Diamond micro-milling of lithium niobate for sensing applications

Experiments for this work were carried out on an ultra-precision desktop micro machining centre (Nanowave MTS5R). The machine is equipped with a high speed aerostatic bearing spindle (Air Bearings Ltd) offering a speed of 18 000 rpm–180 000 rpm. The high speed spindle allows a high cutting velocity even when small diameter cutters are used. The XYZ sliders provide a precision of 0.1 μm. This experimental set-up ensures that both the spindle errors such as vibration and run-out, and slideway inaccuracy were minimised. Therefore spindle and slideway errors on surface quality will not be explicitly taken into account in the analysis. A multi-component piezoelectric cutting force dynamometer (Kistler MiniDyn type 9256C2) was mounted on the top of a Z slide to monitor the cutting force during machining and also assist the cutting tool set-up. The experimental set-up is illustrated in figure 1.

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Polished Z-cut LiNbO₃ samples (dimension 10 mm  ×  10 mm  ×  0.5 mm) were used in this research. The samples were adhesively bonded onto a ground stainless steel fixture and removed using acetone after machining. Single flute single crystal diamond micro milling tools (Contour Fine Tooling) with a nominal diameter of 0.3 mm were used in the experiments. A uniform tool shank diameter of 3 mm is used for all micro tools to fit a 3 mm ultra-precision spindle collet. Figure 2 shows the micro end mills used in the experiments.

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Prior to the machining experiments, the levelness of the square LiNbO₃ wafer surface to the cutting tool axis was carefully adjusted using a 1 μm resolution dial gauge. A levelness deviation of less than 5 μm was obtained over the 10 mm  ×  10 mm machining area. To eliminate the effect of levelness deviation on the depth of cut, the NC program (Z feed) was also adjusted to compensate for this geometric error thanks to the 0.1 μm feed precision of the machine tool. Zero position of the cutting tool relative to the LiNbO₃ wafer surface was set with the assistance of a machine vision system (Dino-lite microscope) and initial contact test using the Kistler dynamometer at a very slow feed rate. This procedure allows one to set up the depth of cut at a micron level.

Full immersion slot milling was performed in this experiment. No coolant was used to avoid contamination, and compressed air was supplied throughout the machining experiments to reduce the possibility of chip jam induced micro cracks. Two sets of machining experiments were carried out to investigate the influence of the cutting parameters and crystallographic effect on the surface quality, respectively.

In the first set of experiments, 5 mm long and 0.3 mm wide micro slots were milled along a fixed $\left[1\,0\,\bar{1}\,0\right]$ direction. The three controlled quantitative factors used in the experiments are cutting speed (m min⁻¹), feed rate (μm/tooth) and axial depth of cut (μm). Due to the presence of only three controlled factors, full factorial experimental designs were implemented to capture the entire main effects and their interactions. Two levels of cutting speed, three levels of depth of cut, and four levels of feed rate were selected. The cutting parameters in this 2  ×  3  ×  4 mixed level full factorial design is presented in table 1. Each set of cutting parameters was repeated to reduce machining errors and separate the influence due to interactions from the measurement noise. A total of 48 slots were machined for each cutter. In order to reduce the influence of tool wear on the surface quality and edge chipping, a brand new micro tool was used for the experiments.

In the second set of experiments, 5 mm long and 0.3 mm wide micro slots were milled along various crystallographic directions for studying the crystallographic orientation effect. The cutting parameters were fixed using optimal cutting speed and feed rate obtained from the first set of experiments. Figure 3 shows the schematic feed direction in the second experiments.

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After the machining experiments, the machined surface was cleaned in acetone by an ultrasonic bath. The average surface roughness of the bottom surface for each micro-milled slots was then measured using a white light interferometer (Zygo NewView 5020). To reduce the measurement uncertainty, four measurements on different areas were conducted for each slot and an average value of surface roughness (Ra) is used for analysis. The surface morphology and burr formation were analysed on the basis of SEM micrographs. Cutting forces and specific cutting energy were calculated and analysed.

