Abstract
Nanomachining of brittle materials is required in a wide range of applications. This paper reports on the feasibility studies of vibration-assisted nano-impact machining by loose abrasives (VANILA), a novel nanomachining process for target-specific nanomachining of hard and brittle materials. A mathematical model based on Hertzian fracture mechanics theory has been developed to evaluate the feasibility of material removal in the VANILA process, where hard abrasive grains impact the brittle workpiece surface. Experimental investigations are conducted using a commercially available atomic force microscope (AFM), to validate the feasibility of the proposed process. Several nanocavities with circular shape, having depths ranging from 6 to 64 nm and diameters ranging from 78 to 276 nm, are successfully machined. Patterns of nanocavities are machined to confirm the repeatability and controllability of the process. Observation of tool tips using a scanning electron microscope (SEM) reveals that the tool wear in the VANILA process is lesser than that observed in indentation process.
Introduction
Nanomachining has tremendous potential for applications in wide areas such as aerospace (gyroscopes, transducers), biomedical (DNA detection/separation devices, molecular sieves for protein sorting), electronics (paper-like flexible displays, nanowires), automotive (accelerometers, pressure sensors), and healthcare industries (nanotherapeutic devices, catheters, infusion pumps, intrauterine products) [1–7]. Recent advancements in materials research have resulted in an avalanche of materials such as intermetallics, metal matrix composites, functionally graded materials, and advanced ceramic materials with unprecedented properties [8–10]. Advanced engineering ceramics and composites in general are tougher and stronger with improved mechanical, chemical, and wear-resistant properties and have unique ferromagnetic, magnetoresistive, ionical, dielectric, ferroelectric, piezoelectric, pyroelectric, electronical, superconducting, and electro-optical properties [11,12].
Abrasive machining is a proven material removal process capable of machining a wide range of materials, especially hard and brittle materials [13]. Abrasive materials have several advantages such as high hardness, strength, chemical inertness, and high wear resistance which are essential for machining advanced engineering materials. At nanoscales, abrasive-based machining processes have been already applied successfully in traditional finishing operations such as grinding, honing, lapping, and also in advanced finishing processes such as abrasive flow machining, magnetorheological finishing, magnetic float polishing (MFP), magnetorheological abrasive flow finishing, elastic emission machining, and chemomechanical polishing [14]. These processes can be broadly classified as loose abrasive and fixed abrasive processes. Loose abrasive machining (LAM) processes such as lapping [15] use abrasives such as diamond, SiC, boron nitride, and aluminum oxide for nanomachining, wherein the abrasive materials are usually mixed with a liquid medium to form slurry which is introduced between a hard, horizontally rotating wheel and the workpiece. Fixed abrasive processes such as nanogrinding [16,17] and high-speed lapping [18] involve two body abrasions between the workpiece surface and an abrasive embedded rotating tool.
The addition of high-frequency vibrations is found to be very effective in performance enhancement of abrasive-based machining processes [19,20]. Ultrasonic machining is a typical example of vibration-assisted abrasive machining processes that use high-frequency mechanical motion of shaped tools and abrasive slurry to erode materials from hard and brittle workpieces [21,22]. Microultrasonic machining has been gaining popularity as an efficient process in micron-scale machining of nonconductive, brittle and hard-to-machine materials to fine precision and smooth surface finish [23,24]. However, ultrasonic machining at nanoscale is a yet largely unexplored research area. Moreover, the abrasive-based nanofinishing techniques discussed above are not suitable for target-specific machining of features such as holes, slots, and three-dimensional shapes with nanoscale dimensions. Other advanced techniques such as femtosecond laser machining and focused ion beam machining are technically capable but prohibitively expensive alternates for nanomachining [25,26]. Hence, there is a need for alternative solutions such as tip-based nanomanufacturing processes for nanomachining of difficult-to-machine ceramic and brittle materials [27].
