High temperature transport properties of lead chalcogenides and their alloys

This thesis describes a series of experimental studies of lead chalcogenide thermoelectric semiconductors, mainly PbSe. Focusing on a well-studied semiconductor and reporting good but not extraordinary zT, this thesis distinguishes itself by answering the following questions that haven’t been answered: What represents the thermoelectric performance of PbSe? Where does the high zT come from? How (and how much) can we make it better? For the first question, samples were made with highest quality. Each transport property was carefully measured, cross-verified and compared with both historical and contemporary report to overturn commonly believed underestimation of zT. For n- and p-type PbSe zT at 850 K can be 1.1 and 1.0, respectively. For the second question, a systematic approach of quality factor B was used. In n-type PbSe zT is benefited from its high-quality conduction band that combines good degeneracy, low band mass and low deformation potential, whereas zT of p-type is boosted when two mediocre valence bands converge (in band edge energy). In both cases the thermal conductivity from PbSe lattice is inherently low. For the third question, the use of solid solution lead chalcogenide alloys was first evaluated. Simple criteria were proposed to help quickly evaluate the potential of improving zT by introducing atomic disorder. For both PbTe1-xSex and PbSe1-xSx, the impacts in electron and phonon transport compensate each other. Thus, zT in each case was roughly the average of two binary compounds. In p-type Pb1-xSrxSe alloys an improvement of zT from 1.1 to 1.5 at 900 K was achieved, due to the band engineering effect that moves the two valence bands closer in energy. To date, making n-type PbSe better hasn’t been accomplished, but possible strategy is discussed.

Investigation of bulk indium antimonide as heterodyne detector for the submillimeter wavelength region

Bulk n-lnSb is investigated at a heterodyne detector for the submillimeter wavelength region. Two modes or operation are investigated: (1) the Rollin or hot electron bolometer mode (zero magnetic field), and (2) the Putley mode (quantizing magnetic field). The highlight of the thesis work is the pioneering demonstration or the Putley mode mixer at several frequencies. For example, a double-sideband system noise temperature of about 510K was obtained using a 812 GHz methanol laser for the local oscillator. This performance is at least a factor or 10 more sensitive than any other performance reported to date at the same frequency. In addition, the Putley mode mixer achieved system noise temperatures of 250K at 492 GHz and 350K at 625 GHz. The 492 GHz performance is about 50% better and the 625 GHz is about 100% better than previous best performances established by the Rollin-mode mixer. To achieve these results, it was necessary to design a totally new ultra-low noise, room-temperature preamp to handle the higher source impedance imposed by the Putley mode operation. This preamp has considerably less input capacitance than comparably noisy, ambient designs.

In addition to advancing receiver technology, this thesis also presents several novel results regarding the physics of n-lnSb at low temperatures. A Fourier transform spectrometer was constructed and used to measure the submillimeter wave absorption coefficient of relatively pure material at liquid helium temperatures and in zero magnetic field. Below 4.2K, the absorption coefficient was found to decrease with frequency much faster than predicted by Drudian theory. Much better agreement with experiment was obtained using a quantum theory based on inverse-Bremmstrahlung in a solid. Also the noise of the Rollin-mode detector at 4.2K was accurately measured and compared with theory. The power spectrum is found to be well fit by a recent theory of non- equilibrium noise due to Mather. Surprisingly, when biased for optimum detector performance, high purity lnSb cooled to liquid helium temperatures generates less noise than that predicted by simple non-equilibrium Johnson noise theory alone. This explains in part the excellent performance of the Rollin-mode detector in the millimeter wavelength region.

Again using the Fourier transform spectrometer, spectra are obtained of the responsivity and direct detection NEP as a function of magnetic field in the range 20-110 cm^-1. The results show a discernable peak in the detector response at the conduction electron cyclotron resonance frequency tor magnetic fields as low as 3 KG at bath temperatures of 2.0K. The spectra also display the well-known peak due to the cyclotron resonance of electrons bound to impurity states. The magnitude of responsivity at both peaks is roughly constant with magnet1c field and is comparable to the low frequency Rollin-mode response. The NEP at the peaks is found to be much better than previous values at the same frequency and comparable to the best long wavelength results previously reported. For example, a value NEP=4.5x10^-13/Hz^1/2 is measured at 4.2K, 6 KG and 40 cm^-1. Study of the responsivity under conditions of impact ionization showed a dramatic disappearance of the impurity electron resonance while the conduction electron resonance remained constant. This observation offers the first concrete evidence that the mobility of an electron in the N=0 and N=1 Landau levels is different. Finally, these direct detection experiments indicate that the excellent heterodyne performance achieved at 812 GHz should be attainable up to frequencies of at least 1200 GHz.

