Introduction

Since Yeh et al.1 and Cantor et al.2 independently described multicomponent alloys without a principal element in 2004, considerable research efforts have been directed toward this vast and largely unexplored composition space3. This region of chemical space is commonly referred to as complex concentrated alloys, multi-principal element alloys, or high-entropy alloys (HEAs). However, high entropy alloys must contain five or more elements with the goal of increasing the total entropy change (i.e., entropy metric4) toward a negative Gibbs free energy (ΔG) thus resulting in a single phase5,6. To achieve ‘high entropy’, the configurational entropy must be greater than 1.5R, where R is the gas constant4. The impact of this strategy is perhaps best exemplified by the number of material classes where high entropy materials have been discovered, often with unique and desirable properties1,2,5,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27. Unfortunately, the original hypothesis that significantly more multi-component systems would be entropically stabilized into a single-phase solid solution has proven untrue28. The most common single phase microstructures for high entropy alloys to form are face-centered cubic (FCC), body-centered cubic (BCC), and occasionally hexagonal (HEX), while other crystal structures occur very rarely7. Presently, the scientific community considers the BCC phase as most likely to form, owing to its ability to accommodate larger ranges of atomic size in the same lattice29. However, recent reviews of HEAs reveal the FCC crystal structure to be more common than anticipated, accounting for nearly 50% of the aggregated results7,22,29. Furthermore, materials such as the Cantor alloy (CrMnFeCoNi) require further explanation as only Ni is FCC (20 at%), Cr is BCC, and Fe, Mn, and Co are allotrope elements with room temperature and atmospheric pressure structures of BCC, BCC, and HEX, respectively; and yet FCC is the resultant structure2. Miracle et al. performed an overview statistical analysis of HEAs called ‘structure in – structure out’ in which they concluded that most known HEAs are comprised primarily of FCC, BCC, and HEX elements, and thus, it should not be surprising that more complex structures are rarely reported (see Sect. 4.3.1.3 in7. However, the work does not individually assess HEA compositions to determine why they formed a particular structure, nor does it explain why compositions with relatively small amounts of a particular crystal structure still adopt that phase, both of which are addressed herein. An example of the new insight provided by this more in-depth analysis through the lens of allotropy is the perceived relative scarcity of FCC HEAs compared to BCC. There are only 11 non-allotrope FCC elements on the periodic table and excluding the six precious metals and actinium (none of which are generally commercially viable) leaves only Al, Cu, Ni, and Pb. Of those four elements, Pb is another element not typically used for commercial applications and Cu exhibits a miscibility gap with most other elements. Thus, materials engineers are reliant primarily on Al and Ni to form FCC HEAs. The need for more insight into crystal structure formation in HEAs is imperative given the large, complex composition space30 that has been unlocked by the idea of searching for the next impactful material near the largely unexplored center of phase diagrams.

Despite the intense effort to identify new high entropy alloys, the challenge of determining a priori, (which compositions are likely to form a single phase and which crystal structure the phase will adopt) remains non-trivial. This work is primarily focused on the latter part of the HEA design process; assuming a single phase will form, what crystal structure should be expected? A fundamental understanding of this phenomena is expected to serve as an important tool in the screening of materials for specific applications, since the intrinsic properties of alloys are highly dependent on the resultant phase(s)7,19,31. For example, FCC and BCC structured HEAs generally exhibit a tradeoff between good ductility and higher strength32,33. Existing in silico strategies generally employ some combination of first-principles density functional theory (DFT), thermodynamics, machine learning, and compositional descriptors as screening techniques. DFT-based strategies are a useful technique in the search for new alloys; however, the computational expense becomes impractical for dealing with the large simulation cells required to assess HEAs with 5 + elements and can require hundreds of hours of computation per composition10,34,35,36,37. Thermodynamic-based strategies, namely the CALPHAD method38,39,40,41, rely on thermodynamic databases of assessed systems, and therefore, perform best in regions of chemical space where significant data are available. Given the infancy of the high entropy materials field and the current resistance to publishing negative results (i.e., multiphase compositions), the reliability of this method is expected to be reduced for the vast majority of HEA candidates11. Machine learning-based methods are a relatively new approach to searching for HEAs and often leverage data from DFT, CALPHAD, and/or physicochemical descriptors42,43,44,45,46,47,48. The set of attributes most used to predict phase formation of alloys include a combination of: (1) the mixing enthalpy (\(\:\varDelta\:{H}_{mix}\)), (2) valence electron configuration (VEC), (3) atomic size ratios (δ), (4) configurational entropy (S), and (5) Pauling electronegativity (χ)49,50,51. There are a plethora of other descriptors tested during model fitting; however, these five attributes are the most common across multiple HEA-design campaigns and are typically found to be the most important to machine learning models’ decision making process42,43. Despite efforts in the material informatics field to link these descriptors with phase formation, there remains significant overlap of the different predicted phases by application of the derived models (refer to Chap. 2 in Reference36. Additionally, the presence of specific elements (i.e., Al, Cu, Li, Mg, Sn, and Zn) are known to limit the effectiveness of these phase formation rules52. Since existing descriptors are largely derived from the Hume-Rothery rules, their predictive capabilities in the HEA composition space are expectedly limited by their origination from binary alloys53.

