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Using electrochemical impedance spectroscopy, we have devised a method of sensing the microscopic surface conditions on the surface of niobium as it is undergoing an electrochemical polishing (EP) treatment. The method uses electrochemical impedance spectroscopy (EIS) to gather information on the surface state of the electrode without disrupting the polishing reaction. The EIS data is analyzed using a so-called distribution of relaxation times (DRT) method. Using DRT, the EIS data can be deconvolved into discrete relaxation time peaks without any a priori knowledge of the electrode dynamics. By analyzing the relaxation time peaks, we are able to distinguish two distinct modes of the EP reaction. As the polishing voltage is increased, the electrode transitions from the low voltage EP mode, characterized by a single relaxation time peaks, to the high voltage EP mode, characterized by two relaxation time peaks. We theorize that this second peak is caused by the formation of an oxide layer on the electrode. We also find that this oxide induced peak transitions from to a negative relaxation time, which is indicative of a blocking electrode process. By analyzing EPed samples, we show that samples polished in the low voltage mode have significantly higher surface roughness due to grain etching and faceting. We find that the surface roughness of the samples only improves when the oxide film peak is present and in the negative relaxation time region. This shows that EIS combined with DRT analysis can be used to predict etching on EPed Nb. This method can also be performed before or during the EP, which could allow for adjustment of polishing parameters to guarantee a smooth cavity surface finish.

TThe effects of alloying elements on diffusion pathways and migration energies of interstitial carbon in austenite (f.c.c.) and ferrite (b.c.c.) are studied using density functional theory first-principles calculations. The binding energies between carbon and alloying elements are determined through 6th nearest-neighbor (NN) distances. The elements studied are Ni, Mo, V, Cr, Mn, Cu, Al, Ti, and Si, relevant to most high-strength steels. Nickel, Mn, Al, and Si have repulsive binding energies; Mo, V, Cr, Cu, and Ti have attractive binding energies in austenite and ferrite. Alloying elements at 1st NN sites of a C atom in an octahedral site introduce asymmetry into the minimum energy diffusion pathway, causing up to about 1 eV changes in saddle-point energies. This pathway goes from one octahedral site to another via intermediate energy states, differing for austenite and ferrite. We find that the elements with attractive binding energies increase the energy barrier for C migration resulting in decelerated carbon diffusion, while the elements with repulsive binding energies decrease the energy barrier for C migration leading to accelerated C diffusion. The magnitude of changes in C migration energies is proportional to the binding energies between C and alloying elements. Among the three austenite stabilizers, Ni and Mn are C diffusion accelerators, while Cu decelerates C diffusion in austenite. Among the four ferrite stabilizers, Si is a C diffusion accelerator, while V and Ti serve as C diffusion decelerators in ferrite. Aluminum has no significant effect on C's diffusivity, while Mo and Cr decelerate C diffusion.

Despite having advantageous superconducting properties, Nb3Sn superconducting radiofrequency (SRF) cavities still have practical challenges compared to Nb SRF cavities due to the brittle nature of Nb3Sn. Performance degradation can occur when a Nb3Sn SRF cavity experiences mechanical stresses such as during handling and tuning of the cavity. In this study, we present a potential treatment for SRF cavities that have experienced stress induced performance degradation that involves a recoating procedure. The degraded cavity is coated with a small amount of Sn using a single step vapor-diffusion methodology. Using this approach we can recover a significant portion of the lost performance of a Nb3Sn SRF cavity.

We report on atomic-scale analyses of nucleation and growth of Zr oxide precipitates and the microstructural evolution of internally oxidized Nb3Sn wires for high-field superconducting magnet applications, utilizing atom probe tomography (APT), transmission electron microscopy (TEM), and first-principles calculations. APT analyses reveal that prior to interfacial reactions at Nb/Nb3Sn interfaces, Zr atoms in an unreacted Nb-1Zr-4Ta (at.%) alloy form clusters with O atoms owing to their high affinity for oxygen and are segregated at grain boundaries (GBs) in the Nb grains. Then, nucleation of Zr oxide precipitates occurs in Nb3Sn and at Nb3Sn/Nb interfaces, driven by the small solubility of Zr and O in Nb3Sn compared to Nb. Quantitative APT and TEM analyses of Zr oxide precipitates in Nb3Sn layers demonstrate the nucleation, growth, and coarsening processes of Zr oxide precipitates in Nb3Sn layers. A high number density of Zr oxide nanoprecipitates is observed in the Nb3Sn layers, ~10^23 per m^3, with a mean precipitate diam. <10 nm at 625 oC and 700 oC, which provide pinning centers for grain refinement of Nb3Sn, <100 nm diam., and serve as pinning sites for fluxons. First-principles calculations and classical nucleation theory are employed to describe the nucleation of Zr oxide precipitates in Nb3Sn: energy barriers and the critical radius for nucleation of Zr oxide precipitates in Nb3Sn. Our research yields the kinetic pathways for nucleation and growth of Zr oxide precipitates and the microstructural evolution of Nb3Sn layers, which helps to improve the fabrication process of internally oxidized Nb3Sn wires for high-field superconducting magnets.