Scanning probe microscopes have been used over the past two decades for the machining of nanofeatures ranging from ∼100 nm down to atomic dimensions [28]. Nano-indentation and nanoscratching are the two earliest single-point tool based nanomachining processes capable of target-specific machining. The nano-indentation process uses a sharp indenting probe to penetrate the substrate surface to depths ranging in nanoscales [29]. The nanoscratching process can be considered as an extension of the nano-indentation technique, wherein the AFM tip is kept in contact with the substrate and dragged over the surface to form features such as nanochannels [30]. The single-point tool based nanomachining processes involve high forces developed at the tool tip which may lead to frequent breakage of the tool tip. The resultant machined area will have built-up edges and also develop surface stress because of higher machining forces involved [31].
In the present work, the target-specific machining capability of single-point tool based processes is combined with the hard and brittle material machining abilities of abrasives to develop VANILA process—a novel hybrid nanomachining process that uses a single-point AFM probe with loose abrasives and vibration assistance to perform target-specific impact-based machining of nanoscale features on hard and brittle materials. This paper reports on the feasibility studies of this newly developed VANILA process through analytical and experimental methods. An analytical model has been developed for feasibility evaluation and experimental investigations are conducted using a commercially available atomic force microscope (AFM) to validate the nanomachining feasibility of the proposed VANILA process.
Principle of the VANILA Process
The VANILA process developed in this research combines the principles of vibration-assisted abrasive machining and tip-based nanomachining to perform target-specific nano-abrasive impact-based machining of hard and brittle materials. The process is conducted on an AFM and a slurry of nanodiamond particles is introduced between the tool and the workpiece. The machining is conducted in tapping mode in which the tool probe continuously hammers the abrasive nanoparticles, suspended in liquid medium, which in turn impact the workpiece surface. During the machining process, the tool tip is raised by about 100–200 nm in height to avoid direct contact between the tool and the workpiece surface. A schematic of the VANILA process is shown in Fig. 1.

Schematic of VANILA process (a) tool striking the abrasive particle, (b) abrasive particle impacting the workpiece surface, and (c) material removal from the workpiece
Analytical Study
The mathematical model developed to predict the feasibility of the VANILA process is described in this section. The simplification assumptions made in developing the theoretical model are listed below
- (1)
Earlier studies on a closely related process (indentation) report that impact by blunt indenters results in elastic deformation, while impact by sharp indenters causes plastic damage [32,33]. Thus, the shape of the abrasive grain is expected to affect the mode of material removal. Though abrasive grains will not normally be spherical, self-impacts prior to impingement onto the workpiece surface will generally reduce them to a roughly spherical shape [34]. Therefore, for simplification, effect of nonsphericity is not considered in this model and all diamond abrasive particles are assumed to be identical spheres.
- (2)
The tool tip and abrasive particles are considered to have equal hardness, while the workpiece is softer than the abrasive particles.
- (3)
The collision between the tool tip and the abrasive particles is considered to be perfectly elastic.
- (4)
While in contact, the abrasive particle and the workpiece surface are frictionless and nonconforming, i.e., the workpiece surface, being softer than abrasive grains, deforms while in contact. The abrasive particles do not undergo any shape change and the particles remain intact throughout the machining process.
- (5)
The workpiece is assumed to be stationary before and after the impact of the abrasive particles.
- (6)
Energy loss due to the presence of liquid medium is neglected. The dynamic behavior of abrasive grain motion in fluid medium and its impact on the workpiece surface could possibly be affected by several variables such as instantaneous fluid velocity, fluid viscosity, and temperature [35–37]. The effect of liquid medium and subsequent energy loss due to drag would make the theoretical model closer to the actual process. However, this is beyond the scope of this paper and thus not considered in the model developed here.
- (7)
Abrasive grains impact perpendicularly (impact angle α = 90 deg) onto the workpiece surface. Studies show that the nature and extent of damage due to solid particle impact depend on the angle of particle impingement [35,36,38]. In VANILA process, the tool tip could strike the particles on the workpiece surface at an angle which is not necessarily perpendicular to the workpiece surface, but at an inclined angle. The simplest case of particles striking in a perpendicular direction [35] is considered in the model developed here.
- (8)
The workpiece is not atomically flat and its surface is assumed to have flaws at nanoscale.
Mathematical Model for Verifying the Feasibility of the Process.
