Thermal evolution of the metastable r8 and bc8 polymorphs of silicon

Abstract

The kinetics of two metastable polymorphs of silicon under thermal annealing was investigated. These phases with body-centered cubic bc8 and rhombohedral r8 structures can be formed upon pressure release from metallic silicon. In this study, these metastable polymorphs were formed by two different methods, via point loading and in a diamond anvil cell (DAC). Upon thermal annealing different transition pathways were detected. In the point loading case, the previously reported Si-XIII formed and was confirmed as a new phase with an as-yet-unidentified structure. In the DAC case, bc8-Si transformed to the hexagonal-diamond structure at elevated pressure, consistent with previous studies at ambient pressure. In contrast, r8-Si transformed directly to diamond-cubic Si at a temperature of ${255}^{\circ }\mathrm{C}$. These data were used to construct diagrams of the metastability regimes of the polymorphs formed in a DAC and may prove useful for potential technological applications of these metastable polymorphs.

Keywords:

• pressure-induced transitions
• metastable polymorphs
• silicon
• in situ annealing

Acknowledgments

We would like to acknowledge and thank Reinhard Boehler and Amol Karandikar (both Geophysical Laboratory, Carnegie Institution, USA) for their assistance in conceiving and conducting the laser-heating experiment. Additionally, we would also like to thank Brad D. Malone (Harvard University, USA) and Marvin L. Cohen (University of California, Berkeley, USA) for many helpful and stimulating discussions. The XRD was performed at HPCAT (Sector 16), and the gas loading at GSECARS (Sector 13), both Advanced Photon Source (APS), Argonne National Laboratory. We also acknowledge the facilities and the technical assistance of the Australian Microscopy & Microanalysis Research Facility at the Electron Microscopy Unit, University of New South Wales, Australia, and the Center for Advanced Microscopy, Australian National University, Australia.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. Note that traditionally these different Si polymorphs are often denoted by Roman numbers (Si-I, Si-II, Si-III, etc.). In this work, we used the alternative denomination of a phase by its structural description (dc-Si, (β-Sn)-Si, bc8-Si, etc.) instead for two reasons. Firstly, none of the predicted phases are included within this numbering system, and secondly, denomination by structural description simplifies the comparison with other elements that possess structurally equivalent polymorphs such as germanium.

2. Note that the exact nature of the polymorph(s) obtained via such point loading is ambiguous. Namely, the exact ratio of the phases in the transformed volume is not known and it may even be possible that a hybrid mixed bc8/r8 phase is formed. The phases(s) made by point loading will therefore be referred to as bc8/r8-Si henceforth.

3. Note that in both cases, pressure was cycled by a few GPa to achieve the desired phase composition and stabilize the cells.

4. The (200) (β-Sn) peak is sharper in the Ne cell 2 compared to the methanol–ethanol cell 1, presumably due to strain in the latter case. Additionally, comparison of two cases where the (200) (β-Sn) peaks are at the same Q reveals a (101) peak shifted to a slightly lower Q for the Ne cell suggesting a slightly larger $c/a$ ratio in this case.

5. Note that all peaks from allowed reflections have full intensity in electron diffraction, making them readily observable but that the same reflections can have low intensity in XRD. Hence the absence of peaks at $5.6\pm 0.1\text{Å}$, $4.8\pm 0.1\text{Å}$ and $4.4\pm 0.1\text{Å}$ in the XRD data could be attributed to these differences.

6. Note that Figure 8(a) does not consider bc8/r8-Si made from point loading that leads to Si-XIII.

7. Note that such cooling has to take place once r8-Si has already formed from (β-Sn)-Si because decompression from the metallic regime at low temperatures to pressures below 2 GPa does not result in r8-Si, but in (β-Sn)-Si followed by amorphization upon heating to ambient temperature.[54,55]

Additional information

Funding

This work was supported by funding from the Australian Research Council (ARC). JEB is supported by an ARC Future Fellowship. Work by MG was fully supported by EFree, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award No. DE-SC0001057. BH acknowledges current funding through an Alvin M. Weinberg Fellowship (ORNL) and the Spallation Neutron Source (ORNL), sponsored by the U.S. Department of Energy, Office of Basic Energy Sciences. HPCAT operations are supported by DOE-NNSA under Award No. DE-NA0001974 and DOE-BES under Award No. DE-FG02-99ER45775, with partial instrumentation funding by NSF. Use of the COMPRES-GSECARS gas loading system was supported by COMPRES under NSF Cooperative Agreement EAR 11-57758 and by GSECARS through NSF grant EAR-1128799 and DOE grant DE-FG02-94ER14466. APS is supported by DOE-BES, under Contract No. DE-AC02-06CH11357.