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Ryuta Yurishima, [Ayako Ikeda](https://orcid.org/0000-0002-1705-9004), [Teruyuki Ikeda](https://orcid.org/0000-0001-7076-6958)

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[Determination of the Entire Existence Composition Range of CrMnFeCoNi High-Entropy Alloys Using Sintered Diffusion Multiple Method](https://mdr.nims.go.jp/datasets/bc02df2a-3839-4c1a-ab65-2f2c10dfea7f)

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Determination of the Entire Existence Composition Range of CrMnFeCoNi High-Entropy Alloys Using Sintered Diffusion Multiple MethodAcademic Editor: Wei RenReceived: 10 December 2024Revised: 4 January 2025Accepted: 6 January 2025Published: 10 January 2025Citation: Yurishima, R.; Ikeda, A.;Ikeda, T. Determination of the EntireExistence Composition Range ofCrMnFeCoNi High-Entropy AlloysUsing Sintered Diffusion MultipleMethod. Materials 2025, 18, 295.https://doi.org/10.3390/ma18020295Copyright: © 2025 by the authors.Licensee MDPI, Basel, Switzerland.This article is an open access articledistributed under the terms andconditions of the Creative CommonsAttribution (CC BY) license(https://creativecommons.org/licenses/by/4.0/).ArticleDetermination of the Entire Existence Composition Range ofCrMnFeCoNi High-Entropy Alloys Using Sintered DiffusionMultiple MethodRyuta Yurishima 1, Ayako Ikeda 2 and Teruyuki Ikeda 1,*1 Graduate School of Science and Engineering, Ibaraki University, 4-12-1 Nakanarusawa,Hitachi 316-8511, Ibaraki, Japan2 Research Center for Structural Materials, National Institute for Materials Science, 1-2-1 Sengen,Tsukuba 305-0047, Ibaraki, Japan; ikeda.ayako@nims.go.jp* Correspondence: teruyuki.ikeda.hy@vc.ibaraki.ac.jp; Tel.: +81-294-38-5066Abstract: The sintered diffusion multiple (SDM) method, which has been developed inour research group, has been applied to determine the entire composition range of theCrMnFeCoNi high-entropy alloy stereoscopically and continuously over nearly the entirerange. The samples were prepared by sintering mixed elemental powders and wereannealed at 970 ◦C or 800 ◦C. Several hundreds of thousands of points were analyzed atrandom within the samples for chemical compositions using electron probe microanalysis.With the assumption that ideally, only chemical compositions of existing phases at thetemperature of annealing are obtained, the compositional data thus obtained were analyzedto estimate the phase boundaries of the high-entropy phase, including the Cantor alloycomposition, assuming local equilibrium within the samples. The analysis includes thedetermination of point densities and their slopes in the space of chemical composition.The results are shown in the tetrahedral compositional space, with vertices for the Cr,Mn, and Fe atomic fractions and the sum of the Co and Ni fractions. One of the featuresfound in this work is that the high-entropy phase exhibits a wide compositional range inthe Fe-CrMnCoNi direction. The estimated phase boundary compositions are found tobe in good agreement, within an error range 3 at.%, with those obtained using samplesprepared by the conventional method, where the samples with uniform compositions areequilibrated by annealing, and the compositions of their existing phases are analyzed usingEPMA. Thus, the sintered diffusion multiple method is effective in providing an overviewof the quinary phase diagrams.Keywords: high-entropy alloys; phase diagram; sintered diffusion multiple method1. IntroductionHigh-entropy alloys (HEAs) have been expected to exhibit unique physical propertiessince the idea of a high-entropy alloy was introduced in the metallurgy field by Cantor andYeh [1,2]. HEAs are defined as solid-solution alloys composed of more than five elementswith intermediate compositions and hence, stabilized due to extremely high configurationalentropies [3]. Such unique atomic arrangements and atomic interactions have the potentialto give rise to properties creating the so-called cocktail effect, which is not possible froma simple mixture of elements. The Cantor alloy is well known as a prototype of HEAs,with the FCC structure exhibiting a unique mechanical property, which displays highstrength at low temperatures. This FCC phase has been reported to have a wide existenceMaterials 2025, 18, 295 https://doi.org/10.3390/ma18020295https://doi.org/10.3390/ma18020295https://doi.org/10.3390/ma18020295https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://www.mdpi.com/journal/materialshttps://www.mdpi.comhttps://orcid.org/0000-0002-1705-9004https://orcid.org/0000-0001-7076-6958https://doi.org/10.3390/ma18020295https://www.mdpi.com/article/10.3390/ma18020295?type=check_update&version=1Materials 2025, 18, 295 2 of 12compositional range [4] implying the ability to control the physical properties by changingthe composition while retaining the crystal structure. A number of studies examining thestability [5–9] or the composition range [10–20] of the HEA phase have been conductedexperimentally and with the aid of CALPHAD calculations, even for the Cr–Mn–Fe–Co–Nisystem alone. However, all these studies have been conducted on pseudo-binary sections ofthe quinary system and hence, the