外文翻譯： Material Removing Mechanism for Mechanical Lapping of Diamond Cutting Tools LI Zeng-qiang， ZONG Wen-jun， SUN Tao， DONG Shen （ Center for Precision Engineering， Harbin Institute of Technology， Harbin 150001， China） Abstract： The material removing mechanism for mechanical lapping of diamond cutting tools was illuminated at the atomistic scale. In lapping process， phase transformation of the lapping region was the main reason for the material removal. Thus a three-dimensional model of a specimen of the diamond monocrystal and rigid diamond grit was built with the aid ofthe molecular dynamics（ MD） simulation. The force between all of the atoms was calculated by the Tersoff potential. After that， lapping with a certain cutting depth of 1.5 lattice constants was simulated. By monitoring the positions of atoms within the model， the microstructure in the lapping region changes as diamond transformed from its diamond cubic structure to amorphous carbon were identified. The change of structure was accomplished by the flattening of the tetrahedron structure in diamond. This was verified by comparing the radial distribution functions of atoms in the lapping and un-lapping regions.Meanwhile， the debris produced in lapping experiment was analyzed by XRD（ X-ray diffraction） . The results show that the phase transformation happens indeed. Keywords ： diamond cutting tools ； mechanical lapping ； material removing mechanism； molecular dynamics simulation It is an important way to turn the optical surface with natural diamond cutting tools to obtain high accuracy. The processed work-pieces surface has lower surface roughness and residual stress，and smaller metamorphic region than those machined in usual ways. Diamond is the most important material to make cutting tools in the ultra-precision machining， for it is an ideal brittle solid with the greatest hardness and resistance to plastic deformation of any material and has very high dimensional homogeneity. The sharpening method of diamond cutting tools is the key technology to obtain sharp cutting radius， good surface quality and small geometric tolerance1. There are many sharpening methods such as lapping， ion beam sputtering，thermal chemistry polishing， plasma polishing， oxide etching and laser erosion， etc. The most common and effective method is lapping2. The mechanism of the material removal in lapping has a lot of statements such as the micro-cleavage theory3， the thermal abrasion theory4， electro-abrasion theory5 and theory of fracture taking place in the hard direction6， etc. However， these explanations are only satisfactory in the particular situation. The explanation accepted by most people is that the hybridized orbit of the carbon converts from sp3 to sp2 in lapping， as demonstrated by van Bouwelen7， Grillo8， Hird and Field9. As yet， few man has verified it at the atomistic level. The extremely powerful technique of molecular dynamics（ MD）simulation involves solving the classical many-body problem in contexts relating to the study of matter at the atomistic level. Since there is no alternative approach capable of handling this broad range of problems at the required level of detail， molecular dynamics methods have been proved indispensable in both pure and applied research， as demonstrated by Rapaport10. Molecular dynamics analysis is an effective method in studying indentation， adhesion， wear and friction，surface defects and nano-cutting at the atomistic scale. Nowadays， MD analysis has already been employed to investigate the AFM-based nanolithography process using an AFM tool11 and atomic surface modification in monocrystalline silicon12. Therefore， it is an efficient way to approach the mechanism of the material removal in lapping using molecular dynamics simulation. From all the above， this study will focus on the material removing mechanism in diamond mechanical lapping using three-dimensional MD simulation. And the microcosmic phenomena in mechanical lapping will be presented and discussed. 