The operational demands that continue to be placed on machinery are leading researchers to identify new metal alloys that can handle more extreme operating conditions. Traditionally, new alloys contain one dominant metal that is supplemented with much smaller percentages of other materials to increase specific physical and mechanical properties.

An appealing option is to evaluate high-entropy alloys. Wei Chen, associate professor of materials science and engineering at Illinois Institute of Technology in Chicago, says, “The initial definition of high-entropy alloys was a single-phase material that is prepared from equimolar amounts of multiple elements. This definition has now been updated to indicate that high-entropy alloys formed from equimolar amounts of multiple elements can exhibit multiple phases.”

Chen believes that the large number of potential high-entropy alloys means that this is a very large design space. He adds, “With the potential to combine multiple elements, the number of combinations that may produce new alloys is astronomical.”

This can lead to the development of new alloys with potentially beneficial characteristics for use in specific applications. A previous TLT article¹ gives an example of a high-entropy alloy with a hexagonal close-packed structure. Researchers converted a face-centered cubic high-entropy alloy based on chromium, manganese, iron, cobalt and nickel to a hexagonal close-packed structure under high pressure empirical conditions. Once the pressure is relieved, the alloy reverts to a face-centered cubic structure at ambient pressure but retains a high degree of hexagonal close-packed structure. The ratio of the two structures may be adjusted to produce a series of high-entropy alloys with unique properties.

Identification of the structural properties of high-entropy alloys appears to be a significant challenge. Synthesis of candidates in the laboratory is the ideal approach but has limitations. Chen says, “The problem with relying on the experimental approach to evaluate new high-entropy alloys is that most laboratories can produce only 10 candidates per year. This approach is very time consuming and costly and cannot cover all of the possible combinations.”

Modeling studies have been conducted but have only been done on a small scale. Chen says, “Most research makes the assumption that only single-phase alloys are produced, which is a limitation.”

A new theoretical study has now been reported that generates a much larger number of potential high-entropy alloys utilizing the capability of a supercomputer.

High-throughput EMTO-CPA method
Chen and his colleagues determined the physical and mechanical properties for over 370,000 high-entropy alloy compositions through the use of high-throughput first principles calculations. This approach calculates physical properties of high-entropy alloys without empirical parameters using density functional theory.

The researchers produced this large combination of high-entropy alloys from the following 14 elements: aluminum, chromium, cobalt, copper, hafnium, iron, manganese, molybdenum, nickel, niobium, titanium, tungsten, vanadium and zirconium. Chen says, “We selected these metals for our calculations because they are found in 3D and refractory high-entropy alloys, which are the two main types of these alloys currently known.”

The process to produce these calculations was to use the supercomputer to calculate properties for both equimolar and non-equimolar high-entropy alloys by employing the exact muffin-tin orbitals and coherent potential approximation (EMTO-CPA) method. Chen indicates this approach is a quantum mechanical first principles method that utilizes density functional theory.

The initial calculations yielded over 7,000 cubic high-entropy alloy structures. Elasticity properties for over 1,900 of these structures were calculated. Chen says, “We decided to study elasticity because this is an important mechanical property for any metal alloy. Elasticity also can be used as the basis to train a machine learning model using the Deep Sets architecture, which will then enable the supercomputer to predict properties more efficiently for a larger combination of high-entropy alloy compositions.”

Deep Sets exhibits high efficiency and more flexibility than many other machine learning models. For example, the order in which the metals are placed in a proposed high-entropy alloy matters for some models but not for Deep Sets.

Association rule mining is then utilized to better understand trends among combinations of specific metals and elastic properties. Figure 3 summarizes the process used by the researchers starting with selection of the metals (upper left), the use of EMTO-CPA (top middle), the Deep Sets architecture (top right) and association rule mining (bottom left). Following this workflow, the results from the association rule mining are illustrated in the graph representation (bottom middle) leading to potential alloy designs (bottom right).


Figure 3. A process known as association rule mining was used to better understand trends among combinations of specific high-entropy metal alloys theoretically calculated using high-throughput first principles calculation and calculated elastic properties. Figure courtesy of Illinois Institute of Technology.

Chen says, “Results from our study were validated using all available literature and whatever limited experimental data was available. Comparisons between data generated using the EMTO-CPA method and literature sources were compared and found to be comparable to experimental data.”

One example was work done on the widely studied Cantor high-entropy alloy prepared from iron, manganese, cobalt, chromium and nickel. Chen says, “This alloy is very interesting because its ductility increases as the temperature is reduced, which is in direct contradiction to how most metal alloys perform.”



The results from this study produced a public database that researchers can use to gain a better understanding of the potential properties of a specific high-entropy alloy. Chen says, “We are collaborating with other research groups to better understand how our theoretical approach predicts the performance of new high-entropy alloys they are synthesizing in the laboratory.”

Additional information can be found in a recent article² or by contacting Chen at wchen66@iit.edu.

REFERENCES
1. Canter, N. (2017), “Hexagonal close-packed high-entropy alloy,” TLT, 73 (8), pp. 14-15. Available here.
2. Zhang, J., Cai, C., Kim, G., Wang, Y. and Chen, W. (2022), “Composition design of high-entropy alloys with deep sets learning,” npj Computational Materials, 8, 89.