I have just read an article in which they used $\ce{WO3}$ and $\ce{WO_{2.9}}$ as precursors, whose objective was to form $\ce{WS2}$, in an atmosphere of argon by CVD. In one boat there is the powder of $\ce{S}$ and in another boat there is $\ce{WO3}$ or $\ce{WO_{2.9}}$, in an oven with a double temperature zone. In the article they conclude that $\ce{WO_{2.9}}$ forms larger layers of $\ce{WS2}$ in the substrate giving the following justification:

They found that $\ce{W^6+}$ cannot be directly sulfated by $\ce{S},$ unless some intermediates are formed due to the high energy of the $\ce{W-O}$ bond. The reduction from $\ce{W^6+}$ to $\ce{W^5+}$ is mandatory for the incorporation of sulfur in the $\ce{WO3}$ network. For $\ce{WO_{2.9}}$ in our case, its partial $\ce{W^6+}$ ions have been reduced to $\ce{W^5+}$ or $\ce{W^4+}$ ions. Therefore, we find that replacing $\ce{W^5+}$ or $\ce{W^4+}$ with $\ce{W^6+}$ in the initial stage facilitates the growth of the single crystal $\ce{WS2}$ film.

I didn't realize what the difference is between $\ce{WO3}$ and $\ce{WO_{2.9}}$ and where these ions come from that they talk about in this part of the article. I also don't understand what a fractional index means in a chemical formula. Could you help me to interpret that part of the article and explain these doubts that I have please?


There is nothing special about fractional indices in chemistry, it is just a pointer signifying we are dealing with a non-stoichiometric compound. Group 6 metal are known not only for their regular oxides existing in numerous polymorphic modifications, but also for forming homologous series of nonstoichiometric oxides $\ce{\ce{M^{VI}_nO_{3n-1}}}$ and $\ce{\ce{M^{VI}_nO_{3n-2}}}$ with the general formula $\ce{M^{VI}O_{3-x}}$ $(\ce{M} = \ce{Mo}, \ce{W};$ $x \in (0; 1)).$

Now, to make things clear, notation "$\ce{WO_{2.9}}$" does not refer to a molecule; $\ce{WO_{2.9}}$ is a formula unit showing composition of a network solid. To further illustrate the origin of the fractional coefficients here, let's refer to the crystal structures of the stoichiometric and non-stoichiometric tungsten(VI) oxides $(\ce{WO3}$ and $\ce{WO_{2.9}},$ respectively).

Depending on the temperature, $\ce{WO3}$ adopts several polymorphs with various crystal structures; at the room temperature the most common structure it adopts is the one of distorted $\ce{ReO3}$ type, being made of tilted $\ce{[WO6]}$ octahedra cross-linked via the corners (for the illustration, see e.g. Wikipedia).

On the other hand, $\ce{WO_{2.9}}$ is an oxygen-deficient compound in comparison. To account for that and eliminate the presence of point defects, crystal structure undergoes a transformation resulting in increased number of edge-sharing groups of $[\ce{WO6}]$ polyhedra and reduced number of the corner-sharing ones, e.g. the structure gets more "packed", and, more importantly, a crystallographic shear is introduced (which is not an impurity). Let's have a look at the asymmetric unit of $\ce{WO_{2.9}}$ of the crystal structure determined by Magnéli [1]:

Asymmetric unit
Figure 1. Crystal structure of $\ce{WO_{2.9}}$ [1, ICSD-24736] showing an asymmetric unit $\ce{W10O29}.$ Color code: $\color{#FF0D0D}{\Large\bullet}~\ce{O}$; $\color{#2194D6}{\Large\bullet}~\ce{W}$.

Due to the asymmetric unit $\ce{W10O29},$ the chemical formula (formula unit) is reduced to $\ce{WO_{2.9}}.$ One can also fill the entire unit cell knowing the number of formula units $(Z)$ per unit cell; here, $Z = 2$ and this results in equal formula $\ce{W20O58},$ often seen in the literature:

Unit cell
Figure 2. Crystal structure of $\ce{WO_{2.9}}$ [1, ICSD-24736] showing packed unit cell. Color code: $\color{#FF0D0D}{\Large\bullet}~\ce{O}$; $\color{#2194D6}{\Large\bullet}~\ce{W}$.

Finally, to illustrate the location of the aforementioned shear plane, let's complete coordination shells on all tungsten atoms and view the structure along the $b$ axis:

Shear plane
Figure 3. Crystal structure of $\ce{WO_{2.9}}$ [1, ICSD-24736] showing polyhedral representation ($[\ce{WO6}]$ octahedra) with the shear plane along $a$ axis denoted with red arrow. Color code: $\color{#FF0D0D}{\Large\bullet}~\ce{O}$; $\color{#2194D6}{\Large\bullet}~\ce{W}$.

As for the assignment of the formal oxidation numbers for the non-stoichiometric compounds like this, this is typically considered a non-trivial task of a questionable value. Also, see the answer of mine to the related question Oxidation state of tungsten in $\ce{W3O8}$.


  1. Magnéli, A. Structure of β-Tungsten Oxide. Nature 1950, 165 (4192), 356–357. DOI: 10.1038/165356b0.
  • $\begingroup$ There are also references to a $\ce{W_{18}O_{49}}$ such as this one. Would this be a combination of $\ce{W_nO_{3n-1}}$ and $\ce{W_nO_{3n-2}}$ with $n=6$? $\endgroup$ – Oscar Lanzi Feb 15 '20 at 10:47
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    $\begingroup$ @OscarLanzi Judging from the structure (ICSD 202488 by Lamire et al. 1987), $\ce{W18O49}$ is a different story: there is a tungsten with C.N. 7 (pentagonal bipyramid, like in many uranium(VI) componds) forming pentagonal assemblies with other $[\ce{WO6}]$ octahedra, which is even more efficient packing (than shear plane) that can afford to account for further O-deficiency. $\endgroup$ – andselisk Feb 15 '20 at 11:04
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    $\begingroup$ Thanks. One minor point: "Further O deficiency" seems to be a judgment call. $\ce{W_{18}O_{49}}$ is less deficient than $\ce{W3O8}$; the latter, on an equal tungsten basis, would be $\ce{W_{18}O_{48}}$. $\endgroup$ – Oscar Lanzi Feb 15 '20 at 11:17
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    $\begingroup$ @OscarLanzi True, let's just agree on oxygen deficiency. $\endgroup$ – andselisk Feb 15 '20 at 11:20

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