Surface characterisation of the machined slots was performed using an SEM and a 3D surface profilometer. Figure 4 shows the SEM micrographs of the micro machined slots. Surface defects were found on the micro machined surface and edge chipping was observed in most of the slots. The results show that the feed rate and axial depth of cut have significant influence on the surface generation. Higher cutting speed is also found to promote better surface quality. Slow feed rate and small axial depth of cut produce fewer surfaces defects and hence promote ductile mode machining. Figure 5 shows surface measurement results on typical ductile and brittle mode machined surfaces. On the ductile mode machined surface, regular tool marks and less surface defects were observed. Surface roughness measurements indicate that a very smooth surface with surface roughness Ra  =  10 nm can be achieved at f_z  =  0.1 μm/tooth and a_p  =  1 μm. In contrast, on the brittle mode machined surface, regular tool marks are absent and instead irregular streaks were observed, and surface roughness, Ra  =  50–150 nm, was measured.

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As already demonstrated in previous single point diamond turning (SPDT) experiments, an enabling factor for ductile mode machining of brittle materials is the use of very small uncut chip thickness and depth of cut. It is believed that there is a critical uncut chip thickness, below which the energy required to cause fracture is higher than that required for plastic deformation. Therefore, plastic deformation becomes the primary mechanism of material removal instead of brittle fracture (Li et al 2010, Yan et al 2009). When materials undergo ductile shear plastic deformation, lesser surface and subsurface defects are generated and hence better surface roughness can be achieved.

Edge chipping is a type of surface/subsurface defect normally induced in the machining of brittle materials. Machining induced edge chipping affects the geometric accuracy of the finished parts and causes potential functional failure due to the micro cracks left on the finished part (Ng 1996, Gong 2013). Good edge quality in some LiNbO₃ applications is believed to be more desirable than surface roughness. In the micro milling of micro devices, the size of edge chipping defects can be comparable to its feature size, therefore control and suppression of edge chipping formation in micro milling becomes a pressing challenge. The SEM micrographs in figure 4 show a similar trend as surface topography, i.e. lower feed rate and axial depth of cut would produce less edge chipping defects due to ductile mode machining. In a full immersion milling operation, both up and down milling sides of the slot are generated. In the up milling side, the cutting direction is opposite to the workpiece feed direction and the surface is generated at the beginning of the cut, whilst the cutting direction is the same as the feed direction in the down milling side and the surface is generated when the cutting edge exits the workpiece. Therefore, up and down milling have different characteristics in edge chipping formation. Within the machining conditions in this experiment, edge chipping defects were predominantly observed in the down milling side of the slot, and lesser or no edge chipping in the up milling side were formed as shown in figure 6. Brittle materials like LiNbO₃ are more sensitive to impact at workpiece entry. In the case of up milling, the nominal instantaneous uncut chip thickness starts from minimum chip thickness (a few tens of nanometers in this case) and increases gradually, therefore lesser edge chipping defects are formed. This conclusion is in agreement with the micro milling of other brittle materials (Huo 2015).

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The cutting forces were collected by the dynamometer during the machining process to calculate the specific cutting energy. Firstly, raw force data was used to obtain the principle cutting forces and thrust forces, via equation (1):

$$\begin{eqnarray}&&\left(\begin{array}{c} \text{d}Fx\left(\theta \right) \\ \text{d}Fy\left(\theta \right) \end{array}\right)=\left(\begin{array}{c} -\cos \theta \\ \sin \theta \end{array}\,\begin{array}{c} -\sin \theta \\ -\cos \theta \end{array}\right)\left(\begin{array}{c} \text{d}Ft\left(\theta \right) \\ \text{d}Fr\left(\theta \right) \end{array}\right)\end{eqnarray} \tag{ 1 }$$

where Fx and Fy represent the measured cutting forces along the feed and cross feed directions respectively, while Ft and Fr represent the thrust and cutting forces, and θ is the rotation angle of the cutting. Then specific cutting energy, or specific cutting force (unit: MPa), Uc, is defined as follows:

$$\begin{eqnarray}&&Uc=\frac{{{V}_{\text{c}}}}{{{V}_{\text{rem}}}}\times {\int}_{0}^{{{T}_{\text{c}}}}\sqrt{F{{t}^{2}}+F{{r}^{2}}}\text{d}t\end{eqnarray} \tag{ 2 }$$

where V_c and V_rem stand for the cutting speed and material removal volume, with T_c as the cutting time.

It has been proven that the specific cutting energy required by plastic deformation of the material is higher than that required by brittle rupture (Wang 2008). Thus, it would also be an indication of brittle-ductile transition occurring should a drop of the specific cutting force be observed.

Analysis of variance (ANOVA) performed on the cutting force data (figure 7) indicates that, within the experimental machining conditions, a lower depth of cut or a slower feed rate results in higher specific cutting energy, hence indicating that a ductile mode cutting has taken place. As shown in figure 7, when depth of cut of 1 μm is used, a feed rate decrease from a 1 μm/tooth to 0.1 μm/tooth would result in an increase of specific cutting energy from 2000 MPa to 14 000 MPa and also a steep increase from the feed rate of a 0.3 μm/tooth can be observed suggesting that a 0.3 μm/tooth could be the brittle-ductile transition threshold. When a 0.1 μm/tooth is used, a depth of cut decrease from 10 μm to 1 μm would result in an increase of specific cutting energy from 1800 MPa to 14 000 MPa. It can also be seen from figure 7 that a higher cutting speed results in higher specific cutting energy. Therefore, higher specific cutting energy, which has been believed to be a sign of ductile machining, is obtained with higher cutting speed, along with a lower feed rate and cutting depth. This conclusion is consistent with results from the surface topography analysis, which in turn proves that specific cutting energy can be used as an effective indicator of the cutting mode for brittle materials. Attempts were also made to look into the ratio of thrust force and principle cutting force, however, the theory stating that under a critical uncut chip thickness, the thrust force stays larger than the principle cutting force (Davim 2008) was not supported by the results from the micro milling of LiNbO₃ in this experiment.

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In order to study the effect of crystallographic orientation of the material on the surface quality, slots along different crystallographic orientations were machined using single crystal diamond tools using the same cutting parameters, as described in section 3.2. The machining parameters used in the second set of experiments were: spindle speed, n  =  50 000 rpm; feedrate, f_z  =  0.1 μm/tooth; depth of cut, a_p  =  5 μm. Although almost crack-free surfaces were found to be achieved in the first set of experiments (feedrate, f_z  =  0.1 μm/tooth and a depth of cut, a_p  =  1 μm), a slightly deeper depth of cut was used to show the distinct differences along different crystallographic orientations.

Cleavage planes of LiNbO₃ naturally run along the family planes of {0 1 $\bar{1}$ 2} (Boyd 1964, Weis 1985). Since LiNbO₃ has a hexagonal crystalline configuration, it exhibits a three-fold symmetry in which its cleavage planes repeat itself at every 120°. Due to the anisotropy property of the material, a strong crystallographic orientation effect was observed. As shown in figure 8, edge chipping defects were observed in the slots machined along the cleaving directions of $\left[\bar{2}\,1\,1\,0\right]$ (30°) and $\left[1\,1\,\bar{2}\,0\right]$ (150°). This is due to the cleaving directions having lower surface energies and hence having less resistance to edge chipping generation during contact with the cutting tool. Good edge quality without obvious chipping defects were achieved by the slots machined other directions. Evident differences on the edge quality were shown between the up-milling and down-milling sides on the machined slots. Surface roughness of the bottom surface along both the feed and cross feed direction were measured. As shown in figure 9, a clear correlation between surface roughness value and crystallographic directions existed. Those slot surfaces machined along 90° have a surface roughness (Ra) of around 40 nm in contrast to those slot surfaces machined along 30° or 150° on which 90 nm Ra was measured. Hence, micro milling should be performed either along or close to $\left[\bar{1}\,0\,\bar{1}\,0\right]$ direction with an up-milling strategy whenever possible for such materials.

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