Embrittling Potency Research Articles

The effect of solute segregation on stability and strength of Cu symmetrical tilt grain boundaries from the first-principles study

Grain boundary (GB) stability and strength are two essential points for nanocrystalline materials. In this study, the effects and underlying mechanisms of segregation-induced GB stabilization and GB strengthening in various Cu GBs for selected 8 alloying elements (Mg, Ca, Cr, Ni, Zn, Zr, Ag and Sn) were investigated through first-principles total energy calculations. The segregation energy results show that all other elements excluding Ni can segregate to GB thus improving the GB stability. The segregation driving force is associated with the volume of Voronoi cell of solute, in the trend that increases along with the volume of Voronoi cell growth. The stabilizing mechanism should attribute to the decrease in the number of antibonding electrons. As to GB strength, the embrittling potency results show that Mg, Cr, Zr and Ag are enhancers in Σ5 [001](310) GB, while for Σ5 [001](210) and Σ11 [110](113) GBs, only Cr and Zr are enhancers. The embrittling potency is concerned with segregation energy and the volume of Voronoi cell of solute, in a trend that increases with the segregation energy decline and the volume of Voronoi cell growth. The enhancing mechanism lies in the formation of covalent-like bonds between solute and matrix atoms. Furthermore, by comparing the stabilizing and strengthening effectiveness of alloying elements in various Cu GBs. The trend that the worse the stability and strength of GBs, the better the stabilizing and strengthening effects of alloying elements were revealed.

Statistical perspective on embrittling potency for intergranular fracture

Embrittling potency is a thermodynamic metric that assesses the influence of solute segregation to a grain boundary (GB) on intergranular fracture. Historically, authors of studies have reported embrittling potency as a single scalar value, assuming a single segregation site of importance at a GB and a particular cleavage plane. However, the topography of intergranular fracture surfaces is not generally known a priori. Accordingly, in this paper, we present a statistical ensemble approach to compute embrittling potency, where many free surface (FS) permutations are systematically considered to model fracture of a GB. The result is a statistical description of the thermodynamics of GB embrittlement. As a specific example, embrittling potency distributions are presented for Cr segregation to sites at two Ni $\ensuremath{\langle}111\ensuremath{\rangle}$ symmetric tilt GBs using atomistic simulations. We show that the average embrittling potency for a particular GB site, considering an ensemble of FS permutations, is not equal to the embrittling potency computed using the lowest energy pair of FSs. A mean GB embrittlement is proposed, considering both the likelihood of formation of a particular FS and the probability of solute occupancy at each GB site, to compare the relative embrittling behavior of two distinct GBs.

Application of Machine Learning to Predict Grain Boundary Embrittlement in Metals by Combining Bonding-Breaking and Atomic Size Effects.

The strengthening energy or embrittling potency of an alloying element is a fundamental energetics of the grain boundary (GB) embrittlement that control the mechanical properties of metallic materials. A data-driven machine learning approach has recently been used to develop prediction models to uncover the physical mechanisms and design novel materials with enhanced properties. In this work, to accurately predict and uncover the key features in determining the strengthening energies, three machine learning methods were used to model and predict strengthening energies of solutes in different metallic GBs. In addition, 142 strengthening energies from previous density functional theory calculations served as our dataset to train three machine learning models: support vector machine (SVM) with linear kernel, SVM with radial basis function (RBF) kernel, and artificial neural network (ANN). Considering both the bond-breaking effect and atomic size effect, the nonlinear kernel based SVR model was found to perform the best with a correlation of r2 ~ 0.889. The size effect feature shows a significant improvement to prediction performance with respect to using bond-breaking effect only. Moreover, the mean impact value analysis was conducted to quantitatively explore the relative significance of each input feature for improving the effective prediction.

An embedded-atom method potential parameterized for sulfur-induced embrittlement of nickel

The embrittling or strengthening effect of solute atoms at grain boundaries (GBs), commonly known as the embrittling potency, is an essential thermodynamic property for characterizing the effects of solute segregation on GB fracture. One of the more technologically relevant material systems related to embrittlement is the Ni–S system where S has a deleterious effect on fracture behavior in polycrystalline Ni. In this work, we develop a Ni–S embedded-atom method (EAM) interatomic potential that accounts for the embrittling behavior of S at Ni GBs. Results using this new interatomic potential are then compared to previous density functional theory studies and a reactive force-field potential via a layer-by-layer segregation analysis. Our potential shows strong agreement with existing literature and performs well in predicting properties that are not included in the fitting database. Finally, we calculate embrittling potencies and segregation energies for six [100] symmetric-tilt GBs using the new EAM potential. We observe that embrittling potency is dependent on GB structure, indicating that specific GBs are more susceptible to sulfur-induced embrittlement.