In stark contrast to the approaches described in the above discussion, allotropism provides a simple method to reliably predict and explain the physical phenomena underlying the resultant crystal structure. Allotropism is the property of some elements to exist in two or more different structures in the same physical state of matter (e.g., liquid or solid). For example, some allotropic forms of solid carbon are diamond, graphite, lonsdaleite, and fullerenes. In the context of this work, elements are considered to be “allotrope forming” if more than one crystal structure exists for the solid state; no other states of matter will be considered. For instance, solid iron changes from a body-centered cubic structure (ferrite) to a face-centered cubic structure (austenite) above 906 °C. On the other hand, the “non-allotrope” elements (e.g., Ni or V) are only known to exist in one crystal structure as solids. The role of this property on HEA phase formation, to the best of these authors’ knowledge, has not been discussed previously in the literature, and yet, it will be demonstrated that the majority crystal structure of the non-allotrope elements present in a given composition is a dependable predictor of the final structure. While not predictive of whether or not a single-phase will form, allotropy can assist with defining the compositional search space for an HEA with a desired crystal structure. In addition, thermodynamic modeling of compositions containing equal parts FCC and BCC non-allotrope elements will be compared to the modeling of known HEAs to demonstrate that the absence of a dominant (in atom percent) non-allotrope structure (and absence of allotrope forming elements to provide crystal structure “flexibility”) prevents the formation of a single phase. These principles are an effective tool to assist in the development of new HEAs and predict their structure a priori.

Methods

Known single phase HEA materials

The set of materials known to form a single phase is obtained from the 2019 book on HEAs by Murty et al.29 and the 2018 database of HEAs compiled by Gorsse et al.22. The tables of materials in each source were converted to Excel documents using the AWS Textract API and subsequent compositional analyses performed using Python and the Pandas software package54. The datasets are presented separately herein. Between the two datasets, there are 434 unique single phase HEA compositions comprising a diverse region of chemical space.

Selection of new alloys

The new HEA candidates for testing a null hypothesis of the allotropy model (i.e., equal atom percent of FCC and BCC elements will form a single phase) were selected for modeling and potential fabrication using three rules: (i) all of the elements in the composition must be BCC or FCC and not exhibit allotropism; (ii) all of the elements must be available in the ThermoCalc TCHEA5 (high entropy alloys) database; and (iii) the BCC elements must sum to 50 atom percent, and the FCC elements must sum to 50 atom percent. The FCC elements that satisfy these criteria are Al, Cu, Ni, Ir, and Rh; and the BCC elements are Cr, Mo, Nb, Ta, V, and W. All possible 5 + element combinations of these FCC and BCC non-allotrope elements are then input to ThermoCalc. The combinations with only FCC or BCC elements (e.g., CrMoNbTaV) were excluded from the calculation. The intent of these compositions is to demonstrate the importance of allotropism on single versus multi-phase formation.

Thermodynamic modeling

Thermodynamic modeling was performed using the ThermoCalc Software TCHEA5 database55. Each composition is modeled from 2500 °C down to 500 °C in 100 °C steps, and the number of solid phases at each temperature recorded. The presence of a liquid phase is also recorded, and the composition not considered single phase if either a liquid or more than one solid phase is predicted.

