1

CHAPTER 1

INTRODUCTION

The chapters 1 and 2 give a review of Ferromagnetic Shape Memory

Alloys (FSMAs), origin of ferromagnetism and nanostructured materials. The

concepts and definitions introduced below are needed when analyzing the

experimental data, in particular, the optimization of Martensitic Transformation

(MT) in ferromagnetic nanoparticles.

1.1 FERROMAGNETIC SHAPE MEMORY ALLOYS - AN OVERVIEW

Smart materials have received flurry of activity in the last two decades

because of their great technological significance and potential applications (Takagi

1996, Gandhi 1992). Smart material means that it has sensing, actuating and

controlling or information-processing capabilities. With a stimulus, it can respond in

a pre-determined manner and extent in an appropriate time and then revert to its

original state as soon as the stimulus is removed (Wei 1997). Though smart

materials having several classification, Shape Memory Alloys (SMAs) have been

central class of smart materials after the possibility for using the Shape Memory

Effect (SME) in actual applications was realized in a Ti-Ni alloy in 1963 (Buehler et

al). They have successfully been used in actuator and sensor design as well as

biomedical and numerous other technological applications. These materials exhibit

the large strain of 6–10% when being subjected to thermal or mechanical load, is

caused by the change in crystallography associated with a reversible austenite to

martensite phase transformation. In conventional SMAs, which are paramagnetic,

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the martensitic transformation underlying the SME is induced by changes in

temperature or stress or both (Liu 2005). In spite of the large strain achieved, the

activation of the thermo elastic SME is slow and inefficient because it depends on

the transportation of heat, i.e. heating, especially cooling of the sample. On the other

hand, FSMAs alloys have more recently emerged as an interesting addition to this

class of materials. In particular, Ni-Mn-Ga has generated immense interest because

of very large strain in a moderate magnetic field (1 Tesla) (Sozinov 2002, Müllner

2004). Moreover, in Ni-Mn-Ga the actuation is much faster than in conventional

SMA. The martensitic transformation in FSMAs can be triggered not only by

changes in temperature and stress, but also by changes in the applied magnetic field.

This enables the devices to operate at high frequencies and facilitates their remote

control (Nishiyama 1978, Otsuka et al 1987).

FSMAs distinguish themselves from the thermoelastic SMAs by the fact

that the magnetic field induced shape change occurs fully within the

low-temperature martensitic phase. This new FSM effect is associated with the

motion of twin boundaries between regions in which the magnetization direction

differs. It necessitates large magnetocrystalline anisotropy. Therefore, the Magnetic

Field Induced Strain (MFIS) in FSMAs arises from a mechanism different from that

responsible for magnetostrictive materials, i.e. the rotation of the magnetization

direction having appreciable spin-orbit coupling. The large MFIS of 10% in

Ni-Mn-Ga alloy was presented by Sozinov et al (2002a) and Müllner et al (2004a).

This MFIS in Ni-Mn-Ga is generated by twin boundary motion under the influence

of an internal stress produced by a magnetic field through the magnetocrystalline

anisotropy and are different from the conventional magnetostriction.

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In 1968, P.J. Webster was the first to describe in detail the magnetic

properties of a new alloy with stoichiometric composition Ni2MnGa (Webster

1984). Extensive research in Poland (Soltys 1975) and later on in Russia (Kokorin

1989, Zasimchuk 1990) revealed the existence of a martensitic transformation in

this system. Large, reversible, MFISs of order 0.2% were first reported in single

crystals of Ni2MnGa by Ullakko et al in 1996 and a shift in the martensitic

transformation temperature of at most one or two degree under 10 kOe magnetic

field was also reported (Ullako 1996). In 1997, Ullakko and coworkers (Ullako

1997) and a little later Wuttig and James also have been suggested MFIS. In 1999, a

5% shear strain was discovered at room temperature in a field of 4 kOe in 5-layer

tetragonal Ni-Mn-Ga martensite by Murray et al (2000).

Recently, the MFIS close to 10% was found in 7-layer orthorhombic Ni-

Mn-Ga modulated martensite (Sozinov 2002b). The necessary conditions for the

occurrence of FSMAs have been overviewed by Wuttig et al (2000) and a

constrained theory of magnetostriction intended to describe strain versus field and

the associated microstructural changes in these materials is given by Desimone and

James (2002). Various phenomenological models have been proposed to understand

the elastic and magnetic properties in FSMAs. O’Handley (1998) presents a model

for the magnetization process, field-induced strain by twin-boundary and phase-

boundary motion and accounts for the magnetic anisotropy, based on a particular

twinned domain structure. It shows good agreement with experimental data of

Ullakko et al (1996) and suggests that the competition of twin blocking stress and

magnetic driving force leads to a restricted temperature window for magnetic

actuation in Ni2MnGa alloys. L’vov (1998) starts from an expression for the

Helmholtz free energy of a cubic crystal to derive the expressions for the static

magnetic susceptibility and for the magnetization of the martensite. Their analysis

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demonstrates that the magnetization of FSMAs is closely related to the spontaneous

strains arising at martensitic temperature TM, which indicate a strong magneto-

elastic coupling in the vicinity of martensitic phase transformation.

