Understanding Chemical Changes Across the Α‑Cristobalite to Stishovite Transition Path in Silica † † ‡ † † Miguel A
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Article pubs.acs.org/JPCC Understanding Chemical Changes across the α‑Cristobalite to Stishovite Transition Path in Silica † † ‡ † † Miguel A. Salvado,́*, Pilar Pertierra, A. Morales-García, J. M. Menendez,́ and J. M. Recio † Departamento de Química Física y Analítica, Universidad de Oviedo, Oviedo, Spain, and MALTA-Consolider Team ‡ Departamento de Química Física I, Universidad Complutense de Madrid, Madrid, Spain, and MALTA-Consolider Team ABSTRACT: The interplay of structural, energetic, and chemical bonding features across the pressure-induced α- → cristobalite stishovite phase transition in SiO2 is fully characterized by first principles calculations and topological analysis of the electron localization function. Under a martensitic approach, the transition mechanism is theoretically modeled at the thermodynamic transition pressure using the α -cristobalite P41212 space group. A soft and symmetric transition path is determined with an activation barrier lower than 100 kJ/mol. No bond breaking is found, but a synchronous bonding formation process leading to Si 6-fold and O 3-fold coordinations. Only when the third coordination sphere of oxygens approaches a given Si at a distance close to 2.0 Å do new Si−O bonding basins appear. This situation occurs at a transformation stage well beyond the maximum in the energetic profile of the transition path. ■ INTRODUCTION tetrahedral to octahedral silicon coordination change. α- cristobalite structure can be related to the C9 cubic structure Understanding chemical changes induced by thermodynamic 17 variables in crystals is of great interest in solid-state chemistry. through a rotation of SiO4 tetrahedra around their C2 axis. Further rotation leads to a rutile packing of oxygen atoms. On It covers structural, energetic, and chemical bonding character- ’ ff ization of local environments of the atomic constituents of the basis of this idea, O Kee e and Hyde proposed a fi mechanism for the transformation mixing tetraedra rotations solids, and involves the modi cations within the same 17 crystalline structure or between different polymorphs if a and silicon displacements. Later, this mechanism was − successfully modeled using a periodic Hartree−Fock ap- solid solid phase transition occurs. When the transformations 15 are induced by pressure, the outstanding capability of this proach, although the limited basis sets and geometrical variable to promote high metal coordinations in crystalline constraints used in that work do not allow for a global solids leads to densification processes of fundamental interest in quantitative description of the transition path. Huang et al.11 suggested from ab initio and MD calculations areas ranging from planetary sciences to materials engineering. α fi A paradigmatic example of such a capability that merits that -cristobalite under pressure rst transforms into a hp- cristobalite phase with the same tetragonal space group and investigation in detail is the emergence of Si hexacoordinated at ff high pressures from the tetrahedral environment displayed at Wicko positions as the original cristobalite, and associated this new phase with the X-I phase found in experiments. On the normal conditions in silica polymorphs. In fact, thermodynamic 7 and kinetic aspects have been the subject of a number of studies basis of three-dimensional single-crystal data, Dera et al. show dealing with silica transformations under pressure, both that the unit cell for this new phase is not tetragonal but − − experimentally1 7 and theoretically.8 14 However, only few monoclinic, although a structural model remains elusive. efforts have been put forward to the understanding of how the Nevertheless, it is noteworthy to emphasize that an easy transformation between cristobalite and rutile forms of GeO2 chemical bonding network evolves from low to high Si 18 coordination,15,16 an issue that needs to be addressed if a has been also described. global characterization of the densification process is desired. Besides energy and geometry, chemical bonding constitutes Cristobalite has been one of the most widely studied phases the third leg of the triad that fully characterizes the changes α involved in a reconstructive phase transition. The electron of SiO2.Thetetragonal -phase is metastable at room conditions (α-quartz being the stable phase) and is usually localization function (ELF) may be considered, among obtained quenching the cubic β-cristobalite, a stable high quantum chemical topological formalisms, as one of the most ff temperature polymorph. At low temperature and pressures appropriate tools to o er a clear view of those regions within higher than 7.5 GPa, stishovite (octahedral silicon) is the stable phase. Stishovite is also tetragonal, and its space group is a Received: February 23, 2013 supergroup of the α-cristobalite one. For this reason, the Revised: April 2, 2013 transformation between them has been taken as a model for Published: April 5, 2013 © 2013 American