Segregation Energy Research Articles

A universal descriptor to determine the effect of solutes in segregation at grain boundaries

The control of solute segregation at grain boundaries is of significance in engineering alloy properties. However, there is currently a lack of a physics-informed predictive model for estimating solute segregation energies. Here we propose novel electronic descriptors for grain-boundary segregation based on the valence, electronegativity and size of solutes. By integrating the non-local coordination number of surfaces, we build a predictive analytic framework for evaluating the segregation energies across various solutes, grain-boundary structures, and segregation sites. This framework uncovers not only the coupling rule of solutes and matrices, but also the origin of solute-segregation determinants, which stems from the d- and sp-states hybridization in alloying. Our scheme establishes a novel picture for grain-boundary segregation and provides a useful tool for the design of advanced alloys.

First-principles study of solute segregation and its effects on the cohesion of the Fe/Y2Ti2O7 interface in ferritic ODS alloy with He

The solute segregation and its effects on the cohesion of the Fe/Y₂Ti₂O₇ interface in ferritic oxide dispersion strengthened (ODS) alloy have been investigated using first-principles calculations. The computational results indicate that W, Cr, Al, Nb, Zr, and Hf are prone to segregate to the Fe/Y₂Ti₂O₇ interface and enhance the cohesive strength of the Fe/Y₂Ti₂O₇ interface, improving its stability. He atoms exhibit a strong tendency to segregate at the Fe/Y₂Ti₂O₇ interface, leading to embrittlement of the interface. Moreover, in the case of co-existing of W, Cr, Al, Nb, Zr, and Hf with He atoms, it is found that W, Cr, and Al increase the segregation energy of He at the Fe/Y₂Ti₂O₇ interface. This promotes the diffusion of He from the Fe/Y₂Ti₂O₇ interface into the bulk of the Y₂Ti₂O₇, thereby reducing He-induced embrittlement at the Fe/Y₂Ti₂O₇ interface. Finally, the electronic structures of the Fe/Y₂Ti₂O₇ interfaces with and without solute elements, as well as the interaction between metallic solutes and He, have been discussed in detail to reveal the mechanisms of alloying reduction effect on He-segregated embrittlement at the Fe/Y₂Ti₂O₇ interface. The results obtained from this work suggest that adjusting the alloying components in ODS alloys can improve the radiation resistance of the alloy, providing theoretical guidance for the design and optimization of ferritic ODS alloys.

High temperature stress relaxation behavior of high Si, Mo-doped austenitic stainless steels

The resistance to stress relaxation at high temperatures is of importance to fasteners. In this study, the stress relaxation behavior of high Si, Mo-doped austenitic stainless steels at 450, 510, 550, 600 and 650 °C were investigated, taking the microstructure evolution at high-temperature long-term condition into account. It is found that Mo can effectively mitigate the plastic strain rate at high temperatures by impeding the extension of partial dislocations, thus leading to a noteworthy enhancement in the stress relaxation resistance. The first-principles calculations indicated that the addition of Mo can suppress the formation of a multi-phase composed of G phase and ferrite at high temperatures, by increasing the segregation energy of Si, Cr, and Ni at grain boundaries. This multi-phase induces the formation of stacking faults and twins, and therefore is responsible for an abnormal reduction in the residual stress.

Learning grain boundary segregation behavior through fingerprinting complex atomic environments

Although continuum-scale segregation is a well-documented behavior in multi-species materials, detailed site-specific behavior remains largely unexplored. This is partially due to the complexity of analyzing materials at the requisite time and length scales for describing segregation with full atomic accuracy. Here, we better evaluate the segregation behavior of disordered grain boundary (GB) atomic environments through leveraging a set of Strain Functional Descriptors (SFDs) to generate an atomic descriptor (i.e., fingerprint). Using this atomic fingerprint, we resolve key relationships between atomic structure and segregation energy. Machine learning (ML) techniques are utilized in concert with this SFD fingerprint to elucidate complex relationships relating segregation potential to changes in specific features of the local Gaussian density captured by the SFDs. Finally, we identify relationships that indicate both individual and joint structure-property correlations. Linking atomic segregation energy to key structural features demonstrates the value of higher-order descriptors for uncovering complex structure-property relationships at an atomic scale.

First-principles study of the interaction of solutes with ∑3(11-1) symmetric tilt grain boundaries in α-Fe

Abstract The structural, cohesive and magnetic properties of a symmetric Σ3(70.53)[011](11-1) tilt grain boundary in pure bcc iron and with commonly used alloying elements (Si, Co, Mn, Ti, Cu, Mo, Nb, V, Cr and Ni) by means of density functional theory calculations are studied. Solubility and segregation energies were calculated for different positions of dissolved atoms. Calculations show a tendency for impurities to segregate near the boundary. It was found that the substituting Co, Cu and Ni in the layer adjacent to the boundary have an embrittling effect, while other atoms enhance the cohesion of the grains. Magnetic moments on GB atoms are significantly higher than those on bulk atoms.

