Local Deformation Mapping Reveals Diffusion through Microstructures

Local Deformation Mapping Reveals Diffusion through Microstructures | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Local Deformation Mapping Reveals Diffusion through Microstructures Jan Schroers, Arindam Raj, Michael Aderibigbe, Ethen Lund, Yi-Xiang Yang, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7474019/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract Understanding and quantifying microstructure–property relationships, particularly those where plastic deformation is based on atomic diffusion, remains a grand challenge in metallurgy. While existing techniques often tradeoff between spatial resolution, sampling area, and throughput, a method capable of bridging various length scales remains elusive. To address this need, we propose local deformation mapping (LDM) as a high-resolution, high- throughput characterization technique. LDM determines what diffuses locally through microstructures, creating a direct deformation map imprinted on top of the microstructure. These maps can exhibit ~10 nm² resolution across macroscopic areas (~cm²), generating up to ~10¹² data points in a single experiment. This technique maps deformation-related properties such as diffusivity as a function of microstructural features, including grains, grain boundaries, and interphase boundaries. We demonstrate a one-step determination of grain boundary diffusivity as a function of misorientation angle, temperature-dependent deformation behavior, and previously unknown fast diffusion within interphase boundaries in eutectic-containing alloys. Experimentally, LDM is realized by pressing a nanomold onto a microstructure, inducing local stress gradients that drive material from the microstructure into mold pores, forming nanorods. This spatial separation of the plastic response from the microstructure enables sensitive chemical composition mapping of this flux in multicomponent microstructures, previously unachieved with the state of the art. Nanorods’ length and composition form the deformation response maps, converted into diffusivity maps via the hereby developed analytical model. Altogether, LDM is a powerful platform to advance the quantitative understanding of structure–property relationships for a wide range of materials across a broad temperature range. Physical sciences/Materials science/Structural materials/Metals and alloys Physical sciences/Materials science/Techniques and instrumentation/Characterization and analytical techniques Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction and Motivation: Structure-property-processing relations and existing characterization methods Generally, alloys are multiphase and polycrystalline, exhibiting complex microstructures. Their plastic deformation is among the richest problems in materials science. As a result, their structure-property-processing relations have been the center of metallurgical research 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 . Metallic microstructures may include grains and grain boundaries of different structures, chemistry, and orientations, often combined with defects, and local gradients in stress and dislocation density. These features dictate the local variations in a microstructure’s elastic, plastic, thermodynamic, and kinetic properties 12 . To study these relations, a wide range of characterization techniques have been developed to probe materials with different spatial resolutions. These measurement techniques include TEM for locally isolated features 13, 14, 15, 16, 17 , atom probe tomography (APT) and 3D reconstructions from SEM for nanoscale volumes 18, 19, 20, 21, 22 , and EBSD for grain distributions and strain 23, 24, 25, 26, 27, 28 . Additionally, further detailed analyses of microstructures and strain responses are possible through tomography (X-ray, MRI) 29, 30, 31, 32, 33 , nanoindentation 34, 35 , and digital image correlation (DIC) 36, 37, 38 , among others. These techniques probe different length scales, revealing phenomenological details. In large part due to these technical advancements, various aspects of the structure-property-processing relations are well studied, 1, 6, 7, 39, 40, 41, 42, 43, 44 and quantitative theories have been developed 12, 45, 46, 47, 48, 49, 50, 51 . Despite the many strengths of such state-of-the-art characterization techniques, a key gap remains; highly localized and sensitive deformation measurements over large areas and volumes. Thus, even though considerable progress has been made, a general quantitative understanding of this relationship is still lacking due to the fundamentally multiscale and complex nature of the plastic response of alloys’ microstructures. Model descriptions for microstructure-property relations require a high spatial resolution mapping of local microstructure deformation behavior and properties, considering the multi-scale nature of a microstructure response to stress 6, 45, 49, 51, 52, 53, 54, 55 . These models may require measurements over large areas, long times, and high temperatures, particularly when interactions between multiple features are present. Especially for high temperature fatigue or creep studies, sequential measurements have limitations at long time scales and high temperatures. Since the mechanical response of a microstructure depends on the interplay of its microstructural features, a piecemeal approach is generally not appropriate for studying the vast set of possible microstructural features. Broadly speaking, the specifics of plastic deformation in metals and alloys depend largely on their mass transport mechanisms and the related rates, the applied forces, and their boundary conditions. The transport rates, which determine deformation, can vary dramatically across the microstructure of a single material. For example, lattice diffusivity and grain boundary diffusivity values may differ by several orders of magnitude in metals and alloys owing to much lower activation energy along these boundaries 10, 56, 57, 58, 59 . Diffusion-based mechanisms drive a variety of microstructural phenomena in alloys that occur during their preparation and service. These includes phase transformations 60, 61 , segregation 62 , alloy homogenization 63 , and performance related phenomenon such as creep and fatigue 64, 65, 66 . Therefore, engineering alloy microstructures with desired properties hinges on precise understanding of mass transport rates within microstructures. To address this, we propose a new technique to study plastic deformation characteristics of bulk scale microstructures with high resolution (Fig. 1). Within this method, a microstructure is locally deformed at the nanoscale in a massively parallel fashion. We connect these local deformations to the underlying mass transport processes across the microstructure, categorized broadly under diffusion and dislocation-based plasticity mechanisms. Here, we focus primarily on diffusion-based measurements (Fig. 1b,c), though dislocation related measurements are also made. The salient features of this technique are i.) the massively parallel, high-resolution, and chemically sensitive mapping of the mass transport rates as a function of the various microstructural features, and ii.) the quantitative determination of these local mass transport rates such as diffusivity with the same resolution. Experimentally, this is accomplished via the deformation of a bulk scale microstructure at more than one billion locations simultaneously. These locations are regularly spaced over large areas of ~cm 2 , enabling spatial resolution down to ~10 nm 2 (Fig. 1). Each deformation captures the plastic deformation response of the underlying component/feature in the microstructure. Thus, the collection of these deformation spots results in a local deformation map, created in a single step (Fig. 1b,c). We then relate the varying rates of deformation in the different regions of the microstructure to the variation in the microstructural features (Fig. 1c). Thus, we directly measure the local variations in the mass transport mechanism dictating the deformation as a function of the features, e.g., grain boundaries with different misorientation angles, which are present in the different regions of a polycrystalline microstructure. This enables, for example, identification of the microstructural features which exhibit particularly high or low mass transport rates during plastic deformation. In this way, one experiment can offer significant insight into property-structure correlations. Introduction to Local Deformation Mapping (LDM) LDM is experimentally based on Thermomechanical Nanomolding (TMNM), a recently developed technique for fabricating arrays of nanorods for a range of elements and alloys 67, 68, 69, 70 . This technique is realized by pressing a feedstock material against a porous nanomold, creating local stress gradients that force the material into the mold (Fig. 1a). The control parameters of the process are the applied compressive stress, σ , temperature, T , and molding time, t . Appropriate application of these parameters results in an array of nanorods which can be released from the mold through a selective etching process. We demonstrate here that TMNM is modified into a characterization method to map material transport rates within microstructures. The nanomolds used for deforming the microstructure during LDM have pores which range in diameter from 2.5 nm to 150 nm and