**Brute Force Composition Scanning with a CALPHAD Database to Find Low Temperature Body Centered Cubic High Entropy Alloys**

#### **T. P. C. Klaver \*, D. Simonovic and M. H. F. Sluiter**

Department of Materials Science and Engineering, Delft University of Technology, 2628 CD Delft, The Netherlands; darko.simonovic@gmail.com (D.S.); M.H.F.Sluiter@tudelft.nl (M.H.F.S.)

**\*** Correspondence: klaver2@gmail.com; Tel.: +31-15-2784-345

Received: 11 October 2018; Accepted: 26 November 2018; Published: 29 November 2018

**Abstract:** We used the Thermo-Calc High Entropy Alloy CALPHAD database to determine the stable phases of AlCrMnNbTiV, AlCrMoNbTiV, AlCrFeTiV and AlCrMnMoTi alloys from 800 to 2800 K. The concentrations of elements were varied from 1–49 atom%. A five- or six-dimensional grid is constructed, with stable phases calculated at each grid point. Thermo-Calc was used as a massive parallel tool and three million compositions were calculated, resulting in tens of thousands of compositions for which the alloys formed a single disordered body centered cubic (bcc) phase at 800 K. By filtering out alloy compositions for which a disordered single phase persists down to 800 K, composition 'islands' of high entropy alloys are determined in composition space. The sizes and shapes of such islands provide information about which element combinations have good high entropy alloy forming qualities as well as about the role of individual elements within an alloy. In most cases disordered single phases are formed most readily at low temperature when several elements are almost entirely excluded, resulting in essentially ternary alloys. We determined which compositions lie near the centers of the high entropy alloy islands and therefore remain high entropy islands under small composition changes. These island center compositions are predicted to be high entropy alloys with the greatest certainty and make good candidates for experimental verification. The search for high entropy islands can be conducted subject to constraints, e.g., requiring a minimum amount of Al and/or Cr to promote oxidation resistance. Imposing such constraints rapidly diminishes the number of high entropy alloy compositions, in some cases to zero. We find that AlCrMnNbTiV and AlCrMoNbTiV are relatively good high entropy alloy formers, AlCrFeTiV is a poor high entropy alloy former, while AlCrMnMoTi is a poor high entropy alloy former at 800 K but quickly becomes a better high entropy alloy former with increasing temperature.

**Keywords:** high entropy alloy; bcc; phase stability; CALPHAD; composition scanning

#### **1. Introduction**

High entropy alloys (HEAs) are at present a very active field of research within metallurgy. The vast number of possible compositions promises a very broad range of properties. While the vast majority of (near) equi-atomic combinations of alloying elements lead to alloys with poor properties, the small fraction of combinations with good properties still provides very promising prospects, spurring very active research in this area.

Originally, HEAs were defined as alloys with five or more principal elements in (near) equi-atomic amounts, which form a single disordered phase on a simple crystal lattice. Configurational entropy was thought to be the main stabilizing factor, though it was soon shown that other factors can be more important, see e.g., [1]. More recently, the focus of attention has widened. More alloys that are not (near) equi-atomic have been investigated [2]. Carbon and/or nitrogen have been

deliberately introduced to steer ferritic/austenic stability and to form finely dispersed carbides and/or nitrides to improve mechanical properties, see e.g., [3]. Compositions are chosen to deliberately create multi-phase materials that have better mechanical properties [4,5]. Stacking fault energies and relative phase stabilities in multi-phase materials are engineered to induce TRIP and/or TWIP deformation mechanisms [6–12]. Despite the extensive research effort on HEAs, the number of true HEAs found is still rather limited [13]. The vast majority of compositions lead to the formation of alloys with very brittle phases, like Laves and sigma phases [14]. Even many of the compositions that lead to alloys with good properties for applications are not truly HEAs at lower temperature. These alloys (sometimes referred to as compositionally complex alloys) may be HEAs just below the solidification temperature, but at lower temperature their equilibrium state includes additional phases [15,16]. They often have good low temperature properties thanks to the sluggish formation of additional phases, which allows the disordered single phase to persist as a meta-stable state at lower temperature.

In this work we focus on finding HEAs that retain their single disordered phase down to relatively low temperature, consisting in part of elements that promote oxidation resistance (Al up to high temperature, Cr up to intermediate temperature in environments free of water vapour). The number of non-equi-atomic composition variations with five or more elements is so large that experimental testing, even with modern high-throughput screening using samples with composition gradients, is no longer feasible. Computationally however, using CALPHAD databases to determine the stable phases as a function of temperature on a fine grid in the composition space is possible. For the six element alloys AlCrMnNbTiV and AlCrMoNbTiV, and five element alloys AlCrFeTiV and AlCrMnMoTi, and their constituent alloys, we determined in a five (four) dimensional composition space where the 'islands' of low temperature HEA stability are located, i.e., for which compositions a single disordered phase remains stable down to low temperature. Apart from determining islands of low temperature HEA stability we also determine where the 'centers' of the islands are, i.e., which compositions remain HEAs under small compositional changes. These compositions are also likely to have some margin against the inevitable error inherent in the CALPHAD method, see e.g., the mismatches in the comparison between CALPHAD predicitons and experimental results drawn up by Saal et al. [15]. The island centre compositions are predicted to be low temperature HEAs with the greatest certainty and are good candidates for experimental verification. Apart from selecting compositions corresponding to the centers of islands of HEA stability, constraints can be imposed. For example, minimum amounts of Al and/or Cr can be required to promote oxidation resistance. Also, alloys can be selected for a narrow solidification temperature range to limit segregation during solidification.

The outline of this paper is as follows: in Section 2 we provide details on our computational approach. In Section 3 we first explain our choice of the five and six element alloys we investigated and present results of a simple composition optimization for these alloys. We then present results of convergence testing of the concentration step size used in brute force scanning of the composition space for these alloys. After that, we look at the overall HEA forming qualities of the alloys and the roles that individual elements play in them through binary element projections. Finally, we present results about the islands of HEA stability for our alloys, without and with constraints for minimum concentrations of certain elements. Conclusions are reported in Section 4.

#### **2. Computational Details**

The Thermo-Calc (TC) implementation of the CALPHAD method was used to calculate stable phases. The TC high entropy alloy v2.1 database (TCHEA2.1 [17,18]) was used within TC v2017b or 2018a, run under linux. The TCHEA2.1 database contains data for the elements Al, C, Co, Cr, Cu, Fe, Hf, Mn, Mo, N, Nb, Ni, Re, Ru, Si, Ta, Ti, V, W and Zr. For these elements, full information on all binary systems and 135 ternary systems is included, as well as partial information from another 308 ternary systems. Equilibrium data for some of the elements (including Fe) is available only for ~500 ◦C and above. To avoid the hazards of extrapolation, our calculations apply to the temperature range 800–2800 K. Below 800 K diffusion is exceedingly sluggish in transition metal HEAs, so that

equilibrium calculations are in any case more applicable to the higher temperature ranges. We found that calculations over a continuous temperature range with TCHEA2.1 enter into infinite loops every few dozen compositions, making automated high-throughput calculations ineffective. Also, results are at times calculated over incomplete temperature ranges. Calculations did not go into infinite loops when calculated with a different TC database (SSOL) or when data was calculated at discrete temperatures rather than continuously over a temperature range. Hence, we calculated data with TCHEA2.1 every 50 K in the 800–2800 K range (41 temperatures).

We employed a high throughput approach that is in some ways similar to the high-throughput method used by Senkov et al. [19,20]. In their extensive study, the Pandat implementation of the CALPHAD method was used to calculate the equilibrium phases for over 100,000 equi-atomic alloys. Here we determine equilibrium phases for a large number of non-equi-atomic compositions for four alloys. We used the Console.sh command line interface within TC to run typically ~100 calculations in parallel on single cpu cores of a computing cluster. The calculation of the stable phases and their fractions at 41 temperatures takes less than a minute on one cpu core, allowing throughput of a few thousand compositions per core per day. For this work we calculated 3 million compositions in total. While e.g., using a genetic algorithm to find HEA compositions [21], possibly in combination with a constraint satisfaction algorithm [22] or performing a targeted search that optimizes an objective function (e.g., narrow solidification temperature range or single disordered phase stability down to low temperature) under constraints [23] are approaches that are all far less computationally demanding, using TC as a high throughput tool is not much limited by the required cpu time or the disk space required to store input and output files. Analysis can be time consuming if it is done post hoc in serial over hundreds of thousands of output files. Analysis should ideally be included right after each TC calculation so that it is carried out in parallel, either using external tools or the TC\_Python module.

#### **3. Results and Discussion**

#### *3.1. Selection of Alloys, Extending the HEA Temperature Range*

HEAs containing Al, Cr and Ti are rather likely to have a bcc crystal structure. Pure Cr has a bcc crystal structure and while Ti has an hcp structure at room temperature, it assumes a bcc structure above 1155 K. While pure Al has an fcc crystal lattice, it is known to promote the bcc structure in transition metal based HEAs [24]. The work by Senkov et al. [19,20] reported both five element and six element bcc HEAs (Tables 14 and 15 in [19]). TCHEA2.1 did not confirm all bcc HEAs predicted in [22], but several six element HEAs containing Al and Cr, including AlCrMnNbTiV and AlCrMoNbTiV, were confirmed to be HEAs. AlCrMnNbTiV is predicted to be a single disordered bcc phase from ~1550–1750 K, AlCrMoNbTiV from ~1200–2100 K. According to TCHEA2.1 the five element HEA AlCrTaTiV starts to form a sigma phase just before solidification is complete. AlCrFeTiV is predicted to be a disordered single bcc phase from ~1050–1800 K, AlCrMnMoTi from ~1150–1800 K. We focused our work on AlCrMnNbTiV, AlCrMoNbTiV, AlCrFeTiV and AlCrMnMoTi.

For practical applications of these four series of alloys, it is preferable that the temperature at which other (brittle) phases appear is decreased and the amount of other phases formed is reduced. A simple way to achieve this is to determine what the composition of the disordered bcc phase and alternate phases is at a lower temperature, where multiple phases have formed. If the alternate phases were removed, the remaining bcc phase then forms a HEA at the lower temperature. This was tried for multiple iterations for AlCrMnNbTiV, see Figure 1.

Obviously, altering the concentrations of the individual elements within a HEA can be very effective in maintaining the HEA to a lower temperature and reducing the amount of alternate phases once they start to form. However, this way of strengthening the HEA character of an alloy produces a HEA that at low temperature is on the boundary of the HEA single phase region and the two or more phase region containing undesirable secondary phases.

**Figure 1.** Phase fractions as a function of temperature for (**A**) equi-atomic AlCrMnNbTiV (**B**) Al18Cr10Mn13Nb12Ti21V26 (**C**) Al15Cr12Mn17Nb3Ti10V43.

The smallest change in composition in some directions already leads to the formation of secondary phases. In order to find an alloy that is a HEA 'with margin to spare', we want to find the compositions that remain HEAs under all small composition changes.

#### *3.2. Convergence Testing for Scanning Part of the Composition Space*

Scanning all possible five and six element alloy compositions at fine 1% increments requires going through more compositions than is feasible. In order to limit the number of compositions required, we limit the portion of the composition space that we cover and for that limited part of the composition space, we conduct convergence tests of the concentration increment, to see how fine a mesh is required. We limit the part of the composition space by requiring that no element in a HEA should be a majority constituent, i.e., the concentration of any element should be <50 atom%. Within the selected part of the composition space, atom percentages are varied from 1 to 49% for all but one element and the concentration of the last element is set to reach 100% in total. If the concentration of the last element has to be negative or larger than 50%, the composition is rejected. For five/six element alloys, each element has the role of 'filler-up' once and that of 'independent variable' four/five times. It should be noted that while the independent and filler-up elements have the same concentration increment, the possible concentrations of the filler-up element are shifted compared to those of the other elements. For example, the composition closest to a binary alloy has 49% of one element, 1% for four elements, leaving 47% for the filler-up element. Thus with a 4% concentration increment, the independently varied elements have concentrations of 49, 45, ... 5, 1% while the filler-up element has concentrations of 47, 43, ... , 7, 3%. Thus the possible element concentrations of the independently varied and filler-up elements are on sub-grids that have the same spacing but are shifted from each other. Hence a 4% concentration increment will result in some element concentrations being only 2% apart. Following the scheme outlined above, the numbers of compositions for five and six element alloys are as shown in Table 1.


**Table 1.** Numbers of compositions for five and six element alloys for different concentration spacings.

\* not calculated with TC in our study.

The results we are most interested in are the shapes of low temperature islands of HEA stability. The convergence tests should therefore determine how much these vary with the concentration spacing. We show a number of two-dimensional projections for AlaCrbFecTidV1-a-b-c-d in Figure 2 and for AlaCrbMncNbdTieV1-a-b-c-d-e in Figure 3.

**Figure 2.** Two-dimensional projections for AlaCrbFecTidV1-a-b-c-d, showing at which concentrations for two elements the alloy forms a bcc HEA at 800 K. Three concentration dimensions are flattened out to arrive at the two-dimensional projection. The concentrations of the three elements not shown can be any one or multiple combinations, i.e., a circle indicates that for the corresponding concentration of the two elements shown, there is at least one and in most cases there are many combinations of concentrations of the other three elements for which the alloy forms a HEA at 800 K. The concentration increments in the top, middle and bottom figures are 6, 4 and 2%, respectively.