Effect of alloying solutes on hydrogen segregation at pure iron Σ3(111) grain boundary: First-principles calculation

Hydrogen segregation behaviors at BCC-Fe Σ3 (111) grain boundary (GB) as well as the effects of alloying solutes were studied by the first-principles method. The segregation energy of alloying solutes at different periods presents a concave-down parabolic-like relationship with the atomic number, and the 4 d transition alloying solutes show a higher averaged segregation tendency. At the favorable trapping site, hydrogen segregation energy decreased by increasing the number of hydrogen atoms up to 0.85/Å2 in the plane vertical to the GB. Mo, Tc, Ru, Ta, W, Re, Os, and Ir strengthen GB and inhibit hydrogen segregation. Significantly, the interaction between alloying solutes and hydrogen segregation was elucidated by emphasizing the separation of the chemical and the mechanical contributions, and appropriate descriptors on hydrogen segregation energy influenced by alloying solutes were screened. This work offers theoretical backing to comprehend hydrogen segregation behaviors and the effects of alloying solutes to design advanced high-strength steels resistant to hydrogen embrittlement.

Solute Segregation and Pinning Effect on Lateral Twin Boundary in Magnesium

Deformation twinning creates a three-dimensional twin domain via the migration of forward, normal and lateral twin boundaries (TBs) with respect to twin shear direction, normal to twin plane and twin lateral direction. Solute segregation and pinning effect on the forward and normal TBs have been experimentally observed and demonstrated via atomistic simulations. Here, we conducted a comprehensive study of solute segregation and the pinning effect on the lateral TBs in Mg. First-principles density functional theory calculations were used to obtain the segregation and formation energies of 19 alloying elements in coherent regions of lateral TBs. Alloying elements with greater difference in atomic radius from Mg generally show more negative segregation energy. Moreover, alloying elements with good solubility are selected to demonstrate the pinning effect on a coherent interface. Ge, Ga, Y, Gd, La and Ca show negative segregation energy and solubility energy, indicating that these elements can form stable segregation and have a strong pinning effect at the lateral boundary. Molecular dynamics simulations revealed that solutes in coherent regions are more effective in pinning lateral TBs than those in misfit regions. The results provide insight into the selection of solute atoms for tailoring twinning behavior.

Investigating interfacial segregation of [formula omitted]/Al in Al–Cu alloys: A comprehensive study using density functional theory and machine learning

Solute segregation at the interface between the aluminum (Al) matrix and the Ω (Al2Cu) phase decreases the interfacial energy, impedes the coarsening of precipitates, and enhances the thermal stability of such precipitates. In this study, we employ density functional theory to systematically calculate solute segregation energies of 42 solute elements at the coherent and semi-coherent interfaces between the two phases, as well as mixing energies of these elements within the Al and Cu sublattices of the Ω phase. Using correlation analysis and machine learning methods, we establish the relationship between the solute segregation energy and 20 selected atomic descriptors. Metalloid and late transition metal elements are predicted as potential candidates for enhancing the thermal stability of Al–Cu alloys. We observe that the solute segregation energy at the interfacial site of the semi-coherent interface correlates with the atomic size of solute atoms and their solubilities within the Ω phase. The developed machine learning models exhibit the potential to predict solute segregation energies at various sites of the coherent and semi-coherent interfaces. Overall, our study provides valuable insights into the stabilizing potential of individual elements at the Ω/Al interface in Al–Cu alloys.

Point-Defect Segregation and Space-Charge Potentials at the Σ5(310)[001] Grain Boundary in Ceria

The atomistic structure and point-defect thermodynamics of the model Σ5(310)[001] grain boundary in CeO2 were explored with atomistic simulations. An interface with a double-diamond-shaped structural repeat unit was found to have the lowest energy. Segregation energies were calculated for oxygen vacancies, electron polarons, gadolinium and scandium acceptor cations, and tantalum donor cations. These energies deviate strongly from their bulk values over the same length scale, thus indicating a structural grain-boundary width of approximately 1.5 nm. However, an analysis revealed no unambiguous correlation between segregation energies and local structural descriptors, such as interatomic distance or coordination number. From the segregation energies, the grain-boundary space-charge potential in Gouy–Chapman and restricted-equilibrium regimes was calculated as a function of temperature for dilute solutions of (i) oxygen vacancies and acceptor cations and (ii) electron polarons and donor cations. For the latter, the space-charge potential is predicted to change from negative to positive in the restricted-equilibrium regime. For the former, the calculation of the space-charge potential from atomistic segregation energies is shown to require the inclusion of the segregation energies for acceptor cations. Nevertheless, the space-charge potential in the restricted-equilibrium regime can be described well with an empirical model employing a single effective oxygen-vacancy segregation energy.

