# Phase formation prediction in magnetron sputtered Cu(Ti)Zn thin films: Numerical vs experimental approaches

Dimitri Boivin, Andrea Jagodar, Pascal Brault, Thomas Vaubois, Edern Menou, Barthélemy Aspe, Amaël Caillard, Pascal Andreazza, Marjorie Cavarroc-Weimer, Anne-Lise Thomann

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Dimitri Boivin, Andrea Jagodar, Pascal Brault, Thomas Vaubois, Edern Menou, et al. Phase formation prediction in magnetron sputtered Cu(Ti)Zn thin films: Numerical vs experimental approaches. Journal of Applied Physics, 2025, 137 (14), pp.145301. 10.1063/5.0253997. hal-05025837

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# Phase formation prediction in magnetron sputtered Cu(Ti)Zn thin films: Numerical vs experimental approaches

Cite as: J. Appl. Phys. **137**, 145301 (2025); doi: **10.1063/5.0253997**

Submitted: 20 December 2024 · Accepted: 21 March 2025 ·

Published Online: 8 April 2025

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Dimitri Boivin,<fnref n="1" />,<fnref n="2" /> ID Andrea Jagodar,<fnref n="1" /> ID Pascal Brault,<fnref n="1" />,<fnref n="3" />,a) ID Thomas Vaubois,<fnref n="4" /> ID Edern Menou,<fnref n="4" /> ID Barthélemy Aspe,<fnref n="1" /> ID Amaël Caillard,<fnref n="1" /> ID Pascal Andreazza,<fnref n="5" /> ID Marjorie Cavarroc-Weimer,<fnref n="4" />,b) ID and Anne-Lise Thomann<fnref n="1" />,c) ID

## AFFILIATIONS

## ABSTRACT

In this work, we evaluated the ability of three numerical methods to predict the phase formation in Cu–Zn binary and Cu–Ti–Zn ternary alloy thin films deposited by DC-magnetron sputter deposition. Molecular dynamics (MD) simulations were carried out to simulate the growth of the alloy film and study the organization at the atomic level. A Machine Learning (ML) approach trained with a recently published bulk HEA (high-entropy alloy) database was used to determine the presence of an amorphous phase, solid solutions, or/and intermetallics. Finally, CALPHAD (CALculation of PHAse Diagrams) thermodynamic modeling allows one to simulate the phase diagrams. Crystalline phases formed in experimental films were investigated by grazing incidence x-ray diffraction (GIXRD). Comparison with CALPHAD results highlights that for pure Ti or binary Cu–Zn films, the thermodynamically stable phases are formed in the films. Less agreement was found at low or high percentage of Ti introduced in the Cu–Zn system, and drastic differences were observed for elemental compositions close to equimolarity. In those cases, the out of equilibrium nature of the magnetron sputtering deposition technique is evidenced. The very limited agreement between the GIXRD and ML approach is explained by the available database, which is exclusively based on bulk alloys. Elemental composition of the alloy does not itself determine the stabilized phases: elaboration techniques are to be taken into account too. MD simulations bring information on a possible segregation of the Zn element to the surface and grain boundaries. A very good agreement is evidenced between the calculated and experimental diffraction patterns.

© 2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0253997

## I. INTRODUCTION

Medium-Entropy Alloys (MEAs), High-Entropy Alloys (HEAs), and Complex Concentrated Alloys (CCAs) have attracted interest in the last few decades for their original properties related to their elemental composition and structural characteristics. Several review papers on HEA bulk or coatings summarize the

numerous studies published and highlight their outstanding association of properties.<fnref n="1" />⁻<fnref n="3" /> In more recent works, antimicrobial HEA thin films have been synthesized by including active chemical elements, such as silver, copper, zinc, etc., in the alloy elemental composition.<fnref n="4" />,<fnref n="5" /> The structure and phases of thin films control their antimicrobial characteristics. For instance, studies have shown the

<footnote n="1">¹GREMI, UMR7344, CNRS-Université d'Orléans, 14 rue d'Issoudun, F-45067 Orléans, France</footnote>

<footnote n="2">²Nantes Université, CNRS, Institut des Matériaux de Nantes Jean Rouxel, IMN, F-44000 Nantes, France</footnote>

<footnote n="3">³MS4ALL, 1 avenue du Champ de Mars, F-45100 Orléans, France</footnote>

<footnote n="4">⁴Safran Tech, rue des jeunes bois, Châteaufort, CS 80112, F-78772 Magny-les-Hameaux, France</footnote>

<footnote n="5">⁵ICMN, UMR7374, CNRS-Université d'Orléans, 1 Rue de la Ferollerie, F-45100 Orléans, France</footnote>

<footnote>a) Author to whom correspondence should be addressed: pascal.brault@univ-orleans.fr</footnote>

