Multicomponent Alloy Systems Research Articles

A cluster-formula composition design approach based on the local short-range order in solid solution structure

The composition design is of importance for developing high-performance complex alloys and is also the primary step to realize a new mode for material development via theoretical prediction and experimental verification, in comparison with the traditional experience-oriented experiments. Traditional alloy design approaches, including Hume-Rothery rule, electron theories, equivalent method, computer simulation, etc., are first reviewed from the viewpoints of their theoretical basis and applicability to limitations. Almost all the traditional alloys are based on solid solution structures, in which the typical characteristic is the chemical short-range order (CSRO) of the solute distribution. We propose a cluster-plus-glue-atom model for stable solid solutions in light of CSRO. A cluster-formula composition design approach is presented for developing the multi-component high-performance alloys. The cluster-plus-glue-atom model classifies the solid solution structure into two parts, i.e., the cluster part and the glue atom part, where the clusters are centered by solute atoms, showing the strong interactions of clusters with the solvent base and the weak interactions of clusters with solute atoms. The clusters are the nearest-neighbor polyhedrons, being cuboctahedron with a coordination number of 12 (CN12) in FCC structure and rhombic dodecahedron with a CN14 in BCC structure, respectively. Then a uniform cluster-formula of[CN12/14 cluster](glue atom)x is achieved from the cluster model. Its wide applications in different multi-component alloy systems confirm its universality as a simple and accurate tool for multiple-component complex alloy composition design. Such alloy systems include corrosion-resistant Cu alloys, high-performance Ni-base superalloys, high-strength maraging stainless steels, Ti/Zr alloys with low Young's modulus, high-entropy alloys, amorphous metallic glasses, quasicrystals, etc.. The specific alloy design steps are incarnated in the up-Ti alloys with low Young's modulus. Firstly, the necessary alloying elements are chosen according to the service requirements (BCC stability and low Young's modulus). Secondly, the local cluster unit to present CSRO and the corresponding cluster formula of[(Mo, Sn)-(Ti, Zr)14](Nb, Ta)x are built, in which the occupations of the alloying elements in the cluster formula are determined by the enthalpy of mixing H between them with the base Ti. Thirdly, these designed alloys are verified experimentally, and the lowest Young's modulus appears at the up-[(Mo0.5Sn0.5)-(Ti13Zr1)]Nb1. Finally, a new Mo equivalent formula under the guidance of phase diagram features is proposed to characterize the structural stability of Ti alloy. Thus all the Ti alloy compositions with different structural types can be expressed with a uniform cluster formula, in which the structural types of alloys are determined by the Mo equivalent.

Precipitation behavior of AlxCoCrFeNi high entropy alloys under ion irradiation.

Materials performance is central to the satisfactory operation of current and future nuclear energy systems due to the severe irradiation environment in reactors. Searching for structural materials with excellent irradiation tolerance is crucial for developing the next generation nuclear reactors. Here, we report the irradiation responses of a novel multi-component alloy system, high entropy alloy (HEA) AlxCoCrFeNi (x = 0.1, 0.75 and 1.5), focusing on their precipitation behavior. It is found that the single phase system, Al0.1CoCrFeNi, exhibits a great phase stability against ion irradiation. No precipitate is observed even at the highest fluence. In contrast, numerous coherent precipitates are present in both multi-phase HEAs. Based on the irradiation-induced/enhanced precipitation theory, the excellent structural stability against precipitation of Al0.1CoCrFeNi is attributed to the high configurational entropy and low atomic diffusion, which reduces the thermodynamic driving force and kinetically restrains the formation of precipitate, respectively. For the multiphase HEAs, the phase separations and formation of ordered phases reduce the system configurational entropy, resulting in the similar precipitation behavior with corresponding binary or ternary conventional alloys. This study demonstrates the structural stability of single-phase HEAs under irradiation and provides important implications for searching for HEAs with higher irradiation tolerance.