entire picture of the existence range of the high-entropyCr–Mn–Fe–Co–Ni alloys is still unknown. A tremendously vast compositional space of amulticomponent system such as HEAs requires an enormous amount of effort to examinetheir detailed phase diagrams.The novel material exploration, aided by a variety of calculations and data science,has thus been developed. To achieve high precision results using these approaches, a largeamount of experimental data is essential. Regarding experimental techniques for creatingan equilibrium phase diagram, a conventional method is often used, where samples withbasically homogeneous compositions are subject to long-term annealing at constant temper-atures for equilibration, and one set of data on one tie line per sample is obtained [21]. How-ever, for multicomponent alloy systems, too many experiments are required to complete asystem. To accelerate data acquisition, therefore, methods using diffusion multiples [22,23]are available. It is, however, not necessarily easy to prepare samples for this method,since it requires bonding multiple times and may cause interfacial debonding. In addition,the number of constituent elements of the alloy system that can be examined using thediffusion multiples technique is limited geometrically up to four; it cannot be applied tomulticomponent systems with more than five components.Recently, as another option, our group has lately developed a sintered diffusionmultiple method [24,25], in which a mixed powder of multiple elements is sintered. Asample prepared by this method can be considered to be an assemblage of micro diffusioncouples, triplets, quadruplets, and so on. Assuming local equilibrium in an annealedsample, it is possible to obtain information on the equilibrium phase diagram in a widecompositional space from a single sample. The advantage of this method is that thesample preparation is simple, and the number of constituent elements of the alloy underexamination is not limited up to four for geometric reasons. The experimental data for theAl–Fe–Si [24,25] and Ni–Co–Ti–Al system [26] obtained by this method in previous studiesare in good agreement with the reported phase diagrams.In this study, the sintered diffusion multiple method is applied to the quinary phasediagram of the Cr–Mn–Fe–Co–Ni system. This work is the first trial to apply the methodto a quinary system. We determine the compositional range of the high entropy FCCphase, the so-called Cantor alloy, stereoscopically, and discuss the usefulness of the sintereddiffusion multiple method to examine the phase diagrams of multicomponent systems.2. Materials and MethodsTo prepare the SDM samples, chromium powder (99%, 63 µm pass), manganesepowder (99.9%, 300 µm pass), iron powder (99%, 150 µm pass), cobalt powder (99.9%,150 µm pass), and nickel powder (99.9%, 150 µm pass), all of which were from KojundoChemical Laboratory Co., Ltd. (Tokyo, Japan), were mixed at a molar ratio of 1:1:1:1:1 andsintered in a graphite die with a 12 mm diameter at 700 ◦C to 800 ◦C for 5 to 10 min at apressure of 11.3–25.5 MPa. The SDM samples were annealed at 800 ◦C for 256 h or 970 ◦Cfor 1 h to 256 h to introduce compositional gradients among multiple chemical elementsand were water-cooled. To demonstrate, using a standard case of the SDM method, thetemperature needs to be chosen within the range at which the alloy system is composed ofonly solid phases at this temperature. On the other hand, larger diffusivities are preferredin terms of the time required for the experiments. From these two points of view, 970 ◦CMaterials 2025, 18, 295 3 of 12was chosen as the temperature to be examined. In addition, 800 ◦C was chosen because attemperatures around 800 ◦C, phase stability has been observed in the literature [6–9], andhence, it is important to investigate the phase equilibria at 800 ◦C. We actually began theexperiments with annealing at 970 ◦C, without knowledge regarding the diffusion depththat would be obtained. That is why we performed the annealing for various periods.After these experiments, we expected that an annealing for 256 h would be enough toobtain information on phase equilibria of the high entropy phase at 800 ◦C in nearly theentire range. This is the reason why we conducted annealing just for 256 h at 800 ◦C, whileannealing was performed for various periods at 970 ◦C.The samples were cut into halves and embedded in conductive resin, and the cutsurfaces were polished for observation using abrasives #320, #400, and #600, followed bypolishing with a series of diamond slurries with particle sizes of 9 µm, 3 µm, and 0.05 µm,respectively. A schematic view of the experiment is shown in Figure 1.Materials 2025, 18, x FOR PEER REVIEW 3 of 13   preferred in terms of the time required for the experiments. From these two points of view, 970 °C was chosen as the temperature to be examined. In addition, 800 °C was chosen because at temperatures around 800 °C, phase stability has been observed in the literature [6–9], and hence, it is important to investigate the phase equilibria at 800 °C. We actually began the experiments with annealing at 970 °C, without knowledge regarding the diffu-sion depth that would be obtained. That is why we performed the annealing for various periods. After these experiments, we expected that an annealing for 256 h would be enough to obtain information on phase equilibria of the high entropy phase at 800 °C in nearly the entire range. This is the reason why we conducted annealing just for 256 h at 800 °C, while annealing was performed for various periods at 970 °C. The samples were cut into halves and embedded in conductive resin, and the cut surfaces were polished for observation using abrasives #320, #400, and #600, followed by polishing with a series of diamond slurries with particle sizes of 9 μm, 3 μm, and 0.05 μm, respectively. A schematic view of the experiment is shown in Figure 1.  