Introduction to computational science shiflet pdf download

Together with the TEM observations Fig. To evaluate the mechanical properties of the identified eight alloys in a high-throughput manner, we performed compression tests on the eight alloys at room temperature RT Fig. The high-temperature performances of Alloys 1 and 8 were also evaluated and compared to other representative alloys Fig.

Based on the above experimental analyses, we can categorize the eight alloys into two groups. G2: Alloys 2—7 with the L2 1 as the major phase Fig. For easy understanding, our discussion in the following part will base on these two groups. The precipitation-strengthening effect in Alloy 1, but not in Alloy 7, is also demonstrated by the in situ neutron-diffraction results. Figure 3 c, d exhibit the lattice strain versus applied compressive stress curves corresponding to the loading direction in both Alloys 1 and 7.

In contrast, no load transfer was observed in Alloy 7 Fig. The synchronized response of various hkl -specific lattice strains versus applied stress indicates that Alloy 7 behaves like a single L2 1 phase. Therefore, the high yield strengths of Alloys 1 and 8 are attributed to the precipitation strengthening, besides the effect of atomic-level complexity in HEAs.

The morphology of the L2 1 phase strongly affects the mechanical performance of the high-throughput-designed LWHEAs, which is related to the order-disorder transition behavior.

The relative intensity of superstructure peaks for the L2 1 phase decreases upon heating, which is due to the reduced fraction of the L2 1 phase. The label of order means that the reflections are exclusive to the L2 1 structure, while the label of fundamental means that the reflections are common to both the ordered L2 1 and disordered BCC structures.

The black arrows indicate the change of the most abundant, Fe, as the neighbor of all elements. We further conducted the metropolis Monte Carlo MC calculations to understand the order-disorder transitions in Alloys 1 and 7 during solidification, using much larger supercells of atoms at 10 7 MC steps within the nearest-neighbor interaction approximation.

With the concentrations as the only variables for a given system, this method gives a more clear and definitive picture of the influence of constitutions on the order-disorder transition. We define. The L2 1 structure has three different sublattice sites Wyckoff sites : 8c, 4a, and 4b, in which 4a and 4b can be considered as one site and 8c as the other site.

Therefore, for simplification, we can treat an L2 1 structure as a B2 structure to calculate the LRO parameter. The LRO can be expressed as The order-disorder transition can be directly reflected by the LRO parameters Fig.

In both Alloys 1 and 7, as the temperature decreases, Al, Cr, and Ti tend to segregate to one sublattice, while Fe and Mn primarily occupy the other.

This prediction is consistent with the experimental observations Fig. Since Fe is the most abundant element in this system, we consider its changes as the fingerprint of the ordering transition. In both alloys, the temperature-dependent SRO parameters of Fe atoms as the nearest neighbors of Al and Ti increase upon cooling. In contrast, the Cr and Mn have the opposite trend Fig.

The reliability of the MC atom superstructures for both Alloys 1 and 7 are verified by the fitted neutron-scattering pair-distribution function PDF results Supplementary Fig. Ab initio molecular dynamics AIMD simulations were also performed on Alloy 1 in its molten state to support the MC-calculation results. The intensities of pair correlations of the Al—Al and Ti—Ti bonds are significantly lower than the other pair correlations, indicating the strong tendency for Al and Ti atoms to bond with other elements.

On the other hand, the Al—Fe pair correlation has the highest intensity, and the Cr—Fe pair correlation has the second-highest intensity, compared to other pair correlations. The different L2 1 morphologies exhibited between G1 nanoscale precipitates and G2 APDs are strongly correlated to their different chemical compositions Supplementary Table 1 , which directly affect their order-disorder transitions, namely, the atomic-site occupancy of the constituent elements.

