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In today’s digitized world, large amounts of data are becoming available at rates never seen before. This holds true also for materials science where high-throughput simulations and experiments continuously produce new data. Data driven methods are required which can make best use of the information stored in large data repositories. In the present article, two of such data driven methods are presented. First, we apply machine learning to generalize and extend the results obtained from computationally intense density functional theory (DFT) simulations. We show how grain boundary segregation energies can be trained with gradient boosting regression and extended to many more positions in the grain boundary for a complete description. The second method relies on Bayesian inference, which can be used to calibrate models to give data and quantification of the model uncertainty. The method is applied to calibrate parameters in thermodynamic models of the Gibbs energy of Ti-W alloys. The uncertainty of the model parameters is quantified and propagated to the phase boundaries of the Ti-W system.

The embrittlement of metallic alloys by liquid metals leads to catastrophic material failure and severely impacts their structural integrity. The weakening of grain boundaries by the ingress of liquid metal and preceding segregation in the solid are thought to promote early fracture. However, the potential of balancing between the segregation of cohesion-enhancing interstitial solutes and embrittling elements inducing grain boundary decohesion is not understood. Here, we unveil the mechanisms of how boron segregation mitigates the detrimental effects of the prime embrittler, zinc, in a $\Sigma 5\,[0\,0\,1]$ tilt grain boundary in $\alpha-$Fe ($4~at.\%$ Al). Zinc forms nanoscale segregation patterns inducing structurally and compositionally complex grain boundary states. Ab-initio simulations reveal that boron hinders zinc segregation and compensates for the zinc induced loss in grain boundary cohesion. Our work sheds new light on how interstitial solutes intimately modify grain boundaries, thereby opening pathways to use them as dopants for preventing disastrous material failure., Comment: 29 pages, 6 figures in the main text and 10 figures in the supplementary

Nanocrystalline metallic alloy thin films provide a variety of interesting properties. A disadvantage concerns their inherent instability and generation of residual stresses. Here, we present a unique framework incorporating machine learning assisted experimental and modelling methods to perceive the impact of the minority element concentration on the generated residual stresses within a nanocrystalline thin film. As a candidate system we use a W-Ti alloy thin film with different Ti concentrations. We perform machine-learning assisted local residual stress measurements, correlate the results with accompanied microstructure and elemental analysis and apply density functional theory. We inquire why the experimental observed Ti enrichment can be strongly reduced at smaller concentrations and discuss how it significantly effects the stress stored in the nanocrystalline thin film. The presented perception is highly crucial to yield future design guidelines for more stable nanocrystalline thin films.

In this study we investigate Zn liquid metal embrittlement at Fe grain boundaries (GBs) by employing ab initio density functional theory (DFT) simulations. We consider three different GBs and two common alloying elements in steels (Si and Al) and evaluate how the interplay of the elements affects Zn enrichment and embrittlement of the GBs. Our simulations show that Zn has stronger tendency to enrich at both GBs and surfaces than Al and Si. By increasing the amount of Al and Si in the bulk, Zn can be reduced at both GBs and surfaces. This is quantified for a large temperature range by the newly introduced replacement potency, which shows that compared to Al, Si has a larger potency to decrease the amount of Zn at GBs and surfaces. Regarding GB embrittlement, our results demonstrate that Si a small positive, Al a small negative, and Zn a strong negative effect on GB cohesion. In combination with Zn both Al and Si are able to somewhat reduce the detrimental effect of Zn.

We propose a model for predicting the depletion zone arising next to grain boundaries during non-equilibrium segregation. The model directly links to distribution of segregation energies as provided by atomistic simulations. We expose the theoretical framework based on the thermodynamic extremal principle and propose an efficient algorithm to solve the underlying equations. The example of the W-25at%Re is discussed to illustrate the main features of the model. Multi-component segregation kinetics is discussed for segregation of B, C, and N in Mo to illustrate site-competition scenarios. Comparison with earlier results obtained without depletion illustrates the importance of this effects. Finally the depletion zones along GBs are investigated for many different compositions to asses for which material composition and heat treatments they may be observed experimentally. We find that extended depletion zones arise for very small solute concentrations.

Clinical transplantation e14887 (2022). doi:10.1111/ctr.14887, Published by Wiley-Blackwell, Oxford [u.]