1 Methods 1.1 Simulation modeling At the beginning， the mechanical lapping process of diamond cutting tools is introduced. The scaife used was made from a grey cast iron and was medium “ striped”（ radial grooves to hold diamond grit） .It was prepared for use by applying a film of olive oil to the surface， before a few carats of graded diamond grits were rubbed evenly into it. With the scaife running at a high speed， a diamond cutting tool was lapped by applying a load. In this process， the diamond grit was fixed in the scaife. So， the process belongs to the fixed abrasive polishing category13. Therefore， a model of a specimen of the diamond monocrystal and rigid diamond grit was built， as shown in Fig.1. Fig.1 Molecular dynamics simulation model of mechanical lapping of diamond cutting tools The crystal lattice of the specimen and the grit belonged to the diamond cubic system. The lattice constant of this system was 0.356 67 nm， which was represented as a. The control volume of the specimen must be large enough to eliminate boundary effects.Taking this into consideration， an optimum control volume was chosen based on an iterative process of increasing the control volume size until further increases did not affect the displacements and velocities of the atoms due to lapping. An optimum size of 50a 15a 30a was obtained， consisting of 183,930 atoms. Moreover， the periodic boundary condition was used in the z-direction to reduce the effects of the simulation scale. The specimen included three kinds of atoms ，namely ： boundary atoms， thermostat atoms and Newtonian atoms.To restrict the rigid-body motion of the specimen， the boundary atoms in the left and bottom layers of the specimen that were fixed in space were used to contain the Newtonian atoms.Thermostat atoms were also used to ensure reasonable outward heat conduction away from the control volume.Thermostat atoms and the Newtonian atoms obey the Newtons second law.The top surface of the specimen was（ 100）surface， which was exposed to the grit.The spherical diamond grit had a radius of 8a， consisting of 17,116 atoms.And it slid on the specimen with the depth of h. Before carrying out the molecular dynamics simulation on the lapping of diamond， it is important to ensure that the chosen potential function gives a reliable result for the simulation. Tersoff potential was used in the present simulation to dictate the interaction among the diamond atoms in this simulation14. The parameters in Tersoff potential for carbon were as follows ： A=1,393.6 eV， B=347.6 eV，=34.879 nm.1， =22.119nm.1 ， =1.572,4 10.7 ， n=0.727,51 ，c=380,49 ， d=4.384， h=.0.570 58， R=0.18 nm， and S=0.21 nm. Positions and velocities of the atoms were determined by the Verlet method as demonstrated by Maekawa and Itoh15.To simulate lapping under room-temperature conditions， the diamond atoms were arranged in a perfectdiamond cubic structure with the lattice parameters equal to their equilibrium values at an ambient temperature of 293 K. The ambient temperature was maintained by scaling the velocities of the thermostat atoms at every special time step.In this simulation， the 0.5 fs was selected as the time step to obtain a high accuracy. This simulation was calculated by the Lammps software16， and visualized by the VMD software17. The velocity of the lapping was 100a with 1.5a in cutting depth and 40a in lapping length. Before the simulation， the specimen had been relaxed for 10 000 time steps in order to maintain the thermal balance. 