Open Access
Add to BibSonomy
Abstract
Microemulsion abrasive-free jet polishing (MAFJP) technology is a novel non-abrasive removal technique that exhibits unique advantages in polishing nonlinear KDP optical material. During MAFJP, the nanoscale water cores in MAFJP fluid impact and slip on the KDP surface, thus leading to contact with the KDP atoms and achieving defect-free removal of KDP through water dissolution. Dissolution is the inverse process of crystal growth and exhibits significant anisotropy. This work first investigated the orientation-determined KDP dissolution removal characteristics. At first, we gained insights into the impacting process of nanoscale water cores based on molecular dynamics simulation and then established an MAFJP removal function model to describe the removal process for KDP. The model considers the dynamic impacting and slipping dissolutions of (001), (010), (100), (111), I-type, and II-type crystal planes, and the final calculated results match perfectly with actual experimental results. This research elucidates the mechanism of orientation-determined MAFJP on KDP, and will promote the application of MAFJP technology in the polishing of single-crystal anisotropic optical materials.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Single-crystal potassium dihydrogen phosphate (KDP) is a unique nonlinear optical material [1–4]. The crystal planes of single-crystal KDP exhibit significant anisotropy in optical properties, making them suitable for various applications in inertial confinement fusion (ICF) facility [5,6]. Currently, the only practical precise KDP machining technique is single-point diamond turning (SPDT) [7–9]. However, due to the fragile nature of KDP, the SPDT process unavoidably introduces a subsurface damage layer on the cutting surface. This subsurface damage layer could lead to more significant light intensity modulation inside the KDP crystal [10–13], ultimately causing laser-induced damage and reducing the KDP's laser damage threshold. Consequently, this shortens the lifespan of the ICF facility [14–18].
To further improve the surface quality after SPDT, several polishing methods have been developed for ultra-precision KDP, such as magnetorheological finishing (MRF) [19–21], ion-beam figuring (IBF) [22,23], and chemical mechanical polishing (CMP) [24,25]. However, these methods inevitably introduce new defects. MRF, for example, embeds magnetic particles into the fragile KDP surface, causing secondary pollution [21]. Although IBF and CMP are particle-free polishing methods, IBF often generates a temperature gradient field on the KDP surface, leading to thermal cracks [22,23]. CMP, on the other hand, is very hard to ensure surface uniformity for large-size KDP [24,25].
Recently, we developed a novel microemulsion abrasive-free jet polishing (MAFJP) method that successfully removes the subsurface damage layer caused by SPDT on bulk single-crystal KDP, and effectively avoids introducing new defects [26–29]. This was achieved using a newly-designed low-viscosity microemulsion as the MAFJP fluid. In the low-viscosity MAFJP fluid, large amounts of nanoscale water cores with a particle size of about 10∼25 nm are uniformly distributed in a mixture of Bmim [TF2N] and TX-100 [29]. During MAFJP, the nanoscale water cores, carried by the mixture, impact and slip on the KDP surface under the action of velocity field. When the nanoscale water cores contact the KDP surface, they dissolve the KDP material, achieving defect-free removal of KDP [28,29].
MAFJP relies on nanoscale water cores to dissolve the KDP surface [26–29]. This type of removal can be referred to as dissolution removal. Dissolution is an inverse process of crystal growth, while previous studies have shown significant anisotropy in the crystal growth [30–33]. Thereby, it can be inferred that KDP's crystallographic anisotropy will significantly affect the polishing characteristics of MAFJP. Meanwhile, in high-power laser system of ICF facility, different KDP crystal planes are selected for applications [1,3–6]. For example, as to the National Ignition Facility (NIF) in USA, the (001) KDP plane is used as the Switch Crystal, while the I-type and II-type planes are used as the Doubler Crystal and Tripler Crystal, respectively [5,6]. Thereby, various crystal planes require for defect-free fabrication in high-power laser systems. However, in our previous work, we only focused on the demonstration of defect-free MAFJP removal of a bulk single-crystal KDP, without considering the influence of crystal orientation on the removal [26–29].
This study systematically investigates the orientation-determined KDP dissolution removal characteristics. Meanwhile, molecular dynamics simulation is employed to understand the impacting process of nanoscale water cores, upon which a MAFJP removal function model for KDP is established. Based on the removal model, this study discusses the dynamic impacting and dynamic slipping dissolutions of (001), (010), (100), (111), I-type, and II-type KDP planes (shown in Fig. 1), thus elucidating the orientation-determined removal mechanism of KDP. This research will promote the application of MAFJP technology in the polishing of single-crystal anisotropic optical materials.
2. Materials and experimental details
The Chinese State Key Laboratory of Crystal Materials employed the rapid growth technique to produce bulk single-crystal KDP samples [34,35]. These samples were then cut into five pieces with a dimension of 40 mm × 40 mm × 10 mm using a wire cutting machine. The surfaces of the five samples were carefully controlled to be (001), (010), (100), (111), I-type, and II-type planes during the cutting process, aided by an X-ray crystal orientation instrument. Subsequently, ultra-precision machining was performed on the (001), (010), (100), (111), I-type, and II-type surfaces using a SPDT machine. The spindle speed, cutting depth, and feed rate were 280 r/min, 4 µm, and 4 mm/min, respectively.
