# High-Entropy Alloy Design Toward Cobalt Substitution for High Hardness and Low Wear Rate Using X-Cr-Fe-Mn-Ni System

Rafaël Jénot, Laurent Peltier, Fodil Meraghni, Mathieu Marquer, Oriane Baulin, Clotilde Macke-Bart

► To cite this version:

Rafaël Jénot, Laurent Peltier, Fodil Meraghni, Mathieu Marquer, Oriane Baulin, et al., High-Entropy Alloy Design Toward Cobalt Substitution for High Hardness and Low Wear Rate Using X-Cr-Fe-Mn-Ni System. Advanced Engineering Materials, 2025, 10.1002/adem.202502266. hal-05416476

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# High-Entropy Alloy Design Toward Cobalt Substitution for High Hardness and Low Wear Rate Using X-Cr-Fe-Mn-Ni System

Rafaël Jénot, Laurent Peltier,* Fodil Meraghni, Mathieu Marquer, Oriane Baulin, and Clotilde Macke-Bart

In the aerospace, nuclear, and machining industries, alloys require high hardness and excellent wear rate. Most high-performance alloys rely on cobalt for high-temperature properties, despite its political, ethical, and health concerns. High-entropy alloys (HEAs), enabled by structural hardening, lattice distortion, and sluggish diffusion, offer pathways to eliminate this critical element. This study examines cobalt substitution in HEAs to optimize hardness and wear rate. New alloys based on the Cantor system (CoCrFeMnNi) are produced by individually replacing cobalt with copper, aluminum, vanadium, or molybdenum. Four equia-tomic HEAs (AlCrFeMnNi, CrFeMnNiv, CrCuFeMnNi, and CrFeMnMoNi) are compared with two literature alloys (Al₀.₂Co₁.₅CrFeNi₁.₅Ti and CoCrFeMnNi) and with the pure substituent elements, all evaluated in the same metallurgical state. All synthesized HEAs except CoCrFeMnNi are multiphased and do not mimic the structure of their corresponding pure element; CrCuFeMnNi also departs from valence electron concentration predictions. Pure cobalt shows the lowest wear rate, while the Cantor alloy exhibits a higher one. Aluminum, vanadium, and molyb-denum strengthen HEAs despite limited performance in their pure state. Ultimately, pure cobalt, CrFeMnMoNi, and AlCrFeMnNi display similar and superior wear rate compared with the optimized reference alloy Al₀.₂Co₁.₅CrFeNi₁.₅Ti.

## 1. Introduction

In the aerospace, machining, and nuclear industries, alloys must combine high hardness with low wear rate, as demonstrated by

R. Jénot, L. Peltier, F. Meraghni
LEM3, Arts et Métiers Institute of Technology
Université de Lorraine
CNRS. 4 rue Augustin Fresnel, 57070 Metz, France
E-mail: laurent.peltier@ensam.eu

M. Marquer, O. Baulin, C. Macke-Bart
Senlis, Research and Programs Department
Centre Technique Des Industries Mécaniques
52 Av. Félix Louat, 60300 Senlis, France

<figure><img src="image_2.png" /></figure>

The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/adem.202502266.

© 2025 The Author(s). Advanced Engineering Materials published by Wiley-VCH GmbH. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

DOI: 10.1002/adem.202502266

alloys such as EM42 (Erasteel),[1] Inconel 625,[2] Marval 18 (Auber et Duval),[3] or the Stellite alloys (Kannametal).[4] Almost all of these alloys, superalloys, or high-speed steels (HSS) contain cobalt. The use of cobalt in these alloys is motivated by their targeted refractory properties, which means high-temperature resistance and high-temperature hardness.[5]

Yet, cobalt has become an increasingly controversial metal for several reasons. The first one is for political and ethical reasons; cobalt ore distribution on the planet is highly heterogeneous. It is estimated that over 80% of the world's reserves are to be found on the seabed;[6] however, these resources remain technologically and economically out of reach. The leading mining country is the Democratic Republic of Congo: more than half of the world's terrestrial cobalt resources are located in the copper belt. The government currently supplies around 70% of global production. The contribution of other producing countries is much lower: Australia 17%, Cuba 7%,

and Russia 4%.[6] The Democratic Republic of Congo is a torn country,[7,8] which leads to children being forced to mine the ores without any protection or infrastructure, often causing injuries or deaths. The second problem is an economic one. Due to the previous point, cobalt prices vary greatly, inducing economic unpredictability. In the last five years, the cobalt price has been oscillating between 20000 and 82000 $ ton⁻¹. For instance, during the same time gap, aluminum, a less critical element, had its price oscillating between 1500 and 4000 $ ton⁻¹.[9,10] Moreover, against the backdrop of the current energy transition, the demand for batteries is growing, particularly for electric vehicles. Cobalt consumption for producing lithium-ion batteries, of which LiCoO₂ is a frequent constituent, accounts for around 80% of ore extraction and processing.[11,12] Even if its current price tends to decrease, an increase could occur shortly since the battery demand will increase due to the European electric car law of 2035.[13,14] Finally, the third problem is health-related; if cobalt dust comprises more than 0.3 µg m⁻³ of air, it can cause throat and lung cancer[15,16] and is the main radiating element in the nuclear industry.[17] All these arguments explain why the industries are planning to reduce the use of Cobalt in their alloys.
Therefore, this study aims to analyze cobalt substitutes in high-
entropy alloys (HEAs) while optimizing the hardness and wear
rate and observing the mixing properties of these alloys.

Previous studies have shown that HEAs have three common
properties due to their multiple principal elements (at least five)
in equiatomic proportion.[18,19] The first one is the lattice distortion
effect. In fact, with a perfectly random distribution, each atom
is no longer surrounded by atoms of the same element.
Disturbances and tensions in the lattice can, therefore, be caused
by the difference in atomic radius, as well as the different forces of
attraction between the elements. This lattice distortion also pre-
vents the diffusion of elements, leading to the second HEA's prop-
erty, the sluggish diffusion effect. This property is the main reason
for using HEAs to replace cobalt. HEAs tend to form nanocrystal-
line structures or nanoprecipitates, grouping atoms that have only
diffused over very short distances. These nanoprecipitates
harden the alloy and bring about lattice stability, leading to high-
temperature resistance.[20,21] The third property is the cocktail
effect. The cocktail effect describes, on the one hand, the possibil-
ity of cumulating, combining, and/or enhancing the characteris-
tics of pure elements and, on the other hand, the possibility of
obtaining new, unexpected, and nonexistent properties. This effect
is due to the multiple differences in possible microstructural con-
figurations. Previous studies also showed that the microstructure
of HEAs can be predicted by calculating the valence electron con-
centration (VEC).[22] These characteristics are the reason why
HEAs could be good candidates for refractory alloys.[23]

Literature has shown that defining an element substitution is a
common strategy when working with HEAs. For instance, Peltier
et al. have employed this strategy to develop high-entropy shape
memory alloys (HESMAs).[24] This strategy consists of determin-
ing the element to substitute, nickel and titanium for Peltier et al.
study, and cobalt for this one. Then, highlight the chemical prop-
erties common to elements of equivalence and choose the partial
or total replacement of one element by another in a composition.
Other studies, like those by Ding et al. or Chen et al., also used
and explained the substitution method.[25,26] The common prop-
erties used to substitute an element are the chemical properties
inherent to the element structure, mixed with an aimed property
 shape memory, hardness, hydrogen container, etc.).[24]

Chuang et al. have already proved the use of HEAs for wear
rate by working on the AlₓCo₁.₅CrFeNi₁.₅Tiᵧ alloys, with the
Al₂Ti₁₀ sample being the most wear-resistant.[27] Yet, every alloy
studied is composed of cobalt. Bhasakaran Nair et al. have the
same result for tribo-corrosion by comparing Al₀.₁CoCrFeNi to
SS316L.[28] Moreover, Kasar et al.'s review also highlights this
point, as almost every alloy in their review comprises cobalt or
other critical elements.[29] Nevertheless, Li et al. showed the
potential of cobalt-free HEAs for refractory properties.[30]

This study examines the strategic substitution of cobalt in
HEAs, with the dual objectives of optimizing mechanical perfor-
mance, specifically hardness and wear rate, and considering the
element mixing behavior. The investigation focuses on compo-
sitional modifications of the Cantor alloy (CoCrFeMnNi),
wherein cobalt is individually replaced by copper, aluminum,
vanadium, or molybdenum, while preserving an overall equia-
tomic balance among the constituent elements. To this end,
six HEAs are designed and produced, including four novel equia-
tomic HEAs specifically developed for this work. Comprehensive

metallurgical and tribological characterizations are conducted on
all compositions to evaluate their microstructural evolution,
hardness, and tribological properties. The results obtained
for the newly developed HEAs are systematically compared
with two benchmark HEAs from the literature, namely:
Al₀.₂Co₁.₅CrFeNi₁.₅Ti²⁷⁾ and the Cantor alloy.³¹⁾ as well as with
the pure substituent elements, to better understand the role of
each substitution. It is worth noticing that all samples are exam-
ined in the same metallurgical condition to highlight the intrin-
sic characteristics of the HEAs.

