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Magnetostriction
The one example of magnetostriction that is the most familiar whether it is known that it is due to magnetostriction or not, is the ubiquitous hum of transformers. The old fluorescent light starter transformers suffered from this as do roadside power transformers. The iron cores expand and contract with the changing magnetic field, and even though the physical change in size is small, 10 micrometers or less, it is enough to generate audible sounds waves. This is more than just an annoyance as it is an electrical energy loss mechanism in the transformer and research is done to minimize it [6,7]. In this work however, a large magnetostriction is desirable, with the intent of converting electrical energy into useful mechanical work.
Definition
Magnetostriction is defined as a change in the dimension of a substance due to a change in its magnetic state. The first magnetostrictive phenomena encountered is “volume magnetostriction” where all three dimensions of a solid spontaneously change in the same direction upon cooling below the magnetic ordering temperature (the Curie temperature) due to the magnetic ordering of the atoms in the solid. The second is the most commonly referred to property, called “Joule magnetostriction” after its discoverer W. P. Joule, and requires the presence of an external magnetic field. The associated change in dimension preserves volume, i.e., elongation in one direction is accompanied by contraction in the other two orthogonal dimensions (cf. Figure 2.1). It is the latter among other magneto-elastic effects, that is of interest in this work and will be referred to simply as magnetostriction.
The magnetostriction, λ, is defined as the ratio of the change in length to the total length, ΔL/L, also known as strain, and is usually written with the dimensionless units of parts per million (ppm or 10-6). Magnetostriction is a magneto-elastic coupling phenomenon between the classical elastic properties of a material and its quantum mechanical magnetic properties. Described simply, magnetism arises from the spin of an electron, and in some part from the angular momentum of the electronic orbit around an atom. The elasticity of a material is due to how the electron orbits of neighboring atoms interact, i.e., how the constituent atoms bond together. Hence magneto-elastic coupling arises from the coupling between the direction of the spin of the electron and the orientation of its orbit. This is termed spin-orbit coupling and how strongly the spin and orbit are coupled, determines to what extent magnetic ordering of the solid (e.g., due to an external field) causes elastic deformation.
Spin-orbit coupling is present in all solids but is strongest in the rare-earth elements. This is due to the fact that the unpaired electrons that give rise to the magnetism of the atom, are located in the f orbit. This orbit is non-spherical and is much closer to the nucleus than the outer (s, p, and d) electron orbits. Hence, the electrons that occupy it do not participate in bonding between the atoms, and experience the nuclear attraction (more specifically the electric field gradient) to a larger extent. These conditions create a strong link between the spin of an electron and its orbit [8]. Hence, a change in the magnetic (spin) orientation causes a corresponding change in the orientation of the electron orbit. Because of the non-spherical orbit, this change in orientation results in an increase in the electrostatic interaction between it and neighboring electronic orbits. As this is an energetically unfavorable condition, the neighboring atoms move (an extraordinarily small amount of course) to accommodate the new orientation. The concerted motion of all the atoms in the solid creates a macroscopic change in dimension. This is magnetostriction.
Terfenol-D
The material with the highest magnetostriction is the rare-earth element, dysprosium, followed closely by terbium, with λ ≈ 9000 x10-6 though this is for extremely low temperatures, close to 0°K [9]. The reason terbium and dysprosium are not used by themselves for practical applications is that their Curie temperatures (magnetic ordering temperatures) are 220°K and 90°K, respectively, far below room temperature. Alloying the rare earths with transition metals results in an increase in the Curie temperature of the material, due to the longer range magnetic exchange interaction of the transition metal d orbitals. This helps to keep the rare earth atoms magnetically aligned above their normal curie temperature. Hence, the material with the highest room temperature magnetostriction, is single crystal TbFe2 with λ ≈ 3600 x10-6. However, this material is highly anisotropic and has a large magneto-crystalline anisotropy energy, requiring fields on the order of 25 kOe in order to reach saturation and the maximum magnetostriction.
To overcome this, Terfenol-D, an inter-metallic alloy of terbium, iron (Fe), and dysprosium was created at the Naval Ordinance Laboratory in conjunction with the University of Iowa [10]. Dysprosium has the opposite sign of magneto-crystalline anisotropy energy (but the same sign of magnetostriction) as terbium, and so by substituting terbium with dysprosium, the magnetization becomes much easier and the coercivity decreases. Fields only as high as 1.5 kOe are needed to substantially saturate the material. The anisotropy energy is temperature dependent and so the amount of dysprosium that is substituted is chosen such that the resulting anisotropy is a minimum at room temperature. This is important for practical applications and particularly necessary for MEMS devices where the driving coil size and available currents, and consequently the magnetic fields, are small.