Figure 1. Schematic view of sintered diffusion multiple method. The microstructures of the SDM samples were observed using a scanning electron microscope, equipped with an electron-probe microanalyzer with wavelength dispersive X-ray spectroscopy (EPMA; EPMA-8050G, Shimadzu Corp., Kyoto, Japan). The chemical compositions were mapped in a grid pattern at 1–2 μm intervals for several regions with 200 μm × 200 μm areas at an acceleration voltage of 15 kV and a 1 μA current for 8 ms per point. The measured intensities of the characteristic X-rays Cr Kα, Mn Kα, Fe Kα, Co Kα, and Ni Kα were converted to chemical compositions via the ZAF-correction method using intensities from elemental standard samples. In order to examine the validity of the phase diagram determined using the SDM samples, it was compared with the phase equilibria determined by a conventional method, where two-phase samples with various average compositions are prepared and annealed for a long period of time for equilibration, and the compositions of the constitu-ent phases are analyzed. For this purpose, the samples were synthesized by arc melting Figure 1. Schematic view of sintered diffusion multiple method.The microstructures of the SDM samples were observed using a scanning electronmicroscope, equipped with an electron-probe microanalyzer with wavelength dispersiveX-ray spectroscopy (EPMA; EPMA-8050G, Shimadzu Corp., Kyoto, Japan). The chemicalcompositions were mapped in a grid pattern at 1–2 µm intervals for several regions with200 µm × 200 µm areas at an acceleration voltage of 15 kV and a 1 µA current for 8 ms perpoint. The measured intensities of the characteristic X-rays Cr Kα, Mn Kα, Fe Kα, Co Kα,and Ni Kα were converted to chemical compositions via the ZAF-correction method usingintensities from elemental standard samples.In order to examine the validity of the phase diagram determined using the SDMsamples, it was compared with the phase equilibria determined by a conventional method,where two-phase samples with various average compositions are prepared and annealedfor a long period of time for equilibration, and the compositions of the constituent phasesare analyzed. For this purpose, the samples were synthesized by arc melting under anargon atmosphere. The starting materials are chromium chip (99.87%, Tosoh Corp., Shunan,Japan), manganese grain (99.9%, Kojundo Chemical Laboratory Co., Ltd., Itado, Saitama,Materials 2025, 18, 295 4 of 12Japan), iron grain (99.99%, Kojundo Chemical Laboratory Co., Ltd., Itado, Saitama, Japan),cobalt flake (99.92%, Xstrata plc, Zug, Switzerland), and nickel pellets (99.80%, vale, Toronto,ON, Canada). Heat treatments for homogenization and equilibration were performed ina quartz tube sealed in a vacuum at less than 2 Pa. The temperature was maintained at1000 ◦C for 48 h or at 1150 ◦C for 12 h for homogenization and then lowered to 970 ◦Cat 1 K/min, held for 200 h for equilibration, and then quenched in water. Another set ofsamples was held at 800 ◦C for 400 h for equilibration after homogenization. The specimenswere then cut and embedded in conductive resin. The surfaces were then polished in thesame manner as the SDM samples. The phase boundary compositions were obtained byEPMA with a point analysis mode at an acceleration voltage of 15 kV and a current valueof 20 nA for 1 min.3. Results and Discussion3.1. Display of Raw Chemical Composition Data in the CrMnFeCoNi SDM SamplesThis is the first study in which the SDM technique is applied to a quinary system, andso the methods for the construction of phase diagrams and displaying the analytical resultshave not yet been established. The phase diagrams for the multicomponent systems aredrawn with geometric figures, with each pure element as an end component; examplesinclude a line for a binary system, a triangle for a ternary system, and a tetrahedron for aquaternary system. In this work, a tetrahedron is used to display the phase diagrams forthe quinary Cr–Mn–Fe–Co–Ni system. Since a tetrahedron has four vertexes and is lessthan the number of component, one vertex is used for the sum of fractions of two elements,and the ratio between them is shown using a color scale. We chose Co and Ni for thetwo elements because they form a proportional solid solution, and hence, their elementalcharacters are similar to each other. Thus, the equiatomic composition CrMnFeCoNi islocated at (xCr, xMn, xFe, xCo/Ni) = (0.2, 0.2, 0.2, 0.4) in the compositional tetrahedrons usedin the following