Many FSMA systems have been developed such as Ni2MnGa (Chernenko

2011), Ni2MnAl (Manosa 2003), Co–Ni–Ga (Al) (Wuttig 2001, Oikawa 2001) and

Ni–Fe–Ga (Zheng 2011, Barandiaran 2008), Fe-Pd (James 1998), Fe-Pt (Kakeshita

1984), Ni-Mn-In (Liu 2009), Ni-Mn-Sn (Xuan 2008) and Ni-Mn-Sb (Dubenko

2009). There have been many reports on their structure, magnetic properties,

martensitic transformation, magnetically controlled shape memory effect, super

elasticity and MFIS. However, Ni2MnGa is one of the prototypical FSMAs; the

history and development of the Ni-Mn-Ga alloys are well described in Refs

(Chernenko 2008, Söderberg 2005). The martensitic temperature is reported to be

around 210 K, while the Curie temperature (TC) is around 370 K (Vasil'ev 2003). In

the high temperature austenitic phase, the structure of Ni2MnGa has been found to

be cubic L21 ordered structure with a = 5.825 Å and also known as the Heusler

structure. The MT temperature can be controlled by changing chemical composition

of the alloy in relation to e/a ratio.

1.2 MARTENSITIC TRANSFORMATIONS

The word ‘martensite’, named after a German microscopist Adolf

Martens, was originally used to describe the differently oriented banded regions in

hard steels in 1890 (Smith 1992). Since then, the realization that the microstructure

is as important as composition in determining a material’s properties has expanded

the studies of martensitic transformations (MTs) from the formation of the

mysterious hardening constituent in quenched iron to a broad class of solid-state

phase transformations occurring in metals, ceramics, polymers and semiconductors

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(Patrick Kelly 2002, Hornbogen 2006, Roitburd 1992). Simply speaking, the study

of phase transformations concerns those mechanisms by which a system attempts to

reach an equilibrium state and how long it takes. The diffusion of atoms is

obviously one of the most fundamental processes to control the kinetics of most

transformations. Therefore, the diffusional transformations in solids are worth to be

mentioned briefly in the beginning.

MTs are diffusionless structural phase transitions of the cooperative type.

The characteristic features of such transformations are the cooperative

displacements of neighboring atoms by distances smaller than the atomic separation.

MTs were first discovered in iron-based alloys (steel). They were interpreted as

structural transformations of a high-temperature austenitic parent cubic phase into

low-temperature martensitic phase. It was found that transformations similar to the

martensitic transformation in steel occur in solids of a different nature (metals,

insulators, semiconductors, and organic compounds) and belong to one of the main

types of phase transformations in the solid state (Otsuka 1998). The most general

feature of MTs is that they occur in the solid medium at low temperatures during

cooling. The conditions under which martensitic transformations take place (elastic

medium, low temperatures) determine all the main features of the transformations.

1.3 SHAPE MEMORY ALLOY (SMA)

Generally, a phase change is considered to be the change of the state of a

material between its solid, liquid or gaseous form. These phase changes are the

result of molecular rearrangements that take place when the material is heated

above, or cooled below, a certain temperature. The molecules will either move

towards or away from each other, resulting in a different state of the material. On

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the other hand, SMAs are set apart from other metals by the fact that they are able to

undergo a solid-to-solid phase transition, which can be utilized for a variety of

different purposes. This ability enables them to assume two different crystalline

lattice structures, depending on both the applied stress and the temperature. Such a

solid state phase change is similar to typical phase changes in the fact that a

molecular rearrangement is taking place. The main difference, however, is that in

this case the molecules remain closely packed and the substance therefore remains a

solid. This solid state phase change is an instantaneous shear transformation

between a highly twinned martensite structure and a cubic austenite structure. As

result of this solid-to-solid phase transition, SMAs are able to show three special

abilities:

1. Shape Memory Effect (SME)

A SMA element, which has been ‘plastically’ deformed, can recover a

‘memorized’ shape by heating it enough to complete the solid-to-solid phase

transition.

2. Pseudoelastic (or Superelastic) Effect (PE)

A SMA element can be stretched or compressed elastically 5-10 times the

amount of conventional materials.

3. Martensitic Deformability (MD)

A SMA element in its low-temperature martensite state is very pliable and

can therefore be bent over and over without the risk of fracture.

A SMA is a metal that can ‘remember’ its original shape even after

several deformations: once deformed at low temperatures (matensitic phase) these

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materials will stay deformed until heated, whereupon they will spontaneously return

to their original, pre-deformation shape. Shape recovery is the result of

transformation from the low-temperature martensitic phase to the high temperature

austenitic phase when it is heated. Shape memory alloys can thus transform thermal

energy directly to mechanical work. Among all these materials, TiNi based alloys

have been extensively studied and found many commercial applications.