spaced by the same distance. For a typical ~cm 2 nano mold array, this results in up to ~10 12 distinct nanorods (data points) in one LDM experiment. So, LDM is capable of mapping plastic responses with high spatial resolution, high throughput, over a macroscopic sampling area, characterizing microstructure deformation over a temperature range practically spanning from cryogenic temperatures to about 1000°C and can be applied to a wide range of materials. In this work, we introduce LDM and also present a quantitative scheme to measure the local deformation rates, focusing on diffusion related processes, within a microstructure by analyzing nanorod growth. Specifically, we claim and demonstrate that we can deduce quantitative information about the diffusion rates within a microstructure using the nanorods array grown over it. The various features of microstructure influence this transport rate, and this reflects as variations in the length and composition (for multicomponent microstructures) of the nanorods. Thus, the crux of the LDM technique lies in revealing the connection between the nanorod length variation map, termed the L -map, and the mass transport behaviors of the different microstructural features. To accomplish this, we develop analytical models to transform the L -maps into a quantitative mass transport rate (diffusivity) map. Quantification of materials properties using LDM Briefly, these analytical models describe the transport of the material due to the stress gradient imposed during LDM and connect the measured L of the nanorods with the local diffusivity values through the microstructure (Fig. 2a). The material transfer during LDM occurs in two steps. First, under the imposed stress gradient material flux in the microstructure (termed as the “microstructure flux,” J microstructure moves towards the mold’s nanopores. Subsequently, this material enters the nanopores to form rods (termed as the “nanorods’ flux,” J nanorod ) (Fig. 2). This outgoing flux, J nanorod , results in the formation of the nanorods that form the L- map, which is measured and analyzed. We have developed models assuming dislocation slip or diffusion as the underlying mechanism dictating the outgoing flux, J nanorod (Fig. 2b and supplementary section 1). We identify through scaling of L ( d ) (Fig. 2b) which mechanism is at play (Fig. 2c) during LDM. For elevated temperatures (T 0.5 T M ), interface diffusion-controlled equation for L is found to fit the experimental data. Then, under the assumption that J microstructure is the rate limiting step, we can determine from the measured L values, the (local) diffusivity of the microstructure. We develop an analytical model capturing this process and verify it under the assumption that J microstructure is the rate limiting step by using Ag samples (presented in Figs. 1 and 2). We calculate D GB (Ag) = 5×10 -7 cm 2 /s for T = 473°C through LDM using this analysis, which is comparable to literature values of 3×10 -7 cm 2 /s for Ag at this temperature 72 . Thereby we confirm that LDM can be used to determine local D values in a one-shot experiment from the measured L -map. This analytical model developed hereby (supplementary section 2) correlates the measured length through LDM with the intrinsic self-diffusivity in the microstructure, D GB according to: where L : length of the nanorods, σ : applied stress, Ω : atomic volume of the diffusing entity, t : molding time, : diffusivity on the mold-feedstock interface, d : mold diameter¸ : mold-feedstock interface thickness. From (A1, 2) it is clear that a difference in the intrinsic kinetics at the different regions of the microstrcuture leads to an L -map with varying lengths of nanorods. Indeed, we observe that nanorods are longer along the grain boundaries in Fig. 1, indicating the faster diffusion rates in GB regions ( D GB > D lattice ). Further, to analyze diffusive flux in alloys, the nanorods can also be analyzed for their composition to determine the composition of the material flux moving through the microstructure. This unique measurement is possible because LDM spatially separates the flux from the underlying microstructure, making sensitive chemical spectroscopy possible. Thereby, the L -map can be correlated with elemental distribution of the material flux over different regions of the microstructure. Consequently, the experimentally determined L- map encodes the microstructure specific transport rate and chemical variation with high spatial resolution, and we demonstrate this for grain boundaries, interphase boundaries, and segregated phases. We demonstrate the potential and capability of LDM by showing: LDM enables locally precise mapping of transport properties: demonstrated through diffusivities mapping in grains and grain boundaries (GBs), revealing the position of GBs and the local diffusivity value variations (Fig. 1) LDM reveals property-microstructural feature correlations in a high-throughput fashion: demonstrated through one step mapping of the dependence of grain boundary self-diffusivity, D GB on the misorientation angle of the grain boundaries in an FCC polycrystalline microstructure (Fig. 3) LDM enables mass transport measurements all the way until melting: demonstrated through the mapping of the temperature dependent mass transport rates for a wide range of homologous temperatures (Fig. 4). LDM enables chemically sensitive mapping by the spatial separation of the diffusion flux into the nanomold: demonstrated through the mapping of the interphase boundary diffusivities in multiphase microstructures and revealing that this flux can have remarkably different behavior and composition than expected from average behavior of the phases involved (Fig. 5). Misorientation angle dependent diffusivity For most polycrystalline microstructures at lower homologous temperatures, diffusion rates are much higher in grain boundaries compared to the lattice 56 , 57 , 58 , 73 . Thus, material transport properties can vary significantly over small length scales even within a single-phase microstructure, and the GBs with different misorientation angles may display very different kinetic properties 74 , 75 , 76 , 77 . While approaches such as bicrystal studies can provide very detailed and precise measurements of well-defined grain boundaries, they are not particularly suited for covering a wide range of GBs due to the cumbersome preparation and set up required, which have limited the use of this approach to a small number 78 , 79 , 80 . LDM, on the other hand can mimic simultaneously a large series of such bicrystal studies when performed on an equiaxed sample (Fig. 3 ). Different grains, their orientations, and the corresponding GBs characterized by different degrees of misorientation can be “imaged” through LDM, revealing the location of the grain boundaries and the kinetics of the diffusion flux through these GBs. Within the new workflow that LDM provides, a static map of grain boundary distribution is obtained through EBSD. Then, an L -map, L (x,y), is generated in the same area using LDM. By spatially correlating these two maps, we can directly plot the local diffusivity as a function of misorientation angle, D GB (Q GB ), for hundreds to thousands of unique grain boundaries in a single experiment. We demonstrate this capacity of LDM with an equiaxed, polycrystalline Ni sample with GBs spanning a typical range of misorientation angles, Q GB , where their relative kinetics is revealed in a single experiment (Fig. 3 ). An L -map is created by molding the Ni sample at ( T = 720°C, σ = 200 MPa, t = 7200 s) (Fig. 3 a). Comparison of the L -map with the EBSD map reveals markedly longer nanorods (~ 30 µm) along the grain boundaries of the polycrystalline Ag than over the grains (~ 1 µm), confirming the general trend of D GB > > D lattice . Further variations within the long nanorods grown on top of the different types of grain boundaries are present. Such variations within the long nanorods growing over the grain boundaries are then correlated with the corresponding Q GB which reveals in a one-shot measurement the absolute values of D GB ( ϴ GB ). Such LDM determined D GB ( ϴ GB ) is in qualitative and quantitative agreement with literature values 81 , 82 , 83 , suggesting that such an application of LDM can expand experimental grain boundary research beyond the few carefully controlled situations to include most complicated and general situations. Characterizing temperature dependent deformation with LDM LDM can further be used to determine the temperature dependent deformation behavior of microstructures, from dislocation mediated at low temperatures to grain boundary and lattice diffusion at high temperatures. To demonstrate this, experiments are carried out for polycrystalline Ag at various temperatures in the range of T hom = 0.34–0.9. For T hom = 0.34, nanorod growth is very slow, and there is no measurable contrast between grains and grain boundaries (Fig. 4 a), suggesting that deformation is based on dislocation slip. With increasing homologous temperature, >~0.5, nanorods with appreciable aspect ratios can be observed after minutes of LDM, and these nanorods on the grain boundaries are significantly longer than nanorods growing on the grains, suggesting diffusion-controlled deformation. The length ratio is ~ 10–15 for T hom ~ 0.5, which translates into D GB / D lattice ~ 10000 (from equations A3-A6) (see table S1 in supplementary section 3). With increasing T hom , increase in L is observed along grain boundary and along the grains. However, this increase occurs with different rates, d L /d T hom (Fig. 4 b), and for T hom ~ 0.9, D GB / D lattice decreases to ~ 100. The rate of nanorod growth over the grains is higher than that for nanorods growing over grain boundaries with increasing temperature. This reflects the fact that the slopes for self-diffusivity curves scale with temperature for atoms in the GBs are low (low activation energy) and high for atoms diffusing through the lattice 73 . Thus, they converge increasingly when heated to very high homologous temperatures. This demonstrates that via LDM, the temperature dependent deformation mechanism can be revealed which changes from dislocation-slip base, present to ~ 0.4 T hom , to grain boundary diffusion dominated deformation up to ~ 0.75 T hom , to grain boundary and lattice diffusion deformation above ~ 0.8 T hom . Further the diffusivity values can be determined quantitatively as a function of temperature (Fig. 4 c). Mapping the effect of interphase boundaries and different-in-composition grain boundaries on local diffusivity After demonstrating LDM for single phases and polycrystalline microstructures, we turn to the most general alloys which are more complex as they may comprise of multiple elements, multiple phases, and corresponding interphase boundaries. Here, we focus on interphase boundaries and the diffusivity within these interfaces. Due to the large number of different interfaces that are present in the compositional space of alloys, only a minute fraction has been characterized in terms of their diffusion characteristics, despite their effect on controlling a variety of alloy related phenomenon and properties including creep and fatigue 64 , 66 , 86 , 87 , phase transformations 60 , segregation 88 , alloy homogenization 44 , self-healing 89 , nucleation of new phases 90 , and complexion and complexion transitions 75 , 91 , 92 . Drawing on our previous findings 93 , we focus on eutectic alloys particularly those which exhibit a deep depressed liquidus temperature relative to the melting temperatures of its constituents and a large negative heat of mixing between its constituents. For such alloys, we observe long nanorods, indicating a fast diffusion pathway along the interphase boundary of the eutectic counterparts (Fig. 5 a) 93 , 94 . Specifically, we use pure Au and Au 97 Si 3 eutectic system. For identical LDM molding conditions, we observe over 10 times longer nanorods in the Au 97 Si 3 system than in pure Au (Fig. 5 a). The small amount of silicon added to gold has a dramatic effect on the length of the nanorods at some location in the microstructure. We reveal that these locations are the Au-Si interfaces in the Au-Si eutectic region which itself is trapped between almost pure Au grains (Fig. 5 a). This indicates, which has not been observed with today’s state of the art diffusion measurements, that eutectic interfaces enable fast diffusion pathways, and it is the presence of eutectic interphase boundaries and not the overall composition that determines the flux through such microstructures. These eutectic interphases have the lowest thermal stability within one alloy system which is reflected in the lowest melting point within the heterogeneous microstructure and hence, they experience the highest homologous temperature at a given absolute temperature. The LDM results reveal that this local low thermal stability is strongly correlated to fast rates of diffusive flux. As another example to demonstrate the capability of the LDM method to capture local deformation, we select an alloy with high grain boundary segregation which results in significant chemical variation between grain and grain boundaries 75 , 95 , 96 . It is widely accepted that, particularly for elements that exhibit large grain boundary segregation tendencies, very small quantities can have significant impact on the microstructure, stability, and properties of alloys 97 , 98 , 99 . To understand, what specifically causes such strong impact, we select Ni 95 Bi 5 as an alloy with low solute concentration, where the grains are primarily solid solution (Ni), and the grain boundaries are enriched in Bi, due to high segregation enthalpy of Bi in Ni of -111.5 kJ/mol (109). The L -map captured at 500°C reveals very long Bi rich nanorods along the Ni grain boundaries (Fig. 4 b), revealing a grain boundary pre-melting behavior (melting temperature of Bi is 271°C). Conclusions We present local deformation mapping (LDM) as a one-shot method to locally characterize plastic responses of a microstructure with a spatial resolution of down to ~ 10 nm 2 , in a parallel fashion over ~ cm 2 . The physical separation of the deforming material from the microstructure allows for sensitive determination of the flux’s quantity and chemistry. Such chemically sensitive, and spatially mapped measurements are prohibitively cumbersome to determine for a general alloy using state-of-the-art methods and hence have been generally lacking. When carried out at high homologous temperature > 0.5 T m , LDM provides the local diffusivity values within the microstructure. We experimentally demonstrate the potential of LDM, proving the capability to perform high throughput diffusion mapping across various microstructural features. We reveal the misorientation angle dependence of grain boundary diffusivity in a one-shot measurement, the temperature dependence deformation of general microstructures, and novel diffusion mechanisms along phase boundaries. 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Supplementary Files naturecommsupplementary.docx Supplementary Information for Local Deformation Mapping Reveals Diffusion through Microstructures Cite Share Download PDF Status: Under Review Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7474019","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":514383068,"identity":"2b000ece-2c47-43f3-abab-7f2e53db1b3a","order_by":0,"name":"Jan Schroers","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9klEQVRIiWNgGAWjYBACxgYwdQDC+8DAIAOiJYjWwjiDgYGHoBYogGhh5iFGC3P72QOMP2ru5POz9z7+bNtmx8PPwHzwNg8+h/XkJTDzHHtmObPnuJl0blsyj2QDW7I1Xi0NOQbMjA2HDQxupLEx57Yx8xgc4DGTxqul/40B40+QlvvPmD9bttXz2B/g/4Zfy4wcAwZesC1sDNKMbYd5DBh42AhoeWNwmOfYYQPJnjQ2yZ5zx3kkDrMZW87Bo8WwP8fw4Y+awwb87MeYP/woq5bjb29+eOMNPi0N8KgH2ckGJJjxKAcBeVTuHwLKR8EoGAWjYEQCAEeqRm2PNwIAAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0001-5877-6782","institution":"Yale University","correspondingAuthor":true,"prefix":"","firstName":"Jan","middleName":"","lastName":"Schroers","suffix":""},{"id":514383069,"identity":"6e91e8d7-adb6-4952-b07b-f55c5c2e203e","order_by":1,"name":"Arindam Raj","email":"","orcid":"","institution":"Northwestern University","correspondingAuthor":false,"prefix":"","firstName":"Arindam","middleName":"","lastName":"Raj","suffix":""},{"id":514383070,"identity":"45056bb7-fb25-406f-984d-97af2040afd6","order_by":2,"name":"Michael Aderibigbe","email":"","orcid":"","institution":"Yale University","correspondingAuthor":false,"prefix":"","firstName":"Michael","middleName":"","lastName":"Aderibigbe","suffix":""},{"id":514383071,"identity":"b290676e-149e-42f1-bb92-da8bc7638371","order_by":3,"name":"Ethen Lund","email":"","orcid":"https://orcid.org/0000-0002-2834-0547","institution":"Yale University","correspondingAuthor":false,"prefix":"","firstName":"Ethen","middleName":"","lastName":"Lund","suffix":""},{"id":514383072,"identity":"dab7174b-c19f-4374-9057-f346af1afbc5","order_by":4,"name":"Yi-Xiang Yang","email":"","orcid":"","institution":"Yale University","correspondingAuthor":false,"prefix":"","firstName":"Yi-Xiang","middleName":"","lastName":"Yang","suffix":""},{"id":514383073,"identity":"f5ac5ad3-2346-4ada-bec1-f414358b672d","order_by":5,"name":"Sungwoo Sohn","email":"","orcid":"https://orcid.org/0000-0002-5626-8247","institution":"Yale University","correspondingAuthor":false,"prefix":"","firstName":"Sungwoo","middleName":"","lastName":"Sohn","suffix":""}],"badges":[],"createdAt":"2025-08-27 18:05:38","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7474019/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7474019/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":91439205,"identity":"16d66170-96ba-41ab-8250-e0fcc0dfc7cb","added_by":"auto","created_at":"2025-09-16 13:48:03","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":1783500,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eIntroduction to Local Deformation Mapping (LDM).\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e(a)\u0026nbsp; \u003c/strong\u003eLDM involves pressing a nanomold onto a metal or alloy microstructure which may contain different phases, grain orientations, grain and phase boundaries. The nanomold comprises an array of evenly spaced nanopores which induce 10\u003csup\u003e8\u003c/sup\u003e - 10\u003csup\u003e12\u003c/sup\u003e simultaneous deformation spots covering the microstructure over ~cm\u003csup\u003e2\u003c/sup\u003e dimensions. This results in the formation of nanorods over the microstructure, and their lengths vary due to the varying local mass transport rates dictated by the underlying microstructural features at each location. Further, the nanorods’ chemical compositions can also be readily determined which reveals the chemical identity of diffusing flux in a diffusion-controlled deformation.