Abstract
Composite structure with amorphous layer and crystalline substrate is important for nano-machining. In order to study the influence of amorphous layer structure on the nano-cutting mechanism and mechanical properties of single crystal germanium (Ge), molecular dynamics (MD) simulations were carried out on the nano-cutting process of amorphous-crystalline layered structure (A-C model) with different amorphous layer thicknesses. Cutting force fluctuation, stress status, subsurface damage characteristics and material removal, which are the key issues in nano-machining were analyzed. The result shows that as the thickness of amorphous germanium (A-Ge) increases, the cutting force and stress decrease, and the cutting temperature increases. The plasticity of the material is enhanced as the thickness of A-Ge increases, which is due to the softening of A-Ge when the cutting temperature rises. When the thickness of A-Ge is the same as the cutting depth, the material has lower subsurface damage and higher material removal rate, so it has excellent mechanical properties.
Science Press
Single crystal Ge is a typical representative of infrared optical materials, and is widely used in infrared optical and electronic applications[1,2]. Conventionally, single crystal Ge is fabricated through grinding and polishing, but these approaches are not suitable for machining axisymmetric surfaces with complex profiles. Instead, single point diamond turning (SPDT) is more promising as a deterministic method of reproduction to generate optical surfaces with high form accuracy[3,4]. Due to its hard and brittle nature, the surface fractures and short tool life are still serious problems to be solved for nanosurface acquisition of infrared optical materials[5,6].
It has been proven that single crystal Ge can be removed in a ductile mode when the material is under high hydrostatic pressure, and then optical surface quality can be achieved[7,8]. However, to achieve the perfect surface quality, appropriate processing parameters are required. This ductile cutting process can only be carried out when the undeformed chip thickness is less than the critical ductility-brittle transition (DBT) depth[9,10]. According to Lai's[11] research, a certain thickness of amorphous structure will appear on the machined surface of single crystal Ge during ultra-precision turning. It is believed that the amorphous structure is formed by the transformation of the metal phase caused by the intensive hydrostatic pressure during loading[12]. Therefore, the processed crystal actually has an amorphous crystal instead of its original lattice. Due to different mechanical properties, the amorphous layer on the top of the crystals can affect the machining process significantly such as ultra-precision turning, grinding and polishing. Besides, the amorphous layer can also be used to facilitate the machining of brittle materials. For example, using the method of ion implantation to form a modified layer on the surface of some hard-brittle materials (e.g, Ge, Si), the structure of the modified layer is mainly amorphous. The surface modification of ion implantation is achieved by bombarding the surface of the workpiece with high energy ion beam and destroying its initial lattice[13]. The method of nanometric machining of ion implanted materials (NiIM) can effectively increase the brittle-plastic transition thickness of the material and improve its ultra-precision machining performance, and its validity has been proved[14].
It is obvious that the amorphous layer has a great contribution to nano-machining, while the current study cannot fully explain the phenomena and mechanisms in material removal. Therefore, in this study, molecular dynamics (MD) simulation was used to study the effect of the amorphous layer on nanometric cutting of single crystal Ge. The effects of different thicknesses of the amorphous layer on the cutting force, stress state, subsurface damage and material deformation during nano-cutting were analyzed. The purpose of this work is also to determine the thickness of the amorphous layer suitable for nano-machining.
A numerical simulation was conducted using the MD method. In this section, the cutting model and details of making the layered composite structure were presented. Then, cutting parameter information was reported.
1.1 Nanometric cutting model
The cutting model consists of cubic diamond single crystal Ge and rigid diamond tools, as illustrated in Fig.1. The workpiece has a size of 22.628 nm×14.143 nm×11.314 nm and includes three kinds of atoms: Newtonian atoms, thermostat atoms and boundary atoms. Nanometric cutting was performed on the Newtonian layer. The thermostat layer imitated a heat sink with a temperature of 298 K. The boundary layer imposed boundary constraints in the x and y directions to prevent the Ge atoms from moving during the cutting process. Dynamic relaxation was performed to allow the model to be in an equilibrium state before the cutting. Three different atomic interactions in the current simulation of cutting process are shown in Table 1[15,16].
Fig.1 Schematic of the MD simulation model
Table 1 Interatomic potential
| Atomic interaction | Interatomic potential |
|---|
|
Ge-Ge |
Tersoff |
|
Ge-C |
Morse |
|
C-C |
Ignore |
Tersoff potential can be described as follows:
where E is the total energy, represents the potential energy between atoms i and j, stands for the distance between atom i and atom j, describes a repulsive pair potential, represents an attractive pair potential, and is a smooth cut off function.
The Morse potential can be expressed as follows:
where represents the pair energy function; and D corresponds to the elastic modulus and the cohesion energy, respectively; represent the equilibrium distance between atoms i and j. The parameter values of the Morse potential function are[17]: D=0.125 78 eV, α=25.8219 nm-1, γ0=0.223 24 nm-1.