In principle, it is also possible to bring about the martensitic phase

transformation by application of a magnetic field, which enables the devices to

operate at high frequencies and facilitates their remote control. However, the

strength of the field required is prohibitively large for practical applications

(Söderberg 2004). Instead, magnetic field can be a very effective in changing the

twin structure, and hence the sample shape, if the uniaxial easy direction of

magnetization changes across the twin boundary and the anisotropy energy is large.

Subsequently, a new form of magnetic-field-induced strain has been observed in

certain SMAs within their ferromagnetic martensitic phase and these alloys that

exhibit magnetic-field-induced strain (MFIS) are called FSMAs (Heczko 2003).

FSMAs are a recently discovered class of materials. Their prominent features are

magnetically driven actuation and large attainable strains greater than that of any

magnetostrictive, piezoelectric, or electrostrictive material. They exhibit a twinning

mechanism similar to that observed in conventional SMAs. This enables FSMAs to

exhibit the SME, like normal SMAs do. However, in a FSMA the SME can be

initiated using an applied magnetic field which shows promise of relatively high

strain and high frequency capabilities.

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1.3.1 Shape-Memory Effect

Certain materials can exhibit large strains without plastic deformations

when an external force is applied to them. In addition, the materials revert to their

original state when the perturbation is removed. A necessary condition for this SME

is that the so-called martensitic transformation of the crystal lattice takes place. In

this phase transformation, the crystal structure changes from the parent, usually

cubic austenitic phase to a lower-symmetry, often tetragonal or orthorhombic

martensitic phase. If a shape-memory sample in the martensitic state is now

deformed, its original shape can be restored by the reverse transformation process

back to the parent phase. In other words, the material remembers what its shape was

before the transformation process. This effect is based on the solid-to-solid phase

transition of SMAs that takes place within a specific temperature interval. If the

temperature of a SMA element is cooled below the Mf temperature, the SMA will be

completely in the martensite phase, in which it can be easily deformed. After an

obvious ‘plastic’ deformation, the element will remain deformed as long as the

temperature stays below the transition temperature (the SMA stays in the

martensitic phase). However, if the element is heated above the Af-temperature the

structure of the SMA will return to its austenite state, which is configured in the

original shape of the wire. Because of this the element will recover its original

‘memorized’ shape. This is illustrated in Figure 1.1.

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Figure.1.1 SME involves structural transition called MTs and occurs by nucleation

and growth of a lower symmetry (tetragonal/ orthorhombic) martensitic

phase from the parent higher symmetry (cubic austenitic) phase

The martensitic transformation can be induced by decreasing the

temperature of the material below a certain critical point, exerting stress on the

sample, or subjecting it to a magnetic field; the last one applies for ferroelectric or

ferromagnetic materials. This phase transformation is diffusionless, i.e., the

chemical composition of the material does not change: only structural

rearrangements occur in the crystal lattice. Thus, the process is reversible. The

transformation starts by the formation of martensitic regions in the parent phase.

Since the lattice constants of the two phases are different, these regions are distorted

with respect to the surrounding lattice. This leads to a local strain - elongation or

contraction-along some crystallographic direction. The martensitic planes may slip

plastically or, more importantly, an ensemble of twin variants-or domains-separated

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by mobile twin boundaries are formed. The latter process can also be regarded as a

mirror-like stacking fault of neighboring atom layers. Usually, the motion of the

twin boundaries is the easiest way for the sample to deform since, contrary to

slipping, this process involves breaking fewer chemical bonds in the lattice and

provides the clearest explanation to the macroscopic shape change.

1.3.2 Ferromagnetic Shape-Memory Effect

Ferromagnetic Shape Memory Effect (FSME) is a newly invented

concept used in actuator materials. FSME differs from other shape-memory

phenomena in that the rearrangement of the twin variants occurs in the martensitic

phase: no phase transformations are required to induce the macroscopic shape

changes. The FSME was first discovered by Ullakko and his co-workers in 1996. To

explain the FSM behavior, one has to take into account also the magnetic dipole

moments of the twin variants. In the absence of magnetic field, the dipoles point in

the directions of the easy axes of magnetization of the different twin variants. In a

weak applied field, the dipole moments start to rotate to align the dipoles with the

field but at stronger fields the twins are reorganized such that the proportion of the

variant favorably oriented with respect to the field starts to increase (see Figure 1.2

a and b). This latter mechanism is responsible for the observed macroscopic strain,

the maximum value of which depends on the material and the crystal structure of the

martensitic phase (Hakola 2004).

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Figure 1.2 a) Magnetic moments without the external field. b) Redistribution of the

variants in an applied field

1.4 MECHANISM FOR MAGNETIC FIELD INDUCED STRAIN

FSMAs have attracted an increasing interest in the past few years due to

their unique actuation, sensing and power generation capabilities (O’Handley 1998,

Marioni 2005, Atli 2011, Suorsa 2004). Conventional actuator materials such as

piezoceramics and magnetostrictive materials have the advantage of high response

frequencies and actuation stress levels (Dapino 2004, Li 2005) but yield only small

strains. Terfenol-D (Tb0.27Dy0.73Fe2) gives a strain of about 0.2% in a magnetic field

of a few thousand Oe, but rare earth metals are expensive (Dapino 2004a). PZT

(leadzirconate-titanate) results in a strain of about 0.1% in an electric field of several

hundred V/cm (Li 2005a), however, it is an oxide and thus brittle. By contrast,

conventional SMAs can yield high actuation stresses (few hundred MPas) and

strains on the order of 8%, but often show a small thermal or mechanical bandwidth

due to the restriction of heat transfer (Otsuka 1998a). The recently developed

FSMAs offer the characteristic of both large output strains, comparable to that of

conventional SMAs, and response frequencies as rapid as in magnetostrictive

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materials. The comparative chart of bandwidth versus strain is shown in the

Figure 1.3.

