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Lets' say I have a solid system made with N atoms in a box with a volume of V as shown below. In this case, the number density of my system is simply $\frac{N}{Volume\; of \; occupied\;3D\; space}$.

Solid Sphere

but what if I have a system with $N$ atoms in the same box, but $N_{1}$ atoms are in the solid phase and $N_{2}$ atoms are in the gas phase $\left( N_{1} + N_{2} = N \right)$.

enter image description here

How should I calculate the number density in this case? Do I consider the whole box volume $V$?

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    $\begingroup$ This seems to be a question of what definition you choose for number density. $\endgroup$ Commented Oct 10, 2022 at 14:29
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    $\begingroup$ You come up with a criteria to distinguish solid from vapor, which is a pretty standard thing in MD. Matter Modeling SE might be a better place to ask since they have experience over there. $\endgroup$
    – Jon Custer
    Commented Oct 10, 2022 at 15:08

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Yes, you take the whole volume. That is the definition of density $\rho = N/V$. I guess what you are thinking of is in fact local density $\rho(r) = \delta N(r) / \delta V$ where $\delta N(r)$ is the number of particles in the immediate vicinity $(x\pm 0.5dx, y\pm 0.5dy, z\pm 0.5dz)$ of the point $\vec{r} = (x,y,z)$, $\delta V = dx\, dy\, dz$.

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