Study of phase equilibrium of refractory high-entropy alloys using the atomic size di ﬀ erence concept for turbine blade applications

: In the pursuit of advancing turbine blade materials, refractory high-entropy alloys (RHEAs) have emerged as promising candidates, o ﬀ ering superior performance at elevated temperatures compared to conventional super-alloys. With the plateauing of melting temperatures in Ni-based superalloys, the demand for innovative material systems capable of substantial performance enhancements in turbines has increased. The expansive compositional space of high-entropy alloys (HEAs) presents a rich yet underex-plored realm, particularly concerning the intricate phase equilibria pivotal for alloy stability at high temperatures. This research purpose is to elucidate the phase formation dynamics within the W – Re – Ni – Co – Mo HEA system across varying atomic percentages of each constituent element. Employing two-dimensional mapping methodology for correlating atomic size di ﬀ erence and enthalpy mix parameters, enabling the di ﬀ erentiation between intermetallic (IM) phase and single-phase formations in the non-equi-molar W – Re – Ni – Co – Mo system across numerous atomic percentages of each element. Major ﬁ ndings indicate distinct phase formations based on elemental compositions, with elevated nickel and rhenium percentages favouring single-phase solid solution (SPSS) structures, while diminished concentrations yield alternative con ﬁ gurations such as (IM + SPSS). Similarly, variations in tungsten and molybdenum concentrations in ﬂ uence phase stability. The ability to assess phases for diverse atomic percentages of elements in the W – Re – Ni – Co – Mo system will facilitate to analyse HEA systems for high-temperature turbine blades