Here, the segregation and accumulation of hydrogen in Ni grain boundaries, and its effects on cohesion and tensile mechanical strength were studied by means of density functional theory simulations. Three model grain boundaries were considered: the Σ 3 ( 1 1 ¯ 1 ) [ 110 ] , Σ 5 ( 120 ) [ 001 ] and Σ 11 ( 1 1 ¯ 0 ) [ 113 ] , as representatives for the highly coherent twin, high energy random high angle, and “special” low energy highly coherent grain boundaries, respectively. Hydrogen segregation was found to be favourable in the Σ 5 and Σ 11 grain boundaries, but not in the Σ 3. Hydrogen accumulation studied via a comprehensive site-permutation analysis revealed the mechanisms for how H accumulation capacity varies as a function of grain boundary character. We show that the interfacial cohesion of boundaries can diminish by between 6.7-37.5% at varying levels of H-accumulation. The cohesion of the grain boundaries was analysed using a novel chemical bond-order based approach, enabling a quantitative atomistic determination of the fracture paths arising from hydrogen embrittlement. These simulations explain the details of why grain boundary character is the principal determinant of the likelihood of hydrogen segregation and accumulation, and hence their vulnerability to hydrogen-enhanced decohesion. This knowledge can be used in the design of thermomechanical processes to achieve grain boundary engineering for resistance to hydrogen embrittlement.

Journal of Clinical Medicine 11(24), 7271 (2022). doi:10.3390/jcm11247271, Published by MDPI, Basel

The local variation of grain boundary atomic structure and chemistry caused by segregation of impurities influences the macroscopic properties of polycrystalline materials. Here, the effect of co-segregation of carbon and boron on the depletion of aluminum at a Σ5 (3 1 0 )[0 0 1] tilt grain boundary in a α − Fe-4 at%Al bicrystal is studied by combining atomic resolution scanning transmission electron microscopy, atom probe tomography and density functional theory calculations. The atomic grain boundary structural units mostly resemble kite-type motifs and the structure appears disrupted by atomic scale defects. Atom probe tomography reveals that carbon and boron impurities are co-segregating to the grain boundary reaching levels of >1.5 at%, whereas aluminum is locally depleted by approx. 2 at.%. First-principles calculations indicate that carbon and boron exhibit the strongest segregation tendency and their repulsive interaction with aluminum promotes its depletion from the grain boundary. It is also predicted that substitutional segregation of boron atoms may contribute to local distortions of the kite-type structural units. These results suggest that the co-segregation and interaction of interstitial impurities with substitutional solutes strongly influences grain boundary composition and with this the properties of the interface., The local variation of grain boundary atomic structure and chemistry caused by segregation of impurities influences the macroscopic properties of polycrystalline materials. Here, the effect of co-segregation of carbon and boron on the depletion of aluminum in a α − Fe grain boundary is shown.

Physical review materials 5(11), 113609 (2021). doi:10.1103/PhysRevMaterials.5.113609, Thermal expansion of materials is of fundamental practical relevance and arises from an interplay of several material properties. For nanocrystalline materials, accurate measurements of thermal expansion based on high-precision reference dilatometry allow inferring phenomena taking place at internal interfaces such as vacancy annihilation at grain boundaries. Here we report on measurements obtained for a severely deformed 316L austenitic steel, showing an anomaly in difference dilatometry curves which we attribute to the exceptionally high density of stacking faults. On the basis of ab intio simulations we report evidence that the peculiar magnetic state of the 316L austenitic steel causes stacking faults to expand more than the matrix. So far, the effect has only been observed for this particular austenitic steel but we expect that other magnetic materials could exhibit an even more pronounced anomaly., Published by APS, College Park, MD

In this study we systematically study the temperature dependence of interface energies in W using first principles. To that purpose, we compute interface free energies and consider different contributions, i.e., from lattice expansion, vibrational contribution from harmonic and quasiharmonic approximation with explicit phonon calculations, and electronic contribution. We find that interface energies decrease with temperature and that in most cases the harmonic approximation to the free energy is sufficient. The relative decrease of the interface energy at 2000 K for the surfaces varies from $\ensuremath{-}20$% to $\ensuremath{-}30$%, while for grain boundaries, the interface energies decrease from $\ensuremath{-}30$% to $\ensuremath{-}55$%. Our results are compared to models on temperature dependence of interface energies available in literature. We find that they are in qualitative agreement also exhibiting a general decrease with higher temperatures. However, most models neglect anisotropy effects and are not in quantitative agreement. The equilibrium crystal shape matches with experimentally observed particle and pore shapes.

