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Consider a composition such as $\ce{FeCo4Sb12}$.

The atomic weight for a mole of substance is usually simply calculated by looking up the atomic weights (g/mole) for each involved element and adding them together proportionally: $$M_{\ce{FeCo4Sb12}}=1\cdot M_{\ce{Fe}}+4\cdot M_{\ce{Co}}+12\cdot M_{\ce{Sb}}$$

But this compound is not a molecule. It is a representation of the amounts: there are 12 Sb and 4 Co for every Fe atom. I could also have written it as $\ce{Fe2Co8Sb24}$.

Same compound, but the calculation will give a different $M$.

The same issue comes for non-stoichiometric compounds, such as: $\ce{FeNb_{0.88}Hf_{0.12}}$. This just says that there are 88 Nb and 12 Hf for each Fe.

How should I understand the chemical formula when calculation atomic weights of crystalline or other non-molecular compounds as well as non-stoichiometric compounds?

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    $\begingroup$ Atomic weight is a property of atom, not compound. Surely you meant "molecular weight", but that's only good for compounds which have molecules. Go with "formula weight" and don't bother. $\endgroup$ – Ivan Neretin Sep 16 '17 at 13:10