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Crystalline Solids_crystalline and noncrystalline materials

Crystalline Solids_crystalline and noncrystalline materials...

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Materials Science and Engineering MIME 1650 Lecture 6 1 1 Chapter 3 - MIME 1650 Materials Science and Engineering Lecture 6: Crystalline Structure and Miller Indices 2 Chapter 3 - ex: linear density of Al in [110] direction a = 0.405 nm Linear Density Linear Density of Atoms LD = a [110] Unit length of direction vector Number of atoms* # atoms length 1 3.5 nm a 2 2 LD - = = *The sharing of atoms with adjacent unit cells must be considered
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Materials Science and Engineering MIME 1650 Lecture 6 2 3 Chapter 3 - Linear Density Linear Density of Atoms LD = Unit length of direction vector Number of repeat distances Repeat distance: distance between adjacent atoms along the direction. In general LD = 1/r where r is the repeat distance between adjacent atoms 4 Chapter 3 - Planar Density Planar Density of Atoms PD = area of plane # of atoms centered on a plane* *The sharing of atoms with adjacent unit cells must be considered
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Materials Science and Engineering MIME 1650 Lecture 6 3 5 Chapter 3 - Crystallographic Planes We want to examine the atomic packing of crystallographic planes Iron foil can be used as a catalyst. The atomic packing of the exposed planes is important. a) Draw (100) and (111) crystallographic planes for Fe. b) Calculate the planar density for each of these planes. 6 Chapter 3 - Planar Density of (100) Iron Solution: At T < 912 ° C iron has the BCC structure. (100) Radius of iron R = 0.1241 nm R 3 3 4 a = Adapted from Fig. 3.2(c), Callister 7e. 2D repeat unit = Planar Density = a 2 1 atoms 2D repeat unit = nm 2 atoms 12.1 m 2 atoms = 1.2 x 10 19 1 2 R 3 3 4 area 2D repeat unit
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Materials Science and Engineering MIME 1650 Lecture 6 4 7 Chapter 3 - Planar Density of (111) Iron Solution (cont): (111) plane 1 atom in plane/ unit surface cell 3 3 3 2 2 R 3 16 R 3 4 2 a 3 ah 2 area = = = = atoms in plane atoms above plane atoms below plane a h 2 3 = a 2 2D rep eat u nit 1 = = nm 2 atoms 7.0 m 2 atoms 0.70 x 10 19 3 2 R 3 16 Planar Density = atoms 2D repeat unit area 2D repeat unit 8 Chapter 3 - Single Crystals Single crystal – material in which periodic arrangement of atoms extends uninterrupted over the entire specimen Without external constraint, crystal assumes a regular geometric shape
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Materials Science and Engineering
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