In the small sampling of projections in Figures 2 and 3 there are only single islands of HEA stability, there are no small separate islands. Also, the islands are solid without holes in them. Generally the size of the islands is many times larger than the concentration spacing. The concentration spacing therefore only influences the outer edges of the islands. At a coarser spacing, some detail of the shapes of outer edges of the islands is lost, but the overall shapes of the islands are preserved. This means that for the cases shown, a relatively modest number of compositions on a coarse grid in composition space already provide most information about islands of low temperature HEA stability.

#### *3.3. The Different Roles of Alloying Elements*

Figures 4–7 show binary projections as in Figures 2 and 3 for all possible binary combinations in our alloys.

**Figure 4.** Two-dimensional projections for AlaCrbFecTidV1-a-b-c-d, showing at which concentrations for two elements the alloy forms a bcc HEA at 800 K. Three concentration dimensions are flattened out to arrive at the two-dimensional projection. The concentrations of the three elements not shown are as explained in the caption of Figure 2. The concentration increments are 2%.

**Figure 5.** *Cont.*

**Figure 5.** Two-dimensional projections for AlaCrbMncModTi1-a-b-c-d, showing at which concentrations for two elements the alloy forms a bcc HEA at 800 K. Three concentration dimensions are flattened out to arrive at the two-dimensional projection. The concentrations of the three elements not shown are as explained in the caption of Figure 2. The concentration increments are 2%.

**Figure 6.** *Cont.*

**Figure 6.** Two-dimensional projections for AlaCrbMncNbdTieV1-a-b-c-d-e, showing at which concentrations for two elements the alloy forms a bcc HEA at 800 K. Four concentration dimensions are flattened out to arrive at the two-dimensional projection. The concentrations of the four elements not shown are as explained in the caption of Figure 2. The concentration increments are 4%.

**Figure 7.** Two-dimensional projections for AlaCrbMocNbdTieV1-a-b-c-d-e, showing at which concentrations for two elements the alloy forms a bcc HEA at 800 K. Four concentration dimensions are flattened out to arrive at the two-dimensional projection. The concentrations of the four elements not shown are as explained in the caption of Figure 2. The concentration increments are 4%.

In interpreting Figures 4–7, it is worth pointing out that a lot of information is left out of the two-dimensional projections. What appears to be a single island may in fact consists of several separate islands in the dimension perpendicular to the projection (which contains all the information of the other elements than the two being shown), that overlap into a single island when shown as a two-dimensional projection.

Figures 4–7 show that the various elements in the four alloys play distinct roles. On the one hand, Fe and Ti in AlCrFeTiV hardly participate in forming a HEA. Single disordered bcc phases in AlCrFeTiV can form, but they are essentially ternary alloys, without Fe or Ti. On the other hand, Mo and Ti in AlCrMoNbTiV can form HEAs with the other elements at any combination of concentrations. In between these two extremes, a variety of other behaviors can be observed. HEA islands that cover part of the two-element projections may extend mutually over the full 0–50% range for both elements or over the full range for one element but part of the range for the other, or over part of the range for both elements. A minimum concentration of the two elements can be required, indicated by a lack of circles around the origin, such as for TiV in AlCrMnNbTiV, see Figure 6. The HEA island may be formed under an inversely proportional line, such as for CrNb in AlCrMnNbTiV, see Figure 6. The maximum percentage of one element as a function of the other may not follow a monotonous line, there may be minima and maxima such as for AlMn and AlV in AlCrMnNbTiV, see Figure 6. V in AlCrMnNbTiV in particular gives many minima and maxima in the two-dimensional projections in Figure 6. There may even be an archipelago of separate islands of stability, as is the case with the thin, stretched-out islands for AlCrMnMoTi, see Figure 5. Islands are seen to feature a great variety of shapes, including bays, peninsular outcroppings and satellite islands, see AlCr, AlNb and CrV in AlCrMoNbTiV, Figure 7. Contrary to the results of convergence testing in Section 3.2, some of these features would be lost if the calculations were carried out on a coarser grid.

Overall, the two six element alloys appear to be more promising candidates for forming low temperature HEAs than the two five element alloys. For AlCrMnNbTiV and AlCrMoNbTiV 17,830 (3.8%) and 17,289 (3.7%) out of 473,382 compositions sampled were single phase HEAs at 800 K. For AlCrFeTiV and AlCrMnMoTi only 356 (0.041%) and 785 (0.091%) out of 862,750 compositions sampled were single phase HEAs at 800 K. In Figures 6 and 7 on average 64% and 67% of the grid points of the two-dimensional projections for AlCrMnNbTiV and AlCrMoNbTiV have circles on them, while in Figures 4 and 5 these percentages are only 6.8% and 9.4% for AlCrFeTiV and AlCrMnMoTi. The supplementary material contains the list of compositions calculated and for each composition, whether that composition is a HEA at 800 K or not and what the phases and phase fractions are at 800 K for the four alloy systems.

#### *3.4. Temperature Dependence of HEA Stability*

Figure 8 shows the fraction of alloy compositions for which a HEA is formed as a function of temperature.

Figure 8 shows that both six element alloys are strong HEA formers, with 4% of compositions being HEAs at 800 K and the HEA fraction of fully solid alloys reaching over 90% at 2000 K. The much lower melting temperature of Mn (1519 K) compared to Mo (2896 K) increases the fraction of (partly) molten alloys at 2000 K but it does not greatly increase the onset of melting, since melting is likely to occur first for compositions rich in low-melting metals like Al. Also, alloys with little Mn or Mo are almost the same. In contrast to the six element alloys, AlCrFeTiV obviously has poor HEA forming qualities. AlCrMnMoTi is in between the six element alloys and AlCrFeTiV, with a very low fraction of HEAs at 800 K, but the fraction rapidly increases with temperature, surpassing that of the six element alloys and reaching 100% at 1750 K. Figure 9 shows the average concentrations of individual elements in HEAs as a function of temperature.

**Figure 8.** Fractions of alloy compositions for which a HEA is formed, as a function of temperature. Solid curves represent the number of HEAs as a fraction of all compositions, including those that are (partly) molten. Dashed curves represent the number of HEAs as a fraction of compositions for which the alloys are still completely solid.

**Figure 9.** Average atom percentages of elements as a function of temperature, averaged over those compositions that form HEAs.

It is perhaps surprising to observe that in AlCrMnNbTiV and AlCrMnMoTi, Mn is the element that is the most reduced in concentration at higher temperatures, while pure Mn has a far higher melting temperature (1519 K) than pure Al (933 K). At present we are not able to explain this. For AlCrFeTiV the average composition shown in Figure 9 does not actually lie inside a HEA island for most of the temperature range. For the other three alloys the average concentrations shown in Figure 9 do lie inside HEA islands for all but a few of the lowest temperatures.

It should be noted that our calculations assume thermodynamic equilibrium and therefore homogenous phases. During solidification usually concentration gradients in the solid state develop so that our results may deviate from experimentally prepared materials.

#### *3.5. HEA Island Centers*

The center of a HEA island is here defined as the HEA composition that is furthest removed from any composition that is not a HEA. The distance between the island center and the closest non-HEA composition defines a body around the island center that contains a subset of the compositions that form the island. The size of the body indicates how much the concentrations of any element(s) can be varied from the island center while the alloy still remains a HEA. The island center—closest non-HEA distance can be calculated as the Euclidian distance (in which case the body is a high-dimensional spheroid) or Manhattan distance (in which case the body is a high-dimensional polyhedron, with a larger volume than the spheroid). Since we allow concentrations up to 50%, an island center may be close to 50% for one or two elements. Therefore it needs to be decided what to do with compositions on grid points on or outside the 50% boundary, for which there is no data. On the one hand, since the vast majority of compositions are not HEAs, it could be assumed that any composition on or outside the 50% boundary is not a HEA. This means that the sphere or polyhedron around the center must lie entirely within the 50% boundaries. On the other hand, if there is a part of an island of HEA stability bordering the 50% boundary, it is reasonable to assume that the island would not end abruptly at the 50% boundary but extend some distance beyond it as well. Therefore it could be argued that the center of the island needs to lie within the 50% boundary, but that part of the sphere or polyhedron may lie outside it. These two scenarios represent extremes for the smallest and biggest possible spheres/polyhedra and specific cases will usually lie somewhere in between. We shall present results for both scenarios, where all compositions at or beyond 50% are assumed to be non-HEAs ('boundary\_on') or where compositions at or beyond 50% are assumed to be HEAs ('boundary\_off'). For the former scenario, non-HEA composition data points are added (i.e., defined, not calculated with TC) for all compositions where one or two elements have a 50% concentration. As an example, Table 2 shows the island center(s) composition for AlCrMnNbTiV.

The alternative, equally valid island center compositions indicated by the asterisks in Table 2 are compositions like 3, 1, 1, 25, 21, 49% or 1, 1, 3, 21, 25, 49% Al, Cr, Mn, Nb, Ti, V.

Under boundary\_on condition, the Euclidian distance between the island center and the nearest non-HEA compositions is √102 = 10.1%. This is only a few times the concentration increment, hence the figure of 10.1% is not very precise. However, it does mean that the alloy will remain a HEA under limited composition changes. For example, if any one element is changed 9% in one direction and four other elements are changed 2% in the opposite direction and one element is changed 1% in the opposite direction, the resulting alloy should still be a HEA. Table 3 shows the island center compositions for all four of our HEAs and the distances to the closest non-HEA compositions.

As in Figures 4–7, the compositions in Table 3 show that the six element alloys are much better HEA formers than the five element alloys at 800 K. The island radii for the five element alloys are so small that there are not really any HEA islands, just a few isolated HEA compositions, possibly with a very small number of their closest neighbor compositions. Finally in this section we show how HEA islands grow with temperature. Figure 10 shows the radii as a function of temperature for AlCrMnNbTiV and AlCrFeTiV.

**Table 2.** HEA island center composition for AlCrMnNbTiV, determined with different distance and boundary criteria at 800 K. Also shown are the five non-HEA compositions closest to the island center. The elements concentration spacing is 4%. An asterix behind an island center composition indicates there are other island center compositions nearby that have an equally long distance to a nearest non-HEA composition.


Unsurprisingly, the island radius pattern for AlCrMnNbTiV in Figure 10 is rather similar to the pattern of the AlCrMnNbTiV HEA fraction shown for AlCrMnNbTiV in Figure 8.

**Figure 10.** Euclidian (squares) and Manhattan (circles) radii of HEA islands around Al1Cr1Mn1Nb25Ti31V41 and Al11Cr43Fe1Ti1V44 under boundary\_off condition. Radii are here defined as the distances between the island center and the nearest non-HEA composition. Only compositions *less* than a radius away from the island center are guaranteed to be HEAs.

**Table 3.** HEA island center(s) compositions, determined with different distance and boundary criteria at 800 K. Below each composition is the distance to the nearest non-HEA composition. The elements concentration spacing is 4% for the six element alloys and 2% for the five element alloys. An asterix behind an island center composition indicates there are other island center compositions nearby that have an equally long distance to a nearest non-HEA composition.


#### *3.6. HEA Compositions with Minimum Concentration Constraints*

The compositions in Table 3 are all essentially ternary alloys, meaning they are not really conventional HEAs. For the six element alloys, the elements mostly absent from the island center compositions include Al and Cr. While oxidation resistance depends on more than just having significant amounts of Al and/or Cr present in alloys, their presence is an important enabling factor for oxidation resistance. We repeated our search for HEA islands of maximum size, but now under the condition that minimum amounts of Al and/or Cr are present in the alloys or that four or more elements must be present in a concentration equal or greater than 10%. Tables 4 and 5 show HEA island center compositions and sizes determined under these constraints.

**Table 4.** HEA island center(s) compositions, determined with different distance and boundary criteria at 800 K, under the constraint of having minimum amounts of Al and/or Cr present. Below each composition is the distance to the nearest non-HEA composition. The elements concentration spacing is 4% for the six element alloys and 2% for the five element alloys. An asterix behind an island center composition indicates there are other island center compositions nearby that have an equally long distance to a nearest non-HEA composition.



**Table 4.** *Cont.*

**Table 5.** HEA island center(s) compositions, determined with different distance and boundary criteria at 800 K, under the constraint of having four or more elements present in a ≥10% concentration. Below each composition is the distance to the nearest non-HEA composition. The elements concentration spacing is 4% for the six element alloys and 2% for the five element alloys. An asterix behind an island center composition indicates there are other island center compositions nearby that have an equally long distance to a nearest non-HEA composition.


Tables 4 and 5 show that the options for selecting HEAs with minimum Al and/or Cr content or four or more elements present in 10% or higher concentration are limited. Imposing such constraints decreases HEA island sizes, down to 0 when requiring that all elements have a 10% or higher concentration. AlCrMnNbTiV has the largest islands of HEA compositions that contain a high enough percentage of Al to promote oxidation resistance.

#### *3.7. Melting Temperature Ranges*

From a production point of view it is preferable to select alloys with narrow solidification temperature ranges in order to achieve solidification with minimal unmixing, or with unmixing on the smallest possible length scales. Since we only determine data at temperature intervals of 50 K, we can only roughly estimate solidification temperature ranges. Therefore, in Table 6 we list the number of 50 K spaced temperatures that fall within the solidification ranges.

**Alloy Average, All Compos. Average Over HEA Compos. at 800 K Average Over Non-HEA Compos. at 800 K Max. of All Compos. Max. of HEA Compos.** AlCrMnNbTiV 2.42 1.27 2.46 15 4

AlCrMoNbTiV 3.20 3.28 3.19 15 6 AlCrFeTiV 2.42 0.43 2.42 9 2 AlCrMnMoTi 4.21 1.68 4.21 15 4

**Table 6.** Number of 50 K spaced data points in the solidification temperature ranges of alloys.

Table 6 shows that alloy compositions that are a single phase HEAs at 800 K generally have rather narrow solidification ranges, in all cases six intervals of 50 K or less. On average the most promising HEA alloys from the AlCrMnNbTiV and AlCrMoNbTiV type have solidification ranges of just 1.27 and 3.28 50 K intervals. So it appears as if selecting compositions that are single phase HEAs at 800 K simultaneously also selects alloys that have desirable solidification behavior. However, the alloy with by far the narrowest solidification range, AlCrFeTiV, is also the poorest HEA former in our study. As in Section 3.4, the higher temperature results in this section have an extra deviation from experimental observations due to the artificial homogeneity and lack of any concentration gradients in our calculations.