The material removal in VANILA process consists of several simultaneous collisions and impacts as shown in Fig. 2. Initially, the tool probe which is vibrating at high-frequency impacts with the loosely suspended abrasive grains (impact 1). This collision imparts kinetic energy to the abrasive grains which are in the machining zone. The abrasive grains with high kinetic energy then impact the workpiece surface (impact 2).
Impact modeling is often very difficult because the actual impact is a complex physical phenomenon, characterized by very short duration of contact, high force levels reached, rapid dissipation of energy, and large accelerations and decelerations [39]. The dynamic analysis of the VANILA process is done based on the assumption that the process can be considered discrete and that a single impact event of abrasive grains with the workpiece surface is a good understanding of the complex phenomenon of material removal due to impact damage. The VANILA process can be modeled using a simplified approach consisting of separating the effects of the operative variables. Variables affecting the material removal in VANILA process can be broadly classified into three categories: tool tip variables, abrasive grain variables, and workpiece material variables as listed in Tables 1–3. Please see the Nomenclature for the variables used in modeling the VANILA process.
Impact parameters—tool tip vibration parameters
Resonance frequency, ft (KHz) | Amplitude, at (nm) | Velocity, Vt (m/s) | |
---|---|---|---|
Tool tip vibration | 10 | 200 | 0.02512 |
Resonance frequency, ft (KHz) | Amplitude, at (nm) | Velocity, Vt (m/s) | |
---|---|---|---|
Tool tip vibration | 10 | 200 | 0.02512 |
Impact parameters—workpiece properties and feasibility study results
Workpiece material | Poisson's ratio, νw | Young's modulus, Ew (N/m2 · 1010) | Fracture toughness, Kc (MPa · m1/2) | Maximum load, Pmax (N · 10−12) | Critical load, Pc (N · 10−12) | Feasibility |
---|---|---|---|---|---|---|
Soda-lime glass | 0.22 [45,63] | 7.07 [45,63,64] | 0.74 [63–67] | 1.573 | 1.148 | Yes |
Silicon | 0.3 [56] | 18.8 [49,56,64] | 0.7 [49,64–67] | 2.25 | 0.4197 | Yes |
Borosilicate glass (Pyrex) | 0.198 [45] | 6.27 [45] | 0.63 [66,67] | 1.503 | 0.9328 | Yes |
SiO2 | 0.167 [45] | 7.25 [45] | 0.79 [68] | 1.587 | 1.2794 | Yes |
Silicon carbide (SiC) | 0.17 [69] | 45.47 [64,69] | 2.8 [66,67,70] | 2.972 | 3.352 | No |
Zirconia | 0.25 [71] | 21 [72] | 6 [70] | 2.334 | 2.8152 | No |
Workpiece material | Poisson's ratio, νw | Young's modulus, Ew (N/m2 · 1010) | Fracture toughness, Kc (MPa · m1/2) | Maximum load, Pmax (N · 10−12) | Critical load, Pc (N · 10−12) | Feasibility |
---|---|---|---|---|---|---|
Soda-lime glass | 0.22 [45,63] | 7.07 [45,63,64] | 0.74 [63–67] | 1.573 | 1.148 | Yes |
Silicon | 0.3 [56] | 18.8 [49,56,64] | 0.7 [49,64–67] | 2.25 | 0.4197 | Yes |
Borosilicate glass (Pyrex) | 0.198 [45] | 6.27 [45] | 0.63 [66,67] | 1.503 | 0.9328 | Yes |
SiO2 | 0.167 [45] | 7.25 [45] | 0.79 [68] | 1.587 | 1.2794 | Yes |
Silicon carbide (SiC) | 0.17 [69] | 45.47 [64,69] | 2.8 [66,67,70] | 2.972 | 3.352 | No |
Zirconia | 0.25 [71] | 21 [72] | 6 [70] | 2.334 | 2.8152 | No |
Impact 1—Impact Between Tool and Abrasive Particles.
Assuming the phase of the cantilever vibration to be zero, the motion of the tool tip can be expressed as ateiωt [40], where at is the amplitude and ω is the angular frequency of vibration of the tool tip.
where Va1 and Va2 are the velocities of the abrasive particle before and after collision. Vt2 is the velocity of the tool after collision.
Impact 2—Impact Between Abrasive Particles and Workpiece Surface.