The atomic-site occupancy of the formed multicomponent L2 1 structure is revealed as follows. According to the calculated LRO parameters Fig. In the L2 1 structure, the sublattices of Y and Z can be considered equally in terms of site, but differ in terms of composition. However, if the content of Al is more than 25 at. As for Mn, its site occupancy depends on Fe contents, that is, if the Fe content is less than 50 at. Once the Fe content equals 50 at. Note that the solubility of Mn at sites of Z 4b should not exceed 15 at.

When the content of Mn is more than 15 at. From the known atomic-site occupancy, the different L2 1 morphologies between G1 and G2 can be understood from the L2 1 stoichiometric composition, i.

For G2 Alloys 2—7 , their chemical compositions can exactly match the perfect L2 1 stoichiometry, resulting in the formation of the single-phase L2 1 phase in the form of APD. In contrast, for G1 Alloys 1 and 8 , their chemical compositions deviate far away from the perfect L2 1 stoichiometry, leading to the formation of nanoscaled L2 1 precipitates within the BCC matrix.

The atomic-site occupancy in the multicomponent L2 1 structure and the composition-dependent phase-evolution behavior are schematically presented in Fig. A schematic showing the atomic-site occupancy in the multicomponent L2 1 structure and the morphology evolution of the L2 1 phase that depends on the chemical compositions of discovered LWHEAs. The concept of HEAs provides us an unprecedented degree of freedom in the design of advanced alloys with promising properties. For the rapid exploration of the vast compositional space and investigation of the composition and temperature effects on the microstructure, advanced HEA-design strategies and efficient tools are necessary.

The computational software could significantly affect the efficiency of HTC since massive calculations are carried out. Fortunately, the current HTC module can be easily converted to parallel calculations for efficiently utilizing the available computational resource, which is the target that we are working on.

Thus, the organization of the large volume of data will be especially critical for efficiently retrieving the requested subsets of the large datasets. At present, each calculation is stored separately in a workspace and organized by its calculation identity ID. The calculation ID is usually the alloy composition, and the detailed information of each calculation is represented by the predefined features, such as the composition, temperature, phase fraction, etc.

The users can easily access these results via their calculation IDs and efficiently retrieve the requested datasets through the customized features. Here, we would like to emphasize that any algorithms that are able to be ascribed to these features can be employed as the screening criteria for the CALPHAD-calculated datasets.

Moreover, the current HTC tool allows users to customize the outputs of different types of CALPHAD calculations for the possible combination with other datasets for machine learning and the usage of other data mining tools.

The microstructure discrepancy between the thermodynamic prediction and experimental observation indicates that our current thermodynamic database needs further improvement on the stability of the L2 1 phase.

In addition to the current experimental results, long-period annealing on these identified alloys and quantitative characterization will be necessary in order to improve our current thermodynamic database. Especially, the HTC can become more efficient when it is coupled with the deciphered atomic occupancy of the multicomponent L2 1 structure and its related phase-evolution rule. Therefore, the high-throughput design and the fundamental understanding of the discovered LWHEAs will accelerate the pace of discovering promising HEAs, especially for multicomponent systems.

The CALPHAD approach 38 , 39 , 40 is currently the only method that can be used to obtain multicomponent phase diagrams with enough accuracy for practical applications without the need of the heavy experimental work The application of the CALPHAD method requires both the thermodynamic database to provide the Gibbs energies as a function of pressure, temperature, and composition for the individual phases and the computational software to calculate the equilibrium state by an energy-minimization procedure.

Over the past three decades, the development of consistent multicomponent thermodynamic databases has grown steadily, and several commercial software, such as Pandat TM 44 , Thermo-Calc 45 and FactSage 46 , has become available. Although the CALPHAD approach has been well accepted in the design and development of advanced materials 21 , 47 , 48 , 49 , 50 , 51 , its full potential has not been fully released due to the low efficiency to explore the entire composition and temperature space of a multicomponent system.

Alloy compositions that satisfy user-defined criteria can then be identified through mining the thousands of simulated results. Here we would like to emphasize that the current HTC module is a combinatorial tool for both the high-throughput calculation and high-throughput screening.

