Construction of a body-centered cubic unit cell. What fraction of the volume of
ID: 1064988 • Letter: C
Question
Construction of a body-centered cubic unit cell. What fraction of the volume of the center sphere is inside the unit cell, if the corners of the unit cell lie at the centers of the corner spheres? What is the total number of spheres within the unit cell ? In terms of the radius r of one of the spheres, what is the total volume of the spheres inside the unit cell? In terms of the sphere radius r what is the side length a of the unit cell? What is the cell volume ? To answer this question, look at your model and note the direction in the cell along which the spheres are actually in contact. The following geometrical relationships for a cube will be useful: side length = a; face diagonal = f a Squareroot 2: body diagonal = a Squareroot 3 What is the fraction of space occupied by the spheres in a body-centered cubic unit cell ? What is the coordination number of a particle in a body-centered cubic structure ?Explanation / Answer
1. What fraction of the volume of the spheres in the centers of the cube faces is inside the unit cell, if the corners of the unit cell lie at the centers of the corner spheres?
Answer= 1
2. What is the total number of spheres within the unit cell?
Answer= (1/8) +1= 2
3. In terms of the radius, r, of one of the spheres, what is the total volume of the spheres inside the unit cell?
Answer= ( 2 ) =8 pie r^3 /3
4. In terms of the sphere radius, r, what is the side length, a, of the Unit cell? What is the cell volume?
Answer=
A=4r/ sqrt 3
B
V=(4r/ sqrt 3)^3 =64 r^3 /3 sqrt 3 =12.3 r^3
C5. What is the fraction of space occupied by the spheres in a face-centered cubic (fcc) unit cell?
= (8/3) pie r^3 / 64 r^3 /3 sqrt 3
= pie sqrt 3 / 8 =68
What is the coordination number of a particle in a body-centered cubic structure?
Answer =8
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