Introduction
Advanced materials play a crucial role in the development and progress of technology across various industries.Advanced materials often exhibit superior mechanical, thermal, electrical, or optical properties compared to traditional materials.This enhanced performance allows for the development of more efficient and high-performance technologies [1][2][3][4][5][6][7][8][9].As technology advances, there is a trend towards miniaturization of devices and components.Advanced materials with unique properties, such as nanomaterials or metamaterials, enable the design and manufacturing of smaller and more compact devices [10][11][12][13][14][15][16][17].Advanced materials contribute to the development of energy-efficient technologies.Technology encompasses a wide range of industries, internet, and software plays a crucial role in enhancing efficiency, productivity, and innovation across these domains.The specific software needs in technology can vary based on the industry and application.The software needs in technology are dynamic and continually evolving as new technologies emerge.Depending on the specific requirements of a given industry or application, additional specialized software may be employed to address unique challenges and opportunities [2,[18][19][20][21][22][23].These software categories collectively form the technological ecosystem, enhancing various aspects of development, collaboration, security, and decision-making within the technology industry [4,[24][25][26][27][28].In the field of metallurgy, software tools like computational thermodynamics software are helpful in predicting phase transformations, equilibrium conditions, and properties of alloys at different temperatures and compositions.
The necessity for advanced materials exhibiting superior performance at elevated temperatures has become more imperative, given the increasingly intricate and harsh operating conditions in the realm of turbine blade applications, propelled by rapid advancements in technology.The escalating needs for high-temperature applications, the imperative for enhanced properties alloys capable of withstanding elevated temperature conditions in the context of the "space race," the need for materials tailored for gas turbine blade applications, and relevant pursuits are steering the ongoing development of refractory-based high-entropy alloys (HEAs).The efficacy of energy production in industrial gas turbines is contingent upon the operating temperature, where efficiency experiences an upsurge with elevated temperatures.A constraining factor in achieving higher operating temperatures is the formidable environment that turbine blades endure, necessitating resilience against substantial stresses encountered at elevated temperatures [29][30][31][32][33][34].
There exist two primary material properties within the alloys of these blades that require enhancement to facilitate elevated operating temperatures of the turbine blades: (1) enhanced stability at high temperatures and (2) sustained strength at elevated temperatures.Presently, the prevalent utilization of nickel-based superalloys is evident [35][36][37][38]; however, this approach is nearing its limitations in improving the turbine disk's operating temperature due to the approaching constraints of alloy composition in design.With the deceleration in the advancement of melting temperatures in nickel-based superalloys, there arises a demand for innovative material systems capable of manifesting substantial enhancements in turbine performance.Recently identified as a class of materials, refractory high-entropy alloys (RHEAs) demonstrate notable high-strength and hightoughness characteristics at elevated temperatures, thereby showcasing their potential for application in turbine blades [39][40][41][42][43].
Owing to variations in the size of atoms among these elements, HEAs tend to deviate from their optimal lattice positions, resulting in significant local lattice distortion.This phenomenon has the potential to hinder dislocation motion, thereby yielding high configurational entropy that escalates with temperature.Consequently, HEAs demonstrate elevated strength and reduced plasticity at increased temperatures [44][45][46][47][48]. RHEAs, characterized by their elevated melting points, can manifest superior strength at temperatures surpassing 800°C in comparison to widely employed superalloys.This characteristic positions RHEAs as highly promising alternatives for applications in elevated temperature environments, particularly in turbine blade applications, where they hold the prospect of outperforming Ni-based superalloys.Consequently, the exploration of RHEAs emerges not only as a pursuit with cutting-edge academic value but also as a venture with incalculable economic benefits and strategic significance, as they represent novel and promising candidates extending beyond the capabilities of conventional superalloys [49][50][51][52][53][54].
Due to the extensive compositional range within HEAs, the intricate phase equilibria governing the high-temperature stability of the alloy remain largely unexplored [55][56][57][58].
However, the challenge lies in pinpointing the ideal combination of constituent elements to achieve the desired properties.The conventional trial-and-error method, characterized by prolonged experimentation and limited comprehension of HEA's intricate structural aspects, proves inefficient.Hence, there arises a pressing need for innovative alloy-design methodologies capable of predicting phases within W-Re-Ni-Co-Mo alloys, thereby streamlining the arduous experimental process.The novelty of this research lies in establishing a two-dimensional mapping (2DM) relationship between atomic size differences and enthalpy mix.This mapping endeavour aims to unveil the phases within non-equiatomic W-Re-Ni-Co-Mo HEAs across various atomic compositions of each element.Proficiency in discerning phase structures for diverse atomic compositions of elements within W-Re-Ni-Co-Mo HEAs holds significant potential for guiding the development of HEAs tailored for turbine blade applications.The commonly found alloying elements in HEAs include nickel (Ni), cobalt (Co), titanium (Ti), molybdenum (Mo), and vanadium (V).Numerous HEA systems, such as those based on the CrFeNi composition, have been documented in the literature [59][60][61][62][63].However, CrFeNi-based HEA systems, while frequently employed for the development of new HEAs, may not possess superior properties that align with industrial requirements.The incorporation of Ni, Co, Mo, and W elements into HEA systems can significantly influence the formation of precipitates, thereby enhancing the mechanical properties [58,[64][65][66][67].
The pursuit of studying metallurgical properties and advancing materials for industrial technological applications epitomizes a multifaceted endeavour characterized by meticulous inquiry and innovation.Delving into the intricate interplay between material composition and performance, this scholarly pursuit transcends mere exploration, embodying a commitment to pushing the boundaries of scientific understanding and practical utility.Through rigorous experimentation, sophisticated analytical techniques, and mathematical modelling, researchers strive to unravel the intricacies of material behaviour at atomic and macroscopic scales, discerning the fundamental principles governing their mechanical, thermal, and corrosion resistance properties [68][69][70][71][72].This scholarly quest not only enriches our comprehension of materials science but also underpins the development of HEAs to meet the exacting demands of diverse industrial sectors, thereby fostering technological advancement and driving economic progress.Consequently, the primary aim of this research is to devise an innovative non-equimolar HEA (W-Re-Ni-Co-Mo) through varied compositions (5-40 at%) of each constituent element.

Materials and methods
Owing to its compositional versatility, non-equiatomic HEA systems represent a promising class of alloys, particularly in the context of emerging high-temperature materials.Determining the optimal combination of constituent elements necessary for desired properties poses a challenge.The conventional trial-and-error approach, marked by prolonged periodicity and a limited understanding of the intricate structural features of HEAs, is not recommended.Consequently, there is a need to devise innovative alloydesign methodologies that can predict the phases in W-Re-Ni-Co-Mo alloy, thereby circumventing the cumbersome experimental process.Thus, the principal objective of this research is to forge a 2DM correlation between enthalpy mix and atomic size differences to reveal the phases in nonequimolar W-Re-Ni-Co-Mo HEAs across varying atomic compositions of each element.Such an approach holds the promise of facilitating alloy design by evaluating phase structures at different atomic compositions within the W-Re-Ni-Co-Mo HEA spectrum, thereby aiding in the attainment of desired properties crucial for high-temperature applications.
Central to this inquiry are key scientific questions concerning the circumstances under which solid solutions or intermetallic (IM) compounds arise in multi-component HEA alloys, addressing both the why and when of such occurrences.