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e(b)\u0026nbsp; \u003c/strong\u003e\u003cem\u003eL\u003c/em\u003e-maps from an equiaxed, polycrystalline FCC metal microstructure (large image Ni, small images Ag), SEM images showing large spatial variations of \u003cem\u003eL\u003c/em\u003e.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e(c)\u0026nbsp;\u0026nbsp; \u003c/strong\u003eComparison of the Ni microstructure determined by EBSD and LDM reveals that the \u003cem\u003eL\u003c/em\u003e-map correlates with the microstructure and long nanorods form at locations (or in the vicinity) of grain boundaries. Further, the comparison signifies that LDM characterizes the microstructure without inducing any measurable changes in the microstructure, highlighting its non-invasive nature.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-7474019/v1/4d7b29a88b7aaaadb2198f2b.png"},{"id":91440612,"identity":"f831c07e-b46b-451f-89c9-e1e728ca79b0","added_by":"auto","created_at":"2025-09-16 14:04:03","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":373258,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eMechanism dictating mass transport rates during Local Deformation Mapping (LDM).\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e(a)\u003c/strong\u003e During LDM we measure the flux dictating the nanorod growth, \u003cem\u003eJ\u003c/em\u003e\u003csub\u003enanorod\u003c/sub\u003e to determine the flux within the microstructure, \u003cem\u003eJ\u003c/em\u003e\u003csub\u003emicrostructure\u003c/sub\u003e. The underlying driving force in microstructure and nanocavity is the applied stress gradient.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e(b)\u003c/strong\u003e Schematics of the deformation mechanisms that result in the formation of the nanorods during LDM. They can be based on atomic diffusion or dislocation slip. The different mechanisms have different \u003cu\u003e\u003cem\u003eL\u003c/em\u003e\u003c/u\u003e scaling with the nanorod diameter, \u003cem\u003ed\u003c/em\u003e \u003csup\u003e71\u003c/sup\u003e, and these scaling relations can be used to identify the mechanisms that are at play during LDM. The scaling experiments determine which equation must be used to connect \u003cem\u003eL\u003c/em\u003e with the intrinsic properties, \u003cem\u003eD\u003c/em\u003e\u003csub\u003eGB\u003c/sub\u003e, \u003cem\u003eD\u003c/em\u003e\u003csub\u003elattice.\u003c/sub\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e(c)\u003c/strong\u003e Experimental determination of the formation mechanism of the nanorods at low homologous temperature (\u003cem\u003eT\u003c/em\u003e/T\u003csub\u003eM\u003c/sub\u003e), \u003cem\u003eT\u003c/em\u003e\u003csub\u003ehom\u003c/sub\u003e = 0.34.\u0026nbsp; L(d) scaling reveals a dislocation slip based mechanism. The data shown here is for polycrystalline Ag, performed by molding the sample at \u003cem\u003eT\u003c/em\u003e = 147°C, \u003cem\u003es\u003c/em\u003e = 500 MPa, \u003cem\u003et\u003c/em\u003e = 1800 s using different nanocavity sizes.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e(d)\u003c/strong\u003e Experimental determination of the formation mechanism of the nanorods at high homologous temperature, \u003cem\u003eT\u003c/em\u003e\u003csub\u003ehom\u003c/sub\u003e = 0.6 T\u003csub\u003eM,\u003c/sub\u003e \u003cem\u003eL\u003c/em\u003e(d) scaling reveals an interface diffusion-based mechanism. The data shown here is for polycrystalline Ag, performed by molding the sample at \u003cem\u003eT\u003c/em\u003e = 456°C, \u003cem\u003es\u003c/em\u003e = 200 MPa, \u003cem\u003et\u003c/em\u003e = 600 s using different nanocavity sizes.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-7474019/v1/e097369a80bf816b8d6fc98d.png"},{"id":91440333,"identity":"b53fd0d4-14e9-417e-822d-86ccf69c2928","added_by":"auto","created_at":"2025-09-16 13:56:03","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":663857,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eQuantifying misorientation angle dependent grain boundary diffusion kinetics with LDM.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eExperimental realization using LDM to determine \u003cem\u003eD\u003c/em\u003e\u003csub\u003eGB\u003c/sub\u003e(\u003cem\u003eϴ\u003c/em\u003e\u003csub\u003eGB\u003c/sub\u003e). EBSD-map of polycrystalline Ni (a) from which a \u003cem\u003eϴ\u003c/em\u003e\u003csub\u003eGB\u003c/sub\u003e-map\u003csub\u003e \u003c/sub\u003eis determined (b). Elimination of very high (\u0026gt;57°) and very low (\u0026lt;10°) \u003cem\u003eϴ\u003c/em\u003e\u003csub\u003eGB\u003c/sub\u003e from \u003cem\u003eϴ\u003c/em\u003e\u003csub\u003eGB\u003c/sub\u003e -map (c) shows very good spatial correlation with the \u003cem\u003eL\u003c/em\u003e-map (d). The corresponding \u003cem\u003eD\u003c/em\u003e-map (only examples shown (e)) which is extracted through equation A5 from the \u003cem\u003eL\u003c/em\u003e-map is then compared with the \u003cem\u003eϴ\u003c/em\u003e\u003csub\u003eGB\u003c/sub\u003e-map. This allows connecting, for any given location of the grain boundaries in the microstructure, \u003cem\u003eD\u003c/em\u003e\u003csub\u003eGB\u003c/sub\u003e with \u003cem\u003eϴ\u003c/em\u003e\u003csub\u003eGB\u003c/sub\u003e, hence yielding \u003cem\u003eD\u003c/em\u003e\u003csub\u003eGB\u003c/sub\u003e(\u003cem\u003eϴ\u003c/em\u003e\u003csub\u003eGB\u003c/sub\u003e) (f). It is important to mention that when comparing the \u003cem\u003eL\u003c/em\u003e-map (\u003cem\u003eL\u003c/em\u003e(x,y) with the \u003cem\u003eϴ\u003c/em\u003e\u003csub\u003eGB\u0026nbsp; \u003c/sub\u003emap, the grain boundaries with \u003cem\u003eϴ\u003c/em\u003e\u003csub\u003eGB\u003c/sub\u003e 60° are not present. These grain boundaries with \u003cem\u003eϴ\u003c/em\u003e\u003csub\u003eGB\u003c/sub\u003e 60° are predominately coherent twin grain boundaries as can be noted from their shape in the EBSD map. Coherent twin grain boundaries are known to exhibit very low diffusivity \u003csup\u003e84, 85\u003c/sup\u003e, hence the low nanorods lengths in the vicinity. Details of diffusivity calculation are presented in the section 3 of the supplementary material as table S3, with figure S1 with the SEM images showing \u003cem\u003eL\u003c/em\u003e as a function of \u003cem\u003eϴ\u003c/em\u003e\u003csub\u003eGB\u003c/sub\u003e.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-7474019/v1/2851afea94b2f9577abdef9f.png"},{"id":91440613,"identity":"4a2193b7-4f37-4fbc-be15-cd5cef43bc41","added_by":"auto","created_at":"2025-09-16 14:04:03","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":817239,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eUncovering temperature- dependent deformation with LDM in polycrystalline material.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e(a)\u0026nbsp; \u003c/strong\u003eMolding polycrystalline Ag at different temperatures (0.34 - 0.9 \u003cem\u003eT\u003c/em\u003e\u003csub\u003em\u003c/sub\u003e) reveals that at low homologous temperatures, 0.34 the \u003cem\u003eL\u003c/em\u003e-map appears homogenous with short nanorods of very similar lengths. No discernible grain structure can be seen. For, \u003cem\u003eT\u003c/em\u003e\u003csub\u003ehom\u003c/sub\u003e \u0026gt;~ 0.5, significant difference in length between rods over grain and grain boundaries are observed and the rods along the grain boundaries look much longer. At higher temperatures \u0026gt; 0.7 \u003cem\u003eT\u003c/em\u003e\u003csub\u003em\u003c/sub\u003e, the difference in the lengths over lattice and grain boundaries narrows and the length of the rods becomes comparable. All scale bars indicate 10 μm.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e(b)\u0026nbsp; \u003c/strong\u003eNanorod length as a function of \u003cem\u003eT\u003c/em\u003e\u003csub\u003ehom\u003c/sub\u003e for grain and grain boundary regions. Superimposed is the summary of the deformation behavior. Dislocation-based deformation dominates at low \u003cem\u003eT\u003c/em\u003e\u003csub\u003ehom\u003c/sub\u003e, with GB diffusion taking over at intermediate \u003cem\u003eT\u003c/em\u003e range result in longest nanorods over the GBs. At high \u003cem\u003eT\u003c/em\u003e\u003csub\u003ehom\u003c/sub\u003e, lattice and GB diffusivity flux become comparable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e(c)\u0026nbsp;\u0026nbsp; \u003c/strong\u003eThe rate of change in lengths of nanorods at high \u003cem\u003eT\u003c/em\u003e\u003csub\u003ehom\u003c/sub\u003e becomes higher for nanorods over the grains than nanorods over grain boundaries, revealing that the activation energy for diffusive processes resulting in the growth of the nanorods over the grains is higher.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e(d)\u0026nbsp; \u003c/strong\u003eDiffusivities extracted from LDM data present in (a). For \u003cem\u003eT\u003c/em\u003e\u003csub\u003ehom \u003c/sub\u003e\u0026gt; 0.5, self-diffusion activation energy from the slope of ln(\u003cem\u003eD\u003c/em\u003e) vs 1/\u003cem\u003eT\u003c/em\u003e plots, for grain boundaries are 56 kJ/mol, which compares reasonable well with the previously published values for Ag in higher temperature ranges (\u0026gt; 600 K) for the GB in the range of 59-78 kJ/mol \u003csup\u003e72\u003c/sup\u003e (details of diffusivity calculation are presented in the table S2 of the section 3 of the supplementary material).