displays.The raw chemical composition data of 920,000 points at 970 ◦C and 720,000 pointsat 800 ◦C were obtained from SDM sample diffusion annealed at 970 ◦C for 1, 4, 16, 64,and 256 h and 800 ◦C for 256 h. The microstructures obtained by a scanning electronmicroscope are shown in Figure 2. From Figure 2a, tens of micrometers diameter or largerparticles of each element (Cr, Mn, Fe, Co, Ni) are recognized. Composition mixing due tointerdiffusion is limited in very small ranges in the as-sintered sample. Thus, we succeededin preparing a sample of a sintered diffusion multiple. At this stage, in most regions, eachelement still remains as an element. Figure 2b reflects the microstructure after interdiffusionproceeded to larger ranges after the 256 h annealing, where the interfaces between differentparticles of different elements are indistinct because of interdiffusion. Thus, annealingafter 256 h yields considerable information on the phase equilibria of this multicomponentsystem. In Figure 2b, one can recognize tiny dots, which are not considered to reflect realcompositional variations, since a typical X-ray intensity in the current experiments, around800 counts per pixel, gives an error of ±30 counts (~3.5%) and provides the contrast in themapping images.The chemical compositions obtained by WDS mapping analysis shown in Figure 2were plotted in the Cr–Mn–Fe–Co/Ni tetrahedral compositional space of Figure 3. Asone can see from the data at 970 ◦C shown in Figure 3a, as the annealing time increases,the measured compositional points in the sample, on the whole, gradually shift towardsthe equiatomic composition due to interdiffusion, and come together near the centerat the end (~256 h). Therefore, it is reasonable to use data obtained for up to 256 h ofannealing. At 800 ◦C, the only data from the annealing for 256 h seems to cover a largecompositional space (Figure 3b). Since it covers a wide compositional range at eitherMaterials 2025, 18, 295 5 of 12temperature, it is hard to identify the compositional range of the phases present merelyfrom Figure 3. Because the compositional analyses are performed at a large number ofrandom points, the measurement points include those obtained from points on phaseboundaries in the sample space and provide the apparent compositions in the miscibilitygaps in the compositional space.Materials 2025, 18, x FOR PEER REVIEW 5 of 13   At 800 °C, the only data from the annealing for 256 h seems to cover a large compositional space (Figure 3b). Since it covers a wide compositional range at either temperature, it is hard to identify the compositional range of the phases present merely from Figure 3. Be-cause the compositional analyses are performed at a large number of random points, the measurement points include those obtained from points on phase boundaries in the sam-ple space and provide the apparent compositions in the miscibility gaps in the composi-tional space.  Figure 2. Microstructures in the as-sintered state (a) and after annealing at 800 °C for 256 h (b). The monochrome images are backscattered electron images, and colored images are characteristic X-ray maps for the respective elements.  Figure 3. Tetrahedral plots of compositions measured from the Cr–Mn–Fe–Co–Ni sintered diffusion multiple samples annealed at 970 °C (a) and 800 °C (b), respectively. The color scale shows the Ni–Co ratio.  Figure 2. Microstructures in the as-sintered state (a) and after annealing at 800 ◦C for 256 h (b). Themonochrome images are backscattered electron images, and colored images are characteristic X-raymaps for the respective elements.Materials 2025, 18, x FOR PEER REVIEW 5 of 13   At 800 °C, the only data from the annealing for 256 h seems to cover a large compositional space (Figure 3b). Since it covers a wide compositional range at either temperature, it is hard to identify the compositional range of the phases present merely from Figure 3. Be-cause the compositional analyses are performed at a large number of random points, the measurement points include those obtained from points on phase boundaries in the sam-ple space and provide the apparent compositions in the miscibility gaps in the composi-tional space.  Figure 2. Microstructures in the as-sintered state (a) and after annealing at 800 °C for 256 h (b). The monochrome images are backscattered electron images, and colored images are characteristic X-ray maps for the respective elements.  Figure 3. Tetrahedral plots of compositions measured from the Cr–Mn–Fe–Co–Ni sintered diffusion multiple samples annealed at 970 °C (a) and 800 °C (b), respectively. The color scale shows the Ni–Co ratio.  