There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

https://dc.engconfintl.org/cgi/viewcontent.cgi?article=1032&context=superalloys_ii

A critical review of high entropy alloys and related concepts

Alloying has long been used to confer desirable properties to materials. Typically, it involves the addition of relatively small amounts of secondary elements to a primary element. For the past decade and a half, however, a new alloying strategy that involves the combination of multiple principal elements in high concentrations to create new materials called high-entropy alloys has been in vogue. The multi-dimensional compositional space that can be tackled with this approach is practically limitless, and only tiny regions have been investigated so far. Nevertheless, a few high-entropy alloys have already been shown to possess exceptional properties, exceeding those of conventional alloys, and other outstanding high-entropy alloys are likely to be discovered in the future. Here, we review recent progress in understanding the salient features of high-entropy alloys. Model alloys whose behaviour has been carefully investigated are highlighted and their fundamental properties and underlying elementary mechanisms discussed. We also address the vast compositional space that remains to be explored and outline fruitful ways to identify regions within this space where high-entropy alloys with potentially interesting properties may be lurking. High-entropy alloys have greatly expanded the compositional space for alloy design. In this Review, the authors discuss model high-entropy alloys with interesting properties, the physical mechanisms responsible for their behaviour and fruitful ways to probe and discover new materials in the vast compositional space that remains to be explored.

High-entropy alloys

https://scholars.cityu.edu.hk/files/27103119/High_entropy_alloy_challenges_and_prospects.pdf

High-entropy alloy: challenges and prospects

High-entropy alloys are an intriguing new class of metallic materials that derive their properties from being multi-element systems that can crystallize as a single phase, despite containing high concentrations of five or more elements with different crystal structures. Here we examine an equiatomic medium-entropy alloy containing only three elements, CrCoNi, as a single-phase face-centred cubic solid solution, which displays strength-toughness properties that exceed those of all high-entropy alloys and most multi-phase alloys. At room temperature, the alloy shows tensile strengths of almost 1 GPa, failure strains of ∼70% and KJIc fracture-toughness values above 200 MPa  m(1/2); at cryogenic temperatures strength, ductility and toughness of the CrCoNi alloy improve to strength levels above 1.3 GPa, failure strains up to 90% and KJIc values of 275 MPa  m(1/2). Such properties appear to result from continuous steady strain hardening, which acts to suppress plastic instability, resulting from pronounced dislocation activity and deformation-induced nano-twinning.

/pdf/exceptional-damage-tolerance-of-a-medium-entropy-alloy-1ezzci6auz.pdf

Exceptional damage-tolerance of a medium-entropy alloy CrCoNi at cryogenic temperatures

We develop a strategy to design and evaluate high-entropy alloys (HEAs) for structural use in the transportation and energy industries. We give HEA goal properties for low (≤150 °C), medium (≤450 °C) and high (≥1,100 °C) use temperatures. A systematic design approach uses palettes of elements chosen to meet target properties of each HEA family and gives methods to build HEAs from these palettes. We show that intermetallic phases are consistent with HEA definitions, and the strategy developed here includes both single-phase, solid solution HEAs and HEAs with intentional addition of a 2nd phase for particulate hardening. A thermodynamic estimate of the effectiveness of configurational entropy to suppress or delay compound formation is given. A 3-stage approach is given to systematically screen and evaluate a vast number of HEAs by integrating high-throughput computations and experiments. CALPHAD methods are used to predict phase equilibria, and high-throughput experiments on materials libraries with controlled composition and microstructure gradients are suggested. Much of this evaluation can be done now, but key components (materials libraries with microstructure gradients and high-throughput tensile testing) are currently missing. Suggestions for future HEA efforts are given.