<footnote>b) Electronic mail: marjorie.cavarroc@safrangroup.com</footnote>

<footnote>c) Electronic mail: anne-lise.thomann@univ-orleans.fr</footnote>
antiviral properties, especially on the SARS-CoV-2 virus, of binary and ternary alloys from the Cu-Zn, Cu-Ni, Cu-Ti, Cu-Ni-Zn, etc., systems.⁶,⁷ In 2021, Mostaghimi *et al.* tested the effectiveness of Cu-Ni-Zn coatings in a hospital environment (on door handles, armrests, etc.) and proved that it significantly increased the duration of antibacterial activity while requiring less maintenance.⁸ We can note that in his review, V. Govind mentions the strategy, which consists of using families of more complex alloys, such as HEAs, in order to combine numerous functional properties.⁶ Such an approach is also pursued by Li *et al.*, with a Cu-based HEA: CuFeCrCoNi.⁵ Because of the huge number of elemental compositions to be investigated in these multi-element materials, an exploration conducted purely experimentally would be excessively expensive and time-consuming. Many works have, thus, been devoted to find key physical or thermodynamic parameters, or define numerical approaches, which allow predicting the material structure [mainly Body Centered Cubic (BCC), Face Centered Cubic (FCC), or Hexagonal Close-Packed (HCP) solid solutions and intermetallics] and their degree of crystallinity as a function of the elemental composition. Thermodynamic calculations have often been used to determine the stable phases that should form at equilibrium depending on the elemental composition and the operating temperature. In addition, multiple criteria have been defined, including mixing enthalpy and entropy, elemental atomic size mismatch, electronegativity mismatch, etc., to better predict the stabilized structure and thus the final properties.⁹⁻¹¹ More recently, the use of data science tools from the field of artificial intelligence, and, in particular, the construction of machine-learned, data-based models, made possible to establish relationships between elemental compositions and physicochemical properties to design new bulk HEAs with tailored properties.¹² The ability of data-based models, first principles calculations, and calculations of phase diagrams to solve the complex issue of designing optimal multi-element alloys for given applications has been discussed.⁵,¹³

The aim of our work is to design and produce complex metallic alloy thin films by magnetron sputter deposition dedicated to antimicrobial applications. Since a degree of bacteria resistance has been reported for silver,¹⁴ copper was chosen in association to zinc to ensure bactericidal and antiviral properties by “release killing.”¹⁵ Following a methodology based on the progressive increase of the alloy complexity, we have decided to start from the Cu-Zn system and study the evolution of the film structural and morphological properties when other elements, each expected to bring complementary properties (resistance to abrasion, hardness, etc.), are added. In this paper, we report on the Cu-Zn and Cu-Zn-Ti systems.

Our approach is based on the coupling of three numerical methods of a phase formation prediction that will be compared to experimental data. In the first step, the CALPHAD (CALculation of PHAse Diagrams¹⁶) method will be employed to identify the stability domains of the various crystallographic phases based on the alloy elemental composition and on the deposition temperature. CALPHAD predictions will be compared to those of a machine learning (ML) model trained on bibliographic data available for bulk HEAs. In addition, since conditions of film deposition by magnetron sputtering are out of equilibrium compared to classical metallurgy, simulations by molecular dynamics will be carried out. In previous works, we have shown that these calculations allow the

study of the film growth in conditions close to that of magnetron sputter experiments by using the energy distribution functions of each species interacting with the substrate.¹⁷⁻¹⁹ For instance, phase formation has been successfully anticipated in the case of a HEA thin-film growth.²⁰,²¹

## II. METHODS

### A. Thin-film synthesis and physico-chemical characterization

The thin films were prepared in a stainless steel sputtering system made of a deposition chamber and an airlock. The system is equipped with three balanced 4-in. magnetrons furnished with a titanium target (99.99% purity), a copper target (99.99% purity), and a zinc target (99.99% purity). An argon flow rate is kept constant at 10 sccm and pressure at 0.5 Pa. Base pressure in the chamber is $10^{-6}$ mbar or lower as measured by a Pfeiffer Compact Full-Range pressure gauge. Pressure during deposition is measured by a Pfeiffer Baratron gauge and is controlled through a throttle valve between the chamber and the turbopump. A rotating substrate holder is located 11.5 cm away from the targets, facing the magnetrons, 30° tilted. All depositions were performed at room temperature.

For atomic percentages of Ti ranging from 3% to 24%, power values were set to 200 and 160 W on the copper and zinc targets, respectively, while the power applied to the titanium target was varied from 70 to 400 W. Above these Ti at. %, the power of the titanium target was set at 400 W, and the power of copper and zinc targets was reduced to values between 100–50 and 80–40 W, respectively. Thin films were deposited on single-crystal silicon substrates [p-doped Si(100)] cleaned in an ultrasonic bath, 10 min in isopropanol and 10 min in ethanol. All depositions were performed for 10 min leading to film thicknesses comprised between 400 and 900 nm depending on the deposition parameters.

The thin-film crystallographic structure was determined by Grazing Incidence X-Ray Diffraction (GIXRD) using an AXS Bruker D8 Advance diffractometer with the Cu Kα radiation ($\lambda$ = 0.154 06 nm). XRD measurements were performed between 20° and 80° at a 1° grazing incidence. Thickness and morphology were determined using a Zeiss Supra 40 Field Emission Gun-Scanning Electron Microscopy (FEG-SEM) operating at 3 kV. In addition, Energy X-ray Dispersive Spectroscopy (EDS) is carried out on 200 × 200 µm surface areas, using Ti 4.512 and 0.452 keV rays, to estimate the thin-film mean elemental composition. EDS results were compared to Rutherford Backscattering Spectroscopy (RBS) results measurements for four samples. RBS, performed at the CEMHTI²² laboratory on a Pelletron accelerator with 2 MeV alpha particles (with a 166° scattering angle), allowed in-depth elemental composition homogeneity assessment. RBS analysis was performed on thinner thin films than those used for EDS, in order to properly quantify only Ti content, as both Zn and Cu feature close atomic weights. Spectra simulations were carried out with the SIMNRA software.²³

### B. Molecular dynamics simulations

Molecular Dynamics (MD) simulations based on the Newton equations of motion were implemented to describe the growth of alloy thin films at the atomic scale. The Embedded Atom Method
(EAM) is chosen for describing Cu, Ti, and Zn interactions.²⁴ Cross interactions make use of a Johnson mixing rule.²⁵,²⁶ The silicon substrate atoms interact by Tersoff potential,²⁷ while Cu, Zn, and Ti interactions with Si are described using the Lennard-Jones potential²⁸,²⁹ with the Lorentz-Berthelot mixing rule.

