Exploring the Impact of Surface Thermal Treatments on WC-Co Blocks Subjected to Linear Scratching: A Molecular Dynamics Simulation Study

Abstract

High-energy thermal treatments, such as electron beam irradiation, are crucial for enhancing the performance of tungsten carbide–cobalt (WC-Co) composites in cutting tools and wear-resistant coatings. This study utilizes molecular dynamics simulations to analyze the nanoscale effects of such treatments on WC-Co surfaces, focusing on cobalt evaporation and linear scratching phenomena. The results demonstrate that electron beam irradiation significantly accelerates cobalt evaporation, with rates depending on energy flux and local atomic environments. Embedded cobalt atoms within WC grains exhibit higher resistance to evaporation due to stronger bonding, while pure cobalt surfaces show greater susceptibility to material loss. Under high energy flux, WC-Co surfaces experience an interplay of thermal expansion, density reduction, and evaporation, resulting in accelerated degradation. Linear scratching simulations reveal that thermally treated WC-Co surfaces exhibit increased structural instability, as indicated by broader distributions of local entropy and von Mises stress, reflecting heightened susceptibility to deformation and failure. Stress concentrations from indentation and scratching are more pronounced in thermally treated samples, highlighting the influence of thermal history on mechanical behavior. Molecular dynamics simulations enable detailed insights into atomic-scale phenomena, allowing precise quantification of the effects of energy flux, material composition, and thermal treatment on structural and mechanical responses. These findings emphasize the need to optimize thermal treatment protocols to enhance the durability and performance of WC-Co composites, providing valuable guidance for the development of robust materials for industrial applications.

1. Introduction

High-energy thermal treatment technologies, such as electron beam irradiation, have revolutionized surface engineering and material processing in recent years [1,2,3]. These advanced techniques offer unparalleled precision in manipulating surface properties—including hardness, wear resistance, and thermal stability—which are crucial for high-performance industrial applications [4,5,6]. Thus, the machining industry has focused on improving the performance of tools through various surface treatments. Tungsten carbide–cobalt (WC-Co) composites, renowned for their exceptional mechanical and thermal properties, have emerged as indispensable materials in the fabrication of cutting tools, protective coatings, and wear-resistant components [7,8,9].

Electron beam irradiation induces localized energy deposition on WC-Co surfaces, triggering a series of complex structural and mechanical transformations [10,11]. This process can lead to phenomena such as localized melting, evaporation, and recrystallization, which collectively alter surface roughness, mechanical strength, and material integrity [12]. At the nanoscale, these transformations become increasingly intricate due to the interplay between energy flux, grain boundaries, and material composition [13,14,15]. Understanding the precise mechanisms governing these nanoscale changes is essential, yet remains a significant challenge within the field.

To effectively characterize these nanoscale phenomena, metrics such as local entropy (LE) and von Mises stress (${\sigma }_{VMS}$) have gained prominence [16,17,18]. Local entropy quantifies atomic-level randomness, providing valuable insights into the structural order or disorder within a material. In contrast, von Mises stress measures the distortional energy under applied loads, serving as a critical indicator of mechanical stability and potential failure points [18,19,20]. Employing these metrics enables a deeper understanding of structural and mechanical behaviors, particularly in processes like evaporation and scratching, where atomic-scale interactions are dominant.

Molecular dynamics (MD) simulations have proven to be a powerful tool for investigating atomic-scale processes in materials science [21,22]. By modeling the interactions of individual atoms under controlled conditions, MD simulations offer detailed insights into the structural and mechanical responses of materials subjected to high-energy thermal treatments [18,23,24,25,26]. This approach allows for the precise manipulation of variables such as temperature, pressure, and energy flux, facilitating systematic analysis of complex phenomena like cobalt evaporation and grain boundary instability. Moreover, MD simulations enable the direct calculation of properties like local entropy and von Mises stress—quantities that are otherwise challenging to measure experimentally at the nanoscale [18,22]. By replicating real-world conditions at the atomic level, MD simulations provide a unique platform for elucidating the mechanisms underlying the observed changes in WC-Co composites.