To verify the reliability of the current HTC method, eight different alloys identified from thousands of compositions were fabricated via the arc-melting method with The nominal chemical compositions of these alloys are listed in Supplementary Table 1. To ensure chemical homogeneity, the ingot was melted at least six times before drop-casting. The APT specimens were fabricated, employing the method described by Thompson et al.

Each test was repeated three times. To obtain a better d-spacing resolution, the high-resolution HR mode was chosen. The atomic structure in the liquid state can reveal the useful information about the preferred interatomic bonding that may impact the formation of the disordered solid solution during solidification 18 , A lattice-gas model can describe the order-disorder phase transitions for the same and fixed lattice. In principle, sufficiently large lattices with sufficiently accurate interactions between the lattice points can accurately describe the real phase transitions that do not involve only changes of lattice types.

The serious restrictions of lattice-gas models include the effects of lattice distortion and lattice vibration. Still, such models are found to successfully predict the order-disorder phase transitions in a number of conventional and high-entropy alloys HEAs 3 , 33 , 65 , 66 , 67 , In this study, a lattice-gas model was constructed to describe the order-disorder phase transitions in a BCC lattice.

We performed Metropolis MC simulations, using the nearest-neighbor interaction model for simplicity. In the nearest-neighbor interaction model, only the atomic interactions of the nearest neighbors between atoms are considered. Although each atom has 8 nearest-neighbor bonds, two atoms share them. Hence, the number has to be divided by 2. The formation energies are taken from the Aflow database of Curtarolo et al. Applying numbers listed in Table 2 , we performed three Metropolis MC simulations.

Two are for Alloys 1 and 7 using atoms with 10 7 MC steps, the third for the L2 1 phase using atoms with 10 6 MC steps. The data that support the findings of this study are available from the corresponding author upon reasonable request.

Song, G. Ferritic alloys with extreme creep resistance via coherent hierarchical precipitates. Sun, Z. New design aspects of creep-resistant NiAl-strengthened ferritic alloys. Yeh, J. Nanostructured high-entropy alloys with multiple principal elements: novel alloy design concepts and outcomes. Cantor, B. Microstructural development in equiatomic multicomponent alloys.

A , — Zhang, Y. Microstructures and properties of high-entropy alloys. Miracle, D. A critical review of high entropy alloys and related concepts.

Acta Mater. Diao, H. Fundamental deformation behavior in high-entropy alloys: An overview. Solid State Mater. George, E. High-entropy alloys. Lei, Z. Enhanced strength and ductility in a high-entropy alloy via ordered oxygen complexes. Nature , — Yang, T. Multicomponent intermetallic nanoparticles and superb mechanical behaviors of complex alloys. Science , — Sohn, S. Ultrastrong medium-entropy single-phase alloys designed via severe lattice distortion.

Ma, E. Unusual dislocation behavior in high-entropy alloys. Antonov, S. A 49 , — Detrois, M. Alloys Compounds , — Refractory high entropy superalloys RSAs. Liang, Y. High-content ductile coherent nanoprecipitates achieve ultrastrong high-entropy alloys.

Feng, R. Design of light-weight high-entropy alloys. Entropy 18 , Phase stability and transformation in a light-weight high-entropy alloy. Rickman, J. Materials informatics for the screening of multi-principal elements and high-entropy alloys.

Coury, F. High throughput discovery and design of strong multicomponent metallic solid solutions. Exploration and development of high entropy alloys for structural applications. Entropy 16 , — Senkov, O. Accelerated exploration of multi-principal element alloys with solid solution phases.

Krein, R. Stallybrass, C. Ferritic Fe—Al—Ni—Cr alloys with coherent precipitates for high-temperature applications. Zhou, Y. A hierarchical nanostructured Fe 34 Cr 34 Ni 14 Al 14 Co 4 high-entropy alloy with good compressive mechanical properties. Shaysultanov, D. Morris, D. Laser additive manufacturing of iron aluminides strengthened by ordering, borides or coherent Heusler phase. Reed, R. Cowley, J. An approximate theory of order in alloys.

