Question

Given an alloy of $Cu$ , $Ag$ , and $Au$ in which $Cu$ atoms constitute the CCP arrangement. If the hypothetical formula of the alloy is $C{u}_{4}A{g}_{3}Au$ . What are the probable locations of $Ag$ and $Au$ atoms?
A) $Ag$ - all tetrahedral voids; $Au$ - all octahedral voids
B) $Ag$ - ${\displaystyle \frac{3}{8}}$ the tetrahedral voids; $Au$ - ${\displaystyle \frac{1}{4}}$ the octahedral voids
C) $Ag$ - ${\displaystyle \frac{1}{2}}$ octahedral voids; $Au$ - ${\displaystyle \frac{1}{2}}$ tetrahedral voids
D) $Ag$ - all octahedral voids ; $Au$ - all tetrahedral voids

Answer 1

Hint: Three layers (ABCABC...) of hexagonally organised atoms make up a CCP structure. Since they contact six atoms in their layer, plus three atoms in the layer above and three atoms in the layer below, atoms in a CCP configuration have a coordination number of $12$ .

Complete answer:
We know that Copper atoms ( $Cu$ ) form a CCP (Cubic Close Packed) structure, which is equivalent to an FCC (Face Centered Cubic) arrangement, according to the question.
Amount of copper atoms in a unit cell
 $$\begin{gathered} \Rightarrow {\displaystyle \frac{1}{8}}\left(Number.of.corners\right)+{\displaystyle \frac{1}{2}}\times 6 \\ \Rightarrow {\displaystyle \frac{1}{8}}\left(8\right)+{\displaystyle \frac{1}{2}}\times 6 \\ \Rightarrow 1+3 \\ \Rightarrow 4copper.atoms \end{gathered}$$
The number of octahedral voids (spaces) equals the number of atoms in the FCC arrangement, which is $4$ .
The Ag atoms appear to be at the centres of the cube's sides since the structure is oriented.
Since Ag has three atoms and a cube has eight corners, the fraction would be $Ag$ has ${\displaystyle \frac{3}{8}}$ tetrahedral voids and $Au$ has ${\displaystyle \frac{1}{4}}$ octahedral voids.
Hence, the correct option is B) $Ag$ - ${\displaystyle \frac{3}{8}}$ the tetrahedral voids; $Au$ - ${\displaystyle \frac{1}{4}}$ the octahedral voids.

Note:
Cubic Close Packed (CCP) or Face Centered Cubic (fcc) The same lattice is known by two different names. This cell is created by injecting another atom into each face of a simple cubic lattice, thus the term "face centred cubic."