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156 records · Page 9

Local and global approaches to treat the torsional barriers of 4-methylacetophenone using microwave spectroscopy

The Fourier transform microwave spectrum of 4-methylacetophenone recorded from 8 GHz to 18 GHz under jet-cooled conditions has revealed large tunneling splittings arising from a low barrier to internal rotation of the ring methyl group and small splittings from a high torsional barrier of the acetyl methyl group. The large splittings are especially challenging to model, while the small splittings are difficult to analyze due to the resolution limit of 120 kHz. The combination of two methyl groups undergoing internal rotations caused each rotational transition to split into five torsional species, which were resolved and fitted using a modified version of the XIAM code and the newly devel- oped ntop code to a root-mean-square deviation close to measurement accuracy, providing an estimate of the V 3 potential barriers of about 22 cm -1 and 584–588 cm -1 for the ring and the acetyl methyl groups, respectively. The assignment was aided by separately fitting the five torsional species using odd-power order operators. Only one conformer in which all heavy atoms are located on a symmetry plane could be identified in the spectrum, in agreement with results from conformation analysis using quantum chemical calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Spectral Radiative Properties of Polydispersed SiO 2 Particle Beds

The focus of this work is on the measurement and analysis of the radiative properties of polycrystalline SiO 2 particle beds with various layer thicknesses. The particles are polydispersed with average diameters of 222, 150, and 40 μm . The spectral, directional–hemispherical reflectance and transmittance of the particle bed are measured at wavelengths from 0.4 to 1.8 μm using a monochromator, and the reflectance measurement is extended to 15 μm using a Fourier-transform infrared spectrometer. Particles are closely packed between two transparent windows for measuring the radiative properties. In the visible and near-infrared region up to 1.8 μm, the inverse adding–doubling method yields the effective absorption and scattering coefficients. The results suggest that short wavelength absorption needs to be included in modeling the behavior of particle beds due to multiple scattering. A discrete-scale Monte Carlo ray-tracing method is developed to model the radiative properties by assuming monodispersed spherical particles, and the simulated results compare well with measurements. The effective absorption and scattering coefficients of the particle beds obtained from the independent scattering theory are compared to those from the inverse method. As a result, the impact of dependent scattering on the packed beds is observed for smaller-sized particles.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Foundations of machine learning for low-temperature plasmas: methods and case studies

Abstract Machine learning (ML) and artificial intelligence have proven to be an invaluable tool in tackling a vast array of scientific, engineering, and societal problems. The main drivers behind the recent proliferation of ML in practically all aspects of science and technology can be attributed to: (a) improved data acquisition and inexpensive data storage; (b) exponential growth in computing power; and (c) availability of open-source software and resources that have made the use of state-of-the-art ML algorithms widely accessible. The impact of ML on the field of low-temperature plasmas (LTPs) could be particularly significant in the emerging applications that involve plasma treatment of complex interfaces in areas ranging from the manufacture of microelectronics and processing of quantum materials, to the LTP-driven electrification of the chemical industry, and to medicine and biotechnology. This is primarily due to the complex and poorly-understood nature of the plasma-surface interactions in these applications that pose unique challenges to the modeling, diagnostics, and predictive control of LTPs. As the use of ML is becoming more prevalent, it is increasingly paramount for the LTP community to be able to critically analyze and assess the concepts and techniques behind data-driven approaches. To this end, the goal of this paper is to provide a tutorial overview of some of the widely-used ML methods that can be useful, amongst others, for discovering and correlating patterns in the data that may be otherwise impractical to decipher by human intuition alone, for learning multivariable nonlinear data-driven prediction models that are capable of describing the complex behavior of plasma interacting with interfaces, and for guiding the design of experiments to explore the parameter space of plasma-assisted processes in a systematic and resource-efficient manner. We illustrate the utility of various supervised, unsupervised and active learning methods using LTP datasets consisting of commonly-available, information-rich measurements (e.g. optical emission spectra, current–voltage characteristics, scanning electron microscope images, infrared surface temperature measurements, Fourier transform infrared spectra). All the ML demonstrations presented in this paper are carried out using open-source software; the datasets and codes are made publicly available. The FAIR guiding principles for scientific data management and stewardship can accelerate the adoption and development of ML in the LTP community.

