Characterization of the High-Pressure Structures and Phase Transformations in SnO 2 .A Density Functional Theory Study L. Gracia, A. Beltra ´ n,* and J. Andre ´ s Departament de Quı ´mica Fı ´sica i Analı ´tica, UniVersitat Jaume I, Campus de Riu Sec, Castello ´ E-12080, Spain ReceiVed: NoVember 10, 2006; In Final Form: March 28, 2007 Theoretical investigations concerning the high-pressure polymorphs, the equations of state, and the phase transitions of SnO 2 have been performed using density functional theory at the B3LYP level. Total energy calculations and geometry optimizations have been carried out for all phases involved, and the following sequence of structural transitions from the rutile-type (P4 2 /mnm) driven by pressure has been obtained (the transition pressure is in parentheses): f CaCl 2 -type, Pnnm (12 GPa) f R-PbO 2 -type, Pbcn (17 GPa) f pyrite-type, Pa3 h (17 GPa) f ZrO 2 -type orthorhombic phase I, Pbca (18 GPa) f fluorite-type, Fm3 hm (24 GPa) f cotunnite-type orthorhombic phase II, Pnam (33 GPa). The highest bulk modulus values, calculated by fitting pressure-volume data to the second-order Birch-Murnaghan equation of state, correspond to the cubic pyrite and the fluorite-type phases with values of 293 and 322 GPa, respectively. 1. Introduction There have been sustained interests in investigations of pressure-induced phase transitions and in the associated struc- tural changes because they are of both fundamental and technological importance. 1 Most studies in materials chemistry and in high-pressure research have been focused on oxides, which have provided the largest group of inorganic compounds leading to technologically important materials. In particular, metal oxides exhibit extensive polymorphism at high pressures, and different phase transitions that yield highly coordinated structures have been uncovered 2 and have attracted much attention because of their potential as superhard materials. 3-5 In particular, the metal dioxides MO 2 , where M can be cations from groups 4 and 14, present a similar sequence of phase transitions from rutile (P4 2 /mnm), to CaCl 2 -type (Pnnm), to R-PbO 2 -type (Pbcn), and to pyrite-type (Pa3 h) that have been found or predicted. 6-11 SnO 2 together with PbO 2 and SiO 2 are the most representative materials of the homologous group 14 dioxides for potential applications in numerous fields. After previous knowledge on the SnO 2 system has been surveyed, its phase transformations will be explored by the density functional theory (DFT) approach, within the theoretical frame outlined below. Several works on the high-pressure polymorphs of SnO 2 have been published. 7-9,12-18 Pioneering studies by Liu 13 reported the phase transformation of the rutile tetragonal phase to the orthorhombic with the R-PbO 2 structure at above 12 GPa, whereas at around 25 GPa this R-PbO 2 system is transformed to a cubic phase, which was assigned as the fluorite-type structure. Suito et al. 14 synthesized the high-pressure phase (orthorhombic) of SnO 2 in a dense form at 15.8 GPa and 1073 K. Kusaba et al. 18 reported a mechanism for the shock-induced phase transitions from rutile to fluorite-type and then to the R-PbO 2 type structures. While performing cubic SnO 2 room-temperature compression of SnO 2 to 49 GPa, Haines and Leger 7 observed three structural phase transitions with increasing pressure, from its most stable tetragonal rutile-type phase, to the orthorhombic CaCl 2 -type phase at 11.8 GPa under hydrostatic conditions, and to the R-PbO 2 -type phase at 12 GPa under non-hydrostatic conditions, obtaining only a small amount of the latter. Then, both R-PbO 2 and CaCl 2 -type phases were transformed to a cubic modified fluorite-type phase at 21 GPa. They also reported that the cubic phase was actually a pyrite-type structure, with space group Pa3 h, not only in the case of SnO 2 but in other metal dioxides as well. 6,7 Ono and colleagues 8,9 have carried out high pressure- temperature (P-T) studies on SnO 2 using the diamond cell and a large-volume press to ∼30 GPa and 1500 K to investigate the transformations to the R-PbO 2 -type and the pyrite-type phases. The transition from the rutile to the CaCl 2 -type structures was observed for SnO 2 19 by using Brillouin and Raman scattering spectroscopy to pressures of 30 GPa at ambient temperatures. Recently, Shieh et al., 20 by means of X-ray diffraction analysis, have demonstrated the existence of four phase transitions (following the sequence rutile, CaCl 2 -type, pyrite-type, ZrO 2 -type, and cotunnite-type) during compression and heating of SnO 2 to 117 GPa. The studies of pressure-induced phase transitions have been enabled by remarkable advances in techniques of crystallography that are carried out in situ under high-pressure conditions. First- principles calculations 21 can become a powerful complement to experimental techniques to provide detailed structural infor- mation and to understand, at the atomic level, phenomena such as polymorphism and pressure-induced transformations. The validity of the theoretical studies has been demonstrated. 22-27 To the best of our knowledge there is only one recent theoretical work based on DFT with the FP-LAPW method, which only explores two structural phase transitions in SnO 2 with increasing pressure, from the rutile to the CaCl 2 -type phase and to the cubic Pa3 h phase. 28 Although detailed knowledge has been accumulated on the high-pressure behavior of SnO 2 , the transformation pathways between its high-pressure structures remain an issue of debate. 9,20 In this paper, on the basis of quantum chemical simulations, we provide the first systematic study on the structural and the electronic aspects of high-pressure polymorphs of SnO 2 , as an alternative to experimental techniques. To obtain more insights * To whom correspondence should be addressed. E-mail: beltran@uji.es. 6479 J. Phys. Chem. B 2007, 111, 6479-6485 10.1021/jp067443v CCC: $37.00 © 2007 American Chemical Society Published on Web 05/22/2007