# Chemically-driven control of electrical resistivity of high-entropy alloys

Salah-Eddine Benrazzouq, Jaafar Ghanbaja, Sylvie Migot, Valentin A Milichko, Jean-François Pierson

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Salah-Eddine Benrazzouq, Jaafar Ghanbaja, Sylvie Migot, Valentin A Milichko, Jean-François Pierson. Chemically-driven control of electrical resistivity of high-entropy alloys. Applied Materials Today, 2025, 44, pp.102726. 10.1016/j.apmt.2025.102726. hal-05042044

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# Chemically-driven control of electrical resistivity of high-entropy alloys

Salah-Eddine Benrazzouq,Jaafar Ghanbaja, Sylvie Migot, Valentin A. Milichko*,
Jean-François Pierson

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Université de Lorraine, CNRS, IJL, F-54000 Nancy, France

## ARTICLE INFO

**Keywords:**

High entropy alloys, Thin films
Chemical tuning, Electrical resistivity, Tunable
resistance

## ABSTRACT

Chemical control of electrical properties in high-entropy alloys (HEAs) remains largely unexplored despite their potential for next-generation electronic devices. Herein, we demonstrate unprecedented tuning of electrical characteristics in CrMnFeCoNi thin films by systematically incorporating elements with distinct metallic radii (Cu, Al, Ag, and Zr). Comprehensive structural analysis reveals composition-dependent phase evolution: Cu maintains a face-centered cubic (fcc) structure with reduced nanotwins, Al induces fcc-to-bcc transition, Zr drives amorphization, and Ag forms distinctive nanoprecipitates. Through these targeted chemical modifications, we achieve a remarkable resistivity range of 89–324 µΩ-cm and exceptional TCR control, including a near-zero value of -2.86 ppm/K in CrMnFeCoNiCu37 that outperforms conventional low-TCR alloys like Constantan and Manganin. This chemically-driven approach enables remarkable TCR tunability from +355 to -480 ppm/K, establishing HEAs as promising candidates for sustainable thermocouple devices and integrated circuits, offering superior performance and scalability compared to traditional materials.

## 1. Introduction

In the era of advanced electronics and automation, materials with precisely tunable and temperature-independent or temperature dependent electrical properties are crucial for a wide range of applications, from high-precision sensors and resistors to next-generation electronic devices and Global Positioning Systems [1,2]. The growing demands of massive automation, digitalization, and communication technologies have intensified the need for materials that maintain stable electrical characteristics across broad temperature ranges [3,4]. At the core of this requirement lies the temperature coefficient of resistance (TCR), a critical parameter quantifying how a material's electrical resistance changes with temperature.

Traditional metallic alloys like Constantan (Cu-Ni) and Manganin (Cu-Mn-Ni) have long been the standard for low TCR applications. However, their performance is typically limited to temperatures below 473–573 K, falling short of the extreme environments encountered in cutting-edge technologies[2]. This limitation underscores the pressing need for innovative materials offering superior electrical stability over wider temperature spans, while simultaneously possessing excellent mechanical properties such as strength, ductility, and oxidation resistance [5–7].

High-entropy alloys (HEAs), a novel class of materials composed of

five or more principal elements in near-equiatomic concentrations, have emerged as promising candidates to address these challenges [8,9]. The CrMnFeCoNi alloy, known as Cantor alloy, has garnered significant attention for its exceptional combination of strength and ductility [10]. However, the potential of this alloy system for electrical applications, especially in terms of tuning its electrical properties through elemental additions, remains largely unexplored [4]. Recent investigations across diverse HEA systems reveal remarkable control over TCR, surpassing conventional alloys. In the AlₓCoCrFeNi system, Wang et al. achieved an ultralow TCR of –5 ppm K⁻¹ in thin films [11], while Chen et al. demonstrated temperature-dependent behavior in bulk Al₂₀₈CoCrFeNi, with TCR varying from 128 ppm K⁻¹ (50–150 K) to a notably low 42 ppm K⁻¹ (300–360 K) [12]. Dong et al. groundbreaking work on refractory HEAs with body-centered cubic structures unveiled unprecedented stability, with TiZrNbHf exhibiting TCR values in order of 10 ppm K⁻¹ at 300 K [13]. This stability extends across a wide compositional range, including TiVTa, TiVNbTa, and TiZrNbHfTa systems to achieve a value of 800 ppm K⁻¹. Poliakov et al. further expanded the compositional space with CoCrFeNiTiₓ thin films, achieving TCR values between –78 and –6.6 ppm K⁻¹ over a broad temperature range (–60 to 130 °C) [14]. Contrastingly, Pal et al. exploration of AlCoCrFeMo-based coatings revealed higher but diverse TCR values (–382 to –3189 ppm K⁻¹), underscoring the complex interplay between composition and electrical

<footnote>* Corresponding authors.
E-mail addresses: valentin.milichko@univ-lorraine.fr (V.A. Milichko), jean-francois.pierson@univ-lorraine.fr (J.-F. Pierson).</footnote>
properties [15]. Zhu et al. developed a Fe₅₅Cr₂₈Al₁₂Ti₃Si₂ alloy using magnetic levitation melting, which demonstrated a resistivity of 183 ± 2 µΩ-cm and a TCR of -35 ± 10 ppm K⁻¹ from 298 to 673 K in the as-cast condition containing cubic L21 nanoprecipitates [16]. These findings collectively highlight the exceptional tunability of HEAs, achieved through refined compositional adjustments and varied processing techniques. While previous studies have extensively explored the AlₓCoCrFeNi system and some refractory HEAs for their electrical properties, achieving TCR values as low as -5 ppm K⁻¹, However, systematic studies on elemental additions to the CrMnFeCoNi Cantor alloy for tuning the electrical properties are lacking.

The design of alloys with precisely tunable electrical properties presents formidable challenges, rooted in the fundamental physics of electron transport in metals. As temperature increases, electron-phonon scattering intensifies quasi-exponentially, drastically elevating resistivity [17]. To mitigate this inherent temperature dependence, researchers have pursued innovative strategies centered on engineered lattice defects to induce inelastic conduction electron scattering. These defects manifest in various forms, each offering unique advantages and limitations. Grain-boundary scattering in nanocrystals and surface effects in amorphous materials enhance resistivity while compromising thermal stability and ductility [18].

Dislocations contribute to electron scattering, yet precise control of their density and arrangement across wide temperature ranges remains elusive [19]. In conventional alloys, point defects solute atoms dispersed in a solvent matrix serve as efficient atomic-scale scattering sites. However, this paradigm breaks down in HEAs due to their multi-principal element composition, necessitating a reconceptualization of defect engineering [20]. Traditional approaches involving second-phase precipitate refinement prove inadequate; while nanoprecipitates effectively strengthen the material, they often suffer from thermal instability due to coarsening, leading to undesirable fluctuations in resistivity [21]. Twin defects, characterized by mirror-image crystal structures across a plane, introduce another dimension of complexity. In HEAs, the formation and stability of these twins are intricately linked to the multi-element nature of the alloy, potentially offering unprecedented opportunities for fine-tuning electrical properties [20,22]. This complex interplay of defect types in HEAs opens new avenues for materials design, challenging conventional wisdom and prompting innovative approaches to achieving either constant or tunable resistivity across broad temperature ranges.

Our approach uniquely focuses on systematically investigation of the addition of elements (Cu, Al, Ag, and Zr) with large metallic radii (from 127 to 157 pm) to induce controlled lattice distortions and defect structures in the CrMnFeCoNi thin films. This novel strategy for tuning electrical properties in the Cantor alloy, allows us to explore a wider range of microstructures and their impact on electrical stability, potentially uncovering new mechanisms for achieving ultra-low TCR values (targeting < ±5 ppm K⁻¹) and tunable across an expanded temperature range of 80 to 350 K. Employing a comprehensive analytical approach, we combine X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), and electrical resistivity measurements to probe the structural, microstructural, and electrical properties of these alloys. This multi-faceted investigation provides crucial insights into the fundamental electron transport mechanisms in these complex alloys, elucidating the relationship between atomic-scale structures and macroscopic electrical behavior. By focusing on thin films, we leverage the advantages of controlled deposition techniques, enabling precise manipulation of composition and microstructure. This approach facilitates a systematic study of the correlation between atomic-scale defects and electrical properties in these complex alloys. The thin film format allows for uniform composition and microstructure throughout the sample, minimizing the bulk effects that could complicate analysis in larger specimens.

Our investigation reveals a diverse array of phases, including face-centered cubic (fcc), body-centered cubic (bcc), duplex fcc + bcc

structures, amorphous phases, and segregated phases with precipitates, depending on the type and concentration of the added element. We establish clear correlations between alloy composition, microstructural features, and electrical performance, particularly focusing on room temperature resistivity and TCR. The insights gained from this research could pave the way for a new generation of materials suitable for high-precision electrical applications across an expansive temperature range. Moreover, the principles uncovered in this work may extend beyond electrical properties, offering new strategies for designing multifunctional materials that simultaneously optimize electrical, thermal, and mechanical characteristics. These advancements have the potential to revolutionize fields such as aerospace electronics, energy conversion technologies, and advanced sensors for extreme environments.

## 2. Experimental section

**Thin Film Fabrication:** High-entropy alloy (HEA) thin films of composition CrMnFeCoNiₓ (x = Cu, Zr, Al, or Ag) were deposited via DC magnetron co-sputtering on (100)-oriented Si wafers. Before deposition, substrates underwent a rigorous cleaning protocol: acetone cleaning followed by 5-min Ar⁺ radiofrequency plasma etching. To ensure high purity of deposited films, both the CrMnFeCoNi target (Ampere Industry) and the (Cu, Zr, Al, or Ag) target (purity ≥ 99.99 %) were pre-sputtered with Ar⁺ ions for a minimum of 5 min to remove surface contaminants. The deposition parameters were optimized to ensure film homogeneity and precise composition control. Argon gas flow rate was maintained at 30 sccm, with substrate rotation set at 15 rpm. The sputtering system employed a confocal cathode configuration with a target-to-substrate distance of 9 cm. Working pressure was held constant at 0.3 Pa throughout the 50-min (Cantor alloy) and 40-min (other alloys) deposition process, conducted at ambient temperature in a high-vacuum chamber (base pressure: 10–7 mbar). The compositional tuning was achieved by modulating the DC current applied to each target. The CrMnFeCoNi target current was fixed at 0.4 A, while the x target current was systematically varied to achieve the desired stoichiometry of the sixth element (Cu, Zr, Al, or Cu). The actual film compositions were verified using Energy-Dispersive X-ray Spectroscopy (EDX) analysis, the corresponding EDX-verified elemental compositions are presented in Table S1. Film thicknesses were systematically measured using profilometry on each sample. The pure Cantor alloy films exhibited a thickness of approximately 1200 nm, while the doped films had thicknesses ranging from 805 to 1300 nm, with deposition rates varying between 20–32.5 nm/min depending on the dopant element and applied current. This thickness variation is primarily due to the different sputtering yields of the dopant elements. Through control measurements on samples with different thicknesses within this range, we confirmed that these variations had negligible impact on the comparative electrical properties. The complete dataset of deposition parameters (target currents, deposition time), resulting thicknesses, and deposition rates for all compositions is provided in Table S1.

**Structural Characterization:** X-ray diffraction (XRD) analysis was performed using an AXS Bruker D8 Advance diffractometer in Bragg-Brentano geometry with Cu Kα radiation (λ = 1.5406 Å). High-resolution transmission electron microscopy (HRTEM) was conducted on a JEOL ARM 200F Cold FEG TEM/STEM, operating at 200 kV. The microscope equipped with a spherical aberration (Cs) probe and image correctors, achieved point resolutions of 0.12 nm and 0.078 nm in TEM and STEM modes, respectively. Cross-sectional TEM specimens were prepared using a FEI Helios NanoLab 600i focused ion beam (FIB)-scanning electron microscope dual beam system, ensuring minimal sample damage. Surface morphology and film thickness were analyzed using a ZEISS GeminiSEM 500 scanning electron microscope, operated at 5 kV accelerating voltage.

**Electrical Characterization:** Temperature-dependent electrical properties were measured using an Ecopia HMS5000 Hall effect system. Measurements were conducted over a temperature range of 80 to 350 K,
encompassing both cryogenic (liquid nitrogen) and elevated temperatures.

## 3. Results and discussion

### 3.1. The structure

We first investigated how the addition of metals with larger metallic radii ($r_{Cu} = 0.127$ nm, $r_{Al} = 0.142$ nm, $r_{Ag} = 0.144$ nm, and $r_{Zr} = 0.157$ nm) influenced the structure and microstructure of CrMnFeCoNi Cantor alloy ($r_{avr} = 0.125$ nm). It is worth noting that the enthalpy of mixing between these elements and the Cantor alloy components varies significantly, from highly positive values (Ag-Cr: +29 kJ/mol) to strongly negative values (Zr-Ni: -49 kJ/mol), as shown in Table S2. This variation in mixing enthalpy contributes to the diversity of phases and microstructures observed in the films. The X-ray diffractograms of the Cantor alloys with the additions of Cu, Al, Zr, and Ag are shown in Fig. 1. Our investigation reveals a diverse array of phases: a face-centered cubic (fcc) phase for Cu addition (Fig. 1a), a body-centered cubic (bcc) phase, a duplex phase combination of fcc and bcc and finally a bcc phase for Al addition (Fig. 1b), a dimixing of fcc phases for Ag addition (Fig. 1c) [23] as well as an amorphous phase for Zr addition (Fig. 1d). This phase diversity aligns with existing literature that posits the equiatomic CrMnFeCoNiAl HEAs to exhibit both fcc and bcc phases [24–26].

The original Cantor alloy, before elemental addition and as initially deposited, exhibits a fcc structure, which is substantiated by both XRD (the appearing of an intense peak at 43.6° corresponding to the diffraction of (111) crystal planes) and selected area electron diffraction (SAED). Furthermore, delving into the microstructural details, Fig. 2 presents TEM investigations of pure Cantor films and with 10 at. % Cu addition and also with 5 at. % addition of Al. For pure Cantor films, the TEM cross section evidences a columnar microstructure (Fig. 2a1). The SAED pattern, inset in the same figure, shows annular diffraction pattern in agreement with the fcc structure evidenced by XRD. A higher magnification TEM image taken from a specified region in Fig. 2a1, showcasing columnar grains with an average width of app. 45 nm

(Fig. 2a2). Further inspection through this high-resolution TEM micrograph reveals the occurrence of nanotwins as usually encountered in sputtered Cantor thin films [27]. Fig. 2a3 evidences the nanometer scale of the nanotwins, which span only several atomic layers. The twin spacing varies from 1 to 2 nm. These nano twins are predominantly oriented along [111] direction perpendicularally to the film surface. This structural feature is attributable to the atomic peening effect [20], whereby the different high-energy atoms ejected from the sputtering target bombard the growing film, instigating defect formation and promoting nanotwin development due to the inherently low stacking fault energy of CoCrFeMnNi alloys, estimated at 20–30 mJ m⁻² as reported by Zhiming Li et al. [28].

With the introduction of Cu, the X-ray diffractograms (Fig. 1a) and SAED (Fig. 2b1) confirm the preservation of the fcc structure within the Cantor alloy. The observed diffraction peaks shift towards lower 2θ values corroborates the successful integration of copper into the fcc structure. This behavior is attributable to the larger metallic radius of copper compared to the average of the Cantor alloy constituents. The microstructure of Cu incorporation into the Cantor alloy induces homogeneous distribution of pyramidal grains on the top surface of the films and less crystal defects nanotwins as found in TEM cross-section micrographs (Fig. 2b1 and 2b2) compared with the pure Cantor alloy. This decrease in twin density is due to the highest stacking fault energy of the copper approximately (45–58 mJ m⁻²) [29] than the Cantor alloy.

The effect of Al addition can be described in two steps. In the first one, when a few atomic percent of Al (below 10 at. %) is added to the Cantor alloy, the fcc structure is maintained, as indicated by a sharp, strong peak at 43.8° corresponding to the (111) crystal plan diffraction. The TEM analysis reveals that the 5 at. % sample exhibit well columnar fcc phase with a column width of app. 25 nm and a homogeneous distribution of abundant fine nanotwins and stacking faults throughout the sample cross-section (Fig. 2c1 and 2c2). However, it is noteworthy that the intrinsic stacking fault energy ($\gamma_{isf}$) of the alloy increases with Al addition, which generally makes the formation of stacking faults and twins more difficult. Despite this, the overall reduction in unstable stacking fault energy ($\gamma_{utf}$) and unstable twinning fault energy ($\gamma_{utf}$) with

<figure><img src="image_5.png" /><figcaption>**Fig. 1.** X-ray diffraction patterns of CrMnFeCoNi (Cantor alloy, light purple curve) thin films with additional (a) Cu, (b) Al, (c) Ag, and (d) Zr. Inset in (b) shows a magnified view of the 10 at. % Al sample, highlighting the duplex phase structure.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>**Fig. 2.** Transmission electron microscopy (TEM) investigation of different alloy compositions. (a1-a3) CrMnFeCoNi (Cantor alloy), (b1-b3) (CrMnFeCoNi)₉₀Cu₁₀, (c1-c3) (CrMnFeCoNi)₉₅Al₅. For each composition: (1) Bright-field TEM (BF TEM) micrographs and corresponding selected area (inset) electron diffraction (SAED) patterns, (2) High-Resolution TEM (HRTEM) micrographs and corresponding (inset) Fast Fourier Transform (FFT) patterns, and (3) High angle annular dark field scanning transmission electron microscopy (HAADF STEM) micrographs.</figcaption></figure>

Al addition suggests that initiating stacking faults and twins require less energy. Using first-principles methods to calculate the generalized stacking fault energy (GSFE) of fcc CrMnFeCoNi doped with Al, Sun et al. show that while some GSFE parameters decrease with increasing Al content, the intrinsic stacking fault energy actually increases [30]. In the second step, upon augmentation of the Al concentration beyond 10 at. %, a phase transition is observed where the bcc phase becomes pre-dominant within the CrMnFeCoNiAl alloys, along with diminishing the presence of the fcc phase. This is evidenced by the XRD peak intensities (Fig. 1b) which suggest a higher volumetric fraction of the bcc phase. The tendency of Al to foster the formation of a disordered bcc structure while suppressing fcc phase formation is thus demonstrated. However, contrary to the XRD findings, cross-sectional TEM investigation reveals a higher occurrence of the fcc phase, characterized by large grains with app. 400 nm in diameter, as illustrated in Fig. 3a. The cross-section TEM investigation for the film containing 10 at. % Al reveals a high occurrence of the fcc phase, characterized by larger grains with increased density of defects especially nano twins compared to the bcc phase, the twin spacing this time is higher by three-order of magnitude as the twin spacing in Cantor. Moreover, the bcc regions do not contain twin defects. TEM investigation has also been carry out for the sample containing 20 at. % Al (Fig. 3d). In agreement with XRD, only the bcc phase has been evidenced by electron diffraction when the Al content is fixed to 20 at. %. The column width is approx. 40 nm (Fig. 3d2). The diffraction patterns, inset in the same figure, evidences a growth of the bcc grains along the [110] direction. The HAADF-STEM micrograph in

Fig. 3d3 reveals the details of these columnar grains, with the grain boundaries exhibiting no defects.

To further investigate phase formation caused by the Al addition, the surface microstructures of the as-deposited alloys with different Al contents are presented in Figure S1. As previously demonstrated using XRD and TEM, the addition of 5 at. % of Al allow to keep a single fcc phase. The increase of the Al content comes with a change of the surface morphology. At 10 at. %, new shape elongated microstructural morphologies are evidenced. When the Al concentration is fixed to 15 at. %, only the bcc phase is evidenced by X-ray diffraction (Fig. 1b) and the surface morphology can only be described with these elongated grains (Figure S1). The same is true for higher Al content. With Al addition, the morphology of the initial fcc phase further evolves from a round shape to an elongated pyramidal shape (bcc).

The addition of Zr presents a notable departure from the crystalline phases observed with other elements. As shown in Fig. 1d, the high metallic radius of Zr atoms leads to a strong lattice distortion and structural instability. Even for low Zr content (5 at. %) the films are X-ray amorphous. The TEM investigation of the film with 10 at. % evidences a glassy-like microstructure (Fig. 3e). However, some nano-crystals with a very low grain size can be observed during high resolution STEM investigation.

In the case of Ag addition, the X-ray diffractograms disclose a distinct non-mixing behavior with the Cantor alloy. This is evidenced by the emergence of pronounced peaks corresponding to the (111) planes of both silver and the Cantor alloy (Fig. 1c), suggesting the formation of a
<figure><img src="image_7.png" /><figcaption>**Fig. 3.** Transmission electron microscopy (TEM) investigation of different alloy compositions: (a) Bright-field TEM (BF-TEM) micrograph and corresponding selected area electron diffraction (SAED) pattern (inset), (b) BF-TEM micrograph showing a large grain with twins and corresponding SAED pattern (inset), (c) Dark-field TEM micrograph of the twinned grain in (CrMnFeCoNi)₉₀Al₁₀. (d1-d3) (CrMnFeCoNi)₈₀Al₂₀, (e1-e3) (CrMnFeCoNi)₉₀Zr₁₀, and (f1-f3) (CrMnFeCoNi)₉₀Ag₁₀. For each composition: (1) Bright-field TEM (BF TEM) micrographs and corresponding selected area (inset) electron diffraction (SAED) patterns, (2) High-Resolution TEM (HRTEM) micrographs and corresponding (inset) Fast Fourier Transform (FFT) patterns, and (3) High angle annular dark field scanning transmission electron microscopy (HAADF STEM) micrographs.</figcaption></figure>

silver rich phase within the Cantor matrix rather than a homogeneous solid solution. Cross-section bright-field TEM micrograph and SAED patterns (Fig. 3f1) revealed a dense structure with Ag precipitates dispersed throughout the 900-nm-thick film. HRTEM micrographs (Fig. 3f2) showed a nanoprecipitate morphology with fine-scale linear precipitates. STEM-HAADF imaging (Fig. 3f3) highlighted the internal structure, revealing a characteristic modulated pattern with striations parallel to the basal plane, indicative of a nanoprecipitate material with

cuboidal particles or tweed-like contrast patterns. TEM characterization of Cantor films with Ag addition including a thermodynamical approach is detailed in ref [23]. The addition of silver into Cantor thin films shows a spinodal decomposition behavior.

## 3.2. Room temperature electrical resistivity

The room temperature resistivity of pure Cantor thin film and its
variations with the addition of the four elements were measured using the Hall effect technique, as shown in Fig. 4. The pure Cantor alloy exhibited a low resistivity value of 89 µΩ·cm. As the concentration of additional elements increased, the resistivity also increased, reaching maximum values of approximately 324 µΩ·cm for (CrMnFeCoNi)75Al25, 165 µΩ·cm for (CrMnFeCoNi)75Zr25, 132 µΩ·cm for (CrMnFeCoNi)85Cu15, and 174 µΩ·cm for (CrMnFeCoNi)95Ag5. Interestingly, silver films displayed a decrease in electrical resistivity with increasing silver content. This behavior is mainly due to the distinct non-mixing of silver with the Cantor phase, resulting in nano-precipitates of silver that enhance its electrical properties. In high-entropy alloy thin films, the resistivity is influenced by a combination of factors including grain boundary scattering, lattice distortion, sd scattering effect, and local spin interactions, all of which are affected by the nature and concentration of the added elements as illustrated in Fig. 5.

In more details, the increase in resistivity is primarily attributed to the increased disorder within the system due to the incorporation of elements with larger atomic radii. For instance, comparing the resistivity values at 5 at. % for all elements, Zr and Ag, who have the largest atomic radius, resulted in the highest resistivity. The electrical resistivity of a material is directly related to the degree of disorder within the structure. Severe lattice distortion, caused by the random distribution of atoms, leads to deviations of atoms from their lattice sites. This deviation is considered the main reason for the high resistivity, as it results in strong scattering of electrons by the displaced atoms. Additionally, grain boundary scattering significantly contributes to the resistivity. The introduction of elements like Al and Ag increases the number of grain boundaries and defects due to the formation of different phases and microstructures, such as the duplex phase combination of fcc and bcc and segregated phases with precipitates. For example, the addition of Al beyond 10 at. % leads to a phase transition to a predominantly bcc structure, significantly increasing grain boundary scattering. It is noteworthy that while lattice distortion contributes to increased resistivity, our results indicate that structural transitions have a more dominant effect. This is most evident when comparing Al films to Zr films. Despite Zr having a larger metallic radius (0.157 nm vs. 0.142 nm for Al), the Al25 sample exhibits substantially higher resistivity (324 µΩ·cm) than the Zr25 sample (165 µΩ·cm). This difference can be attributed to the fcc-to-bcc phase transition induced by Al addition, which introduces additional electron scattering mechanisms beyond simple lattice distortion. In contrast, Zr addition primarily induces

<figure><img src="image_8.png" /><figcaption>Fig. 4. Electrical resistivity of HEA thin films (Cantor, CrMnFeCoNiAl, CrMnFeCoNiCu, CrMnFeCoNiZr, CrMnFeCoNiAg) measured at room temperature.</figcaption></figure>

amorphization of the film, with only minor presence of nanocrystals as evidenced by HAADF STEM, leading to enhanced electron scattering through a different mechanism than grain boundary scattering.

The relationship between microstructural features and electrical properties across our different compositions reveals complex trends that cannot be explained by simple defect scattering models alone. Comparing samples with 10 at. % additions reveals striking differences in resistivity (Al10: 175.5 µΩ·cm, Zr10: 150.4 µΩ·cm, Ag10: 129.1 µΩ·cm, and Cu10: 123 µΩ·cm) despite each creating distinctly different microstructures. Particularly noteworthy is the Al-series, where Al5 shows densely packed columnar grains with abundant nanotwins, Al10 exhibits larger grains with fewer twins, and Al20 presents columnar structures with virtually no visible defects, yet resistivity increases monotonically with Al content. Similarly, Zr films show relatively modest resistivity increases from 152.5 µΩ·cm (Zr5) to 168.6 µΩ·cm (Zr25) despite transitioning to an amorphous structure, while Cu films show comparable trends (106.6 µΩ·cm for Cu5 to 130.3 µΩ·cm for Cu37) regardless of maintaining crystalline fcc structure. These observations indicate that phase-specific electronic structure effects likely dominate over simple defect density or grain boundary scattering in determining the electrical behavior of these complex alloys.

In addition to lattice distortion and grain boundary scattering, the sd scattering effect also plays a crucial role. In transition metals, conduction electrons involve both the filled s band and the unfilled d band. The addition of different elements influences the electronic structure of the alloy, enhancing the sd scattering effect. Under an external field, s electrons scatter and transition to the d band, reducing the mean free path of electrons and increasing resistivity. The varying degrees of resistivity observed with different element additions can be partially explained by differences in how each element affects sd scattering.

Local spin interactions further contribute to the increased resistivity. Magnetic elements within the alloy, such as Fe, Co and Ni, contribute to resistivity through local spin interactions. The introduction of additional elements, which do not significantly alter the magnetic properties, can still increase disorder, enhancing electron scattering by magnetic atoms. This multiple scattering process creates substantial barriers to electron motion, contributing to higher resistivity.

### 3.3. Temperature-dependent resistivity

The temperature-dependent resistivity curves of the CrMnFeCoNi films with Zr, Al, Cu, and Ag addition are presented in Fig. 6. The electrical resistivity (R) was analyzed over a temperature range from 80 to 350 K. The data was fitted using the following equation:

$$R = R_0 + R_1 * T + R_2 * T^2, \quad (1)$$

where R₀ is the resistivity at 80 K, R₁*T accounts for changes in the structure factor (generalized Faber-Ziman theory), and R₂*T² originates from Mott s-d scattering. The results summarized in Table 1 provide insights into the mechanisms affecting resistivity in these high-entropy alloys. The pure Cantor film demonstrates a relatively low resistivity value at room temperature (89 µΩ·cm) and exhibits metallic behavior with a linear increase of the resistivity as temperature increases, indicated by a positive temperature coefficient of resistivity (TCR) of 355 ppm K⁻¹. The significant R₂ value (84.7 × 10⁻⁵ µΩ·cm K²) suggests substantial Mott s-d scattering, where conduction electrons scatter into partially filled d-states of transition metals. This scattering mechanism dominates at higher temperatures, leading to an increase in resistivity.

The addition of Al to the Cantor film significantly affects its electrical resistivity. The film containing 5 at. % Al shows similar behavior as for pure Cantor. The resistivity increases with temperature with a small decrease in TCR value (258 ppm K⁻¹), suggesting that the alloy retains metallic behavior. A decrease in R₂ value (58 × 10⁻⁵ µΩ·cm K²) is observed due to non-transition metal addition (Al), albeit with increased scattering due to slight lattice distortion introduced by Al atoms. At 10
<figure><img src="image_9.png" /><figcaption>**Fig. 5.** Schematic representation of the four factors influencing high entropy alloy resistivity (grain boundary scattering, lattice distortion, s-d scattering effect, and local spin interactions).</figcaption></figure>

at. % Al, the alloy exhibits a duplex structure fcc+bcc, with nano twins in the fcc grains that are oriented differently (Fig. 3b). This structural transition introduces more significant lattice distortions and grain boundaries scattering, leading to a decrease in resistivity with temperature, and resulting in a negative TCR value (–113 ppm K⁻¹). At higher Al concentrations (15 to 25 at. %), the structural transition to a predominantly bcc phase, exhibiting additional grain boundaries that contribute to a continuous decrease in resistivity with temperature, indicative of non-metallic behavior. The increased resistivity at room temperature for these alloys (up to 324 µΩ-cm for Al25) can be attributed to severe lattice distortion and the introduction of more grain boundaries, leading to enhanced scattering of conduction electrons. To further investigate the electronic origins of these TCR changes, we analyzed the correlation between Valence Electron Concentration (VEC) and TCR across our compositions (Figure S2). The Al-series shows a clear inverse relationship between VEC and TCR, with decreasing VEC (from 8.0 for pure Cantor to 7.25 for Al25) correlating with increasing TCR. This trend is pronounced in other films, further supporting our conclusion that structural effects dominate over simple electronic considerations in determining resistivity behavior.

Cu addition affects the Cantor film's resistivity while maintaining the fcc structure. The alloys exhibit nano twins within the grains, which contribute to the scattering mechanisms. For Cu5 to Cu15, the resistivity increases or remains relatively stable with temperature, indicating that the primary scattering mechanisms are consistent, with phonon-electron interactions playing a dominant role. The R₁ values are low (e.g., 1.29×10⁻² µΩ cm for Cu5 and -0.05×10⁻² µΩ cm for Cu15), indicating minor changes in the structure factor. The R₂ values are also relatively small, suggesting minimal Mott s-d scattering influence. The TCR values, such as 179 ppm K⁻¹ for Cu5 and 72.6 ppm K⁻¹ for Cu15, reflect a

low temperature dependence. At higher Cu concentrations (20 to 37 at. %), the resistivity behavior becomes nearly constant with little variation, suggesting that copper metallic size and electronic properties lead to a balance between lattice distortion and improved electron mobility, reflected in low R₁ and R₂ values. The TCR values range from 54.3 ppm K⁻¹ for Cu20 to near-zero TCR (near-zero TCR < 25 ppm K⁻¹) –2.86 ppm K⁻¹ for Cu37, indicating minimal temperature dependence. Negligible values of R₁ and R₂ constants for Cu indicates good linearity in this temperature range.

Zr addition presents a third distinct mechanism through the formation of an amorphous-nanocrystalline structure. The consistent negative TCR values (–45 to –58 ppm K⁻¹) across compositions reflect dominant electron-disorder scattering. The negligible R₁ and R₂ values at higher Zr concentrations (15–25 at. %) indicate that traditional crystalline scattering mechanisms become irrelevant, replaced by strong localization effects as a characteristic of amorphous metals. This is supported by the broad XRD peaks and STEM observations of ~0.3 nm nanocrystallites.

The addition of Ag to the Cantor film results in a unique microstructure characterized by Ag precipitates within the HEA matrix. This non-mixing behavior leads to interesting electrical properties. All Ag-containing samples (Ag5 to Ag25) display negative TCR values, ranging from –74.1 ppm K⁻¹ for Ag5 to –42.9 ppm K⁻¹ for Ag25. The room temperature resistivity of Ag-containing alloys initially increases to 174.9 µΩ-cm for Ag5, then decreases with increasing Ag content, reaching 120.8 µΩ-cm for Ag25. This trend can be explained by the competing effects of increased electron scattering at Ag-matrix interfaces and the contribution of highly conductive Ag precipitates. Moreover, the R₁ and R₂ values for Ag-containing alloys are generally small and negative, similar to the Zr-containing alloys. However, the Ag5 sample shows a notably higher R₂ value (9.98×10⁻⁵ µΩ cm K⁻²),
<figure><img src="image_10.png" /><figcaption>Fig. 6. Temperature-dependent electrical resistivity of Cantor, a) CrMnFeCoNiAl, b) CrMnFeCoNiCu, c) CrMnFeCoNiAg, and d) CrMnFeCoNiZr.</figcaption></figure>

suggesting a more significant contribution from Mott s-d scattering at lower Ag concentrations.

To evaluate the practical reliability of our optimized compositions, we have conducted thermal cycling tests (25–200 °C, 5 complete cycles) on CrMnFeCoNiCu37 and CrMnFeCoNiAl5 films. As shown in Figure S3, both compositions demonstrate excellent stability with maximum resistivity deviations of only 2.30 % and 2.28 %, respectively, across all cycles. The drift between first and last cycle at maximum temperature (200 °C) was particularly low: 0.99 % for Cu37 and just 0.25 % for Al5. This remarkable thermal cycling stability further enhances the practical applicability of these HEA films for precision electronic components that must maintain consistent performance under variable thermal conditions.

### 3.4. Tunable resistivity

Building upon the comprehensive analysis of resistivity behavior of HEA with tunable composition, we visualized these data as a TCR function of the electrical resistivity compared with conventional metals and alloys. Fig. 7 shows that, unlike conventional metals (Al, Ni, Fe, Ag, Cu, Co, Zr, and Mn with TCR values from 350 to 5000 ppm K¹), CrMnFeCoNi system and other HEA are ranked in the positive and negative areas of TCR (from 350 to –550 ppm K¹), crossing near-zero values. The latter is important for making highly-endurant electronic components with temperature-independent resistivity. Unlike conventional alloys such as Constantan (Cu-Ni) and Manganin (Cu-Mn-Ni) with 20–15 ppm K¹ value of TCR respectively, our HEA films demonstrate near-zero TCR values (–2.86 ppm K¹ in Cu37) while maintaining higher

resistivity. Beyond the specific electrical performance metrics, our systematic approach using the Cantor alloy as a base platform with targeted elemental additions demonstrates a significant practical advantage over traditional TCR-tunable materials. In contrast to ceramic thin films (such as ZrB₂, TiB₂, or TaN) that often require high-temperature processing, specialized deposition techniques, and precise stoichiometry control, our HEA films are produced using standard room-temperature magnetron sputtering, widely available and industrially scalable technique. Similarly, while doped semiconductors and oxide materials (like ITO) can achieve various TCR values (Table S3), they involve complex processing steps, higher production costs, and frequently suffer from mechanical brittleness or thermal instability. Our approach stands out for its remarkable simplicity: a single base alloy target combined with elemental targets enables tuning across a broad spectrum of electrical properties (from +355 to –480 ppm/K) through straightforward composition adjustments. This method significantly reduces manufacturing complexity while maintaining process compatibility with standard microelectronics fabrication. Additionally, the excellent mechanical properties inherent to HEAs including superior adhesion, wear resistance, and thermal shock tolerance further enhance their practical viability compared to ceramic or semiconductor alternatives. This combination of processing simplicity, cost-effectiveness, and superior mechanical performance.

The continuous tunability demonstrated here, unachievable in conventional systems, underscores the transformative potential of HEAs in electronic materials design. By leveraging the complex interplay of elemental additions, microstructural evolution, and electron scattering mechanisms, we have unveiled a new dimension in the tailoring of
<caption>**Table 1**</caption>

Temperature dependence of electrical resistivity of different alloys, fit by $ρ = R_0 + R_1*T + R_2*T^2$, and their temperature coefficient of resistance (TCR) calculated from the range (80–350 K).