The first part of this article outlines the selection of the studied samples, their preparation, and the fabrication process. This is followed by a detailed description of the experimental methodology and testing procedures. Finally, the results dealing with hardness and tribology features are presented and discussed, including metallurgical analyses using scanning electron microscope (SEM), energy dispersive X-ray spectroscopy (EDX), and X-ray diffraction (XRD). A discussion on predictive tools for HEAs and the thermodynamics of phase formation is provided to help explain the metallurgical results obtained.

## 2. Material Design and Fabrication Process

Cantor et al. pioneered the design of the first HEA, CoCrFeMnNi,
in 2004. Brian Cantor had worked on these alloys since the 1980s,
when he became very interested in their potential properties.[31]

Although Cantor alloy appears single-phased with the XRD
analysis, the **Figure 1** providing the atomistic map, showing
the dendrite phase composed of Cantor's alloy (blue) and the
interdendritic phase composed of high Cr, high Mn, and low
Fe (red). It proves the existence of a homogeneous stable phase
composed of 5 elements in equiatomic proportion. Zhou et al.[32]
modified the view of strict component equiatomicity by extend-
ing the acceptable range of atomic concentration from 5-35% as
long as ΔS<sub>mix</sub> > 1.5R with R, the ideal gas constant.

<figure><img src="image_3.png" /><figcaption>**Figure 1.** Cantor's Fe X-ray map for CoCrFeMnNi 20 at.% each.[31]</figcaption></figure>
As shown by the number of citations of Cantor et al. article, the Cantor alloy is the most studied HEA. Fortunately, Cantor alloy is partially composed of cobalt, making it a suitable reference alloy for cobalt substitution.

The substitution method explained in the introduction was used to substitute the cobalt in Cantor.[31] The equivalent elements proposed throughout this manuscript have been chosen according to several criteria that we have determined and used:[33,34] 1) Hardening metal properties; 2) atomic radius and covalent radius; 3) pauling electronegativity; 4) metal classification: non-rare, metal transition, or alkaline earth metals; 5) melting temperature and melting energy; and 6) evaporation temperature and evaporation energy.

In the literature, two elements have proven their hardening properties. The first one is aluminum, well-known for its hardening properties by producing precipitates and its age-hardening properties.[35] Moreover, every element forming the Cantor alloy is on the fourth row of the periodic table, whereas aluminum is on the third row. This difference might favor the occurrence of a multiphased alloy, thus hardening the macroscale alloy. The second element known for its hardening properties is chromium.[35] As chromium is already in Cantor alloy, finding elements of substitution for the chromium while keeping its proportion might enhance the alloy's properties, bearing the lack of cobalt. Another element that could be used is titanium,[36] but many studies have proven that the mix of Ni-Ti can cause a shape memory effect, which is avoided in this study.[24,37] Theoretical substitution elements have been found by analyzing the atomistic structure of every element highlighted,[33] and the following Figure 2 shows them.

In Figure 2, it has first been shown that every element constituting the Cantor alloy is in the fourth row and is near each other. The Co-Fe-Ni structure is also relatively similar, each being a substitute element for the others. Some of the elements of substitution shown are classified as rare or unethical, which implies that they have not been studied in this context for similar reasons that cobalt needs to be substituted. These elements are gold (Au), indium (In), palladium (Pd), platinum (Pt), and tungsten (W).[38-44] Using the melting and evaporation temperature criteria, Gallium (Ga) and zinc (Zn) were also excluded. On the one hand, gallium has a

melting temperature of 29.76 °C,[45] which makes it almost liquid at room temperature and, therefore, uncastable with the elaboration process used in this study. On the other hand, zinc has a boiling point of 906.9 °C,[46] which means it boils before most other elements liquefy, thereby preventing the formation of an alloy through the process used. Finally, the remaining elements have been used to substitute the cobalt in new HEAs, designing and producing the following alloys: 1) Cantor alloy: a single-phased HEA composed of CoCrFeMnNi in equiatomic proportion; 2) AntruC: Cantor alloy with copper (CrCuFeMnNi) substituting the cobalt in equiatomic proportion; 3) AntrAl: Cantor alloy with aluminum (AlCrFeMnNi) substituting the cobalt in equiatomic proportion; 4) AntraV: Cantor alloy with vanadium (CrFeMnNiV) substituting the cobalt in equiatomic proportion; 5) AntroM: Cantor alloy with molybdenum (CrFeMnMoNi) substituting the cobalt in equiatomic proportion; and 6) Al₀₂Ti₁₀. The reference HEA designed by Chuang et al. Al₀₂Co₁.₅CrFeNi₁.₅Ti.[27] This alloy is used to compare the results of the tribology test.

Unlike the other samples, AntrAl has already been studied by Munitz et al. and Zhang et al.,[47,48] yet it has been tested as if it were new in this study. In their study, Chuang et al. have proven that HEAs could be used for low wear rates. The alloy with the minimum wear rate in their article is the Al₀.₂Co₁.₅CrFeNi₁.₅Ti alloy, named Al₀₂Ti₁₀.[27] As it is partly composed of cobalt and optimized for low wear rate, Al₀₂Ti₁₀ stands out as a strong reference alloy for our study. A test on the pure elements substituting the cobalt and the cobalt itself has also been studied to verify a correlation between the pure elements and the HEAs, thus confirming the cocktail effect property of HEAs.

Using the VEC criteria, the microstructure of these HEAs can be anticipated.[22,49] To calculate it, the following formula has been used

$$VEC = \sum_{i=1}^{n} c_{i}(VEC)_{i} \qquad (1)$$

where $c_i$: atomic concentration of element i and $VEC_i$: VEC of element i

The results are shown in Table 1:

<figure><img src="image_4.png" /><figcaption>Figure 2. Periodic table of highlighted element substituents. This table was proposed by combining the atomistic properties and configurations of each element. This table has been found using a reverse engineering method formerly used by Peltier et al.[33]</figcaption></figure>
<table><caption>**Table 1.** Besides the VEC calculation and theoretical microstructure of the designed HEAs, this table recalls the acronyms of the studied alloys as well as their targeted chemical compositions.</caption><thead><tr><th>Alloy</th><th>Targeted composition</th><th>VEC</th><th>Microstructure expected</th></tr></thead><tbody><tr><td>Cantor</td><td>CoCrFeMnNi</td><td>8.2</td><td>FCC</td></tr><tr><td>AntruC</td><td>CrCuFeMnNi</td><td>8.6</td><td>FCC</td></tr><tr><td>AntrAl</td><td>AlCrFeMnNi</td><td>7</td><td>Multiphased</td></tr><tr><td>AntraV</td><td>CrFeMnNiV</td><td>7.4</td><td>Multiphased</td></tr><tr><td>AntroM</td><td>CrFeMnMoNi</td><td>7.2</td><td>Multiphased</td></tr><tr><td>Al<sub>0.2</sub>Ti<sub>10</sub></td><td>Al<sub>0.2</sub>Co<sub>1.5</sub>CrFeNi<sub>1.5</sub>Ti</td><td>7.69</td><td>Multiphased</td></tr></tbody></table>

Several fabrication processes can be used for producing HEAs,[50–52] among them, we can cite the hot-pressure powder alloying.[53,54] In this study, the cold crucible has been used. The elaboration process could commence after studying the formation criteria and analyzing the binary diagrams. The alloys examined were produced using high-purity raw materials; the purity of various metals exceeded 99.9 wt% (Figure 3a,c,g). A CFSYS cold crucible (or levitation furnace) combined with a 50 kW CELES induction furnace was used to produce the alloys (Figure 3b,d,f,h). It is equipped with a laser pyrometer that measures the alloy’s melting temperature (Tm). Before heating, the cold crucible was evacuated five times to a vacuum pressure of 5e–2 mbar and then filled with ultrapure Argon gas. To ensure the miscibility of the elements in the cold crucible, the fabrication of binary or ternary suballoys is mandatory before being mixed (Figure 3a,c,e). Melting was conducted in ultrapure Argon at a pressure of 9 mbar. Subsequently, each ingot was flipped into the crucible using an ejection system inside the cold crucible before the five melting cycles, which were performed to ensure the homogeneity of the produced alloy. Once the suballoys are designed and fabricated, they are mixed with a potential element addition if needed, before following the same casting procedure to produce the targeted HEA (Figure 3e–h). The ingot was then cast

in a square mold with a volume of Vf (8 cm³ in this case) (Figure 3i).[20] The ingot is cooled in the ultrapure Argon atmosphere at a rate of 30 °C min⁻¹.