Figure 3. Tetrahedral plots of compositions measured from the Cr–Mn–Fe–Co–Ni sintered diffusionmultiple samples annealed at 970 ◦C (a) and 800 ◦C (b), respectively. The color scale shows theNi–Co ratio.3.2. Analysis to Identify the Compositional Range of PhasesThe concept of SDM is to form many micro-diffusion couples, triplets, and quadrupletsin a sample in a simple way. Assuming that local equilibrium holds within the samples afterMaterials 2025, 18, 295 6 of 12diffusion annealing, compositions existing within the sample reflect composition rangesof the existing phases of the equilibrium phase diagrams of the alloy system among theelements used as endmembers of SDM. Based on this idea, compositions within the sampleare measured at random by EPMA. However, compositions thus collected involve those incases where the electron probe happens to be located on the phase boundaries, which areof apparent compositions of mixed phases. Therefore, all measured compositions cannotbe regarded as those of the current existing phases as they are.To address this issue, we introduce point density in the compositional space. Thetetrahedral compositional space among Cr–Mn–Fe–Co/Ni, Figure 4b, is divided intoelemental cubes, with an edge the length of which is one hundredth of an edge of thewhole tetrahedral compositional space, and the number of measured compositional pointsper elemental cube is defined as the point density. As shown Figure 4a, point densitieswithin compositional ranges of existing phases are expected to be higher than those in themiscibility gaps, since measured points are located in miscibility gaps only in cases wherethe electron probe happens to be located on the phase boundaries. Therefore, the absolutevalue of the slope of point density is thought to be maximal at the phase boundaries. Thus,the phase boundary surfaces can be represented by the maximal slope of point density.Materials 2025, 18, x FOR PEER REVIEW 7 of 13    Figure 4. Schematic illustration of the concepts used to analyze composition data obtained from the sintered diffusion multiple samples of the A-B-C-D system: the relationship between measured compositions and point density, the former of which include apparent compositions (a), elemental cubes used to determine point density (b), and slope of point density (c) in the compositional space.  Figure 5. Analysis results of SDM samples showing the point density (a) and the slope of point density (b) obtained at 970 °C and 800 °C, respectively. In the figure (b), tie lines obtained by the conventional method are shown together: segments with purple end points and triangles with blue vertices show two-phase and three-phase equilibria, respectively. The color scales show respective quantities, i.e., point density (a) and slope of point density (b). The numbers I, II, III, and I′ were labeled to regions where data points gather. Figure 4. Schematic illustration of the concepts used to analyze composition data obtained fromthe sintered diffusion multiple samples of the A-B-C-D system: the relationship between measuredcompositions and point density, the former of which include apparent compositions (a), elementalcubes used to determine point density (b), and slope of point density (c) in the compositional space.In the practical analysis, the slope of the point density,√∆dx2+∆dy2+∆dz2, where∆di (i = x, y, and z) is the difference in the point density of the adjacent cubes in the x, y, andz directions, is defined as shown in Figure 4c. A threshold was then set as the lower limitof this point density slope to see the phase boundary surfaces, and the common logarithmof the point density slope was taken between the maximum and the lower limit of thepoint density slope, displayed using a continuous gradient color scale in Figure 5. Thesurfaces with colder colors indicate larger slopes of point density and can be considered asMaterials 2025, 18, 295 7 of 12a phase boundary surface. The reason for choosing the common logarithm is as follows:experimental point densities are different phase by phase, and hence, the differencesbetween those of the regions within a phase (that is, the existence range of a phase) andoutside a phase (the probe of EPMA is located on a phase boundary by chance in the samplespace, and hence, the measured points are plotted in-between phases in the compositionalspace, but their point densities are basically low) could be different phase by phase. Inorder to highlight the maximal surfaces of the slope of point density, even with low pointdensities, it should be effective to look at the slope of point density in a logarithm scale.While the information on the Co/Ni ratio is lost, since this analysis was performed withinthe compositional space of a tetrahedron, with the sum of Co and Ni as one vertex, it canbe obtained by referring to the raw chemical composition data.Materials 2025, 18, x FOR PEER REVIEW 7 of 13    Figure 4. Schematic illustration of the concepts used to analyze composition data obtained from the sintered diffusion multiple samples of the A-B-C-D system: the relationship between measured compositions and point density, the former of which include apparent compositions (a), elemental cubes used to determine point density (b), and slope of point density (c) in the compositional space.  