Browsing by Subject "Hysteresis"
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Item Influence of compatibility conditions on the microstructure at phase transformation(2013-07) Chen, XianThe purpose of this research is to study systematically compatibility conditions and their implications for the microstructure of a phase-transforming material. The phase transformation in this thesis is restricted to crystalline solid-to-solid phase transformation. The conditions of compatibility refer to compatibility in the sense of the nonlinear elastic theory of martensite. Different versions of these conditions of compatibility are studied in this thesis, ranging from "weak compatibility'' (continuity along lines aligned with precipitates) to very strong conditions of compatibility as expressed by the "cofactor conditions''. In the case of a diffusionless, reversible martensitic phase transformation, the free energy of the undistorted body is described as the volume integral of the free energy density function, which depends on the temperature and deformation gradient of the continuous body. This free energy at continuum level describes the elastic and chemical energy stored in the lattice. Macroscopic deformations are related to lattice deformation by the Cauchy-Born rule.This rule yields a deformation gradient F relating a sublattice of the austenite phase to the primitive lattice of the martensite phase. We derive a heuristic algorithm to find F directly from X-ray diffraction measurement for both phases. For such a transformation both the lattice parameters and the symmetry of the crystal structure change. We assume that the free energy is invariant under rigid rotations and symmetry operations. The transformation stretch matrix U is calculated from the deformation gradient F by polar decomposition. The associated crystallographically equivalent variants U1, ..., Un are determined by symmetry arguments (We can choose U1 = U.). The matrices I (austenite) and U1, ..., Un (variants of martensite) determine the_para>energy wells of the free energy density. The formation of microstructure arises from the simultaneous requirements of energy minimization, i.e., being near the energy wells, and compatibility. The Widmanstatten type precipitation process produces a microstructure of elongated precipitates. For this microstructure we propose a weaker condition of compatibility than is used in the study of martensite. This weaker condition implies a rank-two connection between energy wells and predicts directions of elongation for the precipitates. This condition can be interpreted as a mathematical condition of semi-coherence. The transformation stretch matrix is calculated by the same algorithm mentioned above. The weak compatibility condition is equivalent to the statement that the smallest and largest eigenvalues of U satisfy &lambda1 &le 1 &le &lambda3, which in turn implies that there is an undistorted direction e. We study this condition in the thermoelectric material PbTe/Sb2Te3, which consists of Sb2Te3 precipitates in a PbTe matrix. This material shows typical Widmanst"atten microstructure. The satisfaction of the rank-two condition for this material implies that the undistorted directions of the precipitates lie on the lateral surface of a cone determined by the eigenvalues of U. By symmetry, there are four crystallographically equivalent cones, that all together restrict the spacial distribution of the Widmanstatten precipitates Sb2Te3. A 3D image reconstructed from a set of SE images of the precipitates by means of slice-and-view technique shows a good agreement with this theory. For the martensitic phase transformation, we discuss the cofactor conditions. These are currently the strongest achievable conditions of compatibility for the formation of microstructure of austenite and twinned martensite. The satisfaction of the cofactor conditions implies the existence of infinitely many compatible ways that twinned martensite laminates of any volume fraction can coexist with austenite at a low-energy interface. In this thesis we show that, in fact, many of these energy minimizing microstructures have zero elastic energy at all length scales. Experimentally, we have successfully achieved the first example Zn45Au30Cu25 whose lattice parameters closely satisfy the cofactor conditions for both Type I and Type II twin systems. This material shows enhanced reversibility and extremely low hysteresis upon cyclic phase transformation. Strikingly, the martensitic microstructure has no reproducibility from cycle to cycle.This phenomenon contrasts sharply with the traditional martensite for a polycrystalline solid, which shows a detailed martensite memory effect for cyclic phase transformation. The zero elastic energy microstructures can be used as the building blocks of a set of compatible triple junctions between a pair of Type I twin/austenite and quad junctions consisting of a pair of Type I twin/Type II twins. From X-ray diffraction measurements, we calculate these building blocks for Zn45Au30Cu25, which are then used to construct a complex mosaic of microstructure. This microstructure is apparently observed under optical microscopy, but this awaits detailed confirmation by Electron Backscatter Diffraction (EBSD) and Transmission Electron Microscopy (TEM), currently underway by the author in collaboration with researchers at Carnegie Mellon University and the