X-Ray measurement of order in single crystals of Cu 3 Au. Warren, B. X-ray Diffraction Courier Corporation, Santodonato, L. Predictive multiphase evolution in Al-containing high-entropy alloys. Wittmann, M. The structure and mechanical properties of Fe 2 AlMn single crystals.

Abu-Odeh, A. Efficient exploration of the high entropy alloy composition-phase space. Tancret, F. Designing high entropy alloys employing thermodynamics and Gaussian process statistical analysis.

Accelerated exploration of multi-principal element alloys for structural applications. Hillert, M. Phase Transformations ASM, Kaufman, L. Chang, Y. We use the ultimate stress and ultimate strain as metrics not quantitative values for relative comparison of strength and ductility.

Atomic configurations, colored according to the structure of the local atomic environments 39 , are shown in Fig. Supplementary Figure 2a—f present atomic configurations near the ultimate strain to capture the structural transitions immediately prior to and posterior to the ultimate stress.

The HCP structure regions seen in Fig. The propagation of these partial dislocations occurs in relatively lower stress until blocked by phase boundaries or other dislocations Supplementary Figure 2f , requiring an increase in stress for further motion, i. Figure 2 and Supplementary Figures 1 and 2 show that the dominant deformation mechanism is associated with FCC to BCC phase transitions in localized regions prior to the ultimate stress, while the post-ultimate stress deformation is dominated by dislocation slip within the untransformed FCC phase.

Hence, the ultimate stress in the HEA corresponds to the nucleation and propagation of partial dislocations. The observation that strain-induced phase transformations dominate the deformation in our CoCuFeNiPd HEA prior to the ultimate stress suggests that a relatively low tensile stress is required to nucleate BCC regions, compared with the larger stress required for partial dislocation nucleation.

A previous experimental study showed that the high strength of a CoCu 0. The variation of the BCC volume fraction phase transformation with strain during tensile deformation is exhibited in Fig. Figure 2f also shows that a larger volume fraction of the BCC-type structure formed in samples with SRO than no SRO over the entire strain range, including at zero strain. These BCC-type structures form as a result of local lattice distortion-induced instabilities and are dispersed randomly throughout the whole sample.

On the other hand, the sample with no SRO exhibits no initial BCC-like structure, and hence, nucleation is necessary prior to growth. To clarify the phase transformation processes observed above, we evaluate the relative stability of the FCC and BCC phases. In Step 2, we determine the mean composition around each atom including atoms in the first and second neighbor shells in the HEA with and without SRO.

In Step 3, we calculate the local phase stability i. All relevant data can be found in Supplementary Data 1. Figure 3b , e show the atomic configurations colored according to their relative phase stability for structures without and with SRO. Figure 3b demonstrates that in the system without SRO the 0 samples , most of the local atom configurations prefer the FCC structure, while a few regions of a limited spatial extent prefer the BCC structure.

Comparing Fig. Therefore, phase transformation can be understood through the relative stability of the FCC and BCC structures, as determined by the local elemental concentrations.

Regions of large composition variations from the mean occur preferentially in the systems with large SRO. In the system without SRO, few transformed regions are observed, and they are typically very small in their spatial extent, and occur more uniformly throughout the sample. The energy reduction in forming stronger FCC-preferred configurations is offset by a similar tendency for BCC-preferred configurations. These configurations qualitatively indicate that regions of high Co-Ni concentrations i.

It is interesting to note that some of the BCC domains undergo reversible transformation to the FCC phase upon unloading. Since the simulations are isothermal, this phase transformation is strain-induced rather than thermoelastic.

We performed additional simulations of bicrystal samples with grain boundaries, as shown in Supplementary Figures 8 and 9. Many strategies have been proposed to tailor structural heterogeneities to promote the strength-ductility synergy in HEAs 8.