Hall coefficient and resistivity of an amorphous palladium-silicon alloy

The Hall coefficient and resistance in several specimens of an amorphous metallic alloy containing 80 at.% palladium and 20 at.% silicon have been investigated at temperatures between 4.2°K and room temperature. An ideal limiting behavior of these transport coefficients was analyzed on the basis of the nearly free electron model to yield a carrier density of 9 x 10²² cm.^-3, or about 1.7 electrons per palladium atom, and a mean free path of about 9Å which is almost constant with temperature. The deviations of the individual specimens from this ideal behavior, which were small but noticeable in the relative resistivity and much greater in the Hall coefficient, can be explained by invoking disk-shaped crystalline regions with low resistivity and a positive Hall coefficient. A detailed calculation shows how a volume fraction of such crystalline material too small to be noticed in X-ray diffraction could have a significant effect on the resistivity and a much greater effect on the Hall coefficient.

Proximity effect in Ag-Pb alloys

The superconducting properties and the microstructure of the Ag_100-xPb_x alloys, 1 ≤ x ≤ 5, prepared by rapid quenching from the liquid state with and without subsequent heat treatments, have been studied. The x-ray diffraction measurements show that supersaturated solid solutions of Pb in Ag can be obtained up to 3.2 at.% Pb as compared to less than 0.1 at.% Pb at equilibrium. It was found that by suitable heat treatment it is possible to vary the size and distribution of the Pb precipitates in the Ag matrix and reproducible superconducting properties in the alloy can be observed. The superconducting transition temperature of these samples can be qualitatively explained by the Silvert and Singh's theoretical calculation. The theory developed for the case of layer structure can be extended to three dimensions to explain the critical current versus temperature behavior. The critical current versus field behavior of these alloys can be explained by the modification of the Josephson effect. Combining these results together with the critical magnetic field measurements and the microstructure studies of the alloys, it can be concluded that the three-dimensional proximity effect is the main mechanism for the superconductivity in the Ag-Pb alloys. Based on the Hilsch empirical formula which was based on experimental results obtained on layer structures, the experimental data in this investigation show that the electron-phonon-electron interaction in silver is attractive. The interaction parameter NV obtained is approximately 0.06, which would lead to a value of 10^-5 °K for the superconducting transition temperature of Ag. These values are in agreement with other determinations which were done on vapor-deposited metallic film sandwiches. Hence, the Hilsch empirical relation valid for layer structures is also valid in the three-dimensional case. Because the transition temperature and the critical current can be varied in a wide range by controlling the heat treatments, the Ag-Pb superconductors might have some useful applications.

Band structure and transport properties of simple cubic tellurium-base alloys

The electrical transport properties and lattice spacings of simple cubic Te-Au, Te-Au-Fe, and Te-Au-Mn alloys, prepared by rapid quenching from the liquid state, hove been measured and correlated with a proposed bond structure. The variations of superconducting transition temperature, absolute thermoelectric power, and lattice spacing with Te concentration all showed related anomalies in the binary Te-Au alloys. The unusual behavior of these properties has been interpreted by using nearly free electron theory to predict the effect of the second Brillouin zone boundary on the area of the Fermi surface, and the electronic density of states. The behavior of the superconducting transition temperature and the lattice parameter as Fe and Mn ore added further supports the proposed interpretation as well as providing information on the existence of localized magnetic states in the ternary alloys. In addition, it was found that a very distinct bond structure effect on the transition temperatures of the Te-Au-Fe alloys could be identified.

