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Understanding binary phase separation towards Cu-C nanocrystalline-amorphous composites

The nanocrystalline-amorphous textures are commonly observed in the coatings synthesized by energetic deposition. We report a binary phase separation towards Cu-C nanocrystalline-amorphous composites by the FCVA deposition. The experimental results highlight that the average size of Cu nanocrystallines mainly depends on the C2H2 content. By performing a MD simulation using the LAMMPS, we theoretically explained how the initial reagent concentration fundamentally determines Cu nanocrystalline's final morphology and size during phase separation. This finding may give insight into the formation of nanocrystalline-amorphous structures by energetic deposition.


I. INTRODUCTION
The nanocrystalline-amorphous composite structures are commonly found in the metal-nonmetal coatings fabricated by energetic deposition, including filtered cathodic vacuum arc (FCVA), high power impulse magnetron sputtering (HiPIMS), and direct current (DC) magnetron sputtering. This is ascribed to the rapid heating and quenching at the atomic scale governed by the thermal spike effect during deposition [1] . Without an external heat bath, the substrate temperature during deposition is relatively low, and long-range atomic diffusion has been rigidly confined. This phenomenon impedes crystal growth and spontaneously contributing to the formation of nanocrystallines or amorphous structures.
The formation of nanocrystalline-amorphous textures is considered as one of the significant factors contributing to the extraordinary mechanical properties of superhard composite coatings [2,3] , and the average nanocrystalline size typically decreases with an increasing amorphous content [4][5][6] . However, a profound understanding of the structure evolution from homogenous blends to nanocrystalline-amorphous coexisting structures remains unclear. These processes involve a thermodynamic phase separation. Fortunately, the binary phase separation has been experimentally studied, including but not limited to binary metal composites like Cu-Ag [7] , Cu-Ta [8] , and Cu-Mo [9] , and binary metal-nonmetal composites Cu-C [10] , Ni-C [11] , and Cr-C [12] . Theoretical studies have also pointed out that the ultimate morphology of these separate phases can be mathematically described by using partial differential equations (PDEs) like a well-known Cahn-Hilliard (CH) equation that is driven by chemical potential gradients [13,14] .
In binary alloy mixtures or polymer blends, the CH equation-based phase-field modeling has been commonly performed to study phase separation, like classical spinodal decomposition [15][16][17] . Notably, by using phase-field modeling, the structures like lateral concentration modulations (LCMs) and vertical concentration modulations (VCMs) as a result of spinodal decomposition during film deposition can be theoretically explained [18][19][20][21] . Besides LCMs and VCMs, the spherical or spot topography is also commonly observed by energetic deposition. However, little research has been focused on this morphology and size evolution. On the other hand, the phase-field modeling cannot provide more details at the atomic scale during phase separation. Therefore, this work takes the binary Cu-C system as an example, dedicated to unveiling the key factors that fundamentally determine the morphology and size of crystalline during phase separation by using the molecular dynamic (MD) simulation and experimental validation.

