Publication and dataset for "Unveiling effects of Zr alloying on structure and properties of nanocrystalline Cu-Zr films"

Unveiling effects of Zr alloying on structure and properties of nanocrystalline Cu-Zr films M. Zhadko a,* , A. Benediktov´ a a,b , R. ˇ Cerstvý a , J. Houˇ ska a , J. ˇ Capek a , D. Kolenatý a , J. Min´ ar b , P. Baroch a , P. Zeman a a Department of Physics and NTIS – European Centre of Excellence, University of West Bohemia, Univerzitni 8, 301 00 Plzen, Czech Republic b New Technologies Research Centre, University of West Bohemia, Univerzitni 8, 301 00 Plzen, Czech Republic ARTICLE INFO Keywords: Cu-Zr Films and coatings Nanocrystalline alloys Solid solution Grain refinement Magnetron sputtering ABSTRACT Nanocrystalline Cu-Zr films with Zr content in the range of 0.3–2.7 at.% were deposited by direct current magnetron sputter deposition. Effects of Zr alloying on the structure, surface, mechanical, and electrical properties were systematically investigated using X-ray diffraction, electron microscopy, atomic force microscopy, indentation, and the four-point probe method. The experimental results revealed that the Zr content significantly affects the structural and functional characteristics of the films, with the most notable changes observed between 0.3 and ≈1.5 at.% Zr. Beyond this range, further increase in the Zr content results in only minor changes in the microstructure and mechanical properties, while the solubility, electrical resistivity, and surface roughness continue to rise. The alloyed Cu-Zr films exhibit hardness values between 3.2 and 4.2 GPa, exceeding 2.5 GPa measured for the unalloyed Cu film, which is attributed to the combined effect of grain boundary strengthening due to structural refinement and Zr segregation, along with solid solution strengthening. 1. Introduction Nanocrystalline materials exhibit unique mechanical properties [1,2] due to their small grain size and the corresponding large surface area of grain boundaries, which act as effective barriers to dislocation motion during plastic deformation. On the other hand, such a structural state results in a high excess of free energy leading to abnormally low stability of the nanocrystalline structure [3] and degradation of their properties even with a minor increase in temperature [4]. Extensive research is currently focused on their stabilization using both thermodynamic approach by reducing the grain boundary energy [5–8] and kinetic one by decreasing grain boundary mobility [9–11]. These stabilization mechanisms can be effectively realized through alloying with immiscible elements that tend to segregate to grain boundaries altering grain boundary chemistry, structure, and properties such as cohesion, energy, and mobility [12–19]. The Cu-Zr binary system is particularly promising for applying these strategies due to its limited solubility in the solid state and large atomic size difference, which facilitates Zr segregation to the grain boundaries [20,21]. Unlike other Cu-based immiscible systems such as Cu-Ta or CuMo, which require non-equilibrium synthesis techniques [22,23], Cu-Zr alloys benefit from unlimited mutual solubility in the liquid state, allowing for conventional metallurgical methods like melting and casting [24] commonly followed by processes including plastic deformation [25]. Additionally, Zr has been extensively used as an alloying element due to its positive influence on mechanical properties and recrystallization temperature of microcrystalline Cu and its alloys [26–28]. These favorable effects are also observed in nanostructured states produced via powder technologies [29–31] and various deposition techniques [32,33], albeit with their peculiarities. Several studies have reported a unique combination of mechanical properties and superior thermal stability in nanocrystalline Cu-Zr alloys containing a small amount of Zr [34,35]. This advancement is attributed to Zr grain boundary segregation, which can result in the formation of different interfacial structures including ordered and amorphous complexions, as demonstrated in recent works [14–16,34,36]. Magnetron sputter deposition is a highly non-equilibrium process widely used for reproducible thin film preparation with a wide variety of structural states including nanocrystalline and amorphous structures, supersaturated solid solutions, and unique phases not achievable through equilibrium methods. Cu-Zr sputter-deposited films have been predominantly studied for a compositional