Fundamental understanding of H localization in steel is an important step towards theoretical descriptions of hydrogen embrittlement mechanisms at the atomic level. In this paper, we investigate the interaction between atomic H and defects in ferromagnetic body-centered cubic (bcc) iron using density functional theory (DFT) calculations. Hydrogen trapping profiles in the bulk lattice, at vacancies, dislocations and grain boundaries (GBs) are calculated and used to evaluate the concentrations of H at these defects as a function of temperature. The results on H-trapping at GBs enable further investigating H-enhanced decohesion at GBs in Fe. A hierarchy map of trapping energies associated with the most common crystal lattice defects is presented and the most attractive H-trapping sites are identified.

Solute atoms segregate and impose a retarding pressure, also known as solute drag pressure, at the grain boundary (GB) leading to reduced GB migration rates. The solute drag pressure depends critically on the segregation energy and the solute diffusivity across the GB. These parameters are, however, typically used as adjustable parameters to describe experimental observations. Here, we present an approach to analyze solute drag based on density functional theory (DFT) calculations. As an example, we apply the proposed approach to available experimental data for migration rates of the 30 ∘ 111 > GB in Au with Fe and Bi impurities at the ppm level. Based on the DFT calculations, Bi is identified as a strongly segregating element while Fe segregation is weak in comparison. The effective segregation energy for Bi is found to vary from -0.59 eV to -0.72 eV in the experimentally investigated temperature range of 500-610 K. Further, the activation energy for trans-GB diffusion of Bi is calculated with DFT to fall into the range of 0.5- 0.6 eV. These DFT based values are consistent with those obtained by the conventional solute drag analysis of the experimental data using the Cahn-Lucke-Stuwe (CLS) model. The proposed approach is discussed in terms of its strengths for trend predictions as well as its quantitative uncertainties.

The adhesion of protective hard coatings to the substrate is one of the most important parameters that influence the performance of metal cutting tools. By a combination of high-resolution transmission electron microscopy and first principles modelling we determine the interface adhesion between a TiN hard coating and microstructural constituents of a high speed steel on an atomic level for the first time. Based on experimentally observed orientation relationships, multiple structures are studied for each interface and both interface cohesion and resistance to sliding are evaluated for MC and M6C carbides as well as the martensitic matrix to TiN coating. We find that TiN coatings have high adhesion to MC carbides, while lower adhesion is present for M6C and the martensitic matrix. Close agreement with experimental measurements validates this approach and suggests new strategies for developing steels with increased coating adhesion.

A model for kinetics of segregation of several interstitial and substitutional components to different kinds of traps at grain boundaries is derived by applying the Thermodynamic Extremal Principle. Evolution equations for the site fractions of the segregating elements at the grain boundary, considered as independent variables, are presented and solved numerically. The kinetic model is applied to the case of Mo containing C, O, and B as impurities and a spectrum of trapping energies obtained from first principles simulations. This newly developed model offers an efficient tool for understanding segregation from several kinds of components at different types of traps.

The design of metallic alloys with superior properties requires a deep understanding of the atomistic processes governing the materials behavior. In this paper, we present results providing a close link between grain boundary (GB) chemistry and fracture behavior in a Mo-Hf alloy. By combining atom probe tomography and ab-initio simulations of GBs, we unravel the origin for the transition between intergranular and transgranular fracture in technological Mo-Hf alloys. The main agent affecting GB strength is not the primary alloying element Hf, but rather the impurities O, C and B. With larger Hf additions, an intricate interplay between segregation and precipitation leads to a strong GB enrichment of C and B and to a depletion of O and Hf resulting in a higher cohesion of the GBs and thus, leading to a change in fracture mode. Our investigation exemplarily demonstrates that smallest additions of solutes can be decisive for understanding fracture behavior on the macroscale. Keywords: Atom probe tomography, Density functional theory, Grain boundary engineering, Intergranular failure, Molybdenum

Grain boundary engineering (GBE) plays an important role in the design of new polycrystalline materials with enhanced mechanical properties. This approach has been shown to be very effective in design of Ni-base alloys, where grain boundary segregation is expected to play a central role in defining their mechanical behavior. In the present work, we apply a powerful combination of advanced experimental and theoretical methods to reveal the grain boundary chemistry of the 725 Ni-base alloy at the atomic level. The methods of investigation comprise atom probe tomography (APT) measurements and density functional theory (DFT) calculations. We also propose a way to cross-validate DFT and APT results in a DFT-based model approach for evaluation of the interfacial excess as a function of the heat treatment history of the material and its chemistry. Both theoretical and experimental methods are applied to a detailed analysis of the GB chemistry of three modifications of the 725 alloy and the results of this investigation are presented and discussed in detail.