Physics↗

Fermi’s Golden Rule Rate Expression for Transitions Due to Nonadiabatic Derivative Couplings in the Adiabatic Basis

Starting from a general molecular Hamiltonian expressed in the basis of adiabatic electronic and nuclear position states, where a compact and complete expression for the nonadiabatic derivative coupling (NDC) Hamiltonian term is obtained, we provide a general analysis of the Fermi’s golden rule (FGR) rate expression for nonadiabatic transitions between adiabatic states. We then consider a quasi-adiabatic approximation that uses crude adiabatic states and NDC couplings, both evaluated at the minimum potential energy configuration of the initial adiabatic state, for the definition of the zeroth and first-order terms of the Hamiltonian. Although the application of this approximation is rather limited, it allows deriving a general FGR rate expression without further approximation while accounting for non-Condon contribution to the FGR rate arising from momentum operators of NDC terms and its coupling with vibronic displacements. For a generic and widely used model where all nuclear degrees of freedom and environmental effects are represented as linearly coupled harmonic oscillators, we derive a closed-form FGR rate expression that requires only Fourier transform. The resulting rate expression includes quadratic contributions of NDC terms and their couplings to Franck–Condon modes, which require evaluation of two additional bath spectral densities in addition to the conventional one that appears in a typical FGR rate theory based on the Condon approximation. Model calculations for the case where nuclear vibrations consist of both a sharp high-frequency mode and an Ohmic bath spectral density illustrate new features and implications of the rate expression. We then apply our theoretical expression to the nonradiative decay from the first excited singlet state of azulene, which illustrates the utility and implications of our theoretical results.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Optical Phase Recovery and Locking in a PPM Laser Communication Link

Free-space optical communication holds great promise for future space missions requiring high data rates. For data communication in deep space, the current architecture employs pulse position modulation (PPM). In this scheme, the light is transmitted and detected as pulses within an array of time slots. While the PPM method is efficient for data transmission, the phase of the laser light is not utilized. The phase coherence of a PPM optical signal has been investigated with the goal of developing a new laser communication and ranging scheme that utilizes optical coherence within the established PPM architecture and photon-counting detection (PCD). Experimental measurements of a PPM modulated optical signal were conducted, and modeling code was developed to generate random PPM signals and simulate spectra via FFT (Fast Fourier Transform) analysis. The experimental results show very good agreement with the simulations and confirm that coherence is preserved despite modulation with high extinction ratios and very low duty cycles. A real-time technique has been developed to recover the phase information through the mixing of a PPM signal with a frequency-shifted local oscillator (LO). This mixed signal is amplified, filtered, and integrated to generate a voltage proportional to the phase of the modulated signal. By choosing an appropriate time constant for integration, one can maintain a phase lock despite long dark times between consecutive pulses with low duty cycle. A proof-of-principle demonstration was first achieved with an RF-based PPM signal and test setup. With the same principle method, an optical carrier within a PPM modulated laser beam could also be tracked and recovered. A reference laser was phase-locked to an independent pulsed laser signal with low-duty-cycle pseudo-random PPM codes. In this way, the drifting carrier frequency in the primary laser source is tracked via its phase change in the mixed beat note, while the corresponding voltage feedback maintains the phase lock between the two laser sources. The novelty and key significance of this work is that the carrier phase information can be harnessed within an optical communication link based on PPM-PCD architecture. This technology development could lead to quantum-limited efficient performance within the communication link itself, as well as enable high-resolution optical tracking capabilities for planetary science and spacecraft navigation.

Aveline, David C.↗

Upgrades to the ion cyclotron emission diagnostic on the DIII-D tokamak

The ion cyclotron emission diagnostic on the DIII-D tokamak comprises seven single-turn loops that measure high-frequency (1–100 MHz) magnetic field fluctuations that are often excited by energetic particles in the plasma. The raw voltage signals induced in the loops in response to these fluctuations travel through a series of cables, isolation transformer DC blocks, low-pass filters, and finally a digitizer before being analyzed in frequency space. The diagnostic has been recently upgraded, most notably to include four additional graphite tile loops and a new eight-channel digitizer. The previous three loops are all on the low-field side of the tokamak. The measurement capabilities of the system have been expanded by the addition of a new horizontally oriented loop on the low-field side, an additional toroidal loop on the low-field side, and two toroidal loops on the high-field side. These loops will be used to provide approximate mode polarization, improved toroidal mode number calculations, and information on modes in inward-shifted plasmas, respectively.

