Landau theory for stress-induced order-disorder transitions in phase change materials

We propose a Landau theory for phase change materials (PCMs), which describes stress-induced amorphization in vacancy-free, ordered PCMs as a condensation of defects in analogy to equilibrium gas-liquid transitions. Three dimensionless parameters suffice to deduce a highly accurate equation of state for both phases from it. The reference data for our model alloy Ge${}_x$Sb${}_{1-x}$ are produced from molecular dynamics simulations and synchrotron x-ray diffraction. Raman spectroscopy is used to estimate the density of tetrahedrally coordinated germanium atoms, which we relate to the order parameter. All methods provide consistent support for the reversibility of the transition.

Figure 1

Representative x-ray spectra of Ge${}_{0.15}$Sb${}_{0.85}$ during compression and subsequent decompression. The bottom spectrum represents the initial sample.

Figure 2

Typical Raman spectra of Ge${}_{0.15}$Sb${}_{0.85}$ at different pressures. The bottom spectrum represents the initial sample.

Figure 3

Raman spectra of (a) an amorphous sample at 1.0 GPa and (b) a crystalline sample at 2.0 GPa. Dashed blue lines are individual Gaussians fitted to the spectra. Solid red lines represent the sum of the blue lines.

Figure 4

Optical images of the sample giving rise to the spectra shown in Fig. 3.

Figure 5

The equation of state of Ge${}_{0.15}$Sb${}_{0.85}$ as measured experimentally (closed symbols) and determined numerically (open symbols). Full (black) and dotted (gray) lines represent the lattice-gas and displacive-mode Landau approach, respectively. Arrows indicate the instability points. $V_0$ and $B_0$ represent experimental volume per unit cell and bulk modulus at ambient conditions, respectively.

Figure 6

The equation of state of Ge${}_{0.25}$Sb${}_{0.75}$. Symbols as in Fig. 5.

Figure 7

XRD spectra of amorphous Ge${}_{0.25}$Sb${}_{0.75}$ compressed to $p=2.95$ GPa (left) and decompressed back to ambient pressure (right). The partial crystallinity is reversed. The Bragg peaks are related to the NaCl reference crystal included in the DAC. Peak intensities are shown in Fig. 8.

Figure 8

Compression-decompression cycle of Ge${}_{0.25}$Sb${}_{0.75}$. The partial crystallinity attained at $p=3.0$ GPa is essentially lost.

Figure 9

Relative number of tetrahedrally coordinated Ge atoms in Ge${}_{0.15}$Sb${}_{0.85}$ obtained after constant-volume energy minimizations of the $T=973$ K liquid (green crosses) and the $T=300$ K glass (red circles). For clarity, representative error bars are given for one data point only. Full lines reflect Landau theory. Landau theory and Raman data (blue circles) have been normalized to match simulation results near zero pressure. Numbers on the Raman symbols index the scans.

Figure 10

Comparison between local structures for liquid Ge${}_{0.15}$Sb${}_{0.85}$ at (a) 973 K and (b) the quenched amorphous samples at 300 K. (c) Coordination probability for Ge and Sb in each of the simulations. (d) Average-angle distributions around four-coordinated Ge and three-coordinated Sb. The majority of four-coordinated Ge atoms are in tetrahedral configurations, with bond angle distributions centered around ${109}^{\circ }$.

Figure 11

Comparison between local structures for (a) crystalline Ge${}_{0.15}$Sb${}_{0.85}$ and (b) a pressure-annealed “amorphous” samples at 300 K. (c) Coordination probability for Ge and Sb in each of the simulations. (d) Average-angle distributions around four-coordinated Ge and three-coordinated Sb. The majority of four-coordinated Ge atoms are in tetrahedral configurations, with bond angle distributions centered around ${109}^{\circ }$.