In magnesium alloys with multiple substitutional elements, solute segregation at grain boundaries (GBs) has a strong impact on many important material characteristics, such as GB energy and mobility, and therefore, texture. Although it is well established that GB segregation is inhomogeneous, the variation of GB solute composition for random boundaries is still not understood. In the current study, atomic-scale experimental and simulation techniques were used to investigate the compositional inhomogeneity of six different GBs. Three-dimensional atom probe tomography results revealed that GB solute concentration of Nd in Mg varies between 2 to 5 at.%. This variation was not only seen for different GB orientations but also within the GB plane. Correlated atomistic simulations suggest that the inhomogeneous segregation behavior observed experimentally stems from local atomic rearrangements within the GBs and introduce the notion of potential excess free volume in the context of improving the prediction of per-site segregation energies.
Atomic-scale calculations indicate that both stress effects and chemical binding contribute to the redistribution of solute in the presence of vacancy clusters in magnesium alloys. As the size of the vacancy cluster increases, chemical binding becomes more important relative to stress. By affecting the diffusivity of vacancies and vacancy clusters, solute atoms facilitate clustering and stabilize the resulting vacancy clusters, increasing their potential to promote solute segregation and to serve as heterogeneous nucleation sites during precipitation. Experimental observation of solute segrega…
The control of solute segregation at grain boundaries (GBs) is essential in engineering alloy properties, however the structure-activity relationship of the key parameter-the segregation energies-still remains elusive. Here we propose the electronic and geometric descriptors of GB segregation based on the valence, electronegativity and size of solutes and the non-local coordination number of free surfaces, with which we build a predictive framework to determine the segregation energies across different solutes, matrices, GB structures and segregation sites. This framework uncovers not only the…
Active room temperature diffusion-less climb of the <a> edge dislocations in model Mg-Al alloys was observed using molecular dynamics simulations. Dislocations on prismatic and pyramidal I planes climb through the basal plane to overcome solute obstacles. This out-of-plane dislocation motion softens the high resistance pyramidal I glide and significantly reduces the anisotropy of dislocation mobility, and could help improve the ductility of Mg. The flow stress scales linearly with solute concentration, cAl. Dislocations climb predominantly in the negative direction, with climb angle on the ord…
Atomic-scale simulations are performed to study the effect of solute segregation on the shear-induced motion of select grain boundaries in the classical $α$-Fe/C system. At shear rates larger than the solute diffusion rate, we observe a transition from coupled motion to sliding. Below a critical solute excess, the boundaries break away from the solute cloud and move in a coupled motion. At smaller shear rates, we observe extrinsic coupled motion at small stresses indicating that the coupling is aided by convective solute diffusion along the boundary. Our studies underscore the role of solutes …
Solid-solution strengthening results from solutes impeding the glide of dislocations. Existing theories of strength rely on solute-dislocation interactions, but do not consider dislocation core structures, which need an accurate treatment of chemical bonding. Here, we focus on strengthening of Mg, the lightest of all structural metals and a promising replacement for heavier steel and aluminum alloys. Elasticity theory, which is commonly used to predict the requisite solute-dislocation interaction energetics, is replaced with quantum-mechanical first-principles calculations to construct a predi…
Solute segregation plays an important role in formation of long-period stacking ordered (LPSO) structure in Mg-M-RE (M: Zn, Ni etc., RE: Y, Gd, etc.) alloy systems. In this work, the planar segregation in Mg-Al-Gd alloy is characterized by high angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) and three-dimensional atom probe (3DAP). It is found there is no planar fault accompanying the segregation, and the spatial distribution of segregation may resemble the periodicity of LPSO structure. The segregation is further quantified by 3DAP, and it mainly enriches wit…
This paper studies how solute segregation and its relationship to grain boundary energy in binary alloys is captured in the phase field crystal (PFC) formalism, a continuum method that incorporates atomic scale elasto-plastic effects on diffusional time scales. Grain boundaries are simulated using two binary alloy PFC models --- the original binary model by Elder et al (2007) and the XPFC model by Greenwood et al (2011). In both cases, grain boundary energy versus misorientation data is shown to be well described by Read-Shockley theory. The Gibbs Adsorption Theorem is then used to derive a se…
We develop a first-principles model of thermally-activated cross-slip in magnesium in the presence of a random solute distribution. Electronic structure methods provide data for the interaction of solutes with prismatic dislocation cores and basal dislocation cores. Direct calculations of interaction energies are possible for solutes---K, Na, and Sc---that lower the Mg prismatic stacking fault energy to improve formability. To connect to thermally activated cross-slip, we build a statistical model for the distribution of activation energies for double kink nucleation, barriers for kink migrati…