\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-7474019/v1/bc471cef3fc992bc4d89022f.png"},{"id":91440336,"identity":"6609c55d-2c36-44b0-be16-da42da1b1769","added_by":"auto","created_at":"2025-09-16 13:56:03","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":1332427,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eInterface boundaries and compositional-different grain boundaries.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e(a) \u003c/strong\u003eSEM images showing Au\u003csub\u003e97\u003c/sub\u003eSi\u003csub\u003e3\u003c/sub\u003e alloy microstructure featuring large-grained Au with Au-Si eutectic phase between them. After LDM at 250°C, the grains featuring essentially pure Au phase grow very short nanorods with maximum length of ~0.5 μm, while the interfaces within the eutectic region (Si rich phases in EDS) result in much longer nanorods of ~5 micron length, demonstrating faster diffusion due to the presence of Au and Si interphases in the eutectic region.\u003c/p\u003e\n\u003cp\u003e(b) Ni\u003csub\u003e95\u003c/sub\u003eBi\u003csub\u003e5\u003c/sub\u003e alloy, as an example of compositional different grain boundaries, which exhibits high solute segregation tendency. The L-map reveals significantly longer nanorods over the Bi enriched grain boundaries than over the Ni grains. The Bi segregation to the grain boundary, measured in the nanorods, results in a composition of the grain boundaries to ~Ni\u003csub\u003e10\u003c/sub\u003eBi\u003csub\u003e90\u003c/sub\u003e with a corresponding liquidus temperature of 440°C. This suggests, during deformation at 500°C, premelting of the grain boundaries, despite the single-phase Ni microstructure and nominal composition and liquidus temperature of ~1360°C of the alloy.\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-7474019/v1/c855173924e8ae3c4b1a4789.png"},{"id":91441822,"identity":"995093ce-2d88-429e-a1e1-fc6975334e65","added_by":"auto","created_at":"2025-09-16 14:12:07","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5707716,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7474019/v1/e9a98d5d-96f9-41ba-8e61-336aed043b6d.pdf"},{"id":91439208,"identity":"79c03b6e-9bf8-46c1-a3a4-565275f3018f","added_by":"auto","created_at":"2025-09-16 13:48:03","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":1227073,"visible":true,"origin":"","legend":"Supplementary Information for Local Deformation Mapping Reveals Diffusion through Microstructures","description":"","filename":"naturecommsupplementary.docx","url":"https://assets-eu.researchsquare.com/files/rs-7474019/v1/264c53eb02d74e9f73482ac1.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Local Deformation Mapping Reveals Diffusion through Microstructures","fulltext":[{"header":"Introduction and Motivation: Structure-property-processing relations and existing characterization methods","content":"\u003cp\u003eGenerally, alloys are multiphase and polycrystalline, exhibiting complex microstructures. Their plastic deformation is among the richest problems in materials science. As a result, their structure-property-processing relations have been the center of metallurgical research \u003csup\u003e1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11\u003c/sup\u003e. Metallic microstructures may include grains and grain boundaries of different structures, chemistry, and orientations, often combined with defects, and local gradients in stress and dislocation density. These features dictate the local variations in a microstructure\u0026rsquo;s elastic, plastic, thermodynamic, and kinetic properties \u003csup\u003e12\u003c/sup\u003e. To study these relations, a wide range of characterization techniques have been developed to probe materials with different spatial resolutions. These measurement techniques include TEM for locally isolated features \u003csup\u003e13, 14, 15, 16, 17\u003c/sup\u003e, atom probe tomography (APT) and 3D reconstructions from SEM for nanoscale volumes \u003csup\u003e18, 19, 20, 21, 22\u003c/sup\u003e, and EBSD for grain distributions and strain \u003csup\u003e23, 24, 25, 26, 27, 28\u003c/sup\u003e. Additionally, further detailed analyses of microstructures and strain responses are possible through tomography (X-ray, MRI) \u003csup\u003e29, 30, 31, 32, 33\u003c/sup\u003e, nanoindentation \u003csup\u003e34, 35\u003c/sup\u003e, and digital image correlation (DIC) \u003csup\u003e36, 37, 38\u003c/sup\u003e, among others. These techniques probe different length scales, revealing phenomenological details. In large part due to these technical advancements, various aspects of the structure-property-processing relations are well studied,\u0026nbsp;\u003csup\u003e1, 6, 7, 39, 40, 41, 42, 43, 44\u003c/sup\u003e and quantitative theories have been developed\u0026nbsp;\u003csup\u003e12, 45, 46, 47, 48, 49, 50, 51\u003c/sup\u003e. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003eDespite the many strengths of such state-of-the-art characterization techniques, a key gap remains; highly localized and sensitive deformation measurements over large areas and volumes. Thus, even though considerable progress has been made, a general quantitative understanding of this relationship is still lacking due to the fundamentally multiscale and complex nature of the plastic response of alloys\u0026rsquo; microstructures. Model descriptions for microstructure-property relations require a high spatial resolution mapping of local microstructure deformation behavior and properties, considering the multi-scale nature of a microstructure response to stress \u003csup\u003e6, 45, 49, 51, 52, 53, 54, 55\u003c/sup\u003e. These models may require measurements over large areas, long times, and high temperatures, particularly when interactions between multiple features are present. Especially for high temperature fatigue or creep studies, sequential measurements have limitations at long time scales and high temperatures. Since the mechanical response of a microstructure depends on the interplay of its microstructural features, a piecemeal approach is generally not appropriate for studying the vast set of possible microstructural features.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eBroadly speaking, the specifics of plastic deformation in metals and alloys depend largely on their mass transport mechanisms and the related rates, the applied forces, and their boundary conditions. The transport rates, which determine deformation, can vary dramatically across the microstructure of a single material. For example, lattice diffusivity and grain boundary diffusivity values may differ by several orders of magnitude in metals and alloys owing to much lower activation energy along these boundaries \u003csup\u003e10, 56, 57, 58, 59\u003c/sup\u003e. \u0026nbsp;Diffusion-based mechanisms drive a variety of microstructural phenomena in alloys that occur during their preparation and service. These includes phase transformations \u003csup\u003e60, 61\u003c/sup\u003e, segregation \u003csup\u003e62\u003c/sup\u003e, alloy homogenization \u003csup\u003e63\u003c/sup\u003e, and performance related phenomenon such as creep and fatigue \u003csup\u003e64, 65, 66\u003c/sup\u003e. Therefore, engineering alloy microstructures with desired properties hinges on precise understanding of mass transport rates within microstructures.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTo address this, we propose a new technique to study plastic deformation characteristics of bulk scale microstructures with high resolution (Fig. 1). Within this method, a microstructure is locally deformed at the nanoscale in a massively parallel fashion. We connect these local deformations to the underlying mass transport processes across the microstructure, categorized broadly under diffusion and dislocation-based plasticity mechanisms. Here, we focus primarily on diffusion-based measurements (Fig. 1b,c), though dislocation related measurements are also made. The salient features of this technique are i.) the massively parallel, high-resolution, and chemically sensitive mapping of the mass transport rates as a function of the various microstructural features, and ii.) the quantitative determination of these local mass transport rates such as diffusivity with the same resolution.\u003c/p\u003e\n\u003cp\u003eExperimentally, this is accomplished via the deformation of a bulk scale microstructure at more than one billion locations simultaneously. These locations are regularly spaced over large areas of ~cm\u003csup\u003e2\u003c/sup\u003e, enabling spatial resolution down to ~10 nm\u003csup\u003e2\u0026nbsp;\u003c/sup\u003e(Fig. 1). Each deformation captures the plastic deformation response of the underlying component/feature in the microstructure. Thus, the collection of these deformation spots results in a local deformation map, created in a single step (Fig. 1b,c). We then relate the varying rates of deformation in the different regions of the microstructure to the variation in the microstructural features (Fig. 1c). Thus, we directly measure the local variations in the mass transport mechanism dictating the deformation as a function of the features, e.g., grain boundaries with different misorientation angles, which are present in the different regions of a polycrystalline microstructure. This enables, for example, identification of the microstructural features which exhibit particularly high or low mass transport rates during plastic deformation. In this way, one experiment can offer significant insight into property-structure correlations.