Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “k mean”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4

An image-driven machine learning approach to kinetic modeling of a discontinuous precipitation reaction

Micrograph quantification is an essential component of several materials science studies. Machine learning methods, in particular convolutional neural networks, have previously demonstrated performance in image recognition tasks across several disciplines (e.g. materials science, medical imaging, facial recognition). Here, we apply these well-established methods to develop an approach to microstructure quantification for kinetic modeling of a discontinuous precipitation reaction in a case study on the uranium-molybdenum system. Prediction of material processing history based on image data (classification), calculation of area fraction of phases present in the micrographs (segmentation), and kinetic modeling from segmentation results were performed. Results indicate that convolutional neural networks represent microstructure image data well, and segmentation using the k-means clustering algorithm yields results that agree well with manually annotated images. Classification accuracies of original and segmented images are both 94% for a 5-class classification problem. Kinetic modeling results agree well with previously reported data using manual thresholding. The image quantification and kinetic modeling approach developed and presented here aims to reduce researcher bias introduced into the characterization process, and allows for leveraging information in limited image data sets.

36 MATERIALS SCIENCE↗

Covariance Shaping Over Riemannian Manifolds for Massive MIMO Communication

Acquiring accurate instantaneous channel state information (CSI) is a challenging aspect of massive multi-input multi-output (MIMO) communication. Utilizing statistical information, such as channel covariance matrix, to design statistical beamforming vectors is robust when compared to instantaneous CSI. In this paper, we propose a novel MIMO covariance shaping scheme over Riemannian manifolds. It serves as an effective statistical beamforming solution to a number of close proximity user equipment (UE) that are undergoing substantial channel correlation. Proposed algorithm exploits the Hermitian positive definite nature of covariance matrices lying over Riemannian manifold. We introduce Wasserstein distance function as a Riemannian metric to measure distances between channel covariance matrices. Furthermore, K-means clustering technique is utilized to effectively identify the optimal shape of effective optimal covariance matrices. Our findings suggest that maximizing the geodesic distance between covariance matrices ultimately leads to a corresponding increase in the network throughput, as determined by the beamforming vector used to shape the covariance matrices. Simulation results validate that the proposed solution converges faster than Euclidean-based state-of-the-art, while maintaining the same computational complexity. Finally, the sum rate performance asymptotically achieves full capacity for two-UE case and more than 96% of the upper bound exhaustive search benchmark for multi-UE scenario.

42 ENGINEERING↗

Machine-learning-assisted analysis of transition metal dichalcogenide thin-film growth

In situ reflective high-energy electron diffraction (RHEED) is widely used to monitor the surface crystalline state during thin-film growth by molecular beam epitaxy (MBE) and pulsed laser deposition. With the recent development of machine learning (ML), ML-assisted analysis of RHEED videos aids in interpreting the complete RHEED data of oxide thin films. The quantitative analysis of RHEED data allows us to characterize and categorize the growth modes step by step, and extract hidden knowledge of the epitaxial film growth process. In this study, we employed the ML-assisted RHEED analysis method to investigate the growth of 2D thin films of transition metal dichalcogenides (ReSe2) on graphene substrates by MBE. Principal component analysis (PCA) and K-means clustering were used to separate statistically important patterns and visualize the trend of pattern evolution without any notable loss of information. Using the modified PCA, we could monitor the diffraction intensity of solely the ReSe2 layers by filtering out the substrate contribution. These findings demonstrate that ML analysis can be successfully employed to examine and understand the film-growth dynamics of 2D materials. Further, the ML-based method can pave the way for the development of advanced real-time monitoring and autonomous material synthesis techniques.