Random alloy diffusion kinetics for the application to multicomponent alloy systems

In this paper, extensive Monte Carlo simulation results are reported on tracer and collective diffusion correlation effects in the random ternary alloy, as an example of a multicomponent alloy system. The problem of analytically describing both collective and tracer diffusion kinetics is also addressed for the random multicomponent alloy by application of a combination of the Manning theory and Holdsworth and Elliott theory. It is found that the overall results from the combined theory agree reasonably well with Monte Carlo results. This combined approach is much more accurate than Manning’s approach itself and much more manageable than the almost exact, but unfortunately difficult to use, self-consistent theory of Moleko, Allnatt and Allnatt. Some relations between the Onsager phenomenological coefficients and tracer diffusion coefficients are derived and are tested with our Monte Carlo data. Good agreement is found.

Critical evaluation of glass forming ability criteria

The available glass forming ability criteria have been examined by classifying them into four basic categories depending on critical temperatures, thermodynamic quantities, topological and kinetic aspects of glass forming alloys. A large number of glass forming alloys of widely varying natures and origin have been analysed with their experimentally measured properties to assess their glass forming ability. A novel approach using kinetic viscosity of glass forming alloys obtained by the Vogel–Fulcher–Tamman equation and the critical cooling rate calculated from the TTT diagram is demonstrated as an excellent universal glass forming ability criterion. Moreover, thermodynamic and topological modelling results through computation of a novel PHSS parameter for various alloy compositions spanning different alloy systems have rendered qualitative guidelines on propensity for glass formation in multicomponent alloy systems. Besides, the importance of kinetic interpretation of PHSS range observed for glass forming alloys is also elaborated.

Thermodynamic Calculation of Bi-Au-Lu, Nd Ternary Systems

With available melting point and hardness, the Bi-based filler alloy is considered as one choice of high-temperature Pb-free solder. Phase diagram can play an important role in the design of new type of Pb-free solder.In the present work, the thermodynamic assessments of the Au-Nd and the Au-Lu binary systems have been carried out by the Calculation of Phase Diagram (CALPHAD) method based on the available experimental data. The Gibbs free energies of the solution phases were described by subregular solution models with the Redlich-Kister equation, and those of the intermetallic compounds were described by sublattice models. A set of self-consistent and reasonable thermodynamic parameters is obtained for the binary systems, which describes the Gibbs energies of the solution phases and the intermetallic compounds phases. Additionally, combined the reported Bi-Au, Bi-Lu and Bi-Nd binary systems, the thermodynamic database of the Bi-Au-Lu and the Bi-Au-Nd ternary systems have been developed, which will provide important thermodynamic information for the phase equilibria of the multicomponent Bi-based alloy systems.

PHASE DIAGRAMS AND THEIR APPLICATIONS TO Mg ALLOYS

This work summarizes the basics of phase diagrams and their relation to the Calphad method. It is emphasized that the benefits of quantitative prediction of phase formation of selected multicomponent alloys under equilibrium and special off-equilibrium processing conditions require the development of reliable and consistent thermodynamic descriptions forming a Calphad-type thermodynamic database. The implications of intermetallic phases in multicomponent Mg alloys are explained for ternary Mg-Ce-La/Nd alloys. An introduction to applications of this approach to phase formation in as-cast and heat treated Mg alloys is given and discussed in detail for the example of ternary Mg-Al-Zn alloys. The extension to truly multicomponent alloy systems and advanced kinetic calculations is briefly depicted.

Predicting the solid solubility limit in high-entropy alloys using the molecular orbital approach

High-entropy alloys (HEAs) are currently at the research frontier of metallic materials. Understanding the solid solubility limit in HEAs, such a highly concentrated multicomponent alloy system, is scientifically intriguing. It is also technically important to achieve desirable mechanical properties by controlling the formation of topologically or geometrically closed packed phases. Previous approaches to describe the solid solubilities in HEAs could not accurately locate the solubility limit and have to utilize at least two parameters. Here, we propose to use a single parameter, the average energy of d-orbital levels, Md, to predict the solid solubility limit in HEAs. It is found that Md can satisfactorily describe the solid solubilities in fcc structured HEAs containing 3 d transition metals, and also in bcc structured HEAs. This finding will greatly simplify the alloys design and lends more flexibility to control the mechanical properties of HEAs. When 4 d transition metals are alloyed, Md alone cannot describe the solid solubility limit in fcc structured HEAs, due to the large increase of the bond strength that can be gauged by the bond order, Bo. The potential opportunities and challenges with applying the molecular orbital approach to HEAs are discussed.

