Mechanical Alloying as a Way to Produce Metastable Single-Phase High-Entropy Alloys beyond the Stability Criteria

Citation: Santiago-Andrades, L.; Vidal-Crespo, A.; Blázquez, J.S.; Ipus, J.J.; Conde, C.F. Mechanical Alloying as a Way to Produce Metastable Single-Phase High-Entropy Alloys beyond the Stability Criteria. Nanomaterials 2024,14, 27. https:// doi.org/10.3390/nano14010027 Academic Editor: Kenji Kaneko Received: 1 December 2023 Revised: 15 December 2023 Accepted: 18 December 2023 Published: 21 December 2023 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). nanomaterials Article Mechanical Alloying as a Way to Produce Metastable Single-Phase High-Entropy Alloys beyond the Stability Criteria Lucía Santiago-Andrades , Antonio Vidal-Crespo , Javier S. Blázquez * , Jhon J. Ipus and Clara F. Conde Departamento de Física de la Materia Condensada, ICMSE-CSIC, Universidad de Sevilla, P.O. Box 1065, 41080 Sevilla, Spain *Correspondence: [email protected] Abstract: Various stability criteria developed for high-entropy alloys are applied to compositions produced by mechanical alloying. While they agree with the annealed samples, these criteria fail to describe the as-milled metastable systems, highlighting the ability of mechanical alloying to overcome the limitations imposed by these criteria. The criteria are based on atomic size ( Ω≥ 1.1 and δr≤ 6.6%) and/or electronegativity misfit, as well as on mixing enthalpy ( Λ> 0.95 J mol−1K−1 and − 5 kJ mol−1<∆Hmix < 0), or purely thermodynamic ( ϕYe > 20; ϕKing > 1; Te f f < 500 K ). These criteria are applied to several compositions found in the literature and to two metastable fcc solid solutions produced by mechanical alloying with compositions Al 0.75 CoXFeNi with X = Cr and Mn. Single-phase microstructures are stable up to above 600 K, leading to more stable multiphase systems after annealing above this temperature. Mössbauer spectrometry shows that, whereas the alloy with Cr is paramagnetic in the as-milled and annealed state, the alloy with Mn changes from paramagnetic to ferromagnetic behavior (Curie temperature ~700 K) after annealing. Thermomagnetic experiments on annealed samples show for both compositions some hysteretic events at high temperatures (850 to 1000 K), probably ascribed to reversible ordering phenomena. Keywords: high-entropy alloys; mechanical alloying; solid solution; metastability 1. Introduction Almost 20 years ago, Cantor [ 1 ] and Yeh [ 2 ] opened a new branch in Materials Science with the development of high-entropy alloys (HEA) [ 3 ]. HEAs are multielement systems that derive their name from the high configurational entropy directly estimated from the composition ∆Scon f =−R∑xilnxi , where xi represents the atomic concentration of the i-th element and R is the gas constant. For an equiatomic quinary alloy, ∆Scon f =1.6R=13.4 JK−1mol−1, and a compromise threshold of ∆Scon f > 1.5 R is considered for defining HEAs, allowing for the inclusion of quinary alloys slightly deviating from equiatomic compositions [ 4 ]. This threshold can be further relaxed to encompass quinary alloys with 0.05 <xi< 0.35 with ∆Scon f ≥ 1.36 R [ 5 ], thus also incorporating quaternary equimolar alloys. However, it is important to note that the ∆Scon f value is valid and physically meaningful only for fully-disordered single-phase solid solutions, which is not always the case. A more stringent definition requires the formation of a single-phase solid solution with bcc, fcc, or hcp unit cells and a monoatomic motif. To provide clarity, Miracle and Senkov [ 5 ] confined HEAs to single-phase solid solutions and coined other terms, such as Cantor alloys, multi-principal element alloys, complex concentrated alloys, and baseless alloys, to categorize alloys within the extensive compositional space created by multielement systems, regardless of their multiphase nature. In HEAs, the high value of ∆Scon f plays a crucial role in stabilizing the solid solution in contrast to the segregation of pure elements or the formation of intermetallic compounds, both of which offer significantly lower configurational entropy than a solid solution. The segregation of elements is favored when the individual elements exhibit Nanomaterials 2024,14, 27. https://doi.org/10.3390/nano14010027 https://www.mdpi.com/journal/nanomaterials Nanomaterials 2024,14, 27 2 of 21 positive enthalpies of mixing (estimated from binary systems as ∆Hmix =∑i=j4∆Hijxixj , with ∆Hij denoting the mixing enthalpy of a binary melt alloy with elements i and j [ 6 ]). On the other hand, the formation of intermetallic compounds occurs when ∆Hmix << 0. Therefore, ∆Hmix ∼ 0 is the ideal situation to obtain an HEA. Consequently, King et al. [ 7 ] proposed a straightforward thermodynamic criterion for the stabilization of HEA, defining ϕKing =−∆GSS/|∆Gmax| , i.e., the ratio between Gibbs free energies of the solid solution, ∆GSS , and the most extreme absolute value among the potential binary systems in the composition (either ∆Gmax > 0, leading to segregation, or ∆Gmax < 0, leading to intermetallic formation). Therefore ϕKing ≥1 was suggested for stable HEAs. Regarding the stability of single-phase solid solution HEAs, various parameters, in addition to ∆Scon f and ∆Hmix [ 8 – 10 ], have been taken into consideration. Martin et al. [ 11 ] gathered these diverse parameters and developed the HEAPS software tool for predicting the stability and microstructure of multielement systems. The High-Entropy Alloys Predicting Software (HEAPS) project, is led by Pablo Martin St Laurence, from the Politechnical University of Catalonia (Spain), in collaboration with members of the Technical University Federico Santa María (Chile). Some of these parameters can be derived from single atom properties, such as atomic size misfit: δr=r∑n i=1xi1−ri r2, (1) where ri and xi are the atomic radius and fraction of element i , and r is the average radius. Furthermore, other parameters, like ∆Hmix and |∆Gmax| , are determined based on the potential binary alloys formed by the elements within the composition. Table 1collects the parameters currently used to establish thresholds to predict the solid solution stability. Recently, some of the present study’s authors proposed a simple phenomenological model based on the averaging of the coefficients of the metallic bonding