Figure 5. Analysis results of SDM samples showing the point density (a) and the slope of point density (b) obtained at 970 °C and 800 °C, respectively. In the figure (b), tie lines obtained by the conventional method are shown together: segments with purple end points and triangles with blue vertices show two-phase and three-phase equilibria, respectively. The color scales show respective quantities, i.e., point density (a) and slope of point density (b). The numbers I, II, III, and I′ were labeled to regions where data points gather. Figure 5. Analysis results of SDM samples showing the point density (a) and the slope of pointdensity (b) obtained at 970 ◦C and 800 ◦C, respectively. In the figure (b), tie lines obtained by theconventional method are shown together: segments with purple end points and triangles with bluevertices show two-phase and three-phase equilibria, respectively. The color scales show respectivequantities, i.e., point density (a) and slope of point density (b). The numbers I, II, III, and I′ werelabeled to regions where data points gather.3.3. Composition Ranges of Existing Phases in the Cr–Mn–Fe–Co–Ni SystemTo identify the existing ranges of equilibrium phases in the phase diagrams, we focuson the change in the point density in the compositional space, which is defined as thenumber of measurement points per elemental cube across the phase boundary; the pointdensity should change rapidly across a phase boundary, as shown Figure 4a. Therefore, thephase boundaries are expected to be represented by the surface with the maximal slopein point density. Figure 5 shows the point density (a) and the slope of point density (b).Supplemental Figures S1 and S2 show the slope of point density from various directionsdifferent from those of Figure 5 at 800 ◦C and 970 ◦C, respectively. Thus, the phase boundarycompositions were estimated stereoscopically and continuously by extracting compositionswith a large slope of the point density. To confirm the validity of the estimated phaseboundary compositions, we compared them with those obtained using the conventionalmethod. In Figure 5b, the tie lines obtained using the conventional samples are shown,together with the slope of point density. The microstructures of the samples prepared viaMaterials 2025, 18, 295 8 of 12the conventional method are shown in Figure 6, where the measured compositions of therespective phases in the microstructures are indicated as well. As seen in Figure 6, thesize of the microstructure is large enough to determine the compositions of the respectiveconstituent phases by EPMA, in the light of its spatial resolution.Materials 2025, 18, x FOR PEER REVIEW 10 of 13    Figure 6. Microstructures observed in samples prepared in the conventional method. The annealing temperature is 970 °C for (a–c) or 800 °C for (d–f). The compositions shown below each micrograph are those, in atomic fractions, measured by electron-probe microanalysis at green and red dots for respective phases in the images.  Figure 7. The slope of point density at 970 °C, together with the phase boundary data at 1000 °C in the literature: two-phase equilibrium (i)–(j) [12], (c)–(g), and (d)–(e) [13], and three-phase equilib-rium (a)–(b)–(f) [13]. Black segments express tie lines. 4. Conclusions and Remarks We have applied the sintered diffusion multiple method to the quinary Cr–Mn–Fe–Co–Ni system. The composition ranges of the existing phases in the system have been estimated stereoscopically and continuously in the large part of the entire system at 970 °C and 800 °C, including the high entropy alloy, the so-called Cantor alloy. The validity of the method has been examined, resulting in a good agreement between the results ob-tained by the sintered diffusion multiple method and those obtained by a conventional Figure 6. Microstructures observed in samples prepared in the conventional method. The annealingtemperature is 970 ◦C for (a–c) or 800 ◦C for (d–f). The compositions shown below each micrographare those, in atomic fractions, measured by electron-probe microanalysis at green and red dots forrespective phases in the images.There are three regions recognized in the slope of point density map; the first one isthe region which has the largest volume extended to Fe from the Co/Ni–Cr–Mn planeand is labeled as “I” in the figure. The second one, “II”, is the region that is located on theCr-richer side of region “I”. And then, the last one, “III”, is the region close to the Cr-vertex,which is thought to be the Cr phase.As found in Figure 5b and Figure S1, in the 970 ◦C results, many of the phase boundarycompositions obtained by the conventional method are located near the maximal slope ofthe point density surfaces. Figure S3 shows the slope of point density on the cross-sectionalplane, including Fe35(CoNi)65, Mn43(CoNi)57, Cr93Fe7, and Cr90Mn10, together with thephase boundary compositions determined by the conventional method, even in a largerscale, again showing a good agreement between the slope of point density surface andthe phase boundary compositions. Actually, the distance between the phase boundarydetermined by the conventional method and the maximal slope of point density surfaceis ~3 at.%, at most, within Figure S3. This value, ~3 at.