departament d’estructura i constituents de la matèria universitat de barcelona structure and...

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

Structure and magnetism in the premartensitic and martensitic states

in Heusler shape-memory alloys

Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007

Antoni Planes

Collaborators: E. Bonnot, T. Castán, Ll. Mañosa, X. Moya, M. Porta, E. Vives (UB), A. Saxena, T. Lookman, J. Lashley (Los Alamos), M. Acet, T. Krenke, E.F. Wassermann, S. Aksoy (Duisburg), M. Morin (INSA). T.A. Lograsso, J.L. Zarestky (Ames)

Introduction

Magnetic shape-memory effect refers to the change of shape (deformation) of a magnetic material undergoing a martensitic transition caused by either:

inducing the transition or

rearranging the martensitic variantsby means of an applied magnetic field

Prototypical shape-memory alloy: Ni-Mn-Ga

Maximum induced deformation ~ 10% with an applied field ~ 10 kOe two orders of magnitude larger than in magnetosrictive Terfenol-D (Tb0.27Dy0.73Fe2)


Shape-memory properties


Superelasticity Shape-memory effect

Ela

stic

Sup

erel

astic

Ela

stic

Magnetic shape-memory properties


Magnetic superelasticity Magnetic shape-memory effect

H

H

Ela

stic

Sup

erel

astic

Ela

stic

La2-xSrxCuO4 Lavrov et al., Nature, 418, 385 (2002) (antiferro)

Magnetic shape-memory materialsHEUSLER

IRON-BASED

OTHER

Ni-Mn-X Ullakko et al., APL, 69, 1966 (1996) (Ga)

(X= Ga, Al, In, Sn, …) Fujita et al., APL, 77, 3054 (2000) (Al)

Sutou et al., APL, 85, 4358 (2004); Krenke et al., PRB, 72, 014412 (2005); 73, 174413 (2006) (In,Sn)

Co-Ni-Al Oikawa et al., APL, 79, 2472 (2001)

Ni-Fe-Ga Morito et al., APL, 81, 5201 (2002); 83, 4993 (2003)

Fe-Pd James & Wuttig, PMA, 77, 1273 (1998)

Fe-Pt Kakeshita et al., APL, 77, 1502, (2000)

Co-Ni Zhou et al., APL, 82, 760 (2003)


InterplayStructural degrees

of freedomMagnetic degrees

of freedom

Unique pretransitional behaviour

Mesoscopic scale

Elastic domains(variants)

Magnetic domains

Microscopic scale

(spin-phonon interplay)

Magnetic shape-memory Magnetic superelasticity Magnetocaloric effect

Magnetostructural interplay


Outline

Phase diagram and general properties Pretransitional effects: Phonon anomalies and the intermediate transition

Conclusions


Magnetic properties

Heusler, L21 (Fm3m)

Ni

Mn

Ga

Ni2MnGa

• Ferromagnetic order (Tc~ 370 K)

• Total magnetic moment: µtotal 4.1 µB per f.u.

Non-stoichiometric Ni2Mn1+xGa1-x (µNi 0.3 µB per f.u.)

• Weak magnetic anisotropy BNitotal 3.5μx12μμ


Phase diagram

Ni2+xMn1-xGaIntermediate

Martensite

L21-ferro

L21-para

From: Vasil’ev et al., Physics-Uspekhi, 46, 559 (2003)

Phase diagram at constant Ga concentration


Phase diagram

7.0 7.2 7.4 7.6 7.8 8.0 8.20

300

600

900

1200

1500

L21

ferro

T (

K)

e/a

B2

martensitepara

L

L21

para

martensiteferrointermediate

ferro

Relative phase stability controlled (to a large extent) by the average number of valence electrons per atom, e/a


Other effects

From: Khan et al., J. Phys. Condens. Matter, 16, 5259 (2004)


Cubic

Martensitic transition mechanism

Transformation mechanism: Shear + Shuffle on {110} planes along <1-10> directions


10M ([32]2)

14M ([52])

Martensitic structure

From: Lanska et al., J. Appl. Phys., 95, 8074 (2004)

7,0 7,2 7,4 7,6 7,8 8,0 8,20

300

600

900

1200

1500

L 21

ferro

T (

K)

e/ a

B 2

martensitepara

L

L 21

para

martensiteferro

intermediate

ferro

7,5 7,6 7,7 7,8

200

300

400

500

T (

K)

e/ a


By increasing e/a the following structures occur:

10M 14M NM (L10 )

Entropy change


Ni-Mn-SnNi-Mn-InNi-Mn-Ga

paraferro paraferr

o

paraferro

Magnetic properties

e/a

From: Enkovaara et al., PRB, 67, 212405 (2003).

From: Albertini et al., APL, 81, 4032 (2002).