Figure 1.3 The comparative chart of bandwidth versus strain of various smart

materials.

There are two possible mechanisms for obtaining large magnetic

field-induced MFIS in FSMAs. The first one, which has been studied extensively

since 1996 (Ullakko), involves the field-induced reorientation of ferromagnetic

martensite variants. In this mechanism, the magnetic field triggers the motion of

martensite twin interfaces such that twins with favorably oriented easy axis of

magnetization, relative to the external magnetic field, grow at the expense of other

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twins leading to an external shape change (Figure 1.4a). The mechanism requires

simultaneous application of external stress and magnetic field to obtain reversible

shape change. The field-induced martensite twin reorientation is possible in

materials with high magnetic anisotropy energy and low force levels for twin

boundary motion. Near Heusler compositions of the intermetallic Ni2MnGa and

FePd alloys are the most widely explored FSMAs since only these have been

reported to demonstrate MFIS of more than 1% via the aforementioned mechanism.

The main limiting factor in currently available FSMAs which solely use the above

mechanism is low actuation stress levels of usually less than 3 MPa (Murray 2000a,

Sozinov 2002). Moreover, the operating temperature range might be narrow as the

upper temperature limit is the martensite to austenite phase transformation

temperature (As) and the lower limit is a critical temperature where the energy

required for twin boundary motion exceeds the MAE. For many engineering

applications, it is important to increase the operating temperature interval and

actuation stress levels of FSMAs to the order of hundred MPa.

Figure 1.4 Effect of applied magnetic field, H, on the reorientation of the

martensite twin variants (a) and phase transformation (b) in FSMAs

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The second possible mechanism to induce large MFIS in FSMAs is the

magnetic field-induced phase transformation (Figure 1.4b). The field-induced phase

transformation has been detected in several ferromagnetic materials such as Fe-C

and Fe-Ni in the past (Kakeshita 2000, Hao 2005), under very high field magnitudes

(>15 Tesla) without any report of MFIS levels. Certain Fe-Ni-Co-Ti alloys

demonstrated reversible martensitic transformation but only under the application of

a high pulsed magnetic field (~30 Tesla) (Kakeshita 2000a). The issue in the

Fe-based alloys arises from the fact that even though they may posses high Zeeman

energy difference between the transforming phases at low magnetic fields, they also

experience strong resistance against phase front motion. Karaman group (Sehitoglu

2001) have demonstrated in his works that high stress levels (couple of hundred

MPas) or large undercooling are required for phase transformation in these alloys

and the transformation is also accommodated by plastic deformation. Therefore, it is

imperative to find new alloys with low lattice friction against phase transformation

(i.e. low thermal and stress hysteresis) even if the Zeeman energy difference might

be relatively small. FSMAs can be potential candidates as they are much softer for

phase transformation as compared to the above alloys.

1.5 HEUSLER ALLOY Ni2MnGa

Heusler alloys are ternary intermetallic compounds with the general

formula X2YZ. The major combinations of Heusler alloy formation is shown in

Figure 1.5. The Ni2MnGa alloy, which belongs to this family, has the L21 structure

at room temperature. As shown in Figure 1.6, it can be represented by a bcc lattice.

They are ferromagnetic even though the constituting elements are not magnetic (as a

result of the double-exchange mechanism between neighboring magnetic ions),

usually manganese which sit at the body centers in a Heusler alloy.

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Figure 1.5 Major combinations of Heusler alloy formation

Figure 1.6 L21 structure of the austenitic phase of Ni2MnGa

The magnetic moment usually resides almost solely on the manganese

atom in these alloys. (See the Bethe-Slater curve for more information on why this

happens). The term is named after a German mining engineer and chemist Friedrich

Heusler, who studied such an alloy in 1903. It contained two parts copper, one part

manganese, and one part aluminum. Many of the Heusler alloys are ferromagnetic

and possess interesting magnetic properties.

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The formation of such a structure from the melt (the melting point of

Ni2MnGa is roughly 1380 K) is, in principle, possible either from the fully

disordered phase A2 (A2 � L21) or through the partially ordered intermediate phase

B2� (A2 � B2� � L21), in which the Ni atoms already form the frame of the lattice,

while the Mn and Ga atoms still occupy arbitrary positions. But with Ni2MnGa the

situation is different (Faidley 2006). As the temperature decreases, this compound

passes from the melt directly into the partially ordered phase B2�, and this phase

then experiences a second-order phase transition of the disorder–order type.

