 to 2100

- Long piping (up to hundreds of m in domestic units)- Large amounts of refrigerant required (up to 50 kg)- Installation often made by end users- Mandatory leak inspections are often unfeasible- Costly waste management

Leaks!!

RefrigerantFamily

Global WarmingPotential (CO2 = 1)

Ozone-DepletingPotential (CFC = 1)

Regulation

CFC 4500-11000 0.3-1 Prohibited in 1996HCFC 70-3200 0.02-0.06 Phase out by 2020HFC 600-1500 0 Phase out by 2020-2030HFO 4 0 -

Vapor compression refrigeration cycleDrawback: Leakage of harmful refrigerant fluids

Greenhouse effect

- In Germany, stationary air conditioning units caused 717400 tons CO2 equivalent- 60% of world HFC emissions arise from leaks- 2050: Almost 10 % of global greenhouse gas emissions

Vapor compression refrigeration cycleEx: Reverse Brayton cycle: adiabatic + isobaric processes

Entropy S – Temperature T

S

T

S(T )p1

p

v

T1 (>T2)

T2 (>T3)

T3

S1S(T )p

2

T2

S2 (< S1)

p1

Pressure p – Volume v

Vapor compression refrigeration cycleEx: Reverse Brayton cycle: adiabatic + isobaric processes

Entropy S – Temperature T

S

T

S(T )p1

p

v

T1 (>T2)

T2 (>T3)

T3

S1

p2

p1

S(T )p2

T2 T1

S2 (< S1)

+Q

Pressure p – Volume v

Vapor compression refrigeration cycleEx: Reverse Brayton cycle: adiabatic + isobaric processes

Entropy S – Temperature T

S

T

S(T )p1

-Q

p

v

T1 (>T2)

T2 (>T3)

T3

S1S(T )p

2

T3 T2 T1

S2 (< S1)

-Qp2

p1

Pressure p – Volume v

Vapor compression refrigeration cycleEx: Reverse Brayton cycle: adiabatic + isobaric processes

Entropy S – Temperature T

S

T

S(T )p1

-Q

p

v

T1 (>T2)

T2 (>T3)

T3

S1S(T )p

2

T3 T2 T1

S2 (< S1)

-Qp2

p1

Pressure p – Volume v

Vapor compression refrigeration cycleEx: Reverse Brayton cycle: adiabatic + isobaric processes

Entropy S – Temperature T

S

T

S(T )p1

-Q+Q

p

v

T1 (>T2)

T2 (>T3)

T3

S1S(T )p

2

T3 T2 T1

S2 (< S1)

+Q

-Qp2

p1

Pressure p – Volume v

Vapor compression refrigeration cycleEx: Reverse Brayton cycle: adiabatic + isobaric processes

Entropy S – Temperature T

S

T

S(T )p1

p

v

T1 (>T3)

T3

S1S(T )p

2

Pressure p – Volume v

S2 (< S1)

∆Tadiabatic

∆S i

soth

erm

al

Barocaloric effects:Adiabatic ∆T

Isothermal ∆SUpon application

of pressure

Barocaloric effects

Adiabatic ∆TIsothermal ∆S

Upon applicationof pressure

0=dS

∫

−=∆∆

F

I

p

p pdp

TVpTS

∂∂),(isot

Adiabatic (rev.)Isothermal0=dT

dpTV

CTpTT

F

I

p

p ppad ∫

=∆∆

∂∂),(

dpTVTdTCTdS

Tp

−=

∂∂

Entro

pyS

Temperature T

S(T )pI

S(T )pF

∆Tad

∆S i

so

Barocaloric effects

Adiabatic ∆TIsothermal ∆S

Upon applicationof pressure

0=dS

∫

−=∆∆

F

I

p

p pdp

TVpTS

∂∂),(isot

Adiabatic (rev.)Isothermal0=dT

dpTV

CTpTT

F

I

p

p ppad ∫

=∆∆

∂∂),(

dpTVTdTCTdS

Tp

−=

∂∂

pTV

∂∂

Barocaloric effects

Adiabatic ∆TIsothermal ∆S

Upon applicationof pressure

0=dS

∫

−=∆∆

F

I

p

p pdp

TVpTS

∂∂),(isot

Adiabatic (rev.)Isothermal0=dT

dpTV

CTpTT

F

I

p

p ppad ∫

=∆∆

∂∂),(

dpTVTdTCTdS

Tp

−=

∂∂

pTV

∂∂~ Thermal expansion:

large for gases

Vapor compression refrigeration cycle

Barocaloric effects

Adiabatic ∆TIsothermal ∆S

Upon applicationof pressure

0=dS

∫

−=∆∆

F

I

p

p pdp

TVpTS

∂∂),(isot

Adiabatic (rev.)Isothermal0=dT

dpTV

CTpTT

F

I

p

p ppad ∫

=∆∆

∂∂),(

dpTVTdTCTdS

Tp

−=

∂∂

pTV

∂∂~ Thermal expansion:

large for gasesMay be large for solids at

first-order phase transitions

Vapor compression refrigeration cycle

Barocaloric effects

Adiabatic ∆TIsothermal ∆S

Upon applicationof pressure

0=dS

∫

−=∆∆

F

I

p

p pdp

TVpTS

∂∂),(isot

Adiabatic (rev.)Isothermal0=dT

dpTV

CTpTT

F

I

p

p ppad ∫

=∆∆

∂∂),(

dpTVTdTCTdS

Tp

−=

∂∂

pTV

∂∂~ Thermal expansion:

large for gasesMay be large for solids at

first-order phase transitions

Vapor compression refrigeration cycle

Solid-state barocaloric effects:- Overcomes problems of leakage- Offers more compact devices- Fast response- Efficiency?

t

t

SV

dpdT

∆∆

=

dpdT

II

I

I

II

T

p

II

IV

TS

T

)( 1,1 pTSt∆

)( 1,1 pTVt∆

Solid-solid first-order phase transitions: Clausius-Clapeyron

t

t

SV

dpdT

∆∆

=

II

I

)( 1,1 pTSt∆

∆Vt(T2,p2)

∆St(T2,p2)II

Solid-solid first-order phase transitions: Clausius-Clapeyron

II

I

)( 1,1 pTVt∆

V

TS

T

T

p

I

dpdT

Entro

pyS

Temperature T

S(T )pF

Solid-state barocaloric refrigeration cycleEx: Reverse Brayton cycle

S(T )pI

Entro

pyS

Temperature T

S(T )pF

Solid-state barocaloric refrigeration cycleEx: Reverse Brayton cycle

S(T )pI

Entro

pyS

Temperature T

S(T )pF

-Q

Solid-state barocaloric refrigeration cycleEx: Reverse Brayton cycle

S(T )pI

Entro

pyS

Temperature T

S(T )pF

-Q

Solid-state barocaloric refrigeration cycleEx: Reverse Brayton cycle

S(T )pI

Entro

pyS

Temperature T

S(T )pF

-Q+Q

Solid-state barocaloric refrigeration cycleEx: Reverse Brayton cycle

S(T )pI

300 320 340 360

10

20

T (K)

dq/d

T (J

K-1 k

g-1)

L

∫= dTdT

pdqT

pTS )(1),(

Cp

0 GPa

Calculation of isobaric entropy curves: Quasi-direct method

High-pressure calorimetry (DSC-DTA)

280 300 320 340 360 3800

200

400

600

800

1000

1200

S - S

240

K (J

K-1 k

g-1)

T (K)

0 GPa

280 300 320 340 360 3800

200

400

600

800

1000

1200

300 320 340 360

10

20

T (K)

dq/d

T (J

K-1 k

g-1)

L

∫= dTdT

pdqT

pTS )(1),(

Cp

Calculation of isobaric entropy curves: Quasi-direct method

High-pressure calorimetry (DSC-DTA)