The microemulsion was synthesized at a constant temperature of 25 °C. The key materials, Bmim[TF2N] and TX-100 surfactant, were purchased from Sigma Aldrich, guaranteeing a purity level higher than 99%. Deionized water was used in preparation of the microemulsion. The resultant mixture (microemulsion), denoted as H2O/TX-100/Bmim[TF2N] (BT), exhibiting a low viscosity of 140 mpa·s, was used as the MAFJP fluid. Cryo-transmission electron microscopy (cryo-TEM FEI Talos Arctica) was employed to visually confirm the structure of the microemulsion.
Jet spot experiment was conducted on the (001), (010), (100), (111), I-type, and II-type planes using the low-viscosity MAFJP fluid BT. Before jet spot experiment, the (001), (010), (100), (111), I-type, and II-type planes were machined precisely using SPDT. During jet spot experiment, the spraying time, pressure, distance, and nozzle for jet spot were 5 min, 0.5 MPa, 10 mm, and 1 mm, respectively. The morphology features of jet spots on different crystal planes were detected using a laser interferometer (ZYGO, λ = 632 nm).
In the current study, we established a removal function model for MAFJP to describe the anisotropy of KDP removal characteristics. Key parameters of this model, such as the dynamic impacting dissolution rate ($S_{h k l}^I$) and the dynamic slipping dissolution rate ($S_{hkl}^s$), are directly determined or indirectly calculated based on the morphology features of jet spots on different crystal planes. Furthermore, in order to verify the accuracy of the MAFJP removal function model, we used the jet spot morphology of different crystal planes as the actual results of the removal function, and compared them with the theoretical results obtained from the model.
3. Removing mechanism of KDP at microscale
3.1 Structure of MAFJP fluid (microemulsion BT)
The cryo-transmission electron microscope (cryo-TEM) is used to directly confirm the structure of the microemulsion. Figure 2(a) displays a low magnified image of the microemulsion in its frozen state, while Fig. 2(b) presents the corresponding diffraction pattern. Figure 2(b) reveals four polycrystalline diffraction rings, which correspond to the crystallographic family {111}H2O, {220}H2O, {311}H2O, and {331}H2O, indicating the presence of frozen nanoscale water cores. Additionally, Fig. 2(c) provides a high magnified image of these frozen nanoscale water cores, presenting a perfect spherical shape with a diameter of 10∼25 nm, and uniformly distributing in the oil matrix. Figure 2(d) schematically illustrates the structure and distribution of nanoscale water cores in the microemulsion.
Fig. 2. The cryo-TEM images of the microemulsion BT: (a) low magnified image, (b) corresponding diffraction pattern of (a) showing the polycrystalline rings of frozen nanoscale water cores, (c) high magnified image, and (d) schematic illustration of microemulsion distribution.
The TEM results confirm that the MAFJP fluid BT exhibits a water-in-oil structure, where nanoscale water cores are evenly dispersed in an oil mixture of Bmim [TF2N] and TX-100. Specifically, Bmim [TF2N] serves as the ionic liquid, while TX-100 acts as the surfactant facilitating the interaction between Bmim [TF2N] and water. TX-100 surfactant is essential of generating nanoscale water cores in Bmim [TF2N] by reducing the surface energy between water and Bmim [TF2N] [29]. In static state, these nanoscale water cores remain separated from the KDP due to the oil mixture barrier. Thereby, by utilizing cryo-TEM, the structure and distribution of these nanoscale water cores in MAFJP fluid have been effectively validated.
3.2 MAFJP removal mechanism of KDP
Figure 3 schematically illustrates the MAFJP removal mechanism of KDP. So far, it is impossible to directly observe the moving process of nanoscale water cores during MAFJP. Previously, large amounts of experimental and simulation works have been done to preclude the impacting process of macroscale liquid drops [36–39]. It has been demonstrated that the macroscale liquid drops break and then spread on the platform after impacting [36–39]. Thereby, shown in Fig. 3(b), the same as the macroscale drops, it is supposed that the nanoscale water cores conveyed by the oil mixture in MAFJP, will quickly break and spread on the KDP surface during impacting process. After that, it is supposed that the nanoscale water cores stop spreading when their impacting velocity reaches zero, and then slip on the KDP surface. Finally, the bulk single-crystal KDP is removed by dissolution during the impacting and slipping processes of nanoscale water cores. During dissolution, shown in Fig. 3(c), due to the effect of water molecules, the K+, H+, and PO4+ ions on the KDP surface will overcome the interaction force and then diffuse into the water.
Fig. 3. Schematic illustration of the MAFJP removal mechanism of KDP: (a) The MAFJP process of KDP, (b) schematic illustration of nanoscale water core movement on the KDP surface, and (c) schematic illustration of removal mechanism by dissolution.
