Molecular Dynamics Modeling and Simulation of Diamond Cutting of Cerium
© The Author(s). 2017
Received: 18 April 2017
Accepted: 16 July 2017
Published: 25 July 2017
The coupling between structural phase transformations and dislocations induces challenges in understanding the deformation behavior of metallic cerium at the nanoscale. In the present work, we elucidate the underlying mechanism of cerium under ultra-precision diamond cutting by means of molecular dynamics modeling and simulations. The molecular dynamics model of diamond cutting of cerium is established by assigning empirical potentials to describe atomic interactions and evaluating properties of two face-centered cubic cerium phases. Subsequent molecular dynamics simulations reveal that dislocation slip dominates the plastic deformation of cerium under the cutting process. In addition, the analysis based on atomic radial distribution functions demonstrates that there are trivial phase transformations from the γ-Ce to the δ-Ce occurred in both machined surface and formed chip. Following investigations on machining parameter dependence reveal the optimal machining conditions for achieving high quality of machined surface of cerium.
Cerium (Ce) with an atomic number of 58 is one of the most abundant lanthanide metals. Cerium has wide applications for its intriguing mechanical, physical, and chemical properties. It is known that machined surface morphology of metal parts has a strong influence on their functionality, performance, and life cycle. For instance, the corrosion resistance of metal parts can be effectively improved by reducing surface roughness or introducing compressive residual stress in machined surface [1–3]. More recently, Yan et al. employed a novel tip-based mechanical machining technique to fabricate periodic triangular micro-cavities on Cu(111), which is demonstrated to be a surface-enhanced Raman scattering substrate . Specifically for cerium that is used to store hydrogen , the surface finish of cerium strongly influences the reaction between cerium and hydrogen at room temperature. Therefore, achieving high accuracy of machined surface morphology of cerium is crucial for its applications. Ultra-precision diamond cutting is one important manufacturing technique to obtain ultra-smooth surface finish of high surface integrity, ultra-low surface roughness, high flatness, low metallographic structure evolution, and low subsurface damage [6, 7]. However, either experimental or theoretical work about the diamond cutting of cerium had been rarely reported. Furthermore, since in the ultra-precision diamond cutting process, the tool edge radius is comparable with depth of cut, the properties of workpiece material play an important even dominant role in the cutting process. Therefore, the understanding of machining mechanisms of cerium is challenging for its complex deformation behavior.
First, cerium is known for its extraordinary rich pressure-temperature phase diagram driven by the delocalization of 4f electrons. At atmospheric pressure and low temperatures below 110 K, the α-Ce (face-centered cubic (fcc)) is stable. At increased temperatures ranging from 45 to 275 K the α-Ce transforms to the β-Ce (double hexagonal close-packed (dhcp)). The γ-Ce (fcc) is stable at moderate temperatures between 270 and 999 K. At high temperatures between 999 K and the melting temperature of 1071 K the δ-Ce (body-centered cubic (bcc)) is stable [8–11]. In particular, the most fascinating isostructural phase transformation from the trivalent low-density γ-Ce to the much denser α-Ce at 295 K and under 8 kbar is accompanied with a large volume collapse of 20% [8, 12–14]. The phase transformation-induced modification of the electronic structure and bonding configuration in cerium inevitably has a strong impact on its deformation behavior. Specifically, the high temperature and high pressure formed in the contact region between cutting tool and workpiece may result in phase transformation of cerium in the diamond cutting process. Second, metallic cerium has considerable ductility governed by dislocations . It is known that dislocation nucleation and glide play key roles in the plastic deformation of fcc metals under mechanical machining. However, it is still largely unknown about the interaction between phase transformations and dislocations in the diamond cutting of cerium.
The constituents of machining mechanisms consist of microscopic deformation behavior of workpiece material and its correlation with macroscopic machining results in terms of cutting force, chip profile, and machined surface morphology. As an important supplementary to machining experiments, molecular dynamics (MD) simulation has been demonstrated to be a powerful tool for elucidating fundamental mechanical machining mechanisms of different kinds of materials. Li et al. reported that the minimum wear depth of single crystalline Cu(111) under nanoscratching that is equivalent to the critical penetration depth at which plasticity initiates increases with probe radius . More recently, they investigated the mechanical behaviors and deformation mechanisms of AlCrCuFe high-entropy alloys under nanoscratching and reported a larger surface pileup volume than pure metals due to its good high-temperature stability of the alloy material . Gao et al. investigated the generation and evolution of plasticity and defects in orthogonal cutting of a bcc Fe . Zhu et al. reported a size effect on the probe shape dependence of the nanoscratching . Hosseini et al. investigated the effects of tool edge radius on nanomachining of single crystal copper . Liu et al. found that the difference between static and dynamic friction coefficients disappear in single asperity friction of Cu(111) due to the interference between asperities . Romero et al. found that the adhesion during orthogonal cutting of a copper substrate can be reinforced by varying the tool rake angle and by choosing specific lattice orientations . Yang et al. indicated that the abrasive self-rotation velocity and direction have significant influence on the morphology and quality of the machined surface of single crystal copper under polishing . Vargonen et al. reported that the tip height loss per scratching distance during scratching is a function of the normal stress and the tapering angle of the tip . Sun et al. proved impact of GB on the scratching of bi-crystal copper . Chen et al. found that water molecules effectively reduce the friction between the tool and workpiece in the nanometric cutting of copper . Wu et al. reported that the bonding energy has a significant influence on the friction . In addition, as compared to experimental investigations, mechanical properties of each cerium phase can be conveniently studied by means of MD simulations, which is crucial for understanding the interaction between phase transformations and dislocations in cerium. More recently, Zhang et al. investigated the interactions between phase transformation and dislocation at the elastic-plastic transition in silicon nanoindentation by MD simulations . However, to the best of our knowledge, there is no work reported on the MD investigation of mechanical machining of cerium.
