Molecular Dynamics Investigation of Ultra‑Precision Diamond Cutting of Cerium

Abstract

The coupling between structural phase transformations and dislocation dynamics complicates the understanding of cerium’s nanoscale deformation. Here we employ molecular dynamics (MD) to unravel the mechanism of cerium during ultra‑precision diamond cutting. An MD model incorporating empirically‑derived Ce–Ce and Ce–C potentials is constructed, and the elastic response of two fcc cerium phases is evaluated. Simulations show that dislocation slip dominates plastic deformation, while radial‑distribution‑function analysis reveals only minor γ→δ phase changes at the machined surface and chip. Parameter studies identify the optimal machining conditions for achieving a high‑quality surface.

Background

Cerium (Ce, Z=58) is a lanthanide metal prized for its unique mechanical, physical, and chemical properties. Surface morphology critically influences performance, corrosion resistance, and hydrogen‑storage behavior of cerium parts [1–3]. Ultra‑precision diamond cutting can produce ultra‑smooth surfaces with minimal subsurface damage [6,7], yet little experimental or theoretical work has addressed cerium cutting. Because the tool edge radius in ultra‑precision cutting is comparable to the depth of cut, the material’s properties dominate the process, making the mechanism of cerium cutting particularly challenging.

Ce exhibits a rich pressure‑temperature phase diagram driven by 4f‑electron delocalization. At ambient pressure and <110 K the α‑Ce (fcc) phase is stable, transforming to β‑Ce (dhcp) between 45–275 K, γ‑Ce (fcc) between 270–999 K, and δ‑Ce (bcc) between 999–1071 K [8–11]. Notably, the γ→α transformation at 295 K and 8 kbar collapses volume by ~20% [12–14], while the γ→δ transition can be triggered by high temperature and pressure. These transformations alter bonding and elastic properties, affecting deformation. Metallic Ce is also ductile, governed by dislocation activity [15]. However, the interplay between phase changes and dislocations during diamond cutting remains largely unexplored.

MD simulation offers a powerful route to probe fundamental machining mechanisms at the atomic scale. Previous studies have examined nanoscratching and orthogonal cutting of Cu, Al, Fe, and high‑entropy alloys, revealing insights into dislocation nucleation, surface pile‑up, and friction behavior [16–27]. Such work highlights the importance of crystal orientation, tool rake angle, and interaction potentials. Yet no MD study has investigated the mechanical machining of cerium, motivating the present work.

Methods

MD Model of Diamond Cutting

Figure 1 illustrates the simulation setup: a single‑crystal Ce workpiece (41 × 25 × 31 nm) containing ~1 × 10^6 γ‑Ce atoms, and a diamond cutting tool (0.1 × 10^6 C atoms) with a 9° relief angle. The workpiece is divided into a fixed 2 nm bottom layer and a mobile layer that follows Newtonian dynamics with a 1 fs time step. Periodic boundaries are applied only along the longitudinal direction. Three crystallographic orientations—(010), (110), and (111)—are considered. Seven rake angles (−30°, −20°, −10°, 0°, 10°, 20°, 30°) are tested. The diamond tool is treated as a rigid body; thus C–C interactions are omitted.

Atomic interactions are modeled as follows: Ce–Ce forces use the embedded atom method (EAM) parameterization of Sheng et al. [29], accurately reproducing elastic constants of fcc Ce. Ce–C interactions adopt a Morse potential: \n\n$$E_{\text{tot}}=\sum_{ij}D_0\left[e^{-2\alpha(r-r_0)}-2e^{-\alpha(r-r_0)}\right]$$\n\nwith D_0=0.087 eV, α=5.14, and r_0=2.93 Å; a 1.0 nm cutoff is applied [30].

The system is first equilibrated at 30 K, 0 bar in the NPT ensemble, then subjected to diamond cutting at a constant velocity of 100 m/s and depth of cut 4 nm in the NVT ensemble. Cutting forces are resolved along the cutting direction, with the cutting direction indicated by red arrows in the figures. Although the simulated dimensions and cutting speeds are orders of magnitude smaller than experimental ultra‑precision conditions, the MD model captures the essential physics of the process. Common‑neighbor analysis (CNA) distinguishes fcc, hcp, bcc, and defect atoms [31]. Simulations are performed with LAMMPS (1 fs step) and visualized using OVITO [32,33].

Characterizing Cerium Phases

Five cerium phases—γ, α, β, ε, and δ—are modeled using lattice parameters from the literature [8–11]. Bulk configurations undergo uniaxial tension, shear, and compression to extract elastic constants and mechanical properties (Table 2). The calculated Young’s modulus of γ‑Ce (24.17 GPa) aligns with experimental nanoindentation data (36.7 GPa) [10], and the elastic constants agree with inelastic neutron scattering results [34]. Denser α‑Ce exhibits significantly higher stiffness than γ‑Ce.