potential [ 12 ]. One advantage of this simple model lies in its reliance on single element properties, in contrast to the broader description derived from the properties of binary alloys. The metallic bonding can be described by a potential energy in the following form: U(r)=−A d+B d2, (2) where d is the distance to nearest neighbors, and A and B can be phenomenologically determined for a specific alloy using the equilibrium distance d=d0 and the bulk modulus. The theoretical basis of Equation (2) is rooted in the stabilization of single metal atoms [ 13 ], where the attractive term accounts for the attraction of the core ion to the valence electrons shared to the Fermi gas; and the repulsive term arises from the confinement energy of that Fermi gas. By employing average coefficients, an estimation of the equilibrium potential difference with respect to segregation, denoted as ∆U0 , can be parametrized as an effective temperature, Te f f =∆U0/∆Scon f . When comparing this model across different multicomponent compositions, a threshold of Te f f ∼ 500 K emerges. Below this threshold, single-phase fcc phases were observed, whereas for Te f f > 500 K , bcc/B2 or multiphase systems were identified for a set of 70 AlCoCrCuFeNi alloys [12]. Nanomaterials 2024,14, 27 3 of 21 Table 1. Different criteria proposed in the literature to predict the microstructure of multielement alloys. Data obtained with the help of HEAPS software from Martin et al. [ 11 ]. Tm , melting temperature; ∆Scon f , configurational entropy; ∆Hmix , mixing enthalpy; Sxs , excess entropy; ∆U0 , excess bonding energy using average coefficients with respect to average over bonding energy of segregated pure metals. Parameter Ref Comment Range for Single-Phase HEA Ω=Tm∆Scon f |∆Hmix |[10] Ratio between entropic and enthalpic contributions to mix Ω≥1.1 and δr≤6.6% Λ=∆Scon f δr2[6]Ratio between entropy due to mixing and elastic energy stored due to size misfit Λ>0.95 J mol−1K−1and −5 kJ mol−1<∆Hmix <0 ϕYe(f)=∆Scon f −∆Hmix Tm |Sxs(f)|[14] Entropy ratio between mixing and excess energy due to atomic size misfit. bcc ϕYe >20 fcc ϕKing =∆Hmix −Tm∆Scon f −|∆Gmax|[7]|∆Gmax| is the scaled maximum among absolute values of mixing Gibbs enthalpies of the binary alloys and possible intermetallics ϕKing >1 Te f f =∆U0 ∆Scon f [12]Effective temperature at which entropic term equals bonding energy Te f f <500 K This analysis was extended to other compositions, encompassing quinary and sexinary alloys, involving a total of 16 elements, as referred to by Gorban et al. [ 15 ]. It is worth noting that in the case of the equiatomic ReMoWNbTa alloy, a single alloy with a bcc phase was observed with Te f f < 500 K , but with a low atomic radii misfit ( δr∼ 2%). It is important to mention that distinguishing disordered bcc from ordered (or partially-ordered) B2 phases can be challenging due to similar average atomic scattering factors. However, the ordered structure may significantly affect the required parameter δr due to the accommodation of larger and smaller atoms on different sites. Nevertheless, this site preference causes the entropy value to deviate from the estimated ∆Scon f , assuming the global composition. In fact, even in single-phase solid solution systems, the assumption of complete disorder used for ∆Scon f is an idealization. ∆Scon f corresponds to an overestimated limit because the larger atoms tend to distort the lattice in such a way that they are preferentially surrounded by smaller ones. The excess entropy, Sxs , was estimated within the framework of the hard sphere model by Mansoori et al. [ 16 ]. Despite its complex dependence on xi and ri of the constituents, as well as on the packing fraction, f , (see [ 11 , 16 ]), simple linear relations with δr2 can be approximated for bcc and fcc structures (though the slope slightly varies for different alloy series). Figure 1shows this linear fitting (regression coefficient >0.9999) for the CoFeNiCr y Mn z Al x family within the ranges 0 <x< 1, 0 <y< 1, and 0<z<1. Despite the many efforts made, as mentioned earlier, to elucidate the stability of solid solutions in multicomponent alloys, it is well known that supersaturated solid solutions can be traditionally obtained either by rapid quenching [ 17 , 18 ] or by mechanical alloying [ 19 ]. Nowadays, new techniques are used to produce metastable systems such as additive manufacturing [ 20 ] and laser melting [ 21 ]. Concerning mechanical alloying, this technique significantly expands the solubility limits in alloys and thus plays a role in enabling the formation of high-entropy alloys (HEAs) beyond what is predicted for thermodynamically-stable conditions. The development of metastable systems is justified from an application perspective due to the expected enhancement in mechanical properties in HEA systems. This potential was recognized by the group of Murty et al. [ 22 ], who pioneered the production of HEAs by mechanical alloying in 2008 [23]. While the number of articles on the mechanical alloying production of HEAs rapidly increased from 10 papers over a five-year period from 2008 to 2012 to nearly 100 in 2022, this surge has led to the publication of several reviews with a focus on HEA produced by Nanomaterials 2024,14, 27 4 of 21 mechanical alloying. Notable among them are the works from Vaidya et al. [ 22 ], Koch [ 24 ], and Torralba et al. [ 25 ]. It is also worth mentioning the section Suryanarayana dedicated to HEA systems in his recent review on mechanical alloying [ 26 ] and a recent review from the pioneering group on mechanically alloyed HEAs [ 27 ]. Suryanarayana discussed the validity of thermodynamical criteria adopted for rapid quenching and their applicability to mechanical alloyed systems. Concerning HEAs, he proposed a new criterion using the Darken–Gurry plots, where electronegativity difference is plotted versus atomic size difference. These plots predict the formation of solid solutions for specific δr values, with fcc structure occurring when there is a low difference in electronegativity, and bcc structure forming in cases of higher electronegativity differences. This representation is suggested to be valid not only for HEAs produced by mechanical alloying but also for those produced using other techniques. Nanomaterials 2024, 14, x FOR PEER REVIEW 4 of 22 −5 0 