Therefore, in the present work, we first establish the MD model of diamond cutting of cerium by constructing atomic configurations of workpiece and tool, assigning empirical potentials for Ce-Ce and Ce-C atomic interactions, and characterizing two fcc phases of cerium. With the established MD model, we then perform MD simulations of diamond cutting of cerium to elucidate the fundamental machining mechanisms of cerium and investigate the influences of rake angle of cutting tool and crystallographic orientation of workpiece on the cutting process.
MD Model of Diamond Cutting
The as-created simulation system is first equilibrated to its equilibrium configuration at 30 K and under 0 bar in the NPT ensemble (constant number of atoms N, constant pressure P, and constant temperature T). Then, the equilibrated workpiece is subjected to the diamond cutting with a constant velocity of 100 m/s and a depth of cut of 4 nm in the canonical ensemble (constant number of atoms N, constant volume V, and constant temperature T). The cutting direction is indicated by arrows colored by red in different views point of the cutting model. And the cutting force is defined as the force component along the cutting direction. The utilized depth of cut in the ultra-precision machining experiment is a few micrometers. We note that the simulated dimension of workpiece and depth of cut are several orders of magnitude smaller than that utilized in ultra-precision diamond cutting experiments, due to the limitation of length scale in atomistic simulations. We also note that the employed cutting velocity of 100 m/s in current MD simulations of nanometric cutting is several orders of magnitude higher than typical velocities of tens of micrometers per second utilized in ultra-precision diamond cutting experiments, giving the intrinsic requirement of the integration time step to be of the order of femtosecond (fs). The common neighbor analysis (CNA) is utilized to identify types of lattice defects , and the coloring scheme is as follows: green stands for fcc atoms, red for hexagonal close-packed (hcp) atoms, blue for body-centered cubic (bcc) atoms, and gray for other atoms including surface atoms and dislocation cores. All the MD simulations are performed by using the LAMMPS code with an integration time step of 1 fs . And the OVITO is utilized to visualize MD data and generate MD snapshots .
Characterizing of Cerium Phases
Lattice parameters (Å)
Face-centered cubic (fcc)
a = 5.1610
P = 0, T = 270~999 K
Face-centered cubic (fcc)
a = 4.824
P = 0, T < 110 K / P = 8kbar, T = 295 K
Double hexagonal close-packed (dhcp)
a = 3.6810
c = 11.857
P = 0, T = 45~275 K
Body-centered cubic (bcc)
a = 4.11
P = 0, T = 999~1071 K
Body-centered tetragonal (bct)
a = 2.92
b = 4.84
P = 17.5 GPa, 295 K
Elastic constants and mechanical properties of cerium phases
Bulk modulus (GPa)
Young’s modulus (GPa)
Shear modulus (GPa)
Results and Discussion
Machining Mechanisms of Cerium
It is seen from Fig. 3 that both cutting force and normal force have negative values when the cutting tool is right close to the workpiece, due to the adhesion between cutting tool and workpiece. When the cutting tool begins to contact with the workpiece, the material firstly undergoes elastic deformation, accompanied with rapid increases of both cutting force and normal force. Figure 3 shows that both cutting force and normal force drop rapidly at a cutting length of 2.3 nm, indicating the initiation of plastic deformation. Upon further cutting, both cutting force and normal force increase with strong fluctuations caused by successive nucleation events. It is seen from the subfigure in zone II that there are considerable 1/6<112> Shockley partial dislocation generated in the vicinity of the cutting zone. Both cutting force and normal force mainly fluctuates around constant values in the cutting length ranging from 10 to 35 nm, indicating that the cutting process is stable. And dislocations in zone II mainly reside both in front of and beneath the diamond cutting tool. When the cutting length reaches 35 nm, the cutting tool starts to separate from the workpiece, accompanied with significant decreases of both cutting force and normal force. The subfigure in zone III shows there are considerable dislocations blocked by the left side of the workpiece. Both cutting force and normal force become steady until formed chip is completely separated from the workpiece. Figure 3 shows that during the cutting process, normal force is lower than cutting force.
Influence of Rake Angle
Influence of Crystal Orientation of Cerium Workpiece
In summary, we perform MD modeling and simulation to elucidate the underlying mechanisms of cerium under the ultra-precision diamond cutting. The EAM and Morse potentials are respectively employed to describe atomic interactions within cerium workpiece and the interactions between cerium workpiece and diamond cutting tool. The elastic constants, mechanical properties, and propensity of phase transformation of cerium phases are evaluated, which demonstrates the feasibility of predicting phase transformation of cerium by the current established MD model. Subsequent MD simulations of diamond cutting reveal that the plastic deformation of cerium is governed by dislocation nucleation and subsequent glide, which is similar with other fcc metals. In addition, there is γ ➔ δ phase transformation occurred within both machined surface and formed chip. It is found that high quality of machined surface and low machining force can be achieved in the diamond cutting of cerium with the optimal machining conditions, i.e., a rake angle of 30° for a crystal orientation of (010).
The authors gratefully acknowledge financial support from the National Natural Science Foundation of China and the China Academy of Engineering Physics United Foundation (NSAF) (Grant No. U1530105).
JZ, MS, and TS conceived the project. HZ, YL, and YY performed the molecular dynamics simulations and analyzed the data. JZ and HZ wrote the paper. All authors read and approved the final manuscript.
The authors declare that they have no competing interests.
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