Ductile-brittle transition temperature shift controlled by grain boundary decohesion and thermally activated energy in Ni-Cr steels

Abstract Temper embrittlement induced by segregation of metalloid solutes to grain boundary (GB) was evaluated by a shift of the ductile-brittle transition temperature (DBTT). DBTT was found to be linearly correlated with the amount of metalloid on the GB (X gb) for both dynamic and static displacement rates (dδ/dt) in high and medium hardness steels. Recent first-principles calculations have determined the GB embrittling potency (Δe p) of segregated Sb, Sn and P. In both high and medium hardness steels, the slope (α) of DBTT vs. X gb was found to be linearly dependent on Δe p regardless of the segregated solutes. In high hardness steels, the slope is independent of dδ/dt, while in medium hardness steels the α is dependent on dδ/dt. An Arrhenius plot of dδ/dt vs. the reciprocal DBTT was used to drive the thermal activation energy (E act), which represents a barrier to plasticity. It was found that E act correlates to a reduction in the GB fracture surface energy. The E act depends strongly on GB decohesion in high hardness steels but only weakly depends on it in medium hardness steels.

Grain Boundary Segregation of Substitutional Solutes/Impurities and Grain Boundary Decohesion in BCC Fe

The segregation of certain impurities to grain boundaries (GBs) which induced by neutron irradiation in Reactor Pressure Vessel (RPV) steels may have adverse effects upon their mechanical properties. In this work, ten symmetrical <110> and <001> tilt GBs in BCC Fe were created based on Coincident Site Lattice method, the GBs segregation embrittling potency was simulated by adding phosphorus, copper, nickel, and manganese to the boundaries and free surface (FS) using molecular static method. We have addressed both high- and low-angle tilt grain boundaries. Systematic Molecular Statics simulations were performed employing recent Embedded Atom Method (EAM) potentials. We show that P will strongly bind to GBs and FS; P and Cu have a detrimental effect on the GB cohesion, and segregation of these two elements will lead to GB embrittlement.

First-principles study of phosphorus embrittlement in austenitic steels with κ-carbide precipitates

Ab initio density functional theory calculations were performed to study the effect of phosphorus on the structural, electronic, and magnetic properties of bulk, surface, and interface of κ-carbide (Fe3AlC) and fcc Fe. The aim was to shed light on the role of phosphorus in austenitic steels with κ-carbide particles, where its presence promotes both intergranular and transgranular embrittlement. The embrittling potency energy calculated as a difference between phosphorus binding energies at the Fe3AlC or fcc Fe surfaces and at Fe3AlC/Fe interface, indicates that phosphorus promotes embrittling behavior. Phosphorus at the interface has negative segregation energy which strongly depends on the phosphorus location as well as its concentration. The calculated cleavage energy decreases sharply for κ-carbide with substituted phosphorus as well as for the interface with segregated phosphorus; both contribute to the embrittlement. These results elucidate the microscopic reasons why phosphorus favors crack nucleation in κ-carbide, and why a crack propagates along the boundary between κ-carbide and austenite.

A compilation of ab-initio calculations of embrittling potencies in binary metallic alloys.

Segregation-induced changes in interfacial cohesion often control the mechanical properties of metals. The change in the work of separation of an interface upon segregation of a solute to the interface, termed the embrittling potency, is an atomic-level quantity used to predict and understand embrittlement phenomena. We present a compilation of calculations of embrittling potencies, along with references for these calculations. A discussion of this data is made in a separate article (Gibson and Schuh, 2016 [1]).

Is low phosphorus content in steel a product requirement?