1.2 Amorphous and layered model construction
The amorphous phase was prepared by quenching[18,19]. The Ge atoms were first heated to 5000 K in 100 ps. Then, amorphous Ge atoms were obtained with a rapid cooling at 100 K. Finally, the Ge atoms were relaxed to eliminate the residual stress and balance the internal energy.
Fig.2 shows the construction and variety of the layered model. Amorphous Ge and crystalline Ge are sliced to get amorphous and crystalline parts according to the specific thicknesses of tA and tC. After the joining followed by a dynamic relaxation, the model reaches equilibrium. Four A-C models with different amorphous layer thicknesses were used to study the influence of amorphous layer structure on single crystal Ge nano-cutting.
Fig.2 Construction of layered model
1.3 Simulation parameters
In this study, the cutting velocity is 200 m/s, which is unrealistically high in comparison with real ultra-precision scratching experiments in order to save computational cost. However, many works have confirmed that MD simulations of scratches with relatively higher scratching speed can reveal the main characteristics of the subsurface deformation mechanism[20,21]. The thickness of amorphous layers in the A-C model established was 0, 1, 2, 4 nm. More parameters used in the present simulation are listed in Table 2. All MD simulations were performed using an open source code LAMMPS software[22]. The results of MD simulations were visualized by the OVITO software[23].
Table 2 Parameters for the MD simulation with single crystal Ge as the workpiece material and diamond as the tool material
| Parameter | Value |
|---|
|
Dimension of workpiece/nm |
22.63×14.14×11.31 |
|
Tool rake angle/(°) |
10 |
|
Tool back angle/(°) |
7 |
|
tool nose radius/nm |
2 |
|
Depth of cut/nm |
2 |
|
Amorphous layer thickness/nm |
0, 1, 2, 4 |
|
Cutting speed/m·s-1 |
200 |
|
Cutting distance/nm |
0~15 |
|
Initial temperature/K |
298 |
|
Time step/fs |
1 |
2.1 Characteristic of cutting forces
Fig.3 describes the result of cutting force during the whole cutting process for different amorphous layer thicknesses. The lateral force (in the z-direction) is not summarized since it fluctuates around an average value of zero during the cutting process due to the balanced forces from two sides of the groove. It is found that the cutting force for different amorphous layer thicknesses increases as the tool cuts into the workpiece in phase I, as shown in Fig.3a and 3b. As the tool continuously cuts the workpiece in phase II, the cutting force in the tangential and normal directions fluctuates around a constant value after chip formation. The fluctuations of cutting force is related to the phase change, formation and movement of dislocation in Ge. In addition, with increases of the thickness of the amorphous layer, the fluctuation amplitude of the tangential force and normal force curves in the stable cutting stage is reduced, but the fluctuation amplitude of the tangential force decreases more significantly.
Fig.3 Machining forces of amorphous layer models with different thicknesses: (a) tangential force, (b) normal force, (c) average cutting force, and (d) average friction coefficient
To further quantify the difference of force during the nano- cutting process, both the tangential cutting force and normal cutting force are averaged over the cutting distance from 5 nm to 15 nm where cutting is in phase II for different amorphous layer thicknesses, as show in Fig.3c. It can be seen that both the tangential cutting force and normal cutting force decrease with increases of amorphous layer thickness. This is because the amorphous structure on the surface of single crystal Ge will reduce the surface hardness and elastic modulus. Through the above analysis, it can be concluded that increasing the thickness of the amorphous layer on the surface of the workpiece can reduce the cutting force significantly, which is beneficial to the cutting process.
Fig.3d shows the friction coefficient in phase II. It can be seen that when the amorphous layer thickness is less than the cutting depth, the friction coefficient decreases with the thick-ness of the amorphous layer; but as the thickness of the amorphous layer exceeds the cutting depth, the friction coeffi-cient increases with the thickness of the amorphous layer.
Under the condition that the thickness of the amorphous layer is less than the cutting depth, increasing the thickness of the amorphous layer can reduce the tangential force; when the thickness of the amorphous layer exceeds the cutting depth, the rough amorphous surface increases the friction between the tool and the workpiece.
2.2 Characteristic of stress distribution during cutting
Shear strain can characterize the degree of deformation of the material, which can be obtained by calculating the relative amount of the current atomic configuration and the atomic configuration of the previous frame or frames by Ovito software. Fig.4 represents the atomic strain at different amorphous layer thicknesses. As shown in Fig.4a, the shear strain is concentrated in three distinct regions (represented by I, II and III): the rake face of the tool, the cutting area and clearance face of the tool, and there is also a narrow shear strain concentration band at the bottom of the chip. This is because the cutting edge pushes Ge atoms during the cutting process to increase the strain energy in the cutting area. When the strain energy is large enough, the atomic lattice structure fails, the Ge atoms with high strain energy expands to the region with smaller strain energy, leading to the plastic flow, so that the chip and the clearance face form a narrow shear strain band. Besides, as the thickness of the amorphous layer increases, the shear strain in the cutting zone is weakened, especially in region I, and there is also a higher shear strain at region III because of the friction between the flank and workpiece surface.