36 MATERIALS SCIENCE↗

Coronado Ecological Conservation: Assessing Vegetation Change Due to Border Wall Construction and Shifting Social Trails

Species monitoring is essential for mitigating the impacts of plant invasion, such as radical changes in an area’s ecosystem, degraded soil health, increased wildfire severity, landslides, and increased flooding. For this project, NASA DEVELOP partnered with the National Park Service (NPS) to investigate invasive species in disturbed lands: specifically, areas affected by off-trail travel and U.S.-Mexico border construction activities. The team assessed how construction has impacted the distribution of Lehmann’s lovegrass and Russian thistle invasives throughout Coronado National Memorial, AZ from 1986-2022. Using data from Landsat 5 and 8, Sentinel-2, NAIP, and PlanetScope, the team computed NDVI, NDMI, MSAVI2, EVI, and Tasseled Cap Wetness, Brightness, and Greenness transformations as vegetation health indicators to input into various machine learning algorithms. To minimize noise, the team conducted Principal Component Analysis on vegetation indices and spectral bands before running k-means clustering and random forest classification algorithms. Between all datasets, the team found that the median area fully overtaken by invasive plants was 5.37% of the park’s total area in 2022. The NPS will use end products to help increase restoration efforts in disturbed areas with high concentrations of invasive plants, and this project can serve as a jumping off point for future invasive species monitoring. The NPS’s collection of ground data for 2022-2023, in conjunction with future data collection, will notably improve the accuracy of classification models, leading to more precise monitoring of invasive species spread over time.

Coronado National Memorial↗

Sub-10 nm Probing of Ferroelectricity in Heterogeneous Materials by Machine Learning Enabled Contact Kelvin Probe Force Microscopy

Reducing the dimensions of ferroelectric materials down to the nanoscale has strong implications on the ferroelectric polarization pattern and on the ability to switch the polarization. As the size of ferroelectric domains shrinks to the nanometer scale, the heterogeneity of the polarization pattern becomes increasingly pronounced, enabling a large variety of possible polar textures in nanocrystalline and nanocomposite materials. Critical to the understanding of fundamental physics of such materials and hence their applications in electronic nanodevices is the ability to investigate their ferroelectric polarization at the nanoscale in a nondestructive way. We show that contact Kelvin probe force microscopy (cKPFM) combined with a k-means response clustering algorithm enables to measure the ferroelectric response at a mapping resolution of 8 nm. In a BaTiO 3 thin film on silicon composed of tetragonal and hexagonal nanocrystals, we determine a nanoscale lateral distribution of discrete ferroelectric response clusters, fully consistent with the nanostructure determined by transmission electron microscopy. Moreover, we apply this data clustering method to the cKPFM responses measured at different temperatures, which allows us to follow the corresponding change in the polarization pattern as the Curie temperature is approached and across the phase transition. This work opens up perspectives for mapping complex ferroelectric polarization textures such as curled/swirled polar textures that can be stabilized in epitaxial heterostructures and more generally for mapping the polar domain distribution of any spatially highly heterogeneous ferroelectric materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Exploring Geothermal Potential of Great Basin Sub-Regions

The INnovative Geothermal Exploration through Novel Investigations Of Undiscovered Systems (INGENIOUS) project aims to discover new, economically viable hidden geothermal systems in the Great Basin region by building on previous work in play fairway analysis and machine learning. A key objective of this project is to develop an exploration workflow to reduce geothermal exploration risks for hidden geothermal systems. A single preliminary play fairway workflow was developed from the assessment of the regional INGENIOUS geological, geophysical, and geochemical datasets. This workflow provided new preliminary predictive geothermal fairway maps for the INGENIOUS study area, which encompasses most of Nevada, western Utah, southern Idaho, southeastern Oregon, and easternmost California. However, a recent study (incorporating machine learning techniques) of a portion of Nevada identified four geologic domains and determined that the relative importance of individual datasets or features as indicators of geothermal potential may differ across these domains. The INGENIOUS study area includes a much larger and more geologically diverse region; therefore, additional geologic domains or sub-regions are expected. To assess the sub-regions in the INGENIOUS study area, principal component analysis and k-means clustering were applied. Preliminary results indicate that the INGENIOUS regional data cluster into groups that relate to different geologic domains in the Great Basin region. These include domains such as the Walker Lane, extensional western Great Basin region, broad lower strain region in the eastern Great Basin of western Utah and eastern Nevada, Quaternary volcanic fields, and the area adjacent to the Snake River Plain. These clusters are assessed to determine the key geologic drivers of the identified clusters. Understanding this variability can provide key insights for the exploration and characterization of hidden geothermal systems in the Great Basin region and could indicate the need to develop multiple geothermal conceptual models and play fairway workflows for the INGENIOUS study area.