This collision involves impacts of accelerated nanoparticles on the surface of a brittle workpiece. This process has close resemblance to the macroscale erosion process of brittle materials as a result of the impact of solid particles, which has been extensively studied for many years [43–46]. Damage or material removal in brittle materials, as examined by several investigators in great detail, is found to happen in three regimes—elastic regime (Hertzian cone cracks), transition zone of elastic–plastic regime, and plastic regime—depending on several impact parameters in the regime [47,48]. While damage in the plastic regime is strongly influenced by material hardness (H), the Hertzian fracture (elastic regime) is primarily governed by the material's critical stress intensity factor or fracture toughness (KC) [47,49]. The damage in the elastic–plastic transition regime is governed by a combination of variables such as material hardness (H), fracture toughness (KC), and the sphere (abrasive grain) diameter (da) [47,48].
The impacting of brittle material surface by small abrasive grains can lead to strength degradation and consequent material damage caused by fracture and crack formation [34]. Depending on factors such as impact velocity of the abrasive grains, thickness of the workpiece material, and size of existing flaws on the workpiece surface, the fractures can be classified as Hertzian ring cracks (with or without conical fractures), median, radial, and lateral cracks and in some cases star cracks [48,50–52]. The AFM tool tip speed (Vt1) during the VANILA process is of the order of less than 1 m/s [41,53,54] and thus the speed of the abrasive grain just before impact on the workpiece surface is low enough for the consequent fracture to be considered Hertzian cone cracks [50]. The system can thus be analyzed in terms of the fundamental Griffith theory of fracture for elastic-brittle solids, wherein a pre-existing crack propagates into a characteristic cone in accordance with the requirements of an energy balance condition [55].
where ϕ is a dimensionless material constant whose value is obtained experimentally [55,57] and KC is the fracture toughness of the workpiece material. When this critical value (Pc) is exceeded, strength degradation can occur [34,59] and result in development of Hertzian cone cracks [43,44,60].
In order to understand the significance, the analytical model is tested on following hard and brittle materials: soda-lime glass, silicon, borosilicate glass (Pyrex), SiO2, silicon carbide, and zirconia. In this theoretical study, the abrasives used are diamond nanoparticles of 10 nm size and the value of the dimensionless material constant is taken as 5 × 10−5 [55]. The impact parameters along with the results of the feasibility calculations are shown in Tables 1–3. The values of mechanical properties of the materials used for this analytical study are referred from literature [61-72].
Experimentation and Results
The experimental setup to conduct the feasibility study of VANILA process is shown in Fig. 2. The VANILA process is conducted using a Dimension 3100 atomic force microscope (AFM) with a Nanoscope IIIa controller. The workpiece is placed in a machining cell and introduced between the AFM probe head and the AFM sample holder plate. The probe used for machining is a silicon nitride tapping mode probe having a tip radius of 50 nm. A direct-drive fluid cantilever holder (DDFCH) is used while conducting the machining. The tool tip is vibrated at just below its resonant frequency in the range of 3–12 KHz. A representative drive amplitude versus frequency curve during the cantilever tuning for VANILA process is shown in Fig. 3. Nanodiamond grains of 10 nm size are used as the abrasive material which is mixed with de-ionized water to form slurry. The abrasive slurry is introduced on the workpiece surface using a syringe before the machining process. Theoretical predictions listed in Table 3 reveal that the VANILA process is feasible for soda-lime glass, silicon, borosilicate glass, and silicon dioxide for the experimental conditions considered in this study. Among them, single crystal silicon wafers (type 100) of rectangular shape with sharp corners are chosen as the work material in this feasibility study. The experimental conditions used are listed in Table 4.