Chemical Society 8950 dx.doi.org/10.1021/jp401901k | J. Phys. Chem. C 2013, 117, 8950−8958 The Journal of Physical Chemistry C Article the unit cell that are especially sensitive in terms of chemical unit cell can be chosen to describe the transformation with the activity under pressure.19 The topology induced by the ELF requirement of belonging simultaneously to a common field provides a partition of the space into basins or regions that subgroup of the initial and final structures. Once the unit cell follow the language of Lewis’ theory: atomic-like core shells is defined, a transformation coordinate and a transition path can (C), lone pairs (LP), and bonds (B).20 Using ELF analysis, it is be proposed. Under this view, the whole process is modeled in possible to track how these basins are modified and when new a way very similar to a chemical reaction. α α bonds are formed as we move forward along the -cristobalite -Cristobalite belongs to the P41212 space group. Its to stishovite transition path. conventional unit cell contains 4 Si and 8 O atoms with Si at In this work, our contribution is aimed at a full under- 4a(x,x,0) and O at general 8b(x,y,z) positions. Stishovite standing of the interplay between unit cell structural changes, belongs to the P42/mnm space group. Its conventional unit cell energetic profiles, and chemical bonding reorganization of silica contains 2 Si and 4 O atoms with Si at 2a(0,0,0) and O at from α-cristobalite to stishovite. To this end, we will carry out: 4f(x,x,0). Both structures have been described in detail (i) electronic structure first principles calculations of a number elsewhere (see, for example, refs 17,29). of periodic systems following a transformation coordinate that In the present microscopic study of the α-cristobalite to α links -cristobalite and stishovite structures under a common stishovite transformation, a P41212 common unit cell with four space group, and (ii) ELF topological analysis of all electron formula units can be chosen to describe the mechanism because solutions of the optimized structures across the transition path. the space group of α-cristobalite is a subgroup of that of The main outcome of these calculations consists of atomic stishovite. In this space group, the stishovite cell volume trajectories, cell shapes, energy barriers, and the quantitative doubles its value, and Si and O atoms occupy the same Wyckoff fi α identi cation of chemical bonding indexes related to the positions as in -cristobalite with xSi = 0.5, yO = xO, and zO = emergence of the new Si−O bonds. 0.25. fl Three more sections complete this Article. Next, we brie y The phase transition mechanism using the P41212 common present the computational parameters used in our electronic unit cell can be monitored through a normalized transformation structure calculations, along with the main ideas of our coordinate, ξ, evolving from 0 (α-cristobalite) to 1 (stishovite) fi ξ − cr st − cr cr st martensitic approach for the transition path and some basic and de ned as follows: =[xSi xSi]/[xSi xSi], xSi and xSi concepts of ELF. Section 3 provides the discussion of the being the x coordinate of silicon in α-cristobalite and stishovite, calculated structural, energetic, and chemical bonding reorgan- respectively, and xSi the x coordinate of Si at each stage of the ization results across the α-cristobalite → stishovite transition transition path. To determine the transition path, we start with path. A brief summary and the main conclusions will be the equilibrium structure of α-cristobalite at 6 GPa, close to the presented in the last section. calculated thermodynamic transition pressure. At each step, we update the xSi value and optimize the cell parameters and the ■ COMPUTATIONAL DETAILS AND MODELING oxygen coordinates (a total of five parameters), keeping the Total Energy. Static total energy (E) calculations at selected silicon coordinate frozen. volumes (V) in the α-cristobalite and stishovite unit cells were Basic Concepts of ELF. The electron localization function 30 carried out under the generalized gradient approximation (ELF), first introduced by Becke and Edgecombe, provides a (GGA) of the density-functional theory as implemented in the measure of the localization of electron pairs in atomic and Vienna ab initio simulation package (VASP).21 The projector- molecular systems that is able to recover the chemical augmented wave (PAW) all-electron description of the representation of a molecule consistent with Lewis’ valence electron−ion−core interaction22,23 and the exchange and picture. The ELF has been defined to have values between 0 correlation functional proposed by Perdew−Burke−Ernzerhof and 1 (1 corresponding to perfect localization) to ease the (PBE)24 were used. Brillouin-zone integrals were approximated visualization of its isosurfaces. The topological analysis of ELF using Γ-centered Monkhorst−Pack meshes25 where the surfaces provides a partition of the three-dimensional space into ⃗ numbers of subdivisions along each reciprocal lattice vector bi nonoverlapping basins, which can be thought of as electronic ×| ⃗| ff were given by Ni = max(1.15 bi + 0.5).