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eIntroduction to Local Deformation Mapping (LDM)\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eLDM is experimentally based on Thermomechanical Nanomolding (TMNM), a recently developed technique for fabricating arrays of nanorods for a range of elements and alloys \u003csup\u003e67, 68, 69, 70\u003c/sup\u003e. This technique is realized by pressing a feedstock material against a porous nanomold, creating local stress gradients that force the material into the mold (Fig. 1a). The control parameters of the process are the applied compressive stress, \u003cem\u003e\u0026sigma;\u003c/em\u003e, temperature, \u003cem\u003eT\u003c/em\u003e, and molding time, \u003cem\u003et\u003c/em\u003e. Appropriate application of these parameters results in an array of nanorods which can be released from the mold through a selective etching process. We demonstrate here that TMNM is modified into a\u0026nbsp;characterization method to map material transport rates within microstructures.\u0026nbsp;The nanomolds used for deforming the microstructure during LDM have pores which range in diameter from 2.5 nm to 150 nm and spaced by the same distance. For a typical ~cm\u003csup\u003e2\u003c/sup\u003e nano mold array, this results in up to ~10\u003csup\u003e12\u003c/sup\u003e distinct nanorods (data points) in one LDM experiment. So, LDM is capable of mapping plastic responses with high spatial resolution, high throughput, over a macroscopic sampling area, characterizing microstructure deformation over a temperature range practically spanning from cryogenic temperatures to about 1000\u0026deg;C and can be applied to a wide range of materials.\u003c/p\u003e\n\u003cp\u003eIn this work, we introduce LDM and also present a quantitative scheme to measure the local deformation rates, focusing on diffusion related processes, within a microstructure by analyzing nanorod growth. Specifically, we claim and demonstrate that we can deduce quantitative information about the diffusion rates within a microstructure using the nanorods array grown over it. The various features of microstructure influence this transport rate, and this reflects as variations in the length and composition (for multicomponent microstructures) of the nanorods. Thus, the crux of the LDM technique lies in revealing the connection between the nanorod length variation map, termed the \u003cem\u003eL\u003c/em\u003e-map, and the mass transport behaviors of the different microstructural features. To accomplish this, we develop analytical models to transform the \u003cem\u003eL\u003c/em\u003e-maps into a quantitative mass transport rate (diffusivity) map.\u0026nbsp;\u003c/p\u003e"},{"header":"Quantification of materials properties using LDM","content":"\u003cp\u003eBriefly, these analytical models describe the transport of the material due to the stress gradient imposed during LDM and connect the measured \u003cem\u003eL\u003c/em\u003e of the nanorods with the local diffusivity values through the microstructure (Fig. 2a). The material transfer during LDM occurs in two steps. First, under the imposed stress gradient material flux in the microstructure (termed as the \u0026ldquo;microstructure flux,\u0026rdquo; \u003cem\u003eJ\u003c/em\u003e\u003csub\u003emicrostructure\u003c/sub\u003e moves towards the mold\u0026rsquo;s nanopores. Subsequently, this material enters the nanopores to form rods (termed as the \u0026ldquo;nanorods\u0026rsquo; flux,\u0026rdquo; \u003cem\u003eJ\u003c/em\u003e\u003csub\u003enanorod\u003c/sub\u003e) (Fig. 2). This outgoing flux, \u003cem\u003eJ\u003c/em\u003e\u003csub\u003enanorod\u003c/sub\u003e, results in the formation of the nanorods that form the \u003cem\u003eL-\u003c/em\u003emap, which is measured and analyzed. We have developed models assuming dislocation slip or diffusion as the underlying mechanism dictating the outgoing flux, \u003cem\u003eJ\u003c/em\u003e\u003csub\u003enanorod\u003c/sub\u003e (Fig. 2b and supplementary section 1). We identify through scaling of \u003cem\u003eL\u003c/em\u003e(\u003cem\u003ed\u003c/em\u003e) (Fig. 2b) which mechanism is at play (Fig. 2c) during LDM. For elevated temperatures (T \u0026nbsp;0.5\u003cem\u003eT\u003c/em\u003e\u003csub\u003eM\u003c/sub\u003e), interface diffusion-controlled equation for \u003cem\u003eL\u003c/em\u003e is found to fit the experimental data.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThen, under the assumption that \u003cem\u003eJ\u003c/em\u003e\u003csub\u003emicrostructure\u003c/sub\u003e is the rate limiting step, we can determine from the measured \u003cem\u003eL\u003c/em\u003e values, the (local) diffusivity of the microstructure. We develop an analytical model capturing this process and verify it under the assumption that\u003cem\u003e\u0026nbsp;J\u003c/em\u003e\u003csub\u003emicrostructure\u003c/sub\u003e is the rate limiting step by using Ag samples (presented in Figs. 1 and 2). \u0026nbsp;We calculate \u003cem\u003eD\u003c/em\u003e\u003csub\u003eGB\u003c/sub\u003e (Ag)\u003csub\u003e\u0026nbsp;\u003c/sub\u003e= 5\u0026times;10\u003csup\u003e-7\u0026nbsp;\u003c/sup\u003ecm\u003csup\u003e2\u003c/sup\u003e/s for T = 473\u0026deg;C through LDM using this analysis, which is comparable to literature values of 3\u0026times;10\u003csup\u003e-7\u0026nbsp;\u003c/sup\u003ecm\u003csup\u003e2\u003c/sup\u003e/s for Ag at this temperature \u003csup\u003e72\u003c/sup\u003e. Thereby we confirm that LDM can be used to determine local \u003cem\u003eD\u003c/em\u003e values in a one-shot experiment from the measured \u003cem\u003eL\u003c/em\u003e-map. This analytical model developed hereby (supplementary section 2) correlates the measured length through LDM with the intrinsic self-diffusivity in the microstructure, \u003cem\u003eD\u003c/em\u003e\u003csub\u003eGB\u003c/sub\u003e according to:\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cimg 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\" width=\"747\" height=\"279\"\u003e\u003c/p\u003e\n\u003cp\u003ewhere \u003cem\u003eL\u003c/em\u003e: length of the nanorods, \u003cem\u003e\u0026sigma;\u0026nbsp;\u003c/em\u003e: applied stress, \u003cem\u003e\u0026Omega;\u003c/em\u003e: atomic volume of the diffusing entity, t : molding time, \u0026nbsp;: diffusivity on the mold-feedstock interface, d : mold diameter\u0026cedil; \u0026nbsp;: mold-feedstock interface thickness.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFrom (A1, 2) it is clear that a difference in the intrinsic kinetics at the different regions of the microstrcuture leads to an \u003cem\u003eL\u003c/em\u003e-map with varying lengths of nanorods. Indeed, we observe that nanorods are longer along the grain boundaries in Fig. 1, indicating the faster diffusion rates in GB regions (\u003cem\u003eD\u003c/em\u003e\u003csub\u003eGB\u003c/sub\u003e \u0026gt; \u003cem\u003eD\u003c/em\u003e\u003csub\u003elattice\u003c/sub\u003e).\u003c/p\u003e\n\u003cp\u003eFurther, to analyze diffusive flux in alloys, the nanorods can also be analyzed for their composition to determine the composition of the material flux moving through the microstructure. This unique measurement is possible because LDM spatially separates the flux from the underlying microstructure, making sensitive chemical spectroscopy possible. Thereby, the \u003cem\u003eL\u003c/em\u003e-map can be correlated with elemental distribution of the material flux over different regions of the microstructure. Consequently, the experimentally determined \u003cem\u003eL-\u003c/em\u003emap encodes the microstructure specific transport rate and chemical variation with high spatial resolution, and we demonstrate this for grain boundaries, interphase boundaries, and segregated phases.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eWe demonstrate the potential and capability of LDM by showing:\u0026nbsp; \u0026nbsp;\u003c/p\u003e\n\u003col class=\"decimal_type\"\u003e\n \u003cli\u003eLDM enables locally precise mapping of transport properties: \u0026nbsp; demonstrated through diffusivities mapping in grains and grain boundaries (GBs), revealing the position of GBs and the local diffusivity value variations (Fig. 1)\u003c/li\u003e\n \u003cli\u003eLDM reveals property-microstructural feature correlations in a high-throughput fashion: demonstrated through one step mapping of the dependence of grain boundary self-diffusivity, \u003cem\u003eD\u003c/em\u003e\u003csub\u003eGB\u003c/sub\u003e on the misorientation angle of the grain boundaries in an FCC polycrystalline microstructure (Fig. 3)\u003c/li\u003e\n \u003cli\u003eLDM enables mass transport measurements all the way until melting: demonstrated through the mapping of the temperature dependent mass transport rates for a wide range of homologous temperatures (Fig. 4).\u003c/li\u003e\n \u003cli\u003eLDM enables chemically sensitive mapping by the spatial separation of the diffusion flux into the nanomold: demonstrated through the mapping of the interphase boundary diffusivities in multiphase microstructures and revealing that this flux can have remarkably different behavior and composition than expected from average behavior of the phases involved (Fig. 5).