Low-dimensional sublattice melting by pressure: Superionic conduction in the phase interfaces of the fluorite-to-cotunnite transition of CaF 2 Salah Eddine Boulfelfel, Dirk Zahn, Oliver Hochrein, Yuri Grin, and Stefano Leoni* Max-Planck-Institute for Chemical Physics of Solids, Nöthnitzer Str. 40, D-01187 Dresden, Germany Received 19 May 2006; published 28 September 2006; corrected 29 September 2006 The pressure-induced phase transformation of calcium fluoride CaF 2  from the cubic-fluorite-type structure Fm3 ¯ m to the orthorhombic cotunnite PbCl 2  type structure  Pnma is investigated from transition path sampling molecular dynamics simulations. Starting from an artificially prepared transformation route connect- ing fluorite to cotunnite, subsequent trajectory rectification evolved to a distinct picture of the favored mecha- nism. The latter is characterized by nucleation and growth of the new phase. The overall transformation mechanism was identified as a symmetry-lowering step from the cubic to the orthorhombic atomic configura- tion which is caused by the reorganization of one half of the octahedral voids. At the interface between the cubic and the orthorhombic structure, a pressure-induced local melting of the fluoride sublattice is observed. This produces defects that allow for the reorganization of the calcium sublattice which eventually leads to the recrystallization of the fluoride ions fixating one of the stable structures. Variation of the thermodynamic parameters shows that the mechanism is conserved over the experimentally relevant range, however with an increasing tendency towards incomplete transformation on lowering the temperature, in accordance with experiments. DOI: 10.1103/PhysRevB.74.094106 PACS numbers: 64.70.Kb, 02.70.Ns, 07.05.Tp, 61.50.Ks INTRODUCTION Transformation processes between liquid and solid phases are phenomena of central importance in nature. The most fundamental transition of this kind is represented by crystal- lization from the melt. While this is one of the main synthetic pathways in solid state synthesis, a more peculiar phenom- enon is reflected by superionic conductors, a fascinating blend of solid and liquid states that arises when only parts of a compound become liquid. In CaF 2 , the fluoride sublattice is well known to melt on raising temperature. The present work is aimed at demonstrating pressure as an important thermo- dynamic variable governing sublattice melting in CaF 2 . Re- cently, the tremendous technological potential of ion con- ducting materials based on distinct transport effects in interface regions has been reviewed. 1 Inspired by these stud- ies we decided to explore the possible similarities between ion conduction in the interface region of CaF 2 -BaF 2 -CaF 2 sandwich structures 1 and phase fronts forming during pressure-induced structural transformations. The polymorphism of CaF 2 encompasses two fundamen- tal structural types, the low pressure face-centered cubic fluorite structure space group Fm3 ¯ m, for which CaF 2 is the prototype compound, and the high pressure PbCl 2 type for the orthorhombic polymorph cotunnite space group Pnma. 2,3 For salt-like compounds of composition AB 2 , these structures offer an attractive combination of a close- packed array of A atoms and interstitial sites of different coordination number available for atom B. In the fluorite structure the Ca ions are in a cubic close-packed ccp ar- rangement, the fluoride ions occupy all the tetrahedral inter- stitial sites. In the cotunnite structure, the array of A atoms is hexagonal close-packed hcp, 4 half of the fluoride ions ex- hibit tetrahedral coordination, the other half is placed off- center in the ideally octahedral voids of hcp, with fivefold coordination. Ca is eightfold coordinated in the fluorite struc- ture, while the coordination number increases to nine in the denser cotunnite structure. The fluorite and cotunnite struc- tures are also realized by the fluorides of the heavier alkaline-earth metals Sr, Ba. The series of high-pressure structures for AB 2 composition is enriched by a plethora of other phases like EuI 2 , -PbO 2 , on varying the halogen moi- ety, like in CaCl 2 , or in oxide compounds like ZrO 2 . Despite the chemical diversity of these compounds, the analogies in their high-pressure behavior, particularly the reappearance of the same atomic pattern among high-pressure polymorphs, hints at common features. Experimental investigations of the mechanistic details of pressure-induced reconstructive phase transitions are compli- cated by the first-order thermodynamics that often causes the destruction of the crystal. Furthermore, these processes dis- play a large pressure hysteresis. For CaF 2 , the fluorite-to- cotunnite phase transition occurs in the range 9.5– 20 GPa, 5 with the cotunnite phase retransforming to the fluorite phase on releasing pressure. The high-pressure polymorph can be quenched from higher temperature, 300 ° C, nonetheless the crystallinity of the obtained material is poor. 3 To shed light on the mechanism of the reconstructive phase transition we have performed isothermic-isobaric mo- lecular dynamics simulations within a recently implemented transition path sampling scheme. 6 The latter allows investi- gating the transformation at the phase coexistence condi- tions, and is particularly suited for observing phase nucle- ation and growth in solid state reconstructive phase transitions. The performance of our approach has been ex- tensively demonstrated for alkaline halogenides. 7–10 SIMULATION DETAILS The simulation scheme as it is described in Ref. 6 requires modeling of a first transition trajectory which is subsequently PHYSICAL REVIEW B 74, 094106 2006 1098-0121/2006/749/0941067 ©2006 The American Physical Society 094106-1