Close packed crystal structures can be thought of as

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Close-Packed Crystal Structures Can be thought of as stacked close-packed planes along the proper crystal direction type. Offer the maximum packing efficiency in 3D for equal sized spheres. An infinite number of stacking sequences are possible, but only a few are important. Consider stacking close-packed planes on and then out of the page:
HCP Unit Cell Hexagonal Close-Packed Note: HCP is not the same as the simple hexagonal structure … See the reduced-sphere and hard-sphere unit cells below: Simple Hexagonal Unit Cell A A A B A a a c a a a c/a = 1.633 c/a = 1
If we stack such that alternating planes cover A,B,C sites, cyclically, we form the Face-Centered Cubic (FCC) crystal structure. Both of these crystal structures feature close-packed planes and close-packed directions. The difference between the structures arises from the stacking sequence of the close packed planes . Close-Packed Crystal Structures Can be thought of as stacked close-packed planes along the proper crystal direction type. Offer the maximum packing efficiency in 3D for equal sized spheres. An infinite number of stacking sequences are possible, but only a few are important. Consider stacking close-packed planes on and then out of the page: If we stack such that alternating planes cover A and B sites, respectively, we form the Hexagonal Close-Packed (HCP) crystal structure.
Close-Packed Crystal Structures Not all crystal planes will be close-packed within a close-packed 3D structure. Not all crystal planes will be planar CN=6 in a 3D structure featuring volume CN=12. FCC constructed by stacking CN=4 planes along <100>: FCC constructed by stacking CN=6 planes along <111>: <100> <111>
Close-Packed Crystal Structures Not all crystal planes will be close-packed within a close-packed 3D structure. Not all crystal planes will be planar CN=6 in a 3D structure featuring volume CN=12. FCC constructed by stacking CN=4 planes along <100>: FCC constructed by stacking CN=6 planes along <111>: <100> <111>
Theoretical Density The APF is constant for a given perfect crystalline structure. If we know how atoms are positioned throughout an entire crystal, we should also be able to calculate the density (mass/volume) of the crystal, as long as we know what element the crystal is made of. Simple Cubic APF = 0.52 Body-Centered Cubic APF = 0.68 Face-Centered Cubic APF = 0.74
Theoretical Density Example: Density of Lead Pb is FCC at room temperature and 1 atmosphere. The atomic radius of Pb is 0.175 nm. = m V
Theoretical Density Example: Density of Lead Pb is FCC at room temperature and 1 atmosphere. The atomic radius of Pb is 0.175 nm. Although any representative volume works, let’s calculate this based on one unit cell:  Find Mass Per Unit Cell Each Pb atom weighs 207 g/mol (from periodic table). There are 4 Pb atoms per unit cell (we’re told it’s an FCC structure). Therefore, there are and thus = m V m = (6 . 64 10 - 24 moles / unit cell)(207 g / mole) = 1 . 37 10 - 21 g / unit cell 4 atoms / unit cell 6.02 × 10 23 atoms / mole = 6.64 × 10 24 moles / unit cell a a a
Theoretical Density Example: Density of Lead Pb is FCC at room temperature and 1 atmosphere.
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