Despite substantial research efforts, several challenges persist in fully understanding the interplay between energy input, material composition, and mechanical responses in WC-Co composites subjected to high-energy thermal treatments. The mechanisms governing cobalt evaporation, grain boundary instability, and the evolution of structural and mechanical properties are not yet fully elucidated. Furthermore, the implications of these nanoscale phenomena on the long-term performance and reliability of WC-Co materials remain inadequately explored. Addressing these gaps is essential for advancing the development of high-performance materials and optimizing thermal treatment processes.

This study aims to bridge these knowledge gaps by leveraging molecular dynamics simulations to investigate the nanoscale effects of high-energy electron beam irradiation on WC-Co surfaces. By analyzing local entropy and von Mises stress during evaporation and linear scratching processes, we seek to uncover the mechanisms driving structural and mechanical property changes. This research not only advances the fundamental understanding of high-energy thermal treatment effects on WC-Co composites but also contributes to the development of more robust and durable materials for industrial applications. The insights gained are anticipated to enhance thermal treatment techniques, ultimately improving the performance and longevity of WC-Co-based components in critical engineering applications.

2. Materials and Methods

2.1. Conformations

Figure 1 depicts two sets of conformations designed to investigate nanoscale phenomena: evaporation (top) and the linear scratching process (bottom). For the evaporation study, blocks with cobalt (Co) and tungsten carbide–cobalt (WC-Co) top layers were prepared to examine the behavior of Co atoms under varying energy flux conditions. The initial crystal structures of WC and Co were modeled as hexagonal close-packed (HCP, a = 2.906 Å, c = 2.837 Å) and face-centered cubic (FCC, a = 3.519 Å), respectively. The Co and WC tops were configured as single-grain structures, while the WC-Co top layer consisted of randomly oriented WC and Co grains [18,23]. Figure 2 provides details of the full-sized blocks, each comprising a top and bottom layer. The dimensions of the blocks were as follows: 11.1 nm × 11.1 nm × 11.5 nm for the Co top layer, and 11.1 nm × 11.1 nm × 11.6 nm for the WC and WC-Co top layers (see

Table 1. Values of dimensions of conformations in Figure 2.

Variable	Value	Variable	Value
lx	11.1 nm	htop	7.0 nm (Co top) 7.1 nm (WC-/WC-Co top)
ly	11.1 nm	hblock	11.5 nm (Co top) 11.6 nm (WC-/WC-Co top)

). The WC-Co blocks contained 15 wt% cobalt. The bottom layer, with a total thickness of 4.5 nm, consisted of three sublayers: a rigid substrate (0.25 nm), a thermal reservoir (2.0 nm), and a buffer layer (2.25 nm). These conformations were prepared for structural and mechanical investigations.

2.2. Interatomic Potential Model: Alaytic Bond Order Potential (ABOP) Model

Accurate interatomic potential models are essential for ensuring both the efficiency and precision of molecular dynamics simulations. This study employed Analytic Bond Order Potential (ABOP) to model the tungsten carbide–cobalt (W-C-Co) system, which features a mix of metallic and covalent bonding. ABOP has been specifically designed to capture such bonding interactions and has been successfully applied to W-C-Co systems in prior studies [18,23,27,28,29]. The ABOP model is based on the bond-order concept, quantifying bonding strength through atomic interactions. This model is a modified empirical tight-binding potential for metals, expressed as:

$$E_{ABOP}=\sum _{\left\{i>j\right\}}{f}_C\left(r_{ij}\right)\left[E_R\left(r_{ij}\right)-{\overline{b}}_{ij}{E}_A\left(r_{ij}\right)\right],$$

(1)

where f_C(r) is the cutoff function defining neighbor interactions, E_R and E_A are repulsive and attractive potentials between atoms i and j, respectively, and ${\overline{b}}_{ij}$ is the averaged bond order. The parameters and functions for the ABOP model were adopted from Erhart et al. [27]. The ABOP model has been widely recognized for its accuracy and transferability across materials without the need for reparameterization, making it particularly suitable for systems with covalent bonding. In this study, the ABOP parameters for the WC-Co system were derived from Petisme et al. [28], incorporating both experimental data and first-principles calculations. Validation of the potential was achieved by comparing melting points from experiments and simulations, as discussed in Section 3.1. Additionally, alternative parameters were proposed to improve melting point accuracy.