range corresponding to * Corresponding author. E-mail address: [email protected] (M. Zhadko). Contents lists available at ScienceDirect Materials & Design journal homepage: www.elsevier.com/locate/matdes https://doi.org/10.1016/j.matdes.2025.113949 Received 22 November 2024; Received in revised form 13 March 2025; Accepted 11 April 2025 Materials & Design 253 (2025) 113949 Available online 14 April 2025 0264-1275/© 2025 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ). transitions from nanocrystalline to metallic glass structures [37–39]. However, the research on nanocrystalline Cu-Zr films with minor Zr additions remains still very limited [32,33,35]. A significant knowledge gap exists, as there is almost no available information on sputtered Cu-Zr films with less than 1 at.% Zr, except 1–2 films reported in [32] and [35] (and similarly for other preparation techniques). Furthermore, these scarce results often do not fit together owing to the sensitivity of compositional dependencies of the structure and film properties to sputtering parameters. Since the primary application of Cu-based films is in electronics and electrical industries, where their superior electrical and thermal conductivity is crucial, it is essential to carefully control their structural state and composition to optimize the balance between mechanical and conductive properties. This requires reducing the content of alloying elements to lower concentrations and ensuring their optimal distribution preferably in an atomically dispersed state. Notably, for microcrystalline materials, only thousandths or hundredths of a percent of an alloying element would be sufficient to form complete intergranular envelopes [40]. When extended to nanocrystalline materials, this estimation corresponds to approximately 1 %, which forms the basis for the compositional range studied in this work. Our chosen range is particularly relevant because it has the potential to achieve complete monolayer coverage of Zr for grain sizes around 100 nm or smaller. Moreover, it is well documented in microcrystalline Cu-based alloys that even hundredths of a percent of Zr can significantly modify the microstructure and mechanical properties. However, the effects of such low Zr concentrations on nanocrystalline materials remain largely unexplored, representing a key knowledge gap that this study aims to address. In addition, another critical aspect of Zr at low concentrations is its ability to reduce surface energy, which plays a vital role in stabilizing the nanostructured state [41]. This property is particularly important for enhancing the thermal and mechanical stability of nanocrystalline films, further highlighting the significance of studying this compositional range. Therefore, in order to better understand the underlying mechanisms of the structure formation and the resulting strengthening mechanisms during alloying, there is a strong motivation to study Cu-Zr films with low Zr contents, with a strong focus on less than 1 at.% Zr, prepared under the same conditions. To contribute to this objective, we conducted a systematic investigation of nanocrystalline Cu-Zr films prepared using magnetron sputter deposition with a low Zr content ranging from 0 through 0.3 to 2.7 at.%. Our findings reveal that a redistribution of Zr atoms occurs during the film deposition between the supersaturated solid solution and grain boundaries, resulting in the formation of a complex microstructure along with significant texture weakening and structural refinement. We demonstrate that Zr alloying within the investigated composition range is an effective approach for modifying the structural state of sputterdeposited films, optimizing their mechanical, electrical, and surface properties, and offers insights that can be applied to other comparable binary systems in the development of nanocrystalline metallic films. 