## 2.1. Experimental Methodology and Test Procedures

SEM observations have been made on a Zeiss SUPRA40 microscope equipped with a tungsten filament. An EDX analysis has been used to ensure the sample’s chemical composition. This experimental technique can be quantitative and qualitative; it provides a map of the spatial distributions of the elements in the sample. These data are essential to verify the phase state of the alloy (homogeneous or not). EDX can also provide a line-scan analysis, which outputs the composition of a line drawn by the user. Knowing the exact composition of a specific phase in the alloy is very useful. The microstructural analysis with this SEM/EDX has been conducted with a magnification of x750, a high-tension electron of 20 keV, a microscope aperture of 60 µm and a temperature of 0 °C.

XRD analysis on the Siemens D5000 machine has been used to determine the internal type of lattice in the alloy. This method uses a beam of X-rays, which, upon encountering a crystal, is reflected in specific directions determined by the X-ray wavelength and the dimensions and orientation of the crystal lattice. The diffractograms were analyzed using the software Maud[55] to get the parameters of this alloy.

Every alloy has been tested for microhardness with a Zwick Roell ZHV machine, following the ASTM E92 standards.[56] A HV1 test is done five times on each alloy; this test consists of applying a mass of 1 kg during 10 s without vibration, with a variation of less than 5%.

This study requires every sample to have the same roughness before the tribology test to ensure a comparable state of each alloy. To achieve this state, the same automatic polishing cycle has been applied to every sample studied. The process involves four polishing steps, each lasting five minutes and using a 25 N load: first with 12 µm polishing paper, then with 9 µm diamond

<figure><img src="image_5.png" /><figcaption>**Figure 3.** The representation of the cast of a high-entropy alloy with the cold crucible. To ensure the miscibility of the elements, suballoys must be compounded by a) placing the pure elements in a cold crucible and b) forming the first suballoy using induction. c) placing other elements in the cold crucible and d) forming the second suballoy. Once done, e) those suballoys are both put in the cold crucible to f) mix together, then g) add an optional last element and h) cast the targeted HEA. Finally, i) placing the cold crucible over a mold and using one last induction to cast the HEA in the desired shape.</figcaption></figure>
polishing paper, followed by 3 µm diamond polishing paper, and finally with 1 µm OPS polishing paper. Roughness tests were performed with a Mitutoyo SJ-201M machine. This test measures the deviation from the arithmetic mean (Ra), the maximum height (Rz), and the deviation from the root mean square (Rq) with a cut of length of 10 mm on a 20 mm length sample. This test has been reproduced three times per sample; if the results diverge, the polishing cycle is done once again.

Tribology studies the mechanical behavior of surfaces (bodies) in contact during relative motion. In particular, the effects of the various parameters linked to the conditions of movement (mechanical force, speed, temperature, and medium in which the movement occurs) on surface damage are analyzed. The focus here is on friction between the two bodies and the wear phenomenon. Limiting the effects of friction through lubrication is another area of tribological study.[57]

A tribological system consists of two surfaces, commonly called first bodies, brought into contact by a normal force, Fn. When one of the first two bodies is in motion relative to the other, a frictional force appears and opposes this motion. This is the tangential force, noted Ft. The Amontons-Coulomb law links these two forces through the coefficient µ, the coefficient of friction.

A low coefficient of friction corresponds to a situation where the relative motion of the first two bodies is easy. However, analyzing the friction coefficient is extremely complicated, as its value depends on the experimental conditions.[58]

A tribological system under wear conditions often contains a third body. This includes all the bodies (debris particles, film adhering to a surface, liquid, etc.) between the first two bodies. The actions produced by the third body depend on their nature: they can prevent or limit damage, but can also aggravate it. For example, a lubricant's role is to reduce the friction coefficient and limit surface wear. Its form and nature differ according to the application, the materials in contact, and the conditions in which contact occurs (environment). Finally, the origin of a lubricant can be “artificial” (if an operator adds it) or “natural” (if it results from physico-chemical interactions within the tribological system, causing phase transformations, corrosion, etc.). On the other hand, harsh particles from one or both bodies can cause tiny cracks in them and further damage them.

The two main experimental methods of tribology are the pin-on-block and pin-on-disk tests. A pin or a ball will contact a moving surface with a force applied for both tests. The main differences are the direction and speed of the test: the first one is unidirectional and has an alternative speed, whereas the second one is circular and has a constant speed.

For this study, the Phoenix Tribology (formerly Plint) TE77 tribometer was used to test the wear rate. The tribology tests were conducted using the ball-on-block method, following ASTM

G-133 standards,[59] as shown in Table 2. It allows us to use any sample shape when the contact surface is longer than 15 mm. The test is also conducted three times, with at least two tests with results differing by less than 25% according to the standards,[59] to ensure the reliability of the result data. The ball specimen used in this study is an alumina ball (Al₂O₃); one ball is used per test, as using the same ball for several tests could change how the ball interacts with the sample (plasticity and strain hardening). The specimens (ball and sample) were weighed before and after every test to determine each test's mass loss or increase.

The tribometer used is composed of several parts, as schematically shown in Figure 4. The carriage is a slightly deformable piece directly linked to the friction force transducer and holds the sample holder. A structure holds the ball specimen to fit it onto the tested sample. A loading arrangement is placed over the roller part of the same structure to ensure a normal load without adding any directional loads. Finally, an oscillating system is connected to the ball-holding structure, ensuring oscillation by converting the rotating movement into linear oscillation through a crank-rod system.

# 3. Results and Observations

## 3.1. Metallurgical Results

As this study concerns HEAs, all the samples are designed in equiatomic proportions. Yet, as these alloys are engineered and produced in the laboratory, they cannot always have the same proportion as designed. An EDX analysis, as shown in Table 3, is required to ensure the composition of each alloy in atomic percent.

These results show that the studied HEAs are not strictly equiatomic but still fall within Zhou et al. less strict definition; an alloy with five or more elements between 5 at.% and 35 at.%.[32] Moreover, the VEC calculation, part of the material preparation and elaboration process, has been performed using the composition determined by the EDS analysis.

Although only one element was changed, the microstructure of those alloys is drastically different.