In this study we will show a new method of polishing for Nb3Sn cavities known as centrifugal barrel polishing (CBP). Using this method, Nb3Sn coated samples are polished to a surface roughness comparable to a traditional Nb cavity after electropolishing (EP). We also investigate different methods of cleaning the Nb3Sn surface after CBP to remove residual abrasive particles. The polished Nb3Sn surface is analyzed using confocal laser microscopy, and scanning electron microscopy (SEM) is used to image the surface and measure the surface roughness after polishing. Transmission electron microscopy (TEM) is also used for high resolution analysis of the surface after polishing. Finally, we show that centrifugal barrel polishing can improve the performance of a Nb3Sn SRF cavity.

To better understand the equilibrium $\gamma^\prime$(L1$_2$) precipitate morphology in Co-based superalloys, a phase field modeling sensitivity analysis is conducted to examine how four phase-field parameters [initial Co concentration ($c_0$), double-well barrier height ($\omega$), gradient energy density coefficient ($\kappa$), and lattice misfit strain ($\epsilon_{\rm misfit}$)] influence the $\gamma^\prime$(L1$_2$) precipitate size and morphology. Gaussian Process Regression (GPR) models are used to fit the sample points and to generate surrogate models for both precipitate size and morphology. In an Active Learning approach, a Bayesian Optimization algorithm is coupled with the GPR models to suggest new sample points to calculate and efficiently update the models based on a reduction of uncertainty. The algorithm has a user-defined objective, which controls the balance between exploration and exploitation for new suggested points. Our methodology provides a qualitative and quantitative relationship between the $\gamma^\prime$(L1$_2$) precipitate size and morphology and the four phase-field parameters, and concludes that the most sensitive phase-field parameter for precipitate size and morphology is the initial Co concentration ($c_0$) and the double-well barrier height ($\omega$), respectively. We note that the GPR model for precipitate morphology required adding a noise tolerance in order to avoid overfitting due to irregularities in some of the simulated equilibrium $\gamma^\prime$(L1$_2$) precipitate morphology., Comment: 24 pages, 10 figures

The temporal evolution of ordered gamma-prime(L12)-precipitates and the compositional trajectories during phase-separation of the gamma(face-centered-cubic(f.c.c.)) and gamma-prime(L12)-phases are studied in a Ni-0.10Al-0.085Cr-0.02Re(mole-fraction) superalloy, utilizing atom-probe tomography, transmission electron microscopy, and the Philippe-Voorhees (PV) coarsening model. As the gamma-prime(L12)-precipitates grow, the excesses of Ni, Cr and Re, and depletion of Al in the gamma(f.c.c.)-matrix develop as a result of diffusional fluxes crossing gamma(f.c.c.)/gamma-prime(L12) heterophase interfaces. The coupling effects on diffusional fluxes was introduced (PV coarsening model) in terms of the diffusion tensor, D, and the second-derivative tensor of the molar Gibbs free energies, G", obtained employing Thermo-Calc and DICTRA calculations. The Gibbs interfacial free energies are (6.9 +- 1.4) mJ/m2 with all terms in D and G", which changes to (18.9 +- 2.1) mJ/m2, (37.7 +- 3.3) mJ/m2, and (-7.5 +- 1.2) mJ/m2 without including the off-diagonal terms in D, G", and both D and G", respectively. The experimental APT compositional trajectories are displayed and compared with the PV model in a partial quaternary phase-diagram, employing a tetrahedron. The compositional trajectories measured by APT exhibit curvilinear behavior in the nucleation and growth regimes, which become vectors, moving simultaneously toward the gamma(f.c.c.) and gamma-prime(L12) conjugate solvus-surfaces, for the quasi-stationary coarsening regime. The compositional trajectories are compared to the PV model with and without the off-diagonal terms in D and G". The directions including the off-diagonal terms in D and G" tensors are consistent with the APT experimental data., Comment: 63 pages, 18 figures, 3tables