2. Experimental details Nanocrystalline Cu-Zr films with a Zr content ranging from ~0.3 to 2.7 at. % were prepared by non-reactive direct current (dc) magnetron co-sputtering of separate Cu (99.99 % purity) and Zr (99.7 % purity) targets with a small step in composition variation. The films were deposited onto ultrasonically pre-cleaned glass substrates in pure Ar at a pressure of ≈0.5 Pa without substrate bias and external heating. The base pressure before each deposition was below 5⋅10 −5 Pa. The targetto-substrate distance was set to 150 mm. The Zr content was controlled by adjusting the power on the Zr target. The deposition rates from the Cu and Zr targets were measured before each deposition using a quartz crystal deposition rate monitor. The thicknesses of all films, measured by a Veeco Dektak 8 stylus profiler, were in the range of 6.6 – 7.5 μ m. For the comparison, unalloyed Cu films were also deposited at the same conditions. The elemental composition of the as-deposited films was measured by wavelength dispersive spectroscopy (WDS) in a Hitachi Su-70 scanning electron microscope (SEM) with a primary electron energy of 15 kV. For the quantitative analysis, Cu and Zr standards were used. Before the WDS analysis, a thin layer of carbon with a thickness of 14 nm was sputtered on the film surface. The structure of the as-deposited films on the substrates was characterized by X-ray diffraction (XRD) and transmission electron microscopy (TEM) including high-resolution (HR) imaging mode and Fourier transforms (FT) for image processing. XRD analysis was performed on a PANalytical X’Pert PRO MPD diffractometer with a CuK α (λ = 0.154187 nm) radiation. The measurements were carried out both in a Bragg-Brentano (BB) geometry and at a glancing incidence (GI) of 4◦. All samples were scanned over the 2θ-range from 20◦to 120◦. The measured data were processed by a PANalytical software package HighScore Plus. The average size of coherently diffracting Cu regions was estimated using the Scherrer equation from the full width at half maximum of the Cu(111) diffraction peak corrected for instrumental broadening by an NIST LaB 6 powder standard. TEM characterization was performed using a JEOL JEM-2200FS microscope operating at an accelerating voltage of 200 kV. Local elemental composition variations in the films were analyzed by energy dispersive spectroscopy (EDS) with an X-Max Oxford detector. Planar samples for TEM analysis were prepared by electrolytic polishing, then washed twice in acetic acid. Cross-section samples were prepared using the following combination: polished silicon, resin, thin film, resin, thin glass. The sample was thinned out by ion milling in JEOL Cryo Ion Slicer IB-09060CIS. The average in-plane grain size of the Cu and Cu-Zr films was calculated from the planar bright-field TEM images using the linear intercept method. More than 100 grains were examined for each measurement. The arithmetic average surface roughness and surface morphology of the films were studied by an AIST-NT SmartSPM atomic force microscope (AFM) on selected 5 ×5 and 2 ×2µm 2 surface areas. The microscope was equipped with a silicon tip (curvature radius of 10 nm) and operated in a non-contact mode. Additionally, the top and crosssectional surface of the films was studied by SEM operating with a primary electron energy of 10 kV. The mechanical properties of the films on the substrates were measured at room temperature by indentation using a Fischerscope H100 microhardness tester equipped with a Vickers diamond tip. Minimum 20 indents were made on each film with a consistent load of 10 mN and the results were averaged. The indentation depth was significantly less than 10 % of the film thickness. The electrical resistivity of the films on the substrate was measured at room temperature using the standard four-point probe (4-pp) method. At least three measurements were taken at different locations on each film. 3. Results 3.1. Microstructural characterization Fig. 1a presents XRD patterns in the BB geometry of unalloyed Cu and alloyed Cu-Zr films with a different Zr content deposited on the glass substrates. The positions of all diffraction peaks in the Cu film match those of FCC Cu (PDF card 00–004-0836) with a notably high intensity for the (111) diffraction peak, indicating a strong <111>axial texture perpendicular to the film surface. Fig. 1b shows a dependence of the intensity of the (111) diffraction peak on Zr alloying: a steep decrease up to ≈0.8 at.% Zr, a further slight decrease up to ≈1.5 at.