Experimental conditions for VANILA process
Workpiece material | Single crystal silicon (type 100) |
Machine | AFM dimension 3100 |
Abrasive | Diamond particles less than 10 nm radius |
Probe used | NSC 16/50 (MikroMasch) Tip radius 10 nm Resonant frequency in air 161 KHz Spring constant 40 N/m Probe material—silicon nitride (uncoated) |
Liquid medium | De-ionized water |
Workpiece material | Single crystal silicon (type 100) |
Machine | AFM dimension 3100 |
Abrasive | Diamond particles less than 10 nm radius |
Probe used | NSC 16/50 (MikroMasch) Tip radius 10 nm Resonant frequency in air 161 KHz Spring constant 40 N/m Probe material—silicon nitride (uncoated) |
Liquid medium | De-ionized water |
Initially, the silicon wafer is cleaned repeatedly with acetone, dried using dry air, and then placed firmly in the machining cell. Target surface details before machining are acquired by scanning the sample in air in tapping mode. The machining spot is identified along with its distance from the corner points and sides in order to facilitate locating the machined nanofeatures during postmachining scans. Then, the scanning probe is replaced with the tool probe which is placed in the probe holder (DDFCH) and, using a syringe, a slurry mixture of de-ionized water and diamond nanoparticles is introduced between the tool probe and the sample. The machining is done in tapping mode while the tip is raised by about 100–200 nm to avoid direct contact with the workpiece surface. Once the machining is done, the sample along with the machining cell is removed, cleaned thoroughly in an ultrasonic cleaner (Branson 5510MT) using acetone and then dried in air. The machined sample is placed on the AFM and the machined area is carefully located using a navigation screen (available in Nanoscope IIIa software) along with the previously recorded information of the distances from corner points and sides and then scanned using the scanning probe to obtain details of the machined features. Figure 4 shows a single nanocavity of circular shape (diameter 102.3 nm and depth 63.7 nm) machined on silicon substrate through VANILA process for a machining time of 20 s.
Pattern Machining.
To examine the repeatability and controllability aspect of VANILA process, nanocavity patterns are machined. Figure 5 shows AFM images of a pattern of nanocavities machined through VANILA process for duration of 20 s per cavity. The pattern design with eight cavities (numbered A–H) and the sequence of machining is shown in Fig. 5(c). The resultant machined pattern (pattern 1) has cavity depths ranging from 5 to 42 nm and diameters ranging from 78 to 276 nm as shown in Table 5. The distance between two consecutive cavities ranged from 3 to 6 μm, while the goal was to create cavities with a spacing of 5 μm. To further confirm the repeatability and controllability of VANILA process, a second pattern (pattern 2) is machined with four cavities (numbered A–D) machined for 20 s as shown in Fig. 6(a) according to the design shown in Fig. 6(d). The cavities obtained in pattern 2 have depths ranging from 16 to 38 nm and diameters in the range of 101–221 nm with intercavity spacing ranging from 3.6 to 5 μm as shown in Table 6.
Dimensions of nanocavities of pattern-1 machined through VANILA process
Cavity number | Diameter (nm) | Depth (nm) |
---|---|---|
A | 275.7 | 35.3 |
B | 78.5 | 6.8 |
C | 110.3 | 17.6 |
D | 246.6 | 22.4 |
E | 223.4 | 28.7 |
F | 165.4 | 4.8 |
G | 198.8 | 41.4 |
H | 220.6 | 40.6 |
Cavity number | Diameter (nm) | Depth (nm) |
---|---|---|
A | 275.7 | 35.3 |
B | 78.5 | 6.8 |
C | 110.3 | 17.6 |
D | 246.6 | 22.4 |
E | 223.4 | 28.7 |
F | 165.4 | 4.8 |
G | 198.8 | 41.4 |
H | 220.6 | 40.6 |
Discussion
Elastic Versus Plastic Deformation.
The theoretical model is developed considering failure only in elastic regime according to Hertzian fracture theory. However, the material removal mechanism may not be limited to elastic-brittle regime and may even extend to plastic deformation. Extensive study using a wider range of process conditions would be required to understand the actual material removal mechanism.
Gap Control During VANILA Process.
In VANILA process, the AFM probe is operated in tapping mode in liquid medium with the cantilever tip vibrated at near resonance frequency. From preliminary studies, it is found that the tip needs be placed at a height range of 100–200 nm from the workpiece surface. Consistently maintaining the optimum gap between the workpiece surface and the probe is a challenge. Before setting the required gap, the z-distance at which the probe makes contacts with the surface needs to be identified. Forces acting on the tip when it is in close proximity to the sample affect the resonance frequency of the cantilever tip. If an AFM tip is moved to contact with a sample, the resonance frequency first decreases slightly due to attractive forces and then increases due to the repulsive forces. Eventually, the repulsive force becomes so high that the tip oscillation is not possible and the contact is achieved.
