Density functional simulations of hexagonal Ge${}_2$Sb${}_2$Te${}_5$ at high pressure

We investigated the structural transformations of the hexagonal phase of Ge${}_2$Sb${}_2$Te${}_5$ under pressure by means of ab initio molecular dynamics with a variable simulation cell. To overcome the enthalpy barriers between the different phases we used metadynamics techniques. We reproduced the hexagonal-to-$\mathrm{bcc}$ transformation under pressure found experimentally. The $\mathrm{bcc}$ phase retains a partial chemical order, as opposed to a second $\mathrm{bcc}$ phase we generated by pressuring the amorphous phase. This structural difference is suggested to be responsible for the memory effect uncovered experimentally, the $\mathrm{bcc}$ phase reverting to the amorphous or to the hexagonal phase upon decompression, depending on the type of precursor phase it originates from.

Figure 1

Upper (lower) panels: snapshots of the $\mathrm{BCC}$1 ($\mathrm{BCC}$2) model. Thicker lines highlight two cubes of the two interpenetrated simple cubic lattices of the $\mathrm{bcc}$ structure. Dark blue, Ge; light green, Sb; light blue, Te.

Figure 2

Total and partial pair correlation functions of the body-centered cubic crystals obtained by pressurizing the amorphous phase generated either from c-GST ($\mathrm{BCC}$1, solid blue line) or by quenching from the melt ($\mathrm{BCC}$1a, dashed black line). The pressure is 30 GPa for both models and the temperature is 300 K. Inset: a Ge${}_2$ dimer and its environment is depicted (see text).

Figure 3

Structure of Ge${}_2$Sb${}_2$Te${}_5$ in the hexagonal cell (stacking B, see text). Two formula units along the $c$ axis, and period replicas of atoms at the edges of the hexagonal cell in the $ab$ plane are shown. In stacking A, the positions of Ge and Sb atoms are interchanged. The weak Te-Te bonds (3.9 Å long) connecting adjacent slabs are not shown to emphasize the presence of Ge${}_2$Sb${}_2$Te${}_5$ stacks.

Figure 4

(a) Enthalpy along the first metadynamics run (run 1). (b) Enthalpy versus volume data collected during the three different metadynamics runs. Each point represents a single metastep and it is the result of a thermal averaging over a fixed-cell NVT simulation.

Figure 5

(a) Lengths and (b) angles of the supercell vectors in the metadynamics runs. Vertical dashed lines denote the observed transitions.

Figure 6

The $Q_4$ and $Q_6$ order parameters for atoms in the models of the different phases of GST optimized at zero temperature. A panel for each species is reported. Each point represents an individual atom. The points for the ideal NaCl and CsCl structures are also reported. The spread of $Q_4$ for Ge atoms in the $\mathrm{BCC}$1 structure (red diamonds) toward values typical of the amorphous phase is due to Ge${}_2$ dimers whose contribution is indicated as $\mathrm{BCC}$1 (Ge${}_2$) (empty red diamonds).

Figure 7

The trajectory of the metadynamics and MD simulations in the ($Q_4$,$Q_6$) plane. A panel for each species is reported. Each point is the centroid of the distributions of the $Q_4$ and $Q_6$ of the different atoms at selected metasteps in the metadynamics simulations leading to $\mathrm{BCC}$2 or at selected volumes in the MD simulations leading to $\mathrm{BCC}$1.

Figure 8

(a) Energy versus volume and (b) enthalpy versus pressure curves for different structures optimized at 0 K. The enthalpy is reported with respect to that of h-GST.

Figure 9

Total and partial pair correlation functions of $\mathrm{BCC}$1 obtained from a-GST (solid blue line) and of $\mathrm{BCC}$2 obtained from h-GST (dashed black line).

Figure 10

(a) Phonon density of states of $\mathrm{BCC}$1a, $\mathrm{BCC}$1, and $\mathrm{BCC}$2. (b) Inverse participation ratio (IPR, see text for a definition) for phonons in the $\mathrm{BCC}$1 (circles), $\mathrm{BCC}$1a (squares), and $\mathrm{BCC}$2 (triangles) models.

Figure 11

Angular positions of the neighboring atoms in the first and second coordination shells in $\mathrm{BCC}$1 (upper panel) and $\mathrm{BCC}$2 (lower panel). Each point corresponds to an atom. The neighboring atoms in the first and second coordination shells of all atoms in the model are collected. Red empty circles and blue triangles correspond, respectively, to atoms in the first and second coordination shells (see text). Black crosses correspond to atoms tagged as noise (see text).

Figure 12

Distribution of interatomic distances for atoms of $\mathrm{BCC}$1 belonging to the spots defined in Fig. 11. The top distribution corresponds to atoms belonging to the second coordination shell, while the central distribution corresponds to atoms belonging to the first coordination shell. The distribution for atoms belonging to the noise (see text) is also shown at the bottom. Vertical dotted lines denote the two average distances obtained for the two groups of clusters. Horizontal solid lines, instead, denote the standard deviation from the average distance. The distribution for the noise shows a first peak at shorter distances due to the presence of Ge${}_2$ dimers.

Figure 13

Angle distribution functions of the $\mathrm{BCC}$1 phase obtained from a-GST and of the $\mathrm{BCC}$2 phase obtained from h-GST. The angle distribution functions for the first and second neighbors are given in the upper and lower panels, respectively. Vertical dashed lines indicate the angles expected for a body-centered cubic structure at 70.5${}^{\circ }$ and 109.5${}^{\circ }$. The bonds formed by Ge atoms belonging to Ge${}_2$ dimers in $\mathrm{BCC}$1 have been omitted. The fact that the distributions in $\mathrm{BCC}$1 are peaked at the expected angles for the body-centered cubic phase demonstrates the validity of the assignment to the first or second coordination shell we made on the basis of the analysis of the spots in Fig. 11 described in the text.

Figure 14

Electronic density of states (DOS) of the different GST structures explored in the simulations. All the models are equilibrated at 30 GPa. The DOS of the monoclinic phase at 20 GPa is also reported for the sake of comparison. The DOSs are computed from the energies of the Kohn-Sham orbitals at the supercell $\Gamma$ point broadened with a Gaussian function of width 54 meV.