4. Orientation-determined KDP removal characteristics in MAFJP
Figure 4 shows the contours and the corresponding cross-sections of the jet spot removal morphology of (001), (010), (100), (111), I-type, and II-type planes. Obviously, the jet spot removal morphology is smooth, presenting a similar Gaussian removal function. In order to evaluate the controllability and stability, there are five jet spots for each crystal plane. Figure 5 shows the 2D morphology features of these five jet spots at one figure. It can be seen that the five jet spots match well with each other, meaning a high controllability and stability. In addition, the surface removal volume ($R$) obtained by integrating the 2D morphology of jet spot, is shown in Table 1. Interestingly, we first observe an obvious crystallographic anisotropy of jet spot removal characteristics in MAFJP, that the removal volume is obviously different for (001), (010), (100), (111), I-type, and II-type planes. According to Table 1, the sequence of removal volume is expressed as follows: ${R_{II - type}} > {R_{111}} > {R_{100}} > {R_{010}} > {R_{I - type}} > {R_{001}}$.
Fig. 4. The 3D removal characteristics and corresponded 2D morphology features of jet spots of (001), (010), (100), (111), I-type, and II-type planes. (λ = 632 nm).
Fig. 5. The 2D morphology features of jet spots of (001), (010), (100), (111), I-type, and II-type planes: (a) (001) jet spots, (b) (010) jet spots, (c) (100) jet spots, (d) (111) jet spots, (e) I-type jet spots, and (f) II-type jet spots.
Table 1. The ${\boldsymbol R\; }({{\boldsymbol nm} \times {\boldsymbol mm}} )$, ${\boldsymbol S}_{{\boldsymbol hkl}}^{\boldsymbol I}{\boldsymbol \; }({{\boldsymbol nm}} )$, and ${\boldsymbol S}_{{\boldsymbol hkl}}^{\boldsymbol S}{\boldsymbol \; }({{\boldsymbol nm}} )$ of different KDP crystal planesa
5. Construction of theoretical modeling
5.1 Movement of nanoscale water core during MAFJP studied by molecular simulation
In order to model the removal process of MAFJP, we first need to address the movement of nanoscale water core. Although we schematically illustrate the removal mechanism of MAFJP, until now there has been no directly observation of the movement of nanoscale water core. In present work, molecular dynamics simulation is employed to understand the impacting process of nanoscale water core, upon which a MAFJP removal function model for KDP is established.
The molecular dynamics simulation puts high demands on water molecule model. Previously, the Transferable Intermolecular Potential (TIP) series models proposed by Jorgenson et al [40–42] have been widely used for simulating water molecular systems. The TIP series models use Lennard-Jones potential to describe the interaction between O atoms and use the Coulomb potential to represent the interaction between all point charges of molecules. The TIP series models are also rigid models, including TIP2P, full atomic TIP3P and refined TIP4P models [41,42]. The TIP4P model can more accurately describe the properties of liquid water among these models [42]. Therefore, in order to well simulate the movement process of liquid water at room temperature, as shown in Fig. 6(a), this study uses the TIP4P model.
Fig. 6. (a) Structure model of water molecule, (b) structure model of KDP crystal, and (c) impact model of nanoscale water. 
KDP crystal belongs to the tetragonal crystal system, while its ferroelectric phase space group is I-42d, and lattice parameters are a = b = 7.4521 Å, c = 6.974 Å [43,44]. Figure 6(b) shows the KDP crystal structure model, in which K+ is connected to H2PO4- through ionic bonds. There is no need to define the ionic bonds, and only accurate charges should be provided. In addition, H atoms are connected to O atoms, while O atoms are connected to P atoms through covalent bonds which need to be defined and relevant parameters should be provided. In present work, the simulation project involves water and KDP, and since there is no specific potential function for these two substances, LJ potential function is used to describe the interaction between atoms [45,46]. Figure 6(c) shows the initial impacting model of the nanoscale water core on the KDP. In consistent with the real dimension, the diameter of the nanoscale water core is defined to be 10 nm.
Figure 7 shows the impacting process based on molecular dynamics simulation. After relaxing for 10 ps, the nanoscale water core rushes to the KDP surface at a speed of 100 m/s, and then reaches the surface at 50 ps. After contacting the KDP surface, the nanoscale water core quickly spreads on the surface. As the impacting velocity gradually decreases to 0, the spreading area also reaches a maximum value. At this time, the maximum spreading radius (${\lambda _m}$) of the nanoscale water core is 4.625 nm, and then the nanoscale water core reaches an equilibrium state with increasing the time.
Fig. 7. The impacting process of nanoscale water core: falling, impacting, spreading, and then maintaining equilibrium.
Figure 8 shows the equilibrium state of the nanoscale water core with different impacting velocities (200 m/s, 500 m/s, and 1000 m/s). The maximum value of spreading area gradually increases with increasing the impacting velocity. Figure 9 shows the relationship between the maximum spreading radius and the impacting velocity. Shown in the figure, the maximum spreading radius and the impacting velocity satisfy a linear relationship, which plays a key role in establishing the removal function model. Based on above simulation results, we will establish a removal function model to describe the MAFJP removal process for KDP in followed chapter.