Substantial disagreement exists for segregation energies between experimentally measured and first principles calculated values. To resolve this standing issue, we computed segregation of five different elements to the same grain boundaries as studied in an previous experimental investigation. We show that the multi-site nature of segregation leads to a strong artificial temperature dependence in the single site effective segregation energy. Taking this into account leads to a highly improved agreement between experiment and theory and clarifies the nature of experimentally determined segregation enthalpies and entropies.

A direct measurement of the surface energy polytherm in Ag + 0.5 at.% Fe alloy and first-principles calculations of segregation energy in silver-based systems with iron, cobalt and nickel were performed. The surface energy was measured in situ on silver foils with 16 μm thickness in the temperature range (0.8 - 0.95) TmAg in Ar+10% H2 atmosphere. Iron was introduced by electrolytic deposition and annealing. The segregation energy calculations were performed using density functional theory (DFT). DFT calculations were used to obtain the segregation energies of Fe, Co and Ni on the (100), (110), and (111) surfaces of Ag. It was shown that alloying of silver with Ni, Co and Fe (~ 0.5 at.%) leads to a significant increase in the surface energy and this effect increased with decreasing temperature. The alloys behaved in a similar way with decreasing temperature: the surface energy of the alloys increased to values close to the surface energy values of the second components in their standard reference states. DFT calculations of the segregation energy showed a strong “anti-segregation” behavior of Ni, Co and Fe in Ag; the segregation energy took positive values of about 0.4 eV/atom for all solute atoms. Surface studies by AFM and AES methods showed that the surface was two-phase, a silver phase and a small fraction of the second bcc-Fe phase particles coated with a thin silver layer. These observations indicated a quite pronounced desorption of iron on silver on one hand and the adsorption of silver on iron on the other hand. The positive segregation energies of Ni, Co and Fe to Ag surfaces, experimentally observed desorption behavior of these solutes as well as an increase of the surface energy with the increasing concentration of the second component, point at the fundamental reversibility of the Gibbs adsorption equation.

We study the Mo 2 C precipitate, a carbide commonly used for secondary hardening in steels, and its interface to the Fe matrix using a combination of ab-initio density functional theory and finite element simulations. For Mo 2 C and Fe, the elastic properties as a function of temperature are determined and different interfaces of the carbide to the matrix are characterized. With finite element simulations that use the derived elastic properties and interface energies as input, the energy contributions from elasticity and creep are evaluated. Combining the results from atomic to micro scale allows to explain the specific needle shape of these precipitates that has been reported experimentally. For one selected interface, also the full elastic properties are determined with ab-initio methods and compared to the Grimsditch-Nizzoli approach, where we find good agreement. Our study shows how a combination of the ab-initio and the finite element method may be used to characterize and understand the micro-mechanical effects of precipitates.

Grain boundary (GB) segregation of solutes can significantly alter material properties, the effects of which have first been observed more than two hundred years ago. After an introduction that shortly summarizes the historic development of the study of segregation, this work conducts an investigation on the segregation tendencies of 27 alloying elements to an Au GB and a surface with first principles calculations, semi-empirical modelling, and a phenomenological model of segregation. The effect of alloying elements on GB cohesion are evaluated and both detrimental (Bi, Cl, As, K) and beneficial elements (Al and the 3d transition metals) for alloying are identified. By comparing to experimental results from over two centuries, the used methodology and the obtained results are validated. The main origin of the GB cohesion effect can be revealed, i.e. the size mismatch between alloying elements and Au.

The influence of all transition element dopants on grain boundary (GB) cohesion in both W and Mo is investigated by means of high throughput density functional theory (DFT) calculations. We present site specific segregation energies to GBs and free surfaces (FS) of W and Mo and evaluate the strength of embrittlement of the individual solutes. The segregation properties for a consistent set of solutes allow an unprecedented comparison to previous DFT data and phenomenological models for segregation. Our DFT data show that the trends are very similar in W and Mo for the different solutes, while the comparison with available phenomenological models highlights the limits of band-filling and elastic models for GB segregation and strengthening.