#### **4. Conclusions**

We used the Thermo-Calc CALPHAD database to computationally investigate the HEA forming qualities between 800 and 2800 K of four alloys, AlCrMnNbTiV, AlCrMoNbTiV, AlCrFeTiV and AlCrMnMoTi. These alloys contain elements that provide oxidation resistance and were previously predicted to be HEAs at high temperature at equi-atomic compositions. Simple variations of the element concentrations away from being equi-atomic can already greatly extend the temperature range over which the alloys are HEAs. However, with a brute force compositions scanning approach, alloy compositions could be found that remain HEAs down to 800 K. By calculating the stable phases for these alloys on grids in five- or six-dimensional composition spaces, we were able to determine islands of low temperature HEA stability. Making binary alloy projections of these high-dimensional islands gives information about the overall HEA forming qualities of the alloys as well as about the roles of individual elements within the alloys. The HEA forming qualities of a combination of elements can also be gleaned from the percentage of compositions that form HEAs as a function of temperature. The compositions of the centers of the HEA islands remain HEAs under small composition changes and thus have some margin of error against inaccuracies in the TC HEA database. Applying our methodology to four alloys, we find that AlCrMnNbTiV and AlCrMoNbTiV are good HEA formers that have HEA islands of non-negligible size at 800 K and that these islands grow rapidly with increasing temperature. AlCrMnMoTi has very few HEA compositions at 800 K but rapidly develops them with increasing temperature. AlCrFeTiV is a poor HEA former at any temperature. For all alloys that have HEA islands, the island centre compositions correspond to what are essentially ternary

alloys. Therefore these most interesting compositions are at best medium entropy alloys rather than high entropy alloys. The elements mostly absent from island centre compositions include Al and Cr for AlCrMnNbTiV and AlCrMoNbTiV. Alloys with these compositions thus lack elements that are important for oxidation resistance. Imposing constraints for minimal amounts of Al and/or Cr or four or more alloying elements with >10% concentration rapidly diminishes the number of available HEA compositions, though there are compositions that meet both the requirements of forming HEAs at 800 K and containing substantial amounts of Al and/or Cr. These requirements can be combined with the additional requirement of having a narrow solidification range. Alloy compositions around Al25Cr7Mn25Nb1Ti1V41 or Al21Cr7Mn21Nb1Ti9V41 offer the best compromise between these three different criteria, according to our CALPHAD predictions. Since CALPHAD predictions are sometimes at odds with experimental results [15], we propose these two compositions for experimental verification.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/1099-4300/20/12/911/s1. The supplementary material contains the list of compositions calculated and for each composition whether that composition is a HEA at 800 K or not and what the phases and phase fractions are at 800 K for the four alloy systems.

**Author Contributions:** T.P.C.K. carried out the TC calculations, the processing of the TC output and prepared the manuscript. D.S. carried out the analysis to determine HEA island locations and sizes in composition spaces. M.H.F.S. contributed the main idea of determining HEA islands with a CALPHAD database, added further ideas during discussions throughout the research and did several rounds of critical reading and making suggestions during the preparation of the manuscript.

**Funding:** This research received funding through the ERA-NET Integrated computational materials engineering (ICME) program under project 4316 "HEAMODELL" as financed by NWO "domein Exacte en Natuurwetenschappen".

**Acknowledgments:** The authors thank Bengt Hallstedt, James Saal and Ake Jansson and others from Thermo-Calc support for their kind help with TC questions. The authors also thank Richard Huizinga for help with the TC license server and Fritz Körmann for general HEA discussions.

**Conflicts of Interest:** The authors declare no conflict of interest. The founding sponsor had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.

#### **References**


© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **First-Principles Design of Refractory High Entropy Alloy VMoNbTaW**

#### **Shumin Zheng 1,\* and Shaoqing Wang <sup>2</sup>**


Received: 28 November 2018; Accepted: 11 December 2018; Published: 13 December 2018

**Abstract:** The elastic properties of seventy different compositions were calculated to optimize the composition of a V–Mo–Nb–Ta–W system. A new model called maximum entropy approach (MaxEnt) was adopted. The influence of each element was discussed. Molybdenum (Mo) and tungsten (W) are key elements for the maintenance of elastic properties. The V–Mo–Nb–Ta–W system has relatively high values of *C*44, bulk modulus (*B*), shear modulus (*G*), and Young's modulus (*E*), with high concentrations of Mo + W. Element W is brittle and has high density. Thus, low-density Mo can substitute part of W. Vanadium (V) has low density and plays an important role in decreasing the brittleness of the V–Mo–Nb–Ta–W system. Niobium (Nb) and tantalum (Ta) have relatively small influence on elastic properties. Furthermore, the calculated results can be used as a general guidance for the selection of a V–Mo–Nb–Ta–W system.

**Keywords:** high-entropy alloys; first-principles calculation; maximum entropy; elastic property

#### **1. Introduction**

In recent years, high entropy alloys (HEAs) have emerged as an interesting area of research [1]. HEAs have superior properties compared to conventional alloys [2]. Refractory high entropy alloys (RHEAs) were developed for high temperature use. RHEAs are mainly composed of Ti, V, Zr, Nb, Mo, Cr, Ta, W, and Hf. According to the literature, most RHEAs exceed the high use temperature of currently used refractory alloys Haynes@230@, MAR-M247@, INCONEL@718 [3], and conventional Ni-based superalloys [4]. This property makes RHEAs a promising candidate for the next generation of high-temperature applications. The VMoNbTaW alloy has received the most attention because of its characteristics, such as its good strength under extreme high temperature, but it is brittle between room temperature and 600 ◦C [5]. In a VMoNbTaW system, element W is a brittle element and has high density. Density is an important factor for transportation, especially for aircraft and aerospace. A high-temperature resistance is needed for turbine disks and blades, because the efficiency of gas turbines increases with working temperature [6].

Recently, many reports have shown that the best properties of RHEAs may generally be displaced from equilibrium compositions; thus, the studied compositions become complicated [7,8]. Some research focuses on the influence of elements on alloy properties, but most studies are often carried out for elements such as Al [9], Ti [10], Mo [11], and V [12]. It is feasible to study the influence of a single element, though single element optimization fails to meet application requirements most of the time. HEAs must have at least four elements in order to exhibit a high entropy effect [13]. Studying the influence of more than one element can enormously increase experimental efforts. First-principles calculation is an effective method for developing new RHEAs. Most data obtained in previous studies for RHEAs provide information for the hardness and compression of elements [3], but little is known

about their elastic properties. Sufficiently large, homogeneous, and defect-free crystals are required to measure experimental elastic constants, so information on elastic properties is only available for a small portion of materials. Special quasi-random structure (SQS) [14] and coherent potential approximation adopted exact muffin-tin orbital (EMTO-CPA) are often used to predict the elastic properties of HEAs [15]. Elasticity is one of the fundamental properties to screen alloys and it directly relates to mechanical properties.

The present study reports a first-principles design of a VMoNbTaW alloy. The aims are to decrease the brittleness and density of a V–Mo–Nb–Ta–W system. The elastic properties of seventy different compositions were calculated. The influence of each element was discussed.

#### **2. Methodology**

CP2K was introduced for first-principles calculation and it is efficient for larger systems. CP2K is a quantum chemistry and solid-state physics software package [16]. QUICKSTEP was introduced to deal with the electronic structure. The Gaussian and plane wave (GPW) was used for the calculation of forces and energies [14]. Single-zeta valence Gaussian (SZV-MOLOPT-SR-GTH) was used as the basis set, while a 500Ry plane wave cutoff was used for the auxiliary grid. Fermi–Dirac smearing was used to accelerate the convergence to self-consistency with an electronic temperature of 300 K. In each self-consistent field (SCF) iteration step, the diagonalized Kohn–Sham matrix was introduced for solving eigenvalue issues. Additionally, Broyden mixing was used to accelerate the convergence to the total energy threshold. The value of the total energy threshold is 10−<sup>7</sup> Hartree. A Broyden–Fletcher–Goldfarb–Shanno (BFGS) minimization algorithm was introduced to deal with the geometry optimization problems. The convergence criteria for the maximum geometry change and force were 1 × <sup>10</sup>−<sup>3</sup> Bohr and 1 × <sup>10</sup>−<sup>3</sup> Hartree/Bohr, respectively.

#### **3. Maximum Entropy (MaxEnt) Model**

MaxEnt structures were generated by a Monte Carlo simulation code in python. A repeat loop was written in the code to make sure all the elements were distributed homogeneously in the model [17]. In order to obtain a relatively homogeneous MaxEnt model, hundreds of structures were generated for selection. The screen criterion is the shortest distance between the same elements should locate in a narrow range—the narrower the better [18]. The most important advantage of the MaxEnt model is that it can demonstrate lattice distortion after relaxation. MaxEnt is a supercell model, while a 4 × 4 × 4 face-centered cubic (FCC) model contains 256 atoms and a 4 × 4 × 4 body-centered cubic (BCC) contains 128 atoms, so the MaxEnt model can present HEAs with complicated element concentrations. In order to test the accuracy and consistency of the MaxEnt model, ten MaxEnt models of BCC (TiZrNbMoV) were generated. Bulk moduli *B* and *C*<sup>44</sup> were also calculated. All bulk moduli fluctuated around 143.3 (±2) GPa and all *C*<sup>44</sup> fluctuated around 36.2 (±3) GPa. The scattered diagram is shown in Figure 1. Thus, the MaxEnt approach demonstrates a good consistence for each model. The MaxEnt approach has been elaborated in Reference [16]. The elastic properties of TaNbHfZrTi and CoCrFeNiMn were predicted based on the MaxEnt approach [18,19]. The accuracy of the predicted data was proven by experimental results [20,21]. Thus, the MaxEnt approach is accurate, believable, and suitable for the study of HEAs.

**Figure 1.** Bulk modulus *B* and *C*<sup>44</sup> of ten maximum entropy (MaxEnt) models of a 4 × 4 × 4 BCC TiZrNbMoV alloy. (**a**) *B*, (**b**) *C*44.

All components of the VMoNbTaW alloy have a BCC lattice and, thus, the formation of BCC substitution solutions was the most probable. This was confirmed by diffraction analysis of these alloys [3]. The 4 × 4 × 4 MaxEnt model of V0.1Mo0.2Nb0.1Ta0.4W0.2 is shown as an example in Figure 2.

**Figure 2.** MaxEnt model of V0.1Mo0.2Nb0.1Ta0.4W0.2.

#### **4. Elastic Properties**

The calculated bulk modulus *B* and equilibrium lattice configuration were determined from the minima of the curves according to the Birch–Murnaghan equation of state (B–M EOS), as presented in Equation (1). *V*, *V*0, *B*, *E*, and *E*<sup>0</sup> are volume, equilibrium volume, bulk modulus, total energy, and equilibrium energy, respectively. In order not to exceed the elastic limit, the changes in *V* should be kept within 3%.

$$E(V) = E\_0 + \frac{9V\_0B}{16} \left\{ \left[ \left(\frac{V\_0}{V}\right)^{\frac{2}{5}} - 1 \right]^3 B' + \left[ \left(\frac{V\_0}{V}\right)^{\frac{2}{5}} - 1 \right]^2 \left[ 6 - 4\left(\frac{V\_0}{V}\right)^{\frac{2}{5}} \right] \right\} \tag{1}$$

The cubic crystal has three independent elastic constants: *C*11, *C*12, and *C*44. They can be calculated by applying small strains to the equilibrium lattice configuration, which transforms the lattice vector **a** according to the rule [22] shown in Equations (2) and (3).

$$\mathbf{a}' = \mathbf{a} \cdot (\mathbf{I} + \varepsilon) \tag{2}$$

$$
\varepsilon = \begin{pmatrix}
\varepsilon\_1 & \varepsilon\_6/2 & \varepsilon\_5/2 \\
\varepsilon\_6/2 & \varepsilon\_2 & \varepsilon\_4/2 \\
\varepsilon\_5/2 & \varepsilon\_4/2 & \varepsilon\_3
\end{pmatrix} \tag{3}
$$

*e* = (*e*1, *<sup>e</sup>*2, *<sup>e</sup>*3, *<sup>e</sup>*4, *<sup>e</sup>*5, *<sup>e</sup>*6) is the strain vector. The different values of *<sup>e</sup>* were applied to the equilibrium lattice configuration according to Table 1. The value of σ should keep within the range of (−0.03, 0.03).


**Table 1.** Vector strain and the corresponding energy.

The following equations were used to calculate Shear modulus *G*, Young's modulus *E*, and Poisson's ratio *υ*.

$$G = \frac{3\mathcal{C}\_{44} + \mathcal{C}\_{11} - \mathcal{C}\_{12}}{5} \tag{4}$$

$$E = \frac{9BG}{3B + G} \tag{5}$$

$$\nu = \frac{3B - 2G}{2(3B + G)}\tag{6}$$

#### **5. Results and Discussion**

Due to the lack of experimental data of VMoNbTaW, the elastic properties of pure V, Mo, Nb, Ta, and W were calculated to prove the accuracy of the calculated data. Table 2 shows the elastic constants and moduli of V, Mo, Nb, Ta, and W. A comparison of calculated elastic properties with experimental data was made, and the agreement was found to be quite good. The accuracy of the calculated data in the present work was also proven by comparing with the calculated results in other studies.