Experimental synthesis and characterization

Nine alloys from those described in Sect. 2.2 are selected for fabrication based on the thermodynamic modeling results. Ingots are fabricated via arc melting > 99.9% purity slugs of the individual elements (Thermo-Fisher) under a Ti-gettered argon atmosphere. High and low melting temperature elements were initially melted separately and subsequently combined to ensure all elements were present in the final compositions at the correct atomic percentages. Samples were flipped and remelted ten times to maximize homogeneity. The sample predicted to be single-phase is then annealed for 24 h in a Red Devil™ vacuum furnace (RD WEBB, USA) at an appropriate temperature as determined by thermodynamic modeling. Target chemistry is verified, and chemistry maps are collected using a Thermo-Fisher Apreo scanning electron microscope (SEM) equipped with an Oxford X-MaxN EDS detector. Phase analysis is performed using an Anton Paar XRDynamic 500 X-ray diffraction (XRD) unit equipped with a one-dimensional detector. XRD data are collected from 20° to 120° (2θ angles) with a 0.02° step size and scan rate of 5°/minute. Copper Kα radiation is used for all x-ray diffraction measurements.

Results

Analysis of known single phase HEAs

The first demonstration of the predictive power of non-allotrope elements is presented in (Table 1). Summary statistics are calculated for the 484 HEAs reported in Murty et al.29 and Gorsse et al.22. Of the 484 reported HEAs, 434 are of a unique composition; however, the data from each source is reported and analyzed in its entirety. The atomic percent of non-allotrope elements in the reported HEAs ranges from 2.50 to 100%. The number of FCC and BCC alloys is reported along with the percentage of alloys for which the structure was correctly predicted using the proposed allotropy-based descriptor (e.g., the column ‘Accuracy for HEAs Primarily Containing BCC Non-allotropes’). An alloy ‘primarily containing BCC non-allotropes’ means there is a greater amount of BCC non-allotrope elements in the composition. The percentage in Table 1 details the percentage of the BCC HEAs reported for which the BCC non-allotrope atom percent is the majority elemental crystal structure present in the HEA and thus are correctly predicted by the allotropy model (i.e., 90% overall for BCC alloys). To provide an example, AlCoCuFeNiV is composed of 66.7 atom percent non-allotrope elements, and 50 atom percent of the composition is FCC elements, 16.7 atom percent are BCC, and the remaining 33.3 atom percent is allotrope-forming elements. Since the composition is reported as FCC, it counts toward the percentage of alloys that crystallize FCC and FCC is the dominant non-allotrope structure (see Table 1). The macro-averaged precision and recall for the allotropy model are 77% and 76%; respectively. The FCC or BCC crystal structure predictions using traditional descriptors VEC and e/a ratio were also tabulated using the criteria from Ref36. The macro-averaged precision and recall for the VEC model are 63% and 47%; respectively. The macro-averaged precision and recall for the e/a ratio descriptor are 66% and 5.6%; respectively. The F1-score, or the harmonic mean of the precision and recall scores, is computed to be 0.76 for allotropism. The F1-score for the VEC descriptor is 0.54 and the F1-score for the e/a ratio is 0.098. Interpreting the F1-score depends on the domain and context of the problem being addressed; however, scores greater than 0.70 generally signify the model is good at identifying both positive and negative cases, which the allotropy descriptor alone achieves. Ultimately, the allotropy descriptor shows at least 10% higher precision, recall, and F1-score than either VEC or the e/a ratio in predicting HEA crystal structure. Refer to Supplementary Table 1 and Supplementary Table 2 for the complete analysis results, including HEAs with crystal structure other than FCC and BCC, the percentage of allotrope forming and non-allotrope elements per composition, and whether the predominant non-allotrope elements are FCC or BCC in each alloy. The data for calculated valence electron concentration (VEC), electron per atom (e/a) ratio, mixing enthalpy (\(\:{\varDelta\:H}_{mix}\)), and atomic size mismatch (δ) are in Supplementary Table 3 and Supplementary Table 4. Figure 1 visually summarizes this data by plotting the atom percent of non-allotrope FCC and non-allotrope BCC elements for each composition, as well as identifies whether the allotropy (Fig. 1A, B), VEC (Fig. 1C, D), or e/a ratio (Fig. 1E, F) model would correctly identify the resultant crystal structure.