0 GPa

S - S

240

K (J

K-1 k

g-1)

T (K)

0.35GPa

0.35 GPa

0 GPa

280 300 320 340 360 3800

200

400

600

800

1000

1200

300 320 340 360

10

20

T (K)

dq/d

T (J

K-1 k

g-1)

L

∫= dTdT

pdqT

pTS )(1),(

Cp

Calculation of isobaric entropy curves: Quasi-direct method

High-pressure calorimetry (DSC-DTA)

0 GPa

S - S

240

K (J

K-1 k

g-1)

T (K)

0.35GPa

0.35 GPa

0 GPa

∫

∂∂

−=→∆p

p patm

atm

dpTVppTS ),(

(High-pressure) X-ray diffraction, dilatometry

260 280 300 320 340 3600.92

0.96

1.00

v (cm

3 g-1)

T (K)

280 300 320 340 360 3800

200

400

600

800

1000

1200

S - S

240

K (J

K-1 k

g-1)

∆S∆T

T (K)

Calculation of barocaloric effects: Quasi-direct method

0 GPa0.35 GPa

280 300 320 340 360 3800

200

400

600

800

1000

1200

S - S

240

K (J

K-1 k

g-1)

∆S∆T

T (K)

280 300 320 340 360 3800

200

400

600

∆S

(J K

-1 k

g-1)

T (K)

0.35 GPa → 0 p → 0

280 300 320 340 360 380

-30

-20

-10

0

∆T (K

)

T (K)

Adiabatic temperature changesIsothermal entropy changes

Calculation of barocaloric effects: Quasi-direct method

0.35 GPa → 0

0 GPa0.35 GPa

0.0 0.2 0.4 0.6

300

320

340

360

p (GPa)

T (K

)300 320 340 360

10

200.5

00.45

0.30

0.25

0.15

0.05

T (K)

dq/d

T (J

K-1 k

g-1)

0.00p (GPa)

High-pressure calorimetry

Transition entropy change

I

II

T-p Phase diagram

Calculation of barocaloric effects: Clausius-Clapeyron

dpdT

0.0 0.2 0.4 0.6280

320

360

400

|∆S t| (

J K-1 k

g-1)

p (GPa)

0.0 0.2 0.4 0.6

0.02

0.04

C-C

|∆V t| (

cm3 g-1

)

p (GPa)

Transition volume change

Calculation of barocaloric effects: Clausius-Clapeyron

SdpdTv ∆=∆

0.0 0.2 0.4 0.6

300

320

340

360

p (GPa)

T (K

)300 320 340 360

10

200.5

00.45

0.30

0.25

0.15

0.05

T (K)

dq/d

T (J

K-1 k

g-1)

0.00p (GPa)

High-pressure calorimetry

Transition entropy change

I

II

T-p Phase diagram

dpdT

0.0 0.2 0.4 0.6280

320

360

400

|∆S t| (

J K-1 k

g-1)

p (GPa)

0.0 0.2 0.4 0.6

0.02

0.04

C-C x-rays

|∆V t| (

cm3 g-1

)

p (GPa)

Transition volume change

Calculation of barocaloric effects: Clausius-Clapeyron

260 280 300 320 340 3600.92

0.96

1.00

v (cm

3 g-1 )

T (K)

Conventional X-ray diffraction

SdpdTv ∆=∆

0.0 0.2 0.4 0.6

300

320

340

360

p (GPa)

T (K

)300 320 340 360

10

200.5

00.45

0.30

0.25

0.15

0.05

T (K)

dq/d

T (J

K-1 k

g-1)

0.00p (GPa)

High-pressure calorimetry

Transition entropy change

I

II

T-p Phase diagram

dpdT

0.0 0.2 0.4 0.6280

320

360

400

|∆S t| (

J K-1 k

g-1)

p (GPa)