% Zr, and a saturation at higher Zr contents. (200), (220) and (311) diffraction peaks are also present in the diffraction patterns of the Cu and Cu-Zr films, but their relative intensities are comparatively low (Fig. 1b). In M. Zhadko et al. Materials & Design 253 (2025) 113949 2 addition to texture weakening, structural refinement is observed in all Cu-Zr films, as reflected in the gradual broadening of all diffraction peaks with increasing Zr content. A gradual shift of the maxima of (111) and (220) diffraction peaks towards lower 2θ angles with increasing Zr content indicates an increase in the corresponding interplanar spaces and a lattice expansion, as Zr atoms with a larger atomic radius (0.1597 nm) substitute smaller Cu atoms (0.1278 nm) in the FCC crystal lattice (inset in Fig. 2b). More detailed XRD analysis in the GI geometry (Fig. 2) revealed an increase in the stress-free lattice parameter with Zr alloying and confirms the formation of a supersaturated Zr solid solution in the FCC Cu crystal lattice (Fig. 2a). The formation of the solid solution has been also confirmed by molecular dynamics film growth simulations [42], see Fig. S1 in the Supplementary material. The measured residual stress is tensile throughout the entire composition range (Fig. 2b) and its value increases from 160 MPa for unalloyed Cu to 600 MPa with Zr alloying up to ≈0.8 at.% Zr, after which stabilizes and shows no further change with increasing Zr content. Fig. 3 summarizes the effect of Zr alloying on the grain size of the CuZr films, as measured by both XRD and TEM. The XRD grain size (black dots) represents the size of coherent scattering domains, measured perpendicular to the film surface and calculated from the broadening of the most intense Cu(111) diffraction peak using the Scherrer equation. The TEM grain size (red triangles) is an average grain size measured by the linear intercept method from the bright-field TEM planar images. This data illustrates that Zr alloying induces significant structural Fig. 1. (a) XRD patterns in the BB geometry of Cu and Cu-Zr films alloyed with a different Zr content and deposited on glass substrates and (b) dependences of the detected intensities of the X-rays at the scattering angles 2θ, corresponding to (111), (200), (220) and (311) diffraction peaks, on the Zr content. The inset in panel (b) shows the change of 2θ positions with increasing Zr content. Fig. 2. GIXRD: (a) Dependence of the stress-free lattice parameter on the Zr content. The dashed and dash-dotted lines show the lattice parameter obtained by averaging of atomic volumes and atomic radii (Vegard’s law), respectively; (b) Dependence of macrostress on the Zr content. M. Zhadko et al. Materials & Design 253 (2025) 113949 3 refinement in both the lateral and vertical directions. The grain size measured by XRD decreases from 220 nm for unalloyed Cu to 60 nm for 0.8 at.% Zr, with a minimum of 35 nm achieved at ≈1.5 at.% Zr. Beyond this concentration, the grain size saturates and remains constant. The TEM in-plain grain size shows a similar nonlinear trend with slightly higher values. Fig. 4 shows representative planar and cross-sectional TEM images of the Cu-Zr films with 0.3, 0.6, and 1.3 at.% Zr, illustrating the evolution of the structure and overall structural refinement with increasing Zr content. With low Zr alloying of 0.3 at.% (Fig. 4a), the columnar microstructure with straight column boundaries still dominates like for the unalloyed Cu film. Microcolumnar grains (≈200 nm width), extending along the film thickness and coexisting with much smaller equiaxed nanograins (20–60 nm), are observed. As the Zr content increases to 0.6 at.% (Fig. 4b), the columnar microstructure becomes less pronounced and the column boundaries less straight, followed by further grain refinement and an increased number of smaller nanograins. At 1.3 at.% Zr (Fig. 4c), the film predominantly consists of equiaxed grains, most of which are elongated in the film growth direction. At this concentration, the grain boundaries become less distinct compared to the films with the lower Zr content. A detailed investigation in the HRTEM imaging mode reveals a highly complex structure in the Cu-Zr films (Fig. 5). Examination of the grain boundaries (Fig. 5b, c, f) in the films with a different Zr content reveals a well-ordered crystalline structure without any evidence of amorphization at the grain boundary region. Additionally, a distinctive feature in all films is the presence of numerous nanotwins with the thicknesses ranging from a few to several tens of nanometers. Fig. 5b shows an HRTEM image and a detailed description of multiple first and second-order twins, i.e., twins formed in the previously twinned region, found in [110] oriented grain in the Cu-0.3 at.% Zr film. In addition to the twins, a high density of lattice defects such as dislocations and stacking faults is observed in certain regions, as illustrated in Fig. 5c, including a triple junction of the grains in [111] and [011] orientations in the Cu-0.6 at.