NMC (nickel-manganese-cobalt) cathodes are the dominant lithium-ion battery chemistry. The composition space is enormous: what ratio of Ni:Mn:Co gives the best tradeoff between capacity and structural stability?
K measures coupling strength between atoms in the crystal lattice. Higher K = more rigid structure = better cycle stability. But higher nickel = more capacity. The Pareto frontier reveals the optimal tradeoff.
| Composition | Capacity | Stability (K) | Cobalt |
|---|---|---|---|
| NMC 811 | 200 mAh/g | 0.472 | no |
| NMC 622 | 175 mAh/g | 0.592 | yes |
| NMC 532 | 155 mAh/g | 0.624 | yes |
| NMC 111 | 150 mAh/g | 0.683 | no |
MM10P correction: the original claim that Pareto-optimal compositions have zero cobalt was wrong. Full Pareto analysis shows 17 of 28 optimal compositions include cobalt. Under alternative stability weights (cobalt more stabilizing), 19/21 Pareto points include cobalt. The zero-cobalt result was an artifact of our Mn > Co > Ni stability weighting. Industry confirms: cobalt is being reduced but not eliminated (Samsung SDI NMC 622, Panasonic NCA both use cobalt). Our model is a fast filter, not a predictor. The stability weights are assumed, not measured.
ABX3 perovskites are the next generation of solar cells. The question: which combination of A-site cation, B-site metal, and X-site halide gives optimal bandgap for solar absorption?
Optimal bandgap is 1.34 eV (Shockley-Queisser limit). K measures the stability of the crystal structure — tolerance factor determines whether the perovskite forms at all.
| Composition | Bandgap (eV) | Tolerance | Stability (K) |
|---|---|---|---|
| FAPbI3 | 1.48 | 1.01 | 0.89 |
| MAPbI3 | 1.55 | 0.91 | 0.85 |
| CsPbI3 | 1.73 | 0.85 | 0.72 |
| FASnI3 | 1.41* | 1.05 | 0.00 |
FAPbI3 wins for single-junction cells — this matches industry consensus. But the result needs caveats:
MM10P correction: *Our bandgap formula gave FASnI3 = 1.85 eV. Literature value is 1.41 eV — actually CLOSER to the 1.34 eV optimum than FAPbI3. FASnI3 scores 0 because Sn2+ oxidizes in air (correct), but the bandgap we used was wrong. FAPbI3 wins for the right conclusion but partially the wrong reason: stability filtering saves us, not bandgap accuracy. Also missing: mixed compositions (FA0.95Cs0.05PbI3) hold actual efficiency records but weren't in our search space. Our screening only tested pure compositions.
Both screening engines use the same core: K (coupling strength) as a structural stability proxy. For cathodes, K comes from the crystal lattice coordination number and bond strength. For perovskites, K comes from the Goldschmidt tolerance factor and octahedral factor. No machine learning. No training data. Just the physics of how atoms couple.
All screening computed on Mac Mini M4, 35W. Code: pip install begump