A. An investigation of the relation between the tensile strength and (Brinell) hardness of non-ferrous alloys. B. A design of a fatigue testing machine for a college laboratory

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Theory of s-d exchange scattering in dilute magnetic alloys

The problem of s-d exchange scattering of conduction electrons off localized magnetic moments in dilute magnetic alloys is considered employing formal methods of quantum field theoretical scattering. It is shown that such a treatment not only allows for the first time, the inclusion of multiparticle intermediate states in single particle scattering equations but also results in extremely simple and straight forward mathematical analysis. These equations are proved to be exact in the thermodynamic limit. A self-consistent integral equation for electron self energy is derived and approximately solved. The ground state and physical parameters of dilute magnetic alloys are discussed in terms of the theoretical results. Within the approximation of single particle intermediate states our results reduce to earlier versions. The following additional features are found as a consequence of the inclusion of multiparticle intermediate states;

(i) A non analytic binding energy is pre sent for both, antiferromagnetic (J < o) and ferromagnetic (J > o) couplings of the electron plus impurity system.

(ii) The correct behavior of the energy difference of the conduction electron plus impurity system and the free electron system is found which is free of unphysical singularities present in earlier versions of the theories.

(iii) The ground state of the conduction electron plus impurity system is shown to be a many-body condensate state for J < o and J > o, both. However, a distinction is made between the usual terminology of "Singlet" and "Triplet" ground states and nature of our ground state.

(iv) It is shown that a long range ordering, leading to an ordering of the magnetic moments can result from a contact interaction such as the s-d exchange interaction.

(v) The explicit dependence of the excess specific heat of the Kondo systems is obtained and found to be linear in temperatures as T→ o and T ℓnT for 0.3 T_K ≤ T ≤ 0.6 T_K. A rise in (ΔC/T) for temperatures in the region 0 < T ≤ 0.1 T_K is predicted. These results are found to be in excellent agreement with experiments.

(vi) The existence of a critical temperature for Ferromagnetic coupling (J > o) is shown. On the basis of this the apparent contradiction of the simultaneous existence of giant moments and Kondo effect is resolved.

Geochemistry and resonance ionization of platinum-group elements

Experimental studies were conducted with the goals of 1) determining the origin of Pt- group element (PGE) alloys and associated mineral assemblages in refractory inclusions from meteorites and 2) developing a new ultrasensitive method for the in situ chemical and isotopic analysis of PGE. A general review of the geochemistry and cosmochemistry of the PGE is given, and specific research contributions are presented within the context of this broad framework.

An important step toward understanding the cosmochemistry of the PGE is the determination of the origin of POE-rich metallic phases (most commonly εRu-Fe) that are found in Ca, AJ-rich refractory inclusions (CAI) in C3V meteorites. These metals occur along with γNi-Fe metals, Ni-Fe sulfides and Fe oxides in multiphase opaque assemblages. Laboratory experiments were used to show that the mineral assemblages and textures observed in opaque assemblages could be produced by sulfidation and oxidation of once homogeneous Ni-Fe-PGE metals. Phase equilibria, partitioning and diffusion kinetics were studied in the Ni-Fe-Ru system in order to quantify the conditions of opaque assemblage formation. Phase boundaries and tie lines in the Ni-Fe-Ru system were determined at 1273, 1073 and 873K using an experimental technique that allowed the investigation of a large portion of the Ni-Fe-Ru system with a single experiment at each temperature by establishing a concentration gradient within which local equilibrium between coexisting phases was maintained. A wide miscibility gap was found to be present at each temperature, separating a hexagonal close-packed εRu-Fe phase from a face-centered cubic γNi-Fe phase. Phase equilibria determined here for the Ni-Fe-Ru system, and phase equilibria from the literature for the Ni-Fe-S and Ni-Fe-O systems, were compared with analyses of minerals from opaque assemblages to estimate the temperature and chemical conditions of opaque assemblage formation. It was determined that opaque assemblages equilibrated at a temperature of ~770K, a sulfur fugacity 10 times higher than an equilibrium solar gas, and an oxygen fugacity 10⁶ times higher than an equilibrium solar gas.

