Ab initiostudy of the β-tin→Imma→sh phase transitions in silicon and germanium

Abstract

We have investigated the structural sequence of the high-pressure phases of silicon and germanium. We have focussed on the cd → β-tin → Imma → sh phase transitions. We have used the plane-wave pseudopotential approach to the density-functional theory implemented within the Vienna ab-initio simulation package (VASP). We have determined the equilibrium properties of each structure and the values of the critical parameters including a hysteresis effect at the phase transitions. The order of the phase transitions has been obtained alternatively from the pressure dependence of the enthalpy and of the internal structure parameters. The commonly used tangent construction is shown to be very unreliable. Our calculations identify a first-order phase transition from the cd to the β-tin and from the Imma to the sh phase, and they indicate the possibility of a second-order phase-transition from the β-tin to the Imma phase. Finally, we have derived the enthalpy barriers between the phases.

Phonons in theβ-tin,Imma, and sh phases of silicon fromab initiocalculations

“…Nevertheless, we can estimate the transition pressures from Fig. 1, and we find that the β-tin→Imma transition occurs between 115 and 118 kbar and the Imma→sh one between 142 and 143 kbar, which is in good agreement with the experimental values [2] if those data are evaluated in the same way (for further details and a review of available experimental and theoretical results see [7]). In the following we will inspect the phonon spectra as a possible source for clearer conclusions.…”

“…Here, with ∆ being discontinuous the phase transition β-tin→Imma seems to be of first order, while the Imma→sh transition seems to be of second order because of a missing discontinuity of ∆. The enthalpy barrier between the Imma and the sh phase is only a few meV [7], which is less than the precision of our calculations. Therefore, the determination of the order of the phase transitions from the behaviour of the lattice parameters as a function of the pressure or total energy is unreliable.…”

“…From group-theoretical arguments [6], the phase transition β-tin→Imma can be of second order, whereas the phase transition Imma→sh has to be of first order. This conclusion was strongly supported by an ab initio calculation in our previous work [7].An intermediate phase similar to the Imma phase, with a structure more general than the β-tin and the sh phase was considered theoretically before [8] with a prediction that the phase transitions might be accompanied by soft phonon modes. Since the Imma structure results from a distortion and a relative sublattice shift of β-tin along the c-direction, which corresponds to a soft Γ phonon displacement [9], it is worthwhile to investigate the pressure dependence of the phonon-dispersion curves.…”

Transition pressures and enthalpy barriers for the cubic diamond→β-tin transition in Si and Ge under nonhydrostatic conditions

“…In addition, our method can be extended to, e.g., the β-tin→Imma→sh transitions in Si and Ge. After the extraction of a two-dimensional energy surface from a threedimensional one using the values along the lines where two components of the stress tensor are equal (like in our previous work 46,78 ), the method mentioned here can be applied to this extracted surface. By the choice of two equal components the main pressure direction is chosen.…”

Molecular Dynamics Simulations of Nanoparticle-Surface Collisions in Crystalline Silicon

“…In both cases, very large pressures are reached, around 13 GPa for the slow-elastic regime, and around 18 GPa for the fast-damped one. Such stresses are amply within the range of pressures capable of determining a phase transition in silicon, i.e., 10-15 GPa for the cubic diamond β-tin phase transformation [20,21]. …”