2.3. Simulation Protocols

Figure 3 presents a flowchart summarizing the simulation protocols. All simulations, except for potential model validation, employed periodic boundary conditions in all Cartesian directions. Each periodic unit cell contained a conformation block as defined in Section 2.1 and an empty buffer zone with a height of 15.4 nm. The simulations were performed in three distinct scenarios: potential model validation, evaporation phenomena, and linear scratching phenomena.

Let us start with the first scenario, the validation protocol. The test configuration consisted of a WC-Co top block, as illustrated in Figure 1. To validate the ABOP model, melting points from simulations were compared with experimental values. The canonical ensemble was used to incrementally increase the system temperature from 2300 K to 3600 K at 1 bar over 4.37 ns. Data on atomic positions and stress tensors were collected to compute temperature-dependent von Mises stress and local entropy profiles. These results, along with their standard deviations, are presented in Section 3.1.

The next scenario was the evaporation protocol. Evaporation dynamics were studied by heating the conformations from 300 K to 3200 K at 1 bar over 150 ps and equilibrating them at 3200 K for 140 ps using the canonical (NPT) ensemble. The system was then switched to a microcanonical ensemble with a Langevin thermostat at 3200 K, and a predefined surface domain (up to 2.5 nm in depth) was subjected to a heat flux (q″ = 0, 0.5, 1.0 [keV/ps]) for 100 ps. The heating depth was based on the Kanaya–Okayama formula for tungsten [30]. Snapshots of cross-sections, along with number density and power law analyses, were used to characterize the evaporation phenomena (Section 3.2).

The last scenario was linear scratching. Linear scratching on WC and WC-Co free surfaces was studied using two sets of conformations: untreated samples at 300 K and 1 bar, and thermally treated samples. Thermal treatment included a sequence of heating (300 K to 3200 K), equilibration at 3200 K, and cooling back to 300 K. Figure 4 provides schematic diagrams of the scratching process, highlighting three stages: no indentation, indentation, and linear scratching. The simulations utilized a rigid spherical tip (radius: 1.5 nm) moving at 50 m/s. The parameters used in this study, including the rigid spherical tip with a radius of 1.5 nm and a scratch speed of 50 m/s, were deliberately chosen to simulate atomic-scale phenomena. These include nanoscale systems or processes such as high-energy atomic collisions, nanoparticle bombardment, nano-machining, and surface damage caused by the interaction of an AFM tip with a surface. The choice of these values ensures this study focused on forces and behaviors that dominate at the atomic scale. Bivariate histograms of local entropy and von Mises stress were analyzed to evaluate structural and mechanical instabilities (Section 3.3).

All simulations were conducted using LAMMPS, with post-processing performed using OVITO Pro, Python, and MATLAB [22,31].

2.4. Local Entropy and Von Mises Stress

Local entropy (LE) and von Mises stress (${\sigma }_{VMS}$) were the primary properties used to analyze structural instabilities and mechanical characteristics. Local entropy quantifies atomic randomness based on two-body interactions using the radial distribution function (g(r)):

$$LE=-2\pi \rho k_B{\int }_0^{\infty }\left[g\left(r\right)\left(\mathrm{l}\mathrm{n}g\left(r\right)-1\right)+1\right]r^{2}dr,$$

(2)

$$g\left(r\right)={\displaystyle \frac{1}{2^{5/2}{\pi }^{3/2}N\sigma \rho r^2}}\sum _{i\ne j}{e}^{-{\left(r-r_{ij}\right)}^2/\left(2{\sigma }^2\right)},$$