A 10 wt.% nickel-steel has been developed for high pressures and low-temperature applications, due to its high strength, excellent toughness, and low ductile-to-brittle transition temperature (DBTT). Under dynamic loading conditions this steel is, however, prone to shear localization that manifests as adiabatic shear bands (ASBs). The temperature increases and thermoplastic microstructural evolution in the ASB are studied in detail, from the macroscopic length scale to the atomic-scale employing correlative electron-backscatter diffraction (EBSD), transmission electron microscopy (TEM), and atom-probe tomography (APT). From a calculation of the temperature increase under adiabatic conditions, based on the conversion of plastic-work to heat generation, the microstructural transitions in the ASB are discussed specifically for: (i) a b.c.c.-f.c.c. phase-transformation and their elemental partitioning; (ii) the thermodynamic model for the compositional change of the V(Nb)-rich carbonitride precipitates during a temperature increase; and (iii) grain-refinement and rotation by dynamic/mechanical recrystallization processes. Solute segregation at subgrain boundaries, measured using the Gibbsian interfacial excess methodology, reveals how solute segregation contributes to the instability of localized shear-deformation by promoting the depinning of solute elements and the migration of a grain boundary. Finally, a kinetic model for grain refinement/rotation within an ASB is described by the dynamic recrystallization behavior with: (i) subgrain formation; (ii) rotation/refinement by deformation; and (iii) grain growth by subgrain coalescence with further rotation and a temperature increase. The temperature increase under dynamic deformation in an ASB promotes grain boundary migration and subgrain coalescence to create a large degree of equiaxed grains with a low density of imperfections., Comment: 48 pages, 11 figures

We study mechanisms of vortex nucleation in Nb$_3$Sn Superconducting RF (SRF) cavities using a combination of experimental, theoretical, and computational methods. Scanning transmission electron microscopy (STEM) image and energy dispersive spectroscopy (EDS) of some Nb$_3$Sn cavities show Sn segregation at grain boundaries in Nb$_3$Sn with Sn concentration as high as $\sim$35 at.\% and widths $\sim$3 nm in chemical composition. Using ab initio calculations, we estimate the effect excess tin has on the local superconducting properties of the material. We model Sn segregation as a lowering of the local critical temperature. We then use time-dependent Ginzburg-Landau theory to understand the role of segregation on magnetic vortex nucleation. Our simulations indicate that the grain boundaries act as both nucleation sites for vortex penetration and pinning sites for vortices after nucleation. Depending on the magnitude of the applied field, vortices may remain pinned in the grain boundary or penetrate the grain itself. We estimate the superconducting losses due to vortices filling grain boundaries and compare with observed performance degradation with higher magnetic fields. We estimate that the quality factor may decrease by an order of magnitude ($10^{10}$ to $10^9$) at typical operating fields if 0.03\% of the grain boundaries actively nucleate vortices. We additionally estimate the volume that would need to be filled with vortices to match experimental observations of cavity heating.

A method based on the Gibbs' adsorption isotherm is developed to calculate the decrease in interfacial free energy resulting from solute segregation at an internal interface, built on measured concentration profiles. Utilizing atom-probe tomography (APT), we first measure a concentration profile of the relative interfacial excess of solute atoms across an interface. To accomplish this we utilize a new method based on J. W. Cahn's formalism for the calculation of the Gibbs interfacial excess. We also introduce a method to calculate the decrease in interfacial free energy that is caused by the segregating solute atoms. This method yields a discrete profile of the decrease in interfacial free energies, which takes into account the measured concentration profile and calculated Gibbsian excess profile. We demonstrate that this method can be used for both homo- and hetero-phase interfaces and takes into account the actual distribution of solute atoms across an interface as determined by APT. It is applied to the case of the semiconducting system PbTe-PbS 12 mol.%-Na 1 mol.%, where Na segregation at the PbS/PbTe interface is anticipated to reduce the interfacial free energy of the {100} facets. We also consider the case of the nickel-based Alloy 600, where B and Si segregation are suspected to impede inter-granular stress corrosion cracking (IGSCC) at homo- (GB) and hetero-phase metal carbide (M7C3) interfaces. The concentration profiles associated with internal interfaces are measured by APT using an ultraviolet (wavelength = 355 nm) laser to dissect nanotips on an atom-by-atom and atomic plane-by-plane basis.

