Reply to Martinez-Canales et al.: The structure(s) of lithium at low temperatures

In our recent article (1), we proposed that Fermiology measurements can be used as a complementary probe for determining the low-temperature state of Li. In a letter (2) criticizing our conclusions, Martinez-Canales, Loa, and Ackland (MLA) claim (i) that “obtaining dHvA signals from martensitic microstructures is usually impossible” and (ii) that the experimental data of Hunt et al. (3), in particular, cannot be used to infer useful information about the martensitic phase.

The first assertion is not correct. A clear de Haas–van Alphen (dHvA) signal from a martensitic phase has been experimentally observed and reported by Goddard et al. (4). Furthermore, a careful reading of the earlier references cited by MLA (5, 6) reveals that the disappearance of the dHvA signal is not always associated with a martensitic transition but can be caused by other experimental factors. Finally, we quote Jan et al. (7): “Ability to observe de Haas-van Alphen signals is certainly no criterion that a low temperature transformation had not occurred, since partially (or totally?) transformed $\beta \prime$-AuZn samples give a wealth of de Haas-van Alphen data! (Springford, Jan, Pearson & Templeton 1963).”

Criticism (ii) would be valid if Hunt et al. (3) had suppressed the martensitic transition in the entire sample. However, they did not claim to have achieved it, nor did they need to. Their motivation was to study the distortion of the Fermi surface of bcc Li, which was achieved by suppressing martensitic transition in the majority (but not all) of the grains. The signal that they studied at around 42 kT is indeed characteristic for bcc (and very close to that of fcc). They were not concerned with a dHvA signal characteristic for the martensitic phase.

Hunt et al. (3) discuss the size distribution of the dispersion in several places: “These grains were between 1 and 100 $\mathrm{\mu }$m in diameter, with the majority smaller than 10 $\mathrm{\mu }$m.” Further, “It was found that, if the tail of the size distribution was extended to allow a substantial number of grains in the diameter range 100 to 200 $\mathrm{\mu }$m, then the fluctuations were of the order of 30 to 40%. Although no grains larger than 100 $\mathrm{\mu }$m were noticed in the paste under the microscope, it is entirely possible that the sample itself may have held such grains.” Not only ref. 1, but also a recent publication coauthored by MLA (8) with experimental data at nearly ambient pressure, confirm that natural Li samples of $\sim$100-$\mathrm{\mu }$m size undergo a martensitic transition.

MLA cite ref. 9, stating that “the structure was verified by X-ray diffraction.” However, the X-ray experiments in ref. 9 were conducted 13 y before the dHvA study in ref. 3. The conditions were different—5 K in ref. 9 versus 20 mK in ref. 3, and only two of the less-prominent diffraction peaks were measured in ref. 9.

While a comparison with the existing dHvA data from ref. 3 is certainly not conclusive—as stated in ref. 1—based on the presented analysis and the known experimental conditions in ref. 3 it strongly suggests that 9R should be ruled out.