Structural evolution and mechanical response of multiple Al Σ5(210) grain boundaries with segregation of solute atoms: First-principles study

Grain boundary (GB) segregation of solute atoms is a key factor affecting the microstructure and macroscopic properties of materials. In this study, first-principles calculations were carried out to investigate the effect of solute atoms (Mg and Cu) segregation on the structural evolution and mechanical response of Al ground-state Σ5(210) GB (GB-Ⅰ) and metastable Σ5(210) GBs (GB-Ⅱ and GB-Ⅲ). The GB energy, segregation energy, and the theoretical tensile strength of the multiple Σ5(210) GBs were calculated. The results show that both Mg and Cu atoms tend to segregate in the boundary plane, thus reducing GB energy and improving GB stability. The segregation of Cu atoms reduced the GB energy more significantly than that of Mg atoms. The segregation of solute atoms can change the symmetric GB structure into an asymmetric one or induce GB phase transformation. The theoretical strength of GB-I is weaker than that of the metastable GB-II with higher GB energy, suggesting that grain boundaries with higher energy are not necessarily unstable. In addition, the effect of solute atom segregation on the GB strength depends not only on the type of element but also on the specific GB structure. The weakening effect of Mg segregation in GB-I and GB-II is due to the weak MgAl bond which enlarges the low charge density region of GB and increases the free volume of GB. The strengthening of GB-I and GB-II by Cu segregation mainly depends on the stronger AlCu bond than AlAl bond along the GB fracture path. The enhanced strength of GB-III with Mg and Cu segregation is attributed to the GB structural phase transformation caused by the segregation of solute atoms. The calculation results further elucidate the relationship between element segregation and grain boundary characteristics.

Grain boundary segregation for the Fe-P system: Insights from atomistic modeling and Bayesian inference

In this work we re-assess experimental data for grain boundary (GB) segregation of P in bcc Fe with thermodynamic and statistical methods. The data are based on Auger-Electron-Spectroscopy (AES) measurements which have provided P GB concentrations for various bulk contents and temperatures for ferrite. While in the previous investigations of this system a single-site McLean equation was used to extract segregation enthalpy and entropy, we employ multi-site segregation models as suggested by atomistic simulations. We use a recently introduced methodology based on inter-atomic potentials to calculate the segregation energy spectrum, as well as vibrational entropy and solute-solute interactions of P in polycrystalline Fe, thereby obtaining a three-dimensional distribution of energy, entropy and interactions. Using this trivariate distribution we predict P GB concentrations and compare them to the experimental measurements. Furthermore, we calibrate the parameters of physical models of increasing complexity to the experimental data with an inverse modeling approach based on Bayesian inference. While it is not possible to seamlessly link the results from AES to atomistic modeling, our investigation provides significant new insights for thermodynamic modeling of GB segregation. The vibrational entropy deduced from experiment differs from physics based atomistic simulations even when taking the spectral nature of energy, entropy and interactions into account. However, the correlations of the quantities are in good agreement when considering the trivariate model. Our investigation highlights the need for new and more accurate experimental datasets of GB segregation.

The Effects on Stability and Electronic Structure of Si-Segregated θ′/Al Interface Systems in Al-Cu Alloys

This study systematically investigates the energy and electronic properties of Si-segregated θ′(Al2Cu)/Al semi-coherent and coherent interface systems in Al-Cu alloys using ab initio calculations. By evaluating the bonding strength at the interface, it has been revealed that Si segregated at the A1 site (Al slab) of the semi-coherent interface systems exhibits the most negative segregation energy, resulting in a noticeable decrease in total energy and an increase in interface adhesion. The electronic structure analysis indicates the presence of Al-Cu and Al-Al bonds, with Si occupying the A1 site. The strong bond formation between Al-Cu and Al-Al is essential for improving interface bonding strength. The results of the calculating analyses are consistent with the results of the previous experiments, and Si can be used as a synergistic element to reduce the θ′/Al interface energy and further reduce the coarsening drive of the θ′ precipitated phase, which can provide new perspectives and computational ideas for the compositional design of heat-resistant Al-Cu alloys.