5 10 15 20 25 30 35 40 −1.6 −1.4 −1.2 −1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2 S xs (J mol -1 K -1 ) δ r 2 (% 2 ) S xs (bcc)=-0.022992(6)δ r 2 S xs (fcc)=-0.037196(6)δ r 2 Figure 1. Excess entropy in bcc (dark yellow, data; red line, linear fitting) and fcc (pink, data; blue line, linear fitting) solid solutions as a function of the square of the atom size misfit for the CoFeNiCryMnzAlx family within the ranges 0<𝑥<1, 0<𝑦<1, and 0<𝑧<1 (1331 compositions obtained from HEAPS software [11]). Lines correspond to linear fitting of the data with regression coefficient 𝑅= 0.99990. Despite the many efforts made, as mentioned earlier, to elucidate the stability of solid solutions in multicomponent alloys, it is well known that supersaturated solid solutions can be traditionally obtained either by rapid quenching [17,18] or by mechanical alloying [19]. Nowadays, new techniques are used to produce metastable systems such as additive manufacturing [20] and laser melting [21]. Concerning mechanical alloying, this technique significantly expands the solubility limits in alloys and thus plays a role in enabling the formation of high-entropy alloys (HEAs) beyond what is predicted for thermodynamically-stable conditions. The development of metastable systems is justified from an application perspective due to the expected enhancement in mechanical properties in HEA systems. This potential was recognized by the group of Murty et al. [22], who pioneered the production of HEAs by mechanical alloying in 2008 [23]. While the number of articles on the mechanical alloying production of HEAs rapidly increased from 10 papers over a five-year period from 2008 to 2012 to nearly 100 in 2022, this surge has led to the publication of several reviews with a focus on HEA produced by mechanical alloying. Notable among them are the works from Vaidya et al. [22], Koch [24], and Torralba et al. [25]. It is also worth mentioning the section Suryanarayana dedicated to HEA systems in his recent review on mechanical alloying [26] and a recent review from the pioneering group on mechanically alloyed HEAs [27]. Suryanarayana discussed the validity of thermodynamical criteria adopted for rapid quenching and their applicability to mechanical alloyed systems. Concerning HEAs, he proposed a new criterion using the Darken–Gurry plots, where electronegativity difference is plotted versus atomic size difference. These plots predict the formation of solid solutions for specific 𝛿 values, with fcc structure occurring when there is a low difference in electronegativity, and bcc structure forming in cases of higher electronegativity differences. This representation is suggested to be valid not only for HEAs produced by mechanical alloying but also for those produced using other techniques. Unlike production techniques starting from the molten alloy, the mechanical alloying route can produce a supersaturated solution at low temperatures. Therefore, the stability criteria based on high-temperature thermodynamically-stable systems are not a priori adequate. Certainly, rapid quenching may also produce supersaturated solutions Figure 1. Excess entropy in bcc (dark yellow, data; red line, linear fitting) and fcc (pink, data; blue line, linear fitting) solid solutions as a function of the square of the atom size misfit for the CoFeNiCr y Mn z Al x family within the ranges 0 <x< 1, 0 <y< 1, and 0 <z< 1 (1331 compositions obtained from HEAPS software [ 11 ]). Lines correspond to linear fitting of the data with regression coefficient R2=0.99990. Unlike production techniques starting from the molten alloy, the mechanical alloying route can produce a supersaturated solution at low temperatures. Therefore, the stability criteria based on high-temperature thermodynamically-stable systems are not a priori adequate. Certainly, rapid quenching may also produce supersaturated solutions (metastable solid solutions) as a frozen microstructure from those thermodynamically stable at high temperature. In these cases, stability criteria can be adapted considering the entropic contribution to the free energy balance at the melting point (and, in fact, they are generally used in this way), which maximizes the effect of configurational entropy on the Gibbs energy. In this work, we employed mechanical alloying of pure powders to obtain two distinct metastable quinary HEA compositions: Al 0.75 CoCrFeNi and Al 0.75 CoMnFeNi (in the following: Cr-alloy and Mn-alloy, respectively). It is worth noting that the former composition is known to present a biphasic character when produced by arc melting, resulting in a mixture of bcc and fcc phases [ 28 ]. The results are compared to recent data from the literature to highlight the disparities that arise from mechanical alloying in contrast to the predictions made according to the stability criteria currently in use. Nanomaterials 2024,14, 27 5 of 21 2. Materials and Methods Massesof5g ofpurepowders(>99.5%)weremixed toformcompositionsAl 0.75 CoCrFeNi and Al 0.75 CoMnFeNi (in the following: Cr- and Mn-alloy, respectively) and incorporated in 80 cm 3 hardened steel bowls with 60 g of 10 mm steel balls. The milling process was conducted using a Fritsch Pulverisette P4 Vario planetary mill (Fritsch, Idar-Oberstein, Germany) at 250 rpm disc frequency and 500 rpm bowl frequency, with milling performed in 30-min intervals followed by 15-min pause steps. Sample preparation and extraction were carried out in argon atmosphere in a Saffron Ω glove box (Saffron, London, UK) to control oxygen and humidity levels. The times for extracting samples were chosen according to our previous experiments under these milling conditions. Initially, the powder size decreases from 1 h to 10 h of milling, but then cold welding is the predominant effect and powder size increases up to 1 mm after 30 h of milling. Due to the ductility of the systems, after 50 h of milling, the powder is almost completely adhered to the milling media, making it impossible to extract any samples for analysis. The composition of the powders was analyzed by means of X-ray fluorescence, XRF, in an Eagle III microfluorescence device (EDAX, Mahwah, NJ, USA) with Rh anticatode. The microstructure was studied via X-ray diffraction, XRD, using Cu K α radiation in a Bruker D8 Advance A25 powder diffractometer (Bruker, Karlsruhe, Germany), and Mössbauer spectrometry, using a Wissel spectrometer (Wissel, Starnberg, Germany) in transmission geometry with a 57Co source. NORMOS software (MS-DOS version) was used to fit the spectra (both SITE and DIST programs) [29]. The thermal stability was studied by means of differential scanning calorimetry, DSC, in a Perkin-Elmer DSC7 calorimeter (Perkin-Elmer, Norwalk, CT, USA) calibrated using Pb and K 2 CrO 4 standards and by thermomagnetic gravimetry, TMG, in a Perkin-Elmer TGA7 (Perkin-Elmer, USA), calibrated using the Curie temperatures of alumel (436 K), Ni (627 K), and Fe (1053 K) standards. Magnetic properties were assessed using Mössbauer spectrometry, TMG, and a vibrating sample magnetometer, VSM, in a LakeShore 7407 (LakeShore, Carson, CA, USA), calibrated with a standard sample of Ni. Samples for DSC and magnetic measurements were pressed in a uniaxial Atlas Manual Hydraulic Press (Specac, Orpington, UK) applying 2 tons on discs of 5 mm diameter. This prevented the movement of the powder due to magnetic field. The HEAPS software tool developed by Martin et al. [ 11 ] was used to calculate the different stability parameters, except when explicitly indicated otherwise. 3. Results The experimental compositions determined through XRF closely align with the nominal compositions. The Fe and Cr contents may slightly increase due to contamination from the milling media (in the Cr-free composition, the Cr content remains below 0.5% after 30 h milling). Both Co and Ni exhibit a similar trend, with a slight decrease to compensate for the increase in Fe and Cr content. Finally, Al seems to progressively decrease with milling time, although, as the lightest element among those studied here, its measurement carries a larger margin of error. The estimated experimental compositions after 30 h of milling are Al 0.7 Co 1.0 Cr 1.0 Fe 1.0 Ni 0.9 and Al 0.76 Co 0.96 Cr 0.02 Mn 1.00 Fe 1.06 Ni 0.96 for the Cr- and Mn-alloys, respectively. Figure 2displays the XRD patterns of the as-milled samples after different times of milling for both compositions. In the early stages of milling, the pure phases disappear, and atoms quickly integrate in fcc or bcc phases. However, in the case of Mn-alloy, some Mn-rich phase remains. As milling progresses, the bcc phase fraction reduces, and after 20 h of milling, only a single fcc phase is detected. The lattice parameters of the fcc phase are similar for both compositions (a=3.62 ±0.01 Å after 20 h of milling). Nanomaterials 2024,14, 27 6 of 21 Nanomaterials 2024, 14, x FOR PEER REVIEW 6 of 22 with milling time, although, as the lightest element among those studied here, its measurement carries a larger margin of error. The estimated experimental compositions after 30 h of milling are Al0.7Co1.0Cr1.0Fe1.0Ni0.9 and Al0.76Co0.96Cr0.02Mn1.00Fe1.06Ni0.96 for the Cr- and Mn-alloys, respectively. Figure 2 displays the XRD patterns of the as-milled samples after different times of milling for both compositions. In the early stages of milling, the pure phases disappear, and atoms quickly integrate in fcc or bcc phases. However, in the case of Mn-alloy, some Mn-rich phase remains. As milling progresses, the bcc phase fraction reduces, and after 20 h of milling, only a single fcc phase is detected. The lattice parameters of the fcc phase are similar for both compositions (𝑎= 3.62 ± 0.01 Å after 20 h of milling). The lower limits for crystal size of the fcc phase were determined from the broadening of the (111) maximum (decoupled from the (110) maximum of the bcc phase using two pseudoVoigt functions when necessary). Notably, while the crystal size of the Cr-alloy progressively decreases as milling progresses (from 68 ± 7 to 18 ± 3 nm as milling time increases from 10 to 30 h), this parameter remains stable for the Mn-alloy (about 90–100 nm). 40 60 80 100 120 2θ (º) Cr-containing alloy 1 h 5 h 10 h 20 h 30 h 40 60 80 100 120 2θ ( º ) 1 h 5 h 10 h 20 h 30 h Mn-containing alloy Mn ** * ****** oooo o fcc o bcc * Figure 2. XRD patterns of Al0.75CoXFeNi alloys (X = Cr, upper panel, and Mn, lower panel) as a function of milling time. The noisy XRD pattern of the 30 h milled Cr-alloy sample is due to the large powder particle size, which impedes a good flat surface. The Mössbauer spectra of the as-milled samples are shown in Figures 3 and 4 as a function of milling time. In agreement with the XRD results, the ferromagnetic contribution, ascribed to an FeCo-based bcc phase, gradually diminishes with ongoing milling, while the paramagnetic contribution, linked to the integration of Fe in the fcc phase, Figure 2. XRD patterns of Al 0.75 CoXFeNi alloys (X = Cr, upper panel, and Mn, lower panel) as a function of milling time. The noisy XRD pattern of the 30 h milled Cr-alloy sample is due to the large powder particle size, which impedes a good flat surface. The lower limits for crystal size of the fcc phase were determined from the broadening of the (111) maximum (decoupled from the (110) maximum of the bcc phase using two pseudoVoigt functions when necessary). Notably, while the crystal size of the Cr-alloy progressively decreases as milling progresses (from 68 ± 7 to 18 ± 3 nm as milling time increases from 10 to 30 h), this parameter remains stable for the Mn-alloy (about 90–100 nm). The Mössbauer spectra of the as-milled samples are shown in Figures 3and 4as a function of milling time. In agreement with the XRD results, the ferromagnetic contribution, ascribed to an FeCo-based bcc phase, gradually diminishes with ongoing milling, while the paramagnetic contribution, linked to the integration of Fe in the fcc phase, increases. After 20 h of milling, the contribution to the spectra of Fe atoms in ferromagnetic sites is negligible for both compositions. The stability of the single-phase fcc solid solution achieved after 30 h of milling was studied by means of DSC scans, as depicted in Figure 5. The processes shown are irreversible, as a second run does not reveal any additional deviations from baseline. This figure shows that the Mn-alloy displays a more well-defined transformation with a peak temperature at 640 K and an enthalpy of transformation of 162 J/g. In contrast, the Cralloy exhibits a much broader transformation, with a peak temperature at 768 K and a transformation enthalpy of 54 J/g. Nanomaterials 2024,14, 27 