An attempt is made, on the basis to published literature, to assess the amount of phosphorus that might be present in the steels without making it susceptible to grain boundary embrittlement. Embrittlement occurs when the general resistance to plastic flow is comparable to the stress required to separate crystals at their boundaries. A criterion is developed that enables a simple assessment to be made of the tendency to embrittle as a function of yield strength and the fraction of grain boundary sites that are covered by phosphorus. The latter is also sensitive to chemical composition, since some elements such as carbon segregate preferentially to phosphorus, giving rise to site competition that can permit a greater tolerance to the impurity. Other solutes affect the embrittling potency by different mechanisms, not all of which are clear.

Ab initio study of H, He, Li and Be impurity effect in tungsten Σ3{1 1 2} and Σ27{5 5 2} grain boundaries

Density functional theory calculations were performed to investigate the effect of H, He, Li and Be impurities on the intergranular cohesion of W Σ3〈1 1 0〉{1 1 2} and Σ27〈1 1 0〉{5 5 2} grain boundaries (GBs). A rigorous search of unique interstices was performed to reveal a range of impurity behaviors. It was found that He exhibits the largest defect formation energy, however it is Li that shows the strongest tendency to segregate towards the GBs. The embrittling potency was studied using the ideal GB fracture energy (Rice–Wang) criterion (Rice and Wang 1989 Mater. Sci. Eng. A 107 23). The potency was found to depend significantly on the local atomic environment. A site-dependent concentration was used as the weighing factor to obtain an average potency as a function of temperature. It was found that the potency depends only weakly on temperature. In Σ3 H, He, Li and Be decrease fracture energy by 4%, 27%, 30% and 14%, respectively. In Σ27 H, He and Li also decrease cohesion, albeit less severely: 3%, 14% and 7%. On the other hand, Be increases cohesion in Σ27 by 3%.

First-principles study in Fe grain boundary with Al segregation: variation in electronic structures with straining

First-principles fully relaxed tensile tests were performed on a Σ3 (111)/[10] tilt Fe grain boundary (GB) segregated with Al. The effects of Al segregation on bond breaking in the GB were compared with those of Cu and P, which are typical GB embrittlers because of charge transfer and covalent-like characteristics, respectively. It was suggested by first-principles tensile tests that the intergranular embrittling potency of Al is as strong as that of Cu. However, this result disagreed with an estimation based on the Rice–Wang thermodynamic model. The first bond breaking site in the Al-segregated GB was the Fe-Fe bond neighbouring the Al atom, as in the Cu-segregated GB. This is typical of bond breaking due to charge transfer. However, no charge transfer was observed from the Fe atom to the Al atom, while the Fe atom neighbouring the Al atom showed covalent-like characteristics. It was suggested from investigations of the charge density at the bond critical point that the effect of covalent-like characteristics of Al on the Fe-Fe bond was small in the initial stage of straining, but it increased as the charge density of the Fe-Fe bond decreased with increasing strain. The investigation of the dynamic change in electronic structure also shed light on the difference of bond breaking behaviour in metallic and covalent-like bonding in metallic materials.

Energetics of segregation and embrittling potency for non-transition elements in the Ni Σ5(012) symmetrical tilt grain boundary: a first-principles study

A series of non-transition elements bound to the NiΣ5 (012) symmetrical tilt grain boundary (GB) and the (012) free surface (FS) systems hasbeen studied by first-principles calculation using WIEN2k code, which is based on thefull-potential linearized augmented plane wave method with the generalized gradientapproximation. The multilayer relaxations in the presence and absence of solutes aredetermined by the force minimization procedure. The binding energies at someGB/FS/bulk sites including both interstitial and substitutional sites are calculatedfor all the non-transition elements between H and Rn (from the first-row to thesixth-row elements). The GB/FS segregation energy is obtained by calculatingthe binding energy difference between the GB/FS site and the inner bulk site.The embrittling potency energy is obtained by calculating the difference betweenthe GB and FS segregation energies on the basis of the Rice–Wang model. Thecalculated results show that most of the non-transition elements have negativeGB/FS segregation energies. In our definition, this means that there exists asegregation site in the GB/FS that is more stable for the solute atom than in the bulk.The embrittling potency energies are positive for most of the solutes. However,some exceptions such as Be, B, C, and Si having negative and large embrittlingpotency can enhance the GB cohesion. The calculated results are found to beconsistent with the various experimental findings within the discussion based on thesimple site competition model neglecting the interactions between different solutes.