Except for the Cantor alloy, which is assumed to be singlephased, all other produced HEAs are multiphased, as confirmed by XRD test and summarized in Table 4. An EDS analysis shows that most of these multiphase regions correspond to distinct chemical phases. These obtained results are valuable considering that several studies have shown that an alloy's macro hardness increases whenever it is multiphased.[60–63]

In addition to the microstructure analysis, the result of the XRD test, combined with the calculation of VEC, can add information to this analysis. It is worth noticing that the VEC results

<table><caption>**Table 2.** ASTM G-133 procedure A and the tests parameters of tribology tests.[59]</caption><thead><tr><th>Type</th><th>Normal force [N]</th><th>Stroke length [mm]</th><th>Sample dimensions [mm]</th><th>Counterface diameter [mm]</th><th>Oscillation frequency [Hz]</th><th>Sliding distance [m]</th><th>Ambient temperature [°C]</th><th>Relative humidity [%]</th><th>Lubrication</th></tr></thead><tbody><tr><td>ASTM</td><td>25</td><td>10</td><td>Not described</td><td>Not described</td><td>5</td><td>100</td><td>19 to 25</td><td>40 to 60</td><td>None</td></tr><tr><td>Test</td><td>25</td><td>10</td><td>20, 20, 10</td><td>10</td><td>5</td><td>100</td><td>20 to 22</td><td>40 to 60</td><td>None</td></tr></tbody></table>
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Ball-on-block tribometer schematic diagram showing the different parts of the system.</figcaption></figure>

<table><caption>**Table 3.** EDX at% results of the produced alloys. The obtained results confirm that the studied alloys have the expected composition of the alloying elements with a mean absolute error given by the SEM.</caption><thead><tr><th>Element</th><th>Cr</th><th>Fe</th><th>Mn</th><th>Ni</th><th>Co</th><th>Cu</th><th>Al</th><th>V</th><th>Mo</th><th>Mean abs. error [%]</th></tr></thead><tbody><tr><td>Cantor</td><td>20.44</td><td>20.39</td><td>19.35</td><td>20.20</td><td>19.62</td><td>0.00</td><td>0.00</td><td>0.00</td><td>0.00</td><td>0.19</td></tr><tr><td>AntruC</td><td>18.07</td><td>23.94</td><td>19.45</td><td>20.24</td><td>0.00</td><td>18.31</td><td>0.00</td><td>0.00</td><td>0.00</td><td>0.53</td></tr><tr><td>AntrAl</td><td>21.72</td><td>22.13</td><td>14.95</td><td>22.00</td><td>0.00</td><td>0.00</td><td>19.20</td><td>0.00</td><td>0.00</td><td>0.52</td></tr><tr><td>AntraV</td><td>15.28</td><td>23.16</td><td>23.08</td><td>22.49</td><td>0.00</td><td>0.00</td><td>0.00</td><td>15.98</td><td>0.00</td><td>0.52</td></tr><tr><td>AntroM</td><td>19.40</td><td>20.95</td><td>22.38</td><td>21.78</td><td>0.00</td><td>0.00</td><td>0.00</td><td>0.00</td><td>15.49</td><td>0.57</td></tr></tbody></table>

<table><caption>**Table 4.** XRD and VEC results for the high-entropy alloys studied.</caption><thead><tr><th>Alloys</th><th>VEC</th><th>Crystal type</th><th>Crystal parameters [nm]</th></tr></thead><tbody><tr><td>Cantor</td><td>8.20</td><td>FCC</td><td>3.6</td></tr><tr><td rowspan="3">AntruC</td><td rowspan="3">8.63</td><td>FCC type 1</td><td>3.682</td></tr><tr><td>FCC type 2</td><td>3.65</td></tr><tr><td>BCC</td><td>2.9</td></tr><tr><td>AntrAl</td><td>7.11</td><td>BCC</td><td>2.9</td></tr><tr><td>AntraV</td><td>7.66</td><td>FCC - Tetragonal</td><td>3.69</td></tr><tr><td>AntroM</td><td>7.43</td><td>FCC - Tetragonal</td><td>3.65</td></tr></tbody></table>

have been calculated considering the actual composition of the produced alloys, as given in Table 4.

Most of these results (Table 4) correlate with the images (Figure 5 and Figure 6). The VEC anticipates the single-phased structure of the Cantor alloy (Figure 5a and 6a), as its cartography is similar to the one Cantor proposed (Figure 1). It also anticipates the multiphased structures of AntraV and

AntroM, whose images and XRD show they are multiphased (Figure 6d,e, Table 4).

Although the theoretical calculation of the designed HEAs in Table 1 predicted AntroM's microstructure as single-phased and BCC, the slight difference between the alloy design and its elaboration caused its VEC to increase enough to predict a multiphased microstructure, which occurred. The intriguing case is the microstructure of AntruC. In fact, as its VEC is over 8, the expected microstructure was a single-phased FCC, yet EDS and XRD showed that its microstructure was multiphased (Figure 6b and Table 4). This highlights that the VEC prediction might be inaccurate or too simplified, leading to a deeper analysis of this criterion and the phase formation thermodynamics.

## 3.2. VEC and Phase Thermodynamic Analysis

Recent studies have shown that there were new indicators for HEAs, such as d-orbital energy calculation[30,64] or a bilinear combination of multiple descriptors.[65,66] Yet, these new criteria
<figure><img src="image_7.png" /><figcaption>**Figure 5.** SEM analysis of a) Cantor alloy, b) AntruC, c) AntrAl, d) AntraV, e) AntroM, and f) Al₀₂Ti₁₀ HEA designed by Chuang et al.[27] All these alloys have been casted and fabricated in the cold crucible for the present study. The microstructural analysis with this SEM/EDX has been conducted with a magnification of x750, a high-tension electron of 20 keV, using secondary electron analysis, a microscope aperture of 60 µm and a temperature of 0 °C.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Figure 6.** EDS atom cartography of cobalt or its element of substitution in every HEA studied. a) The cobalt cartography in Cantor alloy. b) The copper cartography in AntruC. c) The aluminum cartography in AntrAl. d) The vanadium cartography in AntraV. e) The molybdenum cartography in AntroM and f) the cobalt cartography in Chuang et al. Al₀₂Ti₁₀ HEA. The microstructural analysis with this SEM/EDX has been conducted with a magnification of x750, a high-tension electron of 20 kV, a microscope aperture of 60 µm, a temperature of 0 °C, and the cartography duration has been five minutes per sample.</figcaption></figure>

bring up debate within the metallurgical community; therefore, this study will focus on a historical analysis of the well-known HEA and metallurgical predictors.

Hume-Rothery did some pioneering work in metallurgy as he proposed in 1926 the four rules toward the design of binary alloys[⁶⁷⁻⁶⁹]: 1) The atomic radius of the solute and solvent atoms
must not differ by more than 15%; 2) the crystal structures of the solute and solvent must be similar; 3) complete solubility occurs when the solvent and solute have the same valency. A metal is more likely to dissolve a metal with a higher valency than the reverse; and 4) the solute and solvent should have similar electro-negativity. Otherwise, metals tend to form intermetallic compounds instead of solid solutions.

Although these rules apply to the design and the production of binary alloys, studies on complex alloys like those of Mizutani et al. and Yeh et al. showed that they also apply to the formation of more complex alloys, including HEAs.[18,70] This is because the electron concentration works similarly in a low-entropy alloy as in a HEA regarding phase stability. Concerning the electron concentration, there are two types of formulation: e/a and VEC. The first one is the average number of itinerant electrons per atom. The other is the mix of the total number of electrons, including those on the valence band.[70] The effect of the e/a on the phase stability is articulated around the Hume-Rothery second rule, as a similar structure occurs at a similar e/a. VEC is more effective in controlling the ordered crystal parameter, as shown experimentally by several studies.[22,71,72] Concerning the HEAs, it has been very difficult, due to their high concentration of several elements, to find a correct e/a. Studies have shown that working with the VEC leads to a more accurate prediction. A test database has therefore been established, resulting in the formation of the phase prediction using the VEC, explained in the elaboration part of this study.

Yet, because this rule is only based on experimental results, it has some limits. The first one is that the law can be applied only to HEAs mainly composed of transition metal elements, more precisely, to those with a 3 d or 4 d valence band.[73] The second limit is that every test HEA formed a BCC and/or FCC crystal structure, implying that the predicted phase can only be those two, or to an extent, an orthorhombic phase. Moreover, in contrast to binary alloys, the enthalpy of configuration (ΔH<sub>mix</sub>) of HEAs and complex-composed alloys is an essential parameter of the formation of intermetallic phases. Indeed, the more negative the mixing entropy, the more complex-composed alloys (including HEAs) tend to form intermetallics, ranging from 0 if ΔH<sub>mix</sub> > 0 kJ/mol to 5 intermetallics if ΔH<sub>mix</sub> < -75 kJ/mol.[74] Lastly, the VEC rule is less efficient in predicting the phases of alloys that do not follow the Hume-Rothery formation rules explained before.[67-69] Although these criteria are questioned by recent

studies, such as Chauhan et al.[75] this study challenges the basis of HEA's phase formation criteria.

