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Irreversibility of the Pressure-Induced Phase Transition of Quartz and the Relation Between Three Hypothetical Post-Quartz Phases

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Irreversibility of the Pressure-Induced Phase Transition of Quartz and the Relation Between Three Hypothetical Post-Quartz Phases PHYSICAL REVIEW B 70, 224101 (2004) Irreversibility of the pressure-induced phase transition of quartz and the relation between three hypothetical post-quartz phases Carlos Campañá and Martin H. Müser Department of Applied Mathematics, University of Western Ontario, London, Ontario N6A 5B7, Canada John S. Tse Steacie Institute for Molecular Sciences, National Research Council of Canada, Ottawa, Ontario K1A 0R6, Canada Daniel Herzbach and Philipp Schöffel Institut für Physik, WA 331, Johannes Gutenberg-Universität, 55099 Mainz, Germany (Received 9 June 2004; published 1 December 2004) Our atomistic computer simulations mainly based on classical force fields suggest that the pressure-induced transition from ␣ quartz to quartz II at 21 GPa is irreversible. While quartz II is ferroelastic in principle, the transition itself is coelastic, as the shape of the newly formed crystal is determined by the handedness of ␣-quartz. Upon releasing the pressure, our model quartz II remains stable down to 5 GPa, where it undergoes an isosymmetric transformation into a less dense polymorph. If the classical force field model of quartz II is compressed quickly to 50 GPa, a yet different post-quartz polymorph results, which can probably best be described as an incommensurate modulation of the quartz II structure. We discuss the equation of state and the thermomechanical stability of all four phases. One of the post-quartz phases can be switched elastically by shear between two symmetrically equivalent shapes; however, ␣-quartz appears as an intermittent phase. DOI: 10.1103/PhysRevB.70.224101 PACS number(s): 61.50.Ks, 81.30.Hd I. INTRODUCTION at the K point seems established, the extent with which quartz softens has been a matter of a recent controversy.8–10 ␣-quartz (also called low quartz and quartz I) is the most Experiments8 found that quartz softens considerably less ͑ ͒ stable silica SiO2 polymorph at ambient conditions. It be- with increasing pressure than predicted theoretically. How- comes unstable when subjected to large external pressures ever, it was argued that the discrepancy between experiment P.1–3 When P is increased quickly at room temperature, and simulation were due to an inconsistent use of stability quartz I transforms into a disordered solid at about 22 GPa. criteria.9 The determination of mechanical stability is a However, when P is increased sufficiently slowly, quartz I subtle issue at nonzero stresses, because the definition of transforms into a new crystalline phase called quartz II. This elastic constants is not unique in that case.11,12 ͑ ͒ transition also occurs at a pressure PI!II T=300K Another conclusion of Ref. 8 was challenged: namely, Ϸ22 GPa.4,5 the classification of the pressure-induced phase transforma- Due to silica’s commercial applications and its abundance tion as ferroelastic.13 A crystal is called ferroelastic when it is in nature, there is a lot of interest in understanding the prop- able to switch its shape if a sufficiently large elastic force is erties and the phase transformations of silica in general and applied to it. This implies broken symmetry related to a of quartz in particular. Concerning the pressure-induced spontaneous distortion of the crystal analogous to a ferro- phase transformation, there are at least three unsettled ques- magnet’s spontaneous magnetization. However, it may well tions. (i) What is the mechanism that drives the transition be that the I!II transition itself is not involved in the sym- from ␣-quartz to quartz II and is the transition ferroelastic? metry breaking. In that case, there would be a shape change (ii) Does quartz II convert back to ␣-quartz when the pres- associated with the transition without shape-related symme- sure is released? (iii) What is the relation between the re- try breaking. Consequently, the phase transformation would cently identified metastable post-quartz6 and quartz I and II? have to be classified as coleastic.14 Before presenting our computational methods and results, we Issue (ii) arises from electron diffraction patterns of de- will discuss these three issues in more detail. compressed quartz II.4 In their work, Kingma et al. reported Issue (i): The pressure-induced instability of ␣-quartz and that “…the high-pressure phase reverts to quartz or a quartz its concurrent densification was predicted theoretically1,2 and like material, upon decompression. Faint, yet distinct non- observed experimentally3,4 a little more than a decade ago. quartz intensities are detected along various reciprocal lattice The theoretical analysis suggested that the elastic constants directions between primary quartz spots….” The analysis of ␣ of -quartz become soft as PI!II is approached. However, it Raman spectra of decompressed quartz led the authors to was concluded that the transition is driven