0.0 0.2 0.4 0.6

0.02

0.04

C-C x-rays H-P x-rays

|∆V t| (

cm3 g-1

)

p (GPa)

Transition volume change

Calculation of barocaloric effects: Clausius-Clapeyron

260 280 300 320 340 3600.92

0.96

1.00

v (cm

3 g-1 )

T (K)

Conventional & synchrotron high-pressure X-ray diffraction

SdpdTv ∆=∆

0.0 0.2 0.4 0.6 0.8 1.0

0.92

0.96

1.00T (K)383333321

p (GPa)

v (cm

3 g-1)

0.0 0.2 0.4 0.6

300

320

340

360

p (GPa)

T (K

)300 320 340 360

10

200.5

00.45

0.30

0.25

0.15

0.05

T (K)

dq/d

T (J

K-1 k

g-1)

0.00p (GPa)

High-pressure calorimetry

Transition entropy change

I

II

T-p Phase diagram

dpdT

0.0 0.2 0.4 0.6280

320

360

400

|∆S t| (

J K-1 k

g-1)

p (GPa)

0.0 0.2 0.4 0.6

0.02

0.04

C-C x-rays H-P x-rays Dilatometry

|∆V t| (

cm3 g-1

)

p (GPa)

0.0 0.2 0.4 0.6 0.8 1.0

0.92

0.96

1.00T (K)383333321

p (GPa)

v (cm

3 g-1)

0.0 0.1 0.2 0.3

0.92

0.96

1.00

p (GPa)

344

317321

338331

v (c

m3 g

-1)

325

T (K)Dilatometry

Transition volume change

Calculation of barocaloric effects: Clausius-Clapeyron

260 280 300 320 340 3600.92

0.96

1.00

v (cm

3 g-1 )

T (K)

Conventional & synchrotron high-pressure X-ray diffraction

SdpdTv ∆=∆

0.0 0.2 0.4 0.6

300

320

340

360

p (GPa)

T (K

)300 320 340 360

10

200.5

00.45

0.30

0.25

0.15

0.05

T (K)

dq/d

T (J

K-1 k

g-1)

0.00p (GPa)

High-pressure calorimetry

Transition entropy change

I

II

T-p Phase diagram

dpdT

0.0 0.2 0.4 0.6280

320

360

400

|∆S t| (

J K-1 k

g-1)

p (GPa)

· First-order solid-state transition involving large latent heat and volume changes

· Small hysteresis to enhance reversibility

· Appropriate temperature regimes

· Cyclability (no breakdown, no fatigue)

· High thermal conductivity to enhance heat transfer

· Cheap, abundant, non-toxic

· High density for more compact devices

Giant barocaloric materialsGeneral requirements of competitive candidates

- Magnetostructural transitions

Giant barocaloric materials: transitions with volume changes and large latent heat

0 1 2 30

20

40

60

p (kbar)|∆

S peak

| (J

K-1 k

g-1)

GdSiGeFeRh

NiMnInNiCoMnGaIn

LaFeCoSi

MnNiSi-FeCoGe

MnCoGeIn

MnGaN

Ordering

of spins

Emergence of

net polarization

- Magnetostructural transitions

- Ferroelectric transitions

Giant barocaloric materials: transitions with volume changes and large latent heat

0 1 2 30

20

40

60

p (kbar)|∆

S peak

| (J

K-1 k

g-1)

GdSiGeFeRh

NiMnInNiCoMnGaIn

LaFeCoSi

MnNiSi-FeCoGe

MnCoGeIn

BaTiO3

(NH4)2SO4

MnGaN

Ba

Ti

O P

Ordering

of spins

Emergence of

net polarization

Melting of

sublattice

- Magnetostructural transitions

- Ferroelectric transitions

Giant barocaloric materials: transitions with volume changes and large latent heat

0 1 2 30

20

40

60

p (kbar)|∆

S peak

| (J

K-1 k

g-1)