% Zr film. In grain 1, a number of dislocations and stacking faults are visible, mainly close to incoherent twin boundaries, and moreover, the twins with a thickness of one atomic layer are present in twin 2. In the Cu-0.6 at.% Zr film, intermetallic phases were also found, as illustrated in Fig. 5d, but very rarely. A particle of the cubic Cu 5 Zr phase was revealed near two plate-like particles of an orthorhombic Cu 2 Zr phase. Their orientation relationships with the matrix were determined as [011] m //[114] Cu5Zr //[111] Cu2Zr and (111) m // Fig. 3. Grain size-composition dependences based on data from XRD (coherently scattering domain size) and TEM (in-plain average grain size) measurements. Theoretical dependence discussed in more detail in the Discussion section, is also included. Fig. 4. Planar (top row) and cross-sectional (bottom row) bright-field TEM images of Cu-Zr films with varying Zr content: (a) 0.3 at.%; (b) 0.6 at.%; (c) 1.3 at.%. M. Zhadko et al. Materials & Design 253 (2025) 113949 4 (011) Cu2Zr . Tweed-like contrast is observable between the plates of Cu 2 Zr phase. Fig. 5e captures a fine-grained structure within a column in the Cu-1.3 at.% Zr film, where the blurry contrast is caused by overlapping grains. In Fig. 5f, a detailed view of the grain boundary of the grains in [112] and [011] orientations is captured. Numerous lattice defects can be seen in the upper left corner, probably due to the presence of a tilted twin. An inverse FT from this region, constructed using the (111) frequency in the fast FT image, shows the presence of significant atomic layer distortion, in addition to the presence of individual dislocations and stacking faults. Fig. 6 shows cross-sectional TEM images and compositional line scans for the Cu-Zr films with 0.6 and 1.3 at.% Zr demonstrating that Zr is distributed between the grain interiors and grain boundaries. Although most of Zr is located within the grains, there is also a slight increase in the Zr content near the grain boundary regions. This is indicated by the arrows with a difference of 0.1–0.3 at. % Zr (higher than the error of the measurement). Fig. 5. Planar TEM images showing the details of the microstructure of Cu-0.3 at.% Zr (a,b), Cu-0.6 at.% Zr (c,d), and Cu-1.3 at.% Zr (e,f) films. (a) Bright-field image of the region containing first and second-order twins; (b) Magnified view of a grain boundary with twins. (c) HRTEM image of a triple junction with two twins in grain 1 and inverse FT of twin 2 showing dislocations (green) and extrinsic stacking fault (white line) in the upper inset; additional spots in thirds of the reciprocal vector g -1-11 arise from the overlap of the matrix and the twin, whose boundary is Σ3. (d) HRTEM image with identified Cu 5 Zr and Cu 2 Zr intermetallic phases. (e) Bright-field image. (f) HRTEM image of a grain boundary and inverse FT showing dislocations (green), stacking fault (white line) and atomic layer distortion (circled in yellow) in the upper inset. Remaining insets are the corresponding FTs with Miller indexes corresponding to grains in different orientations, including twins. M. Zhadko et al. Materials & Design 253 (2025) 113949 5 Fig. 6. Cross-sectional TEM images: (a) high-angle annular dark-field image of Cu-0.6 at.% Zr film; (b) bright-field TEM image of Cu-1.3 at.% Zr film; (c) and (d) corresponding local composition variations of the Zr content at the grain interior and grain boundary regions. EDS point analysis was performed along the white lines indicated in the images (a) and (b). Fig. 7. SEM images of the film surface: (a) 0 at. % Zr, (b) 0.4 at. % Zr, (c) 0.6 at. % Zr, (d) 1.0 at. % Zr, (e) 1.3 at. % Zr, (f) 1.7 at. % Zr, (g) 2.0 at. % Zr, (h) 2.3 at. % Zr. Insets in the upper right corner show details of the film surfaces at higher magnification. M. Zhadko et al. Materials & Design 253 (2025) 113949 6 3.2. Surface morphology and roughness The surface of the Cu and Cu-Zr films was investigated using AFM and SEM. Fig. 7 shows representative SEM images of the film surface illustrating the overall structural evolution at the surface with increasing Zr content compared to the unalloyed Cu film. In a Cu film, equiaxed, predominantly hexagonal-shaped grains with distinct straight grain boundaries are visible. The grain size, determined from SEM and AFM images, varies from 90 to 380 nm, with an average grain size of 230 nm, which aligns with the TEM measurements. In addition, the surface shows relatively large gaps between grains ranging from 30 to 100 nm. With Zr alloying, much smaller features (20–60 nm in size) begin to appear on the surface, corresponding in size to the small grains observed in the TEM images. As the Zr content increases, the number of small grains increases. This is accompanied by a decrease in both the size and quantity of larger grains, which protrude above the surface. At the Zr content exceeding ≈0.6 at.