The simulation box is composed of a silicon substrate with sizes 7.6 × 7.6 × 4.35 nm³ for Cu-Zn films and 5.43 × 5.43 × 4.35 nm³ for Cu-Ti-Zn films. Both sizes gave identical results in terms of phases and diffraction patterns for Cu-Zn. The first two bottom layers of Si atoms are fixed for preventing substrate motion upon impact of depositing atoms. The remaining substrate atoms are subjected to Langevin thermostat at 300 K with 100 fs damping time to properly dissipate the excess energy transferred by the fast-depositing atoms. A flux of ten atoms being either Cu, Zn, and Ti was periodically released toward the surface every 40 000 time steps. The relative content of Cu, Zn, and Ti atoms in the deposition flux is adapted in order to correspond to that of experimentally obtained film chemistry data. The time step is 0.5 fs. The atoms were randomly placed at a height of 1.5 nm above the substrate. This height was increased by steps of 0.5 nm every 40 000 time steps in order to stay noninteracting with the growing film.

The initial velocities of silicon atoms were randomly chosen in a thermal distribution at 300 K. In order to best imitate the experiments, the initial velocities of Cu, Ti, and Zn were randomly chosen in a distribution matching the deposition conditions, following a procedure described previously.¹⁷,¹⁹,³⁰ The sputtered atom energy distribution was evaluated using the SRIM software³¹ with sputter argon ion energy corresponding to the experimental target bias voltage. This SRIM-deduced energy distribution function was then modified by the collision encountered with the gas atoms during the transport from target to substrate. For each targeted elemental composition, 10 000 atoms were released toward the surface. The total elapsed simulation time for each run was 20 ns. Simulations were carried out using the LAMMPS software.³²,³³ X-ray diffraction patterns were calculated using the Debye method included in LAMMPS.³⁴ Snapshots were plotted using OVITO software.³⁵ The crystalline phases of the simulated films were identified using the polyhedral template matching method implemented in OVITO.

### C. Machine learning

A machine learning classifier model for a structure prediction was trained based on recently published data related to bulk HEAs.³⁶ It uses gradient boosting as implemented in the xgboost R library.³⁷ Since the database contains alloys of Cu, Ti, and Zn, it provides some experimental basis to the model. Taking alloy elemental composition (element nature and concentration) as input, the model predicts, similarly to the work of Lee *et al.*,³⁶ seven structure classes: a single solid solution (BCC, FCC, or HCP), intermetallics, mix of BCC/FCC solid solutions, multiple phases (mixture of one or several solid solutions and one or several intermetallics), or amorphous phase(s). A precision similar to that of the work of Lee *et al.*³⁶ was attained (see its supplementary Table 3), with a testing accuracy of approximately 84% (i.e., 84% of structures correctly classified).

### D. Calculation of phase diagrams

CALPHAD is a thermodynamic modeling method based on Gibbs energy calculations to simulate phase diagrams.¹⁶ In this work, thermodynamic calculations were performed in the CALPHAD framework using the TCHEA6 database and version 2023a of the Thermo-Calc software.³⁸ These calculations enabled us to identify the phases that are expected stable in the ternary system Cu-Ti-Zn under equilibrium conditions.

## III. RESULTS

### A. Experimental results—Thin-film elemental composition, morphology, and microstructure

Experimental thin-film elemental compositions, as determined using EDS and RBS, are reported in Table I. The elemental composition is a crucial parameter of complex metallic alloys driving the in-use properties, including the antibacterial activity as shown in the literature.³⁹⁻⁴¹ Similarly, it has been found to play an important role on the mechanical and physicochemical properties, such as the hardness or the corrosion resistance.⁴⁰ By EDS, as shown in Table I, we obtained the mean elemental composition of the deposited films. However, since no in-depth resolution is accessible by this method, we used RBS measurements on three elemental compositions. It was, thus, necessary to deposit thinner films, which has been done for 3, 10, and 24 at. % of Ti. With RBS analysis, it is possible to discriminate elements in function of their weight. Zn and Cu being too close in the periodic table, their respective signals cannot be separated, but the titanium peak is exploitable, and we obtained its atomic percentage with a precision of about 2 at. %. It is shown in Table I that for the three samples, the results are in good agreement with the EDS measurements within 2% error. Moreover, from RBS results, we checked that the alloy elemental composition is constant over the entire thickness of the films. From these cross-analyses, we deduce that confidence can be established in the EDS measurements.

An SEM surface and cross-sectional images are shown in Fig. 1, and the corresponding samples described in Table I SEM images for 37 at. % Ti contents are very close to those at 24 at. % Ti, and thus, a 37Ti image is not shown for clarity. Surface images

<table><caption>TABLE I. Elemental composition at. % of the binary (B) and ternary (xTi) coatings measured by EDS and RBS. The ratio Cu/Cu+Zn calculated from EDS results is also given.</caption><thead><tr><th rowspan="2">Sample</th><th colspan="3">EDS</th><th colspan="3">RBS</th><th>Cu</th></tr><tr><th>Cu</th><th>Ti</th><th>Zn</th><th>Cu</th><th>Ti</th><th>Zn</th><th>Cu + Zn</th></tr></thead><tbody><tr><td>B1</td><td>41</td><td>0</td><td>59</td><td>...</td><td>...</td><td>...</td><td>41%</td></tr><tr><td>B2</td><td>61</td><td>0</td><td>39</td><td>...</td><td>...</td><td>...</td><td>61%</td></tr><tr><td>3Ti</td><td>41</td><td>3</td><td>56</td><td>41</td><td>3</td><td>56</td><td>42%</td></tr><tr><td>10Ti</td><td>46</td><td>10</td><td>44</td><td>44</td><td>9</td><td>47</td><td>51%</td></tr><tr><td>24Ti</td><td>38</td><td>24</td><td>38</td><td>41</td><td>20</td><td>39</td><td>50%</td></tr><tr><td>37Ti</td><td>35</td><td>37</td><td>28</td><td>...</td><td>...</td><td>...</td><td>56%</td></tr><tr><td>42Ti</td><td>33</td><td>42</td><td>25</td><td>...</td><td>...</td><td>...</td><td>57%</td></tr><tr><td>76Ti</td><td>13</td><td>76</td><td>11</td><td>...</td><td>...</td><td>...</td><td>54%</td></tr></tbody></table>
<figure><img src="image_5.png" /><figcaption>**FIG. 1.** SEM images of the plan views and cross sections of (a) the binary (B1 and B2) and (b) ternary films (3Ti, 10Ti, 24Ti, 42Ti, and 76Ti).</figcaption></figure>