GdSiGeFeRh

NiMnInNiCoMnGaIn

LaFeCoSi

MnNiSi-FeCoGe

MnCoGeIn

(NH4)2SO4

BaTiO3

AgI

MnGaN- Superionic transitions

Ba

Ti

O P

Ordering

of spins

Emergence of

net polarization

Melting of

sublattice

- Magnetostructural transitions

- Ferroelectric transitions

Giant barocaloric materials: transitions with volume changes and large latent heat

0 1 2 30

20

40

60

p (kbar)|∆

S peak

| (J

K-1 k

g-1)

GdSiGeFeRh

NiMnInNiCoMnGaIn

LaFeCoSi

MnNiSi-FeCoGe

MnCoGeIn

(NH4)2SO4

BaTiO3

AgI(NH4)2SnF6

MnGaN- Superionic transitions

Ba

Ti

O P

- Fluoride salts

Ordering

of spins

Emergence of

net polarization

Melting of

sublattice

- Magnetostructural transitions

- Ferroelectric transitions

Giant barocaloric materials: transitions with volume changes and large latent heat

0 1 2 30

20

40

60

p (kbar)|∆

S peak

| (J

K-1 k

g-1)

GdSiGeFeRh

NiMnInNiCoMnGaIn

LaFeCoSi

MnNiSi-FeCoGe

MnCoGeIn

MnGaN

(NH4)2SO4

BaTiO3

AgI(NH4)2SnF6

[TPrA][Mn(dca)3]

- Superionic transitions

Ba

Ti

O P

- Fluoride salts- Hybrid organic-inorganic compounds: Metalorganic frameworks

Ordering

of spins

Melting of

sublattice

Emergence of

net polarization

- Magnetostructural transitions

- Ferroelectric transitions

Giant barocaloric materials: transitions with volume changes and large latent heat

0 1 2 30

20

40

60

p (kbar)|∆

S peak

| (J

K-1 k

g-1)

GdSiGeFeRh

NiMnInNiCoMnGaIn

LaFeCoSi

MnNiSi-FeCoGe

MnCoGeIn

MnGaN

(NH4)2SO4

BaTiO3

AgI(NH4)2SnF6

[TPrA][Mn(dca)3]NR- Superionic transitions

Ba

Ti

O P

- Fluoride salts- Hybrid organic-inorganic compounds: Metalorganic frameworks- Polymers: Natural Rubber, PVDF…

Ordering

of spins

Freeing of orien-

tational disorder

Melting of

sublattice

Emergence of

net polarization

- Magnetostructural transitions

- Ferroelectric transitions

Giant barocaloric materials: transitions with volume changes and large latent heat

Ordering

of spins

- Superionic transitions

- Orientationally Disordered Crystals

Ba

Ti

O P

- Fluoride salts- Hybrid organic-inorganic compounds: Metalorganic frameworks- Polymers: Natural Rubber, PVDF…

0 1 2 30

20

40

60

p (kbar)|∆

S peak

| (J

K-1 k

g-1)

Freeing of orien-

tational disorder

Melting of

sublattice

Emergence of

net polarization

- Magnetostructural transitions

- Ferroelectric transitions

Other BC materials

0 2 4

40

20

0|∆

T pea

k| (

K)

p (kbar)

Other BC materials

400

200

0

|∆S p

eak

| (J K

-1kg

-1)

Giant barocaloric materials: transitions with volume changes and large latent heat

Ordering

of spins

- Superionic transitions

- Orientationally Disordered Crystals

Ba

Ti

O P

Orientationally Disordered Crystal NPG

Orientationally Disordered Crystal NPG

- Fluoride salts- Hybrid organic-inorganic compounds: Metalorganic frameworks- Polymers: Natural Rubber, PVDF…

BarocaloricX: Volume VY: Pressure -p

MagnetocaloricX: Magnetization, MY: Magnetic Field, H

ElectrocaloricX: Polarization, PY: Electric Field, E

ElastocaloricX: Strain, ε

Y: uniaxial stress, σ

- High efficiency, quiet- First prototypes- Large magnetic Fields required: Expensive and difficult to generate- Toxic or expensive materials