by an instability at conclude that a decompression transition from the new crys- the K point, which is not in the center of the Brillouin zone.2 talline phase to a twinned quartzlike structure occurs.4 The The microscopic parameters driving such transitions can true structure remains yet to be determined. soften the acoustic modes with which they are associated, Question (iii) is related to issue (ii). Haines et al.6 identi- but not necessarily up to zero.7 While the onset of instability fied a new stable silica polymorph after decompressing a 1098-0121/2004/70(22)/224101(6)/$22.50224101-1 ©2004 The American Physical Society CAMPAÑÁ et al. PHYSICAL REVIEW B 70, 224101 (2004) sample from 45 GPa to ambient conditions. The high- pressure sample was obtained from shock-compressing quartz II. Moreover, one year before those experiments, one of the present article’s authors15 found evidence for a new post-quartz phase resulting from decompressing quartz II. However, these results have not yet been supported by ab initio calculations. In this paper, we intend to address these three central questions. For this purpose, we employ molecular dynamics (MD) simulations based on the model potential suggested by van Beest, Kramer, and van Santen16 (BKS). Some results will be checked with an alternative model potential devel- oped recently by Tangney and Scandolo,17 as well as by ab initio calculations. FIG. 1. Equation of state at room temperature for three quartz species. The arrows mark possible phase transformation paths. II. METHODS Dashed lines are drawn to guide the eye. Open symbols are results from ab initio simulations. The BKS potential is one of the model potentials18,19 that have proved particularly useful in simulating various silica polymorphs in general20 and elastic properties—for example voked via a small pressure change. We run this number of at the transition between ␣- and ␤-quartz, in particular.21 replica to (statistically) explore the effect of handedness on Anharmonic effects at low temperatures,22 pressure-induced the shape of the new pressure-induced crystalline phase. ␣ We also rerun some of our simulations with an alternative distortion of SiO4 tetrahedral units in -quartz under 5 23 force field that was recently developed by Tangney and pressure, and the properties of disordered silica melts are 17 also reproduced reasonably well with the BKS potential. Scandolo (TS). The TS potential does not only contain Unless noted otherwise, all MD simulations are per- two-body interactions, but it also includes inducible dipoles formed at room temperature and at constant external, isotro- on the oxygen atoms and thus has the ability to incorporate effectively many-body effects. A detailed study of the TS pic stress, which means that shape and size of the simulation 25 cell are variable. Initial configurations consist of single crys- potential will be presented elsewhere. At this point, we ␣ may comment that the TS potential gives excellent agree- tals of -quartz composed of 720 SiO2 units. One initial configuration corresponded to left-handed ␣-quartz, the other ment with experimental data for all quantities and phases that ␣ were tested. initial configuration to right-handed -quartz. The crystal 26 axis at zero pressure corresponds to a, b, and cϷ29.8, 34.5, Last, ab initio calculations using the VASP code were and 27.3 Å, respectively. Time steps are 1 fs long, and employed in order to ensure the reliability of our conclu- 10 000 steps are usually discarded for equilibration. Here sions. Full geometry optimizations were made of the MD- predicted unit cell structures. The projected-augmented-wave 50 000 time steps are retained for observation. The equations 27 of motion were thermostated using a Langevin thermostat (PAW) pseudopotentials provided in the library for Si and with coupling ␥=4 THz. This limits the resolution of dy- O were used in these calculations. namical data to a little less than ␦␯Ϸ1 THz. The Parrinello-Rahman method was used for the box dynamics.24 We ensured good thermal averages of the strain III. RESULTS fluctuations by coupling the geometry of the cell to a sto- A. Phase transformations and equation of state ␥ chastic thermostat box of a slightly smaller value than that ␥ Ϸ␥ for the particles—to be specific, typically box /2. The The equation of state resulting from the simulations are box inertia W was chosen small—i.e., so small that the fluc- shown in Fig. 1. We start at P=0 GPa with an ideal ␣-quartz tuations of the box shape occurred on time scale barely larger configuration, increase P gradually to 28 GPa, and go back than those of the particles. A similar procedure resulted in to zero pressure. On increasing pressure, ␣-quartz transforms excellent values for elastic constants of ␣ and ␤ quartz in into quartz II at P=21.7 GPa, in agreement with experimen- previous work.21 We want to point out at this point that tal observations4 and previous molecular dynamics simula- choosing small box inertia W was important to invoke the tion studies.28,29 An interesting observation is that the shape pressure-induced crystal-crystal transitions.
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