Fig.4 Atomic strains of amorphous layer models with different thicknesses : (a) 0 nm, (b) 1 nm, (c) 2 nm, and (d) 4 nm
Fig.5 shows the shear stress inside the material with different amorphous layer thicknesses. It can be seen that the shear stress is mainly concentrated at the front end of the cutting zone, and the maximum shear stress is about 4 GPa. With the increases of the amorphous layer thickness on the surface of the workpiece, the area and stress values of the shear stress concentration region decrease, which indicates that increases of the amorphous layer thickness can soften the surface of the workpiece and enhance the plasticity, and that the amorphous atoms undergo plastic flow to reach the stress value for chip generation.
Fig.5 Stress fields of amorphous layer models with different thicknesses: (a) 0 nm, (b) 1 nm, (c) 2 nm, and (d) 4 nm
2.3 Characteristic of subsurface damage under different thicknesses of amorphous layers
Fig.6 shows the subsurface damage of the machined sur-face of the workpiece with different thicknesses of amorphous layers. The figure does not show the subsurface damage of the workpiece with an amorphous layer thickness of 4 nm, which is considered to be the largest damage, because the thickness of the amorphous layer is greater than the depth of cut. It can be seen that there is an amorphous periodic expansion damage zone on the subsurface, in which the expansion direction of amorphous atoms in the x-y plane is and , and the angle is about 90°, which is because the direction of splitting and sliding of Ge atoms is [110]. The maximum damage depth of single crystal Ge is 1.5 nm, and as the thickness of the amorphous layer increases, the maximum damage depth decreases and the tendency of amorphous atoms to expand in the x-y plane is weakened significantly. This indicates that the appropriate thickness of the amorphous layer on the workpiece surface can inhibit the downward expansion of amorphous atoms, thereby reducing the damage to the subsurface. As shown in Fig.6c, when the thickness of the amorphous layer is close to the depth of cut, the depth of subsurface damage is the smallest, and desirable machinability at the nanoscale will be achieved.
Fig.6 Subsurface damage under different thicknesses of amorphous layer: (a) 0 nm, (b) 1 nm, and (c) 2 nm
The temperature-displacement curve during cutting process is also shown in Fig.7. The cutting heat is generated due to the friction behavior between the tool and the workpiece. During the cutting process, the cutting temperature gradually increases. In addition, it can be clearly seen that the temperature of the workpiece rises with increase in the thickness of the amorphous layer. This is because the thermal conductivity of the amorphous phase is lower than that of the crystalline phase. It is speculated that thermal softening may also be a reason for the plasticity enhancement of A-Ge.
Fig.7 Temperature-displacement curves under different thicknesses of the amorphous layer
2.4 Uncut thickness and elastic recovery rate under different thicknesses of amorphous layers
In this work, the influence of the amorphous layer on the machining quality was analyzed by comparing the uncut thickness and elastic recovery rate during the cutting process. According to Lai's research[24], there is a stagnation point where the branching of the plastic flow occurs during the nano-cutting process. The material below this point will be pressed under the tool, and only the material above this point can flow to form chips. Fig.8 shows the evaluation method of uncut thickness. According to this method. Fig.9 shows the uncut thickness and elastic recovery rate of the cutting models with different amorphous layer thicknesses.
Fig.8 Uncut thickness evaluation
Fig.9 Uncut thickness and elastic recovery rate at different amorphous layer thicknesses
It can be seen from Fig.9 that the uncut thickness of the A-C model is less than that of the C-Ge, which means a higher material removal rate. The uncut thickness decreases first and then increases with increasing the amorphous layer thickness. When the thickness of the amorphous layer is the same as the cutting depth, the uncut thickness reaches the lowest value, indicating that the material removal rate is the highest at this time.
At the same time, it is found that the elastic recovery rate also has the same trend. The elastic recovery rate of the processed area is the smallest when the thickness of the amorphous layer and the cutting depth are the same, indicating that the workpiece surface has a small amount of spring back and a small shape error under this condition. This has high significance and application value in ultra-precision processing. Therefore, the composite structure with this special thickness of the amorphous layer is preferred.
1) For the A-C model, the hardness and elastic
modulus decrease with increase of the A-Ge thickness, which can reduce the stress and cutting force significantly and is beneficial to the ductile machining of brittle materials. The friction between the amorphous surface and the tool is bigger, which causes the cutting temperature to rise.
2) As the thickness of A-Ge increases, the plasticity of the material increases, which is caused by the softening of A-Ge when the cutting temperature rises.
3) The A-C model (tA=2 nm) with specific configurations has low subsurface damage, high material removal rate and small spring back during nano-cutting, which is beneficial for processing materials at the micro-nano scale.
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