7 of 21 Nanomaterials 2024, 14, x FOR PEER REVIEW 7 of 22 increases. After 20 h of milling, the contribution to the spectra of Fe atoms in ferromagnetic sites is negligible for both compositions. The stability of the single-phase fcc solid solution achieved after 30 h of milling was studied by means of DSC scans, as depicted in Figure 5. The processes shown are irreversible, as a second run does not reveal any additional deviations from baseline. This figure shows that the Mn-alloy displays a more well-defined transformation with a peak temperature at 640 K and an enthalpy of transformation of 162 J/g. In contrast, the Cralloy exhibits a much broader transformation, with a peak temperature at 768 K and a transformation enthalpy of 54 J/g. 0102030 0 5 10 15 −10 −5 0 5 10 P (%) HF (T) Velocity (mm/s) 1h 5h 10h 20h 30h 10h ← Cr-containing alloy Figure 3. Mössbauer spectra of Al0.75CoCrFeNi alloy as a function of milling time. Circles correspond to experimental data. Thick red lines correspond to total fitting. Orange curves correspond to ferromagnetic contribution, and green curves correspond to paramagnetic contribution. Inset shows the probability of ferromagnetic contribution for a sample milled for 10 h, the spectrum of which was fitted using a distribution. Other contributions were fitted using a single site. Figure 3. Mössbauer spectra of Al 0.75 CoCrFeNi alloy as a function of milling time. Circles correspond to experimental data. Thick red lines correspond to total fitting. Orange curves correspond to ferromagnetic contribution, and green curves correspond to paramagnetic contribution. Inset shows the probability of ferromagnetic contribution for a sample milled for 10 h, the spectrum of which was fitted using a distribution. Other contributions were fitted using a single site. Nanomaterials 2024, 14, x FOR PEER REVIEW 8 of 22 0 102030 0 5 10 15 −10 −5 0 5 10 P (%) HF (T) Velocity (mm/s) ← 1h 5h 10h 20h 30h Mn-containing alloy 10h Figure 4. Mössbauer spectra of Al0.75CoMnFeNi alloy as a function of milling time. Circles correspond to experimental data. Thick blue lines correspond to total fitting. Orange curves correspond to ferromagnetic contribution, and green curves correspond to paramagnetic contribution. Inset shows the probability of ferromagnetic contribution for a sample milled for 10 h, the spectrum of which was fitted using a distribution. Other contributions were fitted using a single site. 400 500 600 700 800 900 Heat flow Temperature (K) 1 W/g (exo) 0.1 W/g (exo) Cr-containing Mn-containing Figure 5. DSC scans at 20 K/min of Al0.75CoXFeNi alloys (X = Cr, upper curve, and Mn, lower curve) for as-milled samples after 30 h of milling. Note that the upper curve is zoomed ×10 with respect to lower curve. In order to understand the effect of these transformations, XRD experiments (Figure 6) were performed at room temperature after DSC scans (maximum heating temperature, 973 K). The XRD patterns confirm the irreversible nature of the transformations detected via DSC. The microstructures of the annealed samples exhibit a multiphase character, with Figure 4. Mössbauer spectra of Al 0.75 CoMnFeNi alloy as a function of milling time. Circles correspond to experimental data. Thick blue lines correspond to total fitting. Orange curves correspond to ferromagnetic contribution, and green curves correspond to paramagnetic contribution. Inset shows the probability of ferromagnetic contribution for a sample milled for 10 h, the spectrum of which was fitted using a distribution. Other contributions were fitted using a single site. Nanomaterials 2024,14, 27 8 of 21 Nanomaterials 2024, 14, x FOR PEER REVIEW 8 of 22 0 102030 0 5 10 15 −10 −5 0 5 10 P (%) HF (T) Velocity (mm/s) ← 1h 5h 10h 20h 30h Mn-containing alloy 10h Figure 4. Mössbauer spectra of Al0.75CoMnFeNi alloy as a function of milling time. Circles correspond to experimental data. Thick blue lines correspond to total fitting. Orange curves correspond to ferromagnetic contribution, and green curves correspond to paramagnetic contribution. Inset shows the probability of ferromagnetic contribution for a sample milled for 10 h, the spectrum of which was fitted using a distribution. Other contributions were fitted using a single site. 400 500 600 700 800 900 Heat flow Temperature (K) 1 W/g (exo) 0.1 W/g (exo) Cr-containing Mn-containing Figure 5. DSC scans at 20 K/min of Al0.75CoXFeNi alloys (X = Cr, upper curve, and Mn, lower curve) for as-milled samples after 30 h of milling. Note that the upper curve is zoomed ×10 with respect to lower curve. In order to understand the effect of these transformations, XRD experiments (Figure 6) were performed at room temperature after DSC scans (maximum heating temperature, 973 K). The XRD patterns confirm the irreversible nature of the transformations detected via DSC. The microstructures of the annealed samples exhibit a multiphase character, with Figure 5. DSC scans at 20 K/min of Al 0.75 CoXFeNi alloys (X = Cr, upper curve, and Mn, lower curve) for as-milled samples after 30 h of milling. Note that the upper curve is zoomed × 10 with respect to lower curve. In order to understand the effect of these transformations, XRD experiments (Figure 6) were performed at room temperature after DSC scans (maximum heating temperature, 973 K ). The XRD patterns confirm the irreversible nature of the transformations detected via DSC. The microstructures of the annealed samples exhibit a multiphase character, with the coexistence of bcc and fcc phases. Additionally, a sigma phase is detected for the Cr-alloy. This finding aligns with results reported for annealed AlCoCrFeNi at 1073 K after short-duration milling [ 30 ]. In qualitative agreement with the transformation enthalpy measured via DSC, the transformed fraction from fcc to bcc phase is higher in the case of the Mn-alloy. Nanomaterials 2024, 14, x FOR PEER REVIEW 9 of 22 the coexistence of bcc and fcc phases. Additionally, a sigma phase is detected for the Cralloy. This finding aligns with results reported for annealed AlCoCrFeNi at 1073 K after short-duration milling [30]. In qualitative agreement with the transformation enthalpy measured via DSC, the transformed fraction from fcc to bcc phase is higher in the case of the Mn-alloy. 