Diffusion rates between -γNi-Fe and εRu-Fe metal play a critical role in determining the time (with respect to CAI petrogenesis) and duration of the opaque assemblage equilibration process. The diffusion coefficient for Ru in Ni (D^Ru_Ni) was determined as an analog for the Ni-Fe-Ru system by the thin-film diffusion method in the temperature range of 1073 to 1673K and is given by the expression:

D^Ru_Ni (cm² sec^-1) = 5.0(±0.7) x 10^-3 exp(-2.3(±0.1) x 10¹² erg mole^-1/RT) where R is the gas constant and T is the temperature in K. Based on the rates of dissolution and exsolution of metallic phases in the Ni-Fe-Ru system it is suggested that opaque assemblages equilibrated after the melting and crystallization of host CAI during a metamorphic event of ≥ 10³ years duration. It is inferred that opaque assemblages originated as immiscible metallic liquid droplets in the CAI silicate liquid. The bulk compositions of PGE in these precursor alloys reflects an early stage of condensation from the solar nebula and the partitioning of V between the precursor alloys and CAI silicate liquid reflects the reducing nebular conditions under which CAI were melted. The individual mineral phases now observed in opaque assemblages do not preserve an independent history prior to CAI melting and crystallization, but instead provide important information on the post-accretionary history of C3V meteorites and allow the quantification of the temperature, sulfur fugacity and oxygen fugacity of cooling planetary environments. This contrasts with previous models that called upon the formation of opaque assemblages by aggregation of phases that formed independently under highly variable conditions in the solar nebula prior to the crystallization of CAI.

Analytical studies were carried out on PGE-rich phases from meteorites and the products of synthetic experiments using traditional electron microprobe x-ray analytical techniques. The concentrations of PGE in common minerals from meteorites and terrestrial rocks are far below the ~100 ppm detection limit of the electron microprobe. This has limited the scope of analytical studies to the very few cases where PGE are unusually enriched. To study the distribution of PGE in common minerals will require an in situ analytical technique with much lower detection limits than any methods currently in use. To overcome this limitation, resonance ionization of sputtered atoms was investigated for use as an ultrasensitive in situ analytical technique for the analysis of PGE. The mass spectrometric analysis of Os and Re was investigated using a pulsed primary Ar⁺ ion beam to provide sputtered atoms for resonance ionization mass spectrometry. An ionization scheme for Os that utilizes three resonant energy levels (including an autoionizing energy level) was investigated and found to have superior sensitivity and selectivity compared to nonresonant and one and two energy level resonant ionization schemes. An elemental selectivity for Os over Re of ≥ 10³ was demonstrated. It was found that detuning the ionizing laser from the autoionizing energy level to an arbitrary region in the ionization continuum resulted in a five-fold decrease in signal intensity and a ten-fold decrease in elemental selectivity. Osmium concentrations in synthetic metals and iron meteorites were measured to demonstrate the analytical capabilities of the technique. A linear correlation between Os⁺ signal intensity and the known Os concentration was observed over a range of nearly 10⁴ in Os concentration with an accuracy of ~ ±10%, a millimum detection limit of 7 parts per billion atomic, and a useful yield of 1%. Resonance ionization of sputtered atoms samples the dominant neutral-fraction of sputtered atoms and utilizes multiphoton resonance ionization to achieve high sensitivity and to eliminate atomic and molecular interferences. Matrix effects should be small compared to secondary ion mass spectrometry because ionization occurs in the gas phase and is largely independent of the physical properties of the matrix material. Resonance ionization of sputtered atoms can be applied to in situ chemical analysis of most high ionization potential elements (including all of the PGE) in a wide range of natural and synthetic materials. The high useful yield and elemental selectivity of this method should eventually allow the in situ measurement of Os isotope ratios in some natural samples and in sample extracts enriched in PGE by fire assay fusion.

Phase equilibria and diffusion experiments have provided the basis for a reinterpretation of the origin of opaque assemblages in CAI and have yielded quantitative information on conditions in the primitive solar nebula and cooling planetary environments. Development of the method of resonance ionization of sputtered atoms for the analysis of Os has shown that this technique has wide applications in geochemistry and will for the first time allow in situ studies of the distribution of PGE at the low concentration levels at which they occur in common minerals.

