Fractional Subscripts?

What is the physical meaning when we have an empirical formula with fractional subscripts such as $\ce{LiMn\_{1-x}Fe\_{x}PO4}$ $(0 \le x \le 1)$? 


This an example of the paper the notation above is used:


Bai, J.; Hong, J.; Chen, H.; Graetz, J.; Wang, F. *J. Phys. Chem. C* **2015**, 119 (5), 2266–2276. DOI [10.1021/jp508600u](http://dx.doi.org/10.1021/jp508600u).




These indicate "[doping](http://en.wikipedia.org/wiki/Doping_(semiconductor))" or [non-stoichiometric compounds](http://en.wikipedia.org/wiki/Non-stoichiometric_compound).


In this case, there's some fraction of Fe, and some fraction of Mn in a [lithium iron phosphate battery](http://en.wikipedia.org/wiki/Lithium_iron_phosphate_battery). If I remember correctly, you need to dope a different ion to increase the conductivity of $\ce{LiFePO4}$.


See also here: [How are non-Stoichiometric compounds determined?](https://chemistry.stackexchange.com/questions/6913/how-are-non-stoichiometric-compounds-determined)


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