40 60 80 100 120 2θ (º) Mn-containing Cr-containing ++ * + + + *** o oo oo Figure 6. Room-temperature XRD patterns after DSC experiments. Black asterisks correspond to fcc phase; red circles correspond to bcc phase; and blue crosses in Cr-alloy identify the σ phase. The Mössbauer spectra of annealed samples (Figure 7), after heating to 973 K during DSC, indicate that Fe atoms mainly remain in the fcc paramagnetic phase. In the case of the Cr-alloy, no ferromagnetic Fe sites are detected, while for the Mn-alloy, some magnetically-ordered contribution is observed, which corresponds with the larger amount of bcc phase in this composition. −10−8−6−4−20246810 0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35 velocity (mm/s) P(%) HF (T) P (%) Cr-containing Mn-containing Figure 6. Room-temperature XRD patterns after DSC experiments. Black asterisks correspond to fcc phase; red circles correspond to bcc phase; and blue crosses in Cr-alloy identify the σphase. Nanomaterials 2024,14, 27 9 of 21 The Mössbauer spectra of annealed samples (Figure 7), after heating to 973 K during DSC, indicate that Fe atoms mainly remain in the fcc paramagnetic phase. In the case of the Cr-alloy, no ferromagnetic Fe sites are detected, while for the Mn-alloy, some magneticallyordered contribution is observed, which corresponds with the larger amount of bcc phase in this composition. Nanomaterials 2024, 14, x FOR PEER REVIEW 9 of 22 the coexistence of bcc and fcc phases. Additionally, a sigma phase is detected for the Cralloy. This finding aligns with results reported for annealed AlCoCrFeNi at 1073 K after short-duration milling [30]. In qualitative agreement with the transformation enthalpy measured via DSC, the transformed fraction from fcc to bcc phase is higher in the case of the Mn-alloy. 40 60 80 100 120 2θ (º) Mn-containing Cr-containing ++ * + + + *** o oo oo Figure 6. Room-temperature XRD patterns after DSC experiments. Black asterisks correspond to fcc phase; red circles correspond to bcc phase; and blue crosses in Cr-alloy identify the σ phase. The Mössbauer spectra of annealed samples (Figure 7), after heating to 973 K during DSC, indicate that Fe atoms mainly remain in the fcc paramagnetic phase. In the case of the Cr-alloy, no ferromagnetic Fe sites are detected, while for the Mn-alloy, some magnetically-ordered contribution is observed, which corresponds with the larger amount of bcc phase in this composition. −10−8−6−4−20246810 0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35 velocity (mm/s) P(%) HF (T) P (%) Cr-containing Mn-containing Figure 7. Right panel: Mössbauer spectra of 30 h milled samples after heating to 973 K during DSC. Symbols correspond to experimental data, and lines correspond to fitting using a distribution of hyperfine fields (shown in the corresponding left panels). Figure 8shows TMG heating scans at 33 K/min for 30 h as-milled samples, followed by cooling to room temperature and a subsequent second cycle. The temperatures reached were above the limit temperature of DSC. Nanomaterials 2024, 14, x FOR PEER REVIEW 10 of 22 Figure 7. Right panel: Mössbauer spectra of 30 h milled samples after heating to 973 K during DSC. Symbols correspond to experimental data, and lines correspond to fitting using a distribution of hyperfine fields (shown in the corresponding left panels). Figure 8 shows TMG heating scans at 33 K/min for 30 h as-milled samples, followed by cooling to room temperature and a subsequent second cycle. The temperatures reached were above the limit temperature of DSC. In the case of the Mn-alloy, the as-milled sample exhibits weak ferromagnetic behavior (probably due to impurities). Coinciding with the DSC event associated with the development of the bcc phase, a substantial increase in magnetization occurs. Following this rise, detected during the first heating, the magnetization decreases to zero at ~1000 K for the Mn-alloy. However, this decline is not solely attributed to approaching the Curie temperature but may also result from structural transformations (e.g., ordering). In fact, the cooling process registered a first increase in magnetization at ~850 K and a clear Curie transition at ~700 K. In the second cycle, this reversible process occurs at 700 K, but on heating, a decrease in magnetization is observed at 950 K. During cooling, this phenomenon reappears at 700 K (as observed in the first cooling cycle), indicating that the hightemperature decrease in magnetization corresponds to a hysteretic process. Recently, Gao et al. [31] showed that the presence of Al induces a transition from antiferromagnetic to ferromagnetic coupling in Mn atoms, resulting in soft magnetic behavior in Co4Fe2Mn1.5Al1.5 alloy, which exhibits a B2 ordered structure. This could also be occurring once the as-milled sample of Mn-alloy is annealed, leading to thermal stabilization of the Al positions. Regarding the Cr-alloy, although the magnetization is higher for the as-milled samples, there is no sudden process during the first heating, which aligns with the DSC scan. At around 925 K, the magnetization drops to zero in a similar way to that observed in the Mn-alloy. With further cooling, a rise in magnetization is not detected at this temperature but, rather, a gradual increase starting at approximately 800 K. Subsequent heating shows a tiny effect at ~750 K, which is not observed during the first cooling or the second cooling. However, this effect is reversible, as it is observed in subsequent heating scans (not shown here). Therefore, similar to that in the Mn-alloy, it appears that some hysteretic process occurs at elevated temperatures in the Cr-alloy. 