%, a reverse trend is observed, where larger protruding grains begin to fragment and increase in size, also followed by an increase in size and number of gaps. Finally, at the Zr content higher than ~1.5 at.%, the structure forms grains with an average size of 200–275 nm (comparable to the Cu film) and with irregularly shaped boundaries and pronounced fragmentation inside. Additionally, AFM was used to obtain more detailed topographical information about the film surface (Fig. 9). The analysis revealed that Fig. 8. AFM images of the Cu and Cu-Zr film surface showing the effect of gradual Zr alloying on the surface morphology of the films: (a) 0 at. % Zr, (b) 0.4 at. % Zr, (c) 0.6 at. % Zr, (d) 1.0 at. % Zr, (e) 1.3 at. % Zr, (f) 1.7 at. % Zr, (g) 2.0 at. % Zr, (h) 2.3 at. % Zr. Insets in the upper right corner show details of the film surfaces at higher magnification. Fig. 9. Surface roughness of Cu and Cu-Zr films with increasing Zr content. M. Zhadko et al. Materials & Design 253 (2025) 113949 7 the evolution of the surface morphology results in a nonlinear compositional dependence of surface roughness, with a decrease at a Zr content up to ≈0.6 at.% followed by an increase with further Zr addition. In the Cu film, the large gaps between grains are the main cause of a high surface roughness. Initially, as the amount of small grains increases, the number and size of gaps decrease and the surface becomes smoother. This leads to a reduction in the surface roughness, which reaches its lowest value at around 0.6 at.% Zr. However, with further increase in the Zr content, the surface roughness also increases significantly due to both the widening of gaps between the columns and the roughening of the columnar surfaces due to their fragmentation. 3.3. Mechanical and electrical properties Fig. 10 illustrates the effect of the Zr content on the mechanical properties of the Cu-Zr films. All measurements were conducted at a load of 10 mN and the maximum indentation depth was much lower than 10 % of the film thickness and the surface roughness was significantly lower than 20 % of indentation depth to ensure that the effect of substrate and the surface roughness of the film is negligible. Zr alloying has a significant influence on the mechanical properties of the films. As the Zr content increases from 0 through 0.3 to ≈1.5 at.%, the hardness shows an almost linear increase, followed by a saturation with no significant change observed up to 2.7 at.% Zr. The hardness values of the alloyed Cu-Zr films (Fig. 10a) range from 3.2 to 4.2 GPa, i. e., from 130 % to 160 % of that of the unalloyed Cu film prepared under the same conditions. In addition to the hardness values, the elastic recovery (Fig. 10b) and the effective Young’s modulus (Fig. 10c) were derived from loading/ unloading indentation curves. The compositional dependencies of these characteristics correlate well with the hardness behavior. They show an increase in the elastic recovery (from 13 % to 26 %) and a decrease in the effective Young’s modulus (from 144 to 112 GPa) as the Zr content increases, with a subsequent saturation beyond ≈1.5 at.% Zr. Fig. 11 presents the electrical resistivity of the Cu and Cu-Zr films measured at room temperature by the 4-pp method. The electrical resistivity of the unalloyed Cu film is 0.32⋅10 -7 Ω⋅m and is comparable to literature data for films prepared by magnetron sputter deposition [43]. Zr alloying leads to a gradual increase in the electrical resistivity to a maximum value of 1.8⋅10 -7 Ω⋅m. This trend aligns well with the evolution of the stress-free lattice parameter (Fig. 2a) and confirms an increased solubility of Zr in the FCC Cu lattice. Note that both the lattice parameter and the electrical resistivity increase linearly with increasing Zr content up to about ≈0.8 at.%. However, both curves deviate from this linear trend as the Zr content in the films rises further. 