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What is the meaning of a decimal in a subscript in a chemical formulas?

I came across the fractional subscripts in a publication,[1] for example:

We introduce oxygen into a ferromagnetic metallic glass to form a $\ce{Co_{28.6}Fe_{12.4}Ta_{4.3}B_{8.7}O46}$ magnetic semiconductor with a Curie temperature above $\pu{600 K}$. "

How do I interpret these numbers?

References:

  1. Liu, W.; Zhang, H.; Shi, J.; Wang, Z.; Song, C.; Wang, X.; Lu, S.; Zhou, X.; Gu, L.; Louzguine-luzgin, D. V.; Chen, M.; Yao, K.; Chen, N. A room-temperature magnetic semiconductor from a ferromagnetic metallic glass. Nat. Commun. 2016, 7, 13497 DOI: 10.1038/ncomms13497.
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  • $\begingroup$ also, from the paper "In this way, a single metal oxide Co28.6Fe12.4Ta4.3B8.7O46 (in atomic percentage) is produced " $\endgroup$ – permeakra Dec 10 '16 at 20:58
  • $\begingroup$ Permeakra - you are assuming the atons are covalently bonded to eachother. It is possible to have atoms randomly dispersed within a material. A perfect example are clays which usually have non-stoichiometric subscripts in their chemical formulas. It's not 0.5 atoms, it would be 0.5% molarity for that atom within a sample. $\endgroup$ – Efram Goldberg Dec 10 '16 at 21:13
  • $\begingroup$ @EframGoldberg and for that matter, the atoms in the clays are by no means inserted randomly. They are located in some specific positions, even if not all of them are occupied. $\endgroup$ – permeakra Dec 10 '16 at 21:48
  • $\begingroup$ @Permeakra obviously placement can't violate physical laws, but if a unit cell requires a cation, then cationic species can be inserted randomly into that position. I quote from USGS "Other Group IA or Group IIA cations may also be randomly distributed over water-molecule sites" or "In K(UO,AsO,) .3H,O, one potassium ion and three H,O molecules are distributed randomly over four water-molecule sites" In fact when modeling clay structures, random distributions are often used. $\endgroup$ – Efram Goldberg Dec 13 '16 at 18:21
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In the case of complex glasses such as $\ce{Co_{28.6}Fe_{12.4}Ta_{4.3}B_{8.7}O46}$, Instead of normalizing the subscripts to have integer subscripts they normalized them by molar percent such that the sum of subscripts is $100\%$
($28.6+12.4+4.3+8.7+46=100$)

This is fairly common practice in materials science. For many complicated materials such as this, it's hard to gain useful meaning from the chemical formula if the subscripts are normalized to integers so they are normalized to 100. People reading this formula now can compare it to similar materials they have seen and future materials are also more comparable (e.g. if they substituted the tantalum with niobium).

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Many materials, like clays or alloys are not stoichiometric meaning you would not expect whole integers in the subscripts. If for example they weighed out 1 g of material and performed elemental analysis for each element, then the subscripts you see would be the %ratio of that element.

In these materials, the atoms are not necessarily covalently bonded to eachother and this allows for the non whole number integers.

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