Eplanar and linear densities

Eplanar and linear densities - continuous contact Direction...

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BCC – (100) Planar Densities = Effective # of atoms whose center lies in the plane Area of the plane Simple Cubic – (100) a a =(4*1/4)/a 2

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Planar Density BCC – (110) a 2 a = Effective # of atoms whose center lies in the plane Area of the plane =(4*1/4+1)/(a.a√2)
Planar Density a a FCC – (100) FCC – (111) 2 a 2 a 2 a = Effective # of atoms whose center lies in the plane Area of the plane =(4*1/4+1)/(a.a) # of atoms on the plane = 3*1/6+3*1/2=2 Area=1/2(a√2/2)(a√3/ √2)

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Linear Density y x z [110] [100] y x z [110] [111] [100] FCC BCC 2 a a a a a 3 a 2 a 3 a [111]
y x z Most efficiently packed planes: (110) family Most efficiently packed directions: [111] family All Body diagonals BCC

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y x z Most efficiently packed planes: (111) family Most efficiently packed directions: [110] family (All Face diagonals) FCC
Close packed Planes and Directions Planes and directions where atoms are in

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Unformatted text preview: continuous contact Direction Plane SC [100] none BCC [111] none FCC [110] family (111) family HCP-Basal plane Packing of atoms not the same along different planes and directions in a crystal. Grain structure A grain is a crystal with a certain orientation in 3-d space. Since real materials are usually made of billions of crystals each with a different orientation as shown above, we create grain boundaries which are boundaries between crystals of different orientation. The average grain size is an important microstructural characterics that affects all properties. So we measure grain size, n , by using the ASTM standard: N = 2 n-1 where is the average # of grains/sq. inch at a magnification of 100X....
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Eplanar and linear densities - continuous contact Direction...

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