The Effects of Detector Efficiency on Distinguishing Solute Atoms in Random Solid Solution and Solute Clusters
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Miller, Michael K↗
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Absence of long-range chemical ordering in equimolar FeCoCrNi
Equimolar FeCoCrNi alloys have been the topic of recent research as 'high-entropy alloys,' where the name is derived from the high configurational entropy of mixing for a random solid solution. Despite their name, no systematic study of ordering in this alloy system has been performed to date. Here, we present results from anomalous x-ray scattering and neutron scattering on quenched and annealed samples. An alloy of FeNi{sub 3} was prepared in the same manner to act as a control. Evidence of long-range chemical ordering is clearly observed in the annealed FeNi{sub 3} sample from both experimental techniques. The FeCoCrNi sample given the same heat treatment lacks long-range chemical order.
36 MATERIALS SCIENCE↗
Length scales and scale-free dynamics of dislocations in dense solid solutions
The fundamental interactions between an edge dislocation and a random solid solution are studied by analyzing dislocation line roughness profiles obtained from molecular dynamics simulations of Fe 0.70 Ni 0.11 Cr 0.19 over a range of stresses and temperatures. These roughness profiles reveal the hallmark features of a depinning transition. Namely, below a temperature-dependent critical stress, the dislocation line exhibits roughness in two different length scale regimes which are divided by a so-called correlation length. This correlation length increases with applied stress and at the critical stress (depinning transition or yield stress) formally goes to infinity. Above the critical stress, the line roughness profile converges to that of a random noise field. Motivated by these results, a physical model is developed based on the notion of coherent line bowing over all length scales below the correlation length. Above the correlation length, the solute field prohibits such coherent line bow outs. Using this model, we identify potential gaps in existing theories of solid solution strengthening and show that recent observations of length-dependent dislocation mobilities can be rationalized.
36 MATERIALS SCIENCE↗
Ab initio property predictions of quinary solid solutions using small binary cells
The Set of Small Ordered Structures (SSOS) approach is an ab initio technique for modelling random solid solutions in which many small structures are averaged so that their correlation functions match those of a desired composition. SSOS has been shown to be effective in reducing the cost of density functional theory calculations relative to other well-known techniques such as cluster expansions and special quasirandom structures for modelling solid solutions. Here in this work, we demonstrate that SSOS’s can be constructed using cells with only a subset of elements while still accurately modelling multi-component systems. Specifically, we show that small binary cells can effectively model two quinary high entropy alloys – NbTaTiHfZr and MoNbTaVW – accurately capturing properties such as formation energy, lattice parameters, elastic constants, and root-mean-square atomic displacements. Overall, this insight is useful for those looking to construct databases of such small structures for predicting the properties of multi-component solid solutions, as it greatly decreases the number of structures that needs to be considered.
36 MATERIALS SCIENCE↗
Grain Boundary Segregation Suppresses Local Short‐Range Ordering in Nanocrystalline High‐Entropy Alloys
Multi-principal-element alloys like high-entropy alloys (HEAs) have potential applications in many engineering fields due to their unique mechanical/functional properties. While HEAs are generally considered random solid solutions, recent studies revealed that they are prone to short-range-ordering (SRO) due to the complex multi-pair-wise interactions among the constituent elements. Meanwhile, SROs' evolution can sometimes be deleterious, and it is necessary to have control over their evolution. Examining the AlCoCrFe-Zr model alloy, long-range ordering occurs following the expectation of enthalpic predictions. Advanced characterization techniques—transmission electron microscopy, high-energy synchrotron X-ray diffraction/pair distribution function, and atom probe tomography, reveal that SRO is suppressed in as-milled and GB-decorated NC-(AlCoCrFe)100-xZrx (x = 0–1.5 atomic %). Warren-Cowley coefficient calculations are further used to validate the suppression of SRO. Besides the low segregation enthalpies of Cr, Fe, and Zr, and the high-mixing enthalpy of Cr and Fe, the short diffusion path to GBs due to high-GB density in the NC-HEAs and the higher energy state of the GBs than the matrix promotes GB-segregation that further alters the matrix chemistry and consequently disfavors SRO formation within the matrix. Despite the GB-segregation of Cr, Fe, and Zr, the matrices and GBs remain in a random solid solution.