of Cu-Zn binary alloys (left side) present two topographies. The Cu₄₁Zn₅₉ alloy film (B1) features angular and faceted grains that are larger 100-200 nm than those of the Cu₆₁Zn₃₉ alloy film (B2) (smaller than 40 nm). The corresponding cross-sectional image of B1 reveals a columnar structure typical of magnetron sputtered thin films, as widely reported in the literature.⁴,⁵,⁴³ The Cu₆₁Zn₃₉ alloy (B2) cross-sectional morphology presents a very different structure, exhibiting three layers. The first layer from the substrate is about 100 nm thick and has a columnar structure, as B1, with thinner columns. The second layer is about 800 nm thick and shows a porous and foam-like structure (nanocorals).⁴⁴ The top layer is relatively dense and is about 100 nm thick.

With 3 at. % Ti addition (3Ti), the sharp faceted structure of B1 is somewhat preserved, while a disordered cross-sectional columnar structure is visible. Higher titanium contents (10Ti, 24Ti, and 42Ti) lead to the degradation of the crystallinity as the grain morphology becomes rounder and the grain size decreases. The columnar structure disappearance and the denser structures evidenced by cross-sectional views confirm progressive amorphization. The Cu₁₃Ti₇₆Zn₁₁ (Ti76) alloy film surface features irregular patterns. The cross-sectional image exhibits a mix of columnar and vein-like structure, of around 1.4 µm thick. The structure seems to be finer when moving toward the film surface.

X-ray diffraction patterns for binary and ternary films, as well as that of a pure Ti film, are shown in Fig. 2. The B1 film (Cu₄₁Zn₅₉ alloy) contains one single phase as all the observed peaks match those of the γ-Cu₅Zn₈ phase (BCC, JCPDS No. 01-071-0397⁴⁵). Please note that further call to ICCD/JCPDS/COD sheets will refer to Kabekkodu et al.⁴⁵) The diffraction pattern of the B2 film (Cu₆₁Zn₃₉ alloy) matches the peaks of a Zn-enriched

<figure><img src="image_6.png" /><figcaption>**FIG. 2.** GIXRD experimental patterns of the thin films. Note the log scale used for a better overview of the general shape of the all diffractograms. Positions of some expected peaks are indicated below the GIXRD patterns.</figcaption></figure>

α-Cu phase (FCC, JCPDS No. 00-050-1333) with a elemental composition of Cu₆₄Zn₃₆. This structure is a face-centered cubic phase with space group Fm3-m. However, due to their close atomic radii, the lattice parameter of the α-Cu phase does not vary much with zinc additions. Therefore, the presence of other phases, such as a solid solution of Zn, cannot be ruled out.

The diffraction pattern of the 3Ti film is similar to the B1 film, with a slight shift of diffraction peak angles (approximately -0.5°), indicating a variation in lattice parameters probably caused by solubility of titanium in the γ-Cu₅Zn₈ and the disappearance of several peaks (between 45 and 60 and between 70° and 75°). The widening of the peak and its asymmetry can also be explained by the formation of another phase, such as the β-CuZn phase (BCC, JCPDS No. 04-003-4270), in which three peaks lie at the same position as the main ones of the γ-Cu₅Zn₈.

The diffractogram of the 10Ti film displays three main very broad peaks: an asymmetrical peak at 41.6° and two wide peaks between 70 and 80°. The asymmetry of the peak located around 41° tends to indicate that more than one phase is present. The positions could correspond to shifted main peaks of α-Cu (Cu₆₄Zn₃₆) and γ-Cu₅Zn₈ phases or even of the β'-CuZn. Note that the small and thin peak at 52.6°, which appears randomly on the patterns, is attributed to an artifact of measurements. The general shape of the diffraction pattern points out a loss of crystallinity.

This trend is confirmed on the 24Ti and 42Ti films, in which patterns exhibit a very broad peak at 42°, typical of an amorphous or nanocrystalline phase. This is in agreement with the SEM observations where a dense and smooth film is visible.

However, the 76Ti film is entirely crystalline with a pattern indicating the presence of at least two phases. By comparing to the ICCD database, the presence of a mixture of α-Ti (HCP, COD No. 9016190) and CuTi₃ (COD No. 15246555) phases is suspected.
The width of the most intense peak, located below 40°, suggests a combination of contributions from oriented peaks (002) at 38.42° and (101) at 40.17° from α-Ti, but also from the most intense CuTi₃ oriented peak (111) at 39.6°. The peak at 43.49° corresponds to the (200)-oriented CuTi₃ peak. The other peaks from the diagram also correspond to the combination of contributions from the α-Ti and CuTi₃ phases.

The pure titanium thin-film diffractogram indicates that the main present phase is the α-Ti phase.

## B. Numerical method results

### 1. Molecular dynamics simulations of the film growth

Figure 3 displays the snapshots after 20 ns deposition time for all investigated elemental compositions in the Cu–Ti–Zn system. Displayed elemental compositions match the experimental film elemental compositions. For the two binary alloys Cu₄₀Zn₆₀ and Cu₆₂Zn₃₈, Cu and Zn are clearly segregated into different, more or less tortuous, regions with their respective stable crystalline structure, i.e., FCC and HCP, respectively, at ambient temperatures.

