Question
Download Solution PDFAtomic packing factor for FCC structure is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
The atomic packing factor is defined as the ratio of the volume occupied by the average number of atoms in a unit cell to the volume of the unit cell.
Mathematically, Atomic Packing Factor (APF):
APF \( = \frac{{{N_{atoms}} ~\times ~{V_{atoms}}}}{{{V_{unit\;cell}}}}\)
Characteristics of various types of structures are shown in the table below:
|
Characteristics |
BCC |
FCC |
HCP |
|
a to r relation |
\(a = \frac{{4r}}{{√ 3 }}\) |
\(a = 2√ 2 r\) |
\(a = 2r\) |
|
The average number of atoms |
2 |
4 |
6 |
|
Co-ordination number |
8 |
12 |
12 |
|
APF |
0.68 |
0.74 |
0.74 |
|
Examples |
Na, K, V, Mo, Ta, W |
Ca, Ni, Cu, Ag, Pt, Au, Pb, Al |
Be, Mg, Zn, Cd, Te |
Calculation:
No of atoms in f.c.c unit cell = 4
\(APF = \frac{{{N_{atoms}}{V_{atom}}}}{{{V_{crystal}}}} = \frac{{4\left( {\frac{4}{3}} \right)\pi {r^3}}}{{{{\left( {a } \right)}^3}}}= \frac{{4\left( {\frac{4}{3}} \right)\pi {r^3}}}{{{{\left( {{{2√2r}}{}} \right)}^3}}}\)
for FCC a = 2√2 r where a is side of the cube and r is atomic radius.
APF = 0.74
Last updated on Jul 15, 2025
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