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Let s revisit the concepts of conductor and insulator for a moment In 4 we stated that a conductor is an element whose electrons can move freely and an insulator is one whose electrons are stuck tightly in place Now we look at this electron motion just a little bit closer Keep in mind that physics at this low level can get very tricky, so we make simplifying assumptions and gloss over a number of details An atom, you recall, has a nucleus of protons and neutrons This nucleus has a positive charge Whizzing around that nucleus is a cloud of electrons, normally just enough to make the atom s electric charge neutral Earlier, we hinted at the concept of orbital shells The electrons are not free to orbit just anywhere, otherwise they would just spiral into the center and stick to the nucleus.



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interplanar spacing Filled circles are on the plane of the paper [26]

interplanar distance In the bcc structure, these are the {110} planes, and in the fcc structure, these are the {111} planes (Figures 222 and 223)





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Each electron has an energy level which could refer to how fast it is moving (but doesn t really), and these energy levels are almost digital in nature An electron could have an energy of 1 or 2 but never 125 This discrete separation of energy levels is known as energy quanta, and quanta lead us into the realm of quantum physics Each orbital shell is associated with a particular energy level Only electrons with the correct amount of energy can live in a given shell If you add a quantum of energy e to an electron by, perhaps, banging on it with a hammer or shining a light on it, the electron can no longer stay in its current shell but must jump to a higher energy shell (Fig 12-1) Each orbital shell can hold a limited number of electrons and no more.

Fig 223: Interplanar spacing of {111} planes in (a) bcc and (b) fcc structures [26, 27]

The inner shells of an atom are normally all full We work with the outer.

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A diamond can be cleaved along any plane parallel to the 111 plane or an octahedral plane (Figure 224) It behaves as if it consists of an infinite number of very thin laminations which can be

Fig 224: The cleavable planes of a diamond [25]

Fig. 12-1.

separated by a sharp blow along any parallel plane, but will resist such a thrust on any other plane Therefore, the stone must be mounted in such a way that the tool approaches the workpiece at a plane that is not parallel to a cleavage plane or else the tool will immediately start to flake and chip at the edge [25] A diamond is a solitary anisotropic particle whose properties such as elastic modulus, shearing modulus and hardness change along and within each and every crystallographic plane As a result, the friction forces and the wear directions also change [28] Different coefficients of friction exist for different directions, defined as follows: m =

where F is the drag force and L, the normal force The drag force is a function of the shear strength t of the broken particles and of the real contact area, Ar F = f ( Ar) If we assume that the relationship between t and the shear modulus G is of a linear nature, then t = Gg, where g is the shear angle Combining the previous equations, the relationship between the coefficient of friction and the shear modulus is as shown below: m =

Fig. 12-2.

mhkl = kG hkl , where k is a constant Porat [28] has studied the value of the shear modulus on different planes of a diamond, and the summary of the minimum shear modulus is as given in Table 26

Aab(x, y)

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