Other than the high temperatures, the problem with liquid-liquid batteries is
probably the electrolyte layer has to be somewhat thicker than other technologies, so that slows ion movement. For large storage-to-discharge (e.g., solar or utility) that might not be an issue. Not for cars ;-)
Update: The Standford video says the rest current is 600 amps per cm², so possibly not an issue.
Sounds like it's exothermic on discharge, so the charging also has to add energy to heat the cells which will reduce round trip efficiency.
Insulation could help reduce that, as the net thermal loss should be minimal, but then the batteries would have a large operating temperature range which will undoubtedly affect efficiency (the claim is 75 to 80%).
How hot is hot? Here are melting / boiling points for the elements:
Antimony: 1,167°F / 2,888°F
Calcium: 1,548°F / 2,703°F (Annode)
Calcium chloride: 1,422°F / 3,515°F (Electrolyte)
Magnesium: 1,202°F / 1,996°F
So the operating range sounds like it would be around 1600 to 1500°F.
Except they did some alloys... so the actual temperature is around 900°F. That's a lot of lead mixed in.
They should be inexpensive to manufacture since the layers are self-separating, just drop the solid metals in as bricks, seal it up, and ship. Not seeing the claims of any large economy of scale as the manufacturing should be simple. What it's packaged in needs to be non-reactive to the metals. Glass melts at 2800°F, so possibly glass-lined carbon steel (2600°F melting point) shells? It's not a crazy hot temperature for a utility. For example, a coal furnace runs around 3900°F.
Funded by the Gates Foundation. 80 Ah in a 4" cube, a 53' semi-trailer is 2 MWh. 300 mA/cm² and nearly zero degradation (0.00009% fade/cycle) after 1000s of cycles at 93% DoD. So that's really impressive (99% capacity after 3650 cycles).
They're thinking at scale they'll be below $500 kWh, so still more than pumped hydro, although it's unclear from the video if that's a levelized lifetime cost. But, they're working on "Zebra Unchained" and thinking it'll be $25 kWh and a 4" cell would be 240 Ah, so a semi-trailer size would be 6 MWh. $25/kWh for energy storages changes everything, it would be nice if they can pull it off.
Also see discussions/videos:
Bill Gates put a bunch of money into this company. https://ambri.com/technology/
diysolarforum.com
MIT Video
Luddite Video