Conditions for the formation of the single-phase solid solution (SPSS) and IM in HEAs
Criteria for the IM and single-phase formation in HEAs are detailed in Table 1.Both the calculated atomic size difference and enthalpy mix values must meet the requirements for solid solution phases.Merely satisfying the atomic size difference conditions is inadequate for determining the SPSS.Consequently, it is evident that establishing scientifically satisfactory conditions for the SPSS necessitates an understanding of the relationship between atomic size difference and enthalpy mix.From the perspective of HEA design, comprehending the correlation between atomic size difference and thermodynamic parameters requires the development of a 2DM correlating atomic size difference and enthalpy mix [47].This map serves to distinguish between IM and single-phases in non-equiatomic [W-Re-Ni-Co-Mo] across various atomic percentages of each element.In this research, the prediction of phase types for various compositions of the [W-Re-Ni-Co-Mo] system is facilitated through the development of two-dimensional maps for the parameters atomic size difference (δ) and enthalpy mix (ΔH mix ).Utilizing this mapping technique, , n is the number of component elements, C i and r i are compositions and atomic radii of ith element, and r ̅ is the average atomic radius 2 Enthalpy of mixing (ΔH mix ) where H Δ ij mix indicates the enthalpy of mixing of the pair i−j, calculated using Miedema's model, C i and C j are the atomic percentages of the ith and jth component elements, respectively Phase equilibrium of refractory high-entropy alloys  3 the phase type can be anticipated for any unknown composition within W-Re-Ni-Co-Mo HEA systems for hightemperature turbine blades.Table 2 shows a collection of non-equiatomic HEAs distinguished by diverse compositions within the (W-Re-Ni-Co-Mo) system

Results and discussion
Table 3 presents the calculated results obtained from the parameters enthalpy mix and atomic size difference, which are computed using equations ( 1) and (2).

Impact of rhenium atomic percentage in the (W-Re-Ni-Co-Mo) HEA
Table 4 displays the symbol values corresponding to Figure 1 for the HEA systems 1-8 series, illustrating the fluctuations in rhenium atomic percentages.Table 4 illustrates the variation in rhenium atomic percentages (5-40 at%) across the HEA series.
Figure 1 illustrates the impact of varying atomic percentages of rhenium on the enthalpy mix in the (W-Re-Ni-Co-Mo)  The strengthening of the Laves phase, which is an IM phase, contributes to the enhancement of the properties of HEAs [61].This strengthening effect is particularly notable at higher atomic percentages of rhenium.The Laves phase reinforcement is known to improve the mechanical properties of the alloy, making it more durable and resistant to deformation.The less favourable enthalpy mix indicates a heightened bond among the alloying elements.This enhanced bonding is advantageous for designing IM compounds, which may exhibit unique and desirable properties.Understanding the enthalpy mixing of main components in HEAs is crucial for characterizing their chemical interactions [73], which ultimately influence the alloy's properties and performance.In essence, how variations in rhenium content influence the enthalpy mixing values, which in turn impact the properties and performance of HEA systems.It also underscores the importance of considering these factors in the design and development of advanced alloy materials.

Influence of nickel atomic percentage in
the (W-Re-Ni-Co-Mo)  Phase equilibrium of refractory high-entropy alloys  5 Table 5 elucidates that within the HEA 9 to HEA 15 series, there is a discernible range in the atomic percentages of nickel, spanning from 5 to 40 at%.
Figure 2 illustrates the impact of nickel atomic percentage on the enthalpy mix in (W-Re-Ni-Co-Mo).As the nickel atomic percentage varies from 5 to 40 at%, the enthalpy mix value demonstrates an increase.The maximum enthalpy mix value is observed at a 40 at% of nickel, meeting the criteria for SPSS.However, at minor nickel atomic percentages, specifically below 40 at%, the enthalpy mix values are measured at −21.45 kJ•mol −1 , failing to meet the specified criteria (Table 1).Nickel has a tendency to segregate into dendritic areas, resulting in the emergence of Laves within the phases of the HEA.This precipitation of the Laves phase brings about substantial changes in the features of the HEA.