In alloys Cu₄₂Ti₃Zn₅₅ and Cu₄₈Ti₉Zn₄₃, Zn remains segregated in an HCP phase, while a disordered Ti-enriched FCC Cu phase develops. At 9% Ti, the FCC/HCP phase ratio is significantly reduced as Cu atoms moves in an HCP structure. A low level of an FCC Cu phase is observed corresponding to nearly isolated atoms. This is a limitation of a polyhedral template matching method that only takes into account the first neighbor environment of atoms. A change of behavior occurs for higher Ti additions with a transition between 10% and 24% Ti. The FCC phase changes to either a Cu-enriched Ti BCC phase or a CuTi BCC intermetallic compound (also determined on isolated atoms), whereas the BCC phase was not present for low % Ti. It should also be noted that numerous Cu atoms are then in an HCP position. The predominant phase remains HCP, and the secondary one (also including isolated atoms) turns from FCC to BCC.

For deeper insight into the crystallographic structure, the XRD patterns are simulated using the Debye method included in the LAMMPS software. Figure 4 displays the XRD patterns of the films presented in Fig. 3. Binary film simulated XRD patterns are consistent with a Zn-enriched α-Cu (Cu₆₄Zn₃₆) ICCD sheet. This could appear counterintuitive since MD suggests Cu and Zn segregation. This is attributed to the similarity of atomic radii between copper and zinc, leading to diffraction of a zinc-enriched copper solid solution similar to that of a mixture of two distinct copper and zinc solid solutions. Increasing amounts of titanium trigger phase transformations from HCP+FCC for low Ti contents to HCP+BCC and almost only BCC at the highest Ti content as shown in Fig. 3. MD simulations predict the disappearance of the 42.3° and 49.3° peaks and the formation of a 39.2° peak matching the BCC β-Ti phase (Im3-m symmetry, sheet no. mp-73 from the Materials Project database<sup>46,47</sup>) for the 76Ti alloy. The comparison between experimental and simulated patterns is discussed further below.

### 2. Structure prediction with machine learning

A structure diagram of the Cu–Ti–Zn system, computed using the machine learning model, highlights the existence of a solid

<figure><img src="image_7.png" /><figcaption>FIG. 3. Results from MD simulations. Color coding: brown Cu, light gray Ti, dark gray Zn, light brown Si substrate. First and third rows display the snapshot of each film, in which elemental composition is shown at the top Cu<sub>x</sub>(Ti<sub>y</sub>)Zn<sub>z</sub>. Second and fourth rows display colored regions corresponding to phase structures [green FCC, blue BCC, red HCP, light gray unattributed (disordered) structure, light blue diamond phase of the silicon substrate]. The crystalline phase ratios are displayed below the corresponding snapshots. The balance corresponds to disordered regions.</figcaption></figure>

solution or multiphase domains, as illustrated in Fig. 5. The diagram is built through a complete mapping of Cu–Ti, Cu–Zn, Ti–Zn, and Cu–Ti–Zn alloying systems with each element content ranging from 0% to 100% with a variation step of 2.5%, using data on bulk HEAs. A projection of the experimental elemental compositions on the diagram predicts the formation of a single FCC phase for Ti contents ranging from 10 to 42 at. %. Elemental composition of 3Ti and B1 samples lies in a domain where a mixture of
<figure><img src="image_8.png" /><figcaption>**FIG. 4.** Simulated x-ray patterns of the MD films reported in Fig. 3, superimposed on the corresponding experimental GIXRD patterns of Fig. 2.</figcaption></figure>

solid solutions and intermetallics (MP) is expected, whereas elemental composition of B2 and 76Ti is at the frontier between a single FCC or BCC phase domain, respectively, and a multiphase domain. No elemental composition lies in the very limited amorphous domain (AM).

### 3. Phase prediction with CALPHAD

The calculated binary phase diagram, along with the thin film elemental compositions obtained in this work, is presented in Fig. 6. The Cu–Zn diagram is in good agreement with the published experimental data and the most recent CALPHAD assessments.48–52 Zn exhibits large solubility in the FCC copper solid solution, up to 36 at. % at 400°, while the HCP zinc solid solution can only accommodate up to 2% Cu. Several intermetallic phases are reported on the phase diagram, respectively, $\beta$ (BCC), $\gamma$-Cu$_5$Zn$_8$ (FCC), $\varepsilon$ (HCP), and $\delta$ (BCC). Below 450°, a second order phase transition occurs in the $\beta$ phase leading to the formation of the ordered $\beta'$ (BCC) phase (prototype: CsCl).

<figure><img src="image_9.png" /><figcaption>**FIG. 5.** Prediction of phase domains using the machine learning approach described in Sec. II C for the binary and ternary alloys. Blue dots correspond to experimental elemental compositions. BCC and FCC labels define domains where a single solid solution of the said structure is expected, while MP and AM labels, respectively, define the domain of mixed phase formation or amorphous phase formation.</figcaption></figure>

The 300°C isothermal section of the ternary Cu–Ti–Zn system is presented in Fig. 7 along with the deposited elemental compositions. These elemental compositions are located in different phase regions; thus, we expect the coatings to display different phase equilibria. We can see that many of them contain a varying

<figure><img src="image_10.png" /><figcaption>**FIG. 6.** Copper–zinc phase diagram calculated using the TCHEA6 database and the Thermo-Calc software. Vertical dotted lines represent the experimental elemental compositions (B1 and B2) reached in this work.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>FIG. 7. Isothermal section at 300 °C of the Cu–Ti–Zn phase diagram calculated using the TCHEA6 database and the Thermo-Calc software. The black dots indicate the coating elemental compositions reached in this work.</figcaption></figure>

amount of the β' phase (BCC) in equilibrium with Ti–Cu binary phases. For the Ti-richest coating, thermodynamic calculations predict an equilibrium between pure hexagonal titanium and a Ti₂ (Cu,Zn) compound. It is interesting to note the large solubility of titanium in the β' phase, as the stability of this phase goes from the Cu–Zn binary section up to the Cu–Ti binary section.

