
Interpretation:
The density and the packing factor of the given alloy is to be determined.
Concept introduction:
The relationship between the theoretical density
Here,
Volume of a unit cell
The formula to calculate the packing factor of an alloy is:
Here,
The formula to be used to calculate the volume of a single atom is:
Here,

Answer to Problem 4.14P
The density of the given alloy is
The packing factor of the alloy is
Explanation of Solution
Given information:
Use equation (2) to calculate the volume of a unit cell from its lattice parameter as:
The number of iron atoms present in a unit cell having BCC structure is
Atomic weights of iron and carbon are
Use equation (1) to calculate the density of the alloy as:
Atomic radius of iron and carbon atoms are
Use equation (4) to calculate the volume of a single atom as:
Now, use equation (3) to calculate its packing factor as:
The density of the given alloy is calculated as
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Chapter 4 Solutions
Essentials of Materials Science and Engineering, SI Edition
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