Fig. 8. The equilibrium state of nanoscale water core with different impacting velocities: (a) 200 m/s, (b) 500 m/s, and (c) 1000 m/s.
Fig. 9. Relationship between the maximum spreading radius and the impacting velocity of nanoscale water core.
5.2 Theoretical modeling
As shown in Fig. 10, the movement of the nanoscale water core during MAFJP is divided into two stages: 1. impacting stage, 2. slipping stage. In impacting stage, it can be known from the results of molecular dynamics simulation that the nanoscale water core quickly spreads on the KDP surface under the impact and reaches an equilibrium state. In slipping stage, the nanoscale water core undergoes slipping motion with the support of oil mixture. The impacting velocity is zero at slipping stage, while the slipping velocity depends on the horizontal velocity field distribution of MAFJP fluid.
Fig. 10. The movement of nanoscale water core during MAFJP: stage 1-impacting stage, and stage 2-slipping stage.
Shown in Fig. 10, the nanoscale water core impacts the KDP surface at a certain incident angle ($\gamma $) and quickly spreads to an equilibrium state. The total removal volume (${R^I}$) of a single nanoscale water core during the impacting stage is expressed as follows:
where t is time, ${A^{\prime}}\; $ is the instantaneous contacting area, $A_m^{\prime}$ is the maximum contacting area at the equilibrium state, and ${S_{hkl}}$ is the dissolution rate of (hkl) crystal plane. By substituting following parameters into Eq. (1): the maximum contacting radius ($r_m^{\prime}$), the average velocity ($\bar{v}$) of radius expansion, and the time (${t_m}$) required to reach the equilibrium state, the total removal volume of a single nanoscale water core during the impacting stage can be expressed as follows:According to formula (2), we can obtain the removal rate ($R_t^I$) of a single nanoscale water core as follows:
The oblique incidence of nanoscale water core is a complex process. To simplify the process, we convert the oblique incidence to vertical incidence. The contacting area (${A^{\prime}}\; $) and maximum contacting radius ($r_m^{\prime}$) of the oblique incidence have the following relationship with the contacting area ($A$) and maximum contacting radius (${r_m}$) of vertical incidence:
During the spreading process of a nanoscale water core, it is assumed that the contacting radius and spreading radius satisfy the following linear relationship:
The impacting velocity (${v_y}$) and the initial velocity (${v_0}$) satisfy the following relationship: ${v_y} = {v_0}\cos \theta $, where $\theta $ is the angle between the impacting velocity and initial velocity. In MAFJP, assuming that the number of nanoscale water cores acting on unit area per unit time is N, the macroscopic removal rate can be expressed as follows:
The slipping stage initiates when the contacting area reaches its maximum value, thus the slipping removal rate is expressed as follows:
By substituting Eq. (6) into (12), the macroscopic slipping removal rate can be expressed as follows:
Accordingly, the macroscopic removal rate (${R_{t(x )}}$) of MAFJP, including the impacting and slipping removal rates can be expressed as follows:
Figure 12 shows the variation of ${F_{(x )}}$ and ${v_{(x )}}$ with the center distance x. ${F_{(x )}}$ can be directly calculated from its expression, while ${v_{(x )}}$ is obtained through ANSYS Fluent software simulation. The simulation result of ${v_{(x )}}$ is consistent with numerous FJP flow field distribution simulation [28,47–49]. Shown in Fig. 12(b), the normalized ${v_{(x )}}$ presents a zero velocity at the jet center, and then increases rapidly with increasing x. After reaching a maximum value, the normalized ${v_{(x )}}$ gradually decreases and finally approaches zero.
Fig. 12. The variation of ${F_{(x )}}$ and normalized slipping velocity ${v_{(x )}}$ with distance x: (a) ${F_{(x )}}$ vs x, and (b) ${v_{(x )}}$ vs x.
6. Results and discussion
6.1 Orientation-determined dynamic impacting and slipping dissolution rates of KDP
According to the macroscopic removal function model of MAFJP, it can be concluded that the MAFJP removal rate of KDP mainly depends on the dynamic impacting dissolution rate ($S_{hkl}^I$) and the dynamic slipping dissolution rate ($S_{hkl}^s$). $S_{hkl}^I$ and $S_{hkl}^s$ are both constant multiples of the static dissolution rate (${S_{hkl}}$), and thus expressed as ${k_i}{S_{hkl}}$ and ${k_s}{S_{hkl}}$, respectively. As mentioned earlier, ${k_i}$ and ${k_s}$ are constants related to impacting and slipping processes, respectively. Previously, although there were significant differences in ${S_{hkl}}$ for different crystal planes, we could only macroscopically measure an average dissolution rate ($S$). In present work, the same as ${S_{hkl}}$, $S_{hkl}^I$ and $S_{hkl}^s$ also reflect the dissolution rate of different crystal planes. Meanwhile, $S_{hkl}^I$ and $S_{hkl}^s$ can reflect the influence of impacting and slipping on the dissolution characteristics of different crystal planes. What’s more, $S_{hkl}^I$ can be directly determined from the jet polishing morphology feature, and $S_{hkl}^s$ can be indirectly calculated based on the following formula:
Fig. 13. The $S_{hkl}^I$ and $S_{hkl}^s$ of (001), (010), (100), (111), I-type, and II-type crystal planes: (a) $S_{hkl}^I$ and (b) $S_{hkl}^s$.