Influence of cobalt atomic percentage in the (W-Re-Ni-Co-Mo) HEA
Table 6 displays the symbol values corresponding to Figure 3, illustrating fluctuation in atomic percentages of cobalt within the range of 5-40 at%.
Table 6 presents a detailed breakdown of the atomic percentages of cobalt across various compositions denoted by different symbols.The compositions are characterized by their atomic percentages of cobalt ranging from 5% to 40%, with the remaining percentages distributed among other elements such as HEA, Re, Ni, Mo, and W. It exhibits a systematic variation in atomic percentages of cobalt across different compositions, allowing for a thorough exploration of its impact on material properties.The compositions are arranged in ascending order of cobalt content, providing a clear progression for analysis.Concurrently, the enthalpy mix values corresponding to each composition are provided, elucidating the thermodynamic stability and energy characteristics associated with the different cobalt concentrations.The enthalpy mix values serve as crucial indicators of the material's behaviour under specific conditions.
By examining the enthalpy mix values across the range of cobalt percentages, notable trends emerge.It becomes evident that variations in the atomic percentage of cobalt directly affect the enthalpy mix values, with higher cobalt concentrations generally resulting in lower enthalpy mix values.This suggests a significant influence of cobalt content on the overall energy landscape and stability of the material.Of particular interest is the observation that the highest enthalpy mix value occurs at 5 at% of cobalt.This underscores the intricate interplay between cobalt and other alloying elements, such as cobalt, in determining the material's thermodynamic properties.Such insights are crucial for tailoring compositions to achieve desired performance characteristics.
The consistency of enthalpy mix values with the SPSS condition, as outlined in Table 1, underscores the reliability and relevance of this criterion in guiding material design and selection.This consistency across different cobalt percentages reaffirms the robustness of the SPSS criterion in  predicting material behaviour like thermodynamic stability and energy characteristics of the materials, facilitating informed decision-making in material design and engineering applications.Moreover, referring to Figure 3, which presumably illustrates the relationship between atomic percentage of cobalt and enthalpy mix values, it is evident that the enthalpy mix values consistently adhere to the SPSS condition across all atomic percentage ranges of cobalt.

Influence of atomic percentage of molybdenum in the (W-Re-Ni-Co-Mo) HEA
Table 7 elucidates the changes in atomic percentages of molybdenum, ranging from 5 to 40%. Figure 4 illustrates the impact of the atomic percentage of molybdenum on the enthalpy mix in W-Re-Ni-Co-Mo alloy.As the atomic percentage of molybdenum fluctuates from 5 to 40 at%, there is a corresponding decrease in the enthalpy mix value.
The enthalpy mixing value shows a decline with higher atomic percentages of molybdenum, with similar results observed in experiments conducted by other researchers investigating HEAs [53].
The maximum enthalpy mix value is identified at 5 at % of molybdenum, aligning with the ΔH mix criterion specified for SPSS, as outlined in Table 1.The graphical representation in Figure 4 reveals that enthalpy mix values conform to the SPSS condition for the varied atomic percentages of molybdenum.However, at higher atomic percentages of molybdenum in the (W-Re-Ni-Co-Mo) HEA, the enthalpy mix values fail to meet the condition, as indicated in Table 1.When there are increased atomic percentages of molybdenum in HEA, molybdenum tends to precipitate and leads to Laves formation in HEA.As depicted in Figure 4, it becomes evident that at lower atomic percentages of molybdenum, the enthalpy mix value is large.In contrast, Lave effects become apparent at large atomic percentages of molybdenum in HEA.

Influence of tungsten atomic percentage
in the (W-Re-Ni-Co-Mo) HEA Table 8 displays the symbol values corresponding to Figure 5, illustrating the fluctuation in atomic percentages of tungsten within the range of 5-40 at%.Table 8 illustrates the fluctuation in atomic percentages of tungsten (ranging from 5 to 40 at%).
From the data provided in Table 8, it is evident that there is a range of atomic percentages for tungsten across different compositions of the HEA, with values varying from 5 to 40% in W-Re-Ni-Co-Mo alloy.Furthermore, it is indicated that there is a fluctuation in the atomic percentages of tungsten in the alloy, and this fluctuation has an impact on the enthalpy mix of the alloy.This impact is elucidated in Figure 5, which illustrates how the atomic  Phase equilibrium of refractory high-entropy alloys  7 percentage of tungsten influences the enthalpy mix in the W-Re-Ni-Co-Mo alloy.According to the description, the enthalpy mix values exhibit a decline as the atomic percentage of tungsten varies from 5 to 40%.The peak enthalpy mix value is observed at 5 at% of tungsten, meeting a specified criterion for the formation of a special solid solution (SPSS), as mentioned in Table 1.The enthalpy mixing value shows a decline with higher atomic percentages of tungsten, with similar results observed in experiments conducted by other researchers investigating HEAs [74].
Figure 5 provides a visual representation of this relationship, showing how the enthalpy mix values change with varying atomic percentages of tungsten.It demonstrates that the enthalpy mix values satisfy the SPSS condition for different atomic percentages of tungsten in the W-Re-Ni-Co-Mo HEA.Additionally, the examination of Figure 5 indicates that at minor atomic percentages of tungsten within the HEA, the enthalpy mix values do not meet the specified condition, as outlined in Table 1.This suggests that certain compositions of the alloy may not exhibit the desired properties unless the atomic percentage of tungsten is within a certain range.

