Pressure dependence of the static structure of liquid GeTe based on ab initio molecular dynamics simulations

We have investigated the pressure dependence of the static structure of liquid GeTe based on ab initio molecular dynamics simulations. The pressure range is between ambient pressure and 250 GPa, and their temperatures between 1000 K and 4000 K, which keep the liquid state. In this study, we found two transition stages caused by the compression. At the first stage, below 12 GPa, atomic distances elongate and Peierls-type distortion is dissolved with increasing pressure. At the second stage, above 12 GPa, atomic distances shorten and the electronic states shows metallic.


Introduction
Germanium tellurides (GeTe) are interesting materials because of their semi-conducting properties and the fast phase transition, e.g., Ge-Sb-Te. Crystalline GeTe at room temperature has A7 structure, which is distorted from fcc rocksalt (B1) to expand (111) direction. This distortion is named as Peierls distortion. In this state, Ge atoms and Te atoms are threefold coordinated each other. When the temperature increases up to about 700 K, GeTe changes from A7 to B1 structure, where Ge and Te atoms are sixfold coordinated each other. When the temperature increases up to about 1000 K, crystalline GeTe melts and its coordination number becomes approximately 3-4, i.e., the Peierls-type A7 structure appears again [1].
On the other hand, compression also induces the structural change of crystalline GeTe. When pressure increases up to around 3 GPa, GeTe changes from A7 to rocksalt structure. It has been suggested that, under further compression, GeTe eventually becomes bcc (CsCltype) structure at 40-50 GPa, through several structural changes [2]. The pressure dependence of the structure of the liquid state was also reported by X-ray diffraction measurements [3], which suggest that the structural change in the liquid state is different from that in the crystalline state. However, the details are not clarified yet.
In this study, we investigate the pressure dependence of the static structure of liquid GeTe based on ab initio molecular dynamics (AIMD) simulations, in which the electronic structure is calculated in the framework of the density functional theory with the generalized gradient approximation. The temperature and pressure ranges are from 1000 to 4000 K and from 0 to 250 GPa, respectively.

Numerical details
We have carried out the calculations by using AIMD simulations, in which the electronic states were calculated by the projector-augmented-wave (PAW) method [4,5] within the framework of the density functional theory (DFT) in which the generalized gradient approximation (GGA) [6] was used for the exchange-correlation energy. The plane wave cutoff energies are 9 and 90 Ry for the electronic pseudo-wave functions and the pseudocharge density, respectively. The energy functional was minimized using an iterative scheme [7,8]. The ī point was used for Brillouin-zone sampling. Projector functions of the s, p, and d types were generated for the 4s, 4p, and 4d states of Ge, and the 5s, 5p, and 5d states of Te. By investigating the energy dependence of the logarithmic derivatives of the pseudo-wave functions, we verified that our data sets have good transferability, and do not possess any ghost states in the energy range considered.
Molecular-dynamics simulations were carried out at pressures from approximately 0 to 250 GPa and the temperature T = 1000-4000 K. The number densities ȡ, the pressures P and the temperature T used in our simulations are listed in Table I. They were determined from the averaging result of the isothermal-isobaric MD simulations at least 1500 MD steps (4.35 ps). We used a 128-atom systems in a cubic supercell with periodic boundary conditions. Using Nosé-Hoover thermostat technique [9,10], the equations of motion were solved via an explicit reversible integrator [111] with a time step of ǻt = 2.9 fs. The quantities of interest were obtained by averaging over 29 ps after an initial equilibration taking at least 1.5 ps. Figure 1 shows the pressure dependence of the static structure factors (a) S X (k) using X-ray form factor and (b) S n (k) neutron scattering length. Our results shown by solid lines are in good agreement with experimental results [3] illustrated by circles at wide pressure range.

Static structure factors
The height of the first sharp diffraction peak (FSDP) of S n (k) at about k = 1.0 Å -1 decreases with increasing pressure, and the FSDP disappears at 4.1 GPa. The disappearance of the FSDP suggests the change of the medium range order. The first peak position shifts from k = 2.2 to 3.0 Å -1 with increasing pressure.

Pair distribution functions
The pressure dependence of the total and partial pair distribution functions g(r) and g Įȕ (r) are shown in Fig. 1(c) and 1(d)-(f), respectively.
The first and second peaks of g(r) exist at approximately r = 2.8 and 4.2 Å. The second peak shifts toward smaller r with increasing pressure, and it becomes a shoulder of the first peak between 4.1-5.9 GPa. Under further compression, the first peak position shifts toward smaller r. The partial correlation functions g GeGe (r) and g GeTe (r) have their first peaks at about r = 2.6 and 2.8 Å. The pressure dependence of the first peak positions of g(r) and gDE(r) is shown in Fig. 2. Figure 2 suggests that there are two stages compression process. The first stage appears below 12 GPa. In this stage, the peak position of g(r) elongates from r = 2.8 to 2.9 Å. While peak positions of g GeGe (r) and g GeTe (r) do not change so much. On the other hand, that of g TeTe (r) shortens drastically, however, this change is caused by the difficulty to determine precisely the peak position of g TeTe (r) and growth of the first peak at around r = 3 Å. In the second stage, above 12 GPa, all positions of the first peaks shift monotonically to smaller r with increasing pressure. The temperature effect of the change between 12-24 GPa is discussed in the section 3.8.   Figure 3 shows the pressure dependence of the coordination numbers (a)-(b) ND and (c)-(e) NDE. Solid lines with circles and dotted lines with squares correspond to cutoff distances r c = 3.0 and 3.2 Å, respectively. The former, r c = 3.0 Å, and the latter, r c = 3.2 Å, correspond to the short bond length caused by Peierls distortion in the crystalline state, where the coordination number should be 3, and the first minimum position of g(r), respectively. Dashed lines with diamonds show values obtained by integration of gDE(r) until the first peak position r peak , and then the values are doubled, i.e., if the shape of first peak of gDE(r) would be symmetric, the pressure dependence of dashed lines would show a similar tendency as that of the other lines.