1.2 Experiment The test apparatus of lapping experiment is shown in Fig.2.The abrasive used was diamond grit with an average radius of 0.1 m.They were coated on the scaife in a ring with a radius of 120 mm.The diamond cutting tool was fixed on the arm by a special fixture.Then， the tool was lapped with the scaife running at 3 000r/min(ca.38 m/s)，under a load of 5 N which was obtained by adjusting the place of the weight. The debris was collected after 30 min lapping.Thereafter， the XRD studies were carried out by SHIMADZU XRD-6000. Fig.2 Schematic diagram of the lapping apparatus 2 Results and discussions 2.1 Molecular dynamics analysis The 3D view and cross-section view of the simulation are shown in Fig.3. The crystal lattices near the diamond grit are distorted when the diamond grit cuts into the specimen.The region including these crystal lattices is half-ellipse in shape.The region is under the diamond grit and a bit left to the center o. And the major axis of the ellipse is in the same direction as the composition of forces. Furthermore， this region moves left as the diamond grit slides. As shown in Fig.4 ， A1+A2A3 ， where O1O2 represents the surface of the workpiece.It shows that the removal materials do not pole up on both sides of the groove completely.Some materials are removed and form chips. It is a cutting process. Whereas， the existing A1 and A2 show that ploughing also occurs.So this state is the cutting state accompanied by ploughing. Fig.3 Microstructure of specimen after the grit sliding Fig.4 Section of the grooves in the longitudinal direction There are three key points in lapping， as shown in Fig.5. Firstly，atoms near the diamond grit are forced to make some displacement from their initial position.The crystal lattices including these atoms distort a little.The boundary between the distorted lattices and the perfect lattices is along the diamond（ 111） surface（ the black lines）as shown in Fig.5（ a） .The displacements of the atoms become bigger and bigger along with the diamond grit sliding left.More and more atoms deviate from their initial position.The lattices including these atoms distort seriously.The phase transformation that the diamond cubic diamond transforms into amorphous graphite starts on a few atoms （ in the dark circles） at the end of this moment.That is to say that the hybridized orbit converts from sp3 to sp2. Secondly， the lattices below the diamond grit have the worst distortion and the boundary faceting along the（ 111） surface extend to the deeper layer， as shown in Fig.5（ b） . More atoms transform from diamond cubic diamond to amorphous graphite ， especially those in the dark circle. Besides，some atoms are taken away by the diamond grit.Thirdly， some lattices revert a little with the force minimizing， as shown in Fig.5（ c） . However，the atoms which have the phase transformation cannot revert to their initial phase， especially those in the dark circle. Therefore， the groove is to the left on the surface of the diamond specimen. Fig.5 Scattergrams of atoms in longitudinal section A in different states 2.2 Bond formation From the simulation， it is found that the phase transformation is due to the flattening of the tetrahedron structure in diamond cubic diamond， as shown in Fig.6.The position transformation at progressive time steps is demonstrated in Fig.7. Fig.6 Crystal cell of the diamond crystal lattice taken out from the circular region in Fig.5（ a） As shown in Fig.7（ a）， the tetrahedron is deformed when the grit slides close. And the deformation is serious when the grit cuts into