47 OTHER INSTRUMENTATION↗

Laboratory-Scale Coal-Derived Graphene Process (Final Report)

The Energy & Environmental Research Center (EERC) conducted a laboratory-scale coal-derived graphene (CDG) project focused on developing a technological process for making graphene from four U.S. domestic coal or coal wastes, including lignite from North Dakota, subbituminous coal from Wyoming, bituminous coal from Utah, and anthracite from Pennsylvania. The project was divided into two performance or budget periods (BPs), with BP1 comprising the up-front laboratory experiments to make graphene materials from coal beginning on May 1, 2020, to April 30, 2022. BP2 was conducted from May 1, 2022, to April 30, 2023, and was focused on analyzing the CDG process economic feasibility and the technical gaps for technological scale-up and commercialization. During this project, a few different coal-derived high-value products have been demonstrated, including graphite, graphene oxide (GO), reduced graphene oxide (rGO), and graphene quantum dots (GQDs). A new graphite microstructure was discovered and named “croissant graphite” because of the exterior morphological and textural resemblance to croissant food items sold in commercial groceries stores. The new graphite structure and the associated preparation from coal or coal waste feedstocks has been the subject of a U.S. patent application. The systematic experimental processes involving coal cleaning, upgrading, and conversion to high-value carbon products culminated into a developed upgraded coal-to-products (UCP) technology that is being pursued for potential fast-track commercialization, if funding is available. It is envisioned that commercialization of the UCP technology would increase consumption of U.S. domestic coals or coal wastes to make environmentally sustainable high-value products for the electronics industry, high-energy-storage applications, and clean energy technologies such as electric vehicle (EV) lithium-ion batteries (LIBs), for which graphite has become a critical mineral commodity. Croissant graphite microstructures, when observed by field emission scanning electron microscopy (FESEM), display wavy surface morphology and often grow from a base that is made of graphitized particles with honeycomb-like layers, which are believed to be graphene layers. While more studies are needed to fully ascertain the mechanisms of the croissant graphite microstructure formation, it is postulated that their growth may begin from curling of the graphene sheets into ribbon-like structures, and continuous growth and densification of the ribbon-like structures forms croissant microstructures. Additional studies are ongoing to evaluate the electrochemical performance of croissant graphite for LIB applications and to determine the experimental conditions necessary to tune on/off croissant formation so that it can be either optimized or suppressed depending on performance evaluation results. In addition to the discovery of croissant graphite, the graphitization process from the four coal ranks in general was successful. X-ray diffraction (XRD) analysis showed that the degree of graphitization (DoG) ranged from 12% to 80% in an early sample set, and further optimization on lignite coal produces a DoG of about 92%, which was spectacular to see as lignite is the lowest-rank coal. Thus, it is expected that the graphitization performance for higher-rank coals will be similar or better when optimized as well. The coal-derived graphite was used to make GO and rGO. Analytical characterization, e.g., by methods such as Raman spectroscopy, XRD, Fourier transform infrared (FTIR) spectroscopy and FESEM, showed that the sequence of converting the coal to graphite, exfoliating it to GO, and then chemically reducing the GO to rGO was successful. Although coal naturally contains aromatic compounds and some relatively small-sized condensed aromatic units, it does not contain graphene sheets. In the UCP process, the aromatic domains in the coals, particularly low-rank coals, are concentrated and condensed further into graphene sheets, which are ordered into a 3D stack during graphitization. The synthesized graphite is then unpacked by methods such as exfoliation to various graphene products. GQDs were synthesized from all four coal types, and their optical properties were demonstrated to be tunable by the coal precursor preprocessing treatments. In all four coal types, enhanced optical properties were observed for the produced GDQs with incremental improvements made to the coal precursors. GQDs produced from raw coal samples displayed lower ultraviolet–visible (UV–Vis) spectroscopy absorbance intensity compared to those obtained from cleaned and upgraded coal residues. The photoluminescence (PL) intensities also varied with pretreatment conditions and with the concentration of GQDs in aqueous solutions. GQDs obtained from anthracite show longer emission wavelengths and can be excited by visible light as opposed to GQDs derived from the other coal ranks. UV fluorescence 3D maps and spectra revealed that the emission wavelength at which the GQDs solutions display the highest intensity was slightly redshifted based on the coal precursor pretreatments. In low-rank coal (lignite and subbituminous) samples, two clusters were observed in