Density Functional Theory (DFT) is the prevalent first principles computational method for determining the stacking fault energy (SFE) of face centered cubic (fcc) metals and alloys. Due to several theoretical and computational challenges, SFE determination for interstitial alloys with alloying elements such as carbon, nitrogen, and hydrogen, has so far been limited to few studies at relatively high interstitial content. We propose a new method, rooted in the axial interaction model, that allows rapid and robust mapping of SFE for virtually arbitrary interstitial contents. Instead of computing the total energy of a very large supercell to represent dilute interstitial solutions, representative interstitial-affected and bulk regions are treated separately at the equivalent volume. The SFE is obtained by balancing the SFE values of the regions with a lever rule approach. The method matches SFE values from the axial interaction model within ≤4 mJ.m−2 error, as validated for non-magnetic fcc Fe-N and paramagnetic fcc Fe-N and AISI 304 alloys. The significantly reduced computational workload and equidistant SFE mapping vs. interstitial content down to extremely low values allows accurate fitting of the SFE vs. interstitial content with only few datapoints. This further improves the computational efficiency. So far DFT-based SFE mapping was limited to purely substitutional alloys; we demonstrate the first-time DFT-based SFE mapping in fcc AISI 304 vs. N and Ni, revealing a non-additive contribution of N and Ni to the SFE. Finally, the remaining challenges and future application for high-throughput DFT SFE computation in interstitial alloys is discussed.

Intrinsic stacking fault energy (SFE) values of gamma-Fe and AISI 304 austenitic stainless steels were determined as a function of carbon and nitrogen content using ab initio calculations. In contrast to previous investigations, the analysis was conducted incorporating the paramagnetic state to account for the magnetic constitution of real austenitic stainless steels. The effect of finite temperature was partially accounted for by performing ab initio calculations at the experimental volumes at room temperature. Including paramagnetism in gamma-Fe increases the SFE of non-magnetic gamma-Fe by similar to 385 mJ.m(-2). Interstitial alloying of non-magnetic gamma-Fe causes a linear increase in intrinsic stacking fault energy with interstitial content. In comparison, interstitial alloying of paramagnetic gamma-Fe increases the SFE at only about half the rate. The SFE of paramagnetic interstitial-free AISI 304 is within the range of -12 to 0 mJ.m(-2) and only deviates slightly from the SFE of paramagnetic gamma-Fe. It follows a similar, albeit flatter linear dependency on the interstitial content compared to gamma-Fe. Both gamma-Fe and gamma-AISI 304 were found to be metastable in their interstitial-free condition and are stabilized by interstitial alloying. The possible effect of short range ordering between interstitials and Cr on the SFE was discussed. The calculated threshold nitrogen content necessary to stabilize austenite in AISI 304 is in good agreement with experimental investigations of deformation microstructures in dependence of the nitrogen content. Finally, the calculated negative SFE values of AISI 304 were reconciled with experimentally determined positive SFE values using a recent method that accounts for the kinetics of stacking fault formation.

First-principles calculations were performed to investigate the elastic and thermodynamic properties for multi-component Co-based superalloy systems and explored the effect of alloying on stabilizing the γ′ phase. First, the comparisons were carried out for the γ′ phase in Co3(Al,TM) (TM being transition metals) and Ni3Al systems between the present computational results using the EMTO-CPA method and other available DFT calculations as well as experimental data. The lattice parameters, elastic constants, and Debye temperatures are consistent with experimental results and other calculations. The predicted thermodynamic properties, e.g., the Gibbs free energy, excess entropy, and linear thermal expansion coefficient, agree well with CALPHAD results, experimental results, and other available first-principles calculations. A combination of EMTO-CPA method and Debye–Grüneisen model is utilized in this work to ensure that the alloying effect on the stability of the γ′ phase in a multi-component Co-based system is captured efficiently. This could open the path for designing novel multi-component Co-based alloys based on first-principles calculation. To demonstrate this, predictions for the properties of multicomponent systems were undertaken. Our results show that Ni aids in the stabilization of the (CoNi)3(Al, Mo, Nb) phase. Graphical Abstract: [Figure not available: see fulltext.]

Stacking fault energy and twinning stress are thought to be closely correlated. All currently available models predict a monotonous decrease in twinning stress with decreasing stacking fault energy and depart from the assumption that the intrinsic stacking fault energy has a positive value. Opposite to this prediction, for mediumand high-entropy alloys the twinning stress was shown to increase with decreasing SFE. Additionally, for metastable materials, first principles methods predict negative intrinsic stacking fault energy values, whilst experimentally determined values are always positive. In the present communication, it is postulated that the twinning stress scaled by the Burgers vector bridges the difference between intrinsic and experimentally measured stacking fault energy. The assumption is tested for Cu-Al alloys, for pure metals and for medium- and high-entropy alloys and, for the first time, provides a consistent quantitative interpretation of data for both alloys with positive and negative stacking fault energy.