exploration↗

Crystallographic variant mapping using precession electron diffraction data

In this work, we developed three methods to map crystallographic variants of samples at the nanoscale by analyzing precession electron diffraction data using a high-temperature shape memory alloy and a VO2 thin film on sapphire as the model systems. The three methods are (I) a user-selecting-reference pattern approach, (II) an algorithm-selecting-reference-pattern approach, and (III) a k-means approach. In the first two approaches, Euclidean distance, Cosine, and Structural Similarity (SSIM) algorithms were assessed for the diffraction pattern similarity quantification. We demonstrated that the Euclidean distance and SSIM methods outperform the Cosine algorithm. We further revealed that the random noise in the diffraction data can dramatically affect similarity quantification. Denoising processes could improve the crystallographic mapping quality. With the three methods mentioned above, we were able to map the crystallographic variants in different materials systems, thus enabling fast variant number quantification and clear variant distribution visualization. The advantages and disadvantages of each approach are also discussed. We expect these methods to benefit researchers who work on martensitic materials, in which the variant information is critical to understand their properties and functionalities.

Crystallographic variant mapping↗

Accelerating the Structure Exploration of Diverse Bi–Pt Nanoclusters via Physics‐Informed Machine Learning Potential and Particle Swarm Optimization

Bimetallic Bi–Pt nanoclusters exhibit diverse structural motifs, including core-shell, Janus, and mixed alloy configurations, due to the unique bonding characteristics between Bi and Pt atoms. Using density functional theory refinements from ChIMES physically machine-learned potential and CALYPSO particle swarm optimization global searches, 34 Bi20-Pt20 nanoclusters are systematically classified. The results reveal that Bi atoms predominantly occupy surface sites, driven by charge transfer effects. Cohesive energy trends alone prove insufficient for structure differentiation, necessitating a data-driven approach employing principal component analysis and K-means clustering. Furthermore, vibrational, electronic, and infrared spectral analyses provide additional insights into structure-property relationships. The findings offer an original framework for the automated classification and analysis of bimetallic nanoclusters, enhancing the understanding of their stability and functional properties.

bimetallic nanoparticles↗

Shared Use Travel Behavior for Improving Rural Mobility: Insights from Greene County, Pennsylvania

Rural communities are considered disadvantaged communities as they suffer from a lack of transport options. Thus, rural regionsprovide less accessibility for commuters to reach their destination as opposed to urban regions. However, the issues of transport disadvantageand shared use mobility in rural areas within the United States (US) have not been well investigated. Furthermore, transport disadvantagediffers between communities and regions across the globe; thus, there is a need to study the behavioral choices of rural commuters within theUS context. This study contributes by analyzing the behavioral choices of rural communities within the US through a case study site ofWaynesburg, Pennsylvania, for adopting a shared use shuttle service. K-means clusters showed that trips from the survey data were a goodrepresentation of real trips from Ecolane. Furthermore, random parameter-based binary logit models were calibrated using data collected fromstudents, faculty, and residents in Waynesburg, Greene County, to study the behavioral choices of commuters. The findings for the faculty andstudents group revealed that prior experience with shared services increases the likelihood of using a shared shuttle. An important personalcharacteristic of inconvenience showed a higher propensity toward using existing modes as opposed to a shared shuttle. Such commutersvalue personal vehicles as more convenient as they have childcare responsibilities and varying schedules for work that require them to moveback and forth across locations, thus making a shared shuttle less attractive for them. The socioeconomic factors of age and gender show ahigher propensity for using shared shuttles. Furthermore, the findings from this study could be helpful for agencies in improving rural mobility andconsidering such shared mobility services for rural communities

42 ENGINEERING↗

Anomalously high elastic modulus of a poly(ethylene oxide)-based composite electrolyte