(3)

where $\rho$ is the average density of the system, $k_B$ is the Boltzamann constant, $N$ is the number of atoms in the system, and $\sigma$ is the broadening parameter [16]. The von Mises stress quantifies mechanical stress to predict the yielding stage of a structure under external forces, and its magnitude is relevant to the intensity of distortional energy within a structure under loading. Stable atoms have relatively low von Mises stress values, and plastic deformation or failure occurs for atoms with high von Mises stress. We used elements of the virial stress tensor in a Cartesian coordinate system, as shown:

$${\sigma }_{VMS}=\sqrt{{\displaystyle \frac{1}{2}}\left[{\left({\sigma }_{xx}-{\sigma }_{yy}\right)}^2+{\left({\sigma }_{yy}-{\sigma }_{zz}\right)}^2+{\left({\sigma }_{zz}-{\sigma }_{xx}\right)}^2\right]+3\left({\tau }_{xy}^2+{\tau }_{yz}^2+{\tau }_{zx}^2\right),}$$

(4)

where ${\sigma }_{ii}$ is the normal stress along the i-axis, and ${\tau }_{ij}$ is the shear stress in the j direction on the i plane [22]. Virial stress, in general, is much larger than experimental stress because it reflects localized, atomic-scale interactions with contributions from both kinetic and potential energy [32,33]. Experimental stress, on the other hand, is a macroscopic, averaged quantity that smooths out these localized effects. Proper averaging, scaling, and interpretation are essential to bridge the gap between virial stress and experimentally measured stress.

3. Results and Discussions

3.1. Validation of ABOP Model

The validation of interatomic potentials is a crucial step in ensuring reliable and accurate molecular dynamics simulations. In this study, the Analytic Bond Order Potential (ABOP) model was validated by comparing simulated melting points with experimental data, as shown in Figure 3. The Lindemann index, which quantifies atomic vibrational displacements, has been widely used in prior studies to evaluate structural stability and predict melting points [18,34,35]. For example, Yi et al. demonstrated the utility of the Lindemann index in determining the melting point of WC-Co alloys, achieving results consistent with experimental findings [18]. To enhance sensitivity and robustness, this study introduced alternative indicators—specifically, the standard deviations of von Mises stress and local entropy—to characterize atomic structural disorder. The experimental melting point of tungsten carbide with 15 wt% cobalt (approximately 3140 K) was used as a reference for comparison [36]. The conformation employed for validation was consistent with previous research setups [18]. Figure 5a and Figure 6a illustrate the temperature-dependent behavior of von Mises stress and local entropy, respectively. These profiles reveal distinct phase transitions between 3050 K and 3150 K. Below 3050 K, the profiles exhibit steep gradients, indicating increasing atomic randomness and structural instability as the temperature approaches the melting range. Beyond 3150 K, the slopes flatten, consistent with liquid-phase behavior characterized by less pronounced structural changes. Figure 5b and Figure 6b depict the standard deviations of von Mises stress and local entropy, which effectively capture the structural instability during melting. The melting point, identified as the deflection point in the sequential profiles of standard deviations shown in Figure 5b and Figure 6b, was determined by calculating the first and second derivatives of the data sets. The index corresponding to the maximum absolute value of the second derivative marks the point of maximum curvature, representing the most significant change in the data. This distinct transition, observed near 3150 K, aligns well with the experimentally determined melting point. The calculated error margin for the simulated melting point, derived using the equations in Figure 3, ranged between 0% and 2.87%, indicating a high degree of accuracy. These findings validate the ABOP model as reliable for simulating the structural and mechanical properties of WC-Co systems, enabling its use in subsequent analyses.

3.2. Structural and Mechanial Characteristics Variations Subject to Linear Scratch

Cobalt evaporation in condensed phases represents a key transport phenomenon driven by elevated temperatures and energy flux. This process causes atoms to migrate from their initial positions into the vapor phase. Such evaporation weakens the structural integrity and functional performance of WC-Co tools, leading to increased brittleness, wear, and failure. Understanding and mitigating this phenomenon is vital for extending tool longevity, improving efficiency, and minimizing associated health and environmental risks. Snapshots of thermally treated structures near cobalt’s boiling point (T = 3200 K) are shown in Figure 7. These images highlight the accelerated evaporation process under high-temperature conditions. Cross-sectional views of the simulation cells and corresponding number density distributions (${\rho }_N$)—calculated within 0.5 Å thick slabs along the z-axis—are presented for (a) a fully cobalt-covered micro-grain and (b) a WC-Co nano-polycrystalline structure. The results indicate that electron beam (e-beam) irradiation significantly enhances evaporation compared to the no-irradiation condition. Atoms beyond the Gibbs dividing plane of the free surface, defined as the point where the number density drops to 30% of the bulk crystal value, were classified as vapor-phase atoms for further analysis. Figure 8 depicts the time-dependent evaporation behavior of cobalt atoms, quantified by the number of evaporated atoms (N_X(t)) for each scenario. The evaporation process follows a power law relationship:

$$N_X\left(t\right)=C{t}^{n_X},$$

(5)

where C is a fitting parameter and n_X represents the power law index.