Grain boundary energy (GBE) and its temperature dependence in body-centered cubic (bcc) metals are investigated using ab initio calculations. We reveal a scaling relationship between the GBEs of the same grain boundary structure in different bcc metals and find that the scaling factor can be best estimated by the ratio of the low-index surface energy. Applying the scaling relationship, the general GBEs of bcc metals at 0 K are predicted. Furthermore, adopting the Foiles's method which assumes that the general GBE has the same temperature dependence as the elastic modulus c44 [Scr. Mater., 62 (2010) 231–234], the predicted general GBEs at elevated temperatures are found in good agreement with available experimental data. Reviewing two experimental methods for determining the general GBEs, we conclude that the two sets of experimental GBEs for bcc metals correspond to different GB structural spaces and differ by approximately a factor of 2. The present work puts forward an efficient methodology for predicting the general GBEs of metals, which has the potential to extend its application for homogeneous alloys without strong segregation of the alloying element and facilitates GB engineering for advanced alloy design.

High-density and nanosized deformation twins in face-centered cubic (fcc) materials can effectively improve the combination of strength and ductility. However, the microscopic dislocation mechanisms enabling a high twinnability remain elusive. Twinning usually occurs via continuous nucleation and gliding of twinning partial dislocations on consecutive close-packed atomic planes. Here we unveil a completely different twinning mechanism being active in metastable fcc materials. The transformation-mediated twinning (TMT) is featured by a preceding displacive transformation from the fcc phase to the hexagonal close-packed (hcp) one, followed by a second-step transformation from the hcp phase to the fcc twin. The nucleation of the intermediate hcp phase is driven by the thermodynamic instability and the negative stacking fault energy of the metastable fcc phase. The intermediate hcp structure is characterized by the easy slips of Shockley partial dislocations on the basal planes, which leads to both fcc and fcc twin platelets during deformation, creating more twin boundaries and further enhancing the prosperity of twins. The disclosed fundamental understanding of the complex dislocation mechanism of deformation twinning in metastable alloys paves the road to design novel materials with outstanding mechanical properties.

Compositional tuning of phase stability of the body-centered cubic (BCC) matrix is an effective way to improve mechanical properties of refractory medium/high entropy alloys, which are generally brittle or lack of strain hardening capability. Here, reducing Zr content in Ti(80-x)ZrxHf10Nb10 (at.%) alloys was demonstrated to destabilize the BCC phase and trigger the BCC to hexagonal close-packed (HCP) phase transformation. Two metastable Ti50Zr30Hf10Nb10 and Ti60Zr20Hf10Nb10 medium entropy alloys were designed, which exhibit superior strength-ductility combination and evident strain hardening due to the transformation induced plasticity effect.

The composition and magnetic dependent interfacial energy in Cu-Co immiscible alloys is investigated within a coherent interface model using ab initio calculations. We translate the composition dependence of the interfacial energy to the temperature dependence considering the variations of the equilibrium compositions of precipitate and matrix with respect to temperature. The obtained results are in reasonable agreement with those obtained by experiments and thermodynamic calculations. Reviewing the experimental methods for determining the interfacial energy based on kinetic models for precipitate nucleation and coarsening, as well the thermodynamic models based on broken-bond models, we point out that the temperature effect on the interfacial energy in the above models is primarily due to the composition change of the interface. The present work emphasizes the effort to understand the meaning of the speciously same quantity in different methods.

Grain refinement increases yield strength, but usually at the cost of ductility reduction. In the present work, we explored the strategy of grain refinement and composition tuning in CoCrNi alloys to optimize mechanical properties. Grain refinement was found to strongly suppress deformation-induced martensitic transformation in metastable CoCrNi alloys, which was utilized to modulate the transformation-induced plasticity (TRIP) effect in combination with composition tuning guided by theoretical calculations. We demonstrated in a non-equiatomic CoCrNi TRIP medium-entropy alloy (MEA) that our approach resulted in an excellent combination of strength and ductility. The proposed strategy is expected to be useful in exploring superior mechanical properties of MEAs and high-entropy alloys in varying systems.

Solid solution strengthening (SSS) is one kind of strengthening mechanisms and plays an important role in alloy design, in particular for single-phase alloys including high-entropy alloys (HEAs). The classical Labusch-Nabarro model and its expansions are most widely applicable to treating SSS of solid solution alloys including both conventional alloys (CAs) and HEAs. In this study, the SSS effects in a series of Fe based CAs and HEAs are investigated by using the classical Labusch-Nabarro model and its expansions. The size misfit and shear modulus misfit parameters are derived from first-principles calculations. Based on available experimental data in combination with empirical SSS model, we propose fitting constants (i.e., the ratio between experimental hardness and predicted SSS effect) for these two families of alloys. The predicted host/alloy family-dependent fitting constants can be used to estimate the hardness of these SSS alloys. General agreement between predicted and measured hardness values is satisfactory for both CAs and HEAs, implying that the proposed approach is reliable and successful.