As mentioned above, $S_{hkl}^I$ and $S_{hkl}^s$ are constant multiples of ${S_{hkl}}$, therefore, the difference of $S_{hkl}^I$ and $S_{hkl}^s$ between crystal planes is the result of the anisotropy of ${S_{hkl}}$. Meanwhile, from the orders $S_{II - type}^I > S_{111}^I > S_{100}^I > S_{010}^I > S_{I - type}^I > S_{001}^I$ and $S_{II - type}^s > S_{111}^s > S_{100}^s > S_{010}^s > S_{I - type}^s > S_{001}^s$, it can be inferred that the anisotropy of ${S_{hkl}}$ is $S_{II - type} > S_{111} > S_{100} > S_{010} > S_{I - type} > S_{001}$. The dissolution is the reverse process of crystal growth, so the anisotropic mechanism of the dissolution is essentially consistent with that of the crystal growth. The physical effect of growth anisotropy depends on liquid/solid interface structure, which can be divided into rough interface and smooth interface [50,51]. Due to the kinetic effect, the rough interface grows faster, while the smooth interface grows slower [50,51]. The same as crystal growth, the dissolution rate of rough interface is faster than that of smooth interface. The liquid/solid interface structure is determined by the crystal plane density, with higher density tending to have rough interface, and vice versa tending to have smooth interface [51]. However, KDP crystal also contains a large number of covalent bonds, so in addition to physical effect, the dissolution may also involve chemical effect. Therefore, the dissolution anisotropy is a combined result of physical and chemical effects. In summary, it is the dissolution rate (${S_{hkl}}$) anisotropy that results in the anisotropy of $S_{hkl}^I$ and $S_{hkl}^s$, and finally leads to orientation-determined KDP removal characteristics in MAFJP.
6.2 Comparison between experimental results and theoretical modeling
The removal function model plays a key role in predicting and controlling the removal process with a high accuracy. MAFJP is a recently developed classical method for defect-free removal of KDP. Previously, we initially established a normalized removal model for KDP's MAFJP, which to some extent describes the removal law [28]. However, this model cannot predict the removal volume and does not consider the influence of KDP's anisotropy on the removal process. In this study, based on molecular dynamics simulation, we gained an insight of the movement of nanoscale water core in MAFJP. Based on this, we established the macroscopic removal function model for KDP's MAFJP (Eq. (16)). This model defines the dynamic impacting dissolution rate ($S_{hkl}^I$) and the dynamic slipping dissolution rate ($S_{hkl}^s$). Shown in Fig. 14, we substituted $S_{hkl}^I$ and $S_{hkl}^s$ into the removal function model, and obtained the removal functions for (001), (010), (100), (111), I-type, and II-type crystal planes. Interestingly, the calculation results perfectly match the experimental results. Therefore, the new model can not only accurately predict the removal volume but also describes the influence of KDP's anisotropy on the removal process.
Fig. 14. The comparison between theoretical and experimental removal functions of (001), (010), (100), (111), I-type, and II-type planes: (a) (001), (b) (010), (c) (100), (d) (111), (e) I-type, and (f) II-type.
6.3 Potential application of MAFJP in polishing single-crystal optical materials
In previous studies, we proposed a method for characterizing subsurface damage layer in bulk single-crystal optical materials based on the X-ray grazing incidence technique (GIXRD) [18]. Using this characterization method, we found that the subsurface damage layer in KDP is obviously reduced by MAFJP [29]. Subsurface damage in optical devices has always been an important factor in reducing optical performance. Therefore, as an effective method for removing subsurface damage layer, the MAFJP is expected to be widely applied in other optical materials.
In addition, similar to KDP crystal, there are various single-crystal anisotropic optical materials, such as DKDP, ADP, calcite, and quartz [1,52–54]. These materials also display unique optical properties at different orientations. DKDP and ADP are water-soluble, therefore they can be removed using the MAFJP method with microemulsion BT. Although calcite and quartz are not water-soluble, they can be etched by acidic or alkaline liquids. It is supposed that we could remove calcite and quartz using the MAFJP method by replacing the nano-water cores in the microemulsion with nano-acidic or nano-alkaline cores. Additionally, by utilizing the MAFJP removal function model established in this study, we can accurately predict the removal volume and describe the impact of single-crystal anisotropy on the removal process of these optical materials. Accordingly, the establishment of this model will advance the application of MAFJP technology in polishing single-crystal anisotropic optical materials.