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

Ni50Mn35Sn15 Ni50Mn34In16

ΔSΔM

dHdTM

0ΔS independent of H

Effect of a magnetic field


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)

0H (T)

Precursors in phase transitions• Nanoscale structures which occur above phase transitions. They announce that a system is preparing for the phase transition before it actually takes place.

• Often observed in ferroic and multiferroic materials.

• Revealed by high-resolution imaging techniques well above the (expected) phase transition.

• Detected as anomalies in diffraction experiments (intense diffuse scattering) and in the response to certain exitations.

• Not expected in systems undergoing first-order transions (which are expected to occur abruptly).

• In martensites, related to low restoring forces in specific lattice directions (transition path).


Structural precursors in Ni-Al (similar phenomenology in Fe-Pd, ….., shape-memory alloys)

TEM Neutron Diffraction

From, S.M. Shapiro et al., PRL, 57, 3199 (1986)

Cross-hatched striations (tweed) parallel to {110} planes observed above TM.

(020

)

Example: tweed

(60 nm)


Phonons in Ni-Mn-Ga

L21 5M L21 7M

Acoustic-phonon dispersion curves for the cubic phase of Ni2MnGa. From: Zheludev et al., 54, 15045 (1996).

TA2 branch at selected temperatures.

The position of the dip depends on the selected martensite structure.

From: Mañosa et al. PRB, 64, 024305 (2001)


• The softening is enhanced at the Curie point.

• For systems transforming to the 5M structure, the softening is nearly complete at TI > TM. Upon further cooling the frequency increases.

• At TI the system undergoes the intermediate transition.

TML21 → 5M (low e/a)

TI (higher e/a)

Ni-Al (from Shapiro et al., PRL, 62, 1298 (1989); PRB, 44, 9301 (1991)

Slopes in the two phases

Phonon softening


Elastic constants

L21 5M L21 7M


Diffraction experiments(100)

J. Pons, private communication

T > TI T < TI (111)T < TI

TEM

Neutrons

From A. Zheludev et al., PRB, 54, 15045 (1996)

Elastic scattering along the (ξξ0) direction The transition at TI is associated with the lock-in of the pseudoperiodic tweed phase into a commensurate phase due to the freezing of the anomalous phonon.


Modulation of {110} planes with wave number 1/3 along <1-10> direction.

Preserve cubic symmetry.

Magnetic and thermal anomalies

Further results which prove the existance of the premartensitic transition.

A.c. magnetic susceptibility Calorimetry

Latent heat= 9 J/mol(Martensitic transition:~ 100 J/mol)A. Planes et al., PRL 79, 3926 (1997)

TI

200 220 240 260 280

-80

-70

-60

-50

Latent heat

[Differential] heat capacity (MDSC)

DSC thermal curve

dQ/d

T (

mJ/

g K)

T (K)

The intermediate transition is first-order


Effect of external fields

210 220 230 240 250 260

-0.16

-0.12

-0.08

-0.04

0.00

C

44/C

44

T (K) 0 2 4 6 8 10

230

232

234

236

238

240

(b)

TI

(K)

Stress (MPa)0 1 2 3 4 5

226

228

230

232

234

236

(a)

TI (

K)

Stress (MPa)

Elastic constantTransition temperatures:

ST

RE

SS

MA

GN

ET

IC F

IELD

From: W.H. Wang et al., J. Phys. Condens. Matter, 13, 2607 (2001)

From: Gozàlez-Comas et al., PRB , 60, 7085 (1999)

[001] direction

[1-10] direction

[1-10] direction

0 MPa1 MPa

4.5 MPa

TI ~ M2


Comparison with non-magnetic SMA

High temperature phase (cubic)

Ttw ?

Tweed

TI

Modulated (or intermediate) phase

TM

Martensite

Ni-Mn-Ga Ni-Al


Amplitude of the relevant phonon mode

Order parameters:

Magnetization M

Free energy:

Expansions:

Landau model

ηMFF(M)F(ηF )

...BM4

1AM

2

1F(M) 42

22ηM Mη

2

1F 1χ

6422* cη6

1bη

4

1ηωm

2

1)F(


Minimization with respect to M gives the following effective free-energy:

where:

M0 is the magnetization of the high temperature phase ( = 0):

