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Timothy C. Petersen

Publications and source records attributed to Timothy C. Petersen.

11 recordsLinked to original sources
arXiv2026

Local Structural Signatures of Shear Bands in Metallic Glasses via Electron Nanodiffraction

Structural changes in a glass due to deformation are subtle and difficult to quantify using conventional imaging and diffraction techniques. Additionally, transmission electron microscopy (TEM) sample preparation using energetic ions often causes structural modifications that are challenging to detect in disordered materials. By preparing inverted cross-sectional transmission electron microscopy lamellae of shear bands formed during bending, and employing cryogenic ion polishing to minimize preparation artefacts, we preserve the intrinsic atomic structure. Using sensitive, new parameters derived from electron nano-diffraction, we directly probe the local nano-scale structure in the plastic zone beneath surface shear steps in metallic glasses. Mapping of local centrosymmetry and strain reveals nanoscale, stripe-like regions oriented at 45 degree to the applied strain where strain has localized. These regions exhibit a high density of local atomic structures that have transformed to configurations with reduced centrosymmetry and increased magnitudes of shear and normal strain. Our results demonstrate that plastic deformation in metallic glasses arises from coordinated nanoscale structural transformations, providing direct experimental insight into a long-standing problem.

cond-mat.mtrl-sci↗
arXiv2026

Geometric indicators of local plasticity in glasses measured by scanning small-beam diffraction

The notion of defects in crystalline phases of matter has been extremely powerful for understanding crystal growth, deformation and melting. Many of these discontinuities in the periodic order of crystals are well described by the Burgers vector, derived from the particle displacements, which encapsulates the direction and magnitude of slip relative to the undeformed state. Since the reference structure of the crystal is known a priori, the Burgers vector can be determined experimentally using both imaging and diffraction methods to measure the final lattice distortion, and thus infer the particle displacements. Glasses have structures that lack the periodicity of crystals, and thus a well-defined reference state. Yet, measurable structural parameters can still be obtained from diffraction from a glass. Here we examine the usefulness of these parameters to probe deformation in glasses. We find that co-ordinated transformations in the centrosymmetry of local particle arrangements are a strong marker of plastic events. For a glass, determining the local distortions corresponding to these plastic events requires measurements before and after deformation. We investigate two geometric indicators that can be derived from these distortions, namely the continuous Burgers vector and the quadrupolar strain. We find that the Burgers vector again emerges as a robust and sensitive metric for understanding local structural transformations due to mechanical deformation, even in disordered glasses.

cond-mat.soft↗
arXiv2025

Dopant site occupancy determined by core-loss-filtered, position-averaged convergent beam electron diffraction

In the elastic scattering regime, probe position-averaged convergent beam electron diffraction (PACBED) patterns have proven robust for estimating specimen thickness and mistilt. Through simulation, we show that core-loss-filtered PACBED patterns can be used to measure the site occupancy of a small concentration of dopants in an otherwise known crystal structure. By leveraging the reciprocity between scanning and conventional transmission electron microscopy, we interpret core-loss PACBED patterns using a strategy traditionally used for determining dopant concentrations via energy dispersive X-ray spectroscopy. We show that differences in the interaction range of different elements hinder a purely measurement-based quantification strategy, but that this can be overcome through comparison with simulations that generalize the Cliff-Lorimer k-factors.

cond-mat.other↗
arXiv2025

Quantitative structure determination from experimental four-dimensional scanning transmission electron microscopy via the scattering matrix

Considerable inroads have recently been made on algorithms to determine the sample potential from four-dimensional scanning transmission electron microscopy data from thick samples where multiple scattering cannot be neglected. This paper further develops the scattering matrix approach to such structure determination. Through simulation, we demonstrate how this approach can be modified to better handle partial spatial coherence, unknown probe defocus, and information from the dark field region. By combining these developments we reconstruct the electrostatic potential of a monolithic SrTiO$_3$ crystal showing good quantitative agreement with the expected structure.

cond-mat.mtrl-sci↗
arXiv2024

High-resolution x-ray scanning with a diffuse, Huffman-patterned probe to minimise radiation damage

Scanning objects with a more tightly focused beam (for example of photons or electrons) can provide higher-resolution images. However the stronger localisation of energy deposition can damage tissues in organic samples or may rearrange the chemical structure or physical properties of inorganic materials. Scanning an object with a broad beam can deliver an equivalent probe energy but spreads it over a much wider footprint. Sharp images can be reconstructed from the diffuse implanted signal when a decoding step can recover a delta-like impulse response. Huffman sequences, by design, have the optimal delta-like autocorrelation for aperiodic (non-cyclic) convolution and are well-conditioned. Here we adapt 1D Huffman sequences to design 2D Huffman-like discrete arrays that have spatially broad, relatively thin and uniform intensity profiles that retain excellent aperiodic autocorrelation metrics. Examples of broad shaped diffuse beams were developed for the case of x-ray imaging. A variety of masks were fabricated by the deposition of finely structured layers of tantalum on a silicon oxide wafer. The layers form a pattern of discrete pixels that modify the shape of an incident uniform beam of low energy x-rays as it passes through the mask. The intensity profiles of the x-ray beams after transmission through these masks were validated, first by acquiring direct-detector x-ray images of the masks, and second by raster scanning a pinhole over each mask pattern, pixel-by-pixel, collecting "bucket" signals as applied in traditional ghost imaging. The masks were then used to raster scan the shaped x-ray beam over several simple binary and "gray" test objects, again producing bucket signals, from which sharp reconstructed object images were obtained by deconvolving their bucket images.

