[Dan22]

Hey guys, could you please help me out with something?

When calculating an element's crystal density (for the unit cell) using the equation: ρ=nA/VN_Α

where n: number of atoms in the unit cell,
A=atomic mass
V=volume of the unit cell
N_A: Avogadro's number

why is it that don't get the element's precise (as listed in literature) density?

For example in V, the result we get is 5,96 gr/cm³, whereas the real density is 6.
Why is it that this specific process of calculation gives a slightly different number?

[mjc123]

Is 5.96 different from 6? From 6.0? From 6.00? How precise is your value of "real density"?
A quick look at the internet found values of 5.8, 6.0 and 6.1 for the density of V. All quoted to 2 sig figs, but differing by more than 0.1.
No actual material is actually a perfect single crystal. All samples have defects, grain boundaries, voids, inclusions etc. which make the actual density at least a little different from the theoretical, and maybe different between samples (also affected by e.g. impurities, variability of isotopic composition etc.). And of course it varies with temperature. Practically, I don't think it's that easy to measure density to high accuracy; maybe no more than 2 sig figs are justified. Crystallography can determine the crystallographic density to higher accuracy, but as said, that never exactly corresponds to a real sample.

[Dan22]

Thank you very much for your answer.

I was thinking about possible defects as well (vacancy, inclusion), I guess that is most likely to influence the slight difference in the numbers.

[Enthalpy]

Stacking faults influence a lot the density of graphite, which has no definite value, but for metals and alloys they usually have very little influence. Once an alloy has been compacted (after casting, being by lamination, extrusion, hot isostatic pressing...) - and it usually is to attain the normal strength - further operations that keep the crystal structure don't change the density much, be they annealing, cold deformation... A few kg/m³, not 100. Just by milling or turning a simple shape and weighing the part, we get naturally 4 places accuracy on an alloy's density - one of the best ways to identify an alloy in a workshop.

Refractory metals are produced by sintering rather than melting, and then the density is irregular, but this shouldn't be the case of vanadium.

Natural vanadium consists of just 0.25% of ⁵⁰V, the rest ⁵¹V - that won't justify much.

Let's take (for no reason) a linear thermal expansion of 20ppm/K: from 6100 to 6000 kg/m³, it needs 280K, ouch.

6110 kg/m³ here https://www.webelements.com/vanadium/
5.96 g/cm3 there  https://books.google.de/books?isbn=1111792976 (must be the source of the cell parameters...)
6110 kg/m³ again there http://xpssimplified.com/elements/vanadium.php
other sources just tell 6.0 or 5.8
apparently always BCC.

I'd say: just inaccurate data.