section A， as shown in Fig.7（ b） . The tetrahedron is flattened a little.Soon after， the tetrahedron deforms badly， as shown in Fig.7（ c） .Its four vertexes are almost on a plane and some bonds are broken. At the same time the phase transformation is accomplished. Fig.7 Change of the tetrahedron marked in Fig.6 when the grit slides 2.3 Pair correlation function The pair correlation functions of the specimen and the chip are shown in Fig.8 and Fig.9 respectively.The curve in Fig.8 is syllabified to a lot of clear peaks， which are the same as the diamonds radial distribution fuction(RDF). However， there are only two peaks in Fig.9, and the peaks are continued, which illuminates that amorphous exists in debris atoms. Therefore， it is sure that the phase transformation takes place in lapping. Fig.8 Pair correlation function of specimen atoms Fig.9 Pair correlation function of debris atoms 2.4 XRD Fig.10 shows the X-ray diffraction（ XRD） analysis of the debris produced in the lapping experiment. It demonstrates that the amorphous carbon ， small diamond particles or chips and Fe-C compositions（ like Fe7C3 and Fe5C2） exist together in the debris. Consequently， the amorphous carbon is produced in lapping， which corresponds to the simulation result. Fig.10 XRD analysis of the debris produced in the experiment 3 Conclusions （ 1） A three-dimensional MD model about the atoms of diamond cutting tools and diamond grit is built by using the molecular dynamics. Lapping at a special cutting depth is simulated. （ 2） The boundary of the transformation zone is regular ， faceting along （ 111 ） surface. The microcleavage only occurs inside this boundary. （ 3） Interaction between the diamond grit and diamond specimen leads to a phase transformation event.An amorphous transformation appears as the grit slides.And it is expounded from the comparison between the bond formatting and pair correlation function. Moreover， it has also been proved in the lapping experiment. References： 1 Yuan Z J， Yao Y X， Zhou M， et al. Lapping of single crystal diamond tools J CIRP Annals-Manufacturing Technology， 2003， 52（ 1）： 285-288. 2 Uegami K ， Tamamura K ， Jang K K. Lapping and frictional properties of diamond， and characteristics of diamond cutting tool J Journal of Mechanical Working Technology， 1988， 17（ 8）： 147-155. 3 Tolkowsky M. Research on the Abrading， Grinding or Polishing of Diamond D London： City and Guilds College， University of London， 1920. 4 Bowden F P， Tabor D. Physical Properties of Diamond M Oxford： Clarendon Press， 1965. 5 Brezoczky B ， Seki H. Triboattaction ： Friction under negative load J Langmuir， 1990， 6（ 6）： 1141-1145. 6 Couto M， van Enckevort W J P， Seal M， et al. Scanning tunneling microscopy of polished diamond surfaces J Applied Surface Science， 1992， 62（ 4）： 263-268. 7 van Bouwelen F M. Mechanically Induced Degradation of Diamond D Cambridge ： University of Cambridge， 1996. 8 Grillo S E， Field J E， van Bouwelen F M. Diamond polishing： The dependency of friction and wear on load and crystal orientation J Journal of Physics D： Applied Physics， 2000， 33： 985-990. 9 Hird J R， Field J E. A wear mechanism map for the diamond polishing process J Wear， 2005， 258： 18-25. 10 Rapaport D C. The Art of Molecular Dynamics Simulation M Cambridge： Cambridge University Press， 2004. 11 Yan Y D， Sun T， Dong S， et al. Molecular dynamics simulation of processing using AFM pin tool J Applied Surface Science， 2006， 252： 7523-7531. 12 Zarudi I， Cheong W C D， Zou J， et al. Atomistic structure of monocrystalline silicon in surface nano-modification J Nanotechnology， 2004， 15： 104-107. 13 Li Z Q， Sun T， Shi L Q， et al. Study on lapping process of diamond cutting tool J Key Eng Mater， 2006， 304/305： 104-108. 