First-principles modeling of corrosion current for passive magnesium alloys and its application in Mg-RE alloy

Theoretical calculation could simulate Mg alloy corrosion behavior from electrochemical thermodynamic factors. By considering the kinetic factor as the passivation oxide layer, a comprehensive corrosion current model has been set up in this work. The corrosion current modeling should belgJtot′=lgJa+∆lgJc+km×∑fm×∆Em+ki×∑(fi×∆Ei)−koxCPBR×Winterface−∆Gs−∆GF(ln10)RT)). The formula as koxCPBR×Winterface−∆Gs−∆GF(ln10)RT) is just for passivation factor. Alloying element segregation energy ∆Gs, oxide formation energy ∆GF, oxide PBR value CPBR, interface cleavage work Winterface have all been considered. By this more considerate modeling, the corrosion current lgJtot′ (related to polarization icorr) could be obtained for passivate Mg alloys such as Mg-RE series (RE =Sc, Y, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu). Moreover, the prediction is quite coherent to experimental electrochemical polarization result. The work provides a more precisely prediction for Mg alloy with passivation. It also proposes a passivation criterion for seeking corrosion-resistant Mg alloy in another way.

A machine learning framework for the prediction of grain boundary segregation in chemically complex environments

The discovery of complex concentrated alloys (CCA) has unveiled materials with diverse atomic environments, prompting the exploration of solute segregation beyond dilute alloys. However, the vast number of possible elemental interactions means a computationally prohibitive number of simulations are needed for comprehensive segregation energy spectrum analysis. Data-driven methods offer promising solutions for overcoming such limitations for modeling segregation in such chemically complex environments (CCEs), and are employed in this study to understand segregation behavior of a refractory CCA, NbMoTaW. A flexible methodology is developed that uses composable computational modules, with different arrangements of these modules employed to obtain site availabilities at absolute zero and the corresponding density of states beyond the dilute limit, resulting in an extremely large dataset containing 10 million data points. The artificial neural network developed here can rely solely on descriptions of local atomic environments to predict behavior at the dilute limit with very small errors, while the addition of negative segregation instance classification allows any solute concentration from zero up to the equiatomic concentration for ternary or quaternary alloys to be modeled at room temperature. The machine learning model thus achieves a significant speed advantage over traditional atomistic simulations, being four orders of magnitude faster, while only experiencing a minimal reduction in accuracy. This efficiency presents a powerful tool for rapid microstructural and interfacial design in unseen domains. Scientifically, our approach reveals a transition in the segregation behavior of Mo from unfavorable in simple systems to favorable in complex environments. Additionally, increasing solute concentration was observed to cause anti-segregation sites to begin to fill, challenging conventional understanding and highlighting the complexity of segregation dynamics in CCEs.

Microstructural evolution and spheroidization mechanism of powder metallurgy Ti-6Al-4 V alloys after high-temperature forging

After high-temperature forging and rapidly cooling, the microstructure evolution and spheroidization mechanism of powder metallurgy Ti-6Al-4 V alloy have been clarified. The spheroidization process is divided into two asynchronous stages. The initial stage is primarily characterized by the initial shearing and twisting of GBα grain boundaries, as well as the deformation of lamellar structure. Subsequently, the fragmentation of original GBα grain boundaries and the fracture of intra-granular α lamellae are observed. This process is accompanied by grain twisting and substructure formation, especially the division of lamellae through interface splitting and the segregation of local chemical elements. The differential accumulation of elements around the fractured and twisted grains suggests that element segregation and interfacial energy play a significant role in microstructure evolution. Therefore, the static spheroidization process largely depends on the formation and evolution of dislocation substructures, and the reduction of interfacial energy may be a key factor driving this process. These findings provide a theoretical basis for manufacturing metals with specific anisotropic properties by controlling microstructure evolution.

Grain boundary segregation models for high-entropy alloys: Theoretical formulation and application to elucidate high-entropy grain boundaries

Grain boundary (GB) segregation models are derived for multi-principal element alloys (MPEAs) and high-entropy alloys (HEAs). Differing from classical models where one component is taken as a solvent and others are considered solutes, these models are referenced to the bulk composition to enable improved treatments of MPEAs and HEAs with no principal components. An ideal solution model is first formulated and solved to obtain analytical expressions that predict GB segregation and GB energy in MPEAs and HEAs. A regular solution model is further derived. The GB composition calculated using the simple analytical expression derived in this study and data from the Materials Project agrees well with a prior atomistic simulation for NbMoTaW. The simplicity of the derived analytical expressions makes them useful for not only conveniently predicting GB segregation trends in HEAs but also analyzing nascent interfacial phenomena in compositionally complex GBs. As an application example, the models are used to further derive a set of equations to elucidate an emergent concept of high-entropy grain boundaries.