20

6422*eff AM

4

1ηc

6

1ηb

4

1ηωm

2

1F ~~~

ccA

Mbb

)T(TaMωmωm20

u20

2*2*

~

~

~~~

21

1

χ

χ

c

20

cc

TT for 0

M

TT for T)μ(TB

A

Tc is the Curie temperature


Landau model

• If 12/B is large, can be negative, and a first-order transition is

possible. The transition temperature is:

• The temperature dependence of the anomalous phonon frequency:

1 > 0 softening is enhanced.

• Clausius-Clapeyron equation:

Results in agreement with the experiments if 1 > 0

b~

u

2

I Tca16

b3T

~~

~

0BMaΔS

ΔMdHdT

0

I ~1χ


Landau model: results

0.5 1.0 1.5 2.0 2.5

200

240

280

320

360

400

TI

Tc

T (

K)

x (at. Fe %)

Ni50.85

Mn23.88-x

Ga25.27

Fex

Ms

When an intermediate transition occurs?


Results for Ni-Mn-Ga(Fe)

0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2

200

240

280

320

360

400

Ms

Tc

Ni51.7

Mn22.9

Ga25.23-x

Fex

T (

K)

x (at. Fe %)0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

80

120

160

200

240

280

320

360

400

TIM

s

Tc

Ni52.21-x

Mn22.56

Ga25.23

Fex

T (

K)

x (at. Fe %)

120 160 200 240 280 320

0.0

0.4

0.8

1.2

(a.

u.)

T (K)

' ''

x=1.93

80 120 160 200 240

0.0

0.4

0.8

(a.

u.)

T (K)

' ''

x=3.91

270 300 330 360 390 420

-1000

0

1000

dQ

/dT

(J/

K k

g)

T (K)

x=2.06 Tc

Ms

In Heusler alloys the relative phase stability is (to a large extent)

controlled by e/a.

Compared to other shape-memory alloys, Ni-Mn-Ga shows unique pretransitional behaviour which is a consequence of spin-phonon coupling.

Strong softening of the 1/3[110]TA2 phonon and large magnetisation is required for a first-order intermediate transition to occur.

The intermediate phase almost preserves cubic symmetry and results from the freezing of 1/3[110]TA2 phonon.


Conclusions

• Transition at zero-field: Formation of twin related variant.

• The magnetic easy axis changes from one twin to the other

Cubic → Martensite (twinned)

• Effect of a magnetic field

Twin related variants and magnetic stripe domains inside

From: Ge et al., JAP, 96, 2159 (2004).

Weak anisitropy Strong anisitropy

In systems with strong anisotropy and highly mobile boundaries, field induced rearrangement of martensitic variants is possible Magnetic Shape-Memory


Magnetic shape-memory effect

Field induced deformation in a Ni-Mn-Ga alloy

The residual deformation remaining when the field is removed can be removed by:

1. Heating up through the transition

2. Application of a magnetic field perpendicular to the original

3. Application of a stress that opposes the applied field

From: Likhachev et al., Proc SPIE, 4333, 197 (2001)


Example

0 1 2 3 4 5-60

-40

-20

0

20

Ni2MnGa

Ni50.3

Mn33.8

In15.9

T (

K)

0H (T)


Magnetic superelasticity

From: Krenke et al., PRB, (2007)

Magnetic superelasticity in Ni-Mn-In alloy

ΔSΔM

dHdTM

0

Adiabatic Temperature change, Tadi

Isothermal Entropy change, Siso

when a magnetic field H is applied/removed

H ΔM

ΔM(H)dHΔS(H)e

H

e

H

H TTdH

TM

00

1It is given by:

∆Te is the range over which the transition extends.


Magnetocaloric effect

Controlled by the change of magnetization at the transition

ΔM = MM – MP > 0, Conventional magnetocaloric effect

ΔM = MM – MP < 0, Inverse magnetocaloric effect

170 175 180 185

0

1

2

3

4

5

6

M (1

03 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

0 10 20 30 40

-1.5

-1.0

-0.5

0.0

M (1

03 e

mu/

mol

)

H (kOe)

Ni49.5Mn25.4Ga25.1

∆M = MM - MP


Magnetocaloric effect in Ni2MnGa

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 H=10 kOe

T

S (J

/K m

ol)

T (K)

Inverse magnetocaloric effect

0 10 20 30 40

-1.5

-1.0

-0.5

0

¢M

(10

3 e

mu

/m

ol)

H (kOe)

(a) (b) (c)

Cubic Tetragonal


Physical picture

Historical

• Magnetostructural characterization, Ziebeck’s group [Philos.Mag. B, 49, 295 (1984)]

• Martensitic Transformation and Shape-Memory Properties (Martynov, Kokorin, …)

• Phonon anom. & Intermediate trans., Shapiro’s group PRB, 51, 11310 (1995)

• Magnetic Shape-Memory Effect, O´Handley’s group at MIT, APL, 69, 1966 (1996)

• Magnetoelastic coupling. Vordervisch, Trivisono, UB group (phonons/elas. cnts, 1997)

• Modelling: O’Handley (JAP, 1998), James & Wuttig (PMB, 1998), …..

• First.Principles Calculations: Helsinski group, Duisburg group, …

• Further developments, MIT group, Helsinki group, …..

• Development of other M-SMA: Ishida’s group, Kakeshita’s group, ….

• Magnetic superelasticity: Duisburg & Barcelona, PRB, 2007


departament d’estructura i constituents de la matèria universitat de barcelona structure and...

Documents

magnetic material

magnetic properties

material properties

atomistic simulations

ringberg castle germany

change of shape deformation

fm3m ni mn ga ni

zarestky ames slide