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

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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

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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

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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 diamond’s 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

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