Radial‑distribution‑function (RDF) analysis characterizes structural differences among phases. Figure 2a shows distinct RDF peaks for each phase, corresponding to nearest‑neighbor distances (e.g., γ‑Ce: 3.64, 5.13, 6.30 Å; α‑Ce: 3.41, 4.85, 5.92 Å). Uniform compression of γ‑Ce to achieve a 20% volume collapse yields an RDF matching that of α‑Ce (Figure 2b), confirming the γ→α transition [12–14].

Results and Discussion

Machining Mechanisms of Cerium

MD simulations of diamond cutting on Ce(010) with a 0° rake angle reveal three force regimes (Figure 3). Initially, adhesive forces produce negative cutting and normal forces; elastic deformation follows, leading to a rapid rise in forces. At ~2.3 nm cutting length, a sharp drop indicates the onset of plasticity, dominated by 1/6<112> Shockley partial dislocations nucleated near the free surface and gliding on {111} planes. The cutting and normal forces stabilize between 10–35 nm, while dislocations accumulate ahead of and beneath the tool. Beyond 35 nm, the tool separates from the workpiece, causing force reduction. Throughout, normal force remains lower than cutting force.

Figure 4 depicts the evolution of defect structures and surface morphology at key cutting lengths. Shockley partials generate stacking faults bounded by dislocation cores. As cutting progresses, a dense cloud of partials emanates from the front surface, forming chips along the rake face (Figure 4f). Dislocations behind the tool ascend to the top surface, promoting surface recovery. When the tool approaches the left boundary, dislocation propagation is hindered, increasing chip volume (Figure 4g). After chip separation, the dislocation density diminishes due to annihilation at the free surface (Figure 4h).

RDF analysis of defect zones confirms limited γ→δ phase transformation. The RDF of the defect region beneath the surface aligns with δ‑Ce peaks, indicating a minor γ→δ transition driven by local heating (Figure 5a). Similar δ‑Ce signatures appear in the chip (Figure 5b), but the overall amount remains trivial, suggesting that phase changes are not dominant during cutting.

Influence of Rake Angle

Figure 6 shows that both cutting and normal forces decrease with increasing rake angle, in agreement with Merchant’s theory of shear plane energetics [37]. Higher rake angles also reduce force differential and improve machining stability.

Defect analysis (Figure 7a,b) reveals that a negative rake angle (−30°) yields a higher dislocation density than a positive angle (30°). The number of dislocation segments (Figure 7c) declines monotonically with rake angle, reflecting less complex plastic deformation and lower work hardening.

Surface morphology (Figure 8) corroborates these findings: negative rake angles produce asymmetric, pronounced surface pile‑up, whereas a 30° rake generates the lowest pile‑up volume and a symmetric profile. Consequently, a 30° rake angle is optimal for achieving low cutting force, minimal dislocation density, and superior surface finish.

Influence of Crystal Orientation

Under the optimal 30° rake, we compare Ce(010), Ce(110), and Ce(111) orientations (Figure 9). Ce(010) exhibits the lowest cutting force and dislocation count. Although Ce(111) offers the fewest dislocations, its {111} plane parallel to the surface promotes surface pile‑up, increasing cutting resistance. Machined surface morphology (Figure 10) shows that Ce(010) yields the smallest pile‑up volume and the most symmetric profile, whereas Ce(110) suffers the largest pile‑up.

Conclusions

We have developed an MD framework incorporating EAM and Morse potentials to model ultra‑precision diamond cutting of cerium. Elastic constants, mechanical properties, and phase‑transition behavior of Ce phases are validated, confirming the model’s predictive capability. Simulations reveal that dislocation nucleation and glide dominate plasticity, with only minor γ→δ phase changes observed. Optimal machining conditions—30° rake angle and (010) crystal orientation—produce the lowest cutting forces, minimal dislocation density, and highest surface quality.

References

[1]–[38] (see original article for full citation list)

Figures

Figure 1. MD model of diamond cutting of Ce. (a) Front view, (b) top view. Red = bottom Ce atoms, blue = mobile Ce atoms, gray = C atoms.

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Figure 2. (a) RDF of cerium phases. (b) RDF before and after γ‑Ce compression to 20% volume collapse.

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Figure 3. Variation of cutting and normal forces with cutting length. Subfigures display defect configurations per zone.

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Figure 4. Defect structures and machined surface morphology at various cutting lengths.

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Figure 5. RDF analysis of defect zone (a) and chip (b) after cutting.

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Figure 6. Rake‑angle dependence of average cutting and normal forces.

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Figure 7. Defect structures for rake angles −30° (a) and 30° (b); dislocation count (c).

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Figure 8. Machined surface morphologies for rake angles −10°, −20°, −30°, 10°, 20°, 30°.

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Figure 9. Cutting force and dislocation number versus crystal orientation.

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Figure 10. Machined surface morphologies for Ce(010), Ce(110), Ce(111).

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