Mechanical properties of pure elements from a comprehensive first-principles study to data-driven insights

Shang S., Gao M.C., Alman D.E., Liu Z.

Chen H., Zheng M., Li J., Liu J., Zhou G., Feng X.

Yao J., Wang B., Chen H., Han Z., Wu Y., Cai Z., Manggada G.W., Elsayed M.A., Zhou S.

Johnson D.D., Singh P., Smirnov A. ., Argibay N.

Interstitial electron density ${\ensuremath{\rho}}_{o}$ is offered as a direct metric for maximum strength in metals, arising from universal properties derived from an electron gas. ${\ensuremath{\rho}}_{o}$ sets the exchange-correlation parameter ${r}_{s}$ in density-functional theory. It holds also for maximum shear strength ${\ensuremath{\tau}}_{\mathrm{max}}$ in polycrystals [M. Chandross and N. Argibay, Phys. Rev. Lett. 124, 125501 (2020)]. Elastic moduli and ${\ensuremath{\tau}}_{\mathrm{max}}$ for polycrystalline (amorphous) metals are linear with ${\ensuremath{\rho}}_{o}$ and melting ${T}_{m}$ (glass-transition ${\mathrm{T}}_{g}$) temperature. ${\ensuremath{\rho}}_{o}$ or ${r}_{s}$, even with rule-of-mixture estimate, predicts relative strength for rapid, reliable selection of high-strength alloys with ductility, as confirmed for elements to steels to complex solid solutions, and validated experimentally.

Shimanek J.D., Shang S., Beese A.M., Liu Z.

• Pure alias ideal shear strength first-principles calculations of 26 binary Ni alloys. • Relative importance of atomic properties revealed through feature ranking techniques. • Top features promising for machine learning descriptor of mechanical properties. • Combining Ni and Mg ideal shear data shifted feature importance rankings. • Effect of alloying on ideal shear translates to predicted stress–strain response. The present work examines the effect of alloying elements (denoted X) on the ideal shear strength for 26 dilute Ni-based alloys, Ni 11 X, as determined by first-principles calculations of pure alias shear deformations. The variations in ideal shear strength are quantitatively explored with correlational analysis techniques, showing the importance of atomic properties such as size and electronegativity. The shear moduli of the alloys are affirmed to show a strong linear relationship with their ideal shear strengths, while the shear moduli of the individual alloying elements were not indicative of alloy shear strength. Through combination with available ideal shear strength data on Mg alloys, a potential application of the Ni alloy data is demonstrated in the search for a set of atomic features suitable for machine learning applications to mechanical properties. As another illustration, the calculated Ni ideal shear strengths play a key role in a predictive multiscale framework for deformation behavior of single crystal alloys at large strains, as shown by simulated stress–strain curves.

Chong X., Shang S., Krajewski A.M., Shimanek J.D., Du W., Wang Y., Feng J., Shin D., Beese A.M., Liu Z.

Advances in machine learning (ML), especially in the cooperation between ML predictions, density functional theory (DFT) based first-principles calculations, and experimental verification are emerging as a key part of a new paradigm to understand fundamentals, verify, analyze, and predict data, and design and discover materials. Taking stacking fault energy (γSFE) as an example, we perform a correlation analysis ofγSFEin dilute Al-, Ni-, and Pt-based alloys by descriptors and ML algorithms. TheseγSFEvalues were predicted by DFT-based alias shear deformation approach, and up to 49 elemental descriptors and 21 regression algorithms were examined. The present work indicates that (i) the variation ofγSFEaffected by alloying elements can be quantified through 14 elemental attributes based on their statistical significances to decrease the mean absolute error (MAE) in ML predictions, and in particular, the number of p valence electrons, a descriptor second only to the covalent radius in importance to model performance, is unexpected; (ii) the alloys with elements close to Ni and Co in the periodic table possess higherγSFEvalues; (iii) the top four outliers of DFT predictions ofγSFEare for the alloys of Al23La, Pt23Au, Ni23Co, and Al23Be based on the analyses of statistical differences between DFT and ML predictions; and (iv) the best ML model to predictγSFEis produced by Gaussian process regression with an average MAE < 8 mJ m-2. Beyond detailed analysis of the Al-, Ni-, and Pt-based alloys, we also predict theγSFEvalues using the present ML models in other fcc-based dilute alloys (i.e., Cu, Ag, Au, Rh, Pd, and Ir) with the expected MAE < 17 mJ m-2and observe similar effects of alloying elements onγSFEas those in Pt23X or Ni23X.

Hu Y., Sundar A., Ogata S., Qi L.

