Dependence of Dopant Geometry on Na Concentration in $Na_{x}CoO_{2}$

In this work, we investigated the behaviour of Sb dopants in $Na_{x}CoO_{2}$ for Na concentrations of $x = 0.75, 0.875$ and $1.00$ by density functional theory. We chose $Na_{x}CoO_{2}$ with higher Na concentration of $x > 0.75$ because it has excessively higher thermo-power thus it is appealing for practical applications. The rationale for choosing Sb was its exceedingly higher atomic mass than all elements of the host crystal which enable Sb to rattle phonons considerably.