I. Reactively sputtered Ti-Si-N thin films for diffusion barrier applications. II. Oxidation, diffusion and crystallization of an amorphous Zr_(60)Al_(15)Ni_(25) alloy.

Films of Ti-Si-N obtained by reactively sputtering a TiSi_2, a Ti_5Si_3, or a Ti_3Si target are either amorphous or nanocrystalline in structure. The atomic density of some films exceeds 10^23 at./cm^3. The room-temperature resistivity of the films increases with the Si and the N content. A thermal treatment in vacuum at 700 °C for 1 hour decreases the resistivity of the Ti-rich films deposited from the Ti_5Si_3 or the Ti_3Si target, but increases that of the Si-rich films deposited from the TiSi_2 target when the nitrogen content exceeds about 30 at. %.

Ti_(34)Si_(23)N_(43) deposited from the Ti_5Si_3 target is an excellent diffusion barrier between Si and Cu. This film is a mixture of nanocrystalline TiN and amorphous SiN_x. Resistivity measurement from 80 K to 1073 K reveals that this film is electrically semiconductor-like as-deposited, and that it becomes metal-like after an hour annealing at 1000 °C in vacuum. A film of about 100 nm thick, with a resistivity of 660 µΩcm, maintains the stability of Si n+p shallow junction diodes with a 400 nm Cu overlayer up to 850 °C upon 30 min vacuum annealing. When used between Si and Al, the maximum temperature of stability is 550 °C for 30 min. This film can be etched in a CF_4/O_2 plasma.

The amorphous ternary metallic alloy Zr_(60)Al_(15)Ni_(25) was oxidized in dry oxygen in the temperature range 310 °C to 410 °C. Rutherford backscattering and cross-sectional transmission electron microscopy studies suggest that during this treatment an amorphous layer of zirconium-aluminum-oxide is formed at the surface. Nickel is depleted from the oxide and enriched in the amorphous alloy below the oxide/alloy interface. The oxide layer thickness grows parabolically with the annealing duration, with a transport constant of 2.8x10^(-5) m^2/s x exp(-1.7 eV/kT). The oxidation rate is most likely controlled by the Ni diffusion in the amorphous alloy.

At later stages of the oxidation process, precipitates of nanocrystalline ZrO_2 appear in the oxide near the interface. Finally, two intermetallic phases nucleate and grow simultaneously in the alloy, one at the interface and one within the alloy.

Strength, Deformation and Fracture in Metallic Nanostructures

An understanding of the mechanics of nanoscale metals and semiconductors is necessary for the safe and prolonged operation of nanostructured devices from transistors to nanowire- based solar cells to miniaturized electrodes. This is a fascinating but challenging pursuit because mechanical properties that are size-invariant in conventional materials, such as strength, ductility and fracture behavior, can depend critically on sample size when materials are reduced to sub- micron dimensions. In this thesis, the effect of nanoscale sample size, microstructure and structural geometry on mechanical strength, deformation and fracture are explored for several classes of solid materials. Nanocrystalline platinum nano-cylinders with diameters of 60 nm to 1 μm and 12 nm sized grains are fabricated and tested in compression. We find that nano-sized metals containing few grains weaken as sample diameter is reduced relative to grain size due to a change from deformation governed by internal grains to surface grain governed deformation. Fracture at the nanoscale is explored by performing in-situ SEM tension tests on nanocrystalline platinum and amorphous, metallic glass nano-cylinders containing purposely introduced structural flaws. It is found that failure location, mechanism and strength are determined by the stress concentration with the highest local stress whether this is at the structural flaw or a microstructural feature. Principles of nano-mechanics are used to design and test mechanically robust hierarchical nanostructures with structural and electrochemical applications. 2-photon lithography and electroplating are used to fabricate 3D solid Cu octet meso-lattices with micron- scale features that exhibit strength higher than that of bulk Cu. An in-situ SEM lithiation stage is developed and used to simultaneously examine morphological and electrochemical changes in Si-coated Cu meso-lattices that are of interest as high energy capacity electrodes for Li-ion batteries.