-Thin films: Very large effects- Need of fabrication of multilayers- Bulk materials: Low breakdown fields

- Very large effect- Easy to apply- Plastic deformation and fatigue: Loss and mechanical breakdown

-Pressure: easy to generate- Powder → no fatigue-Very Wide range of materials-Efficiency? No proof-of-concept yet

Caloric effects: Generalization in Ferroic and multiferroic systems

Ba

Ti

O P

Entro

pyS

Temperature T

S(T )HI S(T )HF

-Q+Q

Solid-state magnetocaloric refrigeration cycleEx: Reverse Brayton cycle

Entro

pyS

Temperature T

S(T )HI S(T )HF

-Q+Q

Ex: Reverse Brayton cycle

Adiabaticapplication of H

Adiabaticremoval of H

Solid-state magnetocaloric refrigeration cycle

Sun

et a

l., A

pl 8

9, 1

7251

3 (2

006)

.

Multicaloric strategies

Mor

ello

net

al.,

PRL9

3,13

7201

(200

4)La Fe11.6 Si1.4Tb5Si2Ge2

Enhancement of caloric magnitudes &temperature shift

Liu

et a

l., N

atur

e M

at. 1

1, 6

20 (2

012)

Reduction of the effective hysteresis

Solid-state caloric and multicaloric effects may offer an alternative to current compression methods that use harmful gases.

Additional advantages may be higher efficiencies, more compact devices and faster reponses, as demonstrated by the existing prototypes.

There is a need of finding materials meeting the requirements for a competitive implementation.

To take home

Hysteresis losses in caloric effects

0 2 4 6

300

320

340

360

p (kbar)

T

(K)

Hea

ting

Hysteresis losses in caloric effects

0 2 4 6

300

320

340

360

p (kbar)

T

(K)

Hea

ting

Cooling

Hysteresis losses in caloric effects

0 2 4 6

300

320

340

360

p (kbar)

T

(K)

Hea

ting

Cooling

Decompression

Compression

Consequences of hysteresis losses on caloric effects

280 300 320 340 360 380

200

400

600

800

1000

1200

1400

∆S (J

K-1 k

g-1)

T (K)

3.5 kbar0 kbar280 300 320 340 360 380

-400

-200

0

200

400

∆S (J

K-1 k

g-1)

T (K)

280 300 320 340 360 380

-30

-20

-10

0

10

20

30

∆T (K

)

T (K)

p → 0

p → 0

Consequences of hysteresis losses on caloric effects

280 300 320 340 360 380

200

400

600

800

1000

1200

1400

∆S (J

K-1 k

g-1)

T (K)

3.5 kbar0 kbar280 300 320 340 360 380

-400

-200

0

200

400

∆S (J

K-1 k

g-1)

T (K)

280 300 320 340 360 380

-30

-20

-10

0

10

20

30

∆T (K

)

T (K)

p → 0

p → 0

Consequences of hysteresis losses on caloric effects

280 300 320 340 360 380

200

400

600

800

1000

1200

1400

∆S (J

K-1 k

g-1)

T (K)

3.5 kbar0 kbar280 300 320 340 360 380

-400

-200

0

200

400

∆S (J

K-1 k

g-1)

T (K)

280 300 320 340 360 380

-30

-20

-10

0

10

20

30

∆T (K

)

T (K)

p → 0

p → 0

Consequences of hysteresis losses on caloric effects

280 300 320 340 360 380

200

400

600

800

1000

1200

1400

∆S (J

K-1 k

g-1)

T (K)

280 300 320 340 360 380

-400

-200

0

200

400

∆S (J

K-1 k

g-1)

T (K)

280 300 320 340 360 380

-30

-20

-10

0

10

20

30

∆T (K

)

T (K)

