1. Tardigrade
  2. Question
  3. Chemistry
  4. In an CCP crystal of metal M (diameter = a oversetoA ), we are trying to dope two smaller elements X ( radius =0.16a oversetoA ) and/or Y (radius =0.25a oversetoA ) without disturbing M-M contact, then select correct matching.

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Q. In an $CCP$ crystal of metal $M$ (diameter = $a\overset{o}{A}$ ), we are trying to dope two smaller elements $X$ ( radius $=0.16a\overset{o}{A}$ ) and/or $Y$ (radius $=0.25a\overset{o}{A}$ ) without disturbing $M-M$ contact, then select correct matching.

NTA AbhyasNTA Abhyas 2022

Solution:

$\frac{r_{X}}{r_{M}}=\frac{0 . 16 a}{0 . 5 a}=0.32,$ so $X$ can occupy only $O-$ Voids (ideal $rr$ is $0.414$ ) but not $T-$ void
(ideal $rr$ is $0.225$ )
and $\frac{r_{X}}{r_{M}}=\frac{0 . 25 a}{0 . 5 a}=0.5,$ $Y$ can't occupy either $O-$ voids or $T-$ voids.
On doping $X$ atoms in $O-$ voids, Packing fraction as well as density of crystal will increase as dimensions do not change (no distubing of $M-M$ contact allowed) but total mass increases in the unit cell (we cant comment about $X$ being heavier than $M$ atoms).