7. Conclusions
In present work, the orientation-determined KDP dissolution removal characteristics in MAFJP were investigated. Based on molecular dynamics simulation, a MAFJP removal function model was established to describe the anisotropy, and following can be concluded:
- (1) The MAFJP removal volume is obviously different for (001), (010), (100), (111), I-type, and II-type planes of bulk single-crystal KDP. The sequence of surface removal volume is expressed as follows:$\; {R_{II - type}} > {R_{111}} > {R_{100}} > {R_{010}} > {R_{I - type}} > {R_{001}}$.
- (2) According to molecular dynamics simulation, the nanoscale water core rapidly spreads on the KDP surface at impacting stage, and then reaches an equilibrium. The maximum spreading radius satisfies a linear relationship with the impacting velocity. After that, the nanoscale water core undergoes a slipping stage.
- (3) The removal function model of MAFJP consists of the impacting removal model and slipping removal model, and is expressed as follows: ${R_{t(x )}} = R_{t(x )}^I + R_{t(x )}^s = \frac{{2 \times S_{hkl}^I}}{\pi } \times {F_{(x )}} + S_{hkl}^s \times {v_{(x )}}$, where $S_{hkl}^I$ and $S_{hkl}^s$ are the dynamic impacting dissolution rate and dynamic slipping dissolution rate, respectively. The $S_{hkl}^I$ and $S_{hkl}^s$ present strong anisotropy for different crystal planes, with following orders: $S_{II - type}^I > S_{111}^I > S_{100}^I > S_{010}^I > S_{I - type}^I > S_{001}^I$ and $S_{II - type}^s > S_{111}^s > S_{100}^s > S_{010}^s > S_{I - type}^s > S_{001}^s$. Due to the anisotropy of $S_{hkl}^I$ and $S_{hkl}^s$, the KDP's MAFJP exhibits orientation-determined removal characteristics. This model accurately predicts the removal volume, and describes the influence of KDP's anisotropy on the MAFJP removal process.
Funding
National Natural Science Foundation of China (52175444, 51905506, 61801451, 52001290); Sichuan Science and Technology Program (2021JDJQ0014); Innovation and Development Foundation of CAEP (CX20210006).
Disclosures
The authors declare no conflict of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. J. J. Deyoreo, A. K. Burnham, and P. K. Whitman, “Developing KH2PO4 and KD2PO4 crystals for the world’s most powerful laser,” Int. Mater. Rev. 47(3), 113–152 (2002). [CrossRef]
2. T. N. Thomas, T. A. Land, W. H. Casey, et al., “Emergence of supersteps on KH2PO4 crystal surfaces,” Phys. Rev. Lett. 92(21), 216103 (2004). [CrossRef]
3. S. Mittal, K. Arvind, A. S. Laxmiprasad, et al., “Design and development of Pockels cell driver for Qswitch LASER in space applications,” J. Inst. Electron. Telecommun. Eng. 63, 694–699 (2017).
4. D. Wang, T. Li, S. Wang, et al., “Characteristics of nonlinear optical absorption and refraction for KDP and DKDP crystals,” Opt. Mater. Express 7(2), 533–541 (2017). [CrossRef]
5. G. H. Miller, E. I. Moses, and C. R. Wuest, “The national ignition facility,” Opt. Eng 43(12), 2841–2854 (2004). [CrossRef]
6. J. H. Campbell, R. A. Hawley-Fedder, C. J. Stolz, et al., “NIF optical materials and fabrication technologies: An overview,” Proc. SPIE 5341, 84–101 (2004). [CrossRef]
7. L. Liu, L. Lu, Q. Gao, et al., “External aerodynamic force on an ultra-precision diamond fly-cutting machine tool for KDP crystal machining,” Int. J. Adv. Manuf. Technol. 93(9-12), 4169–4178 (2017). [CrossRef]
8. S. Wang, C. An, F. Zhang, et al., “An experimental and theoretical investigation on the brittle ductile transition and cutting force anisotropy in cutting KDP crystal,” Int. J. Mach. Tools. Manuf. 106, 98–108 (2016). [CrossRef]
9. S. Hatefi and K. Abou-El-Hossein, “Review of hybrid methods and advanced technologies for in-process metrology in ultra-high-precision single-point diamond turning,” Int. J. Adv. Manuf. Technol. 111(1-2), 427–447 (2020). [CrossRef]
10. Q. Liu, J. Cheng, H. Yang, et al., “Modeling of residual tool mark formation and its influence on the optical performance of KH2PO4 optics repaired by micro-milling,” Opt. Mater. Express 9(9), 3789–3807 (2019). [CrossRef]
11. J. Cheng, H. Yang, Q. Liu, et al., “Characterization of manufacturing-induced surface scratches and their effect on laser damage resistance performance of diamond fly-cut KDP crystal,” Results Phys. 15, 102753 (2019). [CrossRef]
