D Simeone et al. / Nucl. Instr. and Meth. in Phys. Res. B 250(2006 )95-100 the irradiation by low energy ions, displacement cascades occur. They produce point defects in the target. A balance between production and recombination of point defects occurs leading to a non-equilibrium defect population. At lution of the population of each defect $[17] d d=(vnoa-4Tr Nb a,5)-4 NDoe g722 where is the ions flux, ad the displacement cross section, n he collision efficiency, re the capture radius, N the number of atoms per unit volume in the samples, b the mean free length associated with recombination collision sequencies 101.52.02.530354.0455.05.560 CS), o, is the RCS cross section [2] and Do the diffusion coefficient of these defects in the target The concentration of defects after irradiation at low Fig 4. Evolution of the Kubelka-Munk function AF(R)as a function of temperature, i.e. where the atomic diffusion can be the photon energy for difierent samples of pure zirconia irradiated by 400 Xe ions at different fluences at room temperature (5x 10cm squares, eglected, is controlled by the first term. The second term 10 triangle). The peak near 2.55ev is identified with Fa color drives the thermal migration of defects. centers [20] Since the experiments were performed at room tempera ture, atomic diffusion can be neglected. Only the first term of Eq(3)has to be taken into account to model the behav s (p)=s tanh(4ItreNb-5) lour of the irradiated samples. In the most general case, an equation of this type must be solved for each kind of s defect. and it is then crucial to determine which kind of 4πrNbσ defect occurs in the material where t is the fluence, t the irradiation time, the As the thickness of damaged areas is relatively small flux. The asymptotic non-equilibrium concentration of de (around 0.5 um for low energy Xe), usual volume tech- fects s does not depend on niques, like NMR, EPR or optical absorption, are not While the diffuse reflexion experiments are sensitive to $ efficient. Nevertheless, optical spectroscopy in diffuse diffraction is sensitive to the symmetry change. Since the reflection mode [18] is very sensitive to the irradiated penetration of low energy ions is very small, we have to volume near the sample surface, and it is an efficient way enhance the response coming from the volume where this to probe the existence of these defects transformation occurs. Therefore, a grazing X-ray diffrac- Different diffuse reflectance spectra were thus collected tion setup [5] was used to probe specifically the irradiated ent fluences. From these experimental results, it is possible zirconia, irradiated at various fluences, were studied to sug to obtain the Kubelka-Munk function, F(R), which is pro- gest a direct relation between the defect concentration and portional to the optical absorption coefficient [18]. In all the observed volumic fraction, Vn, of the tetragonal phase cases,we have recorded the spectra, the non-irradiated Only two phases, the monoclinic and the tetragonal mple being the reference. This allows us to identify pre- ones, were observed in the irradiated samples. The lattice cisely the nature of point defects induced by irradiation. parameters of the tetragonal phase at all fluences for Fig 4 displays AF(R)versus the photon energy for different 400 keV Xe ions were fluence independent. These values irradiated samples. All samples present the same shape for (a,=5.13 A and c,=5.165 A) can be conveniently com- the AF(R) function: a single maximum is observed at about pared to those already measured in zirconia nanocrystals 2.55 eV which is the characteristic signature of Fa colour [16]. From these results, the estimated size of the tetragonal centers [19] already observed in yttria stabilized zirconia domains is about 7 nm. Rietveld refinements of these pat (YSZ) single crystals. These Fa centers, consisting of simple terns do not show any significant change of the position anionic vacancies, are electrically charged and responsible of the refined coordinates zr(O)of the O atom for different for the local strain field as observed in YSZ [20] irradiation fluences. The tetragonal structures of micromet- This analysis suggests that only one kind of defect is ric, nanometric and irradiated ZrO2 are then isostructural produced during the irradiation of zirconia and, conse- Fig. 5 gives the evolution of the tetragonal phase as a quently, only a single(Eq.