# IV. DISCUSSION

## A. CuZn

From experimental GIXRD (Fig. 2), it is seen that the structure of a Cu–Zn alloy greatly depends on the elemental composition close to the equimolarity. In the limited range of power used to deposit B1 and B2 samples, we can state that the energetic conditions at the substrate are similar and that the formation of the Zn-enriched α-Cu (FCC) or γ-Cu₅Zn₈ (BCC) phase is only related to the proportion of Cu and Zn in the film. The appearance of the γ phase (BCC) for B1 at the corresponding elemental composition range is expected from thermodynamics (Fig. 6) at relatively high temperature (600 °C), but is not predicted from MD simulations, operated at room temperature. The XRD pattern calculated from MD (Fig. 4) highlights a FCC phase, whose peaks are shifted from the α-Cu phase due to the Zn enrichment, and is in complete accordance with the ICCD file of a Cu₆₄Zn₃₆ alloy. The same phase is predicted by MD for the B2 film, which is, in this case, in quite good agreement with experimental GIXRD [B2 lies close to the frontier between pure α-Cu and coexistence of α-Cu and β'-CuZn (BCC) phase domains] and machine learning (close to a FCC solid solution domain). These contradictory data for a B1 film suggest that the interaction potential used in MD is unable to predict the formation of this particular γ-Cu₅Zn₈ phase. EAM potentials are not parameterized to form this structure. Thus, in the present simulation conditions, MD will only be valid when the alloy elemental composition leads to the stabilization of the Zn-enriched α-Cu (FCC) phase.

From the above results, predictions from CALPHAD appear in rather good agreement with experimental data. This would suggest that the energetic conditions of deposition, in our case, enable the formation of equilibrium phases. It is interesting to note that the machine learning model also shows its limitation for the B1 sample, predicting the presence of multiple phases where experimental results show a single BCC phase.

## B. CuTiZn thin films

The relative proportion of Cu and Zn is given for all films in Table I to guide the interpretation of the results. Comparison between experimental results and thermodynamic calculations shows a partial agreement for the 3Ti sample (42 at. % of Cu, close to the value in B1) since the presence of the γ-Cu₅Zn₈ phase is predicted and observed. Films with a content of titanium between 10 and 42 at. % clearly lose their crystallinity, and GIXRD results evidence low ordered, nano-sized phases or amorphous domains. This shows that Ti addition disturbs the formation of crystalline phases in the films, whereas for binary alloys (and at very low content of Ti), thermodynamically favorable phases are formed, even in the low energy conditions of magnetron sputter deposition. From 10 to 42 at. % Ti content, the non-equilibrium nature of the magnetron sputter deposition technique, which can be considered a quenching process, is, thus, evidenced. This is the reason for the enhanced glass forming ability usually observed in multielementary alloy thin films deposited by this technique.⁴¹,⁵³,⁵⁴ The machine learning approach predictions anticipate the formation of a FCC solid solution for 24Ti and 42Ti that is not observed experimentally.

For the titanium-richest thin film, the crystalline structure is in agreement with the ML approach (mixed phase domain) and partially matches the CALPHAD predictions, which anticipate the formation of α-Ti + Ti2(Cu,Zn) phases (cf. Table II), in accordance with those evidenced by GIXRD.

## C. Ti thin film

The experimental GIXRD diffractogram shows the presence HCP α-Ti titanium phase (Table II), as expected for magnetron sputtering deposition.⁵⁵,⁵⁶ Both CALPHAD calculations and MD simulation predict the formation of the α-Ti phase, thus in agreement with the present experiments. On the contrary, ML fails in predicting the phase formed in a pure Ti film, as a BCC β-Ti structure is expected. At low temperature, α-Ti is the most stable phase as indicated by CALPHAD, while the β-Ti phase is more common at high temperature as well as film with additional elements.⁵⁶ The limitation of the ML prediction may be related to the fact that the training database is built on binary and ternary alloys, without including pure elements.

## D. Numerical methods vs experiments

All the above results on binary and ternary alloys support that, depending on the alloy elemental composition (complexity of the system), CALPHAD calculations can anticipate the formation of the crystallized phases in sputtered thin films. This point has already been reported by Keuter et al. who states that thin-film phase formation is closer to (at least para-) equilibrium than has
<table><caption>TABLE II. Comparison between phases predicted by machine learning, CALPHAD calculations, molecular dynamics simulations, and experimental determination by GIXRD.</caption><thead><tr><th>Method</th><th>Ti</th><th>B1</th><th>B2</th><th>3Ti</th><th>10Ti</th><th>24Ti</th><th>42Ti</th><th>76Ti</th></tr></thead><tbody><tr><td>GIXRD</td><td>α-Ti<br>HCP</td><td>γ-Cu<sub>5</sub>Zn<sub>8</sub><br>BCC</td><td>α-Cu<br>FCC</td><td>γ-Cu<sub>5</sub>Zn<sub>8</sub><br>BCC</td><td>γ-Cu<sub>5</sub>Zn<sub>8</sub> + β-CuZn<br>FCC + BCC ?</td><td>Amorphous or nano-cryst.<br>Amorphous or nano-cryst.</td><td>α-Cu + Cu<sub>3</sub>Ti<br>HCP + ?</td><td>α-Cu + Cu<sub>3</sub>Ti<br>HCP + ?</td></tr><tr><td>CALPHAD</td><td>α-Ti<br>HCP</td><td>γ-Cu<sub>5</sub>Zn<sub>8</sub><br>BCC</td><td>α-Cu + β'<br>FCC+BCC</td><td>γ-Cu<sub>5</sub>Zn<sub>8</sub> + β'<br>BCC + BCC</td><td>β'<br>BCC</td><td>β' + CuTi<br>BCC + BCT</td><td>α-Ti + Ti<sub>2</sub>(Cu,Zn)<br>HCP + BCT</td><td>α-Ti + Ti<sub>2</sub>(Cu,Zn)<br>HCP + BCT</td></tr><tr><td>ML</td><td>BCC</td><td>MP</td><td>FCC</td><td>MP</td><td></td><td>FCC</td><td>MP</td><td></td></tr><tr><td>MD</td><td>α-Ti<br>HCP</td><td>α-Cu + Zn-HCP</td><td></td><td>Cu(Ti)-FCC+Zn-HCP<br>FCC+HCP</td><td></td><td>Cu(Ti)-HCP+Zn-HCP<br>BCC+HCP</td><td>β-Ti(Cu)<br>BCC</td><td>β-Ti(Cu)<br>BCC</td></tr></tbody></table>