Table 1 Allotropism-based analysis of HEAs. Summary statistics for the FCC and BCC HEAs reported by Murty et al. and Gorsse et al. and the combined data in row ‘Total’. The number of single-phase alloys in each work is reported along with the number that are FCC and BCC. For the FCC (or BCC) alloys, the percentage of alloys that crystallize in the FCC (or BCC) structure when the majority non-allotrope crystal structure is also FCC (or BCC) is detailed. For example, Gorrse et al. contains 95 BCC heas. of which 97.9% contain a greater amount of BCC non-allotrope elements than FCC non-allotrope elements (i.e., BCC dominant).
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Fig. 1
figure 1figure 1

Non-allotrope atom percent compared to phase formation. Each data point details the atom percent of FCC and BCC non-allotrope elements for the HEA compositions in A,C,E) Murty et al.29, and B,D,F) Gorsse et al.22. The allotropy descriptor is applied for phase prediction in panel A and B. The VEC descriptor is applied for phase prediction in panel C and D. The e/a ratio descriptor is applied for phase prediction in panel E and F. Individual compositions marked with a circle are correctly identified by the respective model, while compositions marked with an “X” are not. The color of each data point corresponds to the experimentally reported phase, BCC (blue) or FCC (green). Data points will not add up to 100 atomic percent if any allotrope forming elements are present in the composition.

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Thermodynamic modeling data

Thermodynamic-based modeling of the HEAs from each of the two databases and the 1,414 new compositions containing only equal atom percent of five or more FCC and BCC non-allotrope elements was performed using the ThermoCalc TCHEA5 database. The number of compositions calculated from the Murty and Gorsse works was reduced to 78 and 47 unique compositions, owing to the element restrictions of the thermodynamic database. For a given composition and temperature, it was recorded whether the alloy was predicted to be a single-phase solid-solution (True) or not (False) (see Fig. 2). Supplementary Fig. 1 provides a visual summary of the number of phases predicted for each of the compositions studied. In addition to the bar chart summing the number of True and False readings at each temperature, Table 2 details the percentage of alloys that were modeled to be single phase at any temperature. Furthermore, Table 2 also includes the average and standard deviation of the temperature range for which the alloys are predicted to be single phase. Figure 2A; Table 2 highlight the miniscule likelihood of one of the new non-allotrope compositions being a high entropy alloy. Particularly when compared to the results for the HEAs from the Murty and Gorsse datasets, wherein more than 50% of the modeled HEAs are predicted to be single phase somewhere between 2500 °C and 500 °C and with a wide average single-phase range of ~900 °C ± 500 °C. The accuracy of thermodynamic calculations are, of course, dependent on the modelled and integrated phases and chemical systems that have been evaluated in the thermodynamic TCHEA5 database. However, the magnitude of difference (approximately 1% vs. 55%) in compositions suggested to potentially be single-phase at some temperature when searching nearly 1,500 new compositions suggests the likelihood of fabricating a single-phase material experimentally is unlikely.

Fig. 2
figure 2

Number of compositions predicted single phase in CALPHAD. Thermodynamic modeling is applied to assess the likelihood of equilibrium single phase formation for (A) the previously unreported compositions containing an equal atom percent of five or more FCC and BCC non-allotrope elements, (B) the HEAs from Murty et al.29, and (C) the HEAs from Gorsse et al.22. The inset in (A) is a magnified view showing the miniscule number of compositions predicted to be single-phase HEAs.

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Table 2 Thermodynamic analysis of HEA phase formation. ThermoCalc single phase predictions for HEAs from each literature source and the equiatomic FCC and BCC non-allotrope compositions. The number and percentage of HEAs predicted to form a single phase at any temperature is reported. Additionally, the average and standard deviation of the temperature range for which those compositions are predicted to be single phase is also presented.
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Characterization of fabricated alloys

From the compositions containing an equal atom percent of BCC and FCC non-allotrope elements, only 12 were predicted to be single phase over the modeled temperature range (Table 3). Of those 12, only 1 composition does not contain any of the prohibitively expensive elements Ir or Rh. The composition, Al8.90Cr11.45Nb20.45Ni19.37Ta39.83, is suggested to be stable within an approximately 300 °C window between 1300 and 1600 °C. Intriguingly, the single-phase crystal structure predicted to be stable is the HEX C14 Laves phase. This alloy along with eight other compositions that would be an HEA if single phase were fabricated to experimentally test the computationally supported hypothesis that a given composition, without an atom percent majority of non-allotrope elements having a particular crystal structure, and without the presence of allotrope forming elements, is unlikely to be an HEA. Chemistry maps for these nine alloys showing the multi-phase results are shown (Fig. 3). The phase evolution diagrams from CALPHAD are shown in Supplementary Fig. 2; XRD data is provided in Supplementary Fig. 3. Figure 4 and Supplementary Fig. 4 confirm that the composition Al8.90Cr11.45Nb20.45Ni19.37Ta39.83 remains multi-phase even after annealing at 1475 °C (as suggested by ThermoCalc) for 20 h in a vacuum furnace. The combination of characterization data for these nine compositions highlights the multi-phase result for each sample and the improbability of designing a single-phase alloy with these constraints.

