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1) Assume that the elemental atoms are hard spheres of radius r. Calculate the maximum packing rate t obtained when this element crystallizes into the following structures: (a) simple cubic (sc) (b) body-centered cubic (bcc) (c) face-centered cubic (fcc) (d) diamond (e) hexagonal close packed (hep) (first calculate the optimal c/a relation) Using these results, determine the value of the lattice parameter(s) of the following real crystal systems where dis distance between nearest neighbors: (f) magnesium (hcp), d= 3.20 Å (g) aluminum (fcc), d = 2.86 Å (h) silicon (diamond), d= 2.35 Å www Hints:

1) Assume that the elemental atoms are hard spheres of radius r. Calculate the maximum packing rate t obtained when this element crystallizes into the following structures: (a) simple cubic (sc) (b) body-centered cubic (bcc) (c) face-centered cubic (fcc) (d) diamond (e) hexagonal close packed (hep) (first calculate the optimal c/a relation) Using these results, determine the value of the lattice parameter(s) of the following real crystal systems where dis distance between nearest neighbors: (f) magnesium (hcp), d= 3.20 Å (g) aluminum (fcc), d = 2.86 Å (h) silicon (diamond), d= 2.35 Å www Hints:

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1) Assume that the elemental atoms are hard spheres of radius r. Calculate the maximum packing rate t obtained when this element crystallizes into the following structures: (a) simple cubic (sc) (b) body-centered cubic (bcc) (c) face-centered cubic (fcc) (d) diamond (e) hexagonal close packed (hep) (first calculate the optimal c/a relation) Using these results, determine the value of the lattice parameter(s) of the following real crystal systems where dis distance between nearest neighbors: (f) magnesium (hcp), d= 3.20 Å (g) aluminum (fcc), d= 2.86 Å (h) silicon (diamond), d= 2.35 Å www Hints: (b) For e) (a) Three-dimensi onal filling of the hexagonal close packed (left) and face-centered cubic (right) structures.
Transcribed Image Text:1) Assume that the elemental atoms are hard spheres of radius r. Calculate the maximum packing rate t obtained when this element crystallizes into the following structures: (a) simple cubic (sc) (b) body-centered cubic (bcc) (c) face-centered cubic (fcc) (d) diamond (e) hexagonal close packed (hep) (first calculate the optimal c/a relation) Using these results, determine the value of the lattice parameter(s) of the following real crystal systems where dis distance between nearest neighbors: (f) magnesium (hcp), d= 3.20 Å (g) aluminum (fcc), d= 2.86 Å (h) silicon (diamond), d= 2.35 Å www Hints: (b) For e) (a) Three-dimensi onal filling of the hexagonal close packed (left) and face-centered cubic (right) structures.
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