often been assumed.⁵⁷ One of the sources of uncertainty when comparing CALPHAD predictions to experimental results lies in the choice of the temperature of the system. In our case, we decided to use thermodynamic calculations at 300 °C for the ternary alloy. This value was estimated not too far from the experimental conditions, while ensuring accurate predictions. However, as mentioned above, the exact temperature inside the growing film is not known. A difference between the estimated temperature and the real value could partially explain discrepancies between simulations and experimental results. Moreover, one must keep in mind the paramount importance of the databases used to perform CALPHAD calculations. For instance, in their investigation of phase formation and thermal stability of sputtered AlSiTaTiZr high-entropy alloy thin films, Cemin et al. invoke the lack of updated databases for Si containing compounds, which weakens the phase prediction in these systems.⁵⁸ In our case, the ternary system Cu-Ti-Zn is rather well known and the description is well implemented in the TCHEA6 database; therefore, a good quality of predictions can be expected for equilibrated systems.

In the literature, it is shown that when the number of elements rises, predictions by CALPHAD may not be valid anymore for thin films. Cemin et al. systematically found disagreement between experimental results and predictions in their range of elemental compositions for the AlSiTaTiZr alloy.⁵⁸ They explain the formation of a metastable phase by the extremely fast cooling rates reached in magnetron sputter deposition (non-equilibrium nature), in agreement with our conclusion. They infer that phase formation and selection in complex alloy thin films are determined by both thermodynamic and kinetic factors. They also emphasized that despite this conclusion, deeper thermodynamic investigations should continue in the thin-film literature of HEAs. For instance, Chang et al. developed a model based on experimental and theoretical research coupling DFT and CALPHAD calculations in order to take into account atomic diffusion at the surface, which means kinetic processes, and to predict phase formation in thin films of CuW and CuV.

Data obtained with ML (Fig. 5, Table II) only allows identifying the presence of a mixture of phases, an ordered solid solution (BCC or FCC), or an amorphous phase. What can be observed first in Fig. 5 is that 3Ti and 76Ti lie in elemental composition domains where a multiphase system is expected. This is what is evidenced by GIXRD for 76Ti, whereas a single phase is present for 3Ti. For

10%–42% Ti, an FCC solid solution is predicted by ML, corresponding to the range of elemental composition leading to the synthesis of poor crystallinity thin films. There is, thus, an agreement with the elemental composition domains and frontiers, but the predictions do not match the experimental results. At this step, one has to remind that database accessible to perform such ML calculations is dedicated to bulk alloys elaborated by metallurgical routes, usually including a quenching step in order to stabilize metastable phases. Thus, even if elaboration routes of bulk HEA are usually out of equilibrium (cooling rates below $10^3$ K s⁻¹), they are far from that of magnetron sputter deposition (cooling rates of $10^9–10^{12}$ K s⁻¹). The above observations clearly confirm that using this approach with such databases is not accurate enough for the prediction of phase formation in sputtered films. This has been investigated by several groups on different alloys.⁵⁹ They were able to define domains of agreement but clearly come to the same kind of conclusion. Implementing such a method for PVD techniques would require building specific databases from data available in the literature on thin films.

MD simulations are expected to best match experimental results since they describe the motion of atoms and organization at the atomic scale and also, here, because the energy distribution functions of incoming atoms have been used. Unfortunately, as explained above, the Cu-Zn system tends to form a very stable BCC phase (γ-Cu<sub>5</sub>Zn<sub>8</sub>, at a precise elemental composition) that EAM interaction potentials used for Cu and Zn do not predict. This is the reason why GIXRD of a 3Ti sample does not correspond to the simulated one (Fig. 4). However, the experimental conditions used in the present work to obtain a content of Ti higher than 10% lead to a Cu/Zn proportion (Table I) far from the γ-Cu<sub>5</sub>Zn<sub>8</sub> domain of stability as defined by CALPHAD (Fig. 7). We think that this leads to “α-Cu (FCC) type phase organization” in the films. This could explain the excellent agreement found from 10Ti to 42Ti in the position of the broad peaks present in both experimental and MD diffraction patterns.

Thus, MD simulations reproduce quite well our diffraction experimental results. Previously, a good agreement was found in the case of high-entropy alloy thin films.²¹ Intrinsically, the diffracting volume is very limited in MD simulations, leading to a lack of long range order and thus to broad peaks. It is shown from the snapshots that the films are crystallized at this atomic scale. From GIXRD analysis, we cannot check whether this nano-organization
exists in the films. In the range between 10 and 42 at. %, the crystal-
line structure calculated from MD data is mainly HCP (Fig. 4), and
this phase exists both in the Zn and CuTi zones. This highlights
the formation of a “collective” structure, including all the elements,
even if segregation of Zn atoms is observed at all the elemental
compositions. Experimentally, we have no evidence of such behav-
ior of Zn. GIXRD cannot help since, as mentioned above, peaks
listed in the α-CuZn phase JCPDS file fit exactly those of α-Cu
(FCC) and Zn HCP coexisting nano-phases, as calculated by MD.
However, one must keep in mind that CALPHAD has not pre-
dicted the coexistence of Cu and Zn separated phases, neither the
formation of a HCP phase, whereas the stabilization of a CuTi
phase in a certain range of elemental composition is anticipated by
both techniques.