\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Misorientation angle dependent diffusivity","content":"\u003cp\u003eFor most polycrystalline microstructures at lower homologous temperatures, diffusion rates are much higher in grain boundaries compared to the lattice \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e56\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e57\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e58\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e73\u003c/span\u003e\u003c/sup\u003e. Thus, material transport properties can vary significantly over small length scales even within a single-phase microstructure, and the GBs with different misorientation angles may display very different kinetic properties \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e74\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e75\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e76\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e77\u003c/span\u003e\u003c/sup\u003e. While approaches such as bicrystal studies can provide very detailed and precise measurements of well-defined grain boundaries, they are not particularly suited for covering a wide range of GBs due to the cumbersome preparation and set up required, which have limited the use of this approach to a small number \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e78\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e79\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e80\u003c/span\u003e\u003c/sup\u003e. LDM, on the other hand can mimic simultaneously a large series of such bicrystal studies when performed on an equiaxed sample (Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e). Different grains, their orientations, and the corresponding GBs characterized by different degrees of misorientation can be \u0026ldquo;imaged\u0026rdquo; through LDM, revealing the location of the grain boundaries and the kinetics of the diffusion flux through these GBs.\u003c/p\u003e\n\u003cp\u003eWithin the new workflow that LDM provides, a static map of grain boundary distribution is obtained through EBSD. Then, an \u003cem\u003eL\u003c/em\u003e-map, \u003cem\u003eL\u003c/em\u003e(x,y), is generated in the same area using LDM. By spatially correlating these two maps, we can directly plot the local diffusivity as a function of misorientation angle, \u003cem\u003eD\u003c/em\u003e\u003csub\u003eGB\u003c/sub\u003e(Q\u003csub\u003eGB\u003c/sub\u003e), for hundreds to thousands of unique grain boundaries in a single experiment. We demonstrate this capacity of LDM with an equiaxed, polycrystalline Ni sample with GBs spanning a typical range of misorientation angles, Q\u003csub\u003eGB\u003c/sub\u003e, where their relative kinetics is revealed in a single experiment (Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e). An \u003cem\u003eL\u003c/em\u003e-map is created by molding the Ni sample at (\u003cem\u003eT\u003c/em\u003e\u0026thinsp;=\u0026thinsp;720\u0026deg;C, \u003cem\u003e\u0026sigma;\u003c/em\u003e\u0026thinsp;=\u0026thinsp;200 MPa, \u003cem\u003et\u003c/em\u003e\u0026thinsp;=\u0026thinsp;7200 s) (Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ea). Comparison of the \u003cem\u003eL\u003c/em\u003e-map with the EBSD map reveals markedly longer nanorods (~\u0026thinsp;30 \u0026micro;m) along the grain boundaries of the polycrystalline Ag than over the grains (~\u0026thinsp;1 \u0026micro;m), confirming the general trend of \u003cem\u003eD\u003c/em\u003e\u003csub\u003eGB\u003c/sub\u003e\u0026thinsp;\u0026gt;\u0026thinsp;\u0026gt;\u0026thinsp;\u003cem\u003eD\u003c/em\u003e\u003csub\u003elattice\u003c/sub\u003e. Further variations within the long nanorods grown on top of the different types of grain boundaries are present. Such variations within the long nanorods growing over the grain boundaries are then correlated with the corresponding Q\u003csub\u003eGB\u003c/sub\u003e which reveals in a one-shot measurement the absolute values of \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003eGB\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(\u003c/em\u003eϴ\u003csub\u003eGB\u003c/sub\u003e). Such LDM determined \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003eGB\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(\u003c/em\u003eϴ\u003csub\u003eGB\u003c/sub\u003e) is in qualitative and quantitative agreement with literature values \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e81\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e82\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e83\u003c/span\u003e\u003c/sup\u003e, suggesting that such an application of LDM can expand experimental grain boundary research beyond the few carefully controlled situations to include most complicated and general situations.\u003c/p\u003e"},{"header":"Characterizing temperature dependent deformation with LDM","content":"\u003cp\u003eLDM can further be used to determine the temperature dependent deformation behavior of microstructures, from dislocation mediated at low temperatures to grain boundary and lattice diffusion at high temperatures. To demonstrate this, experiments are carried out for polycrystalline Ag at various temperatures in the range of \u003cem\u003eT\u003c/em\u003e\u003csub\u003ehom\u003c/sub\u003e = 0.34\u0026ndash;0.9. For \u003cem\u003eT\u003c/em\u003e\u003csub\u003ehom\u003c/sub\u003e = 0.34, nanorod growth is very slow, and there is no measurable contrast between grains and grain boundaries (Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ea), suggesting that deformation is based on dislocation slip. With increasing homologous temperature, \u0026gt;~0.5, nanorods with appreciable aspect ratios can be observed after minutes of LDM, and these nanorods on the grain boundaries are significantly longer than nanorods growing on the grains, suggesting diffusion-controlled deformation. The length ratio is ~\u0026thinsp;10\u0026ndash;15 for \u003cem\u003eT\u003c/em\u003e\u003csub\u003ehom\u003c/sub\u003e ~ 0.5, which translates into \u003cem\u003eD\u003c/em\u003e\u003csub\u003eGB\u003c/sub\u003e/\u003cem\u003eD\u003c/em\u003e\u003csub\u003elattice\u003c/sub\u003e ~ 10000 (from equations A3-A6) (see table \u003cspan class=\"InternalRef\"\u003eS1\u003c/span\u003e in supplementary section 3). With increasing \u003cem\u003eT\u003c/em\u003e\u003csub\u003ehom\u003c/sub\u003e, increase in \u003cem\u003eL\u003c/em\u003e is observed along grain boundary and along the grains. However, this increase occurs with different rates, d\u003cem\u003eL\u003c/em\u003e/d\u003cem\u003eT\u003c/em\u003e\u003csub\u003ehom\u003c/sub\u003e (Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003eb), and for \u003cem\u003eT\u003c/em\u003e\u003csub\u003ehom\u003c/sub\u003e ~ 0.9, \u003cem\u003eD\u003c/em\u003e\u003csub\u003eGB\u003c/sub\u003e/\u003cem\u003eD\u003c/em\u003e\u003csub\u003elattice\u003c/sub\u003e decreases to ~\u0026thinsp;100. The rate of nanorod growth over the grains is higher than that for nanorods growing over grain boundaries with increasing temperature. This reflects the fact that the slopes for self-diffusivity curves scale with temperature for atoms in the GBs are low (low activation energy) and high for atoms diffusing through the lattice \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e73\u003c/span\u003e\u003c/sup\u003e. Thus, they converge increasingly when heated to very high homologous temperatures. This demonstrates that via LDM, the temperature dependent deformation mechanism can be revealed which changes from dislocation-slip base, present to ~\u0026thinsp;0.4 \u003cem\u003eT\u003c/em\u003e\u003csub\u003ehom\u003c/sub\u003e, to grain boundary diffusion dominated deformation up to ~\u0026thinsp;0.75 \u003cem\u003eT\u003c/em\u003e\u003csub\u003ehom\u003c/sub\u003e, to grain boundary and lattice diffusion deformation above ~\u0026thinsp;0.8 \u003cem\u003eT\u003c/em\u003e\u003csub\u003ehom\u003c/sub\u003e. Further the diffusivity values can be determined quantitatively as a function of temperature (Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ec).\u003c/p\u003e"},{"header":"Mapping the effect of interphase boundaries and different-in-composition grain boundaries on local diffusivity","content":"\u003cp\u003eAfter demonstrating LDM for single phases and polycrystalline microstructures, we turn to the most general alloys which are more complex as they may comprise of multiple elements, multiple phases, and corresponding interphase boundaries. Here, we focus on interphase boundaries and the diffusivity within these interfaces. Due to the large number of different interfaces that are present in the compositional space of alloys, only a minute fraction has been characterized in terms of their diffusion characteristics, despite their effect on controlling a variety of alloy related phenomenon and properties including creep and fatigue \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e64\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e66\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e86\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e87\u003c/span\u003e\u003c/sup\u003e, phase transformations \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e60\u003c/span\u003e\u003c/sup\u003e, segregation \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e88\u003c/span\u003e\u003c/sup\u003e, alloy homogenization \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e, self-healing \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e89\u003c/span\u003e\u003c/sup\u003e, nucleation of new phases \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e90\u003c/span\u003e\u003c/sup\u003e, and complexion and complexion transitions \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e75\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e91\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e92\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eDrawing