We report on atomic-scale analyses of grain boundary (GB) structures and segregation in Nb3Sn coatings on Nb, prepared by the vapor-diffusion process, for superconducting radiofrequency (SRF) cavity applications, utilizing atom-probe tomography, high-resolution scanning transmission electron-microscopy and first-principles calculations. We demonstrate that the chemical composition of Nb3Sn GBs is correlated strongly with the diffusion of Sn and Nb at GBs during the coating process. In a sample coated with a relatively large Sn flux, we observe an interfacial width of Sn segregation at a GB of ~3 nm, with a maximum concentration of ~35 at.%. After post-annealing at 1100 oC for 3 h, the Sn segregated at GBs disappears and Nb segregation is observed subsequently at GBs, indicating that Nb diffused into the Nb3Sn GBs from the Nb substrate. It is also demonstrated that the amount of Sn segregation in a Nb3Sn coating can be controlled by: (i) Sn flux; and (ii) the temperatures of the Nb substrates and Sn source, which may affect the overall kinetics including GB diffusion of Sn and Nb. An investigation of the correlation between the chemical compositions of GBs and Nb3Sn SRF cavity performance reveals that the Nb3Sn SRF cavities with the best performance (high-quality factors at high accelerating electric-field gradients) do not exhibit Sn segregation at GBs. Our results suggest that the chemical compositions of GBs in Nb3Sn coatings for SRF cavities can be controlled by GB engineering and can be utilized to optimize fabrication of high-quality Nb3Sn coatings for SRF cavities.

The compositional diffusional-trajectories for a phase separation of gamma(f.c.c.)/gamma-prime(L12) phases are studied in a quaternary Ni-10Al-8.5Cr-2Re alloy, aged at 700 deg.C for 0 to 1024 h, utilizing atom-probe tomography (APT). As the gamma-prime(L12)-precipitates grow, the enrichments of Ni, Cr, and Re and depletion of Al on the gamma(f.c.c.) matrix-side develop as a result of diffusional fluxes crossing the gamma(f.c.c.)/gamma-prime(L12) interface.The experimental (APT) compositional trajectories of the two-phases, gamma(f.c.c.)/gamma-prime(L12), are displayed in a quaternary phase-diagram, employing a tetrahedron, and compared with the Philippe-Voorhees (P-V) coarsening model which includes the off-diagonal terms in the diffusion tensor for the multi-component system., Comment: 12 pages, 3 Figures

Atom-probe tomography (APT) facilitates nano- and atomic-scale characterization and analysis of microstructural features. Specifically, APT is well suited to study the interfacial properties of granular or heterophase systems. Traditionally, the identification of the interface between, for precipitate and matrix phases, in APT data has been obtained either by extracting iso-concentration surfaces based on a user-supplied concentration value or by manually perturbing the concentration value until the iso-concentration surface qualitatively matches the interface. These approaches are subjective, not scalable, and may lead to inconsistencies due to local composition inhomogeneities. We propose a digital image segmentation approach based on deep neural networks that transfer learned knowledge from natural images to automatically segment the data obtained from APT into different phases. This approach not only provides an efficient way to segment the data and extract interfacial properties but does so without the need for expensive interface labeling for training the segmentation model. We consider here a system with a precipitate phase in a matrix and with three different interface modalities---layered, isolated, and interconnected---that are obtained for different relative geometries of the precipitate phase. We demonstrate the accuracy of our segmentation approach through qualitative visualization of the interfaces, as well as through quantitative comparisons with proximity histograms obtained by using more traditional approaches., Comment: 23 pages, 6 figures