Regarding the AntruC produced alloy, none of these limits have shown that the VEC could not predict its phase. Another way to predict the formation of single-phased or multiphased complex-composed alloys is to analyze the cohesive energy of every element placed in the studied alloy. The cohesive energy refers to the energy required to isolate constituent elements apart from each other and bring them to an assembly of neutral free atoms, whether a solid or a liquid, calculated in kJ mol⁻¹ at 298.15 K.[76] There is a correlation between this cohesive energy and the melting point of a material. The more similar the cohesive energy between two elements is, the easier it will be to form a homogenous phase between them. Yet, if two elements in a complex-composed alloy are similar and apart from each other, then it tends to produce a chemical multiphased alloy. **Figure 7** shows the cohesive energy calculated by Belin et al.[77]

Figure 7 shows that every element in the AntruC alloy has cohesive energy relatively close to that of the others. Yet, Cu, and Mn's cohesive energy is closer than the rest of the group, which can explain the fact that there is a different chemical phase within the HEA composed of Cu-Mn, as the difference with Cu and the other elements is small. A final way to analyze the formation of phases within an alloy is by analyzing the thermodynamics of phase formation. The CalPhad software has proven its reliability in predicting phases of HEA when the HEA database has been released. According to the thermodynamics of phase formation, a phase formed in the ternary alloy remains while forming a quaternary or quinary alloy.[78] Binary or ternary suballoys must be used to cast an HEA in the cold crucible. In the AntruC case, the copper and manganese were cast together as a suballoy. With the support of **Figure 8** showing the binary diagram, it has been observed that two phases were formed at equiatomicity, therefore probably forming another in the final HEA.[79]

As thermodynamic theories do not ensure that a phase appeared in a binary alloy stays in the quinary phase, it could be interesting to do an analysis of the tested HEAs with numerical metallurgy suballoy per suballoy or with Al-based approaches.[80,81] Another interesting analysis could be to design and produce a normally single-phased HEA in a multiphased HEA by voluntarily forming new phases with the binary suballoys.

The ability to predict phase formation in HEAs represents a significant advantage in their design. In single-phase alloys,

<figure><img src="image_9.png" /><figcaption>**Figure 7.** Cohesive energy (kJ mol⁻¹) of most of the periodic table elements calculated by Belin et al.[77] with the elements composing AntruC alloy highlighted by the red squares.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>**Figure 8.** Cu-Mn binary diagram. The manganese proportion represents the atomic proportion.</figcaption></figure>

certain functional properties such as shape memory may be enhanced, whereas in multiphase alloys, the overall hardness tends to increase,[82] leading to a reduction in abrasive wear rate.

### 3.3. Hardness and Tribology Results

Cantor alloy is known to be a soft alloy; therefore, this phase study does not aim to provide the hardest alloy but focuses on the hardening properties of the elements of substitution. Moreover, comparing the pure elements could verify or refute the HEA's cocktail effect property.[19]

Following the cocktail effect property by just analyzing the pure elements, a good element of cobalt substitution could be molybdenum, as their hardness is quite close (Table 5). However, the results of the HEAs should be considered, too. In fact, by adding cobalt, a hard pure element, the hardness of single-phased Cantor alloy is lowered, finding one similar to the literature.[83] It could still be relevant to the cocktail effect if all the other HEAs had a low hardness, which is invalid here.

While all the substitution elements greatly enhance the hardness of each HEA (compared to the Cantor alloy), two might be alloy-hardening metals. The first one, in line with Yeh's study,[18]

is aluminum, which, compared to its low hardness, enhances the hardness of the HEA by 348HV. The second one is vanadium, which is used for the same reasons as aluminum, giving a 438HV increase. Lastly, unlike cobalt, molybdenum contributes excellent hardness to the HEA, as it already possesses high intrinsic hardness. The addition of molybdenum results in a hardness increase of 309 HV compared to pure molybdenum. Among the tested alloys, Al02Ti10 exhibits the highest hardness, which can be attributed in part to its cobalt content, consistent with the findings reported by Chuang et al.[27]

However, vanadium and molybdenum are similar in both the crystallographic parameters and their alloy hardness-enhancing effect.[84,85] The cocktail effect property of the HEAs is proven to be nonexistent if all elements are considered one by one. It would be interesting to investigate whether this property applies when studying binary or ternary alloys.

To learn more, a tribology study has been done on the same elements and HEAs. As hardness directly correlates to the abrasion wear type, it is interesting to see if the same results apply to this test.

As the experimental methodology explains, a roughness test is required to ensure all the samples can be compared. Otherwise, some tribology results could be due to the roughness of the material rather than its microstructure.

To ensure that the roughness is the same, the same polishing range has been done on the sample before the roughness test. The tests were done three convergent times (more or less 0.1 µm) on every sample to avoid local errors. The mean results are shown in Table 6. The tribology tests could be done because alloys have low and close roughness.

Table 6 shows a significantly higher roughness for the aluminum sample, which is due to its low hardness, making it difficult to achieve the same roughness as the other samples during the polishing steps. This result is not required to be considered, as the study later shows that the aluminum wear rate is too high to be compared to the others.

To follow the ASTM G-133 standards, the samples and the ball specimen were washed with ultrasonic waves just before each test. The tribology tests were done three times per sample, with at least two tests with a relative gap of less than 25%. The tribometer is connected to a friction force transducer. This information is helpful to determine whether the test failed; for instance, if the ball specimen wasn't fixed enough, it can rotate and, therefore, drastically reduce the friction coefficient. Every working test

<table><caption>**Table 5.** Average hardness results in HV1 of the pure elements and the HEAs. All the results used for the average are less than 5% different.</caption><thead><tr><th></th><th>Co</th><th>Cu</th><th>Al</th><th>V</th><th>Mo</th><th>Cantor</th><th>AntruC</th><th>AntrAl</th><th>AntraV</th><th>AntroM</th><th>Al<sub>02</sub>Ti<sub>10</sub></th></tr></thead><tbody><tr><th>HV1</th><td>199</td><td>94</td><td>46</td><td>75</td><td>221</td><td>126</td><td>232</td><td>394</td><td>513</td><td>530</td><td>700</td></tr></tbody></table>

<table><caption>**Table 6.** Roughness test results of every sample studied. All the results are the mean result of three convergent roughness tests.</caption><thead><tr><th></th><th>Co</th><th>Cu</th><th>Al</th><th>V</th><th>Mo</th><th>Cantor</th><th>AntruC</th><th>AntrAl</th><th>AntraV</th><th>AntroM</th><th>Al<sub>02</sub>Ti<sub>10</sub></th></tr></thead><tbody><tr><th>Ra [µm]</th><td>0.04</td><td>0.04</td><td>0.17</td><td>0.08</td><td>0.03</td><td>0.02</td><td>0.04</td><td>0.04</td><td>0.03</td><td>0.04</td><td>0.05</td></tr><tr><th>Rz [µm]</th><td>0.22</td><td>0.43</td><td>0.99</td><td>0.50</td><td>0.19</td><td>0.15</td><td>0.24</td><td>0.22</td><td>0.20</td><td>0.28</td><td>0.32</td></tr><tr><th>Rq [µm]</th><td>0.05</td><td>0.06</td><td>0.22</td><td>0.10</td><td>0.04</td><td>0.03</td><td>0.05</td><td>0.05</td><td>0.04</td><td>0.05</td><td>0.06</td></tr></tbody></table>
had the same friction coefficient pattern, as shown by the friction coefficient recording of every studied alloy in **Figure 9**. Only one friction coefficient, linked to one tribology test, has been shown per alloy in Figure 9.

A peak at the beginning of the tribology test. This can be explained by the beginning of the tribology test, which removes the oxides and the residual stresses induced by the polishing range.[86-88] Then, the friction coefficient drops to its normal value and slowly increases during the test. This increase is explained by the fact that the tribology test induces a new roughness in the material, and the more the ball digs in the material, the more significant the interaction surface between the ball specimen and this new high roughness, increasing the tangential force, which increases the friction coefficient. To synthesize this part of the tribology test, the peak value, the total mean value, and the mean value of the last 10% of the test are presented in Table 6. These are the mean values of the two or three valid tribology tests. No significant correlations exist between the HEAs and the base metals for this part.

