Quasicrystals predicted and discovered by machine learning

Quasicrystals represent a class of ordered materials that have diffraction symmetry forbidden in periodic crystals. Since the first discovery of quasicrystals in 1984, approximately 100 thermodynamically stable quasicrystals have been synthesized. The discovery of new quasicrystals has led to the observation of novel physical phenomena, such as robust quantum criticality, fractal superconductivity, and peculiar long-range magnetic ordering. However, the pace of discovery of new quasicrystals has significantly slowed down, which is attributed to the lack of design principles for exploring new quasicrystals. Here, we demonstrate that machine learning can greatly accelerate the process of material discovery. Our model can predict stable quasicrystalline phases with high accuracy. With this model, we discovered three stable decagonal quasicrystals through an exhaustive screening of more than 1000 ternary aluminum alloy systems.

Figure 1

Machine learning for predicting QC-forming chemical compositions. (a) Schematic of the machine learning workflow. (b) Confusion matrix (top) and three performance metrics (bottom: precision, recall, and $F_1$ scores) summarize the predictive ability of the machine learning algorithm with respect to test datasets. The mean (standard deviation) of each performance metric across 100 models trained on different datasets is shown. (c) Predicted phase diagrams of three aluminum alloys, Al-Ir-Mn, Al-Ir-Fe, and Al-NiOs. The predicted QC-/AC-forming regions are denoted by navy- and light-blue areas, respectively. Straight lines for the rule of $e/a=1.8$ are overlaid. Newly synthesized DQCs are colored in green. (d) Five rules for the formation of QC/AC phases, proposed by the machine learning algorithm, are represented by the straight lines on the predicted phase diagrams.

Figure 2

(a) Basis vectors used for indexing diffraction from DQCs. Selected area electron diffraction patterns taken along (b) $10\mathrm{f}$, (c) $2{\mathrm{f}}^{\prime }$, and (d) $2\mathrm{f}$ axes of a DQC found in an ${\mathrm{Al}}_{70}{\mathrm{Ni}}_{20}{\mathrm{Os}}_{10}$ sample. (e) Powder XRD pattern taken from an ${\mathrm{Al}}_{70}{\mathrm{Ni}}_{20}{\mathrm{Os}}_{10}$ sample with indices (and direction if the diffraction vector is along $10\mathrm{f}, 2{\mathrm{f}}^{\prime }$, or $2\mathrm{f}$) for the DQC phase. Filled triangles indicate the diffraction from phases other than the DQC phase.

Figure 3

Selected area electron diffraction patterns taken from (a) $10\mathrm{f}$, (b) $2{\mathrm{f}}^{\prime }$, and (c) $2\mathrm{f}$ axes of a DQC found in an ${\mathrm{Al}}_{80}{\mathrm{Ir}}_{14}{\mathrm{Mn}}_6$ sample and those taken from (d) $10\mathrm{f}$, (e) $2{\mathrm{f}}^{\prime }$, and (f) $2\mathrm{f}$ axes of a DQC found in an ${\mathrm{Al}}_{79}{\mathrm{Ir}}_{16}{\mathrm{Fe}}_5$ sample. (g) Powder XRD patterns taken from ${\mathrm{Al}}_{80}{\mathrm{Ir}}_{14}{\mathrm{Mn}}_6$ and ${\mathrm{Al}}_{79}{\mathrm{Ir}}_{16}{\mathrm{Fe}}_5$ samples with indices (and direction if the diffraction vector is along $10\mathrm{f}, 2{\mathrm{f}}^{\prime }$, or $2\mathrm{f}$) for the DQC phases. Filled triangles indicate the diffraction from phases other than the DQC phases.