**Table 2.** Elastic constants and moduli of V, Mo, Nb, Ta, and W.


<sup>a</sup> Reference [23]. <sup>b</sup> Reference [24]. <sup>c</sup> Reference [25].

Seventy different compositions of the V–Mo–Nb–Ta–W system were calculated. The results are shown in Table 3. W is brittle and has high density, so three concentrations (0.1, 0.2, and 0.3) of W were studied, while four concentrations each of V, Mo, Nb, and Ta (0.1, 0.2, 0.3, and 0.4) were studied.

All the structures were found to fulfill the mechanical stability criteria. The mechanical stability criterion of the cubic structure is *C*<sup>11</sup> + 2*C*<sup>12</sup> > 0, *C*<sup>11</sup> > *C*12, *C*<sup>44</sup> > 0. *C*44, *B*, *G*, *E*, *B*/*G* and *ν* are presented in scatter-plots in Figures 3–6, respectively. The correspondence between the numbers in Table 3 and the X-axis is shown in Table 4.

**Table 3.** Elastic constants and moduli of RHEAs. *B* (GPa), *E* (GPa), *G* (GPa) and *υ* represent the bulk modulus, Young's modulus, shear modulus, and Poisson's ratio and *a* (Ả) stands for equilibrium lattice constants.



**Table 4.** The correspondence between the numbers in Table 3 and the X-axis. The first point in the X-axis involved with V is the data of number 1 in Table 3. The first point in the X-axis involved with Ta is the data of number 5 in Table 3.

#### *5.1. C44*

According to Reference [26], there is a monotonous relation between hardness and *C*44. In Figure 3, there is a regular distribution of all the points. They are distributed in two areas. The data points have the concentration of W + Mo ≥ 0.4 distributed at the top area. It is obvious that the values of *C*<sup>44</sup> are bigger than the area below. There is also a data blank area between them. *C*<sup>44</sup> increases with the increase of the W + Mo concentration. Thus, W and Mo show significant influence on *C*44. This may be due to the fact that the *C*<sup>44</sup> of Mo (125 Gpa) and W (163 Gpa) are higher than the *C*<sup>44</sup> of V (46 Gpa), Nb (31 Gpa), and Ta (82 Gpa). The densities of W and Mo are 19.350 g/cm<sup>3</sup> and 10.390 g/cm3. In order to decrease the density and keep the high hardness of the V–Mo–Nb–Ta–W system, increasing Mo concentration and decreasing W concentration may be a feasible method.

**Figure 3.** Scatter-plots of *C*<sup>44</sup> of all seventy compositions.

#### *5.2. Bulk Modulus*

According to Reference [27], bulk modulus *B* can be used to describe the average atomic bond strength. The overall trend of the influence of alloying elements on *B* is shown in Figure 4. Figure 4a indicates that with the increase of V concentration, *B* decreases, while Figure 4b indicates *B* increases with the increase of Mo concentration. Additionally, Figure 4c indicates *B* decreases slightly with the increase of Nb concentration. Figure 4d shows that the concentration of Ta has no obvious influence on *B*. *B* increases with the increase of W concentration, as shown in Figure 4e. Furthermore, data points ran periodically with the changes of element concentrations. The trend in each period is the same as the overall trend of each element. For example, in Figure 4c, *B* decreases in the Nb = 0.1 area. This can be attributed to the increase in the concentration of element V. Arrow a in Figure 4e shows *B* decreases with the increase of Nb. Arrow c in Figure 4a shows *B* decreases with the decrease of W. A sharp variation in some points (1, 2, and 3) can be seen in Figure 4. For example, point 1 in Figure 4b shows that the initial concentration of W is 0.1, while the final concentration of W is 0.3. Thus, *B* increases sharply. In summary, Mo and W can help to increase *B*. Elements V and Nb have a negative effect on *B*. *B* has a high value in each period with W + Mo ≥ 0.4.

**Figure 4.** The trend of *B* along with element concentrations: (**a**) V, (**b**) Mo, (**c**) Nb, (**d**) Ta, and (**e**) W.

*5.3. G, E, B/G, ν*

The hardness of materials can be related to Young's modulus *E* and the shear modulus *G* [28]. The general trend is that the larger these two moduli are, the harder the material. According to the Pugh criteria [29], materials with *B*/*G* < 2 are associated with brittleness; otherwise, the materials may behave as ductile. Materials with *υ* > 0.31 have good ductility. Otherwise, the materials are considered brittle.

Figure 5 shows *G* and *E* have the same trend, while *B*/*G* and *ν* also have the same trend. It can also be seen that there is an inverse relationship between them. Element V has a negative effect on *G* and *E*, and a positive effect on *B*/*G* and *ν*. Thus, the trend of *E*, *B*/*G*, and *ν* can be predicted from the trend of *G*. Figure 6 shows the trends of Mo, Nb, Ta, and W. It is obvious that W has a positive effect on *G* and *E* and exhibits a negative effect on *B*/*G* and *ν*, while elements Nb and Ta have no obvious effect. In summary, element V can help to increase the ductility of the V–Mo–Nb–Ta–W system. *G* and *E* have a relatively high value with W + Mo ≥ 0.4.

**Figure 5.** The trends of *G*, *E*, *B*/*G*, and *ν* along with V concentrations.

**Figure 6.** The trend of *G* along with element concentrations: (**a**) Mo, (**b**) Nb, (**c**) Ta, and (**d**) W.

#### **6. Conclusions**

In order to improve the ductility and decrease the density of the V–Mo–Nb–Ta–W system, the elastic properties of seventy different compositions were studied. This work concludes as follows:


**Author Contributions:** All authors contributed extensively to this study. S.Z. did the calculation work and wrote the paper; S.Z. and S.W. conceived the idea and analyzed the data. All authors have read and approved the final manuscript.

**Funding:** This work was supported by the National Natural Science Foundation of China (No.51471164) and the National Key R&D Program of China (No. 2016YFB0701302).

**Acknowledgments:** The authors thank om the Informalization Construction Project of Chinese Academy of Sciences for their computational support during the 11th Five-Year Plan Period (No.INFO-115-B01). The Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (the second phase) is also highly acknowledged. Some of the calculations in this study were done on a Tianhe-II high performance computer system in the National Supercomputer Center in Guangzhou, China.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Review* **Additive Manufacturing of High-Entropy Alloys: A Review**

#### **Shuying Chen \*, Yang Tong and Peter K. Liaw \***

Department of Materials Science and Engineering, The University of Tennessee, Knoxville, TN 37909, USA; ytong1@vols.utk.edu

**\*** Correspondence: schen38@vols.utk.edu (S.C.); pliaw@utk.edu (P.K.L.); Tel.: +1-865-974-6356 (P.K.L.)

Received: 15 November 2018; Accepted: 3 December 2018; Published: 6 December 2018

**Abstract:** Owing to the reduced defects, low cost, and high efficiency, the additive manufacturing (AM) technique has attracted increasingly attention and has been applied in high-entropy alloys (HEAs) in recent years. It was found that AM-processed HEAs possess an optimized microstructure and improved mechanical properties. However, no report has been proposed to review the application of the AM method in preparing bulk HEAs. Hence, it is necessary to introduce AM-processed HEAs in terms of applications, microstructures, mechanical properties, and challenges to provide readers with fundamental understanding. Specifically, we reviewed (1) the application of AM methods in the fabrication of HEAs and (2) the post-heat treatment effect on the microstructural evolution and mechanical properties. Compared with the casting counterparts, AM-HEAs were found to have a superior yield strength and ductility as a consequence of the fine microstructure formed during the rapid solidification in the fabrication process. The post-treatment, such as high isostatic pressing (HIP), can further enhance their properties by removing the existing fabrication defects and residual stress in the AM-HEAs. Furthermore, the mechanical properties can be tuned by either reducing the pre-heating temperature to hinder the phase partitioning or modifying the composition of the HEA to stabilize the solid-solution phase or ductile intermetallic phase in AM materials. Moreover, the processing parameters, fabrication orientation, and scanning method can be optimized to further improve the mechanical performance of the as-built-HEAs.

**Keywords:** high-entropy alloys; additive manufacturing; microstructure; mechanical properties

#### **1. Introduction**

High-entropy alloys (HEAs) and multi-principal-element (MPE) alloys were proposed by Yeh [1] and Cantor [2] in the 2000s, respectively, attracting increasing interest all over the world. It was originally defined as an alloy composed of five or more multi-principal elements, with equi- or near equi-atomic percentages [1]. However, recently, researchers extended the concept of HEAs, which now include alloys with three or four principal elements as well [3]. Usually, they have a single crystal structure, such as a body-centered-cubic (BCC) [4–6], face-centered cubic (FCC) [7–11], or hexagonal-closed packed (HCP) structure [12–15]. HEAs present superior properties, such as a combination of high yield strength and ductility [16], good microstructural stability and retained mechanical strength at elevated temperatures [17–23], strong resistance to wear [24,25], fatigue [26–31], corrosion, and oxidation [32–36].

Most previous studies have focused on cast materials and their microstructure tuning through different post-processing methods, such as cold rolling, forging, or annealing treatment [37]. However, casting defects, such as shrinkages and pores, exist in as-cast materials, thereby requiring further processing to remove these defects. Compared with the conventional up–down fabrication method, additive manufacturing (AM), a flexible processing technique, has been applied to the fabrication of

HEAs to produce materials with a complex geometry. AM, also known as three-dimensional (3D) printing, enables the fabrication of 3D objects based upon computer-aided design (CAD) models, which have been accepted as a transformative technology across multiple industries [38,39]. The AM technique has been becoming increasingly important in the materials science field and has been broadly applied in the industry for manufacturing products with complex shapes. Currently, several engineering materials can be produced by AM, such as aircraft components made of Ti alloys [40,41], Al alloys [42], stainless steel [43], and Polyamide 12 [44], which can significantly increase production efficiency and decrease the production cost due to the combined advantage of the net-shaping capability and design freedom [45]. Especially, several methods based on the AM concept were developed and commonly used in manufacturing products. They are classified as the laser metal deposition (LMD), selective laser melting (SLM, also called laser beam melting, LBM), laser metal fusion (LMF), direct metal laser sintering (DMLS) [46], or selective electron beam melting (SEBM) [39]. Direct metal deposition (DMD) and direct laser fabrication (DLF) are two representative LMD processes.

LMD is characterized by the part being cladded layer by layer [47], as shown in Figure 1. The powders are melted after being carried by the inert gas into a laser beam and are then fed onto the workpiece to fuse with the thin layer deposited previously [47]. LMD can produce the 3D product with the ultrafine microstructure and highly complex geometry based on the layer-by-layer incremental shaping and consolidation of the feedstock to a wide range of configurations. The composition of the feeding powder could be modified by in-situ alloying during LMD, e.g., alloying varied amounts of Al to a CoCrFeMnNi powder blend, which will lead to even higher flexibility and throughput production [48,49].

**Figure 1.** Schematic image of LMD. Image displayed with the permission from the authors in [50].

SEBM is a melting fabrication process by a high-power electron beam in vacuum. Metal powders are normally fed from a hopper and then distributed by a rake across a build plate. A powder layer, which is uniformly supplied on the base plate, is pre-heated by the electron beam raster scanning, as shown in Figure 2. The points built in the slice data obtained from 3D-CAD file are sequentially melted by the focused electron beam. The process of powder feeding, pre-heating, and melting will be repeated until the bulk metallic parts is completed [51]. SEBM has attracted increasingly attention in the past decade due to its unique advantages of the high energy density of the high scan speed, incident electron beam, and reduced operation cost, which make it a suitable method to produce materials used the harsh environment, such as titanium alloys, aluminum alloys, cobalt chromium alloys, and nickel-based alloys [52].

**Figure 2.** Schematic image of the SEBM process. Image displayed with permission from the authors in [53].

SLM is an AM technology applying a high-energy laser beam, by which the part is fabricated in a layer-by-layer mode through the selective melting and consolidation of the metal powder [54], as shown in Figure 3. The layer thicknesses vary in a range of 20 and 100 μm. Compared with the traditional casting and forging method, SLM attracts increasing attention due to its impressive features, such as the ability to net-shape manufacture without the dies and high geometry complexity [55].

**Figure 3.** Schematic image of the SLM process. Image displayed with permission from the authors in [56].

AM has gained increasing attention ascribed to its ability of producing parts with complex shapes. The laser-melting method has been used to HEAs to obtain coatings and bulk materials [57,58]. Brif et al. [55] studied the FeCoCrNi HEA alloy by the powder-bed technology, suggesting that the alloy remained in its single-phase solid-solution state and displayed excellent strength and ductility. Similarly, the phase evolution and mechanical properties of AlCoCrFeNi [52] and CoCrFeMnNi [59] HEAs were reported. In the current study, we review the application of AM in HEAs in terms of their microstructures, mechanical properties, and deformation mechanisms and compare them with conventional cast-HEAs.