The segregation of solute atoms to grain boundaries can have a large influence on the mechanical behavior of polycrystals, particularly in metallic alloys. An overview of 400 calculations of solute-induced changes in grain boundary cohesion from 77 separate studies quantitatively demonstrates that the majority of the variation in solute-induced changes in boundary cohesion is explained by simple bond-breaking arguments. This trend is robust to changes in crystal structure and computational methods. The secondary contributions to embrittlement from other mechanisms, such as atomic size effects …
DFT and MLIP study of solute segregation to coherent and semi-coherent α-Fe/Fe$_3$C interfaces
Christian Doppler Laboratory for Knowledge-based Design of Advanced Steels, Department of Materials Science, Montanuniversität Leoben（奥地利莱奥本矿业大学材料科学系先进钢知识基础设计基督教多普勒实验室）
Grain boundary embrittlement occurs when a solute enriches at a grain boundary and lowers its cohesive energy. While grain boundary enrichment is often attributed to equilibrium segregation effects, most models of embrittlement consider either the energetics of decohesion or the equilibrium adsorption at the boundary, but not both phenomena together. We develop a model for the change in cohesive energy of a grain boundary of a pure metal upon introduction of solute under conditions of equilibrium segregation prior to fracture. A heuristic grain boundary cohesion map is presented to delineate w…
This work unravels the atomic details of the interaction of solute atoms with nanoscale crystalline defects. The complexity of this phenomenon is elucidated through detailed atom probe tomographic investigations on epitaxially-strained, compositionally metastable, semiconductor alloys. Subtle variations are uncovered in the concentration and distribution of solute atoms surrounding dislocations, and their dynamic evolution is highlighted. The results demonstrate that crystal defects, such as dislocations, are instrumental in initiating the process of phase separation in strained metastable lay…
Understanding the composition evolution of grain boundaries and grain boundary precipitation at near-atomic scale in aluminum alloys is crucial to tailor mechanical properties and to increase resistance to corrosion and stress corrosion cracking. Here, we elucidate the sequence of precipitation on grain boundaries in comparison to the bulk in a model Al-Zn-Mg-Cu alloy. We investigate the material from the solution heat treated state (475{\textdegree}C), through the very early stages of aging to the peak aged state at 120{\textdegree}C and further into the overaged regime at 180{\textdegree}C. …
The long wavelength limit of a recent microscopic phase field crystal (PFC) theory of a binary alloy mix- ture is used to derive an analytical approximation for the segregation coefficient as a function of the interface velocity, and relate it to the two-point correlation function of the liquid and the thermodynamic properties of solid and liquid phases. Our results offer the first analytic derivation of solute segregation and solute drag de- rived from a microscopic model, and analytically support recent molecular dynamics and fully numerical PFC simulations. Our analytical result also provid…
Interfacial nucleation is the dominant process of dislocation generation during the plastic deformation of nano-crystalline materials. Solute additions intended to stabilize nano-crystalline metals against grain growth, may segregate to the grain boundaries and triple junctions where they can affect the process of the dislocation emission. In this Letter we demonstrate that the effect of solute addition in a nano-crystalline material containing competing solute segregation sites and dislocation sources can be very complex due to different rates of segregation at different interfaces. Moreover,…
Advanced characterisation techniques were used on LPBF Ti-6Al-4V samples produced on a heated base plate. When the substrate temperature is 100°C the elongation is 6\%, which increases and peaks at 10\% at 570°C, then sharply decreases to zero ductility at 770°C. At 100°C, a heavily strained and twinned microstructure, primarily composed of α+α', was observed and it was comparable to asbuilt microstructures obtained by conventional LPBF methods. At higher temperatures, twins are no longer present and instead nano-scale β precipitates are observed within α' and α, as well as dislocation network…
Segregation-induced structural transitions in metallic grain boundaries are studied with hybrid atomistic Monte Carlo/molecular dynamics simulations using Cu-Zr as a model system, with a specific emphasis on understanding the effect of grain boundary character. With increasing global composition, the six grain boundary types chosen for this study first form ordered complexions, with the local segregation pattern depending on the grain boundary core structure, then transform into disordered complexions when the grain boundary composition reaches a critical value that is temperature dependent. T…
Atomic-Scale Insights into Solute Drag Effects on Grain Boundary Motion in Mg-Al and Mg-Ca Alloys