%, is close to the error range, 3.5%,which is estimated from the statistical analysis mentioned previously (Section 3.1). Thus,it is considered reasonable to regard the maximal slope of point density surfaces fromthe SDM samples as phase boundary surfaces in multicomponent systems. Taking thisroute, one could estimate phase boundary surfaces continuously over the entire range of amulticomponent system with high efficiency.Noting that the equiatomic CrMnFeCoNi composition is located at a point shiftedtoward the Co/Ni vertex from the center of the tetrahedron, the equiatomic composition isfound to be included in region I. Thus, this region is considered to indicate the existencerange of the high-entropy solid solution phase. One of the features found regarding region IMaterials 2025, 18, 295 9 of 12is that it has a wide compositional range, x from 0 to 1, in the Fex-(CrMnCoNi)1−x direction,consistently with the results in the CALPHAD study previously reported [13,27].The existence of a separate phase, as shown as I′ in Figure 5b, in equilibrium with thehigh-entropy solid solution phase in the Mn-rich region in the tetrahedron was revealedby the conventional samples at 970 ◦C, where three-phase equilibrium (I–I′–III) has beenconfirmed, as seen as an equilibrium triangle in Figure 5b and as micrographical contrastin Figure S4. However, the corresponding region in the slope of the point density map isnot clearly separated but connected to the high-entropy solid solution phase. The reasonfor this could be considered as follows: in this study the compositional data analysis wasperformed in the Cr–Mn–Fe–Co/Ni tetrahedron space, where the spatial dimension isreduced by one; as seen in Figure 3, the region corresponding to I′ shows a higher Co ratiothan that of Ni, and hence, the phase equilibria between the Cantor alloy and the Mn-richphase could depend on the Co/Ni, ratio resulting in the dull boundaries in the tetrahedronspace, which neglects the difference between Co and Ni.At 800 ◦C, while it seems as if the existing range of the high-entropy alloys wasacquired over its whole compositional range, it is actually partly lacking, especially inthe high Mn concentration region, as seen in Figure 5b. This is thought to be due to alarger diffusion distance than that at 970 ◦C in the corresponding region, since only thecomposition data from the sample after annealing for 256 h were used at 800 ◦C, while thedata from various annealing conditions from the as-sintered to 256 h annealing sampleswere compiled at 970 ◦C. That is to say, the Mn diffusion distance in the sample annealedat 800 ◦C was too large for its particle size. Thus, in general, it is found that to cover alarge compositional range in a targeted multicomponent system, it is important to prepareSDM samples with various diffusion distances relative to the particle size of the elementalpowder. To achieve this, the usage of powder with a broad distribution of grain sizes inpreparation of the SDM samples or the compilation of data from various annealing times,i.e., diffusion distance, would work, as discussed in Ref. [24].Here, the composition range of the high entropy phase (region I) thus determinedis compared with those in the literature. Figure 7 shows the slope of point density mapat 970 ◦C in this work, together with the phase boundary data at 1000 ◦C reported sofar in the literature [12,13]. There are four sets of equilibrium compositions: two-phaseequilibrium (i)–(j) [12], (c)–(g), and (d)–(e) [13], and three-phase equilibrium (a)–(b)–(f) [13].Compositions (e), (f), (g), and (j) belong to the FCC high-entropy phase and are found to belocated in the vicinity the surface of maximal slope of point density. In addition, points (c)and (i) are from the σ phase and are located in the vicinity of the surface of region II. Thatagain proves that the maximal slope of the point density surfaces can be regarded as phaseboundaries. On the other hand, data points were not acquired in this work in the regionnear the phase boundary data points (a), (b), and (d).At 800 ◦C, it is found that the equiatomic composition is included within region I at800 ◦C, which means the equiatomic composition is the solid solution phase (region I),in this study. This result is consistent with that in several previous works for equiatomiccompositions [6,7,9]. On the other hand, a phase separation occurring at temperaturesbelow 800 ◦C has been reported for the equiatomic alloy [8]. This might mean that thedriving force for the phase separation should be small, even if it occurs.Figure 6c,f indicate the two-phase microstructures consisting of the Cr phase and anintermetallic phase. The intermetallic phase has been reported as an unknown phase byKeil et al. [28]. The results of this study confirm the presence of the phases in both SDMand the conventional method.Materials 2025, 18, 295 10 of 12Materials 2025, 18, x FOR PEER REVIEW 10 of 13    Figure 6. Microstructures observed in samples prepared in the conventional method. The annealing temperature is 970 °C for (a–c) or 800 °C for (d–f). The compositions shown below each micrograph are those, in atomic fractions, measured by electron-probe microanalysis at green and red dots for respective phases in the images.  Figure 7. The slope of point density at 970 °C, together with the phase boundary data at 1000 °C in the literature: two-phase equilibrium (i)–(j) [12], (c)–(g), and (d)–(e) [13], and three-phase equilib-rium (a)–(b)–(f) [13]. Black segments express tie lines. 