Table 3 New alloys predicted to be HEAs by CALPHAD. The twelve compositions predicted to form a thermodynamically stable single phase when modeled from 500 to 2500 °C are listed. Only the temperature range over which any compositions are predicted to be single phase is shown. TRUE denotes only a single phase is predicted to be formed, while FALSE indicates more than one solid phase, or a solid and liquid phase are present. The single phase range column reports the temperature range for which the single phase is thermodynamically predicted to be stable.
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Discussion

A new descriptor for phase formation and crystal structure prediction for high entropy alloys is presented and rigorously evaluated against existing knowledge. The singular descriptor, the phase fraction of non-allotrope elements of each crystal structure type, was foremost demonstrated to predict the FCC or BCC phase formation of known HEAs with overall accuracy of 71%. This level of performance is on par with or better than existing methods10,36,56,57,58,59, does not require threshold values that can vary across alloy systems60, and provides a descriptor based in physiochemistry. The ability to predict accurately the resultant FCC or BCC phase for a wide range of HEAs provides convincing validation and is a marked achievement. Additional compositions outside these datasets demonstrate continued success of the allotropy descriptor: CoCuFeNiPt (FCC)61, CoCrFeNiPd (FCC)62, CoCrFeNiPd2 (FCC)62, and Al20Li20Mg10Sc20Ti30 (HEX)63. Finding further examples of HEAs discovered since these datasets were compiled proved to be challenging owing to the large number of publications that study properties of well-established HEAs or report to have discovered a new “HEA” and then present multi-phase EDS or XRD data. Most incorrect predictions are for alloys containing at least 5 atomic percent Al and at least one other FCC element for which it is known to form the B2 phase (e.g., Ni). The few predictions that are wrong, when the allotropy model predicts the BCC phase, contain Cr or Nb, which are known Laves phase formers. While phases other than BCC and FCC are possible, they rarely occur as demonstrated previously7. Between the two databases of HEAs analyzed in this work, 95% are either FCC or BCC with HCP next most common, appearing in only eight instances. Therefore, elucidating the underlying mechanisms governing FCC and BCC phase formation is expected to play a pivotal role in advancing the design and development of high-entropy alloys. The presence of the light elements Cu, Li, Mg, Sn, and Zn does not reduce the accuracy of the model for FCC and BCC compositions, as it known to using other descriptors52. It is noted that the high temperature crystal structure of the allotrope elements (e.g., FCC for Fe) may also play a role in crystal structure determination, particularly for compositions with small amounts of non-allotrope elements or when the processing route involves high temperatures. This may be useful as a second allotropy-based descriptor in future modeling of HEA phase formation. Despite the few incorrect predictions described, allotropy is likely to become an important feature in future modeling approaches and may further improve their predictive performance.

Fig. 3
figure 3

Characterization of fabricated compositions. An electron image is included with the EDS maps for (A) Al8.90Cr11.45Nb20.45Ni19.37Ta39.83 (B) Al27.00Cr13.01Mo24.00Nb23.24V12.74 (C) Al8.87Nb20.37Ni19.30V11.17W40.30 (D) Mo14.64Nb14.17Ni35.81Ta27.60V7.77 (E) Cr13.61Cu24.93Mo25.10Ni23.03V13.33 (F) Cu19.11Mo14.42Nb13.97Ni17.65Ta27.20V7.66 (G) Cr6.68Cu20.41Mo12.33Nb11.94Ni18.85Ta23.25V6.54 (H) Cr5.08Cu18.65Mo9.37Nb9.07Ni17.21Ta17.68V4.98W17.96 and (I) Al8.87Cr5.69Mo10.50Nb10.17Ni19.28Ta19.80V5.57W20.12. Each sample is observed to be multi-phase as arc melted. All compositions are provided in weight percent. Note that Ta and Cu have overlapping characteristic X-ray peaks. The scale bar in the lower right tungsten EDS map is 25 μm.