A generalized treatment of the order-disorder transformation in alloys and its effects on their magnetic properties

A theory of the order-disorder transformation is developed in complete generality. The general theory is used to calculate long range order parameters, short range order parameters, energy, and phase diagrams for a face centered cubic binary alloy. The theoretical results are compared to the experimental determination of the copper-gold system, Values for the two adjustable parameters are obtained.

An explanation for the behavior of magnetic alloys is developed, Curie temperatures and magnetic moments of the first transition series elements and their alloys in both the ordered and disordered states are predicted. Experimental agreement is excellent in most cases. It is predicted that the state of order can effect the magnetic properties of an alloy to a considerable extent in alloys such as Ni₃Mn. The values of the adjustable parameter used to fix the level of the Curie temperature, and the adjustable parameter that expresses the effect of ordering on the Curie temperature are obtained.

Heteroepitaxy of Group IV and Group III-V semiconductor alloys for photovoltaic applications

Photovoltaic energy conversion represents a economically viable technology for realizing collection of the largest energy resource known to the Earth -- the sun. Energy conversion efficiency is the most leveraging factor in the price of energy derived from this process. This thesis focuses on two routes for high efficiency, low cost devices: first, to use Group IV semiconductor alloy wire array bottom cells and epitaxially grown Group III-V compound semiconductor alloy top cells in a tandem configuration, and second, GaP growth on planar Si for heterojunction and tandem cell applications.

Metal catalyzed vapor-liquid-solid grown microwire arrays are an intriguing alternative for wafer-free Si and SiGe materials which can be removed as flexible membranes. Selected area Cu-catalyzed vapor-liquid solid growth of SiGe microwires is achieved using chlorosilane and chlorogermane precursors. The composition can be tuned up to 12% Ge with a simultaneous decrease in the growth rate from 7 to 1 μm/min^-1. Significant changes to the morphology were observed, including tapering and faceting on the sidewalls and along the lengths of the wires. Characterization of axial and radial cross sections with transmission electron microscopy revealed no evidence of defects at facet corners and edges, and the tapering is shown to be due to in-situ removal of catalyst material during growth. X-ray diffraction and transmission electron microscopy reveal a Ge-rich crystal at the tip of the wires, strongly suggesting that the Ge incorporation is limited by the crystallization rate.

Tandem Ga_1-xIn_xP/Si microwire array solar cells are a route towards a high efficiency, low cost, flexible, wafer-free solar technology. Realizing tandem Group III-V compound semiconductor/Si wire array devices requires optimization of materials growth and device performance. GaP and Ga_1-xIn_xP layers were grown heteroepitaxially with metalorganic chemical vapor deposition on Si microwire array substrates. The layer morphology and crystalline quality have been studied with scanning electron microscopy and transmission electron microscopy, and they provide a baseline for the growth and characterization of a full device stack. Ultimately, the complexity of the substrates and the prevalence of defects resulted in material without detectable photoluminescence, unsuitable for optoelectronic applications.

Coupled full-field optical and device physics simulations of a Ga_0.51In_0.49P/Si wire array tandem are used to predict device performance. A 500 nm thick, highly doped "buffer" layer between the bottom cell and tunnel junction is assumed to harbor a high density of lattice mismatch and heteroepitaxial defects. Under simulated AM1.5G illumination, the device structure explored in this work has a simulated efficiency of 23.84% with realistic top cell SRH lifetimes and surface recombination velocities. The relative insensitivity to surface recombination is likely due to optical generation further away from the free surfaces and interfaces of the device structure.

Finally, GaP has been grown free of antiphase domains on Si (112) oriented substrates using metalorganic chemical vapor deposition. Low temperature pulsed nucleation is followed by high temperature continuous growth, yielding smooth, specular thin films. Atomic force microscopy topography mapping showed very smooth surfaces (4-6 Å RMS roughness) with small depressions in the surface. Thin films (~ 50 nm) were pseudomorphic, as confirmed by high resolution x-ray diffraction reciprocal space mapping, and 200 nm thick films showed full relaxation. Transmission electron microscopy showed no evidence of antiphase domain formation, but there is a population of microtwin and stacking fault defects.