The details of phase separation of a Ni-6.5Al-9.9Mo aged at 978 K for aging times ranging from 0.125 to 1024 h are investigated by atom-probe tomography and lattice-kinetic Monte Carlo (LKMC) simulations. On the basis of the temporal evolution of the nanostructure, three experimental regimes are identified: (1) concomitant precipitate nucleation and growth (t less than 0.25 h); (2) concurrent coagulation and coalescence (t 0.25 to 16 h); and (3) quasi-stationary coarsening of gamma prime(L12)- precipitates (t 16 to 1024 h). The temporal dependencies of the mean precipitate radius and precipitate number density, Nv(t), are determined experimentally, 0.344 (0.012) and -0.95(0.02), respectively, following the predictions of quasi-stationary coarsening models. In this alloy aged at 978 K, Al partitions strongly to the gamma prime(L12)-phase with a partitioning coefficient 4.06(0.04), whereas Mo and Ni partition to the gamma(f.c.c.)-matrix with values of 0.61(0.01) and 0.90(0.01), respectively. In the quasi-stationary regime(t larger than 16h), the temporal exponents of the Al, Mo, and Ni supersaturations in both the gamma(f.c.c.)-matrix and gamma prime(L12)-precipitates are in reasonable agreement with a multi-component coarsening model's prediction of -0.33. Quantitative analyses of the edge-to-edge inter-precipitate distances demonstrate that coagulation and coalescence are consequences of the overlap of the diffusion fields surrounding the gamma prime(L12)-precipitates. Both 3-D APT and LKMC results demonstrate that the interfacial compositional width decrease with increasing values. And the interfacial compositional width at infinite ageing time are estimated to be 1.89(0.22) nm, 2.09(0.12) nm and 2.64(0.03) nm for Ni, Al and Mo, respectively., Comment: 70 pages, 13 figures

The temporal evolution of ordered gamma prime (L12)-precipitates precipitating in a disordered gamma(f.c.c.) matrix is studied in extensive detail for a Ni-12.5 Al at.% alloy aged at 823 K (550 oC), for times ranging from 0.08 to 4096 h. Three-dimensional atom-probe tomography (3-D APT) results are compared to monovacancy-mediated lattice-kinetic Monte Carlo (LKMC1) simulations, which include monovacancy-solute binding energies through 4th nearest-neighbor distances, for the same mean composition and aging temperature. The temporal evolution of the measured values of the mean radius, , number density, aluminum supersaturations, and volume fraction of the gamma prime(L12)-precipitates are compared to the predictions of a modified version of the Lifshitz-Slyozov-Wagner coarsening model due to Calderon, Voorhees et al. The resulting experimental rate constants are used to calculate the Gibbs interfacial free-energy between the gamma(f.c.c.)- and gamma prime(L12)-phases using data from two thermodynamic databases, and its value is compared to all extant values dating from 1966. The diffusion coefficient for coarsening is calculated utilizing the same rate constants and compared to all extant archival diffusivities, not determined from coarsening experiments, and is demonstrated to be the inter-diffusivity, , of Ni and Al. The monovacancy-mediated LKMC1 simulation results are in good agreement with our 3-D APT data. It is demonstrated that the compositional interfacial width, for the {100} interface, between the gamma(f.c.c.)- and gamma prime (L12)-phases, decreases continuously with increasing aging time and , for the 3-D APT results and monovacancy-mediated LKMC1 simulations, in disagreement with an ansatz intrinsic to the trans-interface diffusion-controlled coarsening model, which predicts the opposite trend for binary alloys., Comment: 100 pages, 15 figures

We report an atomic-scale analysis of the microstructure of Nb3Sn coating on Nb prepared by vapor diffusion process for superconducting radiofrequency (SRF) cavity application using transmission electron microscopy (TEM). Epitaxial growth of Nb3Sn on the Nb substrate is found and four types of orientation relationships at the Nb3Sn/Nb interface are identified by electron diffraction or high-resolution scanning transmission electron microscopy (STEM) analysis. Thin Nb3Sn grains are observed in regions with low Sn flux and they have the specific orientation relationship, Nb3Sn (1-20)//Nb (-111) and Nb3Sn (002)//Nb (0-11). The Nb3Sn/Nb interface of thin grains had a large lattice mismatch, 12.3 at.%, and a high density of misfit dislocations was observed by HR-STEM. Based on our microstructural analysis of the thin grains, we conclude that the thin regions are probably a result of a slow interfacial reaction with this particular orientation relationship at the interface. The Sn-deficient regions are seen to form initially at the Nb3Sn/Nb interface and remain in the grains due to the slow diffusion of Sn in bulk Nb3Sn. The formation of Sn-deficient regions and the effects of strain and interfacial energies on the formation of Sn-deficient regions at various interfaces were also estimated by first-principle calculation. The finding of orientation relationships at the Nb3Sn/Nb interface provides important information about the formation of defects in Nb3Sn coatings such as large thin regions, Sn-deficient regions, which are critical to the performance of Nb3Sn superconducting radiofrequency cavities for accelerators.