#### **2. Microstructure Evolution during the AM Process**

#### *2.1. CoCrFeNi HEAs*

Most of the previous studies are the HEA coatings [60,61]. Here, we highlight the performance of AM applications on bulk HEAs. The CoCrFeNi alloy system has been studied most, and more compositions or systems have been developed based on this alloy. For instance, Al*x*CoCrFeNi and CoCrFeNiMn HEAs have been commonly investigated in recent years. Brif et al. [55] studied FeCoCrNi HEAs fabricated by SLM, followed by annealing treatment. X-ray diffraction (XRD) results showed a single BCC solid solution with a uniform chemical composition. No segregation could be found. Later, Karthik et al. [62] proposed a new concept of the metal–metal composite, which consists of an aluminum–magnesium alloy, the AA5083 matrix, and the nanocrystalline CoCrFeNi HEA reinforcement precipitates in 12 vol%. Scanning electron microscope (SEM) images presented a very uniform distribution of HEA particles across the layers in a multi-layer composite. No intermetallic compounds, severe deformation, or accumulation of the HEA particles could be found at the interfaces, which was further confirmed by transmission electron microscope (TEM) examination. Furthermore, the TEM results presented a dynamic recrystallized aluminum matrix with fine equiaxed grains, which illustrated various dislocation densities, and some of the grains exhibited cells and subgrains in their formative processes.

In order to improve their mechanical performance, Zhou et al. [63] obtained the C-containing FeCoCrNi HEAs fabricated by SLM with varying processing parameters. A single-FCC solid solution without the carbide phase was detected, and a uniform distribution of carbon in the matrix was found as well. Equiaxed grains existed mostly in the middle and bottom parts of the sample, and most grains in the top part were columnar. The geometry of grains in the SLM samples was found to be related to the cooling rate and thermal gradient. The electron-backscattered diffraction (EBSD) results revealed that the grain size and microstructure of the SLM specimens were highly dependent upon the laser power and scanning speed. For example, the specimen with a low power presented a larger number of equiaxed grains, and grains became irregular by increasing the scanning speed.

#### *2.2. AlxCoCrFeNi HEAs*

Based on the CoCrFeNi composition, more AM investigations were performed on both composites and simple HEAs. For instance, with the addition of Al to CorCrFeNi, various microstructures were obtained by different processes. A single FCC phase in DLF Al0.3CoCrFeNi alloys was observed by Joseph et al. [64]. A large grain structure was found to be parallel and transverse to the build direction, with a strong texture of <001>, which could be due to the extensional growth of the material along the orientation of the deposition caused by the quick cooling rate and large thermal gradient in the molten pool. It should be noted that a small amount of very fine Ni- and Al-rich particles could be detected at grain boundaries.

By increasing the content of Al to CoCrFeNi, Fujieda et al. [51] reported the BCC and FCC structures in AlCoCrFeNi after SEBM. Further EBSD results showed that the BCC crystal grew along the direction of <100>, which is a preferred orientation for crystal growth in the BCC alloy, which is along the build direction, coinciding with the heat-flux direction. Similarly, Shiratori et al. [65] prepared the AlCoCrFeNi by SEBM as well. More complex solid solutions of B2/BCC and FCC phases were obtained, which is different from the SEBM-specimen with BCC and FCC phases and the casting specimen with B2/BCC phases. Moreover, the confirmed Al–Ni-rich B2/Cr–Fe-rich BCC phases were found to be oriented along the build direction. The detailed elemental distribution in each phase is shown in Figure 4. An AlCoCrFeNi HEA with BCC, B2, and FCC phases along the grain boundaries was fabricated by Kuwabara et al. [52] by applying the SEBM method. Similarly, the SEBM samples presented fine and columnar grains along the building direction with a texture of <100>.

**Figure 4.** (**a**) The high-angle annular dark-field scanning transmission electron microscopy (HAADF–STEM) image and elemental maps obtained from the energy-dispersive X-ray spectroscopy (EDX). (**b**,**c**) Nano-beam diffraction (NBD) patterns obtained from the Al–Ni-rich and Cr–Fe-rich regions, respectively. Image displayed with permission from the authors in [65].

Li et al. [49] further investigated the properties of the ultrafine nanocrystals (UNs)-modified FeCoCrAlCu high-entropy alloy composites (HEACs) fabricated by the LMD, which presented the fine microstructure without the micro-crack with many AlCu2Zr UNs attached to the HEAC matrix. The lattice distortion was observed as well, due to the ultrafine microstructure and high diffusion of UNs destroying the atomic-equilibrium state, which increased the potential/free energy, thus leading to the formation of the lattice distortion. On the one hand, compression stress resulting from the alloying elements of the small atomic radius was generated. On the other hand, tensile stress resulting from the alloying elements of the large atomic radius was also achieved. The reciprocal interaction of these two kinds of stress fields led to decreasing stress and the formation of a relatively stable atomic group, favoring the formation of UNs.

Niu et al. [66] investigated the phase evolution with varying the volumetric-energy density (VED), as shown in Figure 5. During the SLM process, the phase is mainly composed of A2 and B2 phases. Specifically, the B2 phase was mostly found to be distributed on the boundary of the molten pool, indicating that the B2 phase was the original structure due to the strongest combination between Al and Ni elements. Thus, the other elements were homogeneously dispersed around the Al–Ni B2 phase and formed the A2 phase. As the VED increased, the B2 phase increased, while the A2 phase tended to decrease, which was mainly due to the larger VED, inducing a faster cooling rate and thus leading to more B2 phases [66].

**Figure 5.** Phase dispersion of different VEDs in SLM samples: (**a**) 68.4 J/mm3; (**b**) 83.3 J/mm3; (**c**) 97.2 J/mm3; and (**d**) 111.1 J/mm3. Image displayed with permission from the authors in [66].

Sistla et al. [67] studied the Al/Ni ratio effect on the microstructure in Al*x*FeCoCrNi2−*<sup>x</sup>* (*x* = 0.3 and 1) HEAs fabricated by the LMD method. The XRD and SEM results suggest that the studied solid solution transforms from BCC to FCC structures, which is consistent with the casting HEAs [67]. Joseph et al. [68] firstly proposed the HIP effect on the microstructure and mechanical behaviors in DLF Al*x*CoCrFeNi HEAs. The FCC, duplex FCC + BCC, and BCC solid solution were found in Al0.3CoCrFeNi, Al0.6CoCrFeNi, and Al0.85CoCrFeNi HEAs, respectively, which was similar to the casting specimens in previous reports [69]. It turned out that the HIP process removed all second-phase grain-boundary phases and segregation of the Al0.3CoCrFeNi alloy, indicating that the isothermal holding at 1100 ◦C for 2 h during HIP leads to the chemical homogenization of the material and the effectively dissolving of the grain-boundary phases, even though the HIP may induce microstructural coarsening.

#### *2.3. CoCrFeMnNi HEAs*

With the development of the AM research on HEAs, Cantor's alloys have been employed in 3D printing as well. Haase et al. [48] investigated the 3D printing of the elemental powder blend in the CoCrFeMnNi system, producing elongated features with cellular dendrite structures. In fact, the fast cooling rates during the fabrication process could contribute to the formation of a fine cellular dendrite structure. The EDX-elemental mapping suggested a more homogeneous distribution of five principal elements than that in the casting specimens. Li et al. [70] firstly studied the processability of the non-equilibrium microstructure in the SLM CoCrFeMnNi. By increasing the VED, the microstructure became much denser. They showed that the HIP process removed the microcracks, and most micropores were closed, leading to an increased density, large grains, and a more homogeneous elemental distribution. The non-equilibrium processing of SLM resulted in a greater residual-stress difference than that in the HIP specimens. The TEM examination revealed the existence of an original FCC phase and a tetragonal-precipitation phase, which were due to the ultrafine grains and a large amount of dislocations induced in the SLM process. Moreover, nanotwins were found during the SLM process without plastic deformation, which may have been due to the low stacking fault energy caused by rapid solidification.

Guo et al. [71] firstly proposed the post-machining on the SLM CoCrFeMnNi HEA specimens to investigate the machinability. SEM illustrated that the mechanical polishing led to a uniform elemental distribution and smooth surface without clear waviness even though some microcracks and very small pores were present. Piglione et al. [59] proposed the printability of a CoCrFeMnNi HEA with single-layer and multi-layer builds fabricated by the laser-powder-bed fusion. A homogeneous distribution of composition was found in the bulk of the HEA with a single FCC crystal structure and a high degree of consolidation, without the apparent elemental segregation. In the single layer, the high cooling rate resulted in much finer cells, compared with previous reports [72] with the same composition. The high hardness values may be due to the restricted moving dislocation by cell boundaries during plastic deformation. Moreover, the cells were found to be aligned along the <001> orientation because the preferred growth direction is aligned with maximum heat flux. Similar cells with a reduced number could be found in multi-layers. The alternating sequence of columnar grains dominated by two crystallographic orientations was reported, which was caused by the coupling of the extensional growth and grain selection after remelting.

In order to explore the AM materials application in a harsh environment, Qiu et al. [57] firstly reported the deformation mechanism at cryogenic temperature in the CrMnFeCoNi HEA fabricated by the LAM process. A single FCC crystal structure with a typical dendrite structure and a lattice constant of 3.598 Å were observed. The growth direction of the dendrite was found to be perpendicular to the laser-scanning direction due to the quick directional solidification. Zhu et al. [45] investigated the hierarchical microstructure in the CoCrFeNiMn HEA by SLM. The as-built specimens were obtained by controlling the processing parameters of the laser energy density, laser power, and scanning speed. The SEM images revealed that the columnar grains formed along the building direction (BD), with a <001> texture, implying epitaxial growth, which indicates that the formation of the cellular structure was correlated solidification conditions. A sub-micron cellular structure was detected under TEM, which was displayed with a large amount of dislocations and with clean interiors. No obvious segregation could be found from EDS, which was due to a fast cooling rate kinetically suppressing the segregation. After a heat treatment (HT), the cellular structure vanished with a much lower dislocation density left, suggesting their thermodynamically metastable characteristic [45]. Later, Fujieda et al. [73] investigated the SEBM method to prepare the CoCrFeNiTi-based HEA. The XRD results presented Ni3Ti intermetallic compounds with a uniform distribution in the matrix, different from the segregation in casting specimens, as shown in Figure 6. The needle-like NiTi precipitates with a basket-weave morphology contributed to the high yield strength in this SEBM specimen.

**Figure 6.** EPMA elemental maps of Ni and Ti in the as-cast sample and SEBM sample. Image displayed with the permission from the authors in [73].

#### *2.4. Ti25Zr50Nb0Ta25 HEAs*

The Ti25Zr50Nb0Ta25 refractory HEA fabricated by laser-melt deposition has been recently reported. Phase separation was found in the specimen, as shown in Figure 7a. The segregation near the grain boundary was found to be enriched in Ta and depleted in other elements, which was confirmed as a BCC crystal structure, similar to the matrix but with different compositions, shown in Figure 7b. Moreover, it was suggested that the grain size during the fabrication process was more likely influenced by the chemical partitioning of Ta in Zr-rich areas rather than the cooling rate [74]. The other MoNbTaW refractory alloy was prepared by the DMD method, but an additional remelting procedure between the powder deposition was required due to the different melting points of elements. The resultant compositional homogeneity of alloys was improved by preheating, laser parameters, geometries, and heat conduction [75].

**Figure 7.** (**a**) Ta-enriched in the grain boundary and Ta-rich dendritic core inside the grain (illustrated by red arrows). Nb, Zr, and Ti concentrations showing an opposite trend (illustrated by red arrows). (**b**) EBSD presenting the grain-orientation map. Image displayed with permission from the authors in [74].

#### **3. Mechanical Properties of AM-Processed HEAs**

#### *3.1. CoCrFeNi HEAs*

Brif et al. [55] studied the mechanical performance of FeCoCrNi prepared by SLM and compared it with a more traditional processing route of arc melting, as shown in Figure 8. It was apparent that the AM specimen presented a much higher yield strength than that in the arc-melt specimen, while still retaining a significant portion of ductility. The enhanced mechanical properties of AM specimens were ascribed to a fine microstructure, due to the large temperature gradients and rapid solidification in SLM.

**Figure 8.** Representative tensile stress–strain curves of AM specimens with a 20-μm-layer thickness. Image displayed with permission from the authors in [55].

Karthik et al. [62] investigated the mechanical properties of the aluminum-magnesium alloy, an AA5083 matrix reinforced with 12 vol.% of CoCrFeNi HEA nanoparticles, i.e., the HEAp/5083 composite, fabricated by friction deposition. The composite demonstrated a high strength, resulting from the reinforcement precipitates of nanocrystalline CoCrFeNi, with a uniform distribution in the ultra-fine-grained aluminum matrix. It was suggested that the strengthening mechanism in the single-layer/HEAp/5083 composite could be the existing load transfer from the Al matrix to the reinforcement precipitation. The fracture morphology also revealed fine HEA reinforcement particles inside many of the dimples. The encouraging mechanical properties in the HEAp/5083 composite were due to the deficiency of brittle intermetallics at the particle/matrix and layer interfaces. The influence of SLM-processing parameters on mechanical behavior was studied in other C-containing FeCoCrNi

alloys [63]. It was found that the yield strength was not significantly affected by the scanning speed and laser power. By applying the highest scanning speed of 1200 mm/s and a laser power of 400 W, the highest yield strength with a comparable ductility was obtained. It was apparent that the addition of carbon resulted in enhanced strength for FeCoCrNi, due to solid-solution strengthening. Work hardening was suggested to be caused by the interaction of dislocation–dislocation and dislocation–cellular walls since there was no deformation twinning.