A Continuum Model for Slip-Twinning Interactions in Magnesium and Magnesium Alloys

Due to their high specific strength and low density, magnesium and magnesium-based alloys have gained great technological importance in recent years. However, their underlying hexagonal crystal structure furnishes Mg and its alloys with a complex mechanical behavior because of their comparably smaller number of energetically favorable slip systems. Besides the commonly studied slip mechanism, another way to accomplish general deformation is through the additional mechanism of deformation-induced twinning. The main aim of this thesis research is to develop an efficient continuum model to understand and ultimately predict the material response resulting from the interaction between these two mechanisms.

The constitutive model we present is based on variational constitutive updates of plastic slips and twin volume fractions and accounts for the related lattice reorientation mechanisms. The model is applied to single- and polycrystalline pure magnesium. We outline the finite-deformation plasticity model combining basal, pyramidal, and prismatic dislocation activity as well as a convexification based approach for deformation twinning. A comparison with experimental data from single-crystal tension-compression experiments validates the model and serves for parameter identification. The extension to polycrystals via both Taylor-type modeling and finite element simulations shows a characteristic stress-strain response that agrees well with experimental observations for polycrystalline magnesium. The presented continuum model does not aim to represent the full details of individual twin-dislocation interactions, yet it is sufficiently efficient to allow for finite element simulations while qualitatively capturing the underlying microstructural deformation mechanisms.

Spin wave resonance in ferromagnetic films

The objective of this investigation has been a theoretical and experimental understanding of ferromagnetic resonance phenomena in ferromagnetic thin films, and a consequent understanding of several important physical properties of these films. Significant results have been obtained by ferromagnetic resonance, hysteresis, torque magnetometer, He ion backscattering, and X-ray fluorescence measurements for nickel-iron alloy films.

Taking into account all relevant magnetic fields, including the applied, demagnetizing, effective anisotropy and exchange fields, the spin wave resonance condition applicable to the thin film geometry is presented. On the basis of the simple exchange interaction model it is concluded that the normal resonance modes of an ideal film are expected to be unpinned. The possibility of nonideality near the surface of a real film was considered by means of surface anisotropy field, inhomogeneity in demagnetizing field and inhomogeneity of magnetization models. Numerical results obtained for reasonable parameters in all cases show that they negligibly perturb the resonance fields and the higher order mode shapes from those of the unpinned modes of ideal films for thicknesses greater than 1000 Å. On the other hand for films thinner than 1000 Å the resonance field deviations can be significant even though the modes are very nearly unpinned. A previously unnoticed but important feature of all three models is that the interpretation of the first resonance mode as the uniform mode of an ideal film allows an accurate measurement of the average effective demagnetizing field over the film volume. Furthermore, it is demonstrated that it is possible to choose parameters which give indistinguishable predictions for all three models, making it difficult to uniquely ascertain the source of spin pinning in real films from resonance measurements alone.

Spin wave resonance measurements of 81% Ni-19% Fe coevaporated films 30 to 9000 Å thick, at frequencies from 1 to 8 GHz, at room temperature, and with the static magnetic field parallel and perpendicular to the film plane have been performed. A self-consistent analysis of the results for films thicker than 1000 Å, in which multiple excitations can be observed, shows for the first time that a unique value of exchange constant A can only be obtained by the use of unpinned mode assignments. This evidence and the resonance behavior of films thinner than 1000 Å strongly imply that the magnetization at the surfaces of permalloy films is very weakly pinned. However, resonance measurements alone cannot determine whether this pinning is due to a surface anisotropy, an inhomogeneous demagnetizing field or an inhomogeneous magnetization. The above analysis yields a value of 4πM=10,100 Oe and A = (1.03 ± .05) x 10^-6 erg/cm for this alloy. The ability to obtain a unique value of A suggests that spin wave resonance can be used to accurately characterize the exchange interaction in a ferromagnet.

In an effort to resolve the ambiguity of the source of pinning of the magnetization, a correlation of the ratio of magnetic moment and X-ray film thickness with the value of effective demagnetizing field 4πNM as determined from resonance, for films 45 to 300 Å has been performed. The remarkable agreement of both quantities and a comparison with the predictions of five distinct models, strongly imply that the thickness dependence of both quantities is related to a thickness dependent average saturation magnetization, which is far below 10,100 Oe for very thin films. However, a series of complementary experiments shows that this large decrease of average saturation magnetization cannot be simply explained by either oxidation or interdiffusion processes. It can only be satisfactorily explained by an intrinsic decrease of the average saturation magnetization for very thin films, an effect which cannot be justified by any simple physical considerations.

