Four calculations called our candidate unstable. Labs had already made it.

Lithium hafnate (Li2HfO3) was on our internal list of candidate materials. Before going any further with it, we asked a basic question: is the crystal we proposed stable at all?

One standard check is to calculate how the crystal's atoms vibrate (its phonons). At absolute zero, treating each vibration as a simple spring, a stable crystal has only real vibration frequencies. An imaginary frequency, reported as a negative number, means the atoms would rather shift into a different arrangement.

Four calculations, not one measurement

We ran that check on the monoclinic form of lithium hafnate four ways, starting from the computed structure in Materials Project entry mp-755352. A density functional theory (DFT) calculation on a repeating block of 96 atoms gave a lowest frequency of −2.48 THz. That number is the lowest point on a fine grid of vibration patterns interpolated from the block. At the grid's centre all its frequencies were real, and our saved file does not record the other patterns that fit the block exactly.

Three published machine-learned interatomic potentials, MACE, CHGNet and ORB-v3, are trained on data from calculations of that kind. Each was run on its own block of 216 atoms, and each found imaginary frequencies among the patterns that fit its block exactly: −2.23, −3.72 and −0.79 THz. So the four numbers are not the same measurement, and by the stricter rule we now use, the DFT verdict is unknown.

As a check of the setup, we ran the same DFT calculation on two known cases. Magnesium oxide (MgO) came out stable, as it should. Cubic barium titanate (BaTiO3), which is known to distort, came out unstable at −7.37 THz.

Then we read the literature

Then we searched the published literature, which we should have done first. A paper on the crystal structures of Li2ZrO3 and Li2HfO3 appeared in 1969. We found 6 papers from 1969 to 2023 that describe lab-made samples; they are listed below. A 2016 study describes monoclinic Li2HfO3, and the most recent, from 2023, uses it in coatings on nickel-rich cathodes for all-solid-state batteries. We have not read the full 1969 paper, so we do not claim its structure is the one we calculated.

So our reading of these calculations, that this crystal should not exist, was wrong. We have not tested why. Two possible reasons: none of the four calculations included the effect of temperature on the vibrations, and the DFT one used a smaller block (96 atoms) than the others (216 atoms). Lithium hafnate is off our list of new-material candidates, but for a different reason than we first gave: it has a synthesis record in the literature.

What we changed

Check the literature before trusting a calculation, however many methods agree: they can share the same blind spot. And keep every input. Our saved DFT result keeps only a summary of the vibration frequencies, not the forces behind them, so that run cannot be repeated exactly from what we stored.

References

1. Dittrich, Hoppe. Die Kristallstruktur von Li2ZrO3 und Li2HfO3. Z. anorg. allg. Chem. 371, 306–317 (1969). doi:10.1002/zaac.19693710513
2. Georgiev, Misheva, Toumbev. PAC studies of neutron irradiated Li2HfO3. Hyperfine Interactions 60, 735–738 (1990). doi:10.1007/bf02399857
3. Misheva, Toumbev. Temperature dependence of the electric field gradient in Li2HfO3 by the PAC method. Phys. Status Solidi (a) 124, K55–K58 (1991). doi:10.1002/pssa.2211240148
4. Baklanova et al. Photo- and radioluminescence of lithium hafnate Li2HfO3. Optical Materials 34, 1037–1041 (2012). doi:10.1016/j.optmat.2011.12.024
5. Buzlukov et al. Coexistence of two types of lithium motion in monoclinic Li2HfO3: 6,7Li NMR and ab initio calculation results. J. Phys. Chem. C 120, 23911–23921 (2016). doi:10.1021/acs.jpcc.6b06029
6. Zhang et al. Conformal Li2HfO3/HfO2 nanoparticle coatings on layered Ni-rich oxide cathodes for stabilizing interfaces in all-solid-state batteries. Chem. Mater. 35, 6835–6844 (2023). doi:10.1021/acs.chemmater.3c01116