First-Principles Study on Segregation Energy and Embrittling Potency of Hydrogen in NiΣ5(012) Tilt Grain Boundary

The electronic structures of Σ5(012) symmetrical tilt grain boundary (GB) and (012) free surface (FS) systems for nickel including hydrogen are calculated by the full-potential linearized augmented plane wave method with the generalized gradient approximation. The GB/FS energy and the binding energy of hydrogen at an inner bulk site and GB/FS site are calculated. The calculated binding energy of hydrogen on Ni(111) surface is in good agreement with experiment. The difference of the binding energies between the Σ5(012) GB/FS site and the inner bulk site is obtained as the GB/FS segregation energy, and the difference between GB and FS segregation energies as the embrittling potency energy. The segregation position of hydrogen atom is determined by the force minimization. We find that hydrogen atom prefers Σ5(012) GB to inner bulk energetically by about 0.3 eV/H, while it prefers (012) FS to the GB by about 0.3–0.4 eV/H. The open space at GB may be occupied by an additional interstitial Ni atom since it increases the GB energy by only about 10%. In this case, the GB segregation energy of hydrogen reduces, which makes the segregation difficult. The calculated zero-point energies of hydrogen at inner bulk, GB, and FS sites are within 0.12–0.16 eV/H. The difference of the zero-point energies is within 0.04 eV/H, which is small comparing with the segregation energy and embrittling potency.

Influence of alloying additions on the impurity induced grain boundary embrittlement

We have investigated the influence of Mo as a substitutional alloying addition on the grain boundary embrittlement induced by interstitial impurity P by using the first-principles full-potential linearized augmented plane wave total energy/atomic force method within the generalized gradient approximation. With Mo segregated to a clean Fe Σ3(111) grain boundary, the embrittling potency of P increases from +0.19 to +0.88 eV, suggesting a strong detrimental ternary effect in P–Mo couple. Since Mo has a direct strenthening effect of −0.90 eV, the combined effect of a P–Mo couple is −0.02 eV, which confirms the experimental evidence that Mo overcompensates the P embrittlement. Since Mo has a larger atomic size than Fe, it reduces the volume available for P at the grain boundary and hence an increased elastic energy. On the other hand, the strong chemical bonding between Mo and the Fe surface makes the top Fe layers more saturated and hence a weakened vertical P–Fe bonding. Together, they induce a strong embrittling ternary effect in a P–Mo couple. This understanding can also explain the embrittling ternary effect of Mn on P embrittlement and is expected to be applicable to more general cases and instructive in quantum design of ultrahigh-strength alloys.

Effects of Impurities And Alloying Elements on Iron Grain Boundary Cohesion

In metallic materials, where grain boundaries(GB) are of crucial importance, impurities and alloying elements play an important role in determining their physical and mechanical properties because the behavior of a grain boundary may change drastically with the presence of impurities and alloying elements. For example, in iron and its alloys, including industrially important steels, the intergranular embrittlement is usually associated with segregation of impurities, like P and S, toward the GBs. On the other hand, alloying elements, like Mo and Pd, are helpful for intergranular cohesion in iron, due to either direct cohesion effect or effect upon embrittling potency of other impurities. Understanding the mechanisms of impurity-promoted embrittlement and the consequent cohesion(decohesion) effects is becoming more and more important and remains as a challenge for materials scientists. There have been intensive investigations on these mechanisms for a long time and with the progress in computing techniques in recent years, calculations on more realistic representations of impurity-doped grain boundaries have become possible[1–4].

Effects of Alloying Elements on Iron Grain Boundary Cohesion

For a long time, understanding the mechanisms of impurity-promoted embrittlement in iron and the consequent cohesion(decohesion) effects has been a challenge for materials scientists. The role alloying elements play in impurity-promoted embrittlement is important due to either their direct intergranular cohesion(decohesion) effects or effects upon embrittling potency of other impurities. Some alloying elements like Pd and Mo are known to be helpful for intergranular cohesion in iron and some other alloying elements like Mn are known to segregate to and weaken iron grain boundaries dramatically[1]. There have been intensive investigations on these mechanisms for a long time and especially, with the progress in computing techniques in recent years, calculations on more realistic models have become possible[2–4]. In this paper we briefly present our studies on some selected alloying-element/iron grain boundaries(GB) and free surface(FS) systems. The effects of Pd, Mo, Mn and Cr on the Fe Σ5 (031) grain boundary and its corresponding (031) free surface are examined, using a combination of molecular dynamics(MD) and first-principles electronic structure calculations. Section 2 gives a brief introduction to the methods used and Section 3 gives the main results.

