Magnetocaloric and shape- memory properties in ... Science... · Delft Days on Magnetocalorics , Delft, Netherlands October 30-31, 2008 Outline •Shape-memory properties •Magnetic

Delft Days on Magnetocalorics, Delft, Netherlands October 30-31, 2008

Departament d’Estructura i Constituents de la Matèria Universitat de Barcelona

Magnetocaloric and shape-memory properties in

ferromagnetic Heusler alloysAntoni Planes

Collaborators: Ll. Mañosa, X. Moya * (ECM, U. Barcelona)X. Batlle, A. Labarta, F. Casanova ** (FF, U. Barcelona) M. Acet, S. Aksoy, T. Krenke ***, E. Wasserman (U. Duisburg-Essen)

Present address: * Cambridge University** Univ. San Diego *** ThyssenKrupp


Thermodynamics

.......ΩσdεΩHdMµTdSdU +++= 0

Elastocaloricproperties

S

T

HσMε

Magnetocaloricproperties

Shape-memory properties

),(

),(

MS

SMM

εεε

==

Coupling


Outline

• Shape-memory properties

• Magnetic shape-memory and magnetostructural coupling

• First order transitions and magnetocaloric effect

• Results: Ni-Mn-Ga

• Other Heuler alloys

• Conclusions


Shape-memory propertiesShape-memory properties refers to the ability of a material undergoing a martensitic transition to recover from severe deformations:

• in the martensitic phase upon heating above the transition: Shape-memory effect

• upon loading and unloading a large strain associated with the stress-induced martensitic transformation: Superelasticity


Magnetic shape-memory properties

Magnetic shape-memory: Field induced deformation caused by rearranging the martensitic variants.

Requires:

Large magnetic anisotropy

+ High twin boundary mobility

Magnetic superelasticity: Field induced deformation caused by inducing the martensitic transition.

Requires:

Significant shift of the transitionwith magnetic field.


Coupling

Structure Magnetism

Microscopic scale Mesoscopic scale

Interplay

Controlled by the change of J

Controlled by the change of A

Magnetic superelasticity Magnetic shape-memory

Magnetocaloric effect


Magnetocaloric effect: General features

Magnetic system (T, H independent variables):

...dHH

SdT

T

SdS

T,...H,...

+

∂∂+

∂∂=

When magnetic field H is applied/removed:

Adiabatic Temperature change:

Isothermal Entropy change:

∫

∂∂−=

f

i

H

H THadi dH

H

S

C

T∆T

∫

∂∂=

f

i

H

H Tiso dH

H

S∆S

isoH

adi ∆SC

T∆T −≈


∫

∂∂=

∂∂=

∂∂ ⇒

f

i

H

H Hiso

HT

dHT

M∆S

T

M

H

SMaxwell relation

Magnetocaloric effect: Determination• Directly from calorimetric measurements

• Indirectly from magnetization curves

• ⇒ ∆Siso< 0 when Hf – Hi > 0 ⇒ Cooling by adiabatic demagnetization

• ⇒ ∆Siso< 0 when Hf – Hi > 0 ⇒ Heating by adiabatic demagnetization

0<

∂∂

HT

M

0>

∂∂

HT

M

MCE is expected to be large in regions where M shows a fast change with T ⇒vicinity of phase transitions

Considerations


∆Siso

M

TTt(0) Tt(H)

T

( )[ ]HTT∆M hM t−=

h(x) is the Heaviside function

[ ][ ]

∉

∈−=

∂∂= ∫

(H)),T(TT for

(H)),T(T for Tα

∆M

dHT

M∆S

tt

tt

H

iso

00

0

0

For ∆M > 0 (dTt /dH > 0) ⇒ ∆Siso < 0 (for 0 → H)

where α = |dTt /dH|

Example: Ideal first-order phase transition


( )[ ]HTT∆M hM t−=

h(x) is the Heaviside function

For ∆M > 0 (dTt /dH > 0) ⇒ ∆Siso < 0 (for 0 → H)

where α = |dTt /dH|

Example: Ideal first-order phase transition

M

TTt(H)∆Siso

T

Tt(0)

[ ][ ]

∉

∈−=

∂∂= ∫

(H)),T(TT for

(H)),T(T for Tα

∆M

dHT

M∆S

tt

tt

H

iso

00

0

0


∆M

T

Real first-order phase transition

H = 0

H ≠ 0 • The transition spreads over a range of temperatures

• It displays hysteresis

∫∆

∆∆

=∆T

dTHTMHT

HS ),()(

)( 0µ

∫∆

∆∆

−=∆Tt

t dTHTMHS

HT ),()(

)( 0µ

∆T(H)