As a result, **Table 7** and Figure 9 show that AntrAl, AntoM, and AntraV have the lowest mean friction coefficient among the analyzed alloys. Table 7 highlights that AntrAl is the only alloy with values identical to pure cobalt,[83] which is known for having a great friction coefficient. As for AntruC, its friction coefficient is close to that of Cantor alloy.

Concerning the wear rate results, the alloys are analyzed with their mass loss and volume loss during the tribology test. Calculating these two parameters is interesting as they are not directly linked to the sample density. Moreover, the mass loss of the ball specimen helps track whether the analyzed sample tends to wear the other material or wear itself more, as some materials are engineered to wear themselves before the other material. Those three results are shown in **Table 8**. The mass loss of the sample is in milligrams (mg), the volume loss of the sample is in mm³, and the mass loss of the ball specimen is shown as a percentage loss considering the sample one. The color code in Table 8 is directly linked to the volume loss of the tested samples to help analyze these results.

In the G-133 standards, the wear rate is directly analyzed in relation to the sample's volume loss.[59] On the one hand, these results show some similarities with the microhardness test. These similarities are even more highlighted regarding Table 7 (friction coefficient results) and Table 8 (tribology results). In both cases, pure Cobalt and AntrAl alloy have the best results, in contrast to Cantor and AntruC alloys (**Figure 10**). Table 8 shows that Cobalt has the lowest volume loss (0.046 mm³), whereas Cantor has a much more significant loss (1.476 mm³), and even Chuang et al. optimized HEA Al₂Ti₁₀[27] has more volume loss than cobalt (0.196 mm³). Moreover, the pure aluminum sample got destroyed during the test, and

<figure><img src="image_11.png" /><figcaption>**Figure 9.** Friction coefficient over time of all the studied alloys. Only one friction coefficient has been shown per alloy, as this represents the behavior of the alloy during the tribology test. The other two are for ensuring the reliability of the results.</figcaption></figure>

<table><caption>**Table 7.** Friction coefficient results of the valid tribology tests. These results are the mean values of two or three valid tests. The friction coefficient has no unit.</caption><thead><tr><th></th><th>Co</th><th>Cu</th><th>Al</th><th>V</th><th>Mo</th><th>Cantor</th><th>AntruC</th><th>AntrAl</th><th>AntraV</th><th>AntoM</th><th>Al<sub>0.2</sub>Ti<sub>10</sub></th></tr></thead><tbody><tr><th>Peak value</th><td>0.631</td><td>0.541</td><td>Failed</td><td>1.285</td><td>0.855</td><td>1.035</td><td>1.068</td><td>0.639</td><td>0.884</td><td>0.818</td><td>0.984</td></tr><tr><th>Mean value</th><td>0.560</td><td>0.495</td><td>Failed</td><td>0.994</td><td>0.765</td><td>0.722</td><td>0.803</td><td>0.576</td><td>0.623</td><td>0.602</td><td>0.716</td></tr><tr><th>End value</th><td>0.538</td><td>0.513</td><td>Failed</td><td>1.017</td><td>0.799</td><td>0.755</td><td>0.850</td><td>0.535</td><td>0.637</td><td>0.627</td><td>0.708</td></tr></tbody></table>
<table><caption>**Table 8.** Tribology test results of every tested sample.</caption><thead><tr><th></th><th>Number of valid test</th><th>Sample mass loss (mg)</th><th>Ball specimen mass loss (mg)</th><th>Ball specimen mass loss (%)</th><th>Sample volume loss (mm³)</th><th>Color grind of the volume loss</th></tr></thead><tbody><tr><td>Co</td><td>3</td><td>6.563</td><td>-0.403</td><td>-6</td><td>0.046</td><td>- Sample broke<br/>- 4.0 mm³</td></tr><tr><td>Cu</td><td>2</td><td>0.115</td><td>-0.525</td><td>-457</td><td>0.313</td><td>- 3.0 mm³</td></tr><tr><td>Al</td><td>0</td><td>Failed</td><td>Failed</td><td>Failed</td><td>Failed</td><td>- 2.0 mm³</td></tr><tr><td>V</td><td>3</td><td>34.025</td><td>1.600</td><td>5</td><td>1.924</td><td>- 1.0 mm³</td></tr><tr><td>Mo</td><td>3</td><td>38.535</td><td>2.315</td><td>6</td><td>3.135</td><td>- 0.0 mm³</td></tr><tr><td>Cantor</td><td>2</td><td>12.515</td><td>9.820</td><td>78</td><td>1.476</td><td>- 0.0 mm³</td></tr><tr><td>AntruC</td><td>2</td><td>30.340</td><td>0.050</td><td>0</td><td>3.519</td><td>- 0.0 mm³</td></tr><tr><td>AntrAl</td><td>3</td><td>2.530</td><td>0.000</td><td>0</td><td>0.077</td><td>- 0.0 mm³</td></tr><tr><td>AntraV</td><td>2</td><td>11.420</td><td>0.235</td><td>2</td><td>0.330</td><td>- 0.0 mm³</td></tr><tr><td>AntroM</td><td>3</td><td>9.510</td><td>0.283</td><td>3</td><td>0.084</td><td>- 0.0 mm³</td></tr><tr><td>Al₂Ti₁₀</td><td>3</td><td>13.357</td><td>0.113</td><td>1</td><td>0.196</td><td>- 0.0 mm³</td></tr></tbody></table>

<figure><img src="image_12.png" /><figcaption>**Figure 10.** 2D profile of the first tribology scratch from AntruC and AntrAl alloys showing the difference between the most wear-resistant HEA and the least wear-resistant. Both curves were centered around the middle of the profilometer capture without any filtered data.</figcaption></figure>

AntruC has the most important volume loss (3.519 mm³) of the tested sample, yet, in contrast to Cantor, it does not wear the ball specimen at all, meaning it could still be a wearing alloy. Finally, AntraV, AntrAl, and AntroM are three samples with low volume loss, AntroM and AntrAl having less volume loss than Al₂Ti₁₀ while being cobalt-free. These results show once more that vanadium, aluminum, and molybdenum can be cobalt substitutes in HEAs to increase a material's hardness and reduce its wear rate.

On the other hand, some samples show results diverging from those found with the microhardness test. The pure molybdenum and vanadium have an important volume loss; their close microstructure can explain why those results are similar, instead of focusing on the hardness of the tested metals. Finally, the most interesting case is that the pure copper sample has the lowest mass loss, yet a low but average volume loss. The low hardness of the material could not anticipate its low wear rate. The
difference between mass and volume loss shows that other phenomena explain its volume loss, such as some plastic deformation, as shown by several studies on this material.[89–91]

4. Conclusion and Further Work

To summarize, this experimental study involved the production and investigation of six HEAs using metallurgical and tribological analyses. Four of these HEAs were specifically designed for this study with a focus on cobalt substitution. The comparative analysis, particularly with two well-established HEAs, Cantor (CoCrFeMnNi) alloy and Al₂Ti₁₀ (Al₀.₂Co₁.₅CrFeNi₁.₅Ti), leads to the following concluding remarks: 1) The article's main objective is the design of new HEAs without cobalt starting from the Cantor alloy. The hardness and tribology results have shown that molybdenum, vanadium, and aluminum are the potential alloying elements for the cobalt substitution for high hardness and low wear rate. The HEAs designed with these alloying elements (AntroM, AntraV, and AntrAl) show that their hardness and wear properties are enhanced compared to the reference Cantor alloy (five to twenty times more wear-resistant). Moreover, the AntroM and AntrAl alloys exhibit a low volume loss, similar to the pure cobalt one, and lower than the optimized reference alloy Al₀.₂Ti₁₀, which has the highest hardness of the studied samples. On the other hand, using copper as a substitution element of cobalt in the designed HEA (AntruC) slightly increases the hardness compared to Cantor alloy while drastically increasing the wear rate. Yet, thanks to the analysis of the ball specimen used during the tribology test of AntruC, this alloy almost did not wear the other specimen and therefore can be used as a wearing part of a system; 2) this study highlighted correlations between mechanical criteria, such as volumetric loss after a tribology test, and the friction coefficient. Other criteria are uncorrelated, mechanical ones, such as hardness and volume loss, and chemical ones, as pure properties and the same properties as alloying elements; 3) the prediction by the well-established criteria of VEC is not always accurate. Indeed, due to its empirical definition, the anticipation of the results is limited to HEAs composed of metallic elements, high mixing enthalpy, and verifying the Hume-Rothery rules. Moreover, it is worth considering the cohesive energy of every element used in the designed HEA to anticipate the formation of an unwanted phase. Additionally, the phases formed in a suballoy may need to be considered, as these phases could persist in the final HEA; 4) finally, this study has led to several avenues for future research. The first one is a deeper tribological study of the designed HEAs, specifically AntroM and AntrAl alloys, due to their high hardness and low wear rate. This study could target the main wear mode, an analysis of a potential new phase appearing underneath the scratch, and an evolution of the alloy property depending on the number of cycles of the tribology test. The second analysis is based on numerical metallurgy simulation, combined with thermodynamic aspects, to assess and predict the expected structure of the designed alloys, specifically the AntruC alloy. Lastly, a study focusing on the development of a well-known single-phased alloy in a multiphased configuration, to challenge the phase formation criteria and compare with both the base and recent HEA studies. For instance, producing a Cantor alloy with multiphased suballoys to verify whether the