Nature of phosphorus embrittlement of the Fe Sigma 3

Thermodynamic, electronic, and magnetic properties of the P/Fe\ensuremath{\Sigma}3[11\ifmmode\bar\else\textasciimacron\fi{}0](111) grain boundary and the P/Fe(111) free surface are compared using the full potential linearized augmented plane-wave method. The calculated segregation-energy difference of 0.8 eV is consistent with the embrittling effect of P according to the Rice-Wang thermodynamic model. The clean Fe\ensuremath{\Sigma}3[11\ifmmode\bar\else\textasciimacron\fi{}0](111) boundary is found to undergo an \ensuremath{\omega} phase transition which results in an antiferromagnetic coupling within the core of the grain boundary. Structural relaxations in the grain boundary alter the P segregation energy by \ensuremath{\sim}2.0 eV and are found to play an important role in defining the correct sign and value of the segregation energy difference controlling embrittlement. The P/Fe chemical interaction is found to be ``embeddedlike'' electrostatic rather than covalent in both environments. Long-range effects of P impurities are found for the Fe magnetization which reduce the embrittling potency of P.

Dislocation Pinning Effect of Grain Boundary Segregated Solute Atoms at a Crack Tip

We analyze the stressing of a crack along a grain interface on which there have segregated solute atoms which retain a residual misfit volume relative to atoms of the host solid. Results suggest that the critical stress intensity factor necessary to emit a dislocation from the crack tip is increased in proportion to the misfit volume, so that oversized solutes tend to pin crack tip dislocations. This is a complementary embrittling mechanism to the often discussed effects of segregants on reducing the reversible work of interfacial separation. It is consistent with empirical correlations of the embrittling potency of solutes with their atomic size differences relative to the host, e.g., as for Sb, Sn, and S in Fe.

Evaluation of the ductile-to-brittle transition temperature shift due to temper embrittlement and neutron irradiation by means of a small-punch test

By means of a small-punch testing technique, the effects of heterogenous intergranular impurity segregation and neutron irradiation on the ductile-to-brittle transition temperature (DBTT) of impurity-doped and undoped alloy steels were investigated. It was found that antimony-doped steels and, in particular, non-homogenized steels with extremely heterogeneous intergranular dopant segragation frequently show initiation of microcracks as indicated by the appearance of serrations in the load-deflection curves. In this case the ductile to brittle transition is spread out over a wider temperature range than for tin- or phosphorus-doped steels as well as for undoped steel. The upper and lower bounds of the DBTT are uniquely correlated with the maximum and average values of the impurity segregation concentration distributed along grain boundaries. These relationships demonstrate the embrittling potency of the segregants, in agreement with results obtained from Charpy V-notch tests. Neutron irradiation of tin-doped steels caused the DBTT to shift to higher temperatures than that of undoped steels. The experimental results suggest a linear correlation between the DBTTs obtained from small-punch tests and those obtained from Charpy V-notch tests, as predicted by a recently developed kinetic model.

Effect of ageing on properties of pressure vessel steels

Manganese-molybdenum-nickel steels are used in the fabrication of nuclear pressure vessels operating at temperatures up to 350°C. In this work the effects of thermal ageing in the temperature range 300–550°C for durations up to 2 × 10 4 h have been studied in conventionally quenched and tempered, and simulated heat-affected-zone (HAZ) microstructural conditions. Quantitative fractography and Auger spectroscopy have been used to relate changes in mechanical properties with associated changes in fracture mode and grain boundary chemistry. The results show that ageing increases the ductile-brittle transition temperature by an amount dependent on material, prior heat treatment, ageing temperature and time. Embrittlement was associated with the segregation of phosphorus to grain boundaries and was successfully modelled using McLean's approach to equilibrium segregation. The embrittling potency of phosphorus was highly dependent on prior heat treatment; largest in the coarse-grained, higher hardness simulated HAZ condition, and least in the conventionally quenched and tempered conditon.