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Fig. 4
figure 4

Chemistry maps for annealed Al8.90Cr11.45Nb20.45Ni19.37Ta39.83. An electron image is included with the EDS maps for Al8.90Cr11.45Nb20.45Ni19.37Ta39.83 after annealing at 1475 °C in an inert environment. The sample remains multi-phase. The pores are attributed to Kirkendall voids. The scale bar is 25 μm.

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Subsequently, the importance of allotropism on single phase formation was demonstrated via an extensive thermodynamic modeling campaign and fabrication of several alloys with 5 to 8 non-allotrope elements in the ThermoCalc high entropy alloy database. The miniscule subset of non-allotrope compositions predicted to be single phase at any temperature, particularly compared to the known HEAs that could be modeled, suggests none are likely to form a single-phase HEA. The 11 materials not studied, owing to the expense of Ir and Rh, are likely to be incorrect predictions far from the composition space assessed to build the ThermoCalc database. Unfortunately, these elements are prohibitively expensive to study. Ultimately, without a dominant non-allotrope crystal structure, there does not appear to be a driving force toward a particular crystal structure, thus resulting in a multi-phase material. This implies a significant number of complex concentrated alloys can be ruled out as potential single phase HEAs.

One limitation of this study is the sheer number of ways the alloys could be processed in comparison with the methods utilized herein. Differences in processing (e.g., annealing temperature) can result in conflicting reports for the same composition (e.g., some Cantor alloys which are well known to decompose into multiple phases at lower temperatures). For example, the data compiled by Murty et al. lists 43 different processing routes29. The caveat to the numerous processing routes is that several, such as sputtering, mechanical alloying, melt spinning, and suction casting, are known to allow for metastable structures. One such example in the dataset is CrNbTiVZn (60% BCC and 20% HEX non-allotropes) processed by 60 h of mechanical alloying and reported to be single phase FCC by Dwivedi et al.64. In their own work, the authors recognize the metastable nature of the FCC phase achieved under non-equilibrium conditions. It is likely that other reports in the aggregated datasets are for non-equilibrium results. The number of compositions from the literature that ThermoCalc did not predict to be single phase at equilibrium supports but does not prove this statement. Thus, the allotropy model may achieve better performance than derived from analysis of the existing literature when considering whether the reported result is at equilibrium or not.

In the near term, it is expected that this work will be extended to the analysis of other crystal structures, such as the hexagonal phase HEAs. Additionally, this model provides specific guidance for the design of HEAs by offering a chemical basis for targeting specific crystal structures. Since there is no symbol representing allotropism or non-allotrope forming elements, the categorical descriptor \(\:{NAF}_{major}\) for the majority non-allotrope forming crystal structure type (e.g., \(\:{NAF}_{major}=\text{F}\text{C}\text{C}\)) and quantitative descriptors \(\:{NAF}_{fcc}\), \(\:{NAF}_{bcc}\), \(\:{NAF}_{hex}\), etc. (e.g., \(\:{NAF}_{fcc}=43.2\text{\%}\)) of the atomic fractions of the non-allotrope forming elements for each crystal structure are proposed. These descriptors and symbols provide a means for standardizing discussion of the role of allotropy and can be utilized in materials informatics applications. In the long term, further study of the incorrect predictions from this allotropy-based approach may shed new light on the physics governing crystal structures for HEAs and other classes of materials.

Conclusions

The allotropy model for high entropy alloy crystal structure suggests that the non-allotrope elements play a significant and impactful role in the resultant crystal structure in concentrations as little as 5 atomic percent (e.g., the FCC alloy Ni5(CoFeMn)95). This provides a simple model for addressing two of the seminal questions in complex concentrated alloys: (1) will a single-phase form (therefore a high entropy alloy), and if so (2) which crystal structure will prevail. Future analyses of HEAs, including the allotropy descriptor, may shed further light on why some compositions cannot be explained solely by allotropy. Lastly, we present the challenge to the community to identify a single composition containing equal atomic percentages of two or more crystal structures, and only utilizing non-allotrope elements, that solidifies into a single crystal structure HEA.