0 → p

0 → p

280 300 320 340 360 380

200

400

600

800

1000

1200

1400

∆S (J

K-1 k

g-1)

T (K)

Consequences of hysteresis losses on caloric effects

280 300 320 340 360 380

-400

-200

0

200

400

∆S (J

K-1 k

g-1)

T (K)

280 300 320 340 360 380

-30

-20

-10

0

10

20

30

∆T (K

)

T (K)

0 → p

280 300 320 340 360 380

-30

-20

-10

0

10

20

30

∆ T (K

)

T (K)

p → 0

p → 0

0 → p

Consequences of hysteresis losses on caloric effects

280 300 320 340 360 380

200

400

600

800

1000

1200

1400

∆S (J

K-1 k

g-1)

T (K)

280 300 320 340 360 380

-400

-200

0

200

400

∆S (J

K-1 k

g-1)

T (K)

280 300 320 340 360 380

-30

-20

-10

0

10

20

30

∆T (K

)

T (K)

p → 0

0 → p

p → 0

0 → p

Consequences of hysteresis losses on caloric effects

280 300 320 340 360 380

200

400

600

800

1000

1200

1400

∆S (J

K-1 k

g-1)

T (K)

280 300 320 340 360 380

-400

-200

0

200

400

∆S (J

K-1 k

g-1)

T (K)

p → 0

280 300 320 340 360 380

-30

-20

-10

0

10

20

30

∆T (K

)

T (K)

p → 0

0 → p

0 → p

280 300 320 340 360 3800

200

400

600

800

1000

1200

300 320 340 360-5

0

5

10

15

20

25

dq/d

T (J

g-1)

T (K)

∫

∂∂

−=→∆p

p patm

atm

dpTVppTS ),(

S - S

240

K (J

K-1 k

g-1)

(High-pressure) X-ray diffraction, dilatometry

260 280 300 320 340 3600.92

0.96

1.00

v (cm

3 g-1)

T (K)

Cp

L

T (K)

∫= dTdT

pdqT

pTS )(1),(

∆S∆T

0 kbar 3.5 kbar

3.5 kbar0 kbar

Calculation of isobaric entropy curves: Quasi-direct method

High-pressure calorimetry (DSC-DTA)

Vapor compression refrigeration cycleEx: Reverse Carnot cycle: adiabatic + isothermal processes

Entropy S – Temperature T

S

T

-Q+Q

p

v

T1 (>T3)

T3

S1

Pressure p – Volume v (Ideal gas)

T3 T1

S2 (< S1)

+Q

-QS1

S2

S(p=cte)

280 300 320 340 360 3800

200

400

600

800

1000

1200

300 320 340 360-5

0

5

10

15

20

25

dq/d

T (J

g-1)

T (K)

∫

∂∂

−=→∆p

p patm

atm

dpTVppTS ),(

S - S

240

K (J

K-1 k

g-1)

(High-pressure) X-ray diffraction, dilatometry

260 280 300 320 340 3600.92

0.96

1.00

v (cm

3 g-1)

T (K)

Cp

L

T (K)

∫= dTdT

pdqT

pTS )(1),(

∆S∆T

0 kbar 3.5 kbar

3.5 kbar0 kbar

Calculation of isobaric entropy curves: Quasi-direct method

High-pressure calorimetry (DSC-DTA)

H.-G

. Unr

uh &

U. R

udig

er,

J. Ph

ys. C

oll.

33, C

2-77

(197

2)P.

Llov

eras

et a

l.,N

atur

e Co

mm

. 6, 8

801

(201

5)

(NH4)2SO4: electro + barocaloricFe49Rh51 : magneto + barocaloric

Multiferroic systems: Multicaloric effectsJ.

S. K

ouve

l, J.

Appl

. Phy

s. 3

7, 1

257

(196

6)

M. P

. Ann

aora

zove

t al.,

J. Ap

pl. P

hys.