the maps for GQDs, which may suggest that there are potentially two types of fluorophores in solution or two main size populations. The ability to tune the properties of GQDs based on processing methods can be exploited to make GQDs for various optical display or optoelectronics applications. The results also highlight the importance of removing coal-borne impurities to improve the quality of the coal precursor for preparation of graphene products. Coal and/or coal wastes preprocessing methods were developed and applied to clean and upgrade the coal precursors prior to graphitization and subsequent conversion to graphene products. The preprocessing methods involve high specific-gravity separations, mineral acid cleaning (no hydrofluoric acid), and subsequent upgrading by reducing the coal-borne heteroatom (nitrogen, sulfur, and oxygen) content using proprietary chemical agents. Analytical characterization revealed that the preprocessing steps were successful, with ash reductions that range from 38% to 80% and residual ash content that was below the 5 wt% initial target. Based on proximate and ultimate analysis, the heteroatom reduction reactions produced upgraded coal residues with the oxygen content reduced by 8% to 24%, with additional reductions in the nitrogen and sulfur contents. An initial assessment of the waste streams from the UCP process shows very small to negligible environmental impact due to CO 2 , NO x , and SO x because most process steps are performed under inert atmosphere with argon. Consequently, reactive oxygen environments that tend to create these species are avoided. The inorganic and potentially hazardous species are released into aqueous waste streams that are easy to handle for proper disposal. The liquid waste streams were found to contain low-level concentrations of rare-earth elements (REEs), which could be concentrated and recovered as value-added by-products. Additionally, the volatile and gaseous fractions from carbonization and heat treatment contain useful organic compounds that can also be recovered as potential valuable by-products. Thus, the UCP technology is considered an environmentally sustainable and promising emerging technology for making high-value products from coal and coal wastes, with potential additional value-added by-products. Analysis of potential markets for the coal-derived carbon products shows a strong demand in both niche market sectors and across a wide variety of other industrial sectors. Graphite is currently considered a critical mineral commodity that has a large and growing demand in the LIB industry for EV applications. Based on data from Fortune Business Insights (2022) and Marketwatch (2023) reports, the average global graphite market is projected to reach about 33 billion by 2028, growing at a compound annual growth rate (CAGR) of about 7%, with much of this growth expected to be in the LIB industry. GO and rGO have strong market potentials in various application areas, such as coatings for anticorrosion, anti-icing, and antimicrobial protection, thermal barriers, wear resistance, sensors, additive manufacturing such as 3D inks, and others. GQDs are the emerging key player in the bioimaging, photovoltaics, and light-emitting diodes (LEDs) applications, with the potential to replace traditional semiconductor quantum dots (SQDs), which are based on metallic systems that are more toxic and more expensive. Biomedical applications of GQDs are becoming more attractive because of low to no toxicity and extremely low cost compared to SQDs. The major challenges for scale-up and commercialization of coal-derived carbon products such as graphene vary from the inherent attributes of graphene itself to reluctance to accept graphene in new manufacturing processes because of the uncertainty of the unknown. The 2D nature of graphene materials with a thickness of one atom presents significant challenges to proper handling/processing, and process scale-up becomes difficult because it requires high-end, expensive equipment, even for routine handling and analysis for quality assurance and control. Pristine graphene can also be extremely difficult to work into other matrices, thus hindering downstream processibility, especially at large scale. Currently, the cost of graphene and graphene products is still high and presents an economic risk that tends to slow down investment in scaling up emerging technologies. The lack of a standard for graphene materials for quality assurance and quality control poses a great challenge not only for the markets but also for commercialization efforts. A first-look economic feasibility analysis of the UCP technology provided valuable information that suggests the UCP process would be feasible, especially when it is scaled to a pilot scale and could be more competitive at the full scale. Graphitization was found to be the most energy-consuming and most capital-intensive step in the overall process. In small laboratory- and bench-scale experiments, labor is a significant contributor to the total process costs. Although these energy, capital, and labor constraints contribute to a higher selling price for the product, a preliminary economic model suggests that the process would be feasible at large scale when the process is fully integrated, optimized, and automated.