The B2� − L21 transition temperature for Ni2MnGa is about 1070 K. Down to

TM ~ 200 K Ni2MnGa remains in the L21 phase, and this Heusler alloy then

undergoes a first-order phase transition to a martensitic tetragonal phase, with

c/a < 1.

1.6 CRYSTAL STRUCTURE OF Ni-Mn-Ga FSMA

The parent austenitic phase of Ni–Mn–Ga has a cubic crystal structure.

The Ni atoms can be thought to form a simple-cubic (sc) lattice while Mn and Ga

atoms form a NaCl-like structure (face-centered cubic). The two lattices

interpenetrate such that each simple-cubic Ni unit cell encloses one Mn or Ga at its

body-center cite. The point group symmetry of the stoichiometric compound in

austenite is mFm 3 with L21 ordering as shown in Figure 1.7. Off stochiometric

Ni2MnGa alloys are generally used in experimental research on FSMAs because

they can be operated at room temperature due to their higher martensite

transformation temperature. The lattice constant of Ni2MnGa is a = 0.5825 nm at

room temperature, whereas, for Ni51.1Mn28.4Ga20.5, the corresponding value is

a = 0.5837 nm at 373 K (Söderberg 2004a) and for Ni49.7Mn29.1Ga21.2, the value of

a = 0.5840 nm at 323 K. (Heczko 2003a). The transformation to the martensitic

phase can occur in several different ways. The type of the martensite, its crystal

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structure, and the transformation temperature depend on the Ni/Mn/Ga ratio. The

stoichiometric Ni2MnGa has a tetragonal martensitic structure below TM = 202 K

with lattice parameters a = b = 0.5920 nm and c = 0.5566 nm (Hakola 2004a). Thus,

the lattice is contracted such that c/a = 0.94. Other Ni–Mn–Ga structures show a

variety of martensitic structures such as non-modulated tetragonal (T) martensite

with c/a > 1, five-layer-modulated (5M) tetragonal and seven-layer-modulated (7M)

orthorhombic structures with c/a < 1; the modulation means periodic deformation of

the crystal lattice with periods of 5 or 7 atomic layers.

5-layered modulation (5M) Early Neutron diffraction data showed that during MT, a simple

contraction along one of the directions of the cubic unit cell occurred. There

is a strong deformation of the cell (c/a = 0.94), however, accompanied by only 1%

decrease in cell volume. This martensitic structure is formed by the tetragonal

distortion of the parent L21 phase and the martensitic lattice is subjected to periodic

shuffling along the (110) [ 011 ] system and the modulation period is five (110)

planes, which is the so-called 5-layered martensite of body-centered tetragonal

structure (space group: I4/mma) (Martynov 1995). It is the martensitic phase in

which a maximum 6% strain can be induced by a magnetic field.

7-layered modulation (7M)

A variant showing a 7-layered modulation was found in stressed

martensites. It has a body-centered monoclinic (close to orthorhombic) structure

with seven (110) plane modulation (space group: Pnnm). When the long a-axis is

aligned into the short c-axis direction, the martensitic variant produces a 10% strain.

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Non-modulated structure (T)

In Ni-Mn-Ga alloys with a relatively high MT temperature, a

body-centered tetragonal structure having c/a>1 without modulation has been

reported (Martynov 1992). An analysis of the X-ray patterns indicates that the

structure is the face-centered tetragonal (Pons 2002). The non-modulated martensite

receives less attention because both the compressive stress required to obtain

a single variant state and the blocking stress on the twin boundaries for

variant-reorientation are so high that the magnetic field required to induce the shape

change is beyond industrial capacity.

Figure 1.7 Structures of cubic austenite ( mFm 3 ) and tetragonal martensite

)/4( mmmI of Ni2MnGa. Nickel atoms (blue) are located in the interior

tetragonal sites. Manganese atoms (green) are in the outer octahedral

sites and gallium atoms (red) are at the corner positions

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The transformation temperature can be well above 300 K for off

stoichiometric alloys. For example, the 7M Ni50.5Mn29.4Ga20.1 has a TM of 352 K and

lattice constants of a = 0.618 nm, b = 0.580 nm, and c = 0.552 nm (Straka 2003).

Both the MT temperature as well as the Curie temperature for a wide range of

Ni–Mn–Ga alloys can be found in Lanska et al ( 2004).

Magnetically controlled transformation between austenite and martensite

in Fe-Ni at low temperatures were first documented experimental results in this

area. Twin boundary motion in magnetically operated transformation is of primary

interest in the literature today after reported by Ullakko (1996a). The experimental

results showed 0.2% strains below 8 kOe magnetic field for unstressed Ni2MnGa

crystals at 77 K. This original data is reproduced in Figure 1.8.