36 MATERIALS SCIENCE↗
The effect of interstitial carbon on the mechanical properties and dislocation substructure evolution in Fe 40.4 Ni 11.3 Mn 34.8 Al 7.5 Cr 6 high entropy alloys
A systematic study of the effects of up to 1.1 at. % carbon on the mechanical properties and evolution of the dislocation substructure in a series of a high entropy alloys (HEA) based on Fe40.4Ni11.3Mn34.8Al7.5Cr6 is presented. Transmission electron microscopy (TEM), synchrotron X-ray diffraction (XRD) and atom probe tomography (APT) were used to show that all the alloys are single-phase f.c.c. random solid solutions. The lattice constant, determined from synchrotron XRD measurements, increases linearly with increasing carbon concentration, which leads to a linear relationship between the yield strength and the carbon concentration. The dislocation substructures, as determined by a TEM, show a transition from wavy slip to planar slip and, at higher strains, and from cell-forming structure (dislocations cells, cell blocks and dense dislocation walls) to non-cell forming structure (Taylor lattice, microbands and domain boundaries) with the addition of carbon, features related to the increase in lattice friction stress. The stacking fault energy (measured via weak-beam imaging of the separation of dislocation partials) decreases with increasing carbon content, which also contributes to the transition from wavy slip to planar slip. The formation of non-cell forming structure induced by carbon leads to a high degree of strain hardening and a substantial increase in the ultimate tensile strength. The consequent postponement of necking due to the high strain hardening, along with the plasticity accommodation arising from the formation of microbands and domain boundaries, result in an increase of ductility due to the carbon addition. (C) 2016 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Dislocation structures↗
Ab initio investigation of Ti{sub 2}Al(C,N) solid solutions
M{sub n+1}AX{sub n} phases (M: early transition metal, A: IIIA- or IVA-group element, X: carbon or nitrogen) are layered ternary compounds that possess both metal- and ceramic-like properties with numerous potential applications in bulk and thin film forms, particularly under high-temperature conditions. In this work, we use the cluster expansion formalism to investigate the energetics of C-N interactions across the entire Ti{sub 2}AlC-Ti{sub 2}AlN composition range. It is shown that there is a definite tendency for ordering in the C,N sublattice. However, the molar volume and bulk modulus of the ordered structures found along the Ti{sub 2}AlC-Ti{sub 2}AlN composition range show small deviations from the (linear) rule of mixing, indicating that despite the ordering tendencies, the C-N interactions are not strong and the solution becomes disordered at relatively low temperatures. Random solid solutions of Ti{sub 2}AlC{sub 1-x}N{sub x} are simulated using special quasirandom structures (SQS) with x=0.25, 0.50, and 0.75. The thermodynamic properties of these structures are compared to those of the structures found to belong to the ground state through the cluster expansion approach. It is found that the structural properties of these approximations to random alloys do not deviate significantly from Vegard's law. The trend in the structural parameters of these SQS are found to agree well with available experimental data and the predictions of the bulk modulus suggest a very weak alloying effect--with respect to Vegard's law--on the elastic properties of Ti{sub 2}AlC{sub 1-x}N{sub x}.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Data-driven electron-diffraction approach reveals local short-range ordering in CrCoNi with ordering effects
Abstract The exceptional mechanical strength of medium/high-entropy alloys has been attributed to hardening in random solid solutions. Here, we evidence non-random chemical mixing in a CrCoNi alloy, resulting from short-range ordering. A data-mining approach of electron nanodiffraction enabled the study, which is assisted by neutron scattering, atom probe tomography, and diffraction simulation using first-principles theory models. Two samples, one homogenized and one heat-treated, are observed. In both samples, results reveal two types of short-range-order inside nanoclusters that minimize the Cr–Cr nearest neighbors (L1 2 ) or segregate Cr on alternating close-packed planes (L1 1 ). The L1 1 is predominant in the homogenized sample, while the L1 2 formation is promoted by heat-treatment, with the latter being accompanied by a dramatic change in dislocation-slip behavior. These findings uncover short-range order and the resulted chemical heterogeneities behind the mechanical strength in CrCoNi, providing general opportunities for atomistic-structure study in concentrated alloys for the design of strong and ductile materials.