2DM for the W-Re-Ni-Co-Mo alloy
The primary objective of the present research is to forecast the phases in an innovative non-equiatomic HEA comprising W-Re-Ni-Co-Mo across different compositions.A crucial metallurgical aspect of the non-equiatomic HEA lies in understanding the correlation between atomic size differences and the enthalpy mix, which aids in distinguishing the phases in the W-Re-Ni-Co-Mo alloy.It is imperative to elucidate the association between atomic size differences and thermodynamic parameters.Developing a 2DM for associating atomic size differences and enthalpy mix is essential for distinguishing the phase formations in the [W-Re-Ni-Co-Mo] alloy across different atomic percentages of each element.
In this current research endeavour, the anticipation of phase types within the range of non-equiatomic [W-Re-Ni-Co-Mo] HEA compositions, considering varying atomic percentages for each element, involved the creation of 2DM for the specified parameters.

Enthalpy mix (ΔH mix ) vs atomic size difference (δ)
By employing a 2DM of parameters, the prediction of phase types becomes possible for any unidentified composition within the W-Re-Ni-Co-Mo HEA systems.This capability holds significant promise for alloy design, facilitating the attainment of specific properties tailored to meet the requirements of industrial applications.The ability to assess phase structures in non-equiatomic systems of W-Re-Ni-Co-Mo HEA represents a valuable asset in optimizing alloy design for the realization of desired industrial properties.

2DM between enthalpy mix (ΔH mix ) vs atomic size difference (δ)
The correlation between (ΔH mix ) vs (δ) depicted in Figure 6, through a 2DM, furnishes extensive data for the classification and identification of stability regions within HEA systems.These regions are delineated as SPSS, SPSS + IM, or IM, offering a comprehensive understanding of the alloy's stability characteristics.The criterion for SPSS formation is (δ) < 6.5, and the ΔH mix value should be between −20 ≤ ΔH mix ≤ 5 kJ•mol −1 .The requirement for SPSS + IM formation is (δ) < 6.5, and the ΔH mix value should be such that ΔH mix is less than −20.The criterion for IM formation: The atomic size disparity (δ) should exceed 6.5, and the enthalpy mixing condition must be such that ΔH mix is less than −20.
Therefore, the genesis of the SPSS or IM phase is contingent upon the disparity in atomic sizes (δ) and the prevailing conditions of enthalpy mixing.A perpetual rivalry exists between the atomic size differential and the enthalpy mixing, determining the ultimate establishment of either SPSS or IM.Consequently, the interplay between atomic size variance and enthalpy mixing governs the manifestation of IM or SPSS.
When the atomic size difference attains a considerable magnitude, it gives rise to a disproportionate strain energy.Simultaneously, an additional pronounced negative ΔH mix facilitates the IM compound formation.
Table 3 illustrates that the atomic size difference values meet the criterion (δ < 6.5) (refer to Table 1) across all atomic percentages within the HEA.This phenomenon is ascribed to the closely aligned atomic radii of W-Re-Ni-Co-Mo elements in HEA, resulting in a diminished atomic size difference.The reduced atomic-size difference consequently results in less strain energy within the crystal lattice, facilitating the interchangeability of elements and an equal likelihood of occupying lattice sites to form a (SPSS).It is crucial, however, to recognize that adherence to atomic size difference requirements alone does not suffice for determining the formation of (SPSS).Consideration must also be given to enthalpy mix effects, in conjunction with the impacts of atomic size difference, in the process of (SPSS) formation.
For varying atomic percentages ranging from 5 to 40% of nickel and rhenium in the (W-Re-Ni-Co-Mo) HEA, the highest enthalpy mix values are observed at elevated atomic percentages.These values conform to the ΔH mix criterion (−20 ≤ ΔH mix ≤ 5 kJ•mol −1 ) essential for the generation of the SPSS.Conversely, at lower atomic percentages of rhenium and nickel, the enthalpy mix values fail to meet the specified condition, primarily due to their notably more negative values, as illustrated in Table 1.The heightened negativity of the enthalpy mix imparts a more robust binding force among the elements, facilitating the formation of IM compounds in conjunction with the SPSS.
Across the diverse atomic percentages of nickel in the (W-Re-Ni-Co-Mo) alloy, the computed values for both enthalpy mix and atomic size difference consistently meet the specified conditions outlined in Table 1, facilitating the formation of SPSS.Phase equilibrium of refractory high-entropy alloys  9 For varying concentrations of molybdenum and tungsten in the (W-Re-Ni-Co-Mo) HEA, the maximum enthalpy mix value is observed at lower atomic percentages.This alignment fulfils the ΔH mix criteria (−20 ≤ ΔH mix ≤ 5 kJ•mol −1 ) necessary for the SPSS formation.Conversely, at large atomic percentages of molybdenum and tungsten in the (W-Re-Ni-Co-Mo) HEA, the enthalpy mix values do not meet the specified condition due to their more negative values, as depicted in Table 1.