01 COAL, LIGNITE, AND PEAT↗

Generative Physics-Informed Neural Network Solving Multi-Scale and Multi-Phase Plasma Chemical Flow Field

Low-temperature plasmas (LTPs) are non-equilibrium systems with near-room-temperature gas and highly energetic electrons. This makes them ideal for delicate applications in biomedicine and semiconductor manufacturing, enabling processes like wound healing, sterilization, etching, and plasma-enhanced chemical vapor deposition without thermal damage. However, LTPs involve complex chemistries, with hundreds of species and thousands of reactions, complicating their diagnosis, prediction, and control. Conventional diagnostics, such as Fourier-transform infrared spectroscopy (FTIR), laser-induced fluorescence (LIF), and optical emission spectroscopy (OES), offer limited species detection, while mass spectrometry (MS) struggles with low-sensitivity species. Additionally, LTP simulations face multi-scale challenges, as macroscopic fluid dynamics and microscopic particle collisions operate on vastly different timescales. To address these issues, we developed an artificial intelligence (AI) based diagnostic system: a generative physics-informed neural network (PINN-Gen) that can predict spatially resolved species concentrations and temperatures in LTPs by integrating experimental data from planar LIF with microscopic plasma chemical kinetics and macroscopic fluid mechanics, including plasma-liquid interactions at the interface between two phases. PINN-Gen solves no equations but checks the errors of physical laws by substituting the output from neural network, and the comparison with the experimental results. Thus, it naturally avoids the multi-scale difficulty of numerical simulations and predicts the results of conventionally unsolvable multi-scale and multi-phase problems. The real-time prediction will be robust due to the physical information used in the training of such a neural network, and only very limited input of condition required due to its generative feature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Multi-mode lasing in terahertz metasurface quantum-cascade VECSELs

To date, terahertz quantum-cascade vertical-external-cavity surface-emitting lasers (QC-VECSELs) have tended to oscillate in only one or two lasing modes at a time. This is due to the fact that the interaction between all of the longitudinal external cavity modes and the QC gain material is mediated through a single metasurface resonance, whose spatial overlap changes little with frequency; this suppresses spatial-hole-burning induced multi-mode operation. In this Letter, a VECSEL external cavity is demonstrated using an output coupler based upon a high-resistivity silicon etalon, which presents a periodic reflectance spectrum that is nearly matched with the external cavity mode spectrum. As the cavity length is varied, a systematic transition between a single/double-mode lasing regime and a multi-mode lasing regime is realized due to the Vernier effect. Up to nine modes lasing simultaneously with a free-spectral-range of approximately 21 GHz is demonstrated. Furthermore, this result provides a path toward the multi-mode operation necessary for eventual frequency comb operation.

47 OTHER INSTRUMENTATION↗

Scattering and Diffraction of Electromagnetic Radiation: An Effective Probe to Material Structure

Scattered electromagnetic waves from material bodies of different forms contain, in an intricate way, precise information on the intrinsic, geometrical and physical properties of the objects. Scattering theories, ever deepening, aim to provide dependable interpretation and prediction to the complicated interaction of electromagnetic radiation with matter. There are well-established multiple-scattering formulations based on classical electromagnetic theories. An example is the Generalized Multi-particle Mie-solution (GMM), which has recently been extended to a special version ̶ the GMM-PA approach, applicable to finite periodic arrays consisting of a huge number (e.g., >>106) of identical scattering centers [1]. The framework of the GMM-PA is nearly complete. When the size of the constituent unit scatterers becomes considerably small in comparison with incident wavelength, an appropriate array of such small element volumes may well be a satisfactory representation of a material entity having an arbitrary structure. X-ray diffraction is a powerful characterization tool used in a variety of scientific and technical fields, including material science. A diffraction pattern is nothing more than the spatial distribution of scattered intensity, determined by the distribution of scattering matter by way of its Fourier transform [1]. Since all linear dimensions entered into Maxwell's equations are normalized by wavelength, an analogy exists between optical and X-ray diffraction patterns. A large set of optical diffraction patterns experimentally obtained can be found in the literature [e.g., 2,3]. Theoretical results from the GMM-PA have been scrutinized using a large collection of publically accessible, experimentally obtained Fraunhofer diffraction patterns. As far as characteristic structures of the patterns are concerned, theoretical and experimental results are in uniform agreement; no exception has been found so far. Closely connected with the spatial distribution of scattered intensities are cross sections, such as for extinction, scattering, absorption, and radiation pressure, as a critical type of key quantity addressed in most theoretical and experimental studies of radiative scattering. Cross sections predicted from different scattering theories are supposed to be in general agreement. For objects of irregular shape, the GMM-PA solutions can be compared with the highly flexible Discrete Dipole Approximation (DDA) [4,5] when dividing a target to no more than ~106 unit cells. Also, there are different ways to calculate the cross sections in the GMM-PA, providing an additional means to examine the accuracy of the numerical solutions and to unveil potential issues concerning the theoretical formulations and numerical aspects. To solve multiple scattering by an assembly of material volumes through classical theories such as the GMM-PA, the radiative properties of the component scatterers, the complex refractive index in particular, must be provided as input parameters. When using a PA to characterize a material body, this involves the use of an adequate theoretical tool, an effective medium theory, to connect Maxwell's phenomenogical theory with the atomistic theory of matter. In the atomic theory, one regards matter as composed of interacting particles (atoms and molecules) embedded in the vacuum [6]. However, the radiative properties of atomic-scaled particles are known to be substantially different from bulk materials. Intensive research efforts in the fields of cluster science and nanoscience attempt to bridge the gap between bulk and atom and to understand the transition from classical to quantum physics. The GMM-PA calculations, which place virtually no restriction on the component-particle size, might help to gain certain insight into the transition.

Xu, Yu-Lin↗

Rapidity-dependent spin decomposition of the nucleon

We revisit the two-dimensional Fourier transform of generalized parton distributions (GPDs) at nonzero skewness. At 𝜂 = 0 it reduces to the standard impact-parameter density, while at 𝜂 ≠ 0 it is an off-forward amplitude that we interpret as a genuine parton–nucleon correlation. Its overall strength (the transverse-plane integral of the density) is fixed by the GPD at the kinematic point 𝑡 =−𝑐 𝜂 =−4⁢𝜂 2 ⁢𝑚$^{2}_{𝑁}$/(1 − 𝜂 2 ) and decreases monotonically with the rapidity gap Δ⁢𝑦 = ln⁡[(1+𝜂)/(1−𝜂)] = 2 artanh⁡(𝜂). This rapidity dependence implies rapidity-modified Ji identities that connect helicity, orbital, and total angular momenta of the correlation in closed form. To quantify these effects, we construct leading-twist quark and gluon GPDs in a string-based conformal framework: conformal moments are parametrized by linear open- and closed-string Regge trajectories with slopes constrained by parton distribution functions (PDFs), hadron/glueball spectroscopy, and form-factor data, and GPDs are reconstructed over the full (𝑥,𝜂,𝑡) domain by Mellin-Barnes inversion with next-to-leading order evolution. We find qualitative agreement (and fair quantitative agreement within quoted uncertainties) for several moments and selected nonsinglet 𝑥-space channels at 𝜇 = 2 GeV when compared with lattice QCD, while we also identify channels with visible tension and discuss likely sources (PDF priors and 𝑡-slope systematics).

Gauge-gravity dualities↗

Low-temperature state in strontium titanate microcrystals using in situ multireflection Bragg coherent x-ray diffraction imaging

Strontium titanate is a classic quantum paraelectric oxide material that has been widely studied in bulk and thin films. It exhibits a well-known cubic-to-tetragonal antiferrodistortive phase transition at 105 K, characterized by the rotation of oxygen octahedra. A possible second phase transition at lower temperature is suppressed by quantum fluctuations, preventing the onset of ferroelectric order. However, recent studies have shown that ferroelectric order can be established at low temperatures by inducing strain and other means. Here, we used in situ multireflection Bragg coherent x-ray diffraction imaging to measure the strain and rotation tensors for two strontium titanate microcrystals at low temperature. We observe strains induced by dislocations and inclusion-like impurities in the microcrystals. Based on radial magnitude plots, these strains increase in magnitude and spread as the temperature decreases. Pearson's correlation heat maps show a structural transition at 50 K, which could possibly be the formation of a low-temperature ferroelectric phase in the presence of strain. We do not observe any change in local strains associated with the tetragonal phase transition at 105 K.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