Departament d’Estructura i Constituents de la Matèria Universitat de Barcelona Structure and...
-
Upload
sheena-pitts -
Category
Documents
-
view
212 -
download
0
Transcript of 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)
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
Shape-memory properties
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
Superelasticity Shape-memory effect
Ela
stic
Sup
erel
astic
Ela
stic
Magnetic shape-memory properties
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
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)
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
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
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
Outline
Phase diagram and general properties Pretransitional effects: Phonon anomalies and the intermediate transition
Conclusions
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
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
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
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
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
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
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
Other effects
From: Khan et al., J. Phys. Condens. Matter, 16, 5259 (2004)
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
Cubic
Martensitic transition mechanism
Transformation mechanism: Shear + Shuffle on {110} planes along <1-10> directions
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
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
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
By increasing e/a the following structures occur:
10M 14M NM (L10 )
Entropy change
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
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).
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
Ni49.5Mn24.5Ga25.1Ni56.2Mn18.2Ga25.5
Ni50Mn35Sn15 Ni50Mn34In16
ΔSΔM
dHdTM
0ΔS independent of H
Effect of a magnetic field
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
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).
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
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)
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
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)
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
• 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
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
Elastic constants
L21 5M L21 7M
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
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.
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
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
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
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
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
Comparison with non-magnetic SMA
High temperature phase (cubic)
Ttw ?
Tweed
TI
Modulated (or intermediate) phase
TM
Martensite
Ni-Mn-Ga Ni-Al
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
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(
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
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
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
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
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
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?
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
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.
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
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
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
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)
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
Example
0 1 2 3 4 5-60
-40
-20
0
20
Ni2MnGa
Ni50.3
Mn33.8
In15.9
T (
K)
0H (T)
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
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.
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
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
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
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
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007
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
Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007