Structural mechanism leading to a ferroelastic glass state: Interpretation of amorphization under pressure Pierre Tolédano 1 and Denis Machon 2 1 Group “Structure of Materials under Extreme Conditions,” Swiss-Norwegian Beam Lines at ESRF, BP 220, F-38043 Grenoble, France 2 Christopher Ingold Laboratories, University College London, 20 Gordon Street, WC1H 0A3 London, Great Britain sReceived 30 September 2004; published 31 January 2005d The concept of a ferroelastic glass, the mechanical analog of dipole and spin glasses, is introduced. The structural mechanism leading to a ferroelastic glass state, which is formed by a distribution of randomly oriented nanoscale ferroelastic domains, is described and justified theoretically. It is shown to provide a consistent interpretation of the amorphization under pressure of a number of materials, such as Cs 2 HgBr 4 , a-quartz, and ice, and a coherent link between previous models of pressure-induced amorphization. It also clarifies the microstructural properties disclosed in some ferroelectric relaxors. DOI: 10.1103/PhysRevB.71.024210 PACS numberssd: 61.43.Fs, 62.50.1p, 75.30.2m I. INTRODUCTION Ferroelastic transitions are those structural transitions which give rise to a spontaneous strain, 1 the ferroelastic state being characterized by the existence of ferroelastic domains which differ by the components of the spontaneous strain tensor. 2 In this respect ferroelastic transitions are considered as the mechanical analogs of ferroelectric and ferromagnetic transitions which give rise to ferroelectric and ferromagnetic domains corresponding, respectively, to different spontane- ous components of the dielectric polarization and magnetiza- tion. In this article we extend this analogy by showing that under certain conditions a ferroelastic transition can result into the formation of a ferroelastic glass, formed by a ran- dom distribution of randomly oriented nanoscale ferroelastic domains, which constitutes the analog of dipole 3 or spin 4 glasses. In Sec. II we describe the mechanism leading to the formation of a ferroelastic glass from a crystalline paraelastic phase and give a theoretical justification of its stability. We then show sSec. IIId that the preceding mechanism provides a consistent interpretation of the pressure-induced amorphiza- tion observed in a number of materials. 5,6 In Sec. IV, we show that the structural properties observed in the disordered state of some classes of ferroelectric relaxors 7 can also be understood by assuming the formation of a ferroelastic glass state. II. PARAELASTIC-FERROELASTIC GLASS TRANSITION A. Symmetry basis of the ferroelastic glass concept Let us first describe the conditions required for the forma- tion of a ferroelastic glass using as an example a crystalline material which undergoes a paraelastic-ferroelastic transition from an orthorhombic smmmd to a monoclinic s2/ md struc- ture. The monoclinic structure can be realized into three en- ergetically unequivalent crystallographic configurations with the point groups 2 x / m x ,2 y / m y , and 2 z / m z , displaying the spontaneous shear strain component e yz , e xz , and e xy , respec- tively. Each configuration gives rise to two energetically equivalent ferroelastic domains transforming into one an- other by the symmetry operations lost at the transition fFig. 1sadg. If close to the transition an internal stress field is cre- ated in the material corresponding to a stress tensor having nonzero shear stresses components s yz , s xz , and s xy , it may have two different effects: s1d A crystal phase can form which has the most stable monoclinic configuration. s2d A different situation can occur consisting in the formation of a “frustrated” multidomain state in which the six monoclinic domains induced by the stress field take place simulta- neously. Structural mismatches between adjacent differently sheared domains give rise to local distortions and to a dislo- cation array that produce a splitting of the mesoscopic-size domains and their progressive disintegration into nan- odomains fFig. 1sbdg. Orientational fluctuations of the do- mains, due to the decoupling of the proper system of coor- dinates of the internal-stress field tensor with the crystal system of coordinates, lead ultimately to a distribution of randomly oriented nanoscale ferroelastic domains that ap- pears at the length scale of x-ray diffraction experiments as a glassy state. Generalizing, instead of a ferroelastic crystal phase, a fer- roelastic glass may form in a crystalline material under the following conditions: sid The ferroelastic structure can exist in crystallographic configurations corresponding to different spontaneous strain components. siid An internal stress field is created involving the stress components conjugated to the preceding strains and inducing sufficiently large mismatches between the differently sheared domains, which leads to a splitting and disintegration of the mesoscopic-size domains into nanodomains, destroying the long-range order in the crystal. The description of a ferroelastic glass as formed by an inhomogeneous assembly of nanoscale ferroelastic domains implies that although the long-range order is lost in the crys- tal a local order persists in homogeneous single- sor energeti- cally compatibled domain crystallites, with length scales in the range 1 – 100 nm, in which a translational order is pre- served. From one crystallite to another the translational sym- metry varies inhomogeneously with discontinuities in the crystal lattice, giving rise to local distortions and to a dislo- PHYSICAL REVIEW B 71, 024210 s2005d 1098-0121/2005/71s2d/024210s10d/$23.00 ©2005 The American Physical Society 024210-1