)()(

)(

)(

HT

HT

HS

HSt

t ∆∆−=

∆∆

⇒

∆Tt(H)


Materials

Ni2MnGa

Mn

Ni50Mn50-xSnx

Ni50Mn50-xInx

Ni50Mn50-xSbx

Ni50Mn50-xAl x

Prototypical Heusler SMA: Ni2MnGa Other Heusler alloys:

Ni

Ga

Ni-Mn-Sn Ni-Mn-In Ni-Mn-Ga

Cubic 10 M or 5 M (other 7 M, …)


Effect of a magnetic field on the transition

200 250 300

-0,6

-0,4

-0,2

0

240 270 300 330

100 200 300

50 100 150 200-0,6

-0,4

-0,2

0

∆l/l

(%

)

N i50M n27Ga23

µ0H (T )

0 2 5

(a)

(d)

T (K )

N i50.3M n35.9Sb13.8

(b)

Ni50M n34In16

(c)

Ni49.8M n34.7Sn15.5

∆l/l

(%

)

T (K )

Ni-Mn-Ga:• Negligeablelength change at zero field• Negligible shift of the transition• Strong effect of the field on ∆l/l (< 0, easyaxis: short axis)

Black: H = 0 Blue: H = 2 T Red: H = 5 T

Ni-Mn-Sn :• Similar to Ni-Mn-In (smaller changes)

Ni-Mn-In :• Significant shift of the transition with the field• Noticeable length change at zero field • ∆l/l > 0 (easy axis: long axis)

Ni-Mn-In /Sn good candidates to display (reverse) magnetic superelasticity

Ni-Mn-Ga good candidate for magnetic shape-memory effect


0 10 20 30 40 500

0.1

<∆S

> (

J/K

mol

)

H (kOe)

170 175 180 185

0

0.2

0.4

0.6 100 Oe 500 Oe 1 kOe 2 kOe 4 kOe 10 kOe 20 kOe 30 kOe 40 kOe

∆S (

J/m

ol K

)

T (K)

Ni49.5Mn25.4Ga25.1

0 5 10 15 200

1

2

3

4

5

6

T=160K T=170K T=174K T=176K T=177K T=177.5K T=178K T=178.5K T=179K T=179.5K T=180K T=182K T=184K T=186K T=190K

M (

emu/

mol

)

H (kOe)

∫

∂∂=

H

0 H

dHTM

∆S

Magnetocaloric effect: Ni2MnGa

170 175 180 185

0

0.2

0.4

0.6 H=10 kOe

∆T

∆S (

J/K

mol

)

T (K)

Inversemagnetocaloriceffect!

Marcos et al., Phys. Rev. B,66, 224413 (2002)

∫=∆T

H)dH∆S(T,∆T1

∆S


A region exists where (∂M/∂T)H >0

Cubic Tetragonal

170 175 180 185

0

1

2

3

4

5

6

M (

103 e

mu/

mol

)

T (K)

0 100 200 300 400 500 700 1 kOe 2 kOe 4 kOe 6 kOe 10 kOe 20 kOe 40 kOe

∆M ~ 0

∆M < 0

∆M > 0

Explanation

0 1 0 2 0 3 0 4 0

-1 .5

-1 .0

-0 .5

0

¢M

(10

3 em

u/m

ol)

H ( k O e)

(a) (b) (c)

∆M


Contributions

Marcos et al., Phys. Rev. B, 68, 094401 (2003)

Low and intermediate fields: thedominant contribution is related tothe magnetostructural interplayat mesoscale (magneticanisotropy). Gives rise to aninverse magnetocaloric effect .

High fields: the dominantcontribution is related to themicroscopic magnetostructuralcoupling (change of TM with anapplied field). Gives rise to a conventional magnetocaloriceffect.

0 10 20 30 40-0.1

0

0.1

0.2

⟨¢S⟩

(J/K

mol

)

H (kOe)

∆


e/a

(K)

7.4 7.6 7.80

200

400

600

800

TC

L21

ferro-

T

TM

M ferro-

L21

para-

Effect of compositionMarcos et al., Phys. Rev. B, 68, 094401 (2003)

Tc-TM = 0 K

Tc-TM = 26 KTc-TM = 51 KTc-TM = 150 K

Tc-TM ~ 201 K

TC−TM ~ 201 K

TC−TM = 150 K

TC−TM = 26 K

TC−TM ~ 0 K

TC−TM = 51 K

0 10 20 30 40 50-2.0

-1.5

-1.0

-0.5

0

0.5

1.0

1.5

∆M (

103 e

mu/

mol

)

