D Simeone et al. /Nucl. Instr. and Meth. in Phys. Res. B 250(2006 )95-100 transition, the structural behavior of different nanocrystals of zirconia were studied. From this analysis, it seems clear that only a single order parameter controls the phase tran sition. All these facts explain the monoclinic to tetragonal phase transition observed in pure zirconia samples exposed to radiation damage, pointing out the key role of defect created by the radiation exposure and the way they couple to order parameters to induce the monocline to tetragonal phase transition 50472 2. The monoclinic to tetragonal phase transition of zirconia Zirconia undergoes two successive phase transitions on cooling. The former transition occurs at about 2573 K and it is second order or weakly first order [10, 11. The ubic structure becomes tetragonal(P42/nmc)and it is characterized in particular by the onset of a shear strain along the fourfold axis; the coordination polyhedron for Zr in the ideal fluorite structure(Zros unit) is only slightly modified On the other hand, the second phase transition, occurring at about 1330 K on cooling and at about 0.348 500 K on heating, involves important variations of unit 200400 00800100012001400 cell parameters. This transition, associated with an impor- tant volume change, is strongly first order. To understand Fig. 1. Variation of the coordinate of oxygen atoms along the the monoclinic to tetragonal phase transition versus tem- direction (squares)in the m These atomic displacements perature, we have collected several high resolution neutron the Landau framework of phase mperature as expected within difiraction patterns at different temperatures above and (Tc=1500K) below the tetragonal to monoclinic transition. These dia grams were analysed with the rietveld method to extract the behaviour of the structural parameters and to describe their evolution in the framework of the Landau theory of phase transition. Since neutron scattering lengths for O (bo= 5.80 fm)and Zr atoms (bzr=7.16 fm)are of the same order, the accuracies on the structural parameters for all atoms are better than those obtained from X-ray dif- fraction [12, 13] Only the tetragonal and the monoclinic phases were used to index all peaks of the diffraction patterns in the investigated temperature range. The anisotropic mean square displacements of Zr and O atoms associated to the tetragonal phase as well as atomic displacements of Zr and O atoms in the monoclinic phase(Fig. 1)display a square root evolution versus temperature. Moreover,an mportant strain field associated to the evolution of the monoclinic angle B versus the temperature(Fig. 2)appears during the phase transition. From these experimental facts, is possible to discribe this displacive phase transition ithin the Landau theory framework. The mechanism associated to the tetragonal to monoclinic phase transition is the softening of two phonon modes coupled with a strain 006008001000120 field, as expected for displacive phase transitions. The use T。T)(K of the group theory permits us to build a Landau free energy to describe all the possible couplings between these Fig. 2. Evolution of the monoclinic angle, i.e. the strain field, as a function phonon modes-the primary order parameters -and the of temperature(square points and open dots are collected during heating strain field - the secondary order parameter during th as expected within the Landau framework of phase transitions hase transition [14] (Te=1500K)transition, the structural behavior of different nanocrystals of zirconia were studied. From this analysis, it seems clear that only a single order parameter controls the phase tran￾sition. All these facts explain the monoclinic to tetragonal phase transition observed in pure zirconia samples exposed to radiation damage, pointing out the key role of defects created by the radiation exposure and the way they couple to order parameters to induce the monoclinc to tetragonal phase transition. 2. The monoclinic to tetragonal phase transition of zirconia versus temperature Zirconia undergoes two successive phase transitions on cooling. The former transition occurs at about 2573 K and it is second order or weakly first order [10,11]. The cubic structure becomes tetragonal (P42/nmc) and it is characterized in particular by the onset of a shear strain along the fourfold axis; the coordination polyhedron for Zr in the ideal fluorite structure (ZrO8 unit) is only slightly modified. On the other hand, the second phase transition, occurring at about 1330 K on cooling and at about 1500 K on heating, involves important variations of unit cell parameters. This transition, associated with an impor￾tant volume change, is strongly first order. To understand the monoclinic to tetragonal phase transition versus tem￾perature, we have collected several high resolution neutron diffraction patterns at different temperatures above and below the tetragonal to monoclinic transition. These dia￾grams were analysed with the Rietveld method to extract the behaviour of the structural parameters and to describe their evolution in the framework of the Landau theory of phase transition. Since neutron scattering lengths for O (bO = 5.80 fm) and Zr atoms (bZr = 7.16 fm) are of the same order, the accuracies on the structural parameters for all atoms are better than those obtained from X-ray dif￾fraction [12,13]. Only the tetragonal and the monoclinic phases were used to index all peaks of the diffraction patterns in the investigated temperature range. The anisotropic mean square displacements of Zr and O atoms associated to the tetragonal phase as well as atomic displacements of Zr and O atoms in the monoclinic phase (Fig. 1) display a square root evolution versus temperature. Moreover, an important strain field associated to the evolution of the monoclinic angle b versus the temperature (Fig. 2) appears during the phase transition. From these experimental facts, it is possible to discribe this displacive phase transition within the Landau theory framework. The mechanism associated to the tetragonal to monoclinic phase transition is the softening of two phonon modes coupled with a strain field, as expected for displacive phase transitions. The use of the group theory permits us to build a Landau free energy to describe all the possible couplings between these phonon modes – the primary order parameters – and the strain field – the secondary order parameter – during the phase transition [14]. Fig. 1. Variation of the fractional coordinate of oxygen atoms along the z direction (squares) in the monoclinic phase. These atomic displacements follow a square root law (solid line) versus temperature as expected within the Landau framework of phase transitions (Tc = 1500 K). Fig. 2. Evolution of the monoclinic angle, i.e. the strain field, as a function of temperature (square points and open dots are collected during heating and cooling respectively). This angle follows a square root law (solid line) as expected within the Landau framework of phase transitions (Tc = 1500 K). 96 D. Simeone et al. / Nucl. Instr. and Meth. in Phys. Res. B 250 (2006) 95–100