Conclusions
SPSS formation is contingent upon satisfying both the atomic size difference and ΔH mix criteria (Table 1).
• In (W-Re-Ni-Co-Mo) HEAs, an elevated atomic percentage of nickel and rhenium leads to the fulfilment of conditions stipulated for the formation of SPSS, as observed in both enthalpy mix values and atomic size difference values.• For reduced atomic percentages of nickel and rhenium in (W-Re-Ni-Co-Mo) alloy, the atomic size difference adheres to the specified condition (δ < 6.5).Nevertheless, the ΔH mix results fail to encounter the criteria (−20 ≤ ΔH mix ≤ 5 kJ•mol −1 ), leading to the emergence of an IM + SPSS configuration.• For diminished atomic percentages of tungsten and molybdenum within the (W-Re-Ni-Co-Mo) HEA, both the enthalpy mix values and the atomic size difference values conform to the prescribed conditions, facilitating the formation of SPSS.
• With an increased atomic percentage of tungsten and molybdenum in the (W-Re-Ni-Co-Mo) HEA, the values of atomic size difference adhere to the specified condition (δ < 6.5).
the rhenium atomic percentage ranges from 5 to 40 at%, there is an observable increase in the enthalpy mix values.At the elevated atomic percentage of rhenium, enthalpy mixing values satisfy the criteria (−20 ≤ ΔH mix ≤ 5 kJ•mol −1 ) for the formation of an SPSS, whereas at lower rhenium atomic percentages, the enthalpy mixing values do not satisfy the criteria (−20 ≤ ΔH mix ≤ 5 kJ•mol −1 ) for the attainment of an SPSS.

Figure 1 :Table 5 :Figure 2 :
Figure 1: Impact of the rhenium atomic percentage on enthalpy mix.

Table 6 :
Cobalt atomic percentage fluctuations in HEA systems /mol) Atomic percentage of Co (at %) Atomic percentage vs Eanthalpy mix

Figure 3 :
Figure 3: Influence of cobalt atomic percentage on ΔH mix .

Table 7 :
Atomic percentage changes of molybdenum in HEA systems /mol) Atomic percentage of Mo (at %) Atomic percentage vs Enthalpy mix

Figure 4 :
Figure 4: Impact of atomic percentage of molybdenum on enthalpy mix.

Table 8 :%
Tungsten atomic percentage fluctuations in HEA systems Atomic percentage of W (at %) Atomic percentage vs Enthalpy mix

Figure 5 :
Figure 5: Impact of tungsten atomic percentage on enthalpy mix.

Table 1 :
Conditions for the formation of the SPSS and IM in HEAs

Table 3 :
Enthalpy mix and atomic size difference calculations

Table 4 :
Rhenium atomic percentage fluctuations in HEA systems

Table 5
displays the symbol values corresponding to Figure 2, indicating the fluctuation in nickel atomic percentages ranging from 5 to 40 at%.