H (kOe)

Alloy 1 Alloy 2 Alloy 3 Alloy 4 Alloy 5

0 1.0 2.0 3.0 4.0-4

-2

0

2

4

6

<∆S

> (

10-2

J/K

mol

)

H (kOe)


Other Heusler shape-memory alloy

Ni49.5Mn24.5Ga25.1Ni56.2Mn18.2Ga25.5

Ni50Mn35Sn15 Ni50Mn34In16


Results: Ni-Mn-SnKrenke et al., Nature Mater. 4, 450 (2005); Phys Rev. B, 72, 014412 (2005)

285 300 315 330

0

10

20

165 180 195

0

10

20

b)

T (K)

x = 0.13

Mf

Ms T A

C

Ms

a)

∆S

(J

kg-1 K

-1)

T (K)

1 2 3 4 5

x = 0.15µ

0 H (T)

Mf


Results: Ni-Mn-InMoya et al., Phys. Rev. B, 75, 184412 (2007); Krenke et al., Phys. Rev. B, 73, 174413 (2006)


Results: Ni-Mn-InMoya et al., Phys. Rev. B, 75, 184412 (2007); Krenke et al., Phys. Rev. B, 73, 174413 (2006)


Comparison

0 10 20 30 40 50-0.4

-0.2

0

0.2

0.4

0.6

0.8

1.0

⟨∆S⟩/|

∆St|

Ni49.5

Mn25.4

Ga25.1

Ni56.2

Mn18.2

Ga25.6

Ni50

Mn35

Sn15

Ni50.3

Mn33.8

In15.9

H (kOe)

Ni49.5Mn24.5Ga25.1 Ni56.2Mn18.2Ga25.5

Ni50Mn35Sn15 Ni50Mn34In16


0 1 2 3 4 5-60

-40

-20

0

20

Ni2MnGa

Ni53.5

Mn19.5

Ga27

Ni50

Mn35

Sn15

Ni50.3

Mn33.8

In15.9

∆T (

K)

µ0H (T)

Magnetocaloric effect vs. Clausius-Clapeyron

∆St independent of H

0 10 20 30 40 50-0.4

-0.2

0

0.2

0.4

0.6

0.8

1.0

⟨∆S⟩/|

∆St|

Ni49.5

Mn25.4

Ga25.1

Ni56.2

Mn18.2

Ga25.6

Ni50

Mn35

Sn15

Ni50.3

Mn33.8

In15.9

H (kOe)

)()(

)(HT

HS

HSt

t

∆−∝∆∆

∫∆

∆∆

=∆T

dTHTMHT

HS ),()(

)( 0µ∫

∆

∆∆

−=∆Tt

t dTHTMHS

HT ),()(

)( 0µ

Kim et al., Acta Mater., 54, 493 (2005)Jeong et al., Mater. Sci. Engng. A, 359, 253 (2003)


• Heusler alloys show large magnetocaloric effect in the vicinity of the martensitic transition.

• The physics of magnetocaloric effect is controlled by the behaviour of the magnetization change at the transition.

• In nearly stoichiometric Ni2MnGa inverse magnetocaloric effect occurs at low applied fields due to the high magnetic anisotropy of the martensitic phase.

• In non-stoichiometric Ni-Mn-Sn and Ni-Mn-In giant inverse magnetocaloric effect is a consequence of the tendency of the excess of Mn atoms to introduce antiferromagnetic coupling.

Conclusions


Dissipative effects

∫ −=⇒≤ iδSdST

δq

T

δq0

0 → H : Adibatic change of T

C

TS∆S

C

T ∆T

∆SC

T∆T

iirr

rev

+−=

−=

where

∫

∂∂=

H

H

dHT

M∆S

0∆

Tirr

∆T

rev

Ni-Mn-InMoya et al., Phys. Rev. B, 75, 184412 (2007)


Entropy and magnetization changeNi50Mn35Sn15Krenke et alPhys.Rev.B72 (2005) 14412

Ni50Mn34In16Krenke et alPhys. Rev B 73(2006) 174413

Ni49.5Mn24.5Ga25.1Marcos et al., Phys.Rev.B 66(2002) 224413

Ni56.2Mn18.2Ga25.5L. Pareti et al., Eur. Phys.J B 32(2003) 303

Ni-Mn-In

Ni-Mn-Sn

Ni-Mn-Ga

Moya et al., Mat. Sci. Engn. A 438 (2006) 913

Documents

Magnetocaloric and shape- memory properties in ... Science... · Delft Days on Magnetocalorics , Delft, Netherlands October 30-31, 2008 Outline •Shape-memory properties •Magnetic