4. Conclusions and Remarks We have applied the sintered diffusion multiple method to the quinary Cr–Mn–Fe–Co–Ni system. The composition ranges of the existing phases in the system have been estimated stereoscopically and continuously in the large part of the entire system at 970 °C and 800 °C, including the high entropy alloy, the so-called Cantor alloy. The validity of the method has been examined, resulting in a good agreement between the results ob-tained by the sintered diffusion multiple method and those obtained by a conventional Figure 7. The slope of point density at 970 ◦C, together with the phase boundary data at 1000 ◦C inthe literature: two-phase equilibrium (i)–(j) [12], (c)–(g), and (d)–(e) [13], and three-phase equilibrium(a)–(b)–(f) [13]. Black segments express tie lines.4. Conclusions and RemarksWe have applied the sintered diffusion multiple method to the quinary Cr–Mn–Fe–Co–Ni system. The composition ranges of the existing phases in the system have been estimatedstereoscopically and continuously in the large part of the entire system at 970 ◦C and 800 ◦C,including the high entropy alloy, the so-called Cantor alloy. The validity of the methodhas been examined, resulting in a good agreement between the results obtained by thesintered diffusion multiple method and those obtained by a conventional method. Whiledata were partially missing due to the too large diffusion rates, depending on compositionin the sintered diffusion multiple experiments, this matter could be addressed by using apowder with a wider variety of particle sizes in sample preparation or by annealing thesamples for various annealing times.Here, we note the potential applications of the sintered diffusion multiple method. Theresults show that this method could be useful in exploring not only the Cr–Mn–Fe–Co–Nisystem but also a wide variety of multi-component systems, providing initial insightsinto their phase diagrams, even of unknown systems. There is a wide variety of alloysand compounds whose properties depend on chemical compositions. Examples includecompound semiconductors, intermetallic compounds used as structural materials, magneticcompounds, and so on. The transport properties of compound semiconductors, includingthermoelectric materials [29], are sensitive to carrier concentrations, which often dependson chemical compositions. The magnetic properties [30] of compounds often depend ondefect structures, which again depend on chemical compositions. Advanced studies onthese materials are proceeding to multicomponent systems. The sintered diffusion multiplemethod can play a critical role in such multicomponent materials.Supplementary Materials: The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/ma18020295/s1, Figure S1: The slope of point density at 970 ◦C; FigureS2: The slope of point density at 800 ◦C; Figure S3: Comparison results of the slope of point densitysurface and the conventional method at 970 ◦C on cutting section of compositional space of Figure 5b;Figure S4: Microstructure observed in a sample prepared at 970 ◦C in the conventional method.https://www.mdpi.com/article/10.3390/ma18020295/s1https://www.mdpi.com/article/10.3390/ma18020295/s1Materials 2025, 18, 295 11 of 12Author Contributions: Conceptualization, R.Y., T.I. and A.I.; methodology, R.Y. and A.I.; software,R.Y.; validation, R.Y.; formal analysis, R.Y.; investigation, R.Y. and T.I.; resources, A.I.; data curation,R.Y.; writing—original draft preparation, R.Y. and T.I.; writing—review and editing, A.I.; visualization,R.Y.; supervision, T.I.; project administration, T.I.; funding acquisition, T.I. and A.I. All authors haveread and agreed to the published version of the manuscript.Funding: This work was supported by a Grant-in-Aid for Scientific Research on Innovative Areasfrom JSPS KAKENHI, Japan Grant Number 19H05165, and by the NIMS Joint Research Hub ProgramNo. 2024-095.Institutional Review Board Statement: Not applicable.Informed Consent Statement: Not applicable.Data Availability Statement: The original contributions presented in the study are included in thearticle/Supplementary Materials, further inquiries can be directed to the corresponding author.Conflicts of Interest: The authors declare no conflict of interest.References1. Cantor, B.; Chang, I.T.H.; Knight, P.; Vincent, A.J.B. Microstructural development in equiatomic multicomponent alloys. Mater.Sci. Eng. A 2004, 375-377, 213–218. [CrossRef]2. Yeh, J.W.; Chen, S.K.; Lin, S.J.; Gan, J.Y.; Chin, T.S.; Shun, T.T.; Tsau, C.H.; Chang, S.Y. 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MDPI and/or the editor(s) disclaim responsibility for any injury topeople or property resulting from any ideas, methods, instructions or products referred to in the content.https://doi.org/10.1016/j.intermet.2016.09.003https://doi.org/10.1016/j.jallcom.2016.11.376https://doi.org/10.1016/S1369-7021(05)71122-6https://doi.org/10.1016/j.matdes.2019.107816https://doi.org/10.1016/j.jpcs.2018.03.003https://doi.org/10.1016/j.scib.2020.03.035 Introduction  Materials and Methods  Results and Discussion  Display of Raw Chemical Composition Data in the CrMnFeCoNi SDM Samples  Analysis to Identify the Compositional Range of Phases  Composition Ranges of Existing Phases in the Cr–Mn–Fe–Co–Ni System  Conclusions and Remarks  References