#### *3.2. AlxCoCrFeNi HEAs*

The mechanical properties of the addition of Al to CoCrFeNi alloys were extensively investigated in the AM HEAs. Joseph et al. [64] studied the asymmetry of tension/compression in the Al0.3CoCrFeNi alloy with a strong preferred orientation, fabricated by the DLF method. A significant difference in work hardening after yielding could be found in compression and tension curves, even though they had similar yield strengths. The limited work hardening in the tensile experiment was caused by cracks propagating along the grain boundaries, which may have been due to the precipitates enriched in nickel and Al, developing along the grain boundaries, which was observed in the laser-fabricated Rene88DT superalloy as well. Interestingly, deformation twins could be found in compression specimens, rather than tension specimens, because the stress required for the deformation twin could not be reached in the tensile sample before the final fracture. It was suggested that the loading axis in the tensile and compressive specimens were parallel to the depositing direction, which had a significant regulation with the texture of <001>, and was well arranged for deformation twins in the compressive experiment, but failed to orient for twinning in the tension experiment, due to the fact that only in certain directions can the polar deformation twinning accommodate the shape change. Thus, a high working-hardening rate was found in the preferred direction that favors twinning in the compression sample, revealing that the strong texture in the primary material integrated with the activation of twinning contributed to the difference in work-hardening behavior in the tensile and compressive experiments.

With the increase in Al content, the mechanical properties in the AlCoCrFeNi alloy was investigated by the SEBM method [65]. The compressive stress–strain curve presented much better plasticity in SEBM specimens than that in the cast specimens [51,52], due to their finer grains obtained at a higher cooling rate. The cooling rate in the solidification process during the SEBM varied in the range of 10−3–10−5/s, which was much greater than the conventional casting case even with a water-cooled copper mold. This trend could be a reason for the improved deformability in SEBM alloys. Moreover, the generation of the FCC structure could contribute to the good ductility in SEBM materials. It was concluded that the cast specimen of AlCoCrFeNi almost solely consisted of the B2 and BCC phase mixture, which lacks the slip system and leads to a brittle fracture. However, in SEBM specimens, a substantial fraction of the ductile FCC phase was found, which will favor the multi-slip system and thus enhance ductility during the compression experiment, as shown in Figure 9.

**Figure 9.** True stress–strain curves in the cast and SEBM samples. Image displayed with permission from the authors in [65].

Similar work and results were obtained in AlCoCrFeNi alloys [51,52] as well. Moreover, the anisotropy of the compressive specimen was observed, which was ascribed to a large number of grain boundaries [51]. The SEBM sample along the BDs exhibited improved properties, but the reduced yield strength and plasticity were found in samples perpendicular to the build direction (BD). Moreover, their compressive properties were much higher than the tensile properties, which was consistent with previous studies [68]. As previously discussed, FCC and B2 ordered phases existed in the SEBM materials. The fracture of the tensile specimens was ascribed to the preferential formation and propagation of the cracks along BCC/FCC boundaries induced by the significant difference in the elastic properties of these adjacent phases. The micro-voids found in the failed specimen were attributed to the shrinkage induced by the denser FCC phases than BCC or B2 structures [45]. Li et al. [49] proposed the mechanical performance of the composite of the FeCoCrAlCu alloy deposited on the titanium alloy via the LMD method. The excellent wear resistance of materials was primarily attributed to their multiple structure, such as the quasi-crystalline/nanocrystalline phases, and the free micro-crack microstructure. The enhanced strength and ductility induced by adding the proper amount of Y2O3 content could lead to the improvement of the wear resistance. Moreover, the spreading nanoscale particles were capable of withstanding the external normal load, leading to increased wear performance.

#### *3.3. CoCrFeMnNi HEAs*

The mechanical properties and formability of CoCrFeMnNi HEAs were widely investigated by various AM methods [41–51]. Haase et al. [48] revealed the high formability and significant high hardness of CoCrFeMnNi alloys fabricated by the LMD method, producing excellent yield strength and ductility. It was clear that the yield strength of LMD-produced materials presented a much higher value than that in cast materials, which may have been due to the pronounced texture, lowering the mean Schmid factor, thus requiring higher stress to initiate dislocation motion. Furthermore, the initial high density of dislocation caused by the fast solidification and cooling in the LMD process contributed to the increased yield strength as well.

Li et al. [70] studied the mechanical properties of the CoCrFeMnNi HEA by the SLM method. Holes and cracks were reduced by increasing the VED, leading to higher ultimate tensile strength. The tensile strength was improved by HIP, which was ascribed to the closure of micro-pores and micro-cracks, accompanied by the reduced elongation. Overall, the SLM specimen presented a higher tensile strength than that in the slowly solidified HEA, which could be explained in terms of the Hall–Petch theory, which shows that decreasing the grain size leads to high strength. Moreover, the precipitation of the σ phase, preserving from high temperatures owing to rapid solidification, contributed to the improvement of the tensile strength. Furthermore, a similar investigation was performed on the strengthening mechanism in an SLM CoCrFeNiMn HEA with hierarchical microstructures [45]. All the SLM specimens presented much better mechanical properties than that in the as-cast specimens. The postmortem STEM indicated a significant dislocation arrest and retainment mechanism within the deformation cells, resulting in a distinct increase in the dislocation density within the cell walls, which is consistent with Piglione's [59] work. Moreover, the planar sliding interact with the cellular structure substantially for forming a 3D dislocation network, which dominates the deformation process in the as-built HEAs, accompanied by the additional contribution from deformation twinning. Based on the calculation of the yield strength dependent on the dislocation density, they induced that the improved strength was mostly controlled not only by grain-boundary strengthening and friction stress but also by dislocation hardening. Furthermore, the excellent uniform elongation of the as-built HEA was due to the capability of steady strain-hardening at large stress levels. Specifically, dislocations being significantly arrested and retained in the cell interior, and substantial interactions between slip bands and cellular structures, resulted in the generation of a complicated dislocation configuration, which led to a comparable strain-hardening ability.

Another way of studying LAM-fabricated HEAs was investigated to explore the deformation mechanisms at cryogenic temperatures [57]. Their yield strength and ductility were enhanced when the temperature decreased from 298 to 77 K, as shown in Figure 10. The strength in the LAM specimen was found to be higher than that in the as-cast sample, which was due to the suppressed elemental segregation and possible high dislocation density induced by the fast solidification rate in the LAM sample. Deformation twinning was found in the deformed sample. When increasing the plastic strain, the deformation twinning was more obvious. The increased deformation twinning was more dispersed as the strain reached the highest level. However, the deformation mechanism could not be dominated by deformation twinning even at high strain levels due to the limited quantity and its heterogeneous distribution. The local misorientation map indicated that the dislocation is the dominant deformation mechanism, especially with a low strain value. The density of dislocations increased rapidly and uniformly with increasing strain, which revealed that dislocations played an essential role during deformation. It was noticeable that the initial dislocation density in the LAM specimen was substantial, larger than that in the reported materials, which may have been due to rapid solidification and cooling in the LAM process. Such microstructures will undoubtedly produce an enhanced yield strength. It should be noted that, under the cryogenic condition, the deformation twinning at high strain levels could be an obstacle to moving dislocation, resulting in a continuous accumulation of dislocations, thus leading to a high work-hardening rate as well as an increased strength.

**Figure 10.** Tensile engineering stress–strain curves in the CoCrFeMnNi HEA tested at 293 K and 77 K, respectively. Image displayed with permission from the authors in [57].

Fujieda et al. [73] investigated the tensile properties of the CoCrFeNiTi-based HEA, achieved using SEBM and the subsequent solution treatment. The untreated SEBM sample presented a much higher tensile strength than that in the as-cast specimen, due to the uniform distribution of the needle-like Ni3Ti in the matrix, while a reduced ductility was found as well, which should be attributed to the cracks progressing along the boundaries between excessive Ni3Ti intermetallic compounds and the matrix.

**Figure 11.** Engineering stress-engineering strain curves of deposited, and solution-treated SEBM specimens tested at room temperature. Image displayed with permission from the authors in [73].

#### *3.4. Post-Treatment Effect*

It has been proposed that post-treatment has a significant effect on the mechanical properties of AM-processed HEAs. It is believed that defects such as residual stress may exist in a specimen during deposition, which may affect the mechanical properties. For example, after annealing at 750 ◦C, a CoCrFeNi specimen presented a reduced yield and tensile strength with a minor reduction in ductility. When annealing temperature increased to 1000 ◦C, this CoCrFeNi specimen presented a lower yield strength and tensile strength, but improved ductility, which was due to the stress relief and grain growth (shown in Figure 8) [55].

The HIP effects on mechanical properties were studied in the DLF Al*x*CoCrFeNi alloy (*x* = 0.3, 0.6, and 0.85) [68]. The DLF/HIP Al0.3CoCrFeNi presented an enhanced ductility and work-hardening rate, without losing its yield strength. However, the DLF/HIP Al0.3 showed an improved yield strength but reduced ductility. A small volume fraction of deformation twinnings was found in the tension-failed specimens of the DLF/HIP Al0.3CoCrFeNi, which was due to a lower stress compared with the critical stress to activate the twinning. The formation of the hard B2 grain-boundary phase by the HIP process was detrimental to tension, which led to reduced ductility. This result was proved by the fact that the B2 phase in Al*x*CoCrFeNi failed to accommodate shape changes. Sistla et al. [67] studied the heat-treatment effect on the Al*x*FeCoCrNi2−*<sup>x</sup>* prepared by DMD. It was found that the Fe–Cr matrix in the as-deposited, annealed, and as-quenched specimen was enhanced by the precipitates of the Niand Al-rich phases. The Al–Ni composition will transform to a two-phase domain with NiAl + Ni3Al at higher temperatures, resulting in further improvment in the strength of materials.

A SEBM–CoCrFeNiTi-based HEA exhibited good tensile properties [73]. In order to further improve the mechanical properties of SEBM materials, a solution treatment was performed, leading to the disappearance of Ni3Ti. Only small particles composed of Ni and Ti elements were present in the specimen. It is obvious that the ductility was improved without lowering their strengths after solution treatment (ST), as shown in Figure 11. The excellent ductility induced by the delay at the beginning of the plastic instability was attributed to the dynamic recovery induced by the screw-dislocations cross slips or the dislocations coalescence and annihilation during the plastic deformation. Specifically, the air-cooled (A.C.) specimen illustrated a higher yield strength but a lower ductility than that in the water-quenched (W.Q.) specimen, which was ascribed to the different precipitate size of the ordering phases that can act as a weak obstacle to the moving dislocation. The particle size of the sample obtained by the A.C. method was about 40 nm, higher than that of the W.C. sample, with a particle size of 10 nm. It was concluded that the moving dislocation was able to cut through the small particles

with a diameter of several tens of nanometers. Moreover, the critical resolved shear stress increased proportionally to the square root of the precipitate diameter.

#### *3.5. Comparison of Mechanical Properties*

Figure 12 presents the yield strength and ductility obtained from both compression and tension experiments in HEAs, conventional Al, TiAl, and Cu alloys, and steels alloys fabricated by AM [60,76]. It is apparent that HEAs present a much higher yield strength and impressive plasticity than that in Al, TiAl, and Cu alloys and in steels. Even though the AlCoCrFeNi alloy fabricated by casting or by SEBM was found to have a high yield strength in the tensile tests, limited ductility was observed as well, which was due to the brittle phase appearance in the matrix. The modified Co1.5CeFeNi1.5Mo0.1 HEA fabricated by SEBM showed an excellent combination of yield strength and ductility in the tensile experiments due to the uniform dispersion of small Ni3Ti particles in the matrix. The CoCrFeNi alloys prepared by SLM demonstrated a higher yield strength than that in the LMD CoCrFeNi and CoCrFeNi HEA/5083 composite, but comparable to the SLM C-containing FeCoCrNi HEAs, which was ascribed to their fine microstructure in SLM materials. The LAM CoCrFeMnNi HEA suggested that the HIP-post process enhanced yield strength, but slightly lowered elongation. The SLM CoCrFeMnNi HEAs depending on various scanning speeds and heat treatments displayed a wide range of ductility and comparable yield strength. The DLF Al0.3CoCrFeNi alloys revealed a much lower yield strength, compared with other methods, as apparent in Figure 12. We can conclude that different AM methods induce substantial differences in both yield strength and plasticity, and the post-heat-treatment enhances their properties by removing various defects and releasing the residual stress present in the materials.

**Figure 12.** Yield strength vs. elongation using various AM methods. (TS: Tensile; CP: Compression).

#### **4. Future Work**

HEAs are potential materials that can act as functional and structural materials due to their excellent properties. The complex geometries of HEAs cannot be realized by the conventional method. Therefore, AM paves the way to the fabrication of HEAs with complicated shapes. However, defects are present in AM materials, which degrade mechanical properties. Thus, it is essential to explore ways to optimize the microstructure and enhance the mechanical properties of AM-processed HEAs. Suggestions are as follows:


#### **5. Conclusions**

The application of AM in the fabrication of HEAs and the post-heat-treatment were reviewed. The improved mechanical behavior of AM samples, compared with casting materials, is ascribed to the refinement of microstructures caused by large temperature gradients, rapid solidification, and cooling in the fabrication process, which is of significant importance in highly alloyed systems. The post-heat-treatment enhances their properties by removing various defects and releasing the residual stress formed in AM materials. Furthermore, reducing the pre-heating temperature to prevent phase segregation or modifying the composition of the HEA to stabilize one of the phases of BCC, FCC, and B2 structures were considered to improve the mechanical properties in AM materials. It is feasible to further improve the mechanical performance of as-built materials by optimizing the processing parameters, the scanning method, and the fabrication orientation. Promising results pave the way to investigate HEAs as engineering materials by AM methods.

**Author Contributions:** Conceptualization and Writing—Original Draft preparation, S.C. editing: Y.T. and P.K.L.; supervision, P.K.L.