physics.optics↗
arXiv2024

Differential phase contrast from electrons that cause inner shell ionization

Differential Phase Contrast (DPC) imaging, in which deviations in the bright field beam are in proportion to the electric field, has been extensively studied in the context of pure elastic scattering. Here we discuss differential phase contrast formed from core-loss scattered electrons, i.e. those that have caused inner shell ionization of atoms in the specimen, using a transition potential approach for which we study the number of final states needed for a converged calculation. In the phase object approximation, we show formally that differential phase contrast formed from core-loss scattered electrons is mainly a result of preservation of elastic contrast. Through simulation we demonstrate that whether the inelastic DPC images show element selective contrast depends on the spatial range of the ionization interaction, and specifically that when the energy loss is low the delocalisation can lead to contributions to the contrast from atoms other than that ionized. We further show that inelastic DPC images remain robustly interpretable to larger thicknesses than is the case for elastic DPC images, owing to the incoherence of the inelastic wavefields, though subtleties due to channelling remain. Lastly, we show that while a very high dose will be needed for sufficient counting statistics to discern differential phase contrast from core-loss scattered electrons, there is some enhancement of signal-to-noise ratio with thickness that makes inelastic DPC imaging more achievable for thicker samples.

cond-mat.other↗
arXiv2024

Clustering of negative topological charge precedes plastic failure in 3D glasses

The deformation mechanism in amorphous solids subjected to external shear remains poorly understood because of the absence of well-defined topological defects mediating the plastic deformation. The notion of soft spots has emerged as a useful tool to characterize the onset of irreversible rearrangements and plastic flow, but these entities are not clearly defined in terms of geometry and topology. In this study, we unveil the phenomenology of recently discovered, precisely defined topological defects governing the microscopic mechanical and yielding behavior of a model 3D glass under shear deformation. We identify the existence of vortex-like and anti-vortex-like topological defects within the 3D non-affine displacement field. The number density of these defects exhibits a significant anti-correlation with the plastic events, with defect proliferation-annihilation cycles matching the alternation of elastic-like segments and catastrophic plastic drops, respectively. Furthermore, we observe collective annihilation of these point-like defects via plastic events, with large local topological charge fluctuations in the vicinity of regions that feature strong non-affine displacements. We reveal that plastic yielding is driven by several large sized clusters of net negative topological charge, the massive annihilation of which triggers the onset of plastic flow. These findings suggest a geometric and topological characterization of soft spots and pave the way for the mechanistic understanding of topological defects as mediators of plastic deformation in glassy materials.

cond-mat.soft↗
arXiv2021

Families of delta-correlated arrays derived from the Fourier spectra of Huffman sequences

Finite discrete Huffman sequences, together with their extension to n-dimensional arrays, are highly valued because their discrete aperiodic auto-correlations optimally approximate the continuum form of the delta function. We present here several new families of real and integer-valued Huffman sequences, beyond those of the recursive form found by Hunt and Ackroyd. These new sequences are derived using the remarkably uniform discrete Fourier power spectra of Huffman sequences, where the elements are expressed as terms of the Fibonacci sequence.

math.CO↗
arXiv2018

Propagation of fully-coherent and partially-coherent complex scalar fields in aberration space

We consider the propagation of both fully coherent and partially coherent complex scalar fields, through linear shift-invariant imaging systems. The state of such imaging systems is characterized by a countable infinity of aberration coefficients, the values for which can be viewed as coordinates for an infinity of orthogonal axes that span the "aberration space" into which the output propagates. For fully coherent complex scalar disturbances, we study the propagation of the field through the imaging system, while for partially coherent disturbances it is the two-point correlation functions whose propagation we study. For both systems we write down generalized propagators in both real and Fourier space, differential equations for evolution through aberration space, transport equations, and Hamilton-Jacobi equations. A generalized form of the Wolf equations is an important special case of our formalism.

physics.optics↗
arXiv2014

Bloch Sphere Catastrophes

Caustics are optical phenomena which occur when a family of rays creates an envelope of divergent intensity. Here we show that caustic surfaces also appear when a real or complex field is mapped to its order parameter manifold. We study these structures in the context of spin-1/2 fields, where the order parameter manifold is the Bloch sphere. These generic structures are a manifestation of catastrophe theory and are stable with respect to perturbations. The corresponding field configurations are also stable and represent a new type of topological defect. Equations governing the conditions for their existence and unfolding are derived.

physics.optics↗