Recognizing that this decrease of average saturation magnetization could be due to an oxidation process, a correlation of resonance measurements, He ion backscattering, X-ray fluorescence and torque magnetometer measurements, for films 40 to 3500 Å thick has been performed. On basis of these measurements it is unambiguously established that the oxide layer on the surface of purposefully oxidized 81% Ni-19% Fe evaporated films is predominantly Fe-oxide, and that in the oxidation process Fe atoms are removed from the bulk of the film to depths of thousands of angstroms. Extrapolation of results for pure Fe films indicates that the oxide is most likely α-Fe₂O₃. These conclusions are in agreement with results from old metallurgical studies of high temperature oxidation of bulk Fe and Ni-Fe alloys. However, X-ray fluorescence results for films oxidized at room temperature, show that although the preferential oxidation of Fe also takes place in these films, the extent of this process is by far too small to explain the large variation of their average saturation magnetization with film thickness.

Effects of magnetostriction and superlattice formation in ferromagnetic thin films

The contribution to the magnetic uniaxial perpendicular anisotropy which arises from substrate constraint through magnetostrictive effects has been measured in Ni-Fe and Ni-Co thin films evaporated on substrates at room temperature. This was accomplished by measuring the perpendicular anisotropy before and after removal of the film from the substrate. Data are given for the fcc crystal structure regions of both alloy systems, but data for Ni-Co include compositions with less than 60% Ni which have a small percentage of the hcp phase mixed with the fcc phase. The constraint contribution to the perpendicular anisotropy correlates well with the value of the bulk magnetostriction constant using the equation ∆K_˔=3/2λ_sσ. Measured values of isotropic stress for films thicker than 600 Å were 1.6 x 10¹⁰ dyn/cm². In films less than 600 Å thick the isotropic stress decreased with decreasing thickness. After removal of the films from the substrates, the measured perpendicular anisotropy deviated from the expected geometrical shape anisotropy near pure Ni in both alloys. This indicates that additional significant sources of anisotropy exist at these compositions.

The effect of substrate constraint on the crystalline anisotropy K₁ of Ni-Fe epitaxial films has been studied by use of a film removal technique, which involves the evaporation of an epitaxial layer of LiF on MgO, the epitaxial growth of the metallic film on the LiF, and the stripping of the film with water soluble tape. Films ranging in composition from 50% to 100% Ni have been studied. For compositions below 90% Ni the experimental values agree reasonably well with the first order theoretical prediction, ∆K₁=[-9/4(C₁₁-C₁₂)λ² 100+9/2C₄₄λ²111].

In order to compare the magnetic properties of epitaxial thin films more completely with the properties of bulk single crystals, Ni-Fe films ranging in composition from 60% to 90% Ni, which were evaporated epitaxially on (100) MgO substrates, have been subsequently annealed at 400°C in a vacuum of less than 10^-7 Torr to form the ordered Ni₃Fe structure near the 75% composition. This ordered structure has been confirmed by electron diffraction.

The saturation magnetization at Ni₃Fe increased about 6% with ordering which is in good agreement with previous bulk data. Measurements of the magnetocrystalline anisotropy energy K₁ for the epitaxial films show the same large changes with ordering as observed in bulk single crystal samples. In the (001) plane the magnetostriction constants ^λ100, ^λ111 are directly related to the induced anisotropy due to a uniform uniaxial strain in the [100] and [110] directions respectively. Assuming that the elastic constants of a film are the same as in bulk material and are unchanged by ordering, the changes in strain sensitivity with ordering for the epitaxial films are found to be in good agreement with values predicted from bulk data. The exchange constant A as measured by ferromagnetic resonance has been measured at the Ni₃Fe composition and found to increase 25% with ordering. This seems to indicate a significant increase in the Curie temperature which has only been inferred indirectly for bulk material.