Intergranular failure of nickel (Ni) single grain boundaries (GBs) owing to the segregation of sulfur (S), hydrogen (H), and their co-segregation has been investigated by employing micro-cantilever bending tests and density functional theory (DFT) calculations. A pure Ni GB shows completely plastic behavior with no fracture observed in the experiments. Electrochemical H-charging of the sample with no S present in the GB leads to a crack formed at the notch tip, which propagates by means of the mixed plastic–brittle fracture mode. Cantilever testing of the H-charged GB with S results in a clear brittle fracture of the GB. The co-segregation of S and H shifts the sudden drop in the load–displacement curves to smaller values of displacement. This is explained by the combined effect of these elements on the work of separation of the selected GB leading to severely decreased GB cohesion.

The focus of this ab initio study is the interaction between Fe2Al5 particles and WC surfaces in the hot-dip galvanizing processes. In a first step, we compute surface energies of Fe2Al5 to predict the morphology of the particles. In the next step, the most relevant interfaces between Fe2Al5 and WC are characterized in terms of atomic structure and energetics, where different terminations of the two phases at the interface are considered. Finally, we investigate the effect of Zn on the stability and adhesion of the interface, where we find that low Zn coverages can even increase adhesion, but for high Zn coverages the adhesion drops significantly.

Understanding the interactions of solutes in a host material is a key factor for successful alloy design. In this work, we focus on the effect of C, B, O, Fe, and Hf interactions in Mo on grain boundary (GB) segregation and cohesion within an ab initio framework. We show that segregation energies reveal only a weak coverage dependence for the interstitial solutes while for substitutionals a pronounced minimum occurs at 1 ML coverage. For Fe, segregation energies remain negative up to very high coverages of up to 8 ML, which correspond to thick segregation films whose geometric structure and magnetic properties are explored. As a next step we evaluate the binding energy for different solute combinations and show that interactions are mainly repulsive at the GB, while strong attractive interactions occur in the bulk. Origins for this phenomena are discussed and cosegregation energies are extracted for different scenarios. The coverage dependence on cohesion is nearly linear for all investigated solutes and increases for all solutes except for O and Hf.

We use ab initio calculations to analyze the influence of 4d and 5d transition metal alloying elements on cohesive properties of the bulk and a representative grain boundary in Cr within the framework of the Rice–Thomson–Wang approach. The results obtained for Cr are combined with the analogous results for Ni to select Ta and Nb as promising alloying additions to dual-phase (α/γ) Cr-Ni-base high-temperature alloys. Ta and Nb are added to the alloying system of an existing alloy I (Cr-Ni-W-V-Ti) in an attempt to design a chemical composition of a new alloy II (Cr-Ni-W-V-Ti) + (Ta-Nb). Investigation of the microstructure of the Ta-bearing Cr-Ni-alloy reveals a Ta enrichment of large γ-areas near GBs in α-matrix that we consider as potency to increase the cohesive strength of GBs and the cohesive energy of the bulk in γ-phase. Mechanical testing of alloys I and II demonstrates that the alloy II has improved tensile strength and creep resistance at high temperatures.

We investigate grain boundaries (GBs) in W–25 at.% Re alloys with special focus on the segregation of Re to the GBs and the changes in their cohesive properties that arise therefrom. Our simulations rely on density functional theory and a mean-field approximation, the virtual crystal approximation, to model the highly alloyed system. Based on a gamma-surface approach, the geometry of a wide range of GBs, including tilt, twist and mixed GBs, is obtained. Segregation energies are found to vary strongly between different segregation sites, with the strongest segregation energy amounting to −0.75 eVs. We show that bond-order parameters are able to identify strong segregation sites based on purely geometric information only. With a thermodynamic model based on a Bragg–Williams approach, the concentration of Re atoms is calculated as a function of GB character at 1913 K and compared with atom probe experiments. The segregation levels are similar, with a trend towards higher segregation levels observed in the calculations for certain misorientation angles. Finally, Re alloying is found to lead to a general increase in the work of separation of the GBs, suggesting a reduction in the tendency for intergranular fracture.