Table 2. Power law index n for Co and WC-Co top blocks, derived from molecular dynamics simulation results within a constrained time interval.

Power Law Index	q″
	0 keV/ps	0.5 keV/ps	1 keV/ps
nCo	−0.22 ±0.16	1.08 ± 0.11	1.73 ± 0.11
nWC-Co	−0.15 ± 0.22	0.77 ± 0.22	2.01 ± 0.22

summarizes the power law indices for various surface configurations under different irradiation energy fluxes: (1) no irradiation (q″ = 0 keV/ps), where minimal evaporation occurs, as reflected in low power law indices, (2) low flux (q″ = 0.5 keV/ps), where evaporation progresses steadily, with n_X~1, indicating a nearly constant evaporation rate over time, and (3) high flux (q″ = 1.0 keV/ps), where the evaporation rate accelerates significantly, with power law indices exceeding 1 for both cobalt and WC-Co surfaces.

The evaporation rate varied with the bonding environment. Cobalt atoms embedded between WC grains experienced stronger bonding forces (e.g., higher latent heat of evaporation), making them more resistant to vaporization compared to those on a pure cobalt surface. Interestingly, at q″ = 1.0 keV/ps, the WC-Co surface exhibited a higher power law index than the pure cobalt surface. This behavior is attributed to the WC-Co structure’s broader low-density region resulting from localized evaporation and thermal expansion. These findings underscore the intricate interplay between bonding forces, local density, and energy input in driving evaporation dynamics.

3.3. Bivariate Histograms Under Linear Scratching Processes

To investigate structural and mechanical responses during linear scratching, simulations were conducted in three stages (see Figure 4): pre-indentation (Stage 1), indentation (Stage 2), and linear scratching (Stage 3). Bivariate histograms of local entropy and von Mises stress at these stages are presented in Figure 9 and Figure 10 for the configuration with a WC top, and in Figure 11 and Figure 12 for the configuration with a WC-Co top. In each case, Figure 9 and Figure 11 report results for all atoms in a periodic cell, while Figure 10 and Figure 12 focus on atoms within a 2 nm surface block. Notably, we chose a block thickness larger than the indenter’s radius for Figure 10 and Figure 12. The color maps in these histograms indicate data point density [18], providing a combined visualization of structural instabilities and mechanical properties. Three key points are discussed: (1) the effect of deformation due to indenter motion, (2) comparisons of WC and WC-Co top blocks, and (3) effect of surface thermal treatment. The effect of deformation was demonstrated by examining the bivariate maps at the three stages, and we observed that both local entropy and von Mises stress broadened in range during indentation and scratching. Initially (Stage 1), these distributions were relatively narrow, reflecting structural stability. As indentation began (Stage 2), stress concentrations emerged alongside localized atomic-scale instabilities, and during scratching (Stage 3), the entropy distributions widened even further, indicating increasing disorder. The high velocity of the rigid spherical tip (50 m/s) imposed substantial local stresses, which, in turn, highlighted zones of significant plastic deformation and structural instability. The resulting increase in structural disorder and material displacement under the moving indenter provides insights into wear and damage mechanisms at the nanoscale. The next point addresses the comparison of results for different configuration types. Differences in the mechanical responses of WC and WC-Co top blocks were clearly visible. The addition of cobalt in WC-Co altered deformation and stress behaviors due to cobalt’s softer, more ductile character. Compared to WC (Figure 9 and Figure 10), the WC-Co configuration (Figure 11 and Figure 12) exhibited broader distributions of von Mises stress and local entropy. This indicates greater structural instability and an enhanced tendency for plastic deformation, consistent with cobalt’s role as a binder that increases toughness but reduces overall rigidity. Understanding these contrasts is crucial for optimizing WC-Co composites in abrasive applications. The final section examines the influence of thermal treatment. Panels (a) in Figure 9, Figure 10, Figure 11 and Figure 12 represent untreated surfaces, while panels (b) correspond to thermally treated cases. Thermal treatment significantly modified structural and mechanical responses in both WC and WC-Co. The treated WC samples (Figure 9 and Figure 10) showed shifted distributions toward higher entropy values, indicating greater disorder and susceptibility to deformation. Although the WC-Co samples (Figure 11 and Figure 12) exhibited somewhat smaller range expansions, thermal treatment still increased their entropy values, underscoring heat’s influential role in altering structural properties. In WC-Co, thermal exposure led to cobalt evaporation and microstructural changes, ultimately increasing entropy and making treated surfaces more prone to deformation. While thermal treatment may enhance certain properties, such as hardness, it also introduces vulnerabilities due to phase transformations and microstructural degradation. Thus, thermal treatment conditions must be carefully optimized to balance improved performance against long-term durability.