University of Antwerp.Item Position Estimation Using Magnetic Fields(2018-11) Madson, RyanThis thesis develops position estimation systems based on magnetic fields and addresses a number of challenges related to making such systems accurate and robust for real-world applications. The thesis first addresses one-dimensional position estimation using the measurement of piston position inside a cylinder as a benchmark application. The piston is equipped with a permanent magnet and one or more magnetic sensors are embedded on a compact circuit board located on top of the cylinder. Due to large distances between the moving piston and the stationary sensor, the magnetic field as a function of piston position is highly nonlinear. This magnetic field is modeled either analytically or emperically and a nonlinear estimation algorithm, namely the truncated interval unscented Kalman Filter (TIUKF), is utilized for real-time estimation of the position of the piston. Piston position estimation can be useful on hydraulic actuators, pneumatic actuators, IC engines, and a number of other cylinder piston products. The developed estimation algorithm is implemented experimentally on a microprocessor. A compact sensor board containing sensors, the microprocessor, and other components is developed. The developed position estimation system is first evaluated experimentally on pneumatic actuators. The estimation system performs well and an estimation accuracy better that 1% is achieved on pneumatic actuators with stroke lengths of 5 cm and 10 cm. Next an auto-calibration system is developed in order to enable the sensor board to estimate position accurately when installed on new cylinders. Small misalignments and offsets in location can occur on each installation. The new auto-calibration method allows the position estimation system to perform robustly and accurately by identification of new parameters on each installation. This auto-calibration is done without requiring any additional external reference position sensors. A significant challenge to magnetic field based position estimation comes from disturbances due to unexpected ferromagnetic objects coming close to the sensors. A new disturbance estimation method based on modeling the magnetic disturbance as a dipole with unknown location, magnitude, and orientation is developed. A TIUKF is used to estimate all the parameters of this unknown dipole, in addition to estimating piston position from nonlinear magnetic field models. Experimental data from a pneumatic actuator is used to verify the performance of the developed estimator. Experimental results show that the developed estimator is significantly superior to a linear magnetic field model based disturbance estimator. It can reliably estimate piston position and the unknown dipole parameters in the presence of a variety of unknown disturbances. Next the estimation system is implemented for a large hydraulics actuator used on construction machines. The ferromagnetic material of the hydraulic cylinder leads to significant hysteresis, since this material is magnetized and demagnetized repeatedly with the motion of the magnet. A method to model and compensate for the hysteresis in the system is developed. In particular, a modified Preisach model and associated estimation algorithm developed is shown to provide excellent performance. An accuracy better than 2\% is achieved on the large-stroke hydraulic cylinder in spite of significant hysteresis. Finally, the one-dimensional position estimation tools are extended in an attempt to enable 3D position estimation of a magnet. The objective is to estimate magnet position in real-time from a moving sensor board in the neighborhood of the magnet. Applications for this 3D position estimation system include a breast cancer surgery application in which a small magnet can be used to mark tumor location. The significant challenges in the 3D position estimation application are handled by using an accelerometer and gyroscope in addition to magnetic sensors for orientation estimation, by using a particle filter for the estimation task, and by using a neural network for modeling the functional relationships between magnetic field and 3D position and orientation. While the developed system provides reasonable experimental performance, further work with more sensitive magnetic sensors and a better reference 3D position sensor for modeling are needed.Item A Python Implementation of a Drift-Diffusion Model to Capture Ion Migration in Perovskite Solar Cells(2021-06) Anderson, NathanCharge carrier dynamics and ion migration are attributed to the current-voltage hysteresis in perovskite solar cells (PSCs). This study implements a drift-diffusion model in Python to simulate the characteristic current-voltage scans for realistic device architectures. The novel work in this research involve the integration of a transfer-matrix optical model to the drift-diffusion model with ion migration, the implementation of a Radau 5th order solver to the method of lines, and a demonstration that standard Python libraries can handle stiff systems of differential algebraic equations. A comparative analysis with published works was conducted to validate the algorithm. It was found that the simulation was able to capture fast carrier dynamics under a variety of experimental conditions. Lastly, it is shown that the model captures physically relevant trends in PSCs.