Measurement of tracer diffusion coefficients in an interdiffusion context for multicomponent alloys

A recently developed novel approach of simultaneous analysis of isotope and interdiffusion profiles in binary alloy systems is significantly advanced in order to apply to the case of multicomponent alloy systems. The resulting relations for the tracer or self-diffusion coefficients allow for the avoiding of the explicit solution of the interdiffusion equations. This remarkable result means that in the experimental implementation of this new technique there is no need for multiple diffusion couples. Only two profiles of the same component are necessary for the complete analysis. These can be two different isotopes or just two spatially different parts of the same atomic species. Descriptions of three possible experimental implementations of the novel technique combined with the Sauer–Freise method are discussed. Therefore, the new development is ready to be applied experimentally and can provide valuable insight into otherwise very difficult diffusion investigations into multicomponent alloys including high-entropy alloys.

Phase stability of non-equiatomic CoCrFeMnNi high entropy alloys

The objective of this study is to experimentally and theoretically investigate the phase stability of non-equiatomic FexMn62−xNi30Co6Cr2 based high entropy alloys, where x ranges from 22 to 42at.%. Another aim is to systematically and critically assess the predictive capability of the CALPHAD approach for such high entropy alloy systems. We find that the CALPHAD simulations provide a very consistent assessment of phase stability yielding good agreement with experimental observations. These include the equilibrium phase formation at high temperatures, the constituent phases after non-equilibrium solidification processes, unfavorable segregation profiles inherited from solidification together with the associated nucleation and growth of low temperature phases, and undesired martensitic transformation effects. Encouraged by these consistent theoretical and experimental results, we extend our simulations to other alloy systems with equiatomic compositions reported in the literature. Using these other equiatomic model systems we demonstrate how systematic CALPHAD simulations can improve and accelerate the design of multicomponent alloy systems.

An Overview of Selected Phenomena in Multicomponent Diffusion

There exist several interesting phenomena and observations reported in literature for isothermal diffusion in multicomponent systems. Such phenomena include uphill diffusion, development of zero-flux planes and flux reversals for individual components, flux reversals at interfaces, and instability at interfaces and multiphase layer development. In addition, uncommon diffusion structures exhibiting unusual diffusion paths can develop in both single phase and multiphase diffusion assemblies. An overview of such phenomena is presented to highlight the role of interactions among diffusing components with the aid of selected diffusion studies carried out in multicomponent alloy systems, aluminides, silicides, and nuclear fuels.

Modeling of Non-Isothermal Ferrite Transformation in Fe-C-Mn-Si Alloys

Based on Pham’s model, the non-isothermal ferrite transformation start temperature and time of Fe-C-Mn-Si alloys were deduced. The parameters of expression were predicted combined with experimental results. The relationship between ferrite transformation parameters Q , C and composition of Fe-C-Mn-Si alloys was obtained. Then the ferrite transformation start curve of Fe-C-Mn-Si alloys can be accurately predicted by the computational method, which can be extended to more complex multi-component alloy systems.

Atomic-size and lattice-distortion effects in newly developed high-entropy alloys with multiple principal elements

A critical issue of atomic-size effects in the new class of metallic materials, high entropy alloys (HEAs), containing multi-principal alloying elements is addressed by considering the intrinsic lattice distortion. Although the development effort on these new HEAs has revealed the potential of HEAs for elevated temperature applications, a clear physical description of lattice distortions in these advanced alloys containing different atomic sizes is still lacking at the present time. In this study, we proposed a new model to address the lattice distortion of crystalline lattices in these alloys, and a series of physical parameters to address the atomic-size difference can then be defined. The optimal parameter, α2, is found to be effective in explaining the lattice distortion, intrinsic strain energy and excess entropy in HEAs, as well in other multicomponent alloy systems.