14 Tersoff J. Empirical interatomic potential for carbon， with applications to amorphous carbon J Phys Rev， 1988， 61（ 25）： 2879-2882. 15 Maekawa K， Itoh A. Friction and tool wear in nano-scale machining： A molecular dynamics J Wear， 1995， 188： 115-122. 16 Plimpton S J. Fast parallel algorithms for short-range molecular dynamics J J Comp Phys， 1995， 117： 1-19. 17 Humphrey W， Dalke A， Schulten K. VMD： Visual molecular dynamics J J Molec Graphics， 1996， 14： 33-38. 金剛石刀具機(jī)械研磨過(guò)程中材料的去除機(jī)理 李增強(qiáng)，宗文俊，孫 濤，董 申 （哈爾濱工業(yè)大學(xué)精密工程研究所，哈爾濱 150001） 摘要： 該材料，移除為的鉆石切割工具的機(jī)械研磨的機(jī)制被照亮在的原子論的的的的規(guī)模。在研磨過(guò)程中研磨區(qū)，相轉(zhuǎn)變材料去除的主要原因。因此，金剛石單晶和剛性金剛石磨粒的標(biāo)本的三維模型的建立與援助的分子動(dòng)力學(xué)（ MD）模擬。所有的原子之間的力量計(jì)算 Tersoff潛力。后認(rèn)為，與一個(gè) 1.5晶格常數(shù)的的一定的的切削深度研磨進(jìn)行了數(shù)值模擬。通過(guò)監(jiān)測(cè)模型內(nèi)的原子的位置，在金剛石研磨地區(qū)的鉆石立方結(jié)構(gòu)轉(zhuǎn)變?yōu)闊o(wú)定形碳的微觀結(jié)構(gòu)進(jìn)行了鑒定。完成在鉆石的四面體結(jié)構(gòu)的扁平化結(jié)構(gòu)的變化。這驗(yàn)證了原子的徑向分布函數(shù)的研磨和聯(lián)合國(guó)研磨 regions.Meanwhile的，研磨試驗(yàn)產(chǎn)生的碎片，通過(guò) XRD（ X射線衍射）分析比較。的結(jié)果表明，的相位轉(zhuǎn)型會(huì)發(fā)生確實(shí)。 這是一個(gè)重要途徑，把光學(xué)表面與天然金剛石刀具獲得高的精度。處理工作件表面具有較低的表面粗糙度和殘余應(yīng)力，小于常規(guī)方法加工的變質(zhì)地區(qū)。 鉆石是最重要的物質(zhì)，在超精密加工的切削工具，它是一種理想的最大的硬度和耐磨性的任何材料的塑性變形的脆性固體，具有非常高的維同質(zhì)。金剛石刀具刃磨方法的關(guān)鍵技術(shù)，獲得鋒利的切削半徑，良好的表面質(zhì)量和幾何公差小1。有許多方法，如研磨，離子束濺射 ，熱化學(xué)拋光，等離子拋光，氧化腐蝕和激光侵蝕等銳化最常見(jiàn)和最有效的方法是研磨 2。在研磨材料去除機(jī)制有一個(gè)報(bào)表很多，如微切割理論 3，熱磨損理論 4，電磨損理論 5和斷裂理論的努力方向 6，等等。然而，這些解釋是只有在特殊情況令人滿意。大多數(shù)人所接受的解釋是，從 SP3 雜化軌道的碳轉(zhuǎn)換到 SP2 作為由面包車(chē) Bouwelen 證明，在研磨 7，格里洛 8，本手冊(cè)所有提及和現(xiàn)場(chǎng) 9。到目前為止，一些人已證實(shí)它在原子水平。 極其強(qiáng)大的技術(shù)分子動(dòng)力學(xué)（ MD）模擬涉及解決有關(guān)的物質(zhì)在原子水平的研 究背景的經(jīng)典多體問(wèn)題。由于沒(méi)有替代方法能夠在所需水平的細(xì)節(jié)處理這個(gè)問(wèn)題的廣泛，分子動(dòng)力學(xué)方法已被證明是不可或缺的純粹與應(yīng)用研究，由 Rapaport表明 10。分子動(dòng)力學(xué)分析是一個(gè)有效的方法，在學(xué)習(xí)壓痕，附著力，耐磨損和摩擦，表面缺陷，并在原子尺度的納米切割。如今，醫(yī)師分析已經(jīng)被調(diào)查基于AFM 的納米光刻過(guò)程中使用的原子力顯微鏡工具 11和硅原子在單晶硅表面改性 12。因此，它是一種有效的方式來(lái)處理的材料去除機(jī)制，研磨使用分子動(dòng)力學(xué)模擬。 所有上述，本研究將集中在材料，消除金剛石機(jī)械研磨使用三 維的 MD 模擬的機(jī)制。和機(jī)械研磨的微觀現(xiàn)象，將介紹和討論。 1 研究方法 1.1 仿真建模 在開(kāi)始時(shí)，介紹了金剛石刀具機(jī)械研磨過(guò)程。斯凱夫使用了從灰鑄鐵中的 “條紋 ”（徑向槽舉行金剛石磨粒）。 通過(guò)膜表面的橄欖油，之前幾克拉分級(jí)金剛石顆粒均勻揉入準(zhǔn)備使用。斯凱夫在高速運(yùn)行，鉆石刀具研磨應(yīng)用負(fù)載。在這個(gè)過(guò)程中，金剛石磨粒固定在斯凱夫。所以，這個(gè)過(guò)程屬于固定研磨拋光類(lèi) 13。因此，始建金剛石單晶和剛性金剛石磨粒的標(biāo)本模型，如圖 1 所示。圖 7-1 關(guān)于金剛石切割工具機(jī)械研磨的分子動(dòng)力學(xué)仿真模型 晶格的標(biāo)本和砂礫屬于鉆石的立方系統(tǒng)。該系統(tǒng)的晶格常數(shù)為 0.356 67 納米，這是作為一個(gè)代表。試樣的控制量必須足夠大，消除邊界 effects.Taking 考慮到這一點(diǎn)的，被選為最佳控制量的基礎(chǔ)上增加控制音量大小，直到進(jìn)一步增加并不影響原子的位移和速度的迭代過(guò)程由于研磨。一個(gè)最佳規(guī)模為 50A15A30A，183930 原子組成的。此外，周期性的邊界條件是在 z 方向，以減少仿真規(guī)模的影響。標(biāo)本包括原子 3 種，即：邊界原子，恒溫原子和牛頓 atoms.To 的限制的剛體運(yùn)動(dòng)的標(biāo)本，在標(biāo)本固定在空間的左側(cè)和底部層的邊界原 子包含牛頓atoms.Thermostat 原子也被用來(lái)確保合理向外熱傳導(dǎo)遠(yuǎn)離控制 volume.Thermostat原子和牛頓原子服從牛頓第二 law.The 排在前面的標(biāo)本（ 100）表面，這是暴露球形金剛石磨粒 grit.The了一個(gè) 8A的半徑，它與深度 h的標(biāo)本下滑 17,116 atoms.And組成。 開(kāi)展對(duì)金剛石研磨的分子動(dòng)力學(xué)模擬之前，重要的是要確保所選擇的潛在功能提供了一個(gè)可靠的模擬結(jié)果。在目前的模擬 tersoff 潛力，決定在這個(gè)模擬 14鉆石的原子之間的相互作用。 Tersoff 碳勢(shì)參數(shù)如下： = 1,393.6 EV， = 347.6 EV，= 34.879 nm.1， = 22.119nm.1， = 1.572,410.7， N = 0.727,51， C = 380,49， D = 4.384， H = .0.570 58， r = 0.18 納米，和 S = 0.21 納米。位置和原子的速度 Verlet方法，確定由前川和伊藤表明 15為了模擬在室溫條件下研磨，鉆石的原子排列在 perfectdiamond 立方結(jié)構(gòu)的晶格參數(shù)等于其均衡值 0.5 FS，通過(guò)擴(kuò)大在每一個(gè)特殊的時(shí)間 step.In這個(gè)模擬恒溫 原子 的速度保持在 293 K時(shí)的環(huán)境溫度環(huán)境溫度，被選定為時(shí)間步長(zhǎng)，獲得了很高的精度。 這由 Lammps 軟件 16，模擬計(jì)算和可視化的 VMD 軟件 17。的研磨速度 100A 1.5A 切割研磨長(zhǎng)度的深度和 40A。前仿真，標(biāo)本已放寬為 10 000 個(gè)時(shí)間步以保持熱平衡。 1.2 實(shí)驗(yàn) 研磨實(shí)驗(yàn)測(cè)試儀器顯