36 MATERIALS SCIENCE↗
Spin-driven ordering of Cr in the equiatomic high entropy alloy NiFeCrCo
Spin-driven ordering of Cr in an equiatomic fcc NiFeCrCo high entropy alloy (HEA) was predicted by first-principles calculations. Ordering of Cr is driven by the reduction in energy realized by surrounding anti-ferromagnetic Cr with ferromagnetic Ni, Fe, and Co in an alloyed L1{sub 2} structure. The fully Cr-ordered alloyed L1{sub 2} phase was predicted to have a magnetic moment that is 36% of that for the magnetically frustrated random solid solution. Three samples were synthesized by milling or casting/annealing. The cast/annealed sample was found to have a low temperature magnetic moment that is 44% of the moment in the milled sample, which is consistent with theoretical predictions for ordering. Scanning transmission electron microscopy measurements were performed and the presence of ordered nano-domains in cast/annealed samples throughout the equiatomic NiFeCrCo HEA was identified.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Impact of chemical ordering on thermodynamic properties of point defects and Xe substitutional in U-10Mo
The accurate knowledge of defect energetics is critical to understanding the aging and irradiation behavior of U-10Mo nuclear fuel, which is selected as the fuel type for conversion of the United States High-Performance Research Reactors (HPRRs). Furthermore, using hybrid molecular dynamics and Monte Carlo (MDMC) simulation, we studied the impact of chemical ordering on the formation energies of vacancies, interstitials, and the solution energy of the Xe substitutionals. Instead of forming a random solid solution (RSS), substantial short-range-order (SRO) develops in U-10Mo, particularly at low temperatures. Mo atoms are found to repel each other and prefer U-rich local atomic environments within the 1st nearest neighbor (1NN) cutoff. Compared to the case of a RSS, the state with equilibrated Mo ordering shifts the distributions of vacancy and interstitial formation energies due to the dependence of defect energies on the local atomic environment, without a clear effect on Xe solution energy. In the operation temperature range (100–250 °C) of U-Mo fuels, neglecting SRO can lead to an inaccurate estimate of thermal equilibrium point defect concentrations by over an order of magnitude and incorrectly predict the preference among different types of dumbbells, highlighting the critical importance of accounting for the impact of chemical ordering for accurate atomistic calculations of defect properties.
Molecular dynamics and Monte Carlo (MDMC)↗
Exceptional enhancement of mechanical properties in high-entropy alloys via thermodynamically guided local chemical ordering
Understanding the local chemical ordering propensity in random solid solutions, and tailoring its strength, can guide the design and discovery of complex, paradigm-shifting multicomponent alloys. First, we present a simple thermodynamic framework, based solely on binary enthalpies of mixing, to select optimal alloying elements to control the nature and extent of chemical ordering in high-entropy alloys (HEAs). Next, we couple high-resolution electron microscopy, atom probe tomography, hybrid Monte-Carlo, special quasirandom structures, and density functional theory calculations to demonstrate how controlled additions of Al and Ti and subsequent annealing drive chemical ordering in nearly random equiatomic face-centered cubic CoFeNi solid solution. We establish that short-range ordered domains, the precursors of long-range ordered precipitates, inform mechanical properties. Specifically, a progressively increasing local order boosts the tensile yield strengths of the parent CoFeNi alloy by a factor of four while also substantially improving ductility, which breaks the so-called strength–ductility paradox. Finally, we validate the generality of our approach by predicting and demonstrating that controlled additions of Al, which has large negative enthalpies of mixing with the constituent elements of another nearly random body-centered cubic refractory NbTaTi HEA, also introduces chemical ordering and enhances mechanical properties.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Atomic-scale properties of Ni-based FCC ternary, and quaternary alloys
The aim of our study is to characterize some atomic-scale properties of Ni-based FCC multicomponent alloys. For this purpose, we use Monte Carlo method combined with density functional theory calculations to study short-range order (SRO), atomic displacements, electronic density of states, and magnetic moments in equimolar ternary NiCrCo, and quaternary NiCrCoFe alloys. The salient features for the ternary alloy are a negative SRO parameter between Ni Cr and a positive between Cr Cr pairs as well as a weakly magnetic state. For the quaternary alloy we predict negative SRO parameter for Ni Cr and Ni Fe pairs and positive for Cr Cr and Fe Fe pairs. Atomic displacements for both ternary and quaternary alloys are negligible. In contrast to the ternary, the quaternary alloy shows a complex magnetic structure. The electronic structure of the ternary and quaternary alloys shows differences near the Fermi energy between a random solid solution and the predicted structure with SRO. Despite that, the calculated EXAFS spectra does not show enough contrast to discriminate between random and ordered structures. Finally, the predicted SRO has an impact on point-defect energetics, electron phonon coupling and thermodynamic functions and thus, SRO should not be neglected when studying properties of these two alloys.