300 400 500 600 700 800 900 1000 1100 100 110 120 130 140 150 500 1000 100 102 effective mass (%) T ( K ) Cr-alloy 1 st heating Cr-alloy 2 nd heating Mn-alloy 1 st heating Mn-alloy 2 nd heating Cr-alloy 1 st cooling Cr-alloy 2 nd cooling Mn-alloy 1 st cooling Mn-alloy 2 nd cooling Figure 8. TMG scans at 33 K/min of 30 h milled samples. Inset shows a zoomed Y-axis to appreciate the behavior of the Cr-alloy sample. Arrows indicate the sense of temperature change. Figure 8. TMG scans at 33 K/min of 30 h milled samples. Inset shows a zoomed Y-axis to appreciate the behavior of the Cr-alloy sample. Arrows indicate the sense of temperature change. Nanomaterials 2024,14, 27 16 of 21 Table 3. Cont. Composition As-Milled Ω Λ ϕYe Teff/K Annealed Ref. CoCrFe bcc 6.6 78.9 3008 13.5 not reported [68] CoCrFeNi fcc 5.8 130 2988 9.2 not reported [68] CoCrFeNiTi bcc 1.6 0.30 5.1 1907 not reported [68] CoCrFeNiZn fcc+bcc 6.8 0.62 161 not reported [68] CoCrFeNiSi fcc+bcc 0.9 1.42 -- not reported [68] CoCrFeNiAl bcc 1.8 0.40 7.9 937 not reported [68] CoCuFe fcc+bcc 1.9 5.96 65 not reported [68] CoCuFeNi fcc(1)+fcc(2) 3.8 8.90 49 not reported [68] CoCuFeNiTi fcc 2.1 0.32 4.4 1799 not reported [68] CoCuFeNiZn fcc(1)+fcc(2) 11.2 0.66 164 not reported [68] CoCuFeNiSi fcc(1)+fcc(2) 1.3 1.13 -- not reported [68] CoCuFeNiAl fcc 3.9 0.43 8.5 889 not reported [68] AlLiMg0.5Ti1.5 hcp+AlLi 4.0 0.84 17.2 437 intermetallics [69] (AlLiMg0.5Ti1.5)95Sc5hcp 6.7 0.69 16.1 532 intermetallics [69] (AlLiMg0.5Ti1.5)90Sc10 hcp 12.7 0.59 15.0 623 intermetallics [69] (AlLiMg0.5Ti1.5)85Sc15 hcp 44.4 0.53 14.2 703 intermetallics [69] (AlLiMg0.5Ti1.5)80Sc20 hcp 42.6 0.48 13.0 773 hcp+intermet. [69] Al0.5CrFeNiTi fcc+bcc+hcp 1.2 0.24 2279 fcc+bcc+2 hcp [70] FeCoCrNiMn fcc+bcc 5.8 1.25 546 fcc [71] (FeCoCrNi)80Mn10Al10 fcc+bcc 2.8 0.65 800 fcc+bcc+σ[71] CoCrMnNbTi bcc(1)+bcc(2)+tet 2.2 0.32 not reported [72] CoCrFeNiW0.2 bcc+fcc 7.0 2.95 433 bcc+fcc+σ[73] CrFeNiTiV bcc 2.0 0.32 6.9 1802 bcc+Ni3Ti * [74] AlCrFeNiCu bcc+fcc 5.4 0.42 912 B2+fcc+σ[75] AlCrFeNbMo bcc 2.3 0.35 9.1 1587 bcc+fcc+σ[75] WNbMoVTa bcc+WC 8.5 1.35 bcc+others [76] WNbMoVTaCr bcc+WC+NbTa 9.0 0.69 bcc+others [76] WNbMoVTaAl bcc+WC+NbTa 4.0 1.49 bcc+others [76] WNbMoVTaCr0.5 bcc+WC+NbTa 9.1 0.87 bcc+others [76] WNbMoVTaAl0.5 bcc+WC+NbTa 5.2 1.46 bcc+others [76] WNbMoVTaCr0.5Al0.5 bcc+WC+NbTa 5.7 0.94 bcc+others [76] WNbMoVTaCr0.5Al bcc+WC+NbTa 4.4 0.96 bcc+others [76] WNbMoVTaCrAl0.5 bcc+WC+NbTa 5.9 0.73 bcc+others [76] WNbMoVTaCrAl bcc+WC+NbTa 4.5 0.75 bcc+others [76] * There are other phases detected. Finally, there are some compositions where, despite the predicted composition being a single-phase solid solution, a mixture of phases is observed in the as-milled state. The microstructure obtained by mechanical alloying (i.e., starting from a mixture of pure powders or segregated phases) is strongly dependent on the milling time. In fact, despite a solid solution being possible, for short enough milling times, supersaturated or stable solid solutions are not yet achieved. The main difference for the mechanical alloying route with respect to rapid quenching is that the former develops a supersaturated solution at low temperatures. Therefore, the stability criteria based on high-temperature thermodynamically-stable systems, assuming that they are frozen at low temperatures because of rapid quenching, are not straightforwardly applicable to mechanical alloys. In this sense, most of the stability criteria used for HEAs are based on a maximum effect of configurational entropy Nanomaterials 2024,14, 27 17 of 21 on the Gibbs energy (assuming its contribution at the melting temperature). Moreover, an extra complication in mechanical alloyed systems is the possibility of recrystallization effects of the supersaturated solid solutions when the milling time is too long (e.g., due to contamination). Table 3shows that different stability criteria are correlated for a given composition. This is evidenced in Figure 10, where ϕYe is plotted against Te f f . The reported regions for single-phase solid solutions, ϕYe > 20 and Te f f < 500 K, are in good agreement. Nanomaterials 2024, 14, x FOR PEER REVIEW 17 of 22 rapid quenching, are not straightforwardly applicable to mechanical alloys. In this sense, most of the stability criteria used for HEAs are based on a maximum effect of configurational entropy on the Gibbs energy (assuming its contribution at the melting temperature). Moreover, an extra complication in mechanical alloyed systems is the possibility of recrystallization effects of the supersaturated solid solutions when the milling time is too long (e.g., due to contamination). Table 3 shows that different stability criteria are correlated for a given composition. This is evidenced in Figure 10, where ϕ is plotted against 𝑇. The reported regions for single-phase solid solutions, ϕ > 20 and 𝑇 < 500 K, are in good agreement. 10 100 1000 1 10 100 1000 φ Ye T eff (K) Figure 10. Linear correlation between the logarithms of ϕ and 𝑇. Black squares correspond to data taken from Table 3. Red line corresponds to the linear fitting to the data (regression coefficient 𝑅=−0.97). Blue lines indicate the limit values for predicting the development of a singlephase solid solution (ϕ > 20 and 𝑇 < 500 K). Figure 11 shows the Darken–Gurry plot suggested by Suryanarayana [26] as a new criterion for predicting the microstructures of HEAs. However, the plot does not reveal clear demarcation regions between single-phase solid solutions and microstructures formed by mixed phases, neither for the as-milled samples (solid symbols) nor for the annealed ones (hollow symbols enclosing the corresponding solid one of the as-milled counterpart). The absence of distinct regions in the plot emphasizes the complex and multifaceted nature of stability and microstructure formation in HEAs produced via mechanical alloying. This indicates that additional factors or criteria may need to be considered to better understand and predict the behavior of these samples. Figure 10. Linear correlation between the logarithms of ϕYe and Te f f . Black squares correspond to data taken from Table 3. Red line corresponds to the linear fitting to the data (regression coefficient R=− 0.97). Blue lines indicate the limit values for predicting the development of a single-phase solid solution (ϕYe > 20 and Te f f < 500 K). Figure 11 shows the Darken–Gurry plot suggested by Suryanarayana [ 26 ] as a new criterion for predicting the microstructures of HEAs. However, the plot does not reveal clear demarcation regions between single-phase solid solutions and microstructures formed by mixed phases, neither for the as-milled samples (solid symbols) nor for the annealed ones (hollow symbols enclosing the corresponding solid one of the as-milled counterpart). The absence of distinct regions in the plot emphasizes the complex and multifaceted nature of stability and microstructure formation in HEAs produced via mechanical alloying. This indicates that additional factors or criteria may need to be considered to better understand and predict the behavior of these samples. Nanomaterials 2024,14, 27 18 of 21 Nanomaterials 2024, 14, x FOR PEER REVIEW 18 of 22 0 5 10 15 20 0.00 0.05 0.10 0.15 0.20 0.25 0.30 multiphase FCC BCC amorphous Δχ P δ r (%) Figure 11. Darken–Gurry plot showing electronegativity difference (using Pauling values) against atomic size misfit, as suggested by Suryanarayana [26]. Solid symbols correspond to as-milled samples and hollow symbols correspond to annealed samples. 