Generally, these strategies are associated with the manipulation of grain-size heterogeneity, precipitation, dual-phase microstructures, interstitial complex, and short-range ordering Table 1. Oxygen enhanced both the strength and ductility while nitrogen increased the strength but decreased the ductility While the first four of these strategies focus on structural heterogeneities in HEAs over relatively large length scales nanometers to many micrometers , the SRO-based approach focuses on the atomic scale.

It provides a pathway for the manipulation of HEAs at the atomic level that leads to strength-ductility synergy. This approach can, of course, be combined with larger-scale approaches e. On the other hand, the crystal structure and chemical composition of a nanoscale precipitate in a HEA are well defined and generally differ from those of the HEA matrix.

Hence, we do not consider the SRO clusters as precipitates. Prior to reaching the ultimate stress, localized structural FCC to BCC phase transformations occurred that increase both the ultimate strength and ductility. These phase transformations provide the local heterogeneities necessary for dislocation formation in our single-crystal system. While grain boundaries in HEAs may serve as dislocation nucleation sites in polycrystals, the density of such sites is small, compared with that of the high density of heterogeneities induced by the highly localized BCC phases that form on annealing.

We note that phase transformation has been observed in an earlier simulation study This trend supports the deformation mechanism observed here. Figure 6 provides a schematic illustration of the proposed HEA-design strategy for the strength and ductility enhancement via SRO. First, all five elements tend to form a stable FCC structure in the random solid-solution phase i. While the Gibbs phase rule indicates that more phases can co-exist in equilibrium in an alloy with a larger number of components, multiple phases can co-exist in binary and ternary alloys, but such microstructures are fundamentally unstable.

The formation of such a composite microstructure is associated with the SRO previously identified 41 ; the SRO is associated with a large chemical-affinity disparity and high chemical-element exclusivity amongst constituent chemical elements. Clearly, multiple elements are required to form these different atomic configurations and structures; e. These different requirements on the formation of such a composite microstructure require multiple elements. Hence, it is expected that the formation of such a composite microstructure is much more prevalent in HEAs than in simple binary or ternary alloys.

Random FCC NiCo alloys with pre-existing dislocation have yield strengths dominated by solute-misfit However, NiCo has a near-zero misfit such that random NiCo alloys exhibit a very low yield strength Besides, FCCP clusters do not have pre-existing dislocation. With increasing external strain, the elastic interactions lead to a larger stress concentration at the interface, inducing more phase transformation, and thus contributing to the work-hardenability i.

At a critical moment, the nucleation of dislocations occurs at the boundary between the FCC and BCC phases Supplementary Figure 2 , indicating that the elastic interactions are also the driving force for dislocation nucleation. The evolution of a BCC domain is shown in Supplementary Figure 13 , which indicates that the BCC domain expands and phase boundaries move towards the FCC phase prior to dislocation nucleation Supplementary Figures 13b—f due to the increasing phase transformation.

Tensile-deformation simulations indicate that the ultimate strength and ductility of the HEA are both enhanced by the development of the SRO. The origin of these enhancements can be traced to the SRO-induced pseudo-composite microstructure that forms; this consists of both FCCP hardening domains and BCCP toughening domains in a matrix of marginal phase stability. The present study not only reveals the role of SRO in governing the strength and ductility of HEAs, but also provides guidelines for rationally designing HEAs with high-performance mechanical properties for engineering applications.

These potential parameters have been employed in earlier HEA simulations with reasonable results 27 , We have checked the reliability of the atomic potential used in the study from three different aspects: 1 lattice constants, 2 cohesive energies, and 3 melting points.

A good agreement in the lattice constants, cohesive energies Supplementary Table 2 and melting points Supplementary Figure 14 obtained using the atomic potential and from other sources is observed, thus validating the reliability of the atomic potential used in the study detailed analysis and comparison are presented in Supplementary Discussion: validating the reliability of the atomic potential.