36 MATERIALS SCIENCE↗
Effective pair potential for random fcc CoCrFeMnNi alloys
The single-phase equiatomic CoCrFeMnNi alloy is a random solid solution of five elements on the face-centered cubic lattice, whose pure constituents crystallize in very different structures and exhibit diverse magnetic properties. Due to the randomness of the alloy, 80% of nearest neighbor bonds are between unlike elements and thus the details of bonding in pure structures are less important. The elastic moduli of this alloy give rise to small Cauchy pressure C 12 - C 44 , which suggests that the dominant part of bonding may be described by a simple pair potential. We test this hypothesis by developing a long-range Lennard-Jones potential in which the equilibrium crystal structures of pure constituents are taken as reference. The standard mixing rules for regular solutions are then adopted to obtain parameters for bonds between unlike elements in the quinary system. The transferability of this potential to quaternary CoCrFeNi, ternary CoCrNi, and binary FeNi alloys is investigated and the predictions compared with experiments and density functional theory calculations. By sampling over a large number of random configurations, we investigate the effect of compositional randomness on misfit volumes, energies of point defects and stacking faults, and the dislocation friction stresses experienced by moving edge and screw dislocations.
Materials Science↗
Energy and mechanical properties predictions in Fe-Ni binary system by ab initio calculations
Here, the fcc random solid solutions in Fe-Ni binary system were investigated using ab initio calculations. Density functional theory (DFT) was applied along with supercells generated by the Special Quasi-Random Structure (SQS) method to predict the enthalpy of mixing and magnetic and elastic properties. The results were compared with relevant experimental and computational data produced by other groups. The effect of SQS supercell size and relaxation procedure on the predicted properties of the alloys were also studied. Our calculations show that 16-atoms SQS model provides adequate approach to the mixing energy of the alloy. However, calculation of mechanical properties requires larger supercell. Excellent agreement between experimental and calculated elastic properties was found in fcc region of Fe-Ni system.
36 MATERIALS SCIENCE↗
A low-temperature synthetic route to ternary iron-manganese metal fluorides nanoparticles
Ternary metal fluoride Fe{sub x}Mn{sub 1−x}F{sub 2} (x = 0.00, 0.25, 0.50, 0.75, and 1.00), which is a potential cathode material for next-generation Li-ion batteries, were synthesized via a convenient, low-temperature, bottom-up solution-phase method. The lattice dimensions deduced from X-ray diffraction suggested formation of homogeneous solid solutions. With increasing Fe content, the morphology of the solid changed from cubic particles to dendritic, with an average particle size of 20–40 nm. The results suggested that this synthetic method constitutes a translatable route to large-scale production of ternary metal fluoride nanoparticles. - Graphical abstract: Homogeneous random solid solutions of ternary metal fluoride Fe{sub x}Mn{sub 1−x}F{sub 2} can be prepared by room temperature coprecipitation of precursors followed by drying and calcination at 350 °C. Display Omitted - Highlights: • Homogeneous ternary mixed metal iron-manganese fluoride Fe{sub x}Mn{sub 1−x}F{sub 2} nanoparticles prepared by room temperature coprecipitation and calcination. • Fe{sub x}Mn{sub 1−x}F{sub 2} nanoparticles form different morphology aggregates depending on the composition. • Lattice dimensions from X-ray diffraction suggested formation of homogeneous solid solutions.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Research update: Prediction of high figure of merit plateau in SnS and solid solution of (Pb,Sn)S
Direct conversion between thermal and electrical energy can be achieved by thermoelectric materials, which provide a viable route for power generation and solid state refrigeration. Here, we use a combination of energetic, electronic, and vibrational first-principles based results to predict the figure of merit performance in hole doped single crystals of SnS and (Pb,Sn)S. We find high ZT values for both materials, specifically for (Pb,Sn)S along the b -axis. Both SnS and (Pb,Sn)S have excellent power factors when doped, due to a combination of increased electrical conductivity (due to doping) and a significantly enhanced Seebeck coefficient obtained by a doping-induced multiband effect. Anharmonic phonon calculations combined with a Debye-Calloway model show that the lattice thermal conductivity of both compounds is low, due to intrinsic anharmonicity, and is lowered further by the random, solid solution nature of the cation sublattice of (Pb,Sn)S. (Pb,Sn)S exhibits a high ZT plateau ranging from 1.3 at 300 K to 1.9 at 800 K. Finally, the overall ZT of the hole doped (Pb,Sn)S crystals is predicted to outperform most of the current state-of-the-art thermoelectric sulfide materials.