4. Conclusions

This study provides a comprehensive understanding of the nanoscale mechanisms driving the structural and mechanical transformations of tungsten carbide–cobalt (WC-Co) composites under high-energy thermal treatments, specifically electron beam irradiation, through molecular dynamics simulations. From a practical perspective, the findings reveal how electron beam irradiation significantly influences the structural integrity and mechanical properties of WC-Co composites. These insights are critical for optimizing thermal treatment protocols, enhancing the performance and extending the durability of WC-Co-based tools and coatings in industrial applications. From a scientific viewpoint, this study advances our understanding of nanoscale phenomena, including cobalt evaporation and the emergence of structural instability under combined thermal and mechanical stresses. These results contribute to the broader field of materials science by leveraging molecular dynamics to predict and analyze the behavior of complex materials under extreme conditions, paving the way for future innovations in high-performance material design.

• The results demonstrate that high energy flux markedly enhances cobalt evaporation rates, with the extent of evaporation being strongly influenced by the energy flux and the local atomic environment. Cobalt atoms embedded within WC grains exhibit increased resistance to evaporation due to stronger bonding interactions, whereas pure cobalt surfaces are more susceptible to material loss. At elevated energy flux levels, WC-Co surfaces experience a complex interplay of density reduction, thermal expansion, and evaporation processes, leading to accelerated material degradation compared to pure cobalt surfaces.
• Linear scratching simulations reveal that thermally treated WC and WC-Co surfaces exhibit heightened structural instability. This instability is evidenced by broader distributions of local entropy and von Mises stress, indicating an increased susceptibility to deformation and potential failure. The stress concentrations induced by indentation and scratching are more pronounced in thermally treated materials, underscoring the significant impact of thermal history on their mechanical behavior.
• The utilization of molecular dynamics simulations has proven invaluable in capturing atomic-scale phenomena that are challenging to observe experimentally. This approach allowed for precise quantification of the effects of energy flux, material composition, and thermal history on the structural and mechanical responses of WC-Co composites. The detailed insights gained into the mechanisms driving the observed changes enhance the fundamental understanding of high-energy thermal treatments on these materials.
• The findings underscore the importance of optimizing energy flux and thermal treatment protocols to mitigate material degradation and improve the durability of WC-Co-based components. By analyzing the nanoscale interactions and transformations induced by electron beam irradiation, this study provides guidance for the development of more robust and reliable tools and coatings for industrial applications.

Future work should focus on experimentally validating the simulation outcomes and investigating alternative thermal treatment strategies to further improve material performance. Extending this approach to other material systems could broaden the applicability of the findings, benefiting the design and optimization of WC-Co composites in cutting tools and wear-resistant coatings. The identified trends in stress and entropy distributions offer valuable insights into the limits of structural stability under dynamic loading. We expect that this knowledge can guide refined material processing techniques—whether through tailored thermal treatments or compositional adjustments—to enhance both durability and overall performance.