Synthesis and mechanical properties of bulk Al76Ni8Ti8Zr4Y4 alloy fabricated by consolidation of mechanically alloyed amorphous powders

Mechanically alloyed amorphous Al76Ni8Ti8Zr4Y4 (at.%) alloy powder was consolidated by high-pressure sintering process. The influence of the consolidation temperature on the structure and mechanical properties of the consolidated bulk alloys was examined by X-ray diffraction (XRD), Optical microscopy (OM), Scanning electron microscopy (SEM), Vickers Hardness Tester and Nano Indenter. Structural investigations of the bulk materials revealed that most of the amorphous structure was retained after consolidation at 623K, however, compaction at 723K and 823K caused crystallization of the amorphous phase with the appearance of white regions. The results also indicate that application of high pressure affected the crystallization products of the present alloy. Micro mechanical analysis showed that the microhardness of the bulk composites increased from 945HV0.1 to 1177HV0.1 with the consolidation temperature increasing. The evolution trends of nanohardness and Young’s modulus agree well with the Vickers hardness testing results, indentation size effect (ISE) is observed in the multicomponent alloy systems. The yield strength, Meyer exponent and the indentation impressions of these bulk alloys have also been compared.

Atomistic approach to predict the glass-forming ability in Zr–Cu–Al ternary metallic glasses

Prediction of composition-dependent glass-forming ability (GFA) remains to be a key scientific challenge in the metallic-glass community, especially in multi-component alloy systems. In the present study, we apply an atomistic approach to predict the trend of GFA effectively in the Zr–Cu–Al ternary alloy system from alloy compositions alone. This approach is derived from the first-principles calculations based on the density-functional theory and molecular dynamic (MD) simulations. By considering of both the thermodynamic and atomic-structure induced kinetic effects, the predicted GFA trend from this approach shows an excellent agreement with experimental data available in this alloy system, manifesting its capability of seeking metallic glasses with superior GFA in ternary alloy systems.

Low-temperature electrical resistivity and thermal conductivity of binary magnesium alloys

The electrical resistivity and thermal conductivity of some Mg–Al, Mg–Zn and Mg–Mn binary magnesium alloys were measured in the temperature range of 2–300K. The electrical resistivity increased with the increasing alloying content in each binary alloy system, while the thermal conductivity exhibited an opposite trend. The low-temperature thermal conductivity was understood using κ=(A/T+BT2)−1+CT2, which is found to be applicable in various binary and/or multi-component alloy systems. The parameters A, B and C were determined through numerical fitting of the experimental data. Significant differences were found in the effect of three solute atoms on the thermal conductivity of Mg. The reasons for large differences in the thermal conductivity of the three binary magnesium alloy systems are discussed. Variations in the atomic volume and the valence are believed to play an important role on the thermal conductivity of magnesium alloys.

Characterization of Continuous and Discontinuous Precipitation Phases in Pd-Rich Precious Metal Alloys

Aberration-corrected scanning transmission electron microscopy (AC-STEM), X-ray diffraction (XRD), electron backscatter diffraction, and electron probe microanalysis were applied to characterize continuous and discontinuous phase formation in precious metal alloys used in electrical contacts. The Pd-rich Paliney® (®Paliney is tradename of Deringer-Ney Inc., Bloomfield, CT) alloys contain Pd, Ag, Cu, Au, Pt (and Zn or Ni). With aging at 755 K (482 °C), nanometer-scale chemistry modulation was observed indicating spinodal decomposition. An ordered body-centered tetragonal (bct) structure was also observed with AC-STEM after the 755 K (482 °C) aging treatment and another phase, tentatively identified as β-Cu3Pd4Zn, was found by microscopy and XRD after prolonged holds at higher temperatures. During slow cooling or isothermal holds at high temperature [755 K to 973 K (482 °C to 700 °C)], a two-phase lamellar structure develops along grain boundaries by discontinuous precipitation. XRD and AC-STEM showed that the lamellar structure was comprised of Ag-rich and Cu-rich fcc phases (α 1 and α 2). The phases are discussed in relation to a pseudo-ternary diagram based on Ag-Cu-Pd, which provides a simplified representation of the discontinuous phase compositions in the multi-component alloy system.