final microstructure will be multiphased, as observed in
AntruC alloy. If so, tests could be done to verify the *meta*-stability
and properties of this new microstructure.

Acknowledgements

The authors would like to thank the colleagues who run the experimental facilities platforms “Procédés”, “MicroMat”, and “MécaRhéo” at LEM3, Arts et Métiers Institute of Technology, Université de Lorraine, CNRS and the “MMS” platform at CETIM Senlis.

Conflict of Interest

The authors declare no conflict of interest.

Data Availability Statement

The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions.

Keywords

alloy design, cobalt-free, hardness, high-entropy alloys, tribology, valence
electron concentration, wear rate

Received: September 1, 2025

Revised: November 5, 2025

Published online:

[1] J. Badger, CIRP Ann. 2007, 56, 353.

[2] H. L. Eiselstein, D. J. Tillack, "THE INVENTION AND DEFINITION OF ALLOY 625", in *Superalloys 718 625 Var. Deriv. 1991*, TMS **1991**, 1.

[3] F. Cordero, F. Corvasce, R. Franco, G. Paparo, E. Maiorana, P. Rapagnani, F. Ricci, S. Braccini, C. Casciano, R. De Salvo, F. Frasconi, R. Passaquieti, M. De Sanctis, A. Solina, R. Valentini, *J. Alloys Compd. 2000*, **310**, 400.

[4] H. So, C. T. Chen, Y. A. Chen, *Wear* **1996**, *192*, 78.

[5] E. Saikoff, E. Andersson, F. Bengtsson, C. Olausen, M. Galstyan, D. Vikström, J. Lazraq Byström, *Cobalt in High Speed Steels* **2018**.

[6] S. Hannis, T. Bide, *Cobalt*, British Geological Survey **2009**.

[7] A. L. Gulley, *Resour. Policy* **2022**, *79*, 103007.

[8] C. N. Vogel, *Conflict Minerals, Inc.: War, Profit and White Saviourism in Eastern Congo*, Oxford University Press **2022**.

[9] T. L. M. Exchange, *Lme "LME Cobalt | London Metal Exchange"*, https://www.lme.com/Metals/EV/LME-Cobalt (accessed: April 2025).

[10] T. L. M. Exchange, *Lme "LME Aluminium | London Metal Exchange"*, https://www.lme.com/Metals/Non-ferrous/LME-Aluminium (accessed: April 2025).

[11] Q. Wu, B. Zhang, Y. Lu, *J. Energy Chem.* **2022**, *74*, 283.

[12] H.-H. Ryu, H. H. Sun, S.-T. Myung, C. S. Yoon, Y.-K. Sun, *Energy Environ. Sci.* **2021**, *14*, 844.

[13] Eur. Comm, European Commission - European Commission, https://ec.europa.eu/commission/presscorner/detail/en/ip_22_6462 (accessed: April 2025).

[14] L. Lachvajderová, J. Kádárová, *Perners Contacts* **2020**, 15.

[15] R. Lauwerys, D. Lison, *Sci. Total Environ.* **1994**, *150*, 1.

[16] M. Suh, C. M. Thompson, G. P. Brorby, L. Mittal, D. M. Proctor, *Regul. Toxicol. Pharmacol.* **2016**, *79*, 74.
[17] O. US EPA "Radionuclide Basics: Cobalt-60" 2015, https://www.epa.gov/radiation/radionuclide-basics-cobalt-60.

[18] J.-W. Yeh, Eur. J. Control – Eur. J. Control **2006**, *31*, 633.

[19] M. C. Gao, J. W. Yeh, P. K. Liaw, Y. Zhang, *High-Entropy Alloys: Fundamentals and Applications*, Springer International Publishing **2016**.

[20] L. Peltier, P. Lohmuller, F. Meraghni, S. Berveiller, E. Patoor, P. Laheurte, *Shape Mem. Superelasticity 2020*, **6**, 273.

[21] L. Peltier, P. Lohmuller, F. Meraghni, E. Patoor, P. Laheurte, S. Berveiller, *Shape Mem. Superelasticity 2022*, **8**, 335.

[22] S. Guo, C. Ng, J. Lu, C. T. Liu, *J. Appl. Phys.* **2011**, *109*, 103505.

[23] S. Praveen, H. S. Kim, *Adv. Eng. Mater.* **2018**, *20*, 1700645.

[24] L. Peltier, S. Berveiller, F. Meraghni, P. Lohmuller, P. Laheurte, *Shape Mem. Superelasticity 2021*, **7**, 194.

[25] H. Ding, H. Luan, H. Bu, H. Xu, K. Yao, *Materials* **2022**, *15*, 1669.

[26] J. Chen, T. Xu, J. Zhang, H. Huang, J. Yuan, B. Liu, B. Zhang, Y. Wu, *Mater. Chem. Phys.* **2024**, *318*, 129219.

[27] M.-H. Chuang, M.-H. Tsai, W.-R. Wang, S.-J. Lin, J.-W. Yeh, *Acta Mater.* **2011**, *59*, 6308.

[28] R. B. Nair, H. S. Arora, A. Ayyagari, S. Mukherjee, H. S. Grewal, *Adv. Eng. Mater.* **2018**, *20*, 1700946.

[29] A. K. Kasar, K. Scalaro, P. L. Menezes, *Materials* **2021**, *14*, 5814.

[30] Y. Li, A. Olejarz, Kurpaska, E. Lu, M. J. Alava, H. S. Kim, W. Huo, *Int. J. Refract. Met. Hard Mater.* **2024**, *124*, 106834.

[31] B. Cantor, I. Chang, P. Knight, A. J. B. Vincent, *Mater. Sci. Eng. A* **2004**, *375*–377, 213.

[32] Y. Zhou, D. Zhou, X. Jin, L. Zhang, X. Du, B. Li, *Sci. Rep.* **2018**, *8*, 1236.

[33] L. Peltier, Élaboration et étude thermomécanique d'un Alliage à Mémoire de Forme Haute Température et à Haute entropie. Mécanique des matériaux physics.class-ph. HESAM Université, **2022**. Français. NNT : 2022HESAE028.

[34] G. Fu, X. Liu, X. Yi, S. Zhang, X. Cao, X. Meng, Z. Gao, H. Wang, *Metals* **2023**, *13*, 1279.

[35] M. K. Banerjee, *J. Mater. Sci.* **1997**, *32*, 6645.

[36] N. Eißmann, U. Mühle, U. Gaitzsch, G. Walther, T. Weißgärber, B. Kieback, *J. Alloys Compd.* **2021**, *857*, 157610.

[37] R. Chaudhari, J. J. Vora, D. M. Parikh, *Recent Advances in Mechanical Infrastructure*, (Eds: A. K. Parwani, P. L. Ramkumar, K. Abhishek, S. K. Yadav), Springer, Singapore **2021**, 123.

[38] Z. M. Konaré, D. D. Ajayi, S. Ba, A. K. Aremu, *Int. J. Life Cycle Assess.* **2023**, *28*, 684.

[39] A. Weiser, D. J. Lang, T. Schomerus, A. Stamp, *J. Clean. Prod.* **2015**, *94*, 376.

