# What does x mean in (1-x)A – xB composite materials, molar ratio, weight ratio or volume fraction?

I've been collecting data about ceramic materials and often I get to see composite materials are described as $$(1-x)\ce{A} - x\ce{B}$$. I am confused what this $$x$$ means. And I haven't seen any of the papers mention what $$x$$ is unless %wt is given specifically.

For an example in $$(1-x)\ce{MgO} - x\ce{LiF}$$ ceramic material, does $$x$$ mean molar ratio or weight ratio? For me it doesn't make sense to think of $$x$$ as a volume fraction as most of the times powders of these materials are taken for sintering.

1. If nothing is mentioned, is it all right to assume $$x$$ as the molar ratio?

2. Can we assume volume fraction is equal to molar ratio even in solids or liquids?

## 1 Answer

Here, $$x$$ is a variable $$(x\in[0;1])$$ denoting mole fraction of a given constituent in a phase of variable composition (non-stoichiometric compound). This is an algebraic way of denoting a given compound from the phase diagram for a solid solution: $$x$$ corresponds to its abscissa axis.

And no, volume fraction is not equal to mole fraction and is overall a very inconvenient variable to use, so it's usually being avoided. For example, volume fraction would deviate for the different morphologies and allotropes of the same solid, which is not useful for the description of chemical composition, not to mention it's also temperature-dependent.

• Since the OP refers to sintering I don't think that mole fraction can be assumed. In fact the OP mentions that some articles explicitly specify wt %. – MaxW Feb 12 '19 at 17:19
• @MaxW Mole fraction is pretty much a default in the absence of additional remarks. Of course, if there is %wt notation, then it's mass fraction. – andselisk Feb 12 '19 at 17:24
• @MaxW I believe almost all the ceramic compounds are made by sintering. Do you believe 0.8MgO - 0.2LiF could mean weight fractions? Most of the related papers don't mention what x is, although when they do mention about 'weights', they make sure to present it as a percentage, like MgO - 20% LiF. But I'm sure there should be some convention among scientists to understand what x really is unless explicitly specified? – Achintha Ihalage Feb 12 '19 at 18:10
• @avin Again, unless there are any specific notes, $(1-x)\ce{MgO} - x\ce{LiF} ≡ \ce{Li_xMg_{(1-x)}O_{(1-x)}F_x}$, so by default $x$ implicates mole fraction. – andselisk Feb 12 '19 at 18:15