The initial sample was constructed by populating atomic sites randomly with Co, Cu, Fe, Ni, and Pd subject to the near-equiatomic elemental composition constraint, i. The acceptance of each MC swap conforms to the Metropolis criterion 47 , i. Otherwise, it is accepted with probability. Otherwise, it is rejected. The MC steps are interchanged with MD relaxations to efficiently converge site occupancy and atomic displacements we perform MC swaps followed by up to MD relaxations per iteration.

Energy calculations for phase stability. The associated energies are summarized in Supplementary Data 1. To eliminate the influence of lattice distortions in the calculation of the WCPs, the atomic site occupancies are mapped to the corresponding perfect FCC structure no lattice distortion; all atoms on regular lattice sites.

The WCP calculations were performed on this lattice by counting the elemental types of 1 st -nearest neighbors. During tensile deformation, the NPT ensemble was employed in the y- and z-directions to maintain zero lateral pressure i.

Periodic boundary conditions were applied in all three directions. OVITO 39 was used to visualize atomic configurations and analyze simulation results by identifying phase structures common neighbor analysis and calculating atomic strains.

For the binary-alloy, L 1 2 AB 3 , reference system, the cohesive energy is:. Relaxation runs were done by performing spin-polarized calculations and by allowing both the ionic positions, cell volume, and cell shape to relax.

The information of open-source software and input files for simulations that support the findings of this study are available in the Supplementary Information. Zhang, D. Additive manufacturing of ultrafine-grained high-strength titanium alloys. Nature , 91—95 Wu, Z. Mechanistic origin and prediction of enhanced ductility in magnesium alloys. Science , — Martin, J. Nature , Yeh, J. Nanostructured high-entropy alloys with multiple principal elements: novel alloy design concepts and outcomes.

Cantor, B. Microstructural development in equiatomic multicomponent alloys. A , — Lim, X. Metal mixology. Nature , — Datye, A. Opportunities and challenges in the development of advanced materials for emission control catalysts. Ma, E. Tailoring heterogeneities in high-entropy alloys to promote strength-ductility synergy. George, E. High-entropy alloys. Lee, C. Temperature dependence of elastic and plastic deformation behavior of a refractory high-entropy alloy.

Zhang, Y. Microstructures and properties of high-entropy alloys. Yang, T. Multicomponent intermetallic nanoparticles and superb mechanical behaviors of complex alloys. Liang, Y. High-content ductile coherent nanoprecipitates achieve ultrastrong high-entropy alloys. Li, Z. Metastable high-entropy dual-phase alloys overcome the strength—ductility trade-off. Chen, S.

Ultrahigh-strength and ductile superlattice alloys with nanoscale disordered interfaces. Shi, P. Enhanced strength-ductility synergy in ultrafine-grained eutectic high-entropy alloys by inheriting microstructural lamellae. Wei, S. Natural-mixing guided design of refractory high-entropy alloys with as-cast tensile ductility. Wu, S. Enhancement of strength-ductility trade-off in a high-entropy alloy through a heterogeneous structure. Acta Mater. Lei, Z. Enhanced strength and ductility in a high-entropy alloy via ordered oxygen complexes.

Ding, Q. Tuning element distribution, structure and properties by composition in high-entropy alloys. Yin, B. Unusual dislocation behavior in high-entropy alloys. Zhang, F. Local structure and short-range order in a NiCoCr solid solution alloy. Zhang, R. Short-range order and its impact on the CrCoNi medium-entropy alloy. Spurgeon, S. Towards data-driven next-generation transmission electron microscopy. Li, J. Transformation induced softening and plasticity in high entropy alloys.

Influence of chemical disorder on energy dissipation and defect evolution in concentrated solid solution alloys. Jian, W. Effects of lattice distortion and chemical short-range order on the mechanisms of deformation in medium entropy alloy CoCrNi.

Li, Q. Strengthening in multi-principal element alloys with local-chemical-order roughened dislocation pathways. Antillon, E. Chemical short range order strengthening in a model FCC high entropy alloy.

Jiang, C. Efficient ab initio modeling of random multicomponent alloys.