**Acknowledgments:** The authors very much appreciate the support from the Department of Energy (DOE) Office of Fossil Energy, National Energy Technology Laboratory (NETL) (DE-FE-0011194) and the National Science Foundation (DMR-1611180 and 1809640), with J. Mullen, V. Cedro, R. Dunst, S. Markovich, G. Shiflet, and D. Farkas as program managers. P.K.L. very much appreciate the support from the U.S. Army Office Project (W911NF-13-1-0438) with the program managers, M. P. Bakas, S. N. Mathaudhu, and D. M. Stepp. S.C. and P.K.L. would like to acknowledge the financial support of the Center for Materials Processing (CMP), at The University of Tennessee, with the director of Claudia J. Rawn. S.C. and P.K.L. also thanks the support from the University of Tennessee's Open Publishing Support Fund.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **Effect of Annealing on Microstructure and Mechanical Properties of Al0.5CoCrFeMoxNi High-Entropy Alloys**

#### **Yan-Xin Zhuang \*, Xiu-Lan Zhang and Xian-Yu Gu**

Key Laboratory of Electromagnetic Processing of Materials, Ministry of Education, Northeastern University, Shenyang 110819, China; 15204001761@163.com (X.-L.Z.); xianyu062@126.com (X.-Y.G.)

**\*** Correspondence: yxzhuang@epm.neu.edu.cn; Tel.: +86-024-8368-0156

Received: 11 September 2018; Accepted: 19 October 2018; Published: 23 October 2018

**Abstract:** The effect of annealing temperature on the microstructure, phase constituents and mechanical properties of Al0.5CoCrFeMoxNi high-entropy complex alloys has been investigated at a fixed annealing time (10 h). The 600 ◦C-annealing has no obvious effect on their microstructures, while the annealing at 800–1200 ◦C enhances the precipitation of (Al,Ni)-rich ordered BCC phase or/and (Cr,Mo)-rich σ phase, and thereby greatly affects the microstructure and mechanical properties of the alloys. All the annealed Al0.5CoCrFeNi alloys are composed of FCC and (Al,Ni)-rich ordered BCC phases; the phase constituent of the Al0.5CoCrFeMo0.1Ni alloy changes from FCC + BCC (600 ◦C) to FCC + BCC + σ (800 ◦C) and then to FCC + BCC (1100 ◦C); the phase constituents of the Al0.5CoCrFeMo0.2Ni and Al0.5CoCrFeMo0.3Ni alloys change from FCC + BCC + σ to FCC + BCC with the annealing temperature rising from 600 to 1200 ◦C; while all the annealed Al0.5CoCrFeMo0.4Ni and Al0.5CoCrFeMo0.5Ni alloys consist of FCC, BCC and σ phases. The phase constituents of most of the alloys investigated are in good agreement with the calculated results from Thermo-Calc program. The alloys annealed at 800 ◦C under current investigation conditionshave relative fine precipitations and microstructure, and thereby higher hardness and yield stress.

**Keywords:** high-entropy alloys; annealing; microstructure; mechanical properties; phase constituent

#### **1. Introduction**

The recently developed high-entropy alloys (HEAs), also known as multi-principal elements alloys or complex concentrated solid solution alloys, have attracted increasing attention due to their unique microstructures and adjustable properties [1–6]. The HEAs, which contains more than five principal elements with concentrations from 5 to 35 at.% for each principal element [2], tend to form simple solution structures (FCC, BCC, HCP or mixed) rather than many complex phases. To date, many efforts have been made to understand and control the structure and properties within as-cast and/or homogenized HEAs [7–15]. The original concept of HEAs and the strict restriction on the HEA design strategy proposed by Yeh [2] have also been relaxed. Depending on their composition, the as-cast and/or homogenized HEAs can have many interesting mechanical and physical properties, and wide potential applications.

It has been realized that the solid solutions in as-cast HEAs are the firstly formed solid phases upon cooling from the molten liquids, and are generally metastable phases at room temperature [16]. The room-temperature-metastable solid solutions could transform to other phases at an appropriate annealing temperature, and the annealing process can modify the microstructure and properties of the HEAs. Aging the AlCoCrCuFeNi HEA at elevated temperatures causes the structure gradually to transform from stabilized BCC to FCC, decreases the yield strength of the alloy, and increases the plastic strain of the material [17]. Aging the Cu0.5CoCrFeNi alloy at 1100–1350 ◦C induces the precipitation of a

Cr-rich phase in the FCC matrix of the alloy, and improves the anti-corrosion properties of the alloy [18]. The AlNi-based B2 phase and Cr-rich σ phase formed in the Al0.5CrFeCoNiCu HEAs annealed at 700–900 ◦C [19]. A needle-like Cu-rich FCC phase has been precipitated from the BCC dendrite region at the annealing temperatures higher than 973 K in the AlCoCuFeNi HEA [20]. The microstructure and properties of the AlxCoCrFeNi HEAs have a strong dependence on the Al content and annealing temperature [21]. The phase stability of the metastable solid solutions is actually becoming a critical issue for HEAs.

Over the last decades, the single-FCC or BCC HEAs have been intensively investigated and developed. In fact, it is very hard to reach a balance between high strength and high ductility for the single-phase HEAs due to the fact that the single-FCC HEAs normally have good ductility and poor strength, while the single-BCC HEAs generally have poor ductility and good strength. By adjusting the composition of the alloys, a eutectic high-entropy alloy AlCoCrFeNi2.1 with a regular FCC/BCC lamellar structure has been developed, and the alloy has an excellent combination of high strength and high ductility [22], which was attributed to the coupling between the ductile FCC and brittle BCC phases during tension deformation [23]. A transformation-induced plasticity-assisted dual-phase (TRIP-DP) HEA has also been developed, in which two high-entropy phases (FCC γ matrix and laminate HCP ε phase) present [24]. The TRIP-DP HEA combines the solid-solution strengthening effect in HEAs with the TRIP effect, exhibits multiple deformation mechanisms and dynamic strain partitioning behavior [25], and has improved strength and ductility compared to its corresponding single-phase HEA. This combined increases in strength and ductility distinguishes the TRIP-DP-HEA alloy from other structural materials [24]. All these results have showed that the dual- or multi-phase HEAs can display an excellent combination between strength and ductility, and are becoming the future direction for designing advanced HEAs.

The Al0.5CoCrFeNi alloy has a mixed FCC + B2 dual-phase structure with FCC as the dominant structure [7,21]. Our previous results have shown that the addition of Mo into this alloy system could enhance the formation of the σ phase, and tune the mechanical properties of the as-cast Al0.5CoCrFeMoxNi [26]. Although we have evaluated the high-temperature equilibrium phases existing in Al0.5CoCrFeMoxNi alloy using thermodynamic calculation, the results need to be assured by experiments. On the other hand, an appropriate annealing process can further modify the microstructure and improve its mechanical properties. In order to understand the temperature effect on this HEA system, the aged-and-quenched microstructure, phase transformation and mechanical properties have been investigated. The pseudo binary phase diagram derived from Thermo-Calc program has been compared with the experimental results.

#### **2. Materials and Methods**

Ingots with nominal compositions of Al0.5CoCrFeMoxNi (x = 0, 0.1, 0.2, 0.3, 0.4 and 0.5, denoted by Mo0, Mo0.1, Mo0.2, Mo0.3, Mo0.4 and Mo0.5, respectively) were prepared by arc-melting the mixture of constituent elements with purity better than 99.9 wt.% in a water-cooled copper hearth under a titanium-gettered high-purity argon atmosphere. The ingots were remelted at least four times to assure their chemical homogeneity. Samples for microstructural observation and annealing processes were cut from the ingots, mechanically ground and polished through standard routines. Some samples were sealed in quartz tubes under a vacuum better than 1 × <sup>10</sup>−<sup>2</sup> Pa, and then annealed at given temperatures for 10 h. After the annealing process, the samples were quenched in water. The phase constitutions of the alloys were characterized using X-ray diffraction (XRD) with Cu Kα radiation (X'Pert Pro, PANalytical B.V., Almelo, The Netherlands). The microstructure and chemical compositions were examined on the polished samples using scanning electron microscopy (SEM, SSX-550, SHIMADZU corp., Kyoto, Japan) equipped with energy dispersive spectrometry (EDS). Hardness was characterized using a Vickers hardness tester (Wolpert 452SVD, Wolpert Wilson instrument, Shanghai, China) under a load of 5 Kgf for 15 s. The hardness measurements were made on at least seven points to yield an average value for each sample. Room temperature compressive

tests were performed on cylindrical specimens with 5 mm in diameter and 10 mm in length using a SHIMADZU precision universal tester (AG-X, SHIMADZU corp., Kyoto, Japan) with a strain rate of 8.3 × <sup>10</sup>−<sup>4</sup> <sup>s</sup><sup>−</sup>1.

Thermodynamic calculations were conducted using the Thermo-Calc TCCS program in conjunction with a commercial TTNI7 database, which is developed for Ni-based alloys and contains 22 elements including Fe, Co, Ni, Al, Cr, Cu, Nb and Mo. The pseudo binary phase diagram, fraction and composition of each equilibrium phase at different temperatures were derived using the program.

#### **3. Results and Discussion**

#### *3.1. Phase Transformation of Annealed Al0.5CoCrFeMoxNi Alloys*

Figure 1 summaries the XRD patterns of the Al0.5CoCrFeMoxNi multicomponent high-entropy alloys annealed at different temperatures for 10 h followed by water quenching. The XRD patterns of the as-cast alloys are also given in the figure. The addition of Mo and the annealing process affect the phase constituents in the alloys. The addition of Mo enhances the formation of σ and ordered BCC phases in the as-cast Al0.5CoCrFeMoxNi alloys as reported in our previous work [26]. The Bragg peaks in the XRD patterns of the as-cast Al0.5CoCrFeNi alloy can be indexed to a simple FCC phase. When the Al0.5CoCrFeNi alloy was annealed at the temperatures between 600–1200 ◦C for 10 h, the Bragg peaks corresponding to a BCC phase can found on the XRD patterns even though the peak at 2θ of about 44 is very weak for the alloy annealed at 1200 ◦C, meaning that the annealing induces the formation of the BCC phase. Similarly, the as-cast and 600 ◦C-annealed Mo0.1 alloys have a dominant FCC phase and a minor BCC phase, while a σ phase has been found in the Mo0.1 alloys annealed at 800 ◦C and disappears again in the alloys annealed at 1000–1200 ◦C. The as-cast Mo0.2 alloy and the alloys annealed at 600–1100 ◦C consist of three phases, namely FCC, BCC and σ phases, while the Mo0.2 alloys annealed at 1200 ◦C only have FCC and BCC phases. The as-cast Mo0.3 alloy and the alloys annealed at 600–1100 ◦C are composed of the FCC, BCC and σ phases, while only FCC and BCC phases can be found in the alloy annealed at 1200 ◦C. The as-cast and annealed Mo0.4 alloys have the FCC, BCC and σ phases even though the peaks for BCC phase are very weak in the alloy annealed at 1200 ◦C. The as-cast Mo0.5 alloy and the alloys annealed at 600–1200 ◦C have FCC, BCC and σ phases even though the peaks for the BCC phase are very weak in the alloy annealed at 1200 ◦C. It can be concluded that both the Mo content and the annealing temperature affect the phase constituents of the Al0.5CoCrFeMoxNi alloys. On the other hand, some kind of preferred orientation can also be observed in some of the alloys.

**Figure 1.** *Cont.*

**Figure 1.** X-ray diffraction (XRD) patterns of the as-cast Al0.5CoCrFeMoxNi alloys and the alloys annealed at different temperatures for 10 h followed by a water quenching. (**a**) x = 0; (**b**) x = 0.1; (**c**) x = 0.2; (**d**) x = 0.3; (**e**) x = 0.4; (**f**) x = 0.5.

#### *3.2. Microstructures of Annealed Al0.5CoCrFeMoxNi Alloys*

Figure 2 presents the microstructure of the as-cast Mo0, Mo0.1 and Mo0.2 high entropy alloys and the alloys annealed at different temperatures for 10 h. Table 1 lists distribution of element in different phases of the alloys annealed at 1000 ◦C. The as-cast Mo0, Mo0.1 and Mo0.2 alloys have typical dendrite microstructures. The dendrite (DR) phase is FCC phase, while the interdendrite (ID) region consists of (Al,Ni)-rich phase, FCC phase and/or (Cr,Mo)-rich phase [26]. The 600 ◦C annealing has no obvious effect on the microstructure of the three alloys. However, the annealing at temperatures between 800 and 1200 ◦C has a distinct influence on the microstructure of the three alloys. The needle-like precipitations have been found in the Mo0 alloys annealed at 800–1100 ◦C, and the EDS shows that both the needle-like precipitation (marked as NLP in the figure) and the dark matrix phase in the ID region have high Al and Ni, can be regarded as a (Al,Ni)-rich phase (refer to the data in Table 1). The (Al,Ni)-rich phase have an ordered BCC (B2) structure [21,26]. When increasing annealing temperature, the number of needle-like precipitation decreases, while its size increases. When the annealing temperature is up to 1200 ◦C, the needle-like (Al,Ni)-rich precipitation disappears. It is clear that the two phases (FCC and (Al,Ni)-rich ordered BCC) exist in the Mo0 alloy annealed at temperatures of 600–1200 ◦C, which is in good agreement with the observation from XRD patterns. Similarly, many obvious precipitations have been found in the Mo0.1 and Mo0.2 alloys annealed at 800–1100 ◦C. By contrast with the Mo0 alloys, a new phase enriched with Cr and Mo (bright phase marked as WP) has been observed in the Mo0.1 and Mo0.2 alloys. The (Cr,Mo)-rich phase is the σ phase [26]. There are three phases, namely FCC matrix, needle-like (Al,Ni)-rich ordered BCC phase and round-like (Cr,Mo)-rich σ phases, existing in the Mo0.1 alloys annealed at 800–1000 ◦C and the Mo0.2 alloys annealed at 600–1100 ◦C, while there are two phases (FCC and (Al,Ni)-rich ordered BCC phases) in the Mo0.1 alloys annealed at 1100 and 1200 ◦C and the Mo0.2 alloy annealed at 1200 ◦C. It can also be observed that the (Cr,Mo)-rich σ phase exists in the DR and ID regions in the Mo0.1 and

Mo0.2 alloys annealed at 800 ◦C, but only appears together with the (Al,Ni)-rich ordered BCC phase in the alloys annealed at higher temperatures.