/pdf/exploration-and-development-of-high-entropy-alloys-for-3spkgf5vbu.pdf

Exploration and Development of High Entropy Alloys for Structural Applications

Recent multi-principal element, high entropy alloy (HEA) development strategies vastly expand the number of candidate alloy systems, but also pose a new challenge--how to rapidly screen thousands of candidate alloy systems for targeted properties. Here we develop a new approach to rapidly assess structural metals by combining calculated phase diagrams with simple rules based on the phases present, their transformation temperatures and useful microstructures. We evaluate over 130,000 alloy systems, identifying promising compositions for more time-intensive experimental studies. We find the surprising result that solid solution alloys become less likely as the number of alloy elements increases. This contradicts the major premise of HEAs--that increased configurational entropy increases the stability of disordered solid solution phases. As the number of elements increases, the configurational entropy rises slowly while the probability of at least one pair of elements favouring formation of intermetallic compounds increases more rapidly, explaining this apparent contradiction.

/pdf/accelerated-exploration-of-multi-principal-element-alloys-s5r719j0cj.pdf

Accelerated exploration of multi-principal element alloys with solid solution phases

A strategy for accelerated discovery and exploration of multi-principal element alloys was developed and used to identify new alloys within a design window of desired microstructures and properties. As an example, the strategy was applied to analyze thousands of 3- 4-, 5- and 6-component alloys at equiatomic compositions of the alloying elements. Currently available thermodynamic databases were used to assess equilibrium phase diagrams for these alloys. The validity and reliability of the calculated phase diagrams were estimated based on the extent of experimental binary and ternary data used to build the respective thermodynamic databases. Alloys with specific characteristics, such as single-phase solid solution alloys with the use temperature above 1000 °C, were identified using an automated analysis of the calculated phase diagrams. The density, elastic moduli and costs of these alloys were estimated using the rule of mixtures of pure elements and were used as additional criteria for alloy selection. This approach allowed rapid, albeit preliminary, screening of many thousands of alloys and identification of promising candidate compositions, some of which are reported in this paper, for more time intensive experimental validations and assessments.

Accelerated exploration of multi-principal element alloys for structural applications

The effect of alpha/beta solution temperature and cooling rate on the evolution of microstructure during the heat treatment of Ti-6Al-2Sn-4Zr-2Mo-0.1Si (Ti6242Si) with a partially spheroidized starting microstructure of equiaxed + remnant lamellar alpha was established. Experiments comprising induction heating to a peak temperature of 971 °C or 982 °C followed by cooling at a rate of 11 °C/min or 42 °C/min revealed that the volume fraction of the equiaxed alpha grew much more rapidly than the lamellar constituent. These results were explained semiquantitatively using simple diffusion analyses of the growth of either spherical or elliptical particles, taking into account the soft impingement of the concentration fields. Despite the much lower diffusivity of molybdenum, which appears to control the growth of primary alpha in Ti6242Si, the similarity of the overall kinetics compared to those measured previously for Ti-6Al-4V was explained on the basis of the higher supersaturations developed during cooldown in the present alloy.

Alpha/Beta Heat Treatment of a Titanium Alloy with a Nonuniform Microstructure

A single-crystal nickel-base superalloy was directionally solidified over a range of withdrawal rates to assess the benefits of using liquid-metal cooling (LMC) for small-scale castings. Cylindrical bars of 1.6-cm diameter were solidified at a rate of 3.4 mm/min using conventional (Bridgman) radiation cooling and at rates of 8.5, 12.7, and 21.2 mm/min using LMC. PROCAST modeling was used to predict dendrite arm spacings based on local thermal conditions. The LMC process exhibited higher thermal gradients and finer primary and secondary spacings of up to 50 and 70 pct, respectively, in comparison to the Bridgman process. The maximum refinement in dendritic spacings using the LMC process occurred at a withdrawal rate of 12.7 mm/min. Variability in axial and lateral dendrite spacings decreased with increasing withdrawal rate, up to the point of maximum refinement. Withdrawal rates exceeding 12.7 mm/min increased the variability in spacings and produced lateral overgrowth of the primary dendrites by secondaries and promoted formation of high-angle grain boundaries.

J. D. Miller

Papers

Exploration and Development of High Entropy Alloys for Structural Applications

Accelerated exploration of multi-principal element alloys with solid solution phases

Accelerated exploration of multi-principal element alloys for structural applications

Alpha/Beta Heat Treatment of a Titanium Alloy with a Nonuniform Microstructure

Development of Dendritic Structure in the Liquid-Metal-Cooled, Directional-Solidification Process