The Role of Nano
In addition to the use of chemical composition to control the magnetic anisotropy, the crystal grain size of a material can influence the coercivity of polycrystalline soft ferromagnetic materials [11]. When the grain size is on the order of a hundred nanometers, corresponding to single domain particles, the material exhibits large coercivities. However, as the grain size becomes much smaller, on the order of nanometers, (smaller than about 10 nm for iron), the exchange interaction among the magnetic moments is much longer than the grain size and thus causes the moments to align even though the magnetization does not lie along any given grain’s (easy) crystallographic direction. This gives long range magnetic order even over randomly oriented crystal grains and so reduces the crystalline anisotropy and coercivity of the material. Of course an amorphous system where even short range atomic order is suppressed, would be ideal in terms of minimizing the coercivity, though the magnetization and magnetostriction are reduced due to the fact that both are affected by the interatomic distances that tend on average to be larger in amorphous materials [12]. For example, polycrystalline TbFe2 has a magnetostriction of ~2500 ppm at room temperature (already lower than the single crystal magnetostriction) while amorphous TbFe2 has a value of ~450 ppm [13].
In this work the starting feedstock material was Terfenol-D (Tb0.3Dy0.3Fe1.92), as opposed to Terfenol (TbFe2), simply due to the fact that Terfenol was not available for purchase. It would have been preferable to use the binary compound instead of the more complex ternary Terfenol-D, particularly in terms of analysis and comparison with current literature and for the interest in the improved anisotropy due to the nanoparticle size. However, the necessary time, equipment, and expertise to manufacture high quality TbFe2 from individual terbium and iron, was beyond the scope of this research.
Oxidation
Oxidation of the magnetostrictive rare earth iron alloys has been investigated by various authors. In all cases, the inclusion of oxygen in the magnetostrictive material reduced the magnetostriction. Both Snodgrass, et al.[13] and Kim, et al.[14] measured the dependence of the magnetostriction coefficient for bulk Terfenol-D on oxygen, and arrived at a decrease in magnetostriction of 0.012 and 0.017 ppm per atomic ppm of oxygen, respectively. This was a linear dependence though it was measured only for values of oxygen impurities less than 7000 atomic ppm, corresponding to a 10 % decrease in magnetostriction from 1000 ppm in Kim, et al. The oxygen combines preferentially with the rare earth atoms, forming inclusions of R2O3 (R = rare earth) and leaving an iron-rich phase behind.
Quandt, et al.[15], and van Dover, et al.[16], both reported the spontaneous oxide growth on thin films having TbFe and TbDyFe compositions. The oxide layer was seen to grow more slowly over time for films containing a mixture of Tb and Dy, though films having the same rare earth content, but Tb only, started with a larger oxide thickness of about 25 nm as opposed to 15 nm. Van Dover, et al., indicated a segregated native oxide on TbFe2 of 8 nm, consisting of a surface layer of 2 nm Fe2O3 and a sub-layer of 6 nm Tb2O3.
In general, most literature concerning thin films of magnetostrictive material do not report the effect of oxygen and oxidation on the films since after the initial oxide forms the oxidation rate is slow and confined to the surface. However, the initial oxide layer is typically reported to be 10 to 30 nm in thickness; as will be discussed in the following chapters, this oxide thickness is as large as or larger than the diameter of the nanoparticles generated by the LAM process. Should oxygen be present during the nanoparticle formation process or after formation but before impaction into a film, the nanoparticles would oxidize (possibly completely) and the oxygen would be incorporated homogeneously into the film. The susceptibility of the nanoparticles to oxygen prompted much of the research and investigative techniques described in this dissertation.
Table of contents :
Abstract
Abstract en Français
List of Tables
List of Figures
List of Equations
1 Introduction
1.1 Motivation
1.2 “Nano-”
1.3 Objectives.
1.4 Organization
2 Magnetostriction
2.1 Definition
2.2 Terfenol-D
2.3 The Role of Nano
2.4 Oxidation
3 Laser Ablation of Microparticles (LAM)
3.1 Laser Ablation of Microparticles
3.2 Nanoparticle Formation
3.3 Supersonic Impaction
3.4 LAM Applied to Terfenol-D
3.4.1 Process Parameters
3.4.2 Feedstock Microparticles
3.4.3 Nanoparticles from LAM of Terfenol-D
4 Measurement Apparatus and Techniques
4.1 The Cantilever Sample Geometry
4.1.1 Tip Deflection Measurement
4.1.2 Magnetostriction
4.1.3 Elastic modulus
4.1.4 Film Porosity (Density)
4.2 Magnetic Field Source
4.2.1 Motivation
4.2.2 Background
4.2.3 Field Properties
4.4 Optical Emission Spectroscopy
5. Data and Analysis
5.1 Film Properties
5.1.1 Physical Appearance and Geometry
5.1.2 Elastic Modulus
5.1.3 Microstructure and Chemical Composition
5.1.4 Magnetization
5.2 Magnetostriction
5.3 Ablation Spectra
5.4 Data Summary
6 Discussion
6.1 Oxidation
6.1.1 Background Gas Impurities
6.1.2 Microparticle Surface Oxide
6.2 Future work
6.3 Conclusions
References
Vita