II. EXPERIMENTAL DETAILS
The film samples were fabricated on the surface of polished NaCl crystals and Si (100) wafers by employing FCVA deposition for 60 seconds and 30 minutes under the base pressure of~1.0×10 -3 Pa, respectively (Fig. 1a). During the deposition, a pure Cu (99.99 %) target was used as cathodic arc source under 100 A arc current and -100 V negative bias voltage. The C2H2 gas (99.99 %) was pumped into the chamber with a constant flow rate of 10, 15, and 20 sccm, corresponding to a chamber pressure of2 .0×10 -2 , 3.0×10 -2 , and 4.0×10 -2 Pa, respectively. Then, the NaCl substrate was dissolved with deionized water, and transferring the thin film onto support grids for the high-resolution transmission electron microscopy (HRTEM, JEM-2100, 200 kV) test. The specimens on Si substrates were used for the X-ray diffraction (XRD, SmartLab S2) analysis using Cu Ka (λ = 1.5418 Å) incident radiation with a step size of 0.03°at 40 kV and 40 mA. The estimated Cu ion (+1) concentration trend under different chamber pressure is available by solving the Saha ionization equation (Formula 1) [22] , where P is chamber pressure, g is the degenerate state (gi+1/gi=5), Vi is the first ionization energy (7.7264 eV), and the ion kinetic energy kT=57 eV [23] .
In order to reproduce the Cu/C phase separation at an atomic scale, the general MD simulation was performed by using the large-scale atomic/molecular massively parallel simulator (LAMMPS) [24,25] . 10 4 random Cu/C atoms with 0.5 g/cm 3 cell density were first constructed with the Materials Studio (MS) package (Version 8.0) as an estimated amorphous structure at the early stage of deposition. Secondly, the amorphous structure was quenched from 1000 K to 300 K under the NPT ensemble of the Nose thermostat for 1 ns with a time step of 1 fs using the LAMMPS. The hybrid Cu-Cu, Cu-C, and C-C interactions were described by the embedded atom method (EAM) potential [26] , Lennard-Jones (LJ) potential, and the adaptive intermolecular reactive empirical bond order (AIREBO) potential [27] , respectively. By altering the pressure and atomic concentration gradient, we quantitatively investigated the evolution of Cu atomic diffusion, nucleation, and crystal growth. The mean-squared displacement (MSD) of Cu atoms within Δt is given by Formula (2), where r(t) represents the atomic position at time t in the NPT ensemble, and the corresponding atomic diffusion coefficient is derived from Formula (3). All the MD visualization was implemented by using the OVITO Basic [28] .
(3)  Fig. 1f highlights all the Cu nanocrystalline are smaller than~35 nm, and the size will be moderately reduced with increasing C2H2 content. Fig. 1c and 1d present the HRTEM morphologies of as-synthesized specimens with 15 sccm C2H2 flow rate, illustrating the spherical Cu nanocrystalline is embedded by amorphous C, and the selected area electron diffraction (SAED) also confirms these polycrystalline structures. The HRTEM results emphasize an evident phase separation towards the energetic Cu and C atoms rather than forming metallic carbides, which may be attributed to the relatively low formation enthalpy of Cu nanocrystalline compared with the Cu-based carbides. In order to theoretically reproduce the processes of Cu-C phase separation and reveal the Cu grain size evolution, we propose a typical MD simulation using LAMMPS under the NPT ensemble with different concentrations and pressure. Fig. 2 (a)-(i) present the snapshots of atomic distribution by tracking the displacement trajectory with initial Cu:C=1:1 quenching from 1000K to 300K under 1GPa, indicating the hybrid Cu/C atoms will spontaneously form Cu-rich and C-rich phases during atomic diffusion. The radial distribution functions (RDF) shown in Fig.3 (a)-(b) have recorded the evolution of C-C and Cu-Cu atomic distance during phase separation, with the 1 st nearest neighbor of 1.38Å and 2.49Å under equilibrium state, respectively. By converting the RDF with Kirkwood-Buff (KB) method [29] , we further obtain the potential of mean force (PMF) towards Cu-Cu interaction, as depicted in Fig. 3c. The PMF profile demonstrates non-bonded Cu-Cu interaction with time=0 (initial structure). By increasing the MD time, the depth of the potential well will first reach the lowest value of -20.58 kJ/mol (time=1ps) and then rise to -5.75 kJ/mol (time=1ns) till the atoms are bonded. Notably, we use the order parameter of q4 and q6 introduced by Steinhardt et al. to characterize the local bond-orientational order of Cu and C atoms [30] ; as shown in Fig. 3d, the majority of bond order towards Cu exhibits a higher value of q6 than C.

III. RESULTS AND DISCUSSION
As one of the critical factors that may influence atomic distribution during phase separation, the pressure from atomic deposition should be quantitatively studied. Fig.   4 (a)-(c) depict the time-dependence snapshots of Cu crystalline morphology with simulated pressure ranging from 1 kPa to 1 GPa. Assuming the deposited Cu and C atoms are randomly distributed on the substrates under 1000 K at the initial stage (time=0). As the temperature decreases, the diffusive atoms will spontaneously form clusters (time=100ps). The emerging spherical Cu crystals are distinctively separated from the C atoms once the quenching time exceeds 500ps. This morphology is consistent with the as-synthesized nanocrystalline-amorphous structures that observed by HRTEM. Notably, if increasing the pressure from 1 kPa to 1 MPa, the growth of spherical Cu crystalline is dramatically promoted, while the crystalline will be evolved into a spot shape once the pressure rises to 1 GPa. The initial Cu content is the other critical parameter during phase separation. As presented in Fig. 4 (d)-(f) and Moreover, by tracking the atomic displacements during dynamic processes, we obtained the mean-squared displacement (MSD) curves of Cu atoms under different concentration as presented in Fig. 5a, which illustrates a relatively high Cu content will also boost its diffusion ability during phase separation.

IV. CONCLUSIONS
In this work, the Cu-C nanocrystalline-amorphous composites were synthesized by FCVA deposition to study the binary phase separation. The characterization results emphasize the average Cu grain size will be moderately reduced with increasing C2H2 content. In order to unveil the key factors that can fundamentally determine the final phase structures, a classical MD simulation under the NPT ensemble was implemented. The simulation theoretically reproduces the Cu-C phase separation and reveals that initial concentration and pressure play significant role in the morphology and size evolution of Cu nanocrystallines. The higher initial Cu concentration will facilitate rapid crystal growth during phase separation. We hope this finding may provide a practical methodology for depositing functional coatings with designed microstructures and properties.

ACKNOWLEDGMENT
This work is partly supported by the National Natural Science Foundation of