Fig. 1. HRTEM characterization of metastable product phases transformed from β-Sn Ge and the corresponding FFT patterns in regions of 50 × 50 nm². (a) st12 Ge. The Fourier-filtered HRTEM images of the area are outlined with a white box. (b) bc8/r8 Ge. The areas encircled by white lines indicate the amorphous grain boundaries. The interfringe distances and diffraction spots of bc8/r8 Ge and hd Ge are marked by yellow and orange, respectively. (c) a-Ge. The white circles indicate crystal-like short-/medium-range ordered nanostructures with an average distance of 0.32 nm. The scale bar in the HRTEM images is 10 nm. (d)–(f) HRTEM analyses for the normalized distribution of grain size for the metastable phases of st12 Ge, bc8/r8 Ge, and a-Ge, respectively.

Fig. 2. Three distinct transition pathways in the structural evolution of β-Sn Ge under decompression with different compression rates at room temperature. Decompression of β-Sn Ge leads to a phase transformation to (a) st12 Ge at a very low decompression rate (0.001 GPa/s), (b) bc8/r8 Ge at a relatively high rate (∼40 GPa/s), and (c) a-Ge at a high rate (>4 TPa/s). The background has been subtracted for the integrated XRD patterns. The Bragg peaks of NaCl used as a pressure marker and transmitting medium are marked with asterisks. (d) Comparison of the diffraction patterns of st12, bc8, and a-Ge under ambient conditions. (e) Diagram of the phase transformations of β-Sn Ge at various temperatures and strain rates (or decompression rates). The transformation of β-Sn Ge to a-Ge is marked with black squares, the crystalline bc8/r8 phase with red balls, and the crystalline st12 phase with blue blocks. (f) Unit cell volume of β-Sn Ge at transition pressure under decompression at various temperatures and decompression rates. β-Sn Ge transforms to a mixture of st12 and bc8/r8 phases, which are marked with green asterisks.

Fig. 3. XAFS measurements under decompression from β-Sn Ge to the metastable bc8/r8 and st12 phases. (a) XANES absorption spectra for the β-Sn Ge to st12 transition at selected pressures under decompression at nonhydrostatic conditions (those for the β-Sn Ge to bc8/r8 transition at the hydrostatic condition with silicone oil as pressure medium are shown in Figs. S14 and S16, supplementary material). (b) Moduli of the Fourier transform of experimental EXAFS spectra. (c) and (d) Evolution of the absorption edge E₀ (black symbols and dark gray shaded curves) and the radial distance at around 2.0 Å (R₁, red symbols and red shaded curves) in the transformations of β-Sn Ge to st12 Ge and to bc8/r8 Ge, respectively. The blue rectangular area corresponds to the significant change in E₀, the orange rectangular area represents the significant change in R₁, and the light gray area indicates the overlapping region of both.

Fig. 4. (a) Onset transition strain as a function of over-depressurization. The black, red, and blue symbols indicate onset transition strains of β-Sn Ge in the transformations to st12, bc8/r8, and a-Ge, respectively. (b) Normalized nucleation rate as a function of over-depressurization (red dashed line), calculated using I ∼ exp(−C/ΔP²).⁴⁸ The constant C is estimated to be 5, under the assumption that the free energy barrier at ΔP = 1 GPa is equal to the previously calculated enthalpy barrier.⁴⁹ The normalized grain number is shown for comparison. Black, red, and blue symbols represent st12, bc8/r8, and amorphous Ge, respectively.