(3))is necessary to quantify function of the fluence for Xe(400 keV) ions. At high flu- the evolution of defect concentration as a function of the ence. a saturation effect is also observed. because the sizes ion fluence. The analytical solution of Eq (3)at low tem- of the domains associated with the tetragonal phase do not perature IS. evolve versus the fluence. it is reasonable to assume that thethe irradiation by low energy ions, displacement cascades occur. They produce point defects in the target. A balance between production and recombination of point defects occurs leading to a non-equilibrium defect population. At low flux, the following rate equation, taking into account well known recombination processes [2], describes the evo￾lution of the population of each defect n [17]: dn dt ¼ ðgrd 4prcNb2 rrn2 Þ/ 4prcND0e E kBT n2 ; ð3Þ where / is the ions flux, rd the displacement cross section, g the collision efficiency, rc the capture radius, N the number of atoms per unit volume in the samples, b the mean free length associated with recombination collision sequencies (RCS), rr is the RCS cross section [2] and D0 the diffusion coefficient of these defects in the target. The concentration of defects after irradiation at low temperature, i.e. where the atomic diffusion can be neglected, is controlled by the first term. The second term drives the thermal migration of defects. Since the experiments were performed at room tempera￾ture, atomic diffusion can be neglected. Only the first term of Eq. (3) has to be taken into account to model the behav￾iour of the irradiated samples. In the most general case, an equation of this type must be solved for each kind of defect, and it is then crucial to determine which kind of defect occurs in the material. As the thickness of damaged areas is relatively small (around 0.5 lm for low energy Xe), usual volume tech￾niques, like NMR, EPR or optical absorption, are not efficient. Nevertheless, optical spectroscopy in diffuse reflection mode [18] is very sensitive to the irradiated volume near the sample surface, and it is an efficient way to probe the existence of these defects. Different diffuse reflectance spectra were thus collected on various zirconia samples irradiated by Xe ions at differ￾ent fluences. From these experimental results, it is possible to obtain the Kubelka–Munk function, F(R), which is pro￾portional to the optical absorption coefficient [18]. In all cases, we have recorded the spectra, the non-irradiated sample being the reference. This allows us to identify pre￾cisely the nature of point defects induced by irradiation. Fig. 4 displays DF(R) versus the photon energy for different irradiated samples. All samples present the same shape for the DF(R) function: a single maximum is observed at about 2.55 eV which is the characteristic signature of Fa colour centers [19] already observed in yttria stabilized zirconia (YSZ) single crystals. These Fa centers, consisting of simple anionic vacancies, are electrically charged and responsible for the local strain field as observed in YSZ [20]. This analysis suggests that only one kind of defect is produced during the irradiation of zirconia and, conse￾quently, only a single (Eq. (3)) is necessary to quantify the evolution of defect concentration as a function of the ion fluence. The analytical solution of Eq. (3) at low tem￾perature is: nðUÞ ¼ n1 tanhð4prcNb2 rr rd n1UÞ; n1 ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi grd 4prcNb2 rr r ; ð4Þ where U = /s is the fluence, s the irradiation time, / the flux. The asymptotic non-equilibrium concentration of de￾fects n1 does not depend on /. While the diffuse reflexion experiments are sensitive to n, diffraction is sensitive to the symmetry change. Since the penetration of low energy ions is very small, we have to enhance the response coming from the volume where this transformation occurs. Therefore, a grazing X-ray diffrac￾tion setup [5] was used to probe specifically the irradiated volume near the sample surface. Different samples of pure zirconia, irradiated at various fluences, were studied to sug￾gest a direct relation between the defect concentration and the observed volumic fraction, Vt, of the tetragonal phase. Only two phases, the monoclinic and the tetragonal ones, were observed in the irradiated samples. The lattice parameters of the tetragonal phase at all fluences for 400 keV Xe ions were fluence independent. These values (at = 5.13 A˚ and ct = 5.165 A˚ ) can be conveniently com￾pared to those already measured in zirconia nanocrystals [16]. From these results, the estimated size of the tetragonal domains is about 7 nm. Rietveld refinements of these pat￾terns do not show any significant change of the position of the refined coordinates zt(O) of the O atom for different irradiation fluences. The tetragonal structures of micromet￾ric, nanometric and irradiated ZