# Cu-25Cr composites processed by in situ alloying in electron beam powder bed fusion

Lucas Varoto, Elodie Courtois, Mélanie Prost, Pierre Lhuissier, Jean-Jacques

Blandin, Sophie Roure, Anthony Papillon, Mélissa Chosson, Guilhem Martin

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Lucas Varoto, Elodie Courtois, Mélanie Prost, Pierre Lhuissier, Jean-Jacques Blandin, et al. Cu-25Cr composites processed by in situ alloying in electron beam powder bed fusion. Additive Manufacturing, 2025, 109, 10.1016/j.addma.2025.104869. hal-05373719

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https://hal.univ-brest.fr/hal-05373719v1

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# Cu-25Cr composites processed by in situ alloying in electron beam powder bed fusion

Lucas Varoto<sup>a,b,*</sup>, Elodie Courtois<sup>c</sup>, Mélanie Prost<sup>b,D</sup>, Pierre Lhuissier<sup>b,D</sup>,
Jean-Jacques Blandin<sup>b</sup>, Sophie Roure<sup>a</sup>, Anthony Papillon<sup>a</sup>, Mélissa Chosson<sup>a</sup>,
Guilhem Martin<sup>b,**</sup>

<figure><img src="image_3.png" /></figure>

## ARTICLE INFO

### Keywords:

Electron beam powder bed fusion

Cu alloys

Miscibility gap

Microstructure

Mechanical properties

Electrical and thermal properties

## ABSTRACT

Due to their high thermal and electrical conductivity and high resistance to arc erosion, Cu-Cr alloys (Cr >10 wt %) are used as electrical contacts in medium voltage vacuum circuit breakers. Such electrical contacts are industrially processed using solid-state sintering (SSS) from pure Cu and Cr powders or vacuum arc remelting (VAR). In this work, we confirm the possibility of fabricating dense Cu-25Cr samples with a refined and relatively homogeneous microstructure by electron beam powder bed fusion (EB-PBF) using elemental powder blending. The as-printed microstructure is characterized using SEM imaging and EBSD analysis while the mechanical, electrical, and thermal are probed to establish the microstructure-property relationships of the EB-PBF Cu-25Cr composite. The properties of the EB-PBF composite are systematically compared to their VAR counterparts. The as-printed microstructure results from the presence of a metastable miscibility gap that refines the microstructure (micron-sized Cr particles) by an order of magnitude compared to the VAR. The fine EB-PBF microstructure shows superior mechanical properties (hardness, yield strength and ultimate tensile strength), enhanced electrical conductivity, and equivalent thermal conductivity with respect to its VAR counterpart. The microstructure-property relationships are discussed in light of the mechanisms affecting the mechanical, electrical, and thermal properties of metal matrix composites. This work demonstrates the interest in producing Cu-Cr electrical contacts by additive manufacturing.

## 1. Introduction

Various thermo-mechanical applications require materials with a combination of high electrical and thermal conductivity, high voltage resistance, and arc erosion resistance [1]. In this context, Cu-Cr based alloys appear to be promising candidates. These properties result from the good electrical and thermal conductivity of the Cu matrix while the Cr particles improves the arc ablation resistance thanks to its higher melting point and hardness. Such particle-reinforced copper matrix composites with a Cr-content typically between 10 and 50 wt% are often employed as electrical contacts in devices such as vacuum interrupters [2–6]. Cu-Cr electrical contacts are an essential link in the power distribution chain (medium voltage applications). Their role is similar to that of a circuit breaker: under normal conditions the current flows

(electrical contacts closed), but if an overvoltage or short circuit occurs, the power is immediately turned off by separation of the electrical contacts.

Cu-Cr electrical contacts are usually fabricated by powder metallurgy [2,7–10] or solidification-based techniques [3,11–15]. Powder metallurgy (solid-state sintering) [2,7–10] and vacuum-arc remelting (VAR) are the main processing routes used industrially [3,11–15].

When electrical contacts are fabricated via powder metallurgy, Cu and Cr raw powders are first mixed in the desired Cu/Cr ratio. Then, a sintering heat treatment near the Cu melting point, typically at 1050°C for several hours under a secondary vacuum, allows the densification of the green body with a final relative density exceeding 95% [10,16]. The microstructure of such electrical contacts fabricated by powder metallurgy consists of coarse irregular Cr particles embedded in the Cu matrix.

<footnote><sup>a</sup> Schneider Electric Industries, Grenoble F-38000, France</footnote>

<footnote><sup>b</sup> Univ. Grenoble Alpes, CNRS, Grenoble INP, SIMaP, Grenoble F-38000, France</footnote>

<footnote><sup>c</sup> Univ. Bretagne Sud, UMR CNRS 6027, IRDL, Lorient F-56100, France</footnote>

<footnote>* Corresponding author at: Schneider Electric Industries, Grenoble F-38000, France.</footnote>

<footnote>** Corresponding author.</footnote>

<footnote>E-mail addresses: lucasvaroto10@gmail.com (L. Varoto), guilhem.martin@simap.grenoble-inp.fr (G. Martin).</footnote>
The morphology and size of the Cr particles are directly correlated to the Cr powder used. Upon sintering, the densification of the Cu matrix occurs leading to relative density > 95% with the presence of small globular pores within the Cu matrix and large interconnected pores at the Cu/Cr interfaces representing more than 90% out of the overall porosity [16].

VAR is also used to produce metal ingots with increased chemical and mechanical homogeneity. Cu-Cr medium-sized ingots are first produced by solid-state sintering. After the densification of such ingots, vacuum arc remelting of Cu-Cr contact materials is performed. The microstructure of hypereutectic Cu-25Cr alloys inherited from VAR show Cr-dendrites embedded into a eutectic Cu-Cr matrix [14,17–19]. Contrary to the microstructures inherited from powder metallurgy, the microstructure is free of porosity and thus does not contain defects at the Cu/Cr interfaces.

Such processing routes offer limited capabilities to tailor the microstructure by controlling the size, morphology, and spatial distribution of the Cr phase to improve the mechanical and functional properties. For instance, pressing green bodies with micron-sized Cr powders is a challenging operation because the compressive tools are often seized. Achieving very high cooling rates (typically > 10³°C/s) to refine the Cr dendrites during VAR operations turns out to be challenging due to the size of the ingots.

Rapid solidification processes such as melt spinning [17–19] can be interesting to optimize the microstructure of Cu-Cr electrical contacts because of the presence of a metastable miscibility gap providing opportunities to refine the microstructure and achieve superior strength-conductivity trade-off [20–23]. Traditional rapid solidification processes are often limited to simple geometries (thin films, tapes) with one dimension much smaller than the others. Over the past decade, the development of additive manufacturing (AM), especially powder bed fusion (PBF) processes have offered unique opportunities to produce sophisticated geometries with dimensions that can far exceed those achievable by traditional rapid solidification processes while preserving out-of-equilibrium microstructures throughout the parts. In the case of Cu-Cr hypereutectic alloys, one can take advantage of the out-of-equilibrium processing conditions to leverage the large miscibility gap in the Cu-Cr binary system.

Few articles have reported the fabrication of Cu-Cr composites using laser powder bed fusion (LB-PBF) [24–27]. Microstructural heterogeneity is reported due to insufficient energy input (low absorptivity of Cu by infra-red lasers) to melt the Cr phase due to the large difference in melting point between Cu and Cr [25–27]. In the as-printed condition, Chen *et al.* showed that the electrical conductivity of the LB-PBF Cu-25Cr composite was about 11 MS·m⁻¹ while its hardness reached 180 HV [25]. Post-fabrication heat treatments performed at 500°C for 1 h enable to increase the hardness (260 HV) and electrical conductivity (30 MS·m⁻¹). After 1 h at 600°C, the electrical conductivity was further increased (33 MS·m⁻¹) but the hardness was only slightly increased (200 HV) [25].

EB-PBF appears to be a promising manufacturing technique to produce Cu-Cr composites. The fabrication takes place under vacuum (clean atmosphere). It allows the absorptivity issues of Cu to be overcome when using infra-red laser sources and offers the possibility of using high beam power to melt a high melting point metal such as Cr. However, only two studies reported the processing of Cu-Cr composites using electron beam powder bed fusion (EB-PBF) [28,29]. Momeni *et al.* [28] showed for the first time in 2018 the possibility to process Cu-25Cr by EB-PBF using powder blends and reported interesting microstructure observations with a strongly refined Cr phase resulting from a liquid phase separation. However, to the best of our knowledge, the electrical, thermal and mechanical properties were not measured and compared with their VAR counterpart to evaluate the possible benefits of AM. Besides, the microstructure-property relationships are yet to be established. Very recently, Wei *et al.* [29] have successfully produced Cu-50Cr samples by EB-PBF with a relative density > 97%. They showed that the electrical

and thermal conductivity, and the hardness depend on the processing parameters. In some conditions, the hardness can surpass the one of Cu-50Cr fabricated by traditional processing routes (250 HB vs. ≤110 HB) while the electrical conductivity still shows acceptable values (≥16 MS·m⁻¹). However, the microstructure-property relationships were not thoroughly investigated and the current literature lacks of similar studies on Cu-25 or 35 Cr composites.

Herein, we investigate the fabrication of Cu-25Cr composites by EB-PBF using elemental powder blending. Dense and relatively homogeneous microstructures are produced despite the use of powder blends. The properties of the as-printed composites are measured and systematically compared with the Cu-25Cr produced by VAR. The mechanism at the origin of the as-printed Cu-25Cr EB-PBF composite is confirmed and the microstructure-property relationships (mechanical, electrical, and thermal) are established. The improved properties of the EB-PBF composite compared to its VAR counterpart are discussed in terms of the main features of their respective microstructures.

## 2. Materials and methods

### 2.1. Powder characteristics

Pure Cu and Cr powders were mixed in a Turbula® powder mixer for 30 min in a 3:1 mass ratio (25 wt%Cr). The Cu powder was produced by gas atomization under Argon from Cu-OF rods at the LERMPS Laboratory in France, a department of the UTMB (Université Technologique de Belfort-Montbéliard). The Cr powder was provided by Ampere Alloys and was processed by mechanical milling. The chemical composition of the Cu and Cr powders was measured using glow discharge mass spectrometry (GDMS) and instrumental gas analysis (IGA) depending on the elements by Eurofins EAG Laboratories and is given in Table 1. The composition of the EB-PBF Cu-25Cr printed samples was also determined and is reported in Table 1. Both powders are relatively free of impurities.

Standardized methods using the Hall flowmeter funnel (ASTM B212 standard for the relative apparent density and ASTM B213 standard for the flow rate of metal powders) were employed to measure the relative apparent density and flowability. The particle size distribution $D_v10$, $D_v50$, and $D_v90$ of both powder batches are given in Table 2 and the full particle size distributions are given in supplementary materials, see Figure S1. The typical morphology of both powders was characterized by scanning electron microscopy using a Zeiss Gemini SEM500 field emission gun scanning electron microscope (FEG-SEM). The powder characteristics are summarized in Table 2. The morphology of the Cu and Cr powder can be respectively observed in Fig. 1a-b. The Cu powder does not show perfectly spherical morphology because it is not fresh powder but is relatively free of satellites in comparison with the atomized powder, see [30]. The Cu powder was subjected to one recycling step, i.e. the powder has already seen one build and one pass in the powder recovery system (specific device employed in EB-PBF to recycle the powder). The powder processing route of the Cr powder explains why spherical particles are not observed but the flowability of such powder was still relatively good, see Table 2.

### 2.2. EB-PBF processing conditions

The Cu-25Cr samples were fabricated by electron beam powder bed fusion additive manufacturing using a FreemeltONE machine (Freemelt AB, Molndal, Sweden) operating at 60 kV. Preliminary tests were conducted to establish the processing window. The EB-PBF process took place under vacuum (5.10⁻⁶ mbar) at a constant temperature (~610°C), see Table 3 for more details regarding the preheating parameters. Besides the challenge of establishing stable printing conditions (preheating temperature, beam power, and scanning speed) to process dense samples, the objective was to achieve homogeneous microstructures. Indeed, the fabrication of samples by in situ alloying, especially with two
<caption>**Table 1**</caption>

Chemical composition of the Cu and Cr powders used in EB-PBF to produce Cu-25Cr composites and comparison with a sample fabricated by EB-PBF using these powders.

<table><thead><tr><th rowspan="2"></th><th colspan="2">wt%</th><th colspan="9">ppm</th></tr><tr><th>Cu*</th><th>Cr*</th><th>Al*</th><th>Si*</th><th>P*</th><th>Fe*</th><th>Co*</th><th>Ni*</th><th>Zn*</th><th>Sn*</th><th>O*</th></tr></thead><tbody><tr><td>Cu powder</td><td>Bal.</td><td>-</td><td>&lt; 50</td><td>&lt; 50</td><td>&lt; 50</td><td>&lt; 50</td><td>&lt; 5</td><td>&lt; 20</td><td>&lt; 50</td><td>&lt; 50</td><td>&lt; 50</td><td>&lt; 100</td></tr><tr><td>Cr powder</td><td>-</td><td>Bal.</td><td>140</td><td>180</td><td>&lt; 50</td><td>650</td><td>&lt; 5</td><td>&lt; 20</td><td>&lt; 50</td><td>&lt; 50</td><td>&lt; 50</td><td>490</td></tr><tr><td>Cu-25Cr EB-PBF</td><td>Bal.</td><td>24.8</td><td>&lt; 50</td><td>&lt; 50</td><td>&lt; 50</td><td>310</td><td>&lt; 5</td><td>&lt; 20</td><td>&lt; 50</td><td>&lt; 50</td><td>&lt; 50</td><td>380</td></tr></tbody></table>

<caption>**Table 2**</caption>

Cu and Cr powders characteristics used to process Cu-25Cr composites by EB-PBF.

<table><thead><tr><th></th><th>Cu</th><th>Cr</th></tr></thead><tbody><tr><td>D<sub>v</sub>10 (μm)</td><td>46</td><td>30</td></tr><tr><td>D<sub>v</sub>50 (μm)</td><td>70</td><td>45</td></tr><tr><td>D<sub>v</sub>90 (μm)</td><td>107</td><td>72</td></tr><tr><td>Sphericity<sub>v</sub>,50</td><td>&gt; 0.90</td><td>&gt; 0.80</td></tr><tr><td>Flow time (s/50 g)</td><td>13.6 ± 0.2</td><td>26.3 ± 0.2</td></tr><tr><td>Relative Apparent Density (%)</td><td>55.5 ± 0.5</td><td>45.5 ± 0.5</td></tr></tbody></table>

metals, namely Cu and Cr with a large difference in melting temperature sometimes leads to heterogeneous microstructures, see e.g. [27,31–33]. It was thus required to fully melt both Cu and Cr powders. A summary of this preliminary study aiming at determining the processing window is given in Figure S2 provided as Supplementary Materials. Such preliminary work yielded the processing conditions to print dense samples with a homogeneous microstructure using EB-PBF (no contour was applied). The optimized set of parameters is given in Table 3. The scanning strategy used was a snake-like pattern, the latter is rotated by 90° rotation at each layer. Nine samples with the following dimensions: 12 × 12 × 55 mm were printed by EB-PBF (Fig. 2a-b) using the optimized processing parameters on a 10mm-thick build substrate of 316 L austenitic stainless steel.

## 2.3. Vacuum arc remelted Cu-25Cr

Throughout this investigation, we will establish comparisons between the Cu-25Cr processed by EB-PBF and the Cu-25Cr fabricated by VAR. The latter is considered a reference material and was processed by Sirui Advanced Materials Co., Ltd, Xi’an, China. Cylindrical samples with 50 mm in diameter and 8 mm in height were supplied (Figure S3). Their chemical composition is provided in Table 4. The samples were characterized in their as-received state. No post-heat treatment was applied.

## 2.4. Microstructure characterization

Samples were first grinded using SiC abrasive papers, and then polished using diamond suspensions (9, 3, and 1 µm). The final polishing

step was performed using a 0.03 µm colloidal silica solution for 4 h. SEM images were collected using the back scattered electron (BSE) contrast with a Zeiss Gemini SEM500 FEG-SEM. The characteristic length in the Cu ($d_{Cu}$) and Cr ($d_{Cr}$) phase was taken as the average intercept lengths

<caption>**Table 3**</caption>

Processing parameters employed to produce dense and homogeneous Cu-25Cr samples by EB-PBF.

<table><thead><tr><th colspan="2">Preheating</th></tr></thead><tbody><tr><td>Power - P [W]</td><td>1600</td></tr><tr><td>Scanning speed - v [mm/s]</td><td>11000</td></tr><tr><td>Line offset - h [µm]</td><td>1000</td></tr><tr><td>Preheat surface [mm<sup>2</sup>]</td><td>60 × 60</td></tr><tr><td>Processing temperature [°C]</td><td>610 ± 10</td></tr><tr><td>Spot-size [µm]</td><td>700</td></tr><tr><td colspan="2">Melting</td></tr><tr><td>Power - P [W]</td><td>2000</td></tr><tr><td>Scanning speed - v [mm/s]</td><td>2000</td></tr><tr><td>Spot-size [µm]</td><td>300</td></tr><tr><td>Line offset - h [µm]</td><td>80</td></tr><tr><td>Layer thickness - z [µm]</td><td>50</td></tr><tr><td>Rotation of the scanning pattern</td><td>90°</td></tr><tr><td>Sample size: l × w × h [mm<sup>3</sup>]</td><td>12 × 12 × 55</td></tr></tbody></table>

<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Pictures of the nine Cu-25Cr EB-PBF as-built samples on the build plate: (a) top view and (b) side view.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Fig. 1.** SEM-SEM micrographs illustrating the typical size and morphology of (a) the Cu and (b) Cr powders used in EB-PBF to produce Cu-25Cr composites.</figcaption></figure>

<footnote>* Measured by Glow Discharge Mass Spectrometry (GDMS).</footnote>

<footnote>a Measured by Instrumental Gas Analysis (IGA).</footnote>
<table><caption>**Table 4**

Chemical composition of the Cu-25Cr composite produced by VAR.</caption><thead><tr><th rowspan="2"></th><th colspan="2">wt%</th><th colspan="8">ppm</th></tr><tr><th>Cu*</th><th>Cr*</th><th>Al*</th><th>Si*</th><th>P*</th><th>Fe*</th><th>Co*</th><th>Ni*</th><th>Zn*</th><th>Sn*</th><th>O*</th></tr></thead><tbody><tr><td>Cu-25Cr VAR</td><td>Bal.</td><td>25.3</td><td>280</td><td>200</td><td>&lt; 50</td><td>510</td><td>&lt; 5</td><td>&lt; 20</td><td>&lt; 50</td><td>&lt; 50</td><td>350</td></tr></tbody></table>

* Measured by Glow Discharge Mass Spectrometry (GDMS).

a Measured by Instrumental Gas Analysis (IGA).

determined from five segmented SEM images and the statistical dispersion was calculated using the standard deviation. Note that the size distribution of the Cr phase determined using the “Analyze Particles” plugin in ImageJ gives similar results, see Figure S4a. EBSD maps were acquired using a step size of 200 nm for the VAR samples. Regarding the EB-PBF samples, Electron back-scattered diffraction (EBSD) maps with two different steps sizes (80 and 30 nm) were collected. EBSD maps were cleaned up in the EDAX OIM Analysis™ post-processing software using a single neighbor orientation correlation followed by grain dilation.

## 2.5. Characterization of the functional and mechanical properties

The mechanical properties of the as-printed samples and VAR composites were determined through hardness and tensile tests. Vickers hardness mapping was performed to characterize the EB-PBF Cu-25Cr samples (1 kg load and 15 s loading pause) using an Innovatest IMP hardness tester. A 20 × 51 grid consisting of HV/1 indentations spaced by 0.5 mm was performed in the plane containing the build direction allowing us to plot hardness profiles along the build direction in the EB-PBF samples. A 5 kg load was rather employed for the VAR samples due to their coarser microstructures. Flat dog bone tensile specimens (1.5mm-thick, gauge length of 15 mm) were extracted by electron discharge machining from the as-printed EB-PBF samples so that their gauge length is aligned with the build direction as schematically shown in Figure S5. Similar tensile specimens were machined out of the Cu-25Cr as-fabricated VAR composites with their gauge length parallel to the diameter of the cylindrical samples. Mechanical testing was carried out at a constant strain rate of 10⁻³ s⁻¹ using a MTS40 testing machine. Strains were measured by digital image correlation (DIC). The results were analyzed using the GOM Correlate Software using a facet size equal to 25 pixels and a distance separating two facets of 12 pixels. The speckle was made using white and black paintings. Three specimens were deformed under tension up to fracture.

Two different techniques were employed to measure the effective electrical conductivity at room temperature. First, an Eddy current probe was used directly on the polished cross-section surface of the EB-PBF and VAR samples. Measurements were done using a FISCHER-SCOPE MMS using a 8 mm probe at a frequency of 300 kHz resulting in an accuracy of 1MS. For the Cu-25Cr EB-PBF samples, measurements of the local effective electrical conductivity were performed along the 55 mm height. At each height, the average electrical conductivity out of 20 measurements with the corresponding standard deviation was calculated as the local effective electrical conductivity of the EB-PBF Cu-Cr composites. Second, the electrical conductivity was measured using the 4-probes method. A current flow (1 A) was provided by two wires, one connected at each extremity of a 3 × 3 × 20 mm sample machined at the center of the as-built Cu-25Cr EB-PBF samples and the center of VAR cylindrical samples. Two additional copper wires ate then crimped in small holes located at each extremity of the sample. This set-up enables the measurement of the difference in potential (ΔV) in the region of the sample where the cross-sections should be equipotential. Measurements were done at room temperature. The electrical conductivity σ of the sample is deduced from Eq. (1):

$$ \sigma = \frac{l \times I}{\Delta V \times S} \qquad (1) $$

with *l* the sample length *S* the sample cross-section, ΔV the potential difference, and *I* the applied current, see for more details [34,35]. The uncertainties associated with such an experimental protocol are estimated to be approximately 3 %.

The thermal conductivity *k* (W.m⁻¹.K⁻¹) of the Cu-Cr composites was calculated from the experimental measurements of the thermal diffusivity (α - m².s⁻¹), specific heat capacity (*c*<sub>p</sub> - J.kg⁻¹.K⁻¹), and density (ρ - kg.m⁻³) at *T* = 200°C, following Eq. (2):

$$ k = \alpha \cdot \rho \cdot c_p \qquad (2) $$

The thermal diffusivity measurements were achieved using the flash laser method with a NETZSCH LFA 457 apparatus at *T* = 200°C, in an argon atmosphere. Disk-shaped samples of (8 mm in diameter and 3 mm in thickness) were extracted from the EB-PBF Cu-25Cr samples at three different heights (bottom, middle, and top) of the as-built sample. Similar disk-shaped samples were extracted from the VAR Cu-25Cr composites. The specific heat capacity was measured by differential scanning calorimetry (DSC). A Labsys evo SETARAM DSC was used to measure the heat flow from the Cu-Cr samples under Ar. A heating rate of 2 K/min was used until reaching *T* = 200°C and then the temperature was kept constant for 12 min. *c*<sub>p</sub> was then determined by integrating the heat flow signal from the Cu-Cr sample and a reference sample made of silver (Ag), corrected by a blank measurement. The dimensional variation was used to obtain the coefficient of thermal expansion (CTE) of the different samples (EB-PBF and VAR). A LINSEIS L76/10 dilatometer was used to measure the dimensional variation during heating and cooling from RT to 200°C under an argon flow. An average linear CTE was calculated using linear regression from three samples and thus used to calculate the density at *T* = 200°C, ρ(*T* = 200°C). The uncertainties associated with the thermal conductivity calculation are estimated to be approximately 9 %.

In this study, the properties of the EB-PBF and VAR Cu-25Cr composites are also compared to the properties measured in a previous work [30] from a cold-worked and annealed electrolytic tough-pitch copper (Cu-ETP).

# 3. Experimental results

## 3.1. Microstructure of the as-printed EB-PBF microstructure

During EB-PBF, since the first layers are subjected to a longer intrinsic heat treatment at the processing temperature (here 610°C) than the topmost layers, it is important to perform microstructure observations at different heights along the build direction [36–38]. The low-magnification SEM images shown in Fig. 3a,d,g,b,e,h reveal that the material is nearly fully dense. The samples were free of lack-of-fusion defects. Only a few spherical pores randomly distributed were detected. A few microstructure heterogeneities were detected. Locally, unmelted or partially melted Cr particles, e.g. the particle pointed with a black arrow in Fig. 3d are found. Small regions depleted in Cr can also be seen, see typical regions pointed with orange arrows in Fig. 3. However, overall, the microstructure can be considered relatively homogeneous, especially when compared with the microstructure produced using other sets of parameters leading to dense samples but with strong microstructural heterogeneities, see e.g. Figure S2a-d in the supplementary materials. The microstructure in the as-printed samples is better
<figure><img src="image_6.png" /><figcaption>**Fig. 3.** SEM-BSE micrographs taken in the EB-PBF sample at different magnifications along the sample height: (a-c) near the top surface at z = 54.8 mm; (d-f) at the center at z = 30 mm; and near the bottom at z = 5 mm. (j-l) SEM-BSE micrographs taken in Cu-25Cr VAR sample for comparison.</figcaption></figure>

revealed using high-magnification SEM images, see Fig. 3c,f,i. The microstructure consists of fine globular Cr-rich particles (in dark gray) uniformly distributed in the Cu matrix (light gray). Locally, coarser spherical Cr particles are detected, e.g. the Cr particle pointed with the yellow arrows in Fig. 3b,c. Such a microstructure is typical of a liquid-liquid phase separation (LLPS), see e.g. [20,39–42]. The characteristic size of the fine globular Cr-rich particles is homogeneous in the build direction. The latter was found to be $d_{Cr} = 1.2 \pm 0.5$ µm and it was taken as the average intercept length. A slight change in size is observed in the topmost layer, where one can note a relatively finer globular Cr-rich particles compared to the rest of the sample. The characteristic length in the Cu phase, also estimated using the intercept method, was measured at $d_{Cu} = 3 \pm 2$ µm. More details regarding the statistical distribution of the intercept lengths in the Cu and Cr phase can be found in Figure S4b.

A remarkable change in Cr-phase size and morphology is evidenced in comparison with the VAR composite as shown in Fig. 3j-l. The characteristic size (taken as the average intercept length) of the Cr-phase is refined by an order of magnitude: about $d_{Cr} = 1$ µm in the EB-PBF microstructure and $d_{Cr} = 10$ µm in the VAR. Similarly, the average intercept length in the Cu phase of the EB-PBF sample is equal to $d_{Cu} = 3$ µm vs. 25 µm in the VAR. The morphology of the Cr-phase has also drastically changed. While a dendritic morphology is observed in the VAR, the Cr particles exhibit a spherical morphology in the EB-PBF sample.

EBSD maps collected in the bulk material and the topmost layer

provide additional interesting pieces of information (Fig. 4a-f). The Cu matrix grains have a columnar morphology (Fig. 4b,e) with their longer axis exceeding hundreds of microns. A larger EBSD map is also provided in supplementary materials and gives a better idea of the size of the Cu columnar grains, see Figure S6. In the center, the Cu matrix grains grow along the build direction (Fig. 4b) while in the topmost layer, they are tilted with respect to the build direction due to the orientation of the thermal gradient, see Fig. 4. Misorientation within Cu columnar grains can be seen with the presence of color gradients (Fig. 4b,e). Within a given Cu grain, the Cr globular particles show different orientations, see Fig. 4c,f. No specific orientation relationship between Cr and Cu was found.

The area highlighted with the black window in Fig. 4f and containing a spherical 10µm-diameter Cr particle was further characterized using SEM and EBSD, see Fig. 5a-f. Interestingly, in those larger Cr-rich spheroids, one can observe regions appearing with the same grayscale contrast as the Cu matrix in the SEM micrograph, see Fig. 5a. Those regions were indexed as Cu in the EBSD dataset, see Fig. 5b-c. Finally, the kernel average misorientation (KAM) map displayed in Fig. 5d reveals the presence of a high density of misoriented interfaces within the Cu matrix. Those misoriented interfaces are mostly associated with low-angle grain boundaries (LAGBs) represented in white in Fig. 5c.
<figure><img src="image_7.png" /><figcaption>Fig. 4. Phase map and inverse pole figure (IPF) maps of the Cu and Cr phase collected (a-c) in the bulk at z = 50 mm, and (d-f) in the topmost layer at z = 54.5 mm.</figcaption></figure>

## 3.2. Mechanical properties

### 3.2.1. Hardness

The mechanical properties along the height of the sample were first probed using hardness Vickers mapping (HV1). The hardness map determined in a longitudinal cross-section is given in Fig. 6a-b. The average hardness computed over the entire map equals to 116 ± 6 HV1. The error is estimated by computing the standard deviation over the entire hardness map. This is about 25 % higher than the hardness measured in the VAR counterpart (85 ± 3 HV5). In the hardness map shown in Fig. 6b, one can see regions with a hardness lower than the average values (displayed in blue) and regions exhibiting a hardness higher than the average values (displayed in yellow/orange). Those hardness heterogeneities are associated with local microstructural heterogeneities: soft points correspond to Cu-rich regions (i.e. zones depleted in Cr) and harder points are found where the initial Cr powder particles have not been fully melted. Although the heterogeneities appear to be limited, this suggests that there is still room to achieve more homogeneous microstructures, for example by further increasing the energy density to achieve deeper melt pools, using a 67° scan pattern rotation, reducing the hatch spacing, introducing a remelting step or using a pre-alloyed powder. No clear difference in hardness along the build direction was detected between the last printed layers and near the center despite the presence of slightly finer globular micron-sized Cr

particles in the topmost layer (Fig. 3c,f,i).

### 3.2.2. Tensile properties

The engineering tensile stress-strain curves and the true stress-strain curves of the EB-PBF Cu-25Cr are respectively given in Fig. 7a and Fig. 7b along with the tensile responses of the Cu-25Cr VAR and Cu-ETP. The tensile mechanical properties were then extracted and are summarized in Fig. 7c-d. The yield strength taken at 0.2 % plastic strain, ultimate tensile stress (UTS), and uniform elongation were measured from the true stress-strain curves (Fig. 7b). The elongation to failure was determined from the engineering stress-strain curve (Fig. 7a) and the uniform elongation on the true stress-strain curve. The yield strength of the EB-PBF Cu-25Cr composite (210 MPa) is about 25 % higher than the one of its VAR counterparts (155 MPa), see Fig. 7c. The UTS of the EB-PBF Cu-25Cr composite reaches 450 MPa while it is equal to 370 MPa in the VAR. On the contrary, the ductility is reduced in the EB-PBF case with an average elongation to failure of 14 % compared to 35 % for the composite processed by VAR (Fig. 7d). This reduced elongation to failure is strongly related to the few microstructural heterogeneities observed locally in the as-printed samples, see illustrations in supplementary materials (Figure S4a-b). This suggests that there is room for improving the ductility of such composites by further improving the microstructure homogeneity.
<figure><img src="image_8.png" /><figcaption>Fig. 5. Characterization of the ROI highlighted using a black window in Fig. 4f: (a) SEM micrograph; (b) EBSD phase map; (c,e) EBSD IPF map of the Cu and Cr phase respectively; and (d,f) EBSD KAM map of the Cu and Cr phase respectively. LAGBs are defined as interfaces with a misorientation between 5 and 15° and displayed in white. High angle grain boundaries (HAGBs) are defined as interface with a misorientation higher than 15° and are displayed in black.</figcaption></figure>

### 3.3. Electrical conductivity and thermal conductivity

The effective electrical conductivity measured using the Eddy current method along the build direction in the as-printed sample is shown in Fig. 8. A slight decrease in electrical conductivity is observed when approaching the top surface: 36 MS.m⁻¹ vs. 38–39 MS.m⁻¹ near the bottom of the sample. The electrical conductivity of the VAR and Cu-ETP are also given for comparison. The average effective electrical conductivity of the EB-PBF Cu-25Cr composite is equal to 37.8 MS.m⁻¹. This represents a 15% increase in electrical conductivity compared to its VAR counterpart, see Table 5. The results of the measurements of electrical conductivity by the 4-probes method are also given in Table 5. The electrical conductivity measured using the Eddy current and the 4-probes method shows a good agreement.

Finally, the average effective thermal conductivity of the EB-PBF Cu-25Cr composites deduced from the measurements of the thermal diffusivity, specific heat capacity, and density at 200°C was calculated for three different samples extracted along the sample's height. The results are summarized in Fig. 9 where the effective thermal conductivity of the Cu-25Cr VAR (in blue) counterpart is also indicated for comparison. The effective thermal conductivity of the EB-PBF Cu-25Cr composite is slightly lower than the VAR composite.

## 4. Discussion

### 4.1. Microstructural evolution

#### 4.1.1. Microstructure resulting from a liquid-liquid phase separation (LLPS)

It is worth highlighting that the presence of a metastable miscibility gap in the Cu-Cr binary system for composition ranging typically between 5 % and 80 %at was established in the literature [20–22]. When the melt is undercooled below the metastable miscibility gap, a LLPS occurs and the liquid separates into a Cu-rich and a Cr-rich liquid. The phase in a smaller volume fraction (here Cr) takes a spherical shape to decrease the interfacial energy [43]. The observations reported in the present work support the idea that the mechanism responsible for the Cu-25Cr refined microstructure shown in Fig. 3 is indeed a LLPS. The dispersed Cr phase shows a globular morphology (Fig. 3c,f,i) and is about 1 micron in size with no orientation relationship with the Cu phase. The presence of a few large spherical Cr particles with a size 3–10 times larger than the finely dispersed Cr particles as shown in Fig. 5 is another hint supporting the idea of a LLPS. These large Cr spheroids result from the coarsening of several fine droplets of the Cr-rich liquid during the primary LLPS. This coarsening is thought to be promoted by convective flows during EB-PBF. Within these large spherical Cr particles, nanoscale Cu globular precipitates are detected (Fig. 5a). These result from a secondary LLPS where the dispersed phase
<figure><img src="image_9.png" /><figcaption>Fig. 6. (a) Optical micrograph showing in dashed lines the region of interest for hardness mapping. (b) Hardness map taken along the height of the Cu-25Cr EB-PBF samples. (c) Hardness profile along the sample's height where the green star symbol corresponds to the average hardness calculated at each height while the gray points reflect the dispersion of the results at each height. The hardness of Cu-25Cr fabricated using VAR is given using dotted lines in (c) for comparison. The data for Cu-ETP have been extracted from [30].</figcaption></figure>

is now the Cu phase. The primary LLPS is thus responsible for the finely dispersed Cr globular particles in the Cu matrix as shown in Fig. 3 and Fig. 4. The secondary LLPS is at the origin of the nanoscale Cu globular precipitates observed within the large Cr spherical particles (Fig. 5). The mechanisms leading to the as-printed microstructure are summarized in Fig. 10. First, upon cooling below the metastable miscibility gap, Cr-rich liquid droplets form in a Cu-rich liquid. Then, some Cr-rich droplets coarsen resulting in larger Cr spheroids in which a secondary LLPS occurs with the formation of nanoscale Cu-rich droplets within the larger Cr-rich liquid spheroids. Finally, the two liquids, namely the Cr-rich one and the Cu-rich one, solidify.

### 4.1.2. Thermal stability

During the EB-PBF process, the successive heating and cooling stages at each newly printed layer establish a complex thermal history during the layer-by-layer melting. More importantly, the built sample is subjected to continuous heating due to the preheating. In other words, this means that the first-built layers are annealed for a much longer time (about several hours) at the processing temperature (here ~610°C) in comparison with the topmost layer (for about a few minutes), Figure S5. These variations of local thermal conditions can result in microstructure evolutions in the solid state along the build direction. In the present

study, only very faint differences in the size of the Cr particles resulting from the primary LLPS were detected between the topmost layers and the rest of the samples (Fig. 3c,f,i). This is further supported by the nearly constant hardness measured along the build direction (Fig. 6c). The Cu columnar grains are already quite large and are pinned by the high density of Cr particles. Consequently, they are not expected to coarsen significantly at the processing temperature. Those considerations suggest that the microstructure is thermally stable during the EB-PBF process. This is in agreement with previous studies where it is reported that the microstructures of rapidly solidified hypereutectic Cu-Cr alloys (5 <Cr < 50 wt%) are relatively stable at temperatures up to 600°C [44–47] and the Cr phase starts to significantly coarsen at temperatures > 650°C. This means that solid-state coarsening of Cr-particles during EB-PBF fabrication is limited.

## 4.2. Strengthening mechanisms

### 4.2.1. EB-PBF vs. VAR

The EB-PBF as-printed composite shows higher hardness, yield strength, and UTS than its VAR counterpart. The strengthening mechanisms in the Cu-35Cr VAR alloys were deeply investigated in [48]. Three strengthening mechanisms contributing to the strength have been identified: interface strengthening (grain and interphase boundaries), dislocation strengthening (dislocations generated by the difference in the coefficient of thermal expansion between the Cr and the Cu phase upon cooling), and reinforcement of the matrix by the dispersed harder Cr particles (load transfer) [49–52]. We will consider each of these three mechanisms in turn, weighing them individually to highlight the main differences between the EB-PBF composite and its VAR counterpart. The aim here is to determine which of these contributions is predominant, rather than to provide quantitative estimates of the various contributions. In fact, the models used below for the different strengthening mechanisms depend on many parameters that are not necessarily properly measured or that have a non-negligible degree of variability.

Leveraging the out-of-equilibrium LLPS in EB-PBF leads to a significant decrease in the characteristic length in the Cu phase: $d_{Cu} = 3$ µm vs. 25 µm in the VAR. This microstructure refinement by an order of magnitude results in the reduction of the mean free path of dislocations which contributes to increasing the strength. The contribution of this refinement to the yield strength of the VAR and EB-PBF Cu-25Cr was evaluated based on the Hall-Petch relation for pure Cu, see Eq. (3), and the results are given in Table 6:

$$ \Delta\sigma_{HP} = \sigma_0 + k/\sqrt{d_{Cu}} \qquad (3) $$

It is worth highlighting that $d_{Cu}$ is not the grain size here but is rather taken as the average characteristic length in the Cu phase. This gives a better approximation of the mean free path of dislocations in this two-phase composite, as is classically done in eutectic or eutectoid microstructures such as pearlitic steels, see e.g. [53,54]. $\sigma_0$ and $k$ are the Hall-Petch constants ($\sigma_0 = 20$ MPa and $k = 0.16$ MPa.m$^{0.5}$) determined by Hansen [55] for pure Cu. The relative increase in yield strength caused by the refinement of the microstructure between the VAR and the EB-PBF composites is 60 MPa, see Table 6.

Dislocation strengthening in the Cu matrix was then estimated using the Taylor relationship, see Eq. (4):

$$ \Delta\sigma_D = \alpha G_{Cu} b_{Cu} \sqrt{\rho_{Cu}} \qquad (4) $$

where $\alpha$ is a geometric constant taken to be 1.25 [52,56], $G_{Cu}$ is the shear modulus of the Cu phase (45 GPa), $b_{Cu}$ is the Burgers vector of Cu (0.256 nm), and $\rho_{Cu}$ is the dislocation density in the Cu matrix. Here the dislocation density in the Cu matrix was estimated using the Arsenault model [57], see Eq. (5):

$$ \rho = \frac{12V_{Cr} \cdot \Delta T \cdot \Delta CTE}{b_{Cu}(1 - V_{Cr})d_{Cr}} \qquad (5) $$
<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 7. Tensile response of Cu-25Cr samples fabricated by EB-PBF: (a) Engineering stress-strain mechanical response and (b) True stress-strain mechanical response. (c-d) Mechanical properties extracted from the tensile curves shown in (a) and (b): $\sigma_{y0.2\%}$ The tensile response and mechanical properties of Cu-25Cr fabricated using VAR are given in blue for comparison. The data for Cu-ETP have been reproduced from [30].</figcaption></figure>

where $V_{Cr} = 0.3$ is the volume fraction of Cr, $\Delta T$ is the temperature change during which the composite material is subjected to the difference in thermal expansion coefficient between the Cr and Cu phases ($\Delta CTE = 10 \cdot 10^{-6} \text{ K}^{-1}$), and $d_{Cr}$ is the characteristic length of the Cr phase (measured by the intercept method) taken to be 1.2 and 10 µm in the EB-PBF and VAR composites, respectively. The contribution of dislocation strengthening is about three times higher in the case of EB-PBF, see Table 6. This estimate should be treated with extreme caution here as our observations suggest that dislocation strengthening makes a limited contribution to the strength in the EB-PBF composite. Indeed, in the KAM map displayed in Fig. 5d, the misorientations are mostly associated with the LAGBs within the Cu columnar grains (Fig. 5c). Those sub-grain boundaries can be seen as the signature of a softening mechanism called extended recovery or continuous dynamic recrystallization in the literature [58–60]. Continuous recrystallization is characterized by the creation of a recrystallized microstructure through the progressive increase in low-angle grain boundary misorientations, which progressively become high angle grain boundaries during the hot forming of

<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>

metallic materials. However, this can be seen as an intriguing result as Cu is expected to recrystallize by discontinuous recrystallization due to its relatively low stacking fault energy (about 70 mJ/m²). Further work is required here to clarify the exact mechanism responsible for the formation of the LAGBs in the Cu matrix. We hypothesized that such a softening mechanism takes place during EB-PBF and thus significantly reduces the contribution of dislocation strengthening estimated in Table 6.

Finally, the composite effect (load-bearing) due to load transfer from the matrix to the reinforcing Cr particles can be roughly estimated based on the shear-lag models [56,61,62] using Eq. (6):

$$ \Delta\sigma_{LB} = \sigma_{Matrix}^{Cu} \cdot \left(\frac{1+R}{4}\right) \cdot V_{Cr} \qquad (6) $$

where $\sigma_{Matrix}^{Cu} = \Delta\sigma_{HP} + \Delta\sigma_{D}$ is the yield strength of the Cu matrix and R is the aspect ratio of the reinforcing phase, which is taken to be 1 in the EB-PBF case (Cr particles are mostly spherical) and 2 in the VAR case to account for the aspect ratio of the dendrites. The results suggest that the
<figure><img src="image_14.png" /><figcaption>**Fig. 8.** Evolution of the effective electrical conductivity along the Cu-25Cr EB-PBF sample's height measured using the Eddy current method. The schematic on the right indicates the diameter of the probe and the position of the probe during the experiments. The vertical dotted line indicates the electrical conductivity measured using the same method in Cu-25Cr samples processed by VAR.</figcaption></figure>

**Table 5**

Summary of the electrical conductivity of Cu-25Cr EB-PBF measured using the Eddy current method and the 4-probes method. The average value measured in Cu-25Cr samples fabricated using Vacuum Arc Remelting (VAR) is given also for comparison.

<table><thead><tr><th>Cu-25Cr</th><th>Relative Density [%]</th><th>Electrical Conductivity Eddy Current [MS.m<sup>-1</sup>]</th><th>Electrical Conductivity 4-probes [MS.m<sup>-1</sup>]</th></tr></thead><tbody><tr><td>EB-PBF as-printed</td><td>&gt; 99.5 %</td><td>37.8 ± 0.9</td><td>37 ± 1</td></tr><tr><td>VAR</td><td>100 %</td><td>33.4 ± 0.4</td><td>32.9 ± 0.8</td></tr></tbody></table>

<figure><img src="image_15.png" /><figcaption>**Fig. 9.** Effective Thermal conductivity at T = 200°C of the Cu-25Cr samples fabricated by EB-PBF measured at different height. The effective thermal conductivity of Cu-25Cr fabricated using Vacuum Arc Remelting (VAR) and Cu-ETP are given for comparison.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>**Fig. 10.** Schematic summary of the out-of-equilibrium liquid liquid phase separation (LLPS) leading to the microstructure observed in the EB-PBF as-printed samples: (a) Homogeneous Cu-Cr liquid; (b) First LLPS with a dispersion of Cr-rich liquid droplets in the Cu-rich liquid; (c) Coalescence of some Cr-rich liquid droplets; (d) Second LLPS with a dispersion of fine liquid droplets of Cu within the largest Cr-rich spheroids and solidification of first the Cr-rich liquid followed by the solidification of the Cu-rich liquid.</figcaption></figure>

**Table 6**

Estimations of the contribution of the different strengthening mechanisms in the Cu-25Cr EB-PBF and VAR composites.

<table><thead><tr><th></th><th>EB-PBF Cu-25Cr</th><th>Cu-25Cr VAR</th></tr></thead><tbody><tr><td>Δσ<sub>HP</sub> (MPa)</td><td>112</td><td>53</td></tr><tr><td>Δσ<sub>D</sub> (MPa)</td><td>144</td><td>50</td></tr><tr><td>σ<sup>Cu</sup><sub>Matrix</sub> = Δσ<sub>HP</sub> + Δσ<sub>D</sub> (MPa)</td><td>251</td><td>105</td></tr><tr><td>Δσ<sub>LB</sub> (MPa)</td><td>39</td><td>23</td></tr><tr><td>YS<sup>Cu-25Cr</sup><sub>model</sub> = Δσ<sub>HP</sub> + Δσ<sub>D</sub> + Δσ<sub>LB</sub></td><td>295</td><td>126</td></tr><tr><td>YS<sup>Cu-25Cr</sup><sub>experiments</sub></td><td>210</td><td>155</td></tr></tbody></table>
load bearing mechanism does not make a significant contribution to the yield strength in both EB-PBF and VAR Cu-25Cr composites (Table 6).

In summary, the yield strength of the EB-PBF composite (approximately 300 MPa) is significantly overestimated compared to the experimentally measured yield strength (210 MPa), while such a difference is small in the case of the VAR composite, see Table 6. In the case of the EB-PBF composite, the overestimation of the yield strength is attributed to the overestimation of the dislocation strengthening contribution, as dislocation annihilation is not taken into account in EB-PBF, although there is experimental evidence suggesting matrix softening, see Fig. 5b-c.

### 4.2.2. EB-PBF vs. LB-PBF

The hardness of the Cu-25Cr processed by EB-PBF (~115 HV) is higher than its Cu-25Cr VAR counterpart. However, it is still lower than the hardness measured in the Cu-25Cr fabricated by LB-PBF in its as-built condition (180 HV) [25]. It is worth discussing what causes such a difference between the Cu-25Cr fabricated by EB-PBF and LB-PBF. First, the microstructure inherited from LB-PBF is even finer than in the EB-PBF case [25]. Second, as-printed LB-PBF microstructures contain a quite high dislocation density with dislocations arranged in cells, often superimposed with the segregated intercellular regions. It can contribute to the hardness via dislocation strengthening. This was nicely illustrated in alloys such as austenitic stainless steels [63,64] or Ni-based superalloys [65,66] or in pure metals such as Cu [67] and Ni [65]. Contrary to the EB-PBF composite, the dislocations are not annihilated in LB-PBF because the powder bed is not preheated at temperatures approaching 600°C, thus contributing to the hardness. Finally, one can also invoke the supersaturation of the Cu solid solution with a Cr content that can be well above the equilibrium maximum solubility of Cr in Cu at the eutectic temperature (0.7 %wt) due to solute trapping. The supersaturation of the Cu matrix was reflected by a significant decrease in electrical conductivity: 11 MS.m⁻¹ for the as-printed LB-PBF composite [25] vs 37–38 MS.m⁻¹ for the as-printed EB-PBF version. The hardness of the LB-PBF composite can thus be further increased (260 HV) by decomposing this supersaturated solid solution during a direct ageing heat treatment for 1 h at 500°C. After ageing 1 h at 500°C, the nanoscale strengthening Cr-rich phase precipitates in the Cu phase [25]. This increase in hardness goes along with an increase in electrical conductivity of the LB-PBF sample due to the depletion of Cr atoms in the solid solution (30 MS.m⁻¹) after 1 h at 500°C. The high electrical conductivity of the as-printed EB-PBF material (37–38 MS.m⁻¹) suggests that the Cu matrix is not supersaturated. This is due to the high processing temperature (nearly 600°C).

### 4.3. Conduction properties

The Cu-25Cr EB-PBF composite shows a superior effective electrical conductivity (37 MS.m⁻¹) compared to its VAR counterpart (33 MS.m⁻¹). Surprisingly, the effective thermal conductivity, the EB-PBF has a slightly lower conductivity (~220 W.m⁻¹.K⁻¹ at 200°C) compared to its value in the VAR (229 W.m⁻¹.K⁻¹ at 200°C). This is unexpected since the thermal and electrical conductivity usually follow the same trend. We recall here the electrical and thermal conductivity of pure Cu ($\sigma_{Cu} = 59.7$ MS.m⁻¹ at RT and $k_{Cu} = 383$ W.m⁻¹.K⁻¹ at 200°C) and Cr ($\sigma_{Cr} = 7.9$ MS.m⁻¹ at RT $k_{Cr} = 89$ W.m⁻¹.K⁻¹ at 200°C). The idea of this section is to discuss the differences measured and the possible mechanisms that can cause these differences.

Nearly fully dense samples were fabricated by EB-PBF. The impact of porosity on the electrical and thermal conductivity becomes significant when the volume fraction exceeds 2% [68–72]. As a result, here the effect of porosity can be excluded. The grain size is not fine enough [73–76], and the dislocation density [77,78] is not sufficiently high to have an effect on the electrical and thermal conductivity. Two important factors remain to be discussed because they are known to influence the electrical and thermal conductivity: (i) the density of the interfaces [74,

79–81] and (ii) the elements in solid solution in the Cu matrix [82].

### 4.3.1. Theoretical models to predict the conductivity

The effect of impurities and interfacial resistance on the electrical and thermal conductivities can be discussed using analytical theoretical models to predict the effective properties of a two-phase composite. The simplest analytical relationship for estimating the effective properties of composite media is given by the rule of mixtures [83,84]. Its simplest formulation is based on the weighted linear addition of the phase volume fraction and its corresponding property. The assumption of a fiber-reinforced composite simplifies the solution and gives rise to the so-called parallel and series modes. The first translates the effective property of the two-phase composite in the direction of the fibers, while the second predicts the effective property in the direction perpendicular to the principal axes of the fibers. These two simple models are often used to determine the upper ($P_{eff}^{UB}$) and lower ($P_{eff}^{LB}$) bounds of the effective property [82,85,86]. The upper limit corresponds to a stack of slabs of the two constituent phases oriented parallel to the current (electrical) or heat (thermal) flow. In the case of Cu-Cr composites, this equation can be written using Eq. (7):

$$ \frac{P_{eff}^{UB}}{P_{Cu}} = \frac{V_{Cr}P_{Cr}}{P_{Cu}} + (1 - V_{Cr}) \quad (7) $$

where $P_{Cu}$ and $P_{Cr}$ are the properties of the Cu and Cr phases respectively and $V_{Cr}$ is the volume fraction of Cr. The lower bound corresponds to a stack of slabs of the two constituent phases oriented transversely to the current (electrical) or heat (thermal) flow. The lower bound is given by Eq. (8):

$$ \frac{P_{eff}^{LB}}{P_{Cu}} = \frac{1}{P_{Cu}} \left[ \frac{V_{Cr}}{P_{Cr}} + \frac{(1 - V_{Cr})}{P_{Cu}} \right]^{-1} \quad (8) $$

The upper and lower bound equations do not take into account complex morphologies and spatial distribution of the Cr phase in the matrix. They are only used to bound the electrical and thermal conductivities. To model the effective property of our Cu-25Cr composites, we used a more sophisticated model proposed by Torquato [81,87,88], which is a statistical formulation of heterogeneous materials using a 3-point spatial correlation function to describe the microstructure. This model has been successfully applied to study the effective properties of two-phase composite media. Torquato’s formulation for the effective conductivity of particulate composite media can be expressed as in Eq. (9) [87]:

$$ \frac{P_{eff}}{P_{Cu}} = \frac{1 + (d - 1)V_{Cr}\beta - (d - 1)(1 - V_{Cr})\zeta_{2}\beta^{2}}{1 - V_{Cr}\beta - (1 - V_{Cr})\zeta_{2}\beta^{2}} \quad (9) $$

where $\beta = \frac{P_{Cr} - P_{Cu}}{P_{Cr} + (d-1)P_{Cu}}$, d is the spatial dimension and is taken here to be 3 to describe a 3D microstructure, and $\zeta_2$ is a statistical description of the microstructure including the spatial distribution of the second phase. Overall, $\zeta_2$ increases as the complexity (second phase volume fraction and morphology) of the microstructure increases. For the same volume fraction, $\zeta_2$ is smaller for the case of an ordered dispersion of identical spheres than for a disordered dispersion of, for example, identical ellipsoids. In the Cu-25Cr composite processed by EB-PBF, we consider a polydispersion of hard Cr spheres in a Cu matrix, resulting in $\zeta_2 = 0.15$ [87]. In the VAR, in order to account for the more complex morphology and spatial distribution of the dendritic Cr phase, this parameter was set to $\zeta_2 = 0.5$. The effect of impurities in the Cu matrix can be easily studied by deliberately reducing the conductivity of the Cu matrix by X %. The role of the Cu/Cr interfaces can also be studied by introducing an interfacial resistance as shown in [89]. Here, we have used the lower bound of the Torquato’s model which includes a dimensionless parameter R reflecting the interfacial resistance, see Eq. (10) from [89]:
$$ \left(\frac{P_{\text{eff}}}{P_{\text{Cu}}}\right)_{\text{LB}} = \left\{ 1 + \frac{1 - \alpha + 3R}{\alpha} \cdot V_{\text{Cr}} - \frac{B_{\text{LB}}}{C_{\text{LB}}} \right\}^{-1} \quad (10) $$

where $\alpha = P_{Cr}/P_{Cu}$

$$ B_{LB} = V_{Cr} \cdot \left\{ 2 \cdot (1 - V_{Cr}) \cdot \left[ R(4\alpha - 3R - 4) - (\alpha - 1)^2 \right] - 6\alpha R \right\}^2 $$

$$ C_{LB} = \alpha^2(\alpha - 1 - R)^2 \cdot \left[ 6 \cdot (1 - V_{Cr}) + \left(\frac{1}{\alpha} - 1\right) \cdot \left( 4(1 - V_{Cr})^2 + 2\zeta_2(1 - V_{Cr}) \right) \right] $$

$$ + 6\alpha R \cdot \left[ \alpha^2 + 2(R + 1)^2 \right] $$

$$ + \alpha R V_{Cr} $$

$$ \cdot \left\{ (\alpha - 1 - R)^2 \left[ \frac{16}{9} + 3V_{Cr}(1 + V_{Cr}) \right] + 24(\alpha - 1 - R)(R + 1) + 12(\alpha - 1 - R)^2 V_{Cr} \right\} $$

### 4.3.2. Electrical conductivity

Fig. 11 shows the predictions of the effective electrical conductivity of Cu-Cr composites using the Torquato’s model and taking the electrical conductivity of pure Cu ($\sigma_{Cu} = 59.7$ MS.m$^{-1}$) and pure Cr ($\sigma_{Cr} = 7.9$ MS. m$^{-1}$). The lower and upper bounds are also given for comparison. For the EB-PBF Cu-25Cr composite, there is a very good agreement between the effective electrical conductivity predicted by the model (continuous black line in Fig. 11) and the one measured experimentally (green star in Fig. 11) is found. This suggests that the Cu matrix of the EB-PBF samples is nearly free of elements retained solid solution. Indeed, the presence of elements in solid solution in the Cu matrix would necessarily cause a reduction in electrical conductivity [82]. In this case, the electrical conductivity measured experimentally would be lower than that predicted by the model.

However, the model applied to the VAR (black dashed line) overestimates its effective electrical conductivity and that measured

<figure><img src="image_17.png" /><figcaption>Fig. 11. Evolution of the dimensionless electrical conductivity as a function of the volume fraction of Cr as predicted by different theoretical models. The experimental measurements are reported with a blue square and green star symbol for the Cu-25Cr VAR and EB-PBF respectively.</figcaption></figure>

experimentally (blue square in Fig. 11). The effect of elements retained in solid solution in the Cu matrix was investigated by deliberately reducing the electrical conductivity of Cu. Interestingly, by reducing the electrical conductivity of Cu by 10% (-10%$\sigma_{Cu}$), the model shows a good agreement with the experimental value measured in the VAR composite. These results suggest that the effective electrical conductivity in Cu-25Cr composites is mainly determined by the conductivity of the Cu matrix. This is consistent with the ratio of the electrical conductivity of Cr and Cu ($\sigma_{Cr}/\sigma_{Cu}$), which is equal to 0.13. In other words, the dispersed Cr phase can be considered as an electrical insulator to a first approximation. We concluded that the impurities in the Cu matrix in the VAR explain its lower effective electrical conductivity compared to its EB-PBF counterpart. At first sight, this is consistent with our chemical composition measurements, shown in Table 1 and Table 4, where the Cu-25Cr VAR composite has higher Fe, Al and Si contents than the Cu-25Cr EB-PBF composite. The presence of Cr atoms in the Cu solid solution would also lead to a reduction of the conductivity of the matrix. However, more advanced local chemical composition techniques such as atom probe tomography would be required to verify which elements are indeed retained in solid solution in the Cu matrix.

### 4.3.3. Thermal conductivity

Let us now discuss the mechanisms governing the effective thermal conductivity of Cu-Cr composites using Torquato’s theoretical model. Assuming the thermal conductivities of pure metals ($k_{Cu} = 383$ W.m$^{-1}$, K$^{-1}$ and $k_{Cr} = 89$ W.m$^{-1}$,K$^{-1}$ at 200°C), the predicted dimensionless effective thermal conductivity of the Cu-25Cr EB-PBF (continuous black line) is significantly overestimated (0.72), while the experimental value is 0.55 (green star in Fig. 12a). The introduction of an interfacial thermal resistance using Eq. (10) from [89] reduces the predicted values and a relatively good agreement with the experiments is now found when the dimensionless parameter reflecting the interfacial resistance $R = 0.6$, see the red curves with square symbols in Fig. 12b.

For the VAR material there is also a large difference between the predicted dimensionless effective thermal conductivity (0.70) and the experimental dimensionless effective thermal conductivity (0.58), see Fig. 12a. We first artificially reduced the thermal conductivity of the Cu phase by 10% (-10%$k_{Cu}$), as we did for the electrical conductivity, to account for the presence of elements in the Cu matrix of the VAR, see the black dotted lines in Fig. 12a. The discrepancy between model and experiment is reduced, but the model still overestimates the effective thermal conductivity of the VAR composite. Finally, in addition to the 10% reduction in the thermal conductivity of the Cu matrix, we also introduced an interfacial thermal resistance, but this time $R = 0.1$. This is six times less than the dimensionless interfacial resistance found in the EB-PBF case and in agreement with the much lower density of interfaces in the VAR. The combination of the detrimental effects of elements in solid solution in the Cu matrix on the thermal conductivity of the Cu matrix and the introduction of an interfacial thermal resistance gives a good agreement between model and experiment, see the dashed red curve in Fig. 12b. These results highlight the key role of interfacial thermal resistance in predicting thermal conductivity.

The lower impurity content in the Cu matrix of the EB-PBF sample compared to the Cu matrix in the VAR would be expected to result in improved thermal and electrical conductivity. However, this is not what we found experimentally. The insights gained from the model suggests that the presence of interfacial thermal resistance in the EB-PBF-Cu-25Cr composite contributes to a reduction in its thermal conductivity, offsetting the improvement in thermal conductivity due to a lower level of impurities in the Cu matrix. This is consistent with the ratio of the thermal conductivity of Cr and Cu ($k_{Cr}/k_{Cu}$)$_{200°C}$, which is equal to 0.25, indicating that the Cr phases contribute more significantly to the effective thermal conductivity than the effective electrical conductivity.
<figure><img src="image_18.png" /><figcaption>**Fig. 12.** Evolution of the dimensionless thermal conductivity as a function of the volume fraction of Cr as predicted by different theoretical models. The experimental measurements are reported with a blue square and green star symbol for the Cu-25Cr VAR and EB-PBF respectively.</figcaption></figure>

## 5. Conclusion

The main conclusions of the present study can be summarized as follows.

* Cu-25Cr dense samples (relative density > 99.9%) with a rather homogeneous microstructure have been successfully produced by EB-PBF from pure Cu and Cr powder blends.

* The microstructure of EB-PBF Cu-25Cr results from an out-of-equilibrium mechanism, namely a metastable LLPS. The micro-structure resulting from this LLPS is significantly refined (globular micron-sized Cr particles) compared to the dendritic (20 µm) Cr-phase observed in VAR composites. The Cu matrix grains show a columnar morphology with their long axis aligned with the build direction.

* The microstructure is thermally stable during the EB-PBF printing process since no significant changes in microstructure and hardness is observed along the build direction.

* The mechanical strength (yield strength, UTS, and hardness) of the EB-PBF Cu-25Cr microstructure are significantly increased (YS$_{0.2\%}$ = 210 MPa, UTS = 450 MPa, HV1 = 116) compared to its VAR (YS$_{0.2\%}$ = 155 MPa, UTS = 370 MPa, HV5 = 85) counterpart. This increase in strength is mainly attributed to the significant decrease of the mean free path of dislocation in the Cu phase due to the high density of Cu/Cr interfaces created by leveraging the metastable miscibility gap.

* The as-printed EB-PBF Cu-25Cr effective electrical conductivity (37–38 MS.m⁻¹) is higher compared to the conventional Cu-25Cr VAR (33 MS.m⁻¹) composites. The high conductivity of the Cu matrix due to the absence of impurities in solid solution is responsible for the increased effective electrical conductivity of the EB-PBF as-printed material. The higher density of Cu/Cr interfaces in the EB-PBF case does not affect the effective electrical conductivity because of the relatively low electrical conductivity of Cr compared to that of the Cu matrix. Cu-matrix governs the effective electrical conductivity.

* The Cu-25Cr EB-PBF effective thermal conductivity is nearly equivalent to the Cu-25Cr VAR (229 W.m⁻¹.K⁻¹) effective property. Here, the reduction of impurities in solid solution is counterbalanced by the increase in the density of Cu/Cr interfaces due to the refined microstructure, and the non-negligible contribution of Cr to the effective thermal conductivity compared to its contribution to the electrical conductivity. This highlights the key role of the Cu/Cr interfaces for the thermal conductivity.

Finally, it is worth mentioning that the control of the scanning strategy can be an interesting way to tailor the microstructure of Cu-Cr alloys. From the present results, it appears relatively straightforward to produce site-specific microstructures with regions where the LLPS would be exploited and others where we would deliberately only melt the Cu matrix to retain larger Cr inclusions.

## CRediT authorship contribution statement

**Lucas Varoto:** Writing – review & editing, Visualization, Validation, Investigation, Formal analysis, Data curation, Conceptualization. **Elodie Courtois:** Writing – review & editing, Validation, Methodology, Investigation, Data curation. **Mélanie Prost:** Investigation, Data curation. **Pierre Lhuissier:** Writing – review & editing, Validation, Supervision, Conceptualization. **Jean-Jacques Blandin:** Writing – review & editing, Validation, Supervision, Methodology. **Sophie Roure:** Writing – review & editing, Validation, Supervision, Project administration. **Anthony Papillon:** Writing – review & editing, Validation, Supervision, Project administration. **Mélissa Chosson:** Validation, Investigation. **Guilhem Martin:** Writing – review & editing, Writing – original draft, Validation, Supervision, Project administration, Methodology, Investigation, Conceptualization.

## 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

Schneider Electric Industries and the Association Nationale de la Recherche Technologique (ANRT) are gratefully acknowledged for the financial support of this work through the grant CIFRE 2021/1619. Mélanie Prost and Guilhem Martin acknowledges the financial support from the ANR through the research program PEPR - Project DIAMS:
"Design by artificial Intelligence and high throughput data of advanced Alloys and innovative Metallurgical concepts for Structural applications". The authors would like to thank the Centre of Excellence of Multifunctional Architectured Materials "CEMAM" noANR-10-LABX- 44-01 for funding the characterization platform of Grenoble INP.

# Appendix A. Supporting information

Supplementary data associated with this article can be found in the online version at doi:10.1016/j.addma.2025.104869.

## Data availability

Data will be made available on request.

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