I think that they are using the weight of lithium metal rather than the actual battery. That's the only thing that makes sense, as the specific energy of PURE LITHIUM is barely above that 10.5 Wh/g figure. The 10.5 must come from the energy drop to sulfur intercalation, which is at .4v. The 8.5 Wh/g figure comes from the reversable voltage range. It's either that or their numbers are off by 100x.
[1] https://engineering.cmu.edu/media/press/2016/12_13_whitacre_...
It seems like the biggest advance of this one is that the design allows the use of a metallic lithium anode rather than NMC/LMO/LFP etc. They say in the introduction:
"The organic-liquid electrolyte of the lithium-ion battery has an energy-gap window Eg ≈ 3 eV, but its LUMO is below the Fermi level of an alkali-metal anode, it is flammable, and it is not wet by an alkali-metal anode..."
The actual design is lithium metal plated directly onto lithium-doped glass, placed onto sulfur ink on copper as an electrode.
My translation is "The organic-liquid electrolyte will start to spark above 3eV, which is lower than the electron energy if lithium were directly touching it as a metal. Plus, hey, the electrolyte won't wet the metallic lithium anyway so contact is poor."
The glass has a much higher band gap, wets lithium (and sodium, which they also talk about) metal, diffuses sodium and lithium pretty fast, and manufacturability is super high since now you can use all kinds of standard metal working techniques rather than powder handling and sintering -- lithium even melts at 180C, so processing temperatures might be way lower and less costly.
In any case, in this context, the weight density is probably just normalized to anode mass. That would be better to explain clearly what they meant, but it seems fair since the energy density really is higher if you have more lithium in there and that's often the energy density limiting component.
Note: Here's something from just 2014 with a better explanation of why it matters, and a much more complicated sounding solution. https://www.scientificamerican.com/article/pure-lithium-in-b...
The paper itself [1] does mention specific energy, in a form:
>The energy density of the full discharge was 10.5 Wh/g (Li metal); but for the reversible voltage range V_dis > 2.34 V, it was 8.5 Wh/g (Li metal).
That's 8500 Wh/kg, which is absolutely off the charts compared to typical lithium ion, with Wikipedia listing 265 Wh/kg.
That's so off the charts, and and not touted at all, so I wonder if I'm misreading that.
[1] https://news.ycombinator.com/item?id=13778602