<table><thead><tr><th>Film</th><th>R<sub>0</sub><br>(μΩ cm)</th><th>R<sub>1</sub><br>(10<sup>-2</sup> μΩ cm K<sup>-1</sup>)</th><th>R<sub>2</sub><br>(10<sup>-5</sup> μΩ cm K<sup>-2</sup>)</th><th>TCR<br>(80–350 K) (ppm K<sup>-1</sup>)</th></tr></thead><tbody><tr><td>CrMnFeCoNi</td><td>80.0 ± 0.1</td><td>2.85</td><td>84.7</td><td>355</td></tr><tr><td>Al5</td><td>104.4 ± 0.16</td><td>27.2</td><td>58.5</td><td>259</td></tr><tr><td>Al10</td><td>175.5 ± 0.5</td><td>-4.41</td><td>5.30</td><td>-114</td></tr><tr><td>Al15</td><td>206.9 ± 0.4</td><td>-6.58</td><td>5.01</td><td>-220</td></tr><tr><td>Al20</td><td>288.7 ± 0.8</td><td>-8.31</td><td>-6.41</td><td>-397</td></tr><tr><td>Al25</td><td>368.4 ± 1.7</td><td>-6.95</td><td>-0.24</td><td>-480</td></tr><tr><td>Cu5</td><td>106.6 ± 0.1</td><td>1.29</td><td>1.40</td><td>179</td></tr><tr><td>Cu10</td><td>123 ± 0.1</td><td>0.38</td><td>2.21</td><td>106</td></tr><tr><td>Cu15</td><td>130.5 ± 0.1</td><td>-0.05</td><td>2.47</td><td>72.6</td></tr><tr><td>Cu20</td><td>127.6 ± 0.1</td><td>-0.52</td><td>2.75</td><td>54.3</td></tr><tr><td>Cu25</td><td>127.2 ± 0.1</td><td>-0.8</td><td>2.74</td><td>26.2</td></tr><tr><td>Cu37</td><td>130.3 ± 0.1</td><td>-0.9</td><td>1.87</td><td>-2.8</td></tr><tr><td>Ag5</td><td>183.6 ± 0.3</td><td>-5.66</td><td>9.98</td><td>-74.1</td></tr><tr><td>Ag10</td><td>129.1 ± 0.9</td><td>-2.88</td><td>4.06</td><td>-67</td></tr><tr><td>Ag15</td><td>142.3 ± 0.2</td><td>-2.75</td><td>3.89</td><td>-78</td></tr><tr><td>Ag20</td><td>145.8 ± 0.2</td><td>-2.58</td><td>3.98</td><td>-54</td></tr><tr><td>Ag25</td><td>123.6 ± 0.2</td><td>-1.78</td><td>2.74</td><td>-42.9</td></tr><tr><td>Zr5</td><td>152.5 ± 0.2</td><td>-2.69</td><td>4.32</td><td>-52.4</td></tr><tr><td>Zr10</td><td>150.4 ± 0.3</td><td>-2.16</td><td>3.07</td><td>-53.1</td></tr><tr><td>Zr15</td><td>142.1 ± 0.9</td><td>-0.03</td><td>-0.61</td><td>-44.8</td></tr><tr><td>Zr20</td><td>162.3 ± 0.1</td><td>-1.14</td><td>0.51</td><td>-53.2</td></tr><tr><td>Zr25</td><td>168.6 ± 0.2</td><td>-1.44</td><td>0.82</td><td>-58.1</td></tr></tbody></table>

electrical properties. Thus, the work not only expands the fundamental understanding of electron transport in multi-principal element alloys but also lays the foundation for next-generation materials in advanced electronics, particularly for applications demanding precise property control across extreme temperature ranges.

## 4. Conclusion

We demonstrated unprecedented control over electrical properties in high-entropy alloys through systematic elemental additions to the CrMnFeCoNi system. By incorporating Cu, Al, Ag, and Zr, we achieved a remarkable range of temperature coefficient of resistance (TCR) from +355 to -480 ppm K⁻¹, alongside resistivities spanning 89–324 μΩ·cm. Most notably, Cu addition enabled fine-tuning to near-zero TCR (-2.86 ppm K⁻¹) while maintaining higher resistivity than conventional alloys. Through comprehensive structural characterization and electrical measurements, we revealed four distinct mechanisms governing electron transport: lattice distortion, grain boundary scattering, s-d band interactions, and local spin effects. Each additional element induced unique microstructural features, from Cu-induced nanotwin reduction

<figure><img src="image_11.png" /><figcaption>**Fig. 7.** Temperature coefficient of resistance (TCR) versus electrical resistivity for various thin films: CrMnFeCoNi (Cantor alloy), CrMnFeCoNiAl, CrMnFe-CoNiCu, CrMnFeCoNiAg, and CrMnFeCoNiZr. Pure metals [31–33] and conventional alloys (Constantan and Manganin) [34] are included for comparison.</figcaption></figure>

to Zr-driven amorphization, providing new pathways for property control. These findings establish high-entropy alloys as a transformative platform for designing next-generation electronic materials, offering precise property control beyond the capabilities of traditional alloys. The tunable resistivity results enable diverse applications: high copper addition (37 at. %), films with near-zero TCR and stable resistivity are ideal for precision resistors in measuring instruments; Al-containing films with high negative TCR and enhanced resistivity (324 μΩ·cm) are suitable for temperature sensors; while Zr-containing films with consistent negative TCR (-45 to -58 ppm K⁻¹) are valuable for thermal protection circuits. The principles unveiled here extend beyond electrical properties, suggesting new strategies for developing multifunctional materials for extreme environment applications.

Supporting Information

Supplementary material associated with this article can be found, in the online version, at doi:

### CRediT authorship contribution statement

**Salah-Eddine Benrazzouq:** Writing – original draft, Investigation, Formal analysis, Data curation. **Jaafar Ghanbaja:** Investigation. **Sylvie Migot:** Investigation. **Valentin A. Milichko:** Writing – review & editing, Supervision, Project administration, Funding acquisition, Conceptualization. **Jean-François Pierson:** Writing – review & editing, Supervision, Project administration, Formal analysis.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgements

This work was supported by the project CPJ: ANR-22-CPJ1–0010–01 of the French Agence Nationale de la Recherche. The Daum Centre de Compétences of IJL is deeply acknowledged for access to the UHV magnetron sputtering deposition facility, the Centre de Compétences X-gamma for access to the X-ray diffraction system, the Centre de Compétences 3 M for the access to the scanning and transmission
electronic microscopes. The authors thanks Dr. David Pilloud for his
valuable technical support.

Supplementary materials

Supplementary material associated with this article can be found, in
the online version, at doi:10.1016/j.apmt.2025.102726.

Data availability

Data will be made available on request.

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