The alloys annealed at 800 ◦C have fine microstructures, and are supposed to have better mechanical properties. The fine microstructure can be attributed to solid-state decomposition of the B2 phase and FCC matrix. The phenomena can be often found in AlxCoCrFeNi alloys [27–30]. Heat treatment at 620 ◦C for the Al0.3CoCrFeNi alloy caused the transformation of FCC to FCC + L12 or FCC + B2 + σ phases depending on the processing routes, and the microstructural variation realized by different process pathways was attributed to the competition between the thermodynamic driving force and activation barrier for the second-phase nucleation [27]. An aging process lead to the spinodal decomposition reactions of the FCC matrix and the interdendrite (Al,Ni)-rich phase in Al0.5CoCrFeNi alloy, and the phase segregation effect was explained based on the mixing enthalpy between different atom pairs [28]. Recently, Rao et al. found that a (Al,Ni)-rich L12 phase was precipitated from the FCC matrix of Al0.5CoCrFeNi alloy, a Cr-rich BCC nanoprecipitate was observed in its B2 phase, and the Cr-rich BCC nanoprecipitate was the origin of the σ phase [29]. Banerjee et al. also reported that the solid-state decomposition resulted in the formation of FCC + L12 and BCC + B2, accompanied by a compositional partitioning [30]. Cleary, the solid-state decomposition of the FCC matrix and (Al,Ni)-rich ordered BCC in the Mo-free Al0.5CoCrFeNi alloy is responsible for its fine structure at 800 ◦C. In the Mo-containing alloys, the addition of Mo enhances the formation of σ phase. Both Cr and Mo are strong σ-forming elements [31]. The σ phase forms either in a three-step formation from B2 region or directly from the FCC matrix [29].

**Figure 2.** *Cont.*

**Figure 2.** Back-scattering scanning electron microscope (SEM) images of the as-cast Mo0, Mo0.1 and Mo0.2 high entropy alloys and the alloys annealed at different temperatures for 10 h. DR is for FCC dendrite phase, ID is for (Al,Ni)-rich interdendrite phase, NLP is for needle-like (Al,Ni)-rich recipitate, WP is for white (Cr,Mo)-rich precipitate, and BP is for black (Al,Ni)-rich precipitate. (**a**) as-cast Mo0 alloy; (**b**) as-cast Mo0.1 alloy; (**c**) as-cast Mo0.2 alloy; (**d**) Mo0 alloy annealed at 600 ◦C; (**e**) Mo0.1 alloy annealed at 600 ◦C; (**f**) Mo0.2 alloy annealed at 600 ◦C; (**g**) Mo0 alloy annealed at 800 ◦C; (**h**) Mo0.1 alloy annealed at 800 ◦C; (**i**) Mo0.2 alloy annealed at 800 ◦C; (**j**) Mo0 alloy annealed at 1000 ◦C; (**k**) Mo0.1 alloy annealed at 1000 ◦C; (**l**) Mo0.2 alloy annealed at 1000 ◦C; (**m**) Mo0 alloy annealed at 1100 ◦C; (**n**) Mo0.1 alloy annealed at 1100 ◦C; (**o**) Mo0.2 alloy annealed at 1100 ◦C; (**p**) Mo0 alloy annealed at 1200 ◦C; (**q**) Mo0.1 alloy annealed at 1200 ◦C; (r) Mo0.2 alloy annealed at 1200 ◦C.


**Table 1.** Distribution of elements (at.%) in different regions of the alloys annealed at 1000 ◦C.

Figure 3 summarizes the microstructure of the Mo0.3, Mo0.4 and Mo0.5 alloys at various annealing temperature. Table 2 lists the elemental distribution in each phase for the three alloys annealed at 1000 ◦C. All the three as-cast alloys are composed of FCC, (Al,Ni)-rich ordered BCC, and (Cr,Mo)-rich σ phases as stated in our previous work [26]. The 600 ◦C-annealing has also no obvious effect on the microstructure of the three alloys, while 800 ◦C-annealing induces the precipitation of a large amount of fine (Al,Ni)-rich BCC and (Cr,Mo)-rich σ phases in the alloys even though their typical dendrite microstructure remains. Obvious coarsening occurred when the alloys were annealed at 1000–1100 ◦C, and the morphology of BCC and σ phases changes greatly. The BCC and σ phases become larger, and most of them appear together, implying that certain crystallographic orientation exists between the ordered BCC and σ phases. A few precipitations with even higher Mo content can also be found in the Mo0.5 alloy annealed at 1000 ◦C (marked as WP2 in the corresponding image). When the alloys annealed at 1200 ◦C, the amount of ordered BCC and σ phases obviously decrease.

The wide composition range of each phase has been observed in the annealed alloys, as shown in Tables 1 and 2. The addition of Mo into the Al0.5CoCrFeNi alloys can change the liquidus temperature or solvus temperature, the equilibrium phase composition, and even the formation sequence of the equilibrium phases [26]. The variable mixing enthalpy between different atoms and competition among the elements could be possible reasons for the variable composition of each phase. On the other hand, the needle-like (Al,Ni)-rich precipitate has a relatively small size, which might cause the inaccurately measured composition. Further work is going to clarify the reason for the wide composition. However, the wide composition range of each phase has no effect on the phase structure.

**Figure 3.** *Cont.*

**Figure 3.** Back-scattering SEM images of the as-cast Mo0.3, Mo0.4, and Mo0.5 high entropy alloys and the alloys annealed at different temperatures for 10 h. DR is for dendrite FCC, WP1 is for white (Cr,Mo)-rich precipitate with relative low Mo content, WP2 is the whit (Cr,Mo)-rich precipitate with relative high Mo content, and BP is for black (Al,Ni)-rich precipitate. (**a**) as-cast Mo0.3 alloy; (**b**) as-cast Mo0.4 alloy; (**c**) as-cast Mo0.5 alloy; (**d**) Mo0.3 alloy annealed at 600 ◦C; (**e**) Mo0.4 alloy annealed at 600 ◦C; (**f**) Mo0.5 alloy annealed at 600 ◦C; (**g**) Mo0.3 alloy annealed at 800 ◦C; (**h**) Mo0.4 alloy annealed at 800 ◦C; (**i**) Mo0.5 alloy annealed at 800 ◦C; (**j**) Mo0.3 alloy annealed at 1000 ◦C; (**k**) Mo0.4 alloy annealed at 1000 ◦C; (**l**) Mo0.5 alloy annealed at 1000 ◦C; (**m**) Mo0.3 alloy annealed at 1100 ◦C; (**n**) Mo0.4 alloy annealed at 1100 ◦C; (**o**) Mo0.5 alloy annealed at 1100 ◦C; (**p**) Mo0.3 alloy annealed at 1200 ◦C; (**q**) Mo0.4 alloy annealed at 1200 ◦C; (r) Mo0.5 alloy annealed at 1200 ◦C.

**Table 2.** Distribution of elements (at.%) in different regions of the alloys annealed at 1000 ◦C.


#### *3.3. Calculated Pseudo Binary Phase Diagram and Its Comparison with Experiments*

It is clear that the phase constituents in the Al0.5CoCrFeMoxNi alloys depend on the content of Mo and the annealing temperature. Figure 4 is the calculated pseudo-binary phase diagram of Al0.5CoCrFeMoxNi using the Thermo-Calc program, where the calculated equilibrium phase constituents in each region have been labeled. The alloys investigated in this work have also been marked in the diagram as the dash lines. The phase constituents in most of the alloys, which have been derived based on the XRD and microstructures above, are in good agreement with the calculated results. Only 6 samples among the 30 samples have a little difference with the calculated phase constituents from Thermo-Calc program. Careful examination found that the difference happened either near the boundary between different regions or at the low temperatures. For example, the Mo0 alloy at 800 ◦C, the Mo0.1 alloy at 1000 ◦C, the Mo0.2 alloy at 1100 ◦C and the Mo0.4 alloy at 1200 ◦C locate near the boundary between two regions. The difference might be attributed to the unspecified database for the alloy system, which makes the boundary line shift a little. Another reason could be the sluggish diffusion of elements in the high-entropy alloys, whereby the equilibrium state might not be reached in the annealing time used. The examples are the Mo0 and Mo0.1 alloys at 600 ◦C, where the calculated equilibrium phases in these two alloys are FCC, NiAl and σ phases, but only FCC and (Al,Ni)-rich ordered BCC phases have been identified from our experiments. Gwalani et al. reported that a different processing pathway resulted in different phases and the equilibrium phases in Al0.3CoCrFeNi alloy were FCC + B2 + σ phases [27]. Rao et al. also reported that the stable phases

in Al0.5CoCrFeNi alloy are BCC + L12 + σ phases [29]. Anyway, the calculated phase diagram could give us potential help in designing alloys and their corresponding annealing processes.

ƻ **Figure 4.** Pseudo binary phase diagram of Al0.5CoCrFeMoxNi HEAs derived from Thermo-Calc. The dashed line represents the compositions of the alloys experimentally investigated in this work. The symbol ⊗ represents that the phase constituents of the alloys are different from the calculated results, and the text in red is the phase constituents of the alloys identified from experiments. The alloys marked with symbolƻ**dž** have the same phase constituents as calculated results.

#### *3.4. Mechanical Properties of Annealed Al0.5CoCrFeMoxNi Alloys*

Figure 5 depicts the room temperature hardness of the Al0.5CoCrFeMoxNi high entropy alloys annealed at various annealing temperatures. The data at 25 ◦C represent the values of as-cast alloys. The hardness of the alloys increases with the increasing Mo, and this can be attributed to the lattice distortion and formation of BCC and σ phases. On the other hand, with annealing temperature rising, the hardness of the alloys first increases, reaches its maximum at 800 ◦C, and then decreases afterwards. The alloys annealed at 800 ◦C have relatively fine precipitation and microstructure, which could be responsible for their higher hardness. Afterwards, the fine precipitations become larger and the effect of the interface strengthening become smaller.

**Figure 5.** Hardness of Al0.5CoCrFeMoxNi high-entropy alloys annealed at different temperatures for 10 h followed by water quenching.

Figure 6 presents the fracture strain and yield strength of the as-cast Al0.5CoCrFeMoxNi high-entropy alloys and the alloys annealed at 800 ◦C for 10 h. It is clear that the fracture strain decreases, and the yield strength increases with Mo content increasing from 0 to 0.5. The alloys annealed at 800 ◦C have higher yield compressive strength and smaller compressive fracture strain than those of the as-cast alloys, which is attributed to the formation of fine (Al,Ni)-rich ordered BCC and (Cr,Mo)-rich σ phases. Both the Mo content and annealing processes have a great influence on the microstructure and mechanical properties of Al0.5CoCrFeMoxNi high-entropy alloys. For the as-cast alloys, the Mo0.3 and Mo0.4 alloys can have balanced properties of compressive strength and ductility, while an appropriate annealing process can provide more chances to modify the mechanical properties of the alloys. For example, the Mo0.5 alloy annealed at 800 ◦C can have a high compressive yield strength up to 2.1 GPa (ultimate fracture strength of 2.6 GPa) with an accepted fracture strain of 13%. The Mo0.1 alloy annealed at 800 ◦C has a compressive yield strength of 1.2 GPa, an ultimate fracture strength of 2.2 GPa, and an ultimate fracture strain of 17%. Both the Mo content and annealing process can be used to tune the mechanical properties of the alloys.

**Figure 6.** Yield strength (**a**) and fracture strain (**b**) of the as-cast alloys and the alloys annealed at 800 ◦C for 10 h.

#### **4. Conclusions**

The evolution of microstructure, phase and mechanical properties of the Al0.5CoCrFeMoxNi high-entropy alloys have been investigated. Both the Mo content and annealing process can be used to tune the mechanical properties of the alloys. The following conclusions can be established from the current work.

	- (a) Mo0 alloy: mixed structure (FCC + BCC/B2).
	- (b) Mo0.1 alloy: mixed structure (FCC + BCC/B2) below 600 ◦C → FCC + BCC/B2+ σ (800–1000 ◦C) → FCC + BCC/B2 (1100–1200 ◦C).
	- (c) Mo0.2–Mo0.3 alloys: mixed structure (FCC + BCC/B2 + σ) below 1100 ◦C → FCC + BCC/B2 (1200 ◦C).
	- (d) Mo0.4–Mo0.5 alloys: mixed structure (FCC + BCC/B2 + σ).

**Author Contributions:** Y.-X.Z. and X.-L.Z. conceived and designed the experiments. X.-L.Z. prepared the Al0.5CoCrFeMoxNi high entropy alloys and conducted the annealing processes. X.-L.Z. and X.-Y.G. performed the microstructural characterization and mechanical testing. Y.-X.Z. and X.-Y.G. analyzed the data. Y.-X.Z. wrote the paper. All authors have read and approved the final manuscript.

**Funding:** This research was funded by the Fundamental Research Funds for the Central University (Grant No. N150902001), Foundation of Liaoning Educational Committee for key laboratory (Grant No. LZ2015042), and NSF of China (Grant No. 51171041).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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