Again, a recovery of a kind of order is visible in 76Ti where
thinnest peaks are visible on MD simulation. Ti being the main
element, it drives the phase formation. Peaks correspond to the
β-Ti (BCC) phase that is not predicted by thermodynamics and
not usually formed in typical magnetron sputtering deposition con-
ditions. Nevertheless, from the literature, it is known that the β-Ti
(BCC) phase may be obtained at a lower temperature than 880 °C
when a BCC stabilizing element is added. Fe, Cr, Cu, Ni, Co, etc.,
have been identified as a β-Ti (BCC) stabilizer.⁶⁰,⁶¹ Formation of
this β-Ti (BCC) in the simulated film may stand for this stabilizing
effect since Cu low content is randomly mixed in Ti and thus can
act as an impurity. It should be noted that simulating a pure Ti
deposition leads to a HCP film (not represented here but written in
Table II). Experimentally, different results are obtained since the
α-Ti (HCP) phase is detected, similarly to a pure Ti film, in addi-
tion to a CuTi phase.

V. CONCLUSION

The crystalline structure of Cu-Zn and Cu-Ti-Zn films
deposited by a magnetron sputtering technique was analyzed by
means of GIXRD and compared to predictions from three numeri-
cal methods.

The first result is that depending on the elemental composi-
tions around the equimolarity, the phase formed in binary Cu-Zn
alloys is different: α-CuZn or γ-Cu₅Zn₈. When Ti is progressively
added into the binary alloy, the Cu-Zn stabilized phase depends on
the Cu/Zn ratio. Ti was found to be incorporated in this phase,
inducing a modification of the corresponding lattice parameter and
a loss of the crystallinity. For Ti percentages between 24 and
42 at. %, amorphous or nano-crystalline phases are present.

Comparison with CALPHAD results highlights that for pure
Ti or binary Cu-Zn films, the thermodynamically stable phases are
formed in the films. Less agreement was found at low or high per-
centage of Ti introduced in the starting Cu-Zn system, and great
differences were observed for elemental compositions of the ternary
alloy close to equimolarity. The fact that poorly ordered films are
observed in the range 10–42 at. % of Ti is in line with the expected
out-of-equilibrium nature of the magnetron sputter deposition
method.

Only limited agreement was found between ML predictions
and experiments. The main reason that can be invoked is the data-
base used to train the model that is based on bulk HEAs alloys.

This points out the fact that alloys in bulk or thin films do not
behave in the same manner and/or that elaboration routes of bulk
pieces are too different from that of thin films. Since bulk HEAs
are usually synthesized using metallurgical methods, including a
quenching step, conditions could have been comparable to magne-
tron sputter deposition for which high cooling rates are reported.
Our results suggest that this hypothesis is not valid. Developing an
accurate ML approach would require building a dedicated database.
Regarding the growing interest for HEAs, MEAs (medium-entropy
alloys), and CCAs (complex concentrated alloys) thin-film applica-
tions, this work would deserve to be done in the future.

MD simulations, using experimental energy distribution func-
tions of film forming species as inputs, were expected to predict the
phases experimentally obtained. The main result obtained from
MD is the segregation of Zn and the formation of a Cu-Ti phase.
This was not evidenced from the GIXRD analysis but cannot
completely be ruled out in poorly crystalline films. Since
CALPHAD calculations anticipate the formation of Cu-Ti phases,
this possibility has to be considered. A very good agreement is
found between MD and GIXRD for a peak position and a shape
for Ti at. % between 10 and 42. The organization at the nanoscale
cannot be determined from the implemented analysis for compari-
son. However, the general shape of simulated XRD patterns (see
Fig. 4), standing for the level of order in the film, is in good agree-
ment with the experimental results for all the elemental composi-
tions. Our results highlight the crucial impact of the interaction
potentials used in the calculations. This was well known, but partic-
ularly important in the case of the Cu-Zn system for which two
different phases are thermodynamically stable at elemental compo-
sitions around 50/50. All the results show the ability of MD simula-
tions to give interesting trends but highlight the need to check the
validity of the interaction potentials on some selected film and ele-
mental compositions.

ACKNOWLEDGMENTS

Conseil Régional Centre-Val de Loire is acknowledged for
supporting this work through Grant ARD-MATEX No.
2021-00145829.

AUTHOR DECLARATIONS

Conflict of Interest

The authors have no conflicts to disclose.

Author Contributions

**Dimitri Boivin:** Investigation (lead); Visualization (equal); Writing – original draft (equal); Writing – review & editing (supporting). **Andrea Jagodar:** Investigation (equal). **Pascal Brault:** Conceptualization (equal); Formal analysis (lead); Funding acquisition (equal); Investigation (equal); Validation (equal); Visualization (equal); Writing – review & editing (equal). **Thomas Vaubois:** Formal analysis (lead); Investigation (supporting); Visualization (equal); Writing – review & editing (equal). **Edern Menou:** Investigation (equal); Visualization (equal); Writing – review & editing (equal). **Barthélemy Aspe:** Conceptualization (supporting); Visualization (supporting). **Amaël Caillard:** Conceptualization
(supporting). **Pascal Andreazza**: Conceptualization (supporting). **Marjorie Cavarroc-Weimer**: Formal analysis (equal); Funding acquisition (supporting); Writing – review & editing (equal). **Anne-Lise Thomann**: Conceptualization (equal); Funding acquisition (lead); Project administration (lead); Writing – original draft (lead); Writing – review & editing (equal).

DATA AVAILABILITY

The data that support the findings of this study are available
from the corresponding author upon reasonable request.

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