Figure 1.8 (a) Relative orientation of sample, strain gauge, and applied field for

mearsurements shown in (b) and (c). (b) Strain vs. applied field in the

L21 (austenite) phase at 283 K. (c) Same as (b) but data taken at 265 K

in the martensitic phase (Ullakko 1996b)

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Experimental progress continued with testing of off-stoichiometric

Ni-Mn-Ga that showed larger strains at higher temperatures. Tickle et al. studied

Ni51.3Mn24.0Ga24.7 exposed to fields of less than 10 kOe (Tickle 1999). They observed

0.2% strains due to cyclic application of an axial magnetic field and strains of 1.3%

when fields were applied transverse to the sample that started from a stress biased

state.

Work continued on examining compositions and treatments of Ni-Mn-Ga

to optimize for large room temperature strains (Murray 1998b) culminating in the

empirical mapping of the useful compositional ranges presented by Jin et al (2002).

Based on experimental results from various sources, Jin et al identified a range

between Ni52.5Mn24.0Ga23.5 and Ni49.4Mn29.2Ga21.4 in which the martensitic

transformation temperature, TM, is higher than room temperature and lower than the

Curie temperature, TC, and the saturation magnetization is larger than 60 emu/g.

These conditions are suggested by Jin as characterizing samples with the best

capability for large, room temperature strains. The literature reports maximum strain

of 6% for Ni-Mn-Ga samples with tetragonal martensite structure with a five-layer

shuffle-type modulation (Murray 2001, Faidley 2006a). A second microstructure

sometimes found in Ni-Mn-Ga has orthorhombic martensitic phase with a seven-

layered modulation and has been found to exhibit strains of 9.5% (Sozinov 2002c).

Other techniques have also been investigated with the goal of augmenting the strain

output from Ni-Mn-Ga including thermal treatments, texturing, external application

of stress, and variation of operating temperature and sample composition. Though

alloys in the Ni-Mn-Ga system have shown the most promise as FSMAs, other

alloys are also being investigated.

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1.7 MAGNETIC PROPERTIES OF Ni-Mn-Ga

Early determinations of the magnetic properties of Ni-Mn-Ga were made

by Ullakko et al (1996, 1997) in conjunction with the first measurements of

field-induced strain. The saturation magnetization was observed to be 0.6 T in the

martensite phase at 265 K. Kokorin et al (1992) had previously measured the Curie

temperature at 350 K, and similar Curie temperatures have been measured since by

Murray et al (1998c). Both the Curie temperature and martensite temperature are

strongly dependent on alloy composition.

The magnetocrystalline anisotropy is one of the most important material

properties of an FSMA. The mechanism of field-induced strain requires that the

magnetic moment have a preferred direction in the crystal, and the

magnetocrystalline anisotropy is the energy that couples the magnetic moment to

this preferred direction. In the case of very low anisotropy, the magnetization can

rotate in the applied field to its equilibrium orientation without the motion of a twin

boundary. When the anisotropy is sufficiently high, twin boundary motion will be

the favored method to rotate the magnetization, and only under high external

stresses will rotation of the magnetic moment occur within the unit cell. The

magnetocrystalline anisotropy has been measured in single crystals of Ni-Mn-Ga by

both Ullakko (1996) and Tickle and James (1999a). Ullakko et al (1996c)

determined the anisotropy to be 0.12 MJ/m3 from magnetization curves at 265 K.

Tickle and James used a mechanically constrained sample in a single variant state

to measure the anisotropy and found it to be 0.245 MJ/m3 at a temperature of 256 K.

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1.8 ORIGIN OF MAGNETISM

Magnetism originates from the spin and orbital magnetic moment of an

electron. Magnetism can be divided into two groups, group A and group B. In group

A there is no interaction between the individual moments and each moment acts

independently of the others. Diamagnets and paramagnets belong to this group.

1.8.1 Exchange Interactions

Group B consists of the magnetic materials most people are familiar with,

like iron or nickel. Magnetism occurs in these materials because the magnetic

moments couple to one another and form magnetically ordered states. The coupling,

which is quantum mechanical in nature, is known as the exchange interaction and is

rooted in the overlap of electrons in conjunction with Pauli's exclusion principle.

Whether it is a ferromagnet, antiferromagnet of ferrimagnet the exchange

interaction between the neighboring magnetic ions will force the individual

moments into parallel (ferromagnetic) or antiparallel (antiferromagnetic) alignment

with their neighbours. In ferromagnetic materials the individual atomic magnetic

moments interact among themselves, favoring parallel alignment of spins, which is

the magnetically ordered state. There are two models which have been proposed to

explain this interaction in ferromagnetic materials. The first is the Mean field theory

proposed by Weiss, which talks about a non-local internal magnetic field called the

Weiss field which is very strong field but a very short-range field aligning the

moments. This internal field is directly proportional to magnetization.

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Hint � M (1.1)

Hint = �W M (1.2)

The second model is the Heisenberg exchange theory which is a local

interaction between atomic moments in the neighborhood. The model assumes that

the spins interact with the adjacent moments by means of an exchange energy

giving rise to a potential energy

Ep = -Jex Sj x Sj+1 (1.3)

When Jex > 0 parallel alignment of spins is favored and Jex < 0 favors anti

parallel alignment. The ferromagnetic Curie temperature of the material depends on

the strength of these exchange interactions. Three types of exchange which are

currently believed to exist are, a) direct exchange, b) indirect exchange and c) super

exchange.