College of Materials Science and Engineering, State Key Laboratory of Cemented Carbide, Hunan University（湖南大学材料科学与工程学院）；McGill University（麦吉尔大学）；Institute of Solid State Physics, Chinese Academy of Sciences（中国科学院固体物理研究所）；School of Physics and Electronics, Hunan University（湖南大学物理与电子学院）；Hunan University（湖南大学）
A number of experimental and theoretical findings in age hardening alloys suggest that specific solute elements preferentially segregate to and reduce the energy of the interphase boundary (IB). This segregation mechanism can stabilize the precipitation microstructure against coarsening, allowing higher operating temperatures in structural applications. Herein, we present a phase field model of solute segregation to IBs that separate matrix and precipitate phases in binary alloys. The proposed modeling framework is capable of capturing bulk thermodynamics and interfacial free energies, while a…
We propose a new statistical physics model to study equilibrium solute segregation at grain boundaries and the resulting embrittlement effect. This low-temperature expansion model is general and efficient, and its parameters can be obtained from atomistic calculations. It is possible to take into account multiple species, multiple segregation sites with different segregation free energies, account for configurational entropy, grain radius and site competition between solutes. As an example, the model is then applied to the study of phosphorus and hydrogen co-segregation at $\Sigma3$ $109.5°[0\…
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 s…
The Langmuir-McLean isotherm is often interpreted as providing an approximation to the most probable grain boundary segregation as a function of the bulk mole solute fraction $x_B$, even though $x_B$ is not an independant parameter in the free energy minimization on which it is based. In this paper it is shown that the most probable segregation for a specified $x_B$ differs from the standard Langmuir-McLean relation. Numerical solution of the derived equation suggests that two potentially stable interface compositions are associated with most bulk compositions. One solution represents a state …
Radiation-induced segregation (RIS) of solutes in materials exposed to irradiation is a well-known problem. It affects the life-time of nuclear reactor core components by favouring radiation-induced degradation phenomena such as hardening and embrittlement. In this work, RIS tendencies in face-centered cubic (fcc) Ni-X (X = Cr, Fe, Ti, Mn, Si, P) dilute binary alloys are examined. The goal is to investigate the driving forces and kinetic mechanisms behind the experimentally observed segregation. By means of ab initio calculations, point-defect stabilities and interactions with solutes are dete…
Exploiting solute segregation and partitioning to the deformation-induced planar defects and nano-martensite in designing ultra-strong Co-Ni base alloys
In this work, we experimentally establish the isothermal nanofacet evolution at an asymmetric tilt grain boundary in the Cu-Ag system using a diffusion couple approach. We investigate the nanofacet formation along the grain boundary in dependence of the Ag solute excess concentration. The initial grain boundary dissociates into asymmetric Ag-lean segments and Ag-rich symmetric (210) segments. Increasing Ag excess leads to an increase in Ag-rich facet segment length, while the length of the asymmetric facets remains constant. From this, we construct a grain boundary nanofaceting diagram deduced…
Based on ab-initio simulations, we report on the nature of principally different mechanisms for interaction of Mg and Zn atoms with grain boundaries in Al alloys leading to different morphology of segregation. The Mg atoms segregate in relatively wide GB region with heterogeneous agglomerations due to the deformation mechanism of solute-GB interaction. In contrast, in the case of Zn atoms an electronic mechanism associated with the formation of directional bonding is dominating in the solute-GB interaction. As a result, for Zn atoms it is energetically beneficial to occupy interstitial positio…
Grain boundary engineering via dopant segregation can dramatically change the properties of a material. For metallic systems, most current studies concerning interfacial segregation and subsequent transitions of grain boundary structure are limited to binary alloys, yet many important alloy systems contain more than one type of dopant. In this work, hybrid Monte Carlo/molecular dynamics simulations are performed to investigate the behavior of dopants at interfaces in two model ternary alloy systems: Cu-Zr-Ag and Al-Zr-Cu. Trends in boundary segregation are studied, as well as the propensity fo…
Interstitials as a key ingredient for P segregation to grain boundaries in polycrystalline $α$-Fe
Montanuniversität Leoben（维也纳矿业大学）；Christian Doppler Laboratory for Knowledge-based Design of Advanced Steels, Department of Materials Science, Montanuniversität Leoben（维也纳矿业大学材料科学系先进钢知识基础设计克里斯蒂安·道普勒实验室）
A thorough understanding of pattern selection is necessary for the control of solidification structures, which are dissipative structures created by irreversible processes. In this paper, we simulate solidification evolution with different Preferred Crystallographic Orientations (PCOs) through the Phase-Field model. Then we study the effect of solute segregation on the interface energy, as well as the influence of the interface energy on the pattern selection. At the initial stage, the solute segregation influences the interface energy, determining the instability of the planar interface. Duri…
