Consider a face-centered-cubic cell. Construct a primitive cell within this larger cell, and compare the two. How many atoms are in the primitive cell, and how does this compare with the number in the original cell?
Consider a face-centered-cubic cell. Construct a primitive cell within this larger cell, and compare the two. How many atoms are in the primitive cell, and how does this compare with the number in the original cell?
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![7. Consider a face-centered-cubic cell. Construct a primitive cell within this larger
cell, and compare the two. How many atoms are in the primitive cell, and how
does this compare with the number in the original cell?
8. a) Show that a two-dimensional lattice may not possess a 5-fold symmetry.
b) Establish the fact that the number of two-dimensional Bravais lattices is five:
Oblique, square, hexagonal, simple rectangular, and body-centered rectangular.
(The proof is given in Kittel, 1970.)
9. Demonstrate the fact that if an object has two reflection planes intersecting at 1/4,
it also possesses a 4-fold axis lying at their intersection.
10. Sketch the following planes and directions in a cubic unit cell: (122), [122], (IT2),
(172).
11. a) Determine which planes in an fcc structure have the highest density of atoms.
b) Evaluate this density in atoms/cm² for Cu.
12. Repeat Problem 11 for Fe, which has a bcc structure.
13. Show that the maximum packing ratio in the diamond structure is A/3/16. [Hint:
The structure may be viewed as two interpenetrating fcc lattices, arranged such
that each atom is surrounded by four other atoms, forming a regular tetrahedron.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F87103f70-8b7e-45f8-a35b-fc62b41d6817%2F4c7b3449-fcf9-44a8-96da-bf11e688bd84%2Fpjy6j0c_processed.png&w=3840&q=75)
Transcribed Image Text:7. Consider a face-centered-cubic cell. Construct a primitive cell within this larger
cell, and compare the two. How many atoms are in the primitive cell, and how
does this compare with the number in the original cell?
8. a) Show that a two-dimensional lattice may not possess a 5-fold symmetry.
b) Establish the fact that the number of two-dimensional Bravais lattices is five:
Oblique, square, hexagonal, simple rectangular, and body-centered rectangular.
(The proof is given in Kittel, 1970.)
9. Demonstrate the fact that if an object has two reflection planes intersecting at 1/4,
it also possesses a 4-fold axis lying at their intersection.
10. Sketch the following planes and directions in a cubic unit cell: (122), [122], (IT2),
(172).
11. a) Determine which planes in an fcc structure have the highest density of atoms.
b) Evaluate this density in atoms/cm² for Cu.
12. Repeat Problem 11 for Fe, which has a bcc structure.
13. Show that the maximum packing ratio in the diamond structure is A/3/16. [Hint:
The structure may be viewed as two interpenetrating fcc lattices, arranged such
that each atom is surrounded by four other atoms, forming a regular tetrahedron.)
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