In tapping mode, the AFM cantilever tip can experience both attractive and repulsive forces intermittently. Thus, the contact point between the tip and the sample surface can be determined by tracking the shift of the cantilever resonance frequency due to the force field of the surface as shown in Fig. 7. It can be seen that the resonance peaks (in Figs. 7(a)–7(d)) disappear as the tool tip touches the surface. Any further lowering of the tool tip shows no peaks (Figs. 7(e) and 7(f)). Once the contact point is identified, the tip is raised by about 100–200 nm in the positive z-direction and the VANILA process is conducted while this height is maintained.
Indentation Versus VANILA Process.
In order to understand the difference in nanomachining by the VANILA process from that of direct indentation of the tool tip, indentation experiments are conducted by lowering the tool tip onto the workpiece surface. It can be seen from the machining results (shown in Fig. 8) that the shape of nanocavities machined by indentation resembles inverse triangular pyramid shape acquired from the tool tip due to direct contact, whereas the VANILA process, due to its noncontact nature, produces cavities which have near-circular cross sections.

AFM image of inverse triangular pyramid-shaped cavities obtained when the tool tip directly indents the workpiece surface
Tool Wear During the VANILA Process.
In order to understand the material removal mechanism and subsequent tool wear, experiments are conducted for both the VANILA process and the indentation process (in air and in liquid medium with abrasive slurry). The SEM images of the tool tips are shown in Fig. 9. The tool wear suggests that the (softer) silicon nitride probe is undergoing wear in all the cases; however, the wear during the indentation process is more than that during the VANILA processes as shown in Table 7. Moreover, the tool tips in the case of indentation process appear to be blunt as opposed to the sharp ends of the tool tip used in VANILA process. This is suggestive of an increased tool life during the VANILA process as compared to tip-based contact nanomachining techniques such as nano-indentation and nanoscratching processes.
Tool wear study results
Machining time (s) | Tool length (μm) | ||
---|---|---|---|
Before machining | 16.969 | ||
Indentation | |||
In air medium | 20 | 16.529 | |
In liquid medium with nanodiamonds | 20 | 16.474 | |
60 | 15.87 | ||
VANILA process | 20 | 16.694 | |
60 | 16.255 |
Machining time (s) | Tool length (μm) | ||
---|---|---|---|
Before machining | 16.969 | ||
Indentation | |||
In air medium | 20 | 16.529 | |
In liquid medium with nanodiamonds | 20 | 16.474 | |
60 | 15.87 | ||
VANILA process | 20 | 16.694 | |
60 | 16.255 |
Conclusions
A new nanomachining process—VANILA that combines the principles of vibration-assisted abrasive machining and tip-based nanomachining is introduced in this work to perform target-specific nano-abrasive machining of hard and brittle materials. An analytical model based on Hertzian fracture theory is developed to evaluate the feasibility of the process for different workpiece materials. The feasibility of the VANILA process is experimentally verified on single crystal silicon substrate using a commercially available AFM. Nanocavities with circular shape having depths (in the range of 6–64 nm) and diameters (in the range of 78–276 nm) are achieved. Patterns of nanocavities are successfully machined to verify the controllability and repeatability aspect of the process. Observation of tool tips using a scanning electron microscope reveals that the tool wear in the VANILA process is lesser than that observed in indentation processes.
Acknowledgment
This material is based upon the work supported by the National Science Foundation under Grant Nos. CMMI–1137968, CMMI–1120382, and CBET-1239779. The research facilities provided by the Advanced Material Characterization Center at the University of Cincinnati are acknowledged.
- ft =
resonance frequency of vibration of tool tip
- at =
amplitude of vibration of tool tip
- Vt =
velocity of tool tip
- da =
diameter of abrasive grain
- ρa =
density of abrasive grain
- νa =
Poisson's ratio of abrasive grain
- Ea =
Young's modulus of abrasive grain
- Va =
velocity of abrasive grain
- νw =
Poisson's ratio of workpiece material
- Ew =
Young's modulus of workpiece material
- KC =
fracture toughness of workpiece