1. Suppose identical solid spheres are distributed through space in such a way that their centers are lie on the points of a lattice, and spheres on neighboring points just touch without overlapping. (Such an arrangement of spheres is called a close-packing arrangement.) Assuming that the spheres have unit density, show that the density of a set of close-packed spheres on each of the four structures (the "packing fraction") is: fcc: bcc: √√2/6=0.74 √3/8=0.68 SC: π/6=0.52 √√3/16=0.34 diamond:
1. Suppose identical solid spheres are distributed through space in such a way that their centers are lie on the points of a lattice, and spheres on neighboring points just touch without overlapping. (Such an arrangement of spheres is called a close-packing arrangement.) Assuming that the spheres have unit density, show that the density of a set of close-packed spheres on each of the four structures (the "packing fraction") is: fcc: bcc: √√2/6=0.74 √3/8=0.68 SC: π/6=0.52 √√3/16=0.34 diamond:
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![1. Suppose identical solid spheres are distributed through space in such a way that their
centers are lie on the points of a lattice, and spheres on neighboring points just touch
without overlapping. (Such an arrangement of spheres is called a close-packing
arrangement.) Assuming that the spheres have unit density, show that the density of a
set of close-packed spheres on each of the four structures (the "packing fraction") is:
fcc:
bcc:
√√2/6=0.74
√√3/8=0.68
SC:
π/6=0.52
√√3/16=0.34
diamond:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d2fdd51-a813-4b36-89e9-f9581acfc2ee%2Ffbdfc694-2005-49ca-802e-0b9ded688ec8%2Fqu0iok_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Suppose identical solid spheres are distributed through space in such a way that their
centers are lie on the points of a lattice, and spheres on neighboring points just touch
without overlapping. (Such an arrangement of spheres is called a close-packing
arrangement.) Assuming that the spheres have unit density, show that the density of a
set of close-packed spheres on each of the four structures (the "packing fraction") is:
fcc:
bcc:
√√2/6=0.74
√√3/8=0.68
SC:
π/6=0.52
√√3/16=0.34
diamond:
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