Body-centered cubic (bcc) refractory multicomponent alloys are of great interest due to their remarkable strength at high temperatures. Meanwhile, further optimizing the chemical compositions of these alloys to achieve a combination of high strength and room-temperature ductility remains challenging, which would require systematic predictions of the correlated alloy properties across a vast compositional space. In the present work, we performed first-principles calculations with the special quasi-random structure (SQS) method to predict the unstable stacking fault energy ($\gamma_{usf}$) of the $(1\bar10)[111]$ slip system and the $(1\bar10)$-plane surface energy ($\gamma_{surf}$) for 106 individual binary, ternary and quaternary bcc solid-solution alloys with constituent elements among Ti, Zr, Hf, V, Nb, Ta, Mo, W, Re and Ru. Moreover, with the first-principles data and a set of physics-informed descriptors, we developed surrogate models based on statistical regression to accurately and efficiently predict $\gamma_{usf}$ and $\gamma_{surf}$ for refractory multicomponent alloys in the 10-element compositional space. Building upon binary and ternary data, the surrogate models show outstanding predictive ability in the high-order multicomponent systems. The ratio between $\gamma_{surf}$ and $\gamma_{usf}$ is a parameter to reflect the potency of intrinsic ductility of an alloy based on the Rice model of crack-tip deformation. Therefore, using the surrogate models, we performed a systematic screening of $\gamma_{usf}$, $\gamma_{surf}$ and their ratio over 112,378 alloy compositions to search for alloy candidates that may have enhanced strength-ductile synergies. Search results were also confirmed by additional first-principles calculations.

Chen H., Xiao H., Wang Y., Liu J., Yang Q., Feng X.

Unlike temperature-controlled hydrogenation for synthesizing hydrogen storage materials, reactive milling of Mg crystal under hydrogen atmosphere for MgH2 synthesis is often uncontrollable. For the first time, we try to understand the preparation of MgH2 during the reactive ball milling in the perspective of energy conversion and structural evolution. High-energy ball milling can lead to basal slip of Mg crystal, which is controlled to disclose Mg(0001), thus further to enhance its hydriding reaction activity. To trigger the reaction of Mg hydriding without catalyst, the energy transferred by collisions in unit time should be over 148.1 kJ mol−1 according to DFT calculations. Due to structural modulation of Mg crystal, the synthesis of MgH2 from Mg crystal under hydrogen atmosphere by high-energy ball milling can be divided into three periods, and can be optimized for the fine synthesis of MgH2. This work is helpful for the controllable synthesis of MgH2 during high-energy ball milling, and should also inspire how to select conditions to synthesize other functional materials.

Chen H., Ma N., Cheng C., Zhang H., Yuan W., Liu P., Feng X., Liu J., Yang Q., Zhou S.

Traditional catalysts for thermal hydrogenation of CO2 mainly focus on the catalytic activation of CO2 molecule, while the activation of H2 is often neglected. Herein, we report an Al-doped MgH2 nano-catalyst producing negative lattice H− as hydrogen source for CO2 hydrogenation. The Al-doped MgH2 nano-catalyst is synthesized with a reactive ball-milling method equipped with Al-based milling balls to dope Al on MgH2 surface. The surface doping of Al promotes the dissociation of H2 to lattice H− and helps the catalyst to achieve 88.4% CH4 selectivity and 27.1% CO2 conversion under H2/CO2 ratio 5/1 at 320 °C and 1.0 MPa. The atomic-doped-Al weakens the Mg H bond and improves electron transfer on MgH2 surface, by which gives the lattice H− a high reactivity for CO2 hydrogenation. The delocalized large π bond of CO2 molecule is weakened by the combination of the lattice H− to the C atom of CO2 molecule, which promotes the formation of Mg formate, significantly influencing the hydrogenation route.

George E.P., Curtin W.A., Tasan C.C.