5. Conclusions In this work, we showed that high-entropy alloys can be produced via mechanical alloying as single-phase solid solutions even beyond the stability criteria that are currently used to predict the microstructures of multielement alloys. The microstructure after thermal treatment of supersaturated solutions tends to be closer to the one predicted by applying these stability criteria. Nevertheless, these criteria are generally used assuming a maximum contribution of the configurational entropy to the Gibbs free energy (the entropy contribution is added to the energy balance using the melting temperature). However, the supersaturated solution produced via mechanical alloying destabilizes at temperatures below melting. A good correlation was found for those criteria based on thermodynamics and atomic size misfit with one recently proposed by the current authors and based on the average of the potential coefficients describing the metallic bonding. In addition to the analysis of several compositions for which data were taken from the literature, in this work, we produced two single-phase metastable fcc solid solutions by means of mechanical alloying with compositions (Al0.75CoXFeNi with X=Cr and Mn) outside of the ranges predicted by the various criteria. Thermal analysis showed that this microstructure is stable up to above 600 K with a better-defined transition in the alloy with Mn. After annealing, both samples developed a bcc phase coexisting with the remaining fcc phase. Moreover, sigma phase was also detected for the Cr-containing alloy. These post-annealing microstructures agree with the predictions from the discussed stability criteria. In addition to the solid solution stability, magnetic properties were analyzed for these two compositions in the as-milled and annealed stages. The supersaturated fcc solid solutions were paramagnetic at room temperature (except for some impurities probably coming from the milling media and only detected by means of VSM and TMG). After annealing, the biphasic solid solution developed in the Mn-containing alloy exhibited soft magnetism with a high specific saturation magnetization of 100 Am2/kg. Author Contributions: Conceptualization, J.S.B.; methodology, L.S.-A., A.V.-C. and J.J.I.; validation, J.S.B. and L.S.-A.; formal analysis, L.S.-A., A.V.-C. and J.S.B.; investigation, L.S.-A., A.V.-C. and J.J.I.; resources, J.S.B. and C.F.C.; data curation, J.S.B.; writing—original draft preparation, L.S.-A. and Figure 11. Darken–Gurry plot showing electronegativity difference (using Pauling values) against atomic size misfit, as suggested by Suryanarayana [ 26 ]. Solid symbols correspond to as-milled samples and hollow symbols correspond to annealed samples. 5. Conclusions In this work, we showed that high-entropy alloys can be produced via mechanical alloying as single-phase solid solutions even beyond the stability criteria that are currently used to predict the microstructures of multielement alloys. The microstructure after thermal treatment of supersaturated solutions tends to be closer to the one predicted by applying these stability criteria. Nevertheless, these criteria are generally used assuming a maximum contribution of the configurational entropy to the Gibbs free energy (the entropy contribution is added to the energy balance using the melting temperature). However, the supersaturated solution produced via mechanical alloying destabilizes at temperatures below melting. A good correlation was found for those criteria based on thermodynamics and atomic size misfit with one recently proposed by the current authors and based on the average of the potential coefficients describing the metallic bonding. In addition to the analysis of several compositions for which data were taken from the literature, in this work, we produced two single-phase metastable fcc solid solutions by means of mechanical alloying with compositions (Al 0.75 CoXFeNi with X = Cr and Mn) outside of the ranges predicted by the various criteria. Thermal analysis showed that this microstructure is stable up to above 600 K with a better-defined transition in the alloy with Mn. After annealing, both samples developed a bcc phase coexisting with the remaining fcc phase. Moreover, sigma phase was also detected for the Cr-containing alloy. These post-annealing microstructures agree with the predictions from the discussed stability criteria. In addition to the solid solution stability, magnetic properties were analyzed for these two compositions in the as-milled and annealed stages. The supersaturated fcc solid solutions were paramagnetic at room temperature (except for some impurities probably coming from the milling media and only detected by means of VSM and TMG). After annealing, the biphasic solid solution developed in the Mn-containing alloy exhibited soft magnetism with a high specific saturation magnetization of 100 Am2/kg. Nanomaterials 2024,14, 27 19 of 21 Author Contributions: Conceptualization, J.S.B.; methodology, L.S.-A., A.V.-C. and J.J.I.; validation, J.S.B. and L.S.-A.; formal analysis, L.S.-A., A.V.-C. and J.S.B.; investigation, L.S.-A., A.V.-C. and J.J.I.; resources, J.S.B. and C.F.C.; data curation, J.S.B.; writing—original draft preparation, L.S.-A. and J.S.B.; writing—review and editing, L.S.-A., A.V.-C., J.J.I., J.S.B. and C.F.C. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by the VII-PPITU from Universidad de Sevilla (Spain). A. Vidal-Crespo acknowledges the financial support of the VI-PPITU from Universidad de Sevilla (Spain). L. Santiago-Andrades acknowledges an undergraduate student fellowship from the Royal Spanish Physical Society (RSEF). VII-PPITU is acknowledged for its financial support for the use of CITIUS facilities. Data Availability Statement: Data are available on request to the authors. 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