An analytic descriptor for determining the effect of grain-boundary structures of metals on solute segregation

The structure of grain boundaries (GBs) of metals is essential in determining the solute segregation at GBs; however, its complexity prohibits the understanding of the underlying mechanism. We propose a geometric descriptor of GB segregation based on the non-local coordination number of cut surfaces from GBs, which determines the segregation energies of solutes at the grain boundaries of metals across multidimensional GB space, different solutes, and different matrices. The effectiveness of the descriptor originates from the correlation between bonding strength, d-band width, and coordination number. This descriptor only depends on the bond length and angle of pre-segregation sites at GBs and can be readily used for description and prediction. Our scheme builds a novel picture for understanding the role of GB structures in segregation and provides a useful tool for the design of advanced alloys.

Effects of Co on the microstructure evolution and mechanical properties of Ti-4Al-6Cr-5Mo-8 Nb alloy by ultrasonic vacuum melting

An investigation was conducted into the impact of low cobalt content on the microstructure and mechanical properties of titanium alloys. Ti-4Al-6Cr-5Mo-8 Nb-xCo (x = 0, 2, 3, 4, and 5) alloys were prepared by ultrasonic-assisted melting and casting. The changes in microstructure, mechanical properties, and the strengthening and toughening mechanisms were researched. Results show that, when the cobalt content increases from 0 to 5 wt%, the as-cast structure is all β phase. The lattice parameter of the β phase decreases from 0.3663 to 0.3114 nm, a 15% decrease. The size of primary β grains decreases from 676.8 to 310.7 μm, a 54% decrease. When the cobalt content exceeds 3 wt%, the segregation energy of cobalt increases and grain boundary segregation occurs. Grain refinement is due to constitutional supercooling caused by the β-stable element cobalt, as well as the solute drag caused by the differences in intragranular and grain boundary compositions. In addition, the size mismatch between cobalt and titanium atoms leads to lattice distortion. As the cobalt content increases from 0 to 3 wt%, the tensile strength increases from 918.1 to 1147.8 MPa, a 25% increase, while the fracture toughness increases from 51.7 to 59.7 MPa·m1/2, a 15% increase. At 5 wt% cobalt, the tensile strength and fracture toughness diminished to 247.5 MPa and 14.8 MPa·m1/2, respectively. The decrease in lattice parameters mainly lead to an increase in strength. The secondary crack leads to an increase in toughness. The decline in strength and toughness results from cobalt segregating at grain boundaries, leading to embrittlement.

First-principles analysis of intergranular fracture in UN by Σ5(210) grain boundary segregated Xe and vacancy

Segregation of irradiation-generated xenon (Xe) atoms and vacancies to grain boundary (GB) leads to instability and brittleness of uranium mononitride (UN). However, theoretical knowledge about the energetics of its defective interface is lacking, whereas there has been considerable attention on unirradiated UN in experiments. Using first-principles methods, herein we compute the energies of segregation and fracture for typical fission defects. We find that, compared with vacancy, Xe tends more to segregate to Σ5(210) GB, enhancing sensitivity to intergranular fracture. Our predictions clarify the fundamental embrittlement mechanism of irradiated UN GB, which has been discussed so far only on pristine one.

Accelerated First-Principles Calculations Based on Machine Learning for Interfacial Modification Element Screening of SiCp/Al Composites.

SiCp/Al composites offer the advantages of lightweight construction, high strength, and corrosion resistance, rendering them extensively applicable across various domains such as aerospace and precision instrumentation. Nonetheless, the interfacial reaction between SiC and Al under high temperatures leads to degradation in material properties. In this study, the interface segregation energy and interface binding energy subsequent to the inclusion of alloying elements were computed through a first-principle methodology, serving as a dataset for machine learning. Feature descriptors for machine learning undergo refinement via feature engineering. Leveraging the theory of machine-learning-accelerated first-principle computation, six machine learning models-RBF, SVM, BPNN, ENS, ANN, and RF-were developed to train the dataset, with the ANN model selected based on R2 and MSE metrics. Through this model, the accelerated computation of interface segregation energy and interface binding energy was achieved for 89 elements. The results indicate that elements including B, Si, Fe, Co, Ni, Cu, Zn, Ga, and Ge exhibit dual functionality, inhibiting interfacial reactions while bolstering interfacial binding. Furthermore, the atomic-scale mechanism elucidates the interfacial modulation of these elements. This investigation furnishes a theoretical framework for the compositional design of SiCp/Al composites.