36 MATERIALS SCIENCE↗
Density functional study of atomic arrangements in CrMnFeCoNi high-entropy alloy and their impact on vacancy formation energy and segregation
Here, using the density functional theory-coupled Monte Carlo approach, we explored the chemical short-range order (SRO) and element segregation in equimolar CrMnFeCoNi alloy. We found that state-of-the-art approximation of random element distribution is only applicable at > 1100 K close to the melting temperature, while the Cr-Cr repulsion driving the system stabilization and accompanying the formation of cubic Cr sublattice, and mild Ni-Ni attraction are the most prominent pair interactions at lower temperatures. Chemical potential and vacancy formation energy calculations indicate that Cr is most sensitive to the local chemical environment, making Cr atoms most stabilized when the preferred SRO is introduced. While the vacancy formation is predicted equally probable among five constituting elements in the random solid solution, Cr and Ni atoms show the lowest vacancy formation energies in the structure with SRO. Furthermore, distinct element segregation was predicted in the vicinity of planar defects, including symmetric tilt grain boundary and stacking fault, which we correlated to the site- and chemistry-dependent atomic volume and bond lengths. It suggests that the local mechanical strain and bond energy induce the SRO development and element segregation: Namely, the system takes advantage of segregation of Ni atoms having large atomic volume or Cr-Cr pairs having elongated bond lengths to fill in the excess volume at defects that relaxes the mechanical strain field and optimizes bond energy distribution. The correlation between the SRO and properties of CrMnFeCoNi alloy needs further investigations, which is expected to greatly help understand and control the properties of high-entropy alloys.
36 MATERIALS SCIENCE↗
Investigation of the structure and chemical nature of Pd fission product agglomerations in irradiated TRISO particle SiC
Tristructural-isotropic (TRISO)-coated fuel particles are used in high-temperature gas-cooled nuclear reactors. Although the polycrystalline 3C-SiC layer acts as the main barrier to fission product release, post-irradiation examinations have shown that certain metallic fission products are found outside of the TRISO coated particle, with no observable micro-cracks or other mechanical failure feature. In this study, an atomic resolution transmission electron microscopy investigation of a SiC layer of a neutron irradiated (19.38% fissions per initial metal atom average burnup; 1072°C time-averaged temperature) TRISO-coated particle from the first advanced gas reactor experiment at Idaho National Laboratory containing mainly Pd and U was conducted. The fission product Pd was found to be present at dislocation cores associated with twins, stacking faults, and their intersections. The Pd present at the dislocation cores were bonded to Si, suggesting that the diffusion of Pd along the SiC dislocation cores involves the formation of Pd-Si bonds. Evidence of single atom grain boundary migration was also found. Fission product agglomerations at grain boundaries most likely consist of a random solid solution containing Si-FP, Si-C, and C-C type bonding arrangements. No difference in the Si- or C-bonding environment is found for the unoccupied grain boundary adjacent to a fission product agglomeration compared to the bulk SiC.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