The high-entropy alloy (HEA) concept was based on the idea that high mixing entropy can promote formation of stable single-phase microstructures. During the past 15 years, various alloy systems have been explored to identify HEA systems with improved property combinations, leading to an extraordinary growth of this field. In the large pool of alloys with varying characteristics, the first single-phase HEA with good tensile properties, the equiatomic CrMnFeCoNi alloy has become the benchmark material, and it forms the basis of much of our current fundamental understanding of HEA mechanical behavior. As the field is evolving to the more broadly defined complex concentrated alloys (CCAs) and the available data in the literature increase exponentially, a fundamental question remains unchanged: how special are these new materials? In the first part of this review, select mechanical properties of HEAs and CCAs are compared with those of conventional engineering alloys. This task is difficult because of the limited tensile data available for HEAs and CCAs. Additionally, the wider suite of mechanical properties needed to assess structural materials is woefully lacking. Nonetheless, our evaluations have not revealed many HEAs or CCAs with properties far exceeding those of conventional engineering alloys, although specific alloys can show notable enhancements in specific properties. Consequently, it is reasonable to first approach the understanding of HEAs and CCAs through the assessment of how the well-established deformation mechanisms in conventional alloys operate or are modified in the presence of the high local complexity of the HEAs and CCAs. The second part of the paper provides a detailed review of the deformation mechanisms of HEAs with the FCC and BCC structures. For the former, we chose the CrMnFeCoNi (Cantor) alloy because it is the alloy on which the most rigorous and thorough investigations have been performed and, for the latter, we chose the TiZrHfNbTa (Senkov) alloy because this is one of the few refractory HEAs that exhibits any tensile ductility at room temperature. As expected, our review shows that the fundamental deformation mechanisms in these systems, and their dependence on basic physical properties, are broadly similar to those of conventional FCC and BCC metals. The third part of this review examines the theoretical and modeling efforts to date that seek to provide either qualitative or quantitative understanding of the mechanical performance of FCC and BCC HEAs. Since experiments reveal no fundamentally new mechanisms of deformation, this section starts with an overview of modeling perspectives and fundamental considerations. The review then turns to the evolution of modeling and predictions as compared to recent experiments, highlighting both successes and limitations. Finally, in spite of some significant successes, important directions for further theory development are discussed. Overall, while the individual deformation mechanisms or properties of the HEAs and CCAs are not, by and large, “special” relative to conventional alloys, the present HEA rush remains valuable because the compositional freedom that comes from the multi-element space will allow exploration of whether multiple mechanisms can operate sequentially or simultaneously, which may yet lead to the creation of new alloys with a spectrum of mechanical properties that are significantly superior to those of current engineering alloys.

Chen H., Ma N., Li J., Wang Y., She C., Zhang Y., Li X., Liu J., Feng X., Zhou S.

Fe atoms doping in form of adsorption and substitution can improve the hydriding performance of Mg for hydrogen storage, but the underlying mechanism is still unclear. In this work, density functional theory calculation is applied to study the effect of atomic Fe on the hydriding reaction of Mg crystal. The H2 adsorption calculation suggests that the adsorbed and substituted Fe atoms can both enhance the sorption performance of H2 molecule on Mg(0001). The H2 dissociation calculation suggests that the adsorbed Fe is more beneficial for H2 dissociation, in which the electron donation of Fe dz2 orbital and back donation of Fe dxy orbital are helpful to transfer electrons from bonding orbital of H2 to antibonding orbital to weaken H-H bond. The H diffusion calculation suggests that the substituted Fe can promote H atom penetration through Mg surface, which makes bulk diffusion from tetrahedral interstice to octahedral interstice the rate-limiting step. This work clarifies the catalytic mechanism of atomic Fe of different doping types on Mg hydriding, which should contribute to design high quality Mg-Fe system for hydrogen storage.

Shang S., Shimanek J., Qin S., Wang Y., Beese A.M., Liu Z.

Nickel aluminide $(\mathrm{N}{\mathrm{i}}_{3}\mathrm{Al})$ is an important material for a number of applications, especially when used as a strengthening constituent in high-temperature Ni-based superalloys. Despite this, there is minimal information on its mechanical properties such as strength, plasticity, creep, fatigue, and fracture. In the present work, a first-principles based pure alias shear deformation has been applied to shed light on dislocation characteristics in $\mathrm{N}{\mathrm{i}}_{3}\mathrm{Al}$ using the predicted stacking fault energy (i.e., the \ensuremath{\gamma} surface) and ideal shear strength $({\ensuremath{\tau}}_{\mathrm{IS}})$. Results include direct evidence for the splitting of a $1/2[\overline{1}10]$ dislocation into two Shockley partials on the ${111}$ plane, which is further supported by the equivalence of the complex stacking fault (CSF) energy ${\ensuremath{\gamma}}_{\mathrm{CSF}}$ and the antiphase boundary (APB) energy ${\ensuremath{\gamma}}_{\mathrm{APB}111}$. Estimates of the Peierls stresses using ${\ensuremath{\tau}}_{\mathrm{IS}}$ and elastic properties suggest the prevalence of edge dislocations in Ni and screw dislocations in $\mathrm{N}{\mathrm{i}}_{3}\mathrm{Al}$, agreeing with experimental observations regarding the dominance of edge dislocations in the first stage of crystal deformation in fcc metals and the yield-strength anomaly related to screw dislocations in $\mathrm{N}{\mathrm{i}}_{3}\mathrm{Al}$. The present calculations further point out that the CSF and APB111 are easily formed by shear due to the low-energy barriers, although the lowest planar energies are for the superlattice intrinsic stacking fault and the APB001. Through the case of $\mathrm{N}{\mathrm{i}}_{3}\mathrm{Al}$, the present work demonstrates that the pure alias shear methodology is not only computationally efficient but also provides valuable insight into the nature of shear-related properties.

Chen H., Liu P., Li J., Wang Y., She C., Liu J., Zhang L., Yang Q., Zhou S., Feng X.