1.8.1.1 Direct exchange

Direct exchange operates between moments, which are close enough to

have sufficient overlap of their wave functions. It gives a strong but short range

coupling which decreases rapidly as the ions are separated. An initial simple way of

understanding direct exchange is to look at two atoms with one electron each. When

the atoms are very close together the Coulomb interaction is minimal when the

electrons spend most of their time in between the nuclei. Since the electrons are then

required to be at the same place in space at the same time, Pauli's exclusion

principle requires that they possess opposite spins. According to Bethe and Slater

the electrons spend most of their time in between neighboring atoms when the

interatomic distance is small. This gives rise to antiparallel alignment and therefore

negative exchange (antiferromagnetic), Figure 1.9.

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Figure 1.9 Antiparallel alignment for small interatomic distances

If the atoms are far apart the electrons spend their time away from each

other in order to minimize the electron-electron repulsion. This gives rise to parallel

alignment or positive exchange (ferromagnetism), Figure 1.10.

Figure 1.10 Parallel alignments for large interatomic distances

For direct inter-atomic exchange j can be positive or negative depending

on the balance between the Coulomb and kinetic energies. The Bethe-Slater curve

represents the magnitude of direct exchange as a function of interatomic distance.

Cobalt is situated near the peak of this curve, while chromium and manganese are

on the side of negative exchange. Iron, with its sign depending on the crystal

structures probably around the zero-crossing point of the curve, Figure 1.11.

Figure 1.11 The Bethe-Slater curve

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1.8.1.2 Indirect exchange

Indirect exchange couples moments over relatively large distances. It is

the dominant exchange interaction in metals, where there is little or no direct

overlap between neighboring electrons. It therefore acts through an intermediary,

which in metals are the conduction electrons (itinerant electrons). This type of

exchange is better known as the RKKY interaction named after Ruderman, Kittel,

Kasuya and Yoshida. The RKKY exchange coefficient j oscillates from positive to

negative as the separation of the ion changes and has the damped oscillatory nature

shown in Figure 1.12. Therefore depending on the separation between a pair of ions

their magnetic coupling can be ferromagnetic or antiferromagnetic. A magnetic ion

induces a spin polarization in the conduction electrons in its neighborhood. This

spin polarization in the itinerant electrons is felt by the moments of other magnetic

ions within the range leading to an indirect coupling. In rare-earth metals, whose

magnetic electrons in the 4f shell are shielded by the 5s and 5p electrons, indirect

exchange via the conduction electrons gives rise to magnetic order in these

materials.

Figure 1.12 The coefficient of indirect (RKKY) exchange vs. the interatomic

spacing ‘a’

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1.8.1.3 Superexchange

Superexchange describes the interaction between moments on ions too far

apart to be connected by direct exchange, but coupled over a relatively long distance

through a non-magnetic material. We take as an example the coupling between the

moments on a pair of metal cations separated by a diatomic anion as illustrated in

Figure 1.13. The ferric ion has a half filled 3d shell and so has a spherically

symmetric charge distribution (S state ion). The triply rare-earth ion is not

symmetric and has a strong spin-orbit coupling; its charge distribution is coupled to

its moment. The ion's moments are coupled via superexchange, so turning the Fe

moment alters the overlap of the R cation in the molecule. This changes the

magnitude of both the Coulomb and exchange interactions between the cations,

leading to a coupling, which depends on the moment's orientation.

Figure 1.13 Superexchange in ferric-rare earth interaction in a garnet

1.9 SOFT MAGNETIC MATERIALS

Magnetic materials are classified into groups such as soft and hard

magnetic materials. Materials in which magnetic moments could be aligned by

application of very low fields typically ~ 1 Oe or less are termed soft magnetic

materials. Unlike permanent magnetic materials which require large field to

magnetize and demagnetize, soft magnetic materials can be magnetized and

demagnetized very easily by the application of very small field. Such a property

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makes soft magnetic materials the best candidates for components in inductors, low

and high frequency transformers, alternation current machines, motors, generators

and magnetic amplifiers. A good soft magnetic material requires both the saturation

and remanent magnetization to be as large as possible, which would make them

highly suitable for applications. In addition the essential criterion for a good soft

magnetic material is that it should possess extremely low hysteresis losses. This is

why soft magnetic materials are ideal materials for high frequency transformer

applications because usually this energy is dissipated from the material in the form

of heat. So lower the hysteresis loss, lower is the heat produced by the materials

when taken through rapid cycles of magnetizing and demagnetizing. Soft magnetic

materials also posses very high permeability and a high Curie temperature, though

not an essential criterion, is highly favorable. Nanocrystalline soft magnetic

materials have low magnetocrystalline anisotropy resulting in reduced coercivity

and high permeability such as FINEMENT alloys (Prabhu 2007) of the melt-spun

(Fe-Si-B-Nb-Cu), NANOPERM (Fe-M-B-Cu) alloys and high Curie temperature

HITPERM (Fe-Co-Cu-Zr-B) alloys used for high frequency applications. The

magnetization of the homogenized bulk and annealed Ni-Mn-Ga powder is similar,

exhibiting typical soft ferromagnetic behaviour reaching saturation magnetization at

10 kOe (Tian 2008). Ni-Mn-Ga thin films exhibit good soft magnetic properties

characterized by narrow hysteresis loops, low coercivity and high-magnetic

saturation values (Annadurai 2009).