Glass formation, microstructure evolution and mechanical properties of Zr41.2Ti13.8Cu12.5Ni10Be22.5 and its surrounding alloys

Microstructure evolutions were studied as a function of withdrawal velocity and alloy composition for Zr41.2Ti13.8Cu12.5Ni10Be22.5 and its surrounding alloys. The results demonstrate that there is a Zr(Ti)2Cu(Ni)–Zr(Ti)Be2 pseudo-binary eutectic and a Zr(Ti)–Zr(Ti)2Cu(Ni)–Zr(Ti)Be2 pseudo-ternary eutectic in the Zr–Ti–Cu–Ni–Be alloy system. The best glass-forming region was identified to be in the pseudo-binary and pseudo-ternary eutectics. The bulk metallic glass composites with different primary phases can be obtained at the composition which lies in the region between the best glass former and the corresponding primary crystalline phase. This finding confirms that multi-component alloy systems can be considered as pseudo-binary or pseudo-ternary eutectics. A metallographic approach, based on phase selection of the glass over all the competing crystalline phases, can be used to identify the best glass formers and optimum composites in multi-component alloy systems.

A modified Hoch–Arpshofen model for the calculation of enthalpies of formation of multicomponent liquid alloys

A modified model with temperature-dependent parameters is proposed based on the Hoch–Arpshofen model. The enthalpies of formation of multicomponent liquid alloy systems were calculated using the modified model. Results for the Pb-Sn-Zn, Cd-Ga-Sn, Bi-Cd-Ga-Zn, Bi-Cd-Ga-In-Zn, Cd-Ga-In-Sn-Zn and Bi-Cd-Ga-In-Sn-Zn systems are in excellent agreement with experimental data and highly accurate than obtained via the original Hoch–Arpshofen model, which indicate that the method is reliable.

Modeling precipitate growth in multicomponent alloy systems by a variational principle

A physically based state variable model is proposed to simulate precipitate growth encountered in many industry-relevant precipitation processes. The model is derived from the same variational principle used in deriving the phase field method, and is able to efficiently model diffusion-controlled precipitate growth in multicomponent alloy systems. One of the new features of the model is its treatment of the propagation of the diffusion boundary layer surrounding a growing precipitate. The model was applied to simulate spherical precipitate growth in Al–Mg–Si, Ni–Al–Ti and Fe–C alloy systems, and the simulation results were verified by a direct detailed finite volume-based approach. Compared with the approximate growth models that have been reported, e.g., the invariant field model, the SFFK model and the model by Chen et al., the proposed model’s predictions are much closer to the direct detailed approach, especially for growth under high supersaturation conditions. It is concluded that the proposed model is valuable and could be embedded into a multiscale modeling framework to deal with concurrent nucleation, growth, coarsening and macroscopic transportation. This work is also a successful case study demonstrating the potential offered by the variational principle for multiscale microstructural evolution modeling.

Numerical modelling of macrosegregation and shrinkage in large diameter steel roll castings: a mould study

Minimising macrosegregation and shrinkage defects during uphill teeming of medium carbon roll ingots has always presented a major technical challenge. Process improvements have been achieved by balancing the total heat input of a cast roll and the rate of heat extraction from the roll surface. Injecting dilute alloy through a submerged entry nozzle (SEN) into the net shaped roll ingot further mitigated the undesirable consequences of solute enrichment especially at the ingot centreline. Both the centreline segregation problems and midradius channel segregates can be significantly minimised, by combining these techniques. The objectives of this study are to determine the effect of mould thickness and material type (steel versus cast iron) on the centreline and especially on the midradius segregation, the solidification behavior in the transition region between the outer shell and the diluted interior region, as well as the mould durability. To accomplish these objectives, a multiphase multicomponent computational fluid dynamics (CFD) code was developed for studying the macrosegregation and shrinkage under various casting conditions for a 65 tonne, 1·6 m diameter steel roll processed via SEN. The developed CFD framework consists of solving for the volume fraction of phases (air and steel mixture), temperature, flow and solute balance in multicomponent alloy systems.