Thermal conversion of CO2 to value-added chemicals is challenging due to the extreme inertness of the CO2 molecule and the low selectivity of products. We reported a defect-rich MgH2/CuxO hydrogen storage composite from mechanochemical ball-milling for the catalytic hydrogenation of CO2 to lower olefins. The defect-rich MgH2/CuxO hydrogen storage composite achieves a C2=-C4= selectivity of 54.8% and a CO2 conversion of 20.7% at 350 °C under a low H2/CO2 ratio of 1:5, which increases the efficiency of H2 utilization by offering lattice H- species for hydrogenation. Density functional theory calculations show that the defective structure of MgH2/CuxO can promote CO2 molecule adsorption and activation, while the electronic structure of MgH2 is beneficial for offering lattice H- for CO2 molecule hydrogenation. The lattice H- can combine the C site of CO2 molecule to promote the formation of Mg formate, which can be further hydrogenated to lower olefins under a low H- concentration. This work for CO2 conversion by a defect-rich MgH2/CuxO hydrogen storage composite can inspire the catalysts design for the hydrogenation of CO2 to lower olefins.

Zhang S., Xu X., Lin T., He P.

In recent years, Moore’s law had a remarkable effect on predicting the development of semiconductor technology. As the size of devices shrinks to micro scale or nano scale, Intel’s newest 10-nm logic technology is scheduled to start product shipments before the end of 2017. Moore’s law will not die out, as the research scale reaches the atomic scale, “new devices” and new interconnection methods are urgently needed. In this paper, based on emerging interconnection requirement, the contribution to the advanced electronic packaging containing novel nano-materials, such as the carbon nanotubes, nanoparticles sintering, interconnection of nano-solder, nano-silver and surface plasma nano-welding are discussed. For the next 5–10 years, two new types of interconnect solutions are gaining attentions: solder joint alternatives and Cu electrode alternatives. The former uses new materials such as graphene, carbon nanotubes and nanowires to replace traditional solder joints. The latter uses optical media to replace the traditional Cu metal. In general, advanced materials will make more and more outstanding contributions in the development of electronic packaging in the next 10–20 years.

Garg P., Bhatia M.A., Solanki K.N.

The mechanical properties of Ti alloys are significantly affected by the introduction of solute or impurity elements. Thus, the role of impurities on the hardening or softening behavior of α-Ti was investigated through first principles calculations. In particularly, to provide a comprehensive electronic and atomic basis of solute addition in α-Ti, the effect of metallic (V and Al) and non-metallic (C and O) impurities on the ideal shear strength (ISS) and generalized stacking fault energy (GSFE) across different slip systems of Ti were probed. The results revealed that the addition of V atom reduces both ISS and unstable stacking fault energy across various slip systems of α-Ti, whereas Al addition increases the ISS of Ti. Further, the addition of O atom decreases ISS for most of the slip systems while C solute atom increases ISS across all slip systems of α-Ti. To illustrate the underlying factors influencing the observed softening/strengthening behavior, the electronic density of states and valence charge transfer were determined. The electronic density of states calculations showed that the contribution from the d states of V atom decreases the stability of Ti-V solid solution, thereby leading to a decrease in the plastic anisotropy of α-Ti. Finally, the shearability parameter and critical resolved shear stress (CRSS) ratios across different slip systems of Ti solid solutions were calculated to understand the macroscopic effects of impurity addition on the deformation behavior of α-Ti at ambient conditions. Overall, the first-principles study provides an insight into the electronic basis of strengthening/softening effect of solute addition in α-Ti and assesses their implications on the deformation behavior of α-Ti alloys.

Debnath A., Reinhart W.F.

Abstract The design of novel High Entropy Alloys for use in high-temperature applications is an area of active interest due to their potential to provide exceptional properties compared to conventional alloys. Since the increased popularity of machine learning, an important cog in the design process has been training surrogate models on alloy properties. However, these Single-Task models are trained on individual mechanical properties and do not take advantage of the relatedness between properties. Multi-Task models can capture the interdependencies between tasks, leading to potentially more accurate predictions for all tasks. In this paper, we investigate if Multi-Task models can show improvement over Single-Task models when used for predicting the mechanical properties of these alloys. To ensure fair evaluation between the models, we apply L 0 regularization and skip connections to the models, which allows them to adjust the number of model parameters and depth for optimal performance. We find that the Multi-Task models can leverage task relationships to perform better than Single-Task models, especially for high amounts of missing data in the tasks. Furthermore, adding simple auxiliary targets can boost Multi-Task performance even further despite not being effective as input descriptors to single-task models themselves. We anticipate that the proposed strategies can achieve more accurate predictions and consequently enable better design capabilities for such data-constrained domains without incurring much additional computational cost.

Shang S., Gao M.C., Liu Z.

Lin S., Shang S., Shimanek J.D., Wang Y., Beese A.M., Liu Z.