The practical use of lithium metal anodes in solid-state batteries requires a polymer membrane with high lithium-ion conductivity, thermal/electrochemical stability, and mechanical strength. The primary challenge is to effectively decouple the ionic conductivity and mechanical strength of the polymer electrolytes. We report a remarkably facile single step synthetic strategy based on in-situ crosslinking of poly(ethylene oxide) (xPEO) in the presence of a woven glass fiber (GF). Such a simple method yields composite polymer electrolytes (CPE) of anomalously high elastic modulus up to 2.5 GPa over a broad temperature range (20 °C – 245 °C) that has never been previously documented. An unsupervised machine learning algorithm, K-mean clustering analysis, was implemented on the hyperspectral Raman mapping at the xPEO/GF interface. Using such a unique means, we show for the first time that the promoted mechanical strength originates from xPEO and GF interactions through dynamic hydrogen and ionic bonding. High ionic conductivity is achieved by the addition plasticizer (e.g. tetraglyme), where trifluoromethanesulfonate anions are tethered to the xPEO matrix and Li + cations are favorably transported through coordination with the plasticizer. Further, stringent galvanostatic cycling tests indicates the CPE can be stably cycled for >3000 h in a Li-metal symmetric cell at a moderate temperature (nearly 1500 Coulombs/cm 2 Li equivalents), outperforming most of the PEO-based electrolytes. The GF reinforced CPE reported here has multifunctional uses, such as solid electrolytes for all solid-state batteries and membranes for redox-flow batteries. Although the focus of this study is on lithium-based batteries, the results are equally promising for other alkali metal based batteries such as sodium and potassium.

25 ENERGY STORAGE↗

Discovering Hidden Geothermal Signatures using Unsupervised Machine Learning

Discovering hidden geothermal resources is a very challenging task. It requires the mining of large datasets, including various diverse data attributes representing subsurface hydrogeological and geothermal conditions. The commonly used Play Fairway Analysis (PFA) typically relies on subject-matter expertise to analyze site or regional data to estimate geothermal conditions and prospectivity. Here, we demonstrate an alternative approach based on machine learning (ML) to process a geothermal dataset of Southwest New Mexico (SWNM). The study region includes low- and medium-temperature hydrothermal systems. However, most of these systems are poorly characterized because of insufficient existing data and limited past explorative studies. This study aims to discover hidden patterns and relationships in the SWNM geothermal dataset to better understand regional hydrothermal conditions. This is achieved by applying an unsupervised machine learning algorithm based on non-negative matrix factorization coupled with customized k-means clustering (NMFk). NMFk can automatically identify (1) hidden (latent) signatures characterizing datasets, (2) the optimal number of these signatures, (3) dominant data attributes associated with each signature, and (4) spatial distribution of the extracted signatures. Here, NMFk is applied to analyze 18 geological, geophysical, hydrogeological, geothermal attributes at 44 locations in SWNM. NMFk successfully finds data patterns and identifies the spatial associations of hydrothermal signatures with the four physiographic provinces in SWNM (Colorado Plateau, Volcanic Field, Basin and Range, and the Rio Grande rift). The algorithm identified up to 5 hydrothermal signatures in the SWNM datasets that differentiate between low- and medium-temperature hydrothermal systems in different provinces. Also, the algorithm identifies two medium-temperature hydrothermal systems in SWNM that require further exploration for geothermal resource development. Based on our analyses, 12 of the attributes are important to identify medium-temperature hydrothermal systems, and the remaining six attributes are critical to characterize low-temperature hydrothermal systems. Based on the obtained results, we identify potential physiographic provinces for further exploration to characterize them as geothermal resources. The resulting NMFk model can be applied to predict geothermal conditions and their uncertainties at new SWNM locations based on limited data from unexplored areas.

58 GEOSCIENCES↗

Separation of internal and external fields: A new technique of data screening

A method for eliminating transient variation from MAGSAT data is described. Instead of using the conventional Kp index, the Km index is used for the rejection of nonquiet data. To build the Km index, the surface of the Earth is divided in eight sectors. Each sector is defined by two or three magnetic observatories and its geographic limits. For each three hourly interval the MAGSAT tracks were drawn on a map showing the location of the station (the crosses), the limits of the sector, and the value of the mean K index inside each sector. No figure in a sector means that the activity level in this sector is lower than 5 nt; in a sector covered with number 1, the activity lies between 5 and 20 nt; 2 stands for any level greater than 20 nT.

Lemouel, J. L.↗

Passive remote sensing of ocean optical propagation parameters

A method is described for producing a global data of ocean optical properties through the exploitation of optical remote sensing techniques. The diffuse attenuation, K, and the radiance reflectance factor R sub L, of the ocean surface waters can be derived from the radiance data provided by the Coastal Zone Color Scanner and compiled into a computer based atlas of these properties. While these remotely sensed values can only be directly related to the water properties in the first or upper attenuation length, extensive in water measurements have demonstrated that a useful correlation exists between the K that applies to the upper attenuation length, for example, and the mean K over the upper 100 or 200 meters of the ocean. Such an empirical finding greatly enhances the usefulness of this remotely sensed propagation parameter. Examples of the type of information being produced and archived for the atlas are presented.

Austin, R. W.↗

Free convection in the Martian atmosphere

Researchers investigated the free convective regime for the Martian atmospheric boundary layer (ABL). Researchers generalized Schumann's model describing horizontal fluctuations and mean vertical gradients occurring during free convection to include convection driven by water vapor gradients and to include the effects of circulation above both aerodynamically smooth and rough surfaces. Applying the model to Mars, researchers found that nearly all the resistance to sensible and latent heat transfer in the ABL occurs within the thin interfacial sublayer at the surface. Free convection is found to readily occur at low pressures and high temperatures when surface ice is present. At 7 mb, the ABL should freely convect whenever the mean windspeed at the top of the surface layer drops below about 2.5 m s(-1) and surface temperatures exceed 250 K. Mean horizontal fluctuations within the surface layer are found to be as high as 3 m (-1) for windspeed, 0.5 K for temperature, and 10 (-4) kg m (-3) for water vapor density. Airflow over surfaces similar to the Antarctic Polar Plateau was found to be aerodynamically smooth on Mars during free convection for all pressures between 6 and 1000 mb, while surfaces with z sub o approx. equals 1 cm are aerodynamically rough over this pressure range.

Clow, G. D.↗

Uncertainty estimation of bifurcated solutions in the Rayleigh–Bénard problem for advanced nuclear reactors applications

Multiphysics models of nuclear reactors frequently comprise nonlinear systems of equations. The nonlinear nature of these models could lead to solution bifurcations, where a small change in a certain parameter, e.g., the thermophysical properties of the coolant, can lead to a sudden change in the system’s behavior. At the point in parameter space where this happens, called a critical point, the Jacobian matrix of the model’s nonlinear operator becomes singular potentially permitting multiple solutions to coexist. In this paper, we perform uncertainty estimation (UE) in a parameter range that includes bifurcated solutions within the context of Rayleigh–Bénard problem. We perform this analysis assuming uncertain temperature difference, and tilt angle for the iterative solution algorithm with a unit Prandtl number (Pr = 1). Also, we perform this analysis under uncertain thermophysical properties for both FLiBe molten salt and liquid sodium as working fluid. We deploy two approaches to compute statistical moments for the resulting distributions of selected flow-field variables. The first approach is the blind computation of the mean and the standard deviation without any consideration of solution bifurcation, while the second approach utilizes k-means clustering to cluster each branch’s solutions together and compute separate statistical moments for each branch. The statistical distributions are obtained by perturbing the selected parameters about nominal values that correspond to a solution on one of the valid branches, and that solution is used as initial guess for the iterative solution algorithm. We found that perturbation of any parameter when its nominal value is close to its critical point always leads to branch jumping, i.e., the iterations converge to a solution on a branch different from the branch of the initial guess. This produces a statistical ensemble comprised of fundamentally different solutions leading to wrong mean values and uncertainty estimates, whereas clustering provides an efficient way to deal with this type of computation. This work is important for developing Gen IV nuclear systems because many of these systems rely on natural convection for cooling especially in accident conditions.

97 - MATHEMATICS AND COMPUTING↗

Operational Dynamic Configuration Analysis

Sectors may combine or split within areas of specialization in response to changing traffic patterns. This method of managing capacity and controller workload could be made more flexible by dynamically modifying sector boundaries. Much work has been done on methods for dynamically creating new sector boundaries [1-5]. Many assessments of dynamic configuration methods assume the current day baseline configuration remains fixed [6-7]. A challenging question is how to select a dynamic configuration baseline to assess potential benefits of proposed dynamic configuration concepts. Bloem used operational sector reconfigurations as a baseline [8]. The main difficulty is that operational reconfiguration data is noisy. Reconfigurations often occur frequently to accommodate staff training or breaks, or to complete a more complicated reconfiguration through a rapid sequence of simpler reconfigurations. Gupta quantified a few aspects of airspace boundary changes from this data [9]. Most of these metrics are unique to sector combining operations and not applicable to more flexible dynamic configuration concepts. To better understand what sort of reconfigurations are acceptable or beneficial, more configuration change metrics should be developed and their distribution in current practice should be computed. This paper proposes a method to select a simple sequence of configurations among operational configurations to serve as a dynamic configuration baseline for future dynamic configuration concept assessments. New configuration change metrics are applied to the operational data to establish current day thresholds for these metrics. These thresholds are then corroborated, refined, or dismissed based on airspace practitioner feedback. The dynamic configuration baseline selection method uses a k-means clustering algorithm to select the sequence of configurations and trigger times from a given day of operational sector combination data. The clustering algorithm selects a simplified schedule containing k configurations based on stability score of the sector combinations among the raw operational configurations. In addition, the number of the selected configurations is determined based on balance between accuracy and assessment complexity.

Lai, Chok Fung↗

The impact of urban configuration types on urban heat islands, air pollution, CO 2 emissions, and mortality in Europe: a data science approach

The world is becoming increasingly urbanized. As cities around the world continue to grow, it is important for urban planners and policymakers to understand how different urban configuration patterns affect the environment and human health. We aimed at identifying European urban configuration types, based on the Local Climate Zones categories and street design variables from Open Street Map, and evaluating their association with motorized traffic flows, Surface Urban Heat Island (SUHI) intensities, tropospheric nitrogen dioxide (NO 2 ), CO 2 per capita emissions and age-standardized mortality. We considered 946 European cities from 31 countries for the analysis defined in the 2018 Urban Audit database, of which 919 European cities were analysed. Data were collected at a 250 m × 250 m grid cell resolution. We divided all cities into five concentric rings based on the Burgess concentric urban planning model and calculated the mean values of all variables for each ring. First, to identify distinct urban configuration types, we applied the Uniform Manifold Approximation and Projection for Dimension Reduction method, followed by the k-means clustering algorithm. Next, statistical differences in exposures (including SUHI) and mortality between the resulting urban configuration types were evaluated using a Kruskal–Wallis test followed by a post-hoc Dunn's test. We identified four distinct urban configuration types characterising European cities: compact high density (n=246), open low-rise medium density (n=245), open low-rise low density (n=261), and green low density (n=167). Compact high density cities were a small size, had high population densities, and a low availability of natural areas. In contrast, green low-density cities were a large size, had low population densities, and a high availability of natural areas and cycleways. The open low-rise medium and low-density cities were a small to medium size with medium to low population densities and low to moderate availability of green areas. Motorised traffic flows and NO 2 exposure were significantly higher in compact high density and open low rise medium density cities when compared with green low density and open low-rise low density cities. Additionally, green low-density cities had a significantly lower SUHI effect compared with all other urban configuration types. Per person CO 2 emissions were significantly lower in compact high density cities compared with green low density cities. Lastly, green low density cities had significantly lower mortality rates when compared with all other urban configuration types. Our findings indicate that, although the compact city model is more sustainable, European compact cities still face challenges related to poor environmental quality and health. Our results have notable implications for urban and transport planning policies in Europe and contribute to the ongoing discussion on which city models can bring the greatest benefits for the environment, climate, and health.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Nanoscale Polarization-Dependent Young’s Modulus of Ferroelectric BaTiO 3 Single Crystals

Flexoelectric fields produced by strong strain gradients at the nanoscale couple to ferroelectric polarization, promoting changes in the mechanical properties of ferroelectric materials as a function of the direction of the ferroelectric polarization. In this work, we calculate the asymmetry in the Young’s modulus found in oppositely polarized out-of-plane domains of BaTiO 3 single crystals by means of contact resonance AFM, and we evaluate its impact on the electromechanical response as measured by piezoresponse force microscopy, both using band excitation modes. Furthermore, we analyze the electromechanical response of the different BaTiO 3 domains using k-means to build up their mean elastic and electromechanical features and quantify the flexoelectrically induced modulation of the Young’s modulus. Finally, we discuss the use of contact Kelvin probe force microscope measurements to decouple electrostatic artifacts from purely piezoelectric ones when flexoelectric coupling appears.

BaTiO 3 single crystals↗