on our previous findings \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e93\u003c/span\u003e\u003c/sup\u003e, we focus on eutectic alloys particularly those which exhibit a deep depressed liquidus temperature relative to the melting temperatures of its constituents and a large negative heat of mixing between its constituents. For such alloys, we observe long nanorods, indicating a fast diffusion pathway along the interphase boundary of the eutectic counterparts (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ea) \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e93\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e94\u003c/span\u003e\u003c/sup\u003e. Specifically, we use pure Au and Au\u003csub\u003e97\u003c/sub\u003eSi\u003csub\u003e3\u003c/sub\u003e eutectic system. For identical LDM molding conditions, we observe over 10 times longer nanorods in the Au\u003csub\u003e97\u003c/sub\u003eSi\u003csub\u003e3\u003c/sub\u003e system than in pure Au (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ea). The small amount of silicon added to gold has a dramatic effect on the length of the nanorods at some location in the microstructure. We reveal that these locations are the Au-Si interfaces in the Au-Si eutectic region which itself is trapped between almost pure Au grains (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ea). This indicates, which has not been observed with today\u0026rsquo;s state of the art diffusion measurements, that eutectic interfaces enable fast diffusion pathways, and it is the presence of eutectic interphase boundaries and not the overall composition that determines the flux through such microstructures. These eutectic interphases have the lowest thermal stability within one alloy system which is reflected in the lowest melting point within the heterogeneous microstructure and hence, they experience the highest homologous temperature at a given absolute temperature. The LDM results reveal that this local low thermal stability is strongly correlated to fast rates of diffusive flux.\u003c/p\u003e\n\u003cp\u003eAs another example to demonstrate the capability of the LDM method to capture local deformation, we select an alloy with high grain boundary segregation which results in significant chemical variation between grain and grain boundaries \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e75\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e95\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e96\u003c/span\u003e\u003c/sup\u003e. It is widely accepted that, particularly for elements that exhibit large grain boundary segregation tendencies, very small quantities can have significant impact on the microstructure, stability, and properties of alloys \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e97\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e98\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e99\u003c/span\u003e\u003c/sup\u003e. To understand, what specifically causes such strong impact, we select Ni\u003csub\u003e95\u003c/sub\u003eBi\u003csub\u003e5\u003c/sub\u003e as an alloy with low solute concentration, where the grains are primarily solid solution (Ni), and the grain boundaries are enriched in Bi, due to high segregation enthalpy of Bi in Ni of -111.5 kJ/mol (109). The \u003cem\u003eL\u003c/em\u003e-map captured at 500\u0026deg;C reveals very long Bi rich nanorods along the Ni grain boundaries (Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003eb), revealing a grain boundary pre-melting behavior (melting temperature of Bi is 271\u0026deg;C).\u003c/p\u003e"},{"header":"Conclusions","content":"\u003cp\u003eWe present local deformation mapping (LDM) as a one-shot method to locally characterize plastic responses of a microstructure with a spatial resolution of down to ~\u0026thinsp;10 nm\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e, in a parallel fashion over ~\u0026thinsp;cm\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e. The physical separation of the deforming material from the microstructure allows for sensitive determination of the flux\u0026rsquo;s quantity and chemistry. Such chemically sensitive, and spatially mapped measurements are prohibitively cumbersome to determine for a general alloy using state-of-the-art methods and hence have been generally lacking. When carried out at high homologous temperature\u0026thinsp;\u0026gt;\u0026thinsp;0.5\u003cem\u003eT\u003c/em\u003e\u003csub\u003em\u003c/sub\u003e, LDM provides the local diffusivity values within the microstructure. We experimentally demonstrate the potential of LDM, proving the capability to perform high throughput diffusion mapping across various microstructural features. We reveal the misorientation angle dependence of grain boundary diffusivity in a one-shot measurement, the temperature dependence deformation of general microstructures, and novel diffusion mechanisms along phase boundaries. Overall, we demonstrate LDM as a one-shot and radically more efficient method, to study spatially resolved deformation of alloys, suggesting an expansion from today\u0026rsquo;s diffusion science limit of relatively simple model systems to experimental measurements of spatial and chemically highly resolved diffusion in even the most complex alloys.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eFigueiredo RB, Kawasaki M, Langdon TG. Seventy years of Hall-Petch, ninety years of superplasticity and a generalized approach to the effect of grain size on flow stress. \u003cem\u003eProg Mater Sci\u003c/em\u003e \u003cstrong\u003e137\u003c/strong\u003e, (2023).\u003c/li\u003e\n\u003cli\u003eMiracle DB, Senkov ON. A critical review of high entropy alloys and related concepts. \u003cem\u003eActa Mater\u003c/em\u003e \u003cstrong\u003e122\u003c/strong\u003e, 448-511 (2017).\u003c/li\u003e\n\u003cli\u003eHerzog D, Seyda V, Wycisk E, Emmelmann C. 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Effects of Trace-Elements on Mechanical-Properties of Superalloys. \u003cem\u003eMet Technol\u003c/em\u003e \u003cstrong\u003e11\u003c/strong\u003e, 454-464 (1984).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-7474019/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7474019/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eUnderstanding and quantifying microstructure–property relationships, particularly those where plastic deformation is based on atomic diffusion, remains a grand challenge in metallurgy. While existing techniques often tradeoff between spatial resolution, sampling area, and throughput, a method capable of bridging various length scales remains elusive. To address this need, we propose local deformation mapping (LDM) as a high-resolution, high- throughput characterization technique. LDM determines what diffuses locally through microstructures, creating a direct deformation map imprinted on top of the microstructure. These maps can exhibit ~10 nm² resolution across macroscopic areas (~cm²), generating up to ~10¹² data points in a single experiment. This technique maps deformation-related properties such as diffusivity as a function of microstructural features, including grains, grain boundaries, and interphase boundaries. We demonstrate a one-step determination of grain boundary diffusivity as a function of misorientation angle, temperature-dependent deformation behavior, and previously unknown fast diffusion within interphase boundaries in eutectic-containing alloys. Experimentally, LDM is realized by pressing a nanomold onto a microstructure, inducing local stress gradients that drive material from the microstructure into mold pores, forming nanorods. This spatial separation of the plastic response from the microstructure enables sensitive chemical composition mapping of this flux in multicomponent microstructures, previously unachieved with the state of the art. Nanorods’ length and composition form the deformation response maps, converted into diffusivity maps via the hereby developed analytical model. Altogether, LDM is a powerful platform to advance the quantitative understanding of structure–property relationships for a wide range of materials across a broad temperature range.\u003c/p\u003e","manuscriptTitle":"Local Deformation Mapping Reveals Diffusion through Microstructures","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-09-16 13:47:58","doi":"10.21203/rs.3.rs-7474019/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-communications","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"NCOMMS","sideBox":"Learn more about [Nature Communications](http://www.nature.com/ncomms/)","snPcode":"","submissionUrl":"https://mts-ncomms.nature.com/","title":"Nature Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Communications","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"d6073400-a5cc-44ba-ad2e-64babe3221e4","owner":[],"postedDate":"September 16th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":54651615,"name":"Physical sciences/Materials science/Structural materials/Metals and alloys"},{"id":54651616,"name":"Physical sciences/Materials science/Techniques and instrumentation/Characterization and analytical techniques"}],"tags":[],"updatedAt":"2026-04-27T19:50:10+00:00","versionOfRecord":[],"versionCreatedAt":"2025-09-16 13:47:58","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7474019","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7474019","identity":"rs-7474019","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}