79,

168

9 (1

996)

Mag

netiz

atio

n

Multicaloric effects: Hysteresis reduction

J. Liu et al., Nature Mat. 11, 620 (2012)

Ni-Mn-In-Co

Magnetocaloric effect, with simultaneous application of pressure- If dT/dp > 0, application of pressure on cooling- If dT/dp < 0, application of pressure on heating

Entro

pyS

Temperature TTransition at T1, p1

S(T )pI

Solid-solid first-order phase transitions

Entro

pyS

Temperature T

S(T )pI

S(T )pF

Transition at T1, p1 Transition at T2, p2

Solid-solid first-order phase transitions

Entro

pyS

Temperature TTransition at T1, p1 Transition at T2, p2

Pressure-inducedtransition at T=cte

S(T )pF

S(T )pI

Solid-solid first-order phase transitions

- Magnetostructural transitions

Ordering

of spins

Giant barocaloric materials: transitions with volume changes and large latent heat

0 1 2 30

20

40

60

p (kbar)|∆

S peak

| (J

K-1 k

g-1)

GdSiGeFeRh

NiMnInNiCoMnGaIn

LaFeCoSi

MnNiSi-FeCoGe

- Magnetostructural transitions

- Ferroelectric transitions

Giant barocaloric materials: transitions with volume changes and large latent heat

Ba

Ti

O P Emergence of

net polarization

Adiabatic ∆TIsothermal ∆S

Upon application ofan external field Y

p : Pressure → Barocaloricσ : Stress → Elastocaloric H : Magnetic Field → MagnetocaloricE : Electric Field → Electrocaloric

Generalized caloric effects:

∫

=∆∆

1

2

),(isotY

Y YdY

TXYTS

∂∂

dYTX

CTYTT

Y

Y YYad ∫

−=∆∆

1

2

),(∂∂

dYTXTdTCTdS

YY

+=

∂∂

X: Generalized displacement

→ The transition can be driven by electric field↓

ELECTROcaloric effects

→ The transition can be driven by magnetic field↓

MAGNETOcaloric effects

Ordering

of spins

Caloric materials: Ferroic and multiferroic systems

BarocaloricX: Volume VY: Pressure -p

-Pressure: easy to generate- Powder → no fatigue-Very Wide range of materials-Efficiency? No proof-of-concept yet

ElectrocaloricX: Polarization, PY: Electric Field, E

-Thin films: Very large effects- Need of fabrication of multilayers- Bulk materials: Low breakdown fields

Ba

Ti

O P

ElastocaloricX: Strain, ε

Y: uniaxial stress, σ

- Very large effect- Easy to apply- Plastic deformation and fatigue: Loss and mechanical breakdown

MagnetocaloricX: Magnetization, MY: Magnetic Field, H

- High efficiency, quiet- First prototypes- Large magnetic Fields required: Expensive and difficult to generate- Toxic or expensive materials

- Long piping (up to hundreds of m in domestic units)- Large amounts of refrigerant required (up to 50 kg)- Installation often made by end users- Mandatory leak inspections are often unfeasible- Costly waste management

Leaks

RefrigerantFamily

Global Warming Potential (CO2 = 1)

Ozone-Depleting Potential (CFC = 1)

Regulation

CFC 4500-11000 0.3-1 Prohibited in 1996HCFC 70-3200 0.02-0.06 Phase out by 2020HFC 600-1500 0 Phase out by 2020-2030HFO 4 0 -

Vapor compression refrigeration cycleDrawback: Leakage of harmful refrigerant fluids

Drawback: Leakage of harmful refrigerant fluids

Greenhouse effect Ozone depletion

- In Germany, stationary air conditioning units caused 405 tons of HFCemissions in 2010, or 717400 tons CO2 equivalent- 60% of world HFC emissions arise from leaks- 2050: Almost 10 % of global greenhouse gas emissions

Need for a more sustainable technologyProposal: Solid-state caloric effects

Vapor compression refrigeration cycle