Coordination numbers
In Fig. 3(a), the solid line shows that N Ge at ambient pressure is almost 3, however, N GeTe at ambient pressure is 2. If GeTe is in the crystalline state, N GeTe should be 3. While, in the liquid state, although N GeTe is only 2, Ge-Ge homopolar bond appears (N GeGe = 1) and this supplements the lack of Ge-Te bonds. With increasing pressure, ND and NDE does not change much below 12 GPa. However, above 12 GPa, both ND and NDE increase rapidly with compression. The appearance of a difference between NDE using r peak and other r c suggests the existence of a new local order at high pressure. Figure 4 shows the pressure dependence of the three-body bond angle distributions BDED(T). A cutoff distance of r c = 3.0 Å is used. The top panels (a1) and (b1) correspond to the pressure range from 0.0 to 11.9 GPa, and the bottom panels (a2) and (b2) show BDED(T) at the pressures above 11.9 GPa, respectively. At ambient pressure, which shown by black solid lines in the top panels, B GeTeGe (T) and B TeGeTe (T) have each peak at about T = 90°. The profile of B GeTeGe (T) is slightly wider than that of B TeGeTe (T). This is a result of high mobility of Ge atoms. With increasing pressure, the  suggests that the liquid GeTe at 250 GPa is similar to bcc crystalline state. Figure 5 shows the pressure dependence of (a) the charge distribution fD(Q) and (b)-(c) their average values ܳ ത . At ambient and low pressure range, f Ge (Q) and f Te (Q) exist at almost Q = 0. With increasing pressure, the distribution fD(Q) and their averages ܳ ത do not change so much below 12 GPa. However, for furthermore compression, fD(Q) become wider and ܳ ത leave the range of Q ൎ 0. In other words, covalent type liquid GeTe changes to more ionic type at approximately 12 GPa.

Electronic density of states
At ambient pressure, the total electronic density of states D(E) shows that liquid GeTe has semiconductor-type properties because D(E) at E = 0 (Fermi energy) has a dip in Fig.6. With increasing pressure, the dip at E = 0 becomes shallow, and it completely vanishes at 12GPa, i.e., a semiconductor-metal transition occurs at about 12 GPa.

Temperature dependence
In order to discuss the pressure dependence of the structure carefully, additional calculations were performed using the same volume as 12 for GPa. The temperature increases from 1000 to 1250 K, and further to 1500 K. Static structure factors S X (k), partial correlation functions gDE(r), and coordination numbers ND and NDE were obtained by averaging 5000 MD steps (14.2 ps) after an initial equilibration taking at least 1.5 ps.
In Figs. 8(a)-(d), solid and dotted lines show the results at T = 1250 K and 1500 K, respectively. It is found that S X (k) at 1250 and 1500 K are quite similar with that at 1000 K in Fig.8(a). On the other hand, for gDE(r), the heights of the first peaks seem to be slightly lower and the width of g GeGe (r) becomes slightly wider than that at T = 1000 K. Positions of g GeTe (r) and g TeTe (r) at high temperatures slightly shift toward smaller r. However, the temperature effect for S X (k) and gDE(r) is considerably smaller than the pressure induced structural change.
The temperature dependence of the coordination numbers ND and NDE at about 12 GPa is shown in Fig.8

LAM-16
show coordination numbers at about 12 GPa using cutoff distances r c = 3.0 and 3.2 Å, respectively. Closed symbols indicate results at about 24 GPa. It is clearly seen that the temperature effect is much smaller than the pressure effect.

Conclusion
We have investigated the pressure dependence of the static structure of liquid GeTe under pressure based on ab initio molecular dynamics simulations. Our simulation shows that the structure of the liquid changes in two stages under pressure. In the first stage below 12 GPa, the Peierls-type distortion in the liquid state was completely dissolved. In this pressure range, the nearest neighbour distance becomes longer, and the semiconducting properties are maintained. It seems that semiconductor-metallic transition occurs at approximately 12 GPa. In the second stage above 12 GPa, the nearest neighbour distance shortens. The coordination number reaches about 13.7 at 250 GPa, which is quite similar to that of CsCl-type crystalline state with taking the second neighbour into account.