1.10 HARD MAGNETIC MATERIALS

Hard magnetic materials are widely used in contemporary technology.

Depending on the kind of magnetic materials can be divided into: traditional (steels,

Al-Ni-Co magnets, ferrites magnets) and modern (Sm-Co magnets, Nd-Fe-B

magnets). There is still observed the development in permanent magnets especially

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in improving of their magnetic, mechanical, physical and chemical properties that

allows to broader their application (Coey 2001). Permanent magnets are used to

produce strong fields without applying a current to coil. Therefore, they should

exhibit a strong net magnetization, and is stable in the presence of external fields,

which requires high coercivity. Hard-magnetic materials are characterized by high

values of the coercive force Hc, large magnetization, residual induction Br, and

magnetic energy (BH )max in the demagnetization region. After magnetization,

hard-magnetic materials remain permanent magnets because of the high values of

Br and Hc. The large coercive force of hard-magnetic materials may be caused by

restraint of the displacement of domain boundaries because of the presence of

foreign inclusions or strong deformation of the crystal lattice or by the dropping out

in a weakly magnetic matrix of small single-domain ferromagnetic particles that

have strong crystalline anisotropy or form anisotropy.

FePt nanoparticles of face centered tetragonal (fct) structure with high

coercivity have the potential for use as magnetic recording medium. Apart from the

structure, the mechanism for the enhanced properties at the nanoscale could be

different like domain wall pinning or nucleation as in Sm-Co permanent magnetic

materials or exchange coupling as in nanocomposite permanent magnetic materials.

Nanocrystalline Sm-Co permanent magnetic materials with cellular microstructures

are being developed for high temperature applications. Nanocomposites

Nd2Fe14B/�-Fe exhibits enhanced energy product due to the improved exchange

coupling between the two phases when the particle size of the magnetic materials is

reduced to few nanometer.

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1.11 OBJECTIVE OF THE THESIS

The unique properties such as large displacements and fast response time

of FSMAs make these materials, in particular Ni-Mn-Ga attractive as actuator and

sensor elements. FSMAs find promising applications in the field of underwater

communications, structural morphing of unmanned aerial vehicles, acoustic

attenuation, bio medical and vibration control applications. Many of these

applications require FSMA devices of compact size, high energy density, and broad

frequency response. Now a days, nanotechnology is rapidly entering the world of

active materials and taking them to the next level. Nanotechnology influenced

improvements to smart materials will be relatively simple changes to existing

materials. These new materials may incorporate nanosensors, nanocomputers and

nanomachines into their structure. This will enable them to respond directly to their

environment rather than make simple changes caused by the environment. Hence,

nanoscale FSMAs are used in the nano-scale engineering and system integration of

existing materials to continuously develop better materials and better products.

These motivated us to understand the deformation, crystal structure, MT and failure

mechanisms in the nanostructured ferromagnetic Ni-Mn-Ga materials.

Generally, Ni–Mn–Ga bulk alloys are very brittle in nature, which

remarkably hinders their practical applications. To overcome this problem, several

sorts of Ni-Mn-Ga alloy have been proposed and studied, including ribbons, thin

films, and composites using polymer matrix with Ni–Mn–Ga particles. The

composites prepared by mixing Ni–Mn–Ga alloy particles and polymer matrix

exhibit great advantages with good formability and low cost of production,

compared with the thin films and ribbons which are often restricted by their

dimension in applications. Recently, spark erosion has been used to prepare the

Ni–Mn–Ga particles by rapidly solidifying the molten alloy droplets in liquid

30

nitrogen or argon. Clearly, this is a complex and high cost process for preparing

Ni–Mn–Ga particles. In comparison with spark erosion, ball milling is more simple

and cost-effective in preparing the Ni–Mn–Ga particles. The properties of the

polymer composite depend strongly on their filler (particle) structure, size and

internal stress, which develop during the milling and post-annealing process.

Though the effects of composition and pressure on Ni–Mn–Ga bulk alloys have

been studied to date, a systematic investigation of the crystal structure, magnetic

behavior and nanostructure of Ni-Mn-Ga FSMAs is still in progress. Certainly,

increased surface area and modified structure in various nanoparticles have long

been used to optimize the chemical and physical properties.

Therefore, the objective of the present study is to prepare Ni2MnGa

nanoparticles by using ball mill and perform a more fundamental investigation of

the structural and MT of Ni-Mn-Ga alloys to compliment the extensive engineering

properties research that has been performed previously. Through a better

understanding of the crystal structure and MT of the nanostructured Ni2MnGa

alloys, an important outcome will be the impact this work could have on the

practical performance of Ni-Mn-Ga FSMAs.