12. Q. Liu, Z. R. Liao, and D. Axinte, “Temperature effect on the material removal mechanism of soft-brittle crystals at nano/micron scale,” Int. J. Mach. Tools. Manuf. 159, 103620 (2020). [CrossRef]
13. Q. Liu, J. Cheng, Z. R. Liao, et al., “Research on the light intensity modulation and characterizing methods of surface texture on KDP optics generated in fly-cutting and micro ball- end milling processes,” CIRP J. Manuf. Sci. Tec. 41, 30–43 (2023). [CrossRef]
14. M. Chen, M. Li, J. Cheng, et al., “Study on characteristic parameters influencing laser-induced damage threshold of KH2PO4 crystal surface machined by single point diamond turning,” J. Appl. Phys. 110(11), 113103 (2011). [CrossRef]
15. S. Reyné, G. Duchateau, J. Y. Natoli, et al., “Laser-induced damage of KDP crystals by 1omega nanosecond pulses: influence of crystal orientation,” Opt. Express 17(24), 21652–21665 (2009). [CrossRef]
16. S. F. Wang, J. Wang, X. Y. Lei, et al., “Investigation of the laser-induced surface damage of KDP crystal by explosion simulation,” Opt. Express 27(11), 15142–15155 (2019). [CrossRef]
17. J. Cheng, J. H. Wang, E. H. Peng, et al., “Combined modulation of incident laser light by multiple surface scratches and their effects on the laser damage properties of KH2PO4 crystal,” Opt. Express 28(6), 8764–8781 (2020). [CrossRef]
18. Y. Zhang, Q. C. Fan, W. Gao, et al., “Subsurface damage layer of bulk single-crystal potassium dihydrogen phosphate (KDP) after SPDT: studied by the grazing incidence X-ray diffraction technique,” Opt. Mater. Express 12(5), 2041–2052 (2022). [CrossRef]
19. J. A. Menapace, P. R. Ehrmann, and R. C. Bickel, “Magnetorheological finishing (MRF) of potassium dihydrogen phosphate (KDP) crystals: nonaqueous fluids development, optical finish, and laser damage performance at 1064 nm and 532 nm,” Proc. SPIE 7504, 750414 (2009). [CrossRef]
20. F. Ji, M. Xu, B. Wang, et al., “Preparation of methoxyl poly (ethylene glycol) (MPEG)-coated carbonyl iron particles (CIPs) and their application in potassium dihydrogen phosphate (KDP) magnetorheological finishing (MRF),” Appl. Surf. Sci. 353, 723–727 (2015). [CrossRef]
21. H. Yang, J. Cheng, M. Chen, et al., “Optimization of morphological parameters for mitigation pits on rear KDP surface: experiments and numerical modeling,” Opt. Express 25(15), 18332–18345 (2017). [CrossRef]
22. F. Li, X. Xie, G. Tie, et al., “Research on temperature field of KDP crystal under ion beam cleaning,” Appl. Opt. 55(18), 4888–4894 (2016). [CrossRef]
23. F. Li, X. Xie, G. Tie, et al., “Figuring process of potassium dihydrogen phosphate crystal using ion beam figuring technology,” Appl. Opt. 56(25), 7130–7137 (2017). [CrossRef]
24. X. Wang, H. Gao, Y. C. Chen, et al., “A water dissolution method for removing micro-waviness caused by SPDT process on KDP crystals,” Int. J. Adv. Manuf. Technol. 85(5-8), 1347–1360 (2016). [CrossRef]
25. H. Dong, L. Wang, W. Gao, et al., “KDP aqueous solution-in-oil microemulsion for ultra-precision chemical-mechanical polishing of KDP crystal,” Materials (Basel) 10(3), 271 (2017). [CrossRef]
26. W. Gao, L. L. Wang, L. F. Tian, et al., “Novel abrasive-free jet polishing mechanism for potassium dihydrogen phosphate (KDP) crystal,” Opt. Mater. Express 8(4), 1012–1024 (2018). [CrossRef]
27. W. Gao, J. W. Ji, C. Wang, et al., “Mitigation of subsurface damage in potassium dihydrogen phosphate (KDP) crystals with a novel abrasive-free jet process,” Opt. Mater. Express 8(9), 2625–2635 (2018). [CrossRef]
28. W. Gao, Q. L. Wei, J. W. Ji, et al., “Theoretical modeling and analysis of material removal characteristics for KDP crystal in abrasive-free jet processing,” Opt. Express 27(5), 6268–6282 (2019). [CrossRef]
29. Y. Zhang, Q. C. Fan, W. Gao, et al., “Novel abrasive-free jet polishing for bulk single-crystal KDP with a low viscosity microemulsion,” Sci. Rep. 12(1), 8346 (2022). [CrossRef]
30. T. Narumi, Y. Shibuta, and T. Yoshikawa, “Molecular dynamics simulation of interfacial growth of SiC from Si-C solution on different growth planes,” J. Cryst. Growth 494, 36–43 (2018). [CrossRef]
31. A. Yamaguchi, D. Oozeki, N. Kawamoto, et al., “Growth of highly crystalline GaN at high growth rate by trihalide vapor-phase epitaxy,” Phys. Status Solidi B 257(4), 1900564 (2020). [CrossRef]