[40] M.-P. Martínez-Hernando, E. García-Franco, D. Bolonio, M. F. Ortega, M.-J. García-Martínez, *Sustain. Prod. Consum.* **2024**, *46*, 679.

[41] A. H. Tkaczyk, A. Bartl, A. Amato, V. Lapkovskis, M. Petranikova, *J. Phys. Appl. Phys.* **2018**, *51*, 203001.

[42] European Parliament, "Tackling the challenges in commodity markets and on raw materials" 2011, https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX:52011DC0025.

[43] European Parliament, "On the Review of the List of Critical Raw Materials for the EU and the Implementation of the Raw Materials Initiative" 2014, https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX:52014DC0297.

[44] European Parliament, "The 2017 List of Critical Raw Materials for the EU" 2017, https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX:52017DC0490.

[45] H. E. Sostman, *Rev. Sci. Instrum.* **1977**, *48*, 127.

[46] A. Smalcerz, B. Wecki, L. Blacha, J. Labaj, M. Jodkowski, A. Smagor, *Materials* **2021**, *14*, 6641.

[47] A. Munitz, L. Meshi, M. J. Kaufman, *Mater. Sci. Eng. A* **2017**, *689*, 384.

[48] L. J. Zhang, K. Guo, H. Tang, M. D. Zhang, J. T. Fan, P. Cui, Y. M. Ma, P. F. Yu, G. Li, *Mater. Sci. Eng. A* **2019**, *757*, 160.

[49] M.-H. Tsai, K.-Y. Tsai, C.-W. Tsai, C. Lee, C.-C. Juan, J.-W. Yeh., *Mater. Res. Lett.* **2013**, *1*, 207.

[50] Y. Zhang, *High-Entropy Materials: A Brief Introduction* (Ed: Y. Zhang), Springer, Singapore **2019**, 65.

[51] S. Arun, N. Radhika, B. Saleh, *Vacuum* **2024**, *226*, 113314.

[52] D. Castro, P. Jaeger, A. C. Baptista, J. P. Oliveira, *Metals* **2021**, *11*, 648.

[53] M. Çelebi, O. Güler, A. H. Karabacak, A. Çanakçı, S. B. Akçay, M. Kocaman, H. Çuvalcı, T. Varol, *Tribol. Int.* **2025**, *201*, 110277.

[54] A. H. Karabacak, A. Çanakçı, S. Özkaya, S. A. Tunç, O. Güler, M. Çelebi, *J. Alloys Compd.* **2024**, *1008*, 176627.

[55] MAUD - Mater. Anal. Using Diffr. "MAUD - Materials Analysis Using Diffraction (and more)," https://luttertoyo.github.io/maud/ (accessed: April 2025).

[56] Standard Test Methods for Vickers Hardness and Knoop Hardness of Metallic Materials, ASTM https://store.astm.org/e0092-17.html (accessed: October 2025).

[57] P. Kapsa, M. Cartier, Usure des contacts mécaniques - Manifestations de l'usure », Techniques de l'Ingénieur **2001**.

[58] P. Kapsa, M. Cartier, Usure des contacts mécaniques - Manifestations de l'usure », Techniques de l'Ingénieur **2022**.

[59] Standard Test Method for Linearly Reciprocating Ball-on-Flat Sliding Wear, ASTM, https://store.astm.org/g0133-22.html (accessed: April 2025).

[60] Y. Yin, H. Wang, Q. Tan, Q. Sun, Y. Wu, S. Xu, Y. Zhao, M. Li, X. Liao, H. Huang, M. Zhang, *J. Mater. Sci. Technol.* **2010**, *21*, 151.

[61] L. Liu, Y. Zhang, J. Han, X. Wang, W. Jiang, C.-T. Liu, Z. Zhang, P. K. Liaw, *Adv. Sci.* **2021**, *8*, 2100870.

[62] T.-K. Tsao, A.-C. Yeh, C.-M. Kuo, H. Murakami, *Adv. Eng. Mater.* **2017**, *79*, 1600475.

[63] X. An, H. Li, X. Yang, J. Jiang, Z. Liu, L. Kan, L. Zhang, B. Gan, W. Wei, C. Chu, W. Sun, *Adv. Eng. Mater.* **2025**, *27*, 2402102.

[64] Y. Lu, Y. Dong, L. Jiang, T. Wang, T. Li, Y. Zhang, *Entropy* **2015**, *17*, 2355.

[65] L. Thiercelin, L. Peltier, F. Meraghni, *Comput. Mater. Sci.* **2024**, *231*, 112578.

[66] S. A. Krishna, N. Noble, N. Radhika, B. Saleh, *J. Manuf. Process.* **2024**, *109*, 583.

[67] W. Hume-Rothery, *Acta Metall.* **1966**, *14*, 17.

[68] W. Hume-Rothery, G. Mabbott, W. K. M. Channel Evans, H. C. H. Carpenter, *Philos. Trans. R. Soc. Lond. Ser. Contain. Pap. Math. Phys. Character* **1997**, *233*, 1.

[69] Y. M. Zhang, J. R. G. Evans, S. Yang, *J. Cryst. Phys. Chem.* **2010**, *1*, 103.

[70] U. Mizutani, *Surface Properties and Engineering of Complex Intermetallics*, World Scientific **2010**, 323.

[71] W. P. Huhn, M. Widom, *JOM* **2013**, *65*, 1772.

[72] F. Tian, L. Delczeg, N. Chen, L. K. Varga, J. Shen, L. Vitos, *Phys. Rev. B* **2013**, *88*, 085128.

[73] X. Yang, S. Y. Chen, J. D. Cotton, Y. Zhang, *JOM* **2014**, *66*, 2009.

[74] F. R. de Boer, W. C. M. Mattens, R. Boom, A. R. Miedema, A. K. Niessen, *Cohesion in metals. Transition metal alloys*, U.S. Department of Energy - Office of Scientific and Technical Information **1988**.

[75] P. Chauhan, S. Chopra, S. Thangaraju, *Adv. Eng. Mater.* **2019**, *21*, 1900251.

[76] C. Kittel, P. McEuen, *Introduction of Solid State Physics*, John Wiley & Sons **2018**.

[77] E. Belin, A. Traverse, *J. Phys. Condens. Matter* **1991**, *3*, 2157.

[78] H. Baker, *Metals Handbook Desk Edition*, **1998**, 95.

[79] C. He, Y. Du, H.-L. Chen, S. Liu, H. Xu, Y. Ouyang, Z.-K. Liu, *J. Alloys Compd.* **2008**, *457*, 233.

[80] N. M. Eldabah, A. Pratap, A. Pandey, N. Sardana, S. S. Sidhu, M. A.-H. Gepreel, *Adv. Eng. Mater.* **2025**, *27*, 2402504.
[81] S. Zhao, J. Li, W. Liao, R. Yuan, *Mater. Genome Eng. Adv.* **2025**, *3*, e70022.

[82] L. Peltier, G. Le Coz, F. Meraghni, J. Slowensky, *Adv. Eng. Mater.* **2025**, *2501146*.

[83] P. Lohmuller, L. Peltier, A. Hazotte, J. Zollinger, P. Laheurte, E. Fleury, *Materials* **2018**, *11*, 1337.

[84] J. Emsley, *Nature's Building Blocks: "An A-Z Guide to the Elements"*, OUP Oxford **2011**.

[85] D. R. Lide, *CRC Handbook of Chemistry and Physics*, 85th ed., Taylor & Francis **2004**.

[86] D. Wu, H. Wang, K. Zhang, X. Lin, *Int. J. Adv. Manuf. Technol.* **2019**, *103*, 2495.

[87] L. Tan, D. Zhang, C. Yao, D. Wu, J. Zhang, *J. Manuf. Process.* **2017**, *26*, 155.

[88] Z. Chen, Y. Shi, X. Lin, T. Yu, P. Zhao, C. Kang, *Exp. Tech.* **2019**, *43*, 729.

[89] B. Yao, Z. Han, Y. S. Li, N. R. Tao, K. Lu, *Wear* **2011**, *271*, 1609.

[90] H. M. Cao, X. Zhou, X. Y. Li, K. Lu, *Tribol. Int.* **2017**, *115*, 3.

[91] D. A. Rigney, J. P. Hirth, *Wear* **1979**, *53*, 345.