free .net barcode reader library Plane {100} {110} {111} {120} {221} bcc 4 5 3 2 1 fcc 5 6 6 3 1 in Software

Generating Data Matrix in Software Plane {100} {110} {111} {120} {221} bcc 4 5 3 2 1 fcc 5 6 6 3 1

Plane {100} {110} {111} {120} {221} bcc 4 5 3 2 1 fcc 5 6 6 3 1
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An infinite number of planes may be taken through the crystal structure, but most are just geometrical constructions and have no practical importance Remembering that each complete set of parallel planes must account for all the atoms, the most important planes are the ones of a high atomic population and the largest
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Fig 222: Projection of the lattice on a plane perpendicular to the Z-axis to illustrate
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interplanar spacing Filled circles are on the plane of the paper [26]
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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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Fig 223: Interplanar spacing of {111} planes in (a) bcc and (b) fcc structures [26, 27]
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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
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Fig 224: The cleavable planes of a diamond [25]
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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 =
F , L
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 =
f (G Ar ) , L
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
Table 26
Summary of the minimum shear modulus [28]
Plane {100} {110} {111}
Rotation 45 54 44 0
From <100> <100> <111>
G Minimum 451 1011 N/m2 433 1011 N/m2 451 1011 N/m2
Brookes [29] has examined the anisotropy in diamond hardness on the {100} planes It appears that in the <100> directions, the maximum hardness is obtained and in the <110> directions, the minimal hardness This is contrary to the opinion that the difficult polishing directions are those of maximum hardness The properties of diamond are summarized in Table 27
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Table 27
The properties of diamond on the {100} planes [30]
Friction coefficient, (obtained from cast iron wheel at a speed of 64 m/sec) 020 018 014
Directions
Shear modulus (1011 N/m2) G
Hardness (N/mm2)
<100> <120> <110>
518 474 452
9600 8900 6900
242 Natural Diamond
Natural diamond has been in use for grinding very hard non-ferrous materials, notably glass and ceramics, since about 1890 for saws and since about 1940 for cutting tools [31] Natural diamond develops slowly at temperatures from 900 to 1,300 C and pressures from 40 to 60 atm It is extracted from nodules of Kimberlite, which is a variety of mica, peridotite low in silica and high in magnesium, in which natural diamonds are formed and grown Natural diamonds come in various forms and colours: (a) Large single crystals monocrystalline (b) Carbonadoes or balas polycrystalline (c) Borate single crystal monocrystalline Large single crystals, because of their lustre, are used as gems and are extremely costly Borat, an inferior single-crystal diamond, is used for making cutting tools in ductile mode machining However, it suffers from cleavage problems It is easily cleaved on planes that are parallel with the octahedral faces because the density of inter-atomic bonding is the lowest on these faces [32] Thanks to advances in the machining of diamonds, it is possible to locate the strongest plane (ie, the {110} plane) in the main cutting force direction, thus avoiding cleavage and minimizing wear The demands posed by the cleavage problem of single-crystal diamonds have also been met by nature; balas and carbonados, which are natural polycrystalline masses of diamonds They consist of small grains of diamonds 10 100 in size bonded together The random orientation of their grains blocks tile propagation of any cleavage plane that may start in a highly stressed region However, the shortage of these natural polycrystalline diamonds has increased the demand for synthetic diamonds
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