32. H. Liu, S. Zou, S. Dai, et al., “Dopamine sheathing facilitates the anisotropic growth of lysozyme crystals,” J. Mol. Liq. 332, 115826 (2021). [CrossRef]
33. S. S. Mishra, L. C. Chuang, K. Maeda, et al., “Difference in growth rates at {110} and {111} crystal/melt interfaces of silicon,” J. Cryst. Growth 593, 126784 (2022). [CrossRef]
34. Y. J. Fu, Z. S. Gao, X. Sun, et al., “Effects of anions on rapid growth and growth habit of KDP crystals,” Prog. Cryst. Growth Charact. Mater. 40(1-4), 211–220 (2000). [CrossRef]
35. N. P. Zaitseva, J. J. De Yoreo, M. R. Dehaven, et al., “Rapid growth of large-scale (40-55 cm) KH2PO4 crystals,” J. Cryst. Growth 180(2), 255–262 (1997). [CrossRef]
36. M. Bussmann, S. Chandra, and J. Mostaghimi, “Modeling the splash of a droplet impacting a solid surface,” Phys. Fluids 12(12), 3121–3132 (2000). [CrossRef]
37. I. V. Roisman, R. Rioboo, and C. Tropea, “Normal impact of a liquid drop on a dry surface: Model for spreading and receding,” Proc. R. Soc. Lond. A 458(2022), 1411–1430 (2002). [CrossRef]
38. R. Kannan and D. Sivakumar, “Drop impact process on a hydrophobic grooved surface,” Colloids Surf. A 317(1-3), 694–704 (2008). [CrossRef]
39. C. Antonini, A. Amirfazli, and M. Marengo, “Drop impact and wettability: From hydrophilic to superhydrophobic surfaces,” Phys. Fluids 24(10), 102104 (2012). [CrossRef]
40. W. L. Jorgensen, “Transferable intermolecular potential functions for water alcohols, and ethers. Application to liquid water,” J. Am. Chem. Soc. 103(2), 335–340 (1981). [CrossRef]
41. W. L. Jorgensen, J. Chandrasekhar, and J. D. Madura, “Comparison of simple potential functions for simulating liquid water,” J. Chem. Phys. 79(2), 926–935 (1983). [CrossRef]
42. W. L. Jorgensen and J. D. Madura, “Temperature and size dependence for monte carlo simulations of TIP4P water,” Mol. Phys. 56, 1381–1392 (1985).
43. R. J. Nelmes, Z. Tun, and W. F. Kuhs, “A compilation of accurate structural parameters for KDP and DKDP, and a users’ guide to their crystal structures,” Ferroelectrics 71(1), 125–141 (1987). [CrossRef]
44. A. G. Stack, J. R. Rustad, J. J. Deyoreo, et al., “The growth morphology of the {100} surface of KDP (archerite) on the molecular scale,” J. Phys. Chem. B 108(47), 18284–18290 (2004). [CrossRef]
45. S. Y. Yang, L. C. Zhang, H. T. Xie, et al., “Interaction potential function for the deformation analysis of potassium dihydrogen phosphate using molecular dynamics simulation,” Comput. Mater. Sci. 187, 110122 (2021). [CrossRef]
46. S. Y. Yang, L. C. Zhang, and Z. H. Wu, “Subsurface damage minimization of KDP crystals,” Appl. Surf. Sci. 604, 154592 (2022). [CrossRef]
47. A. Beaucamp, Y. Namba, and R. Freeman, “Dynamic multiphase modeling and optimization of fluid jet polishing process,” CIRP Ann.- Manuf. Techn. 61(1), 315–318 (2012). [CrossRef]
48. W. Peng, C. Guan, and S. Li, “Material removal mode affected by the particle size in fluid jet polishing,” Appl. Opt. 52(33), 7927–7933 (2013). [CrossRef]
49. Z. Z. Li, S. Y. Li, Y. F. Dai, et al., “Optimization and application of influence function in abrasive jet polishing,” Appl. Opt. 49(15), 2947–2953 (2010). [CrossRef]
50. R. H. Doremus, B. W. Roberts, and D. Trunbull, Growth and Perfection of Crystals (Wiley, 1958).
51. F. Roseuberger, Fundamentals of Crystal Growth (Springer, 1979).
52. T. T. Sui, L. N. Wei, X. Z. Cao, et al., “Comparison of oxygen vacancy and interstitial oxygen in KDP and ADP crystals from density functional theory calculations,” Comput. Mater. Sci. 182, 109783 (2020). [CrossRef]
53. Z. Shi, Q. Zhao, B. Guo, et al., “A review on processing polycrystalline magnesium aluminate spinel (MgAl2O4): Sintering techniques, material properties and machinability,” Mater. Des. 193, 108858 (2020). [CrossRef]
54. L. Lamberson and K. T. Ramesh, “Dynamic electromechanical behavior of single-crystal α-quartz,” Int. J. Impact Eng. 110, 338–345 (2017). [CrossRef]
stands for the O atoms in H2O, 
stands for the H atoms in H2O, 
stands for the H atoms in KDP (KH2PO4), 
stands for the O atoms which connect to the H atoms in KDP, 
stands for the O atoms which do not connect to the H atoms in KDP, 
stands for the K atoms in KDP, and 
stands for the P atoms in KDP.