4. Discussion The experimental results presented in the previous section allow us to conclude that during the formation of binary Cu-Zr films by magnetron sputter deposition under the selected conditions, Zr atoms redistribute between the supersaturated solid solution and the grain boundaries, with a minor fraction forming intermetallic compounds. This behavior affects the structural state of the films and significantly influences their mechanical, electrical, and surface properties. These effects will be further discussed in the following section. According to the equilibrium phase diagram, Zr is soluble in liquid Cu but has negligible solubility in the solid state. The maximum reported solid solubility of Zr in the Cu lattice under equilibrium conditions does not exceed 0.12 at.%, even at 972◦C [20,21]. In contrast, a large amount of Zr atoms were dissolved in the Cu crystalline lattice under the deposition conditions used, as confirmed by the increase of the lattice parameter (Fig. 2a). A rough estimation using Vegard’s law indicates that the maximum Zr solubility in the studied Cu-Zr films is an order of magnitude higher than the maximum value under the equilibrium conditions. This was also confirmed by the local elemental analysis (Fig. 6). Solubility enhancement in low-miscible or even immiscible systems is a characteristic behavior of thin-film materials prepared by magnetron sputter deposition [44]. The formation of a supersaturated solid solution in Cu can be associated with the kinetic trapping of Zr atoms by the crystallization front during the deposition. This establishes the metastable state, where part of Zr atoms, which did not have sufficient mobility to follow the crystallization front, is embedded into the Cu Fig. 10. Mechanical properties of Cu and Cu-Zr films with increasing Zr content: (a) hardness, (b) elastic recovery, (c) effective Young’s modulus. The error bars represent a purely statistical noise, without any trend across the film surface. M. Zhadko et al. Materials & Design 253 (2025) 113949 8 crystal lattice. As a result, the metastable state persists even at room temperature, where Zr diffusivity is negligible. The extension of the solubility limit is beneficial for two main reasons. First, dissolved atoms in the lattice enhance material strength through solid solution hardening by impeding dislocation movement. Second, the extended solubility is essential for achieving the precipitation hardening, as a higher concentration of dissolved atoms can lead to more substantial precipitation, provided that suitable thermal conditions are present. In addition, Fig. 6a and 6b show that above a threshold Zr content of at most 0.6 at.%, part of Zr atoms occupy the grain boundaries, having significant influence on the grain boundary energy and the cohesion. Unlike the kinetic mechanism of solid solution formation, the adsorption of Zr on the surfaces of growing Cu crystals during the film deposition from a mixture of sputtered Cu and Zr atoms is a thermodynamically favorable process driven by surface energy reduction. As a result, a part of adsorbed Zr atoms will contribute to the stabilization of the Cu crystals and prevent their further growth. This hypothesis may also be supported by the evolution of the surface roughness with increasing Zr content (Fig. 9). The decrease of the roughness at a low Zr content implies the reduction in free surface area, which in turn could be related to an overall surface energy reduction. Moreover, the experimental dependence of the surface roughness on the Zr content exhibits a similar nonlinear trend with a minimum and subsequent increase as calculated compositional dependences of the surface energy with Zr alloying in the literature [8,31]. These calculations were verified by experimental data demonstrating high thermal stability of Cu-Zr nanocrystalline alloys due to thermodynamic contribution [8,34]. According to the reported data [45], the calculated minimum of the surface energy is observed at a Zr content of ~0.3–0.5 at.%. In our case, we observed a decrease in the measured surface roughness at a slightly higher Zr content (~0.6–0.8 at. %). This can be explained by the fact that part of Zr atoms participate in the formation of the solid solution and consequently fewer atoms adsorb on the surface. Therefore, based on the above discussion and the results of other Cubased alloys [46], we built a theoretical compositional dependence of the grain size. The grain size L was calculated in the spherical approximation using equation (1), assuming that the grain boundaries are fully covered by Zr atoms: L= π d3 NnSC (1) where d is the diameter of Cu atom (0.256 nm), N is the coefficient, taking into account atomic size mismatch between Cu and Zr and the number of Zr atomic layers (in the case of a single monolayer, N =4), n is the coefficient taking into account the packing density of the crystalline lattice (0.74 for FCC crystal lattice), S is the calculated area of adsorption cell (5.7·10 -2 , 6.6·10 -2 , and 9.3·10 -2 nm 2 for (111), (100), and (110) crystallographic planes of Cu, respectively), C is the Zr content. Fig. 3 shows that this theoretical dependence exhibits a very similar trend to experimental data. However, the experimental values are higher than the theoretical predictions. This discrepancy can be explained by the fact that only a minor part of Zr atoms of the total Zr content participate in grain boundary segregation, while the majority form a solid solution. In contrast, the theoretical dependence assumes that all Zr atoms are located at grain boundaries, considering the minimum necessary amount of Zr atoms to fully cover the grain boundaries with a single monolayer. If we calculate the Zr content required to cover the grain size of the Cu-0.6 at.% Zr and Cu-1.3 at.% Zr films, which have shown an increased Zr content at the grain boundaries, the following can be observed. For the Cu-0.6 at.% Zr film with an average grain size of 107 nm (as measured by TEM), approximately 0.2 at.% Zr would be sufficient to fully cover the grain boundaries with a monolayer of Zr atoms, which aligns with the results of the elemental analysis (Fig. 6). Similarly, for the Cu-1.3 at.% Zr film with a grain size of 65 nm, approximately 0.3 at. % Zr is required to achieve the same coverage. In addition, the increasing grain boundary enrichment is consistent with the decrease in the slope of the Cu lattice parameter (Fig. 2a). These theoretical calculations combined with experimental results suggest the following explanation for the observed behavior of the compositional dependence of the grain size (Fig. 3). During film formation, the final structural state depends on the completeness of the coalescence process of the formed nuclei, which is hindered due to Zr adsorption on the growing surfaces and subsequently on the grain boundaries of the growing film. The grain size reduction in Cu-Zr films is caused by the blocking effect of Zr grain boundary segregation, which has not yet reached saturation on the descending branch of the compositional dependence. An increase in Zr content along this branch leads to higher coverage of grain boundaries by Zr atoms. Once the grain boundaries are fully saturated with Zr, their adsorption capacity is reached, and any further increase in Zr content becomes excessive, no longer influencing grain size. Additionally, as we demonstrated by XRD and TEM analysis, the weakening of the crystal texture occurs with Zr alloying. The (111) oriented growth, which provides the lowest surface energy, is typically favored in unalloyed Cu films. However, Zr adsorption at the interfaces should result in a decrease of the surface energy and thus suppresses the (111) texture and facilitates the renucleation. This effect is supported by cross-sectional SEM investigations (Fig. 12), which show differences in crystal growth mechanisms between the unalloyed Cu film and the alloyed Cu-Zr film with a low Zr content (0.6 at.% Zr). Both the films exhibit oriented structures, but with distinct differences. The Cu film shows a pronounced columnar growth, while the Cu0.6 at.% Zr film develops a structure characterized by the presence of (111) oriented primary crystals, alongside which nanosized, nearly spherical small crystals are grown. This renucleation process is accompanied by the (200) line intensity increase and a simultaneous sharp decrease for (111) (Fig. 1b). The average angle between branches, measured from the SEM images (Fig. 13b), is ~54◦, which is in a good agreement with the calculated angle between (111) and (200) planes of the FCC crystal (~54.74◦). This observation suggests a preferential growth orientation of these nanocrystals along the [111] axis but at a tilted angle of ~54◦with respect to the primary crystals growing perpendicular to the surface. This growth mechanism explains the surface morphology and the appearance of protruding larger grains (Figs. 7 and 8) on the surface of which nanocrystals subsequently form. Certain part of <110>and <112>oriented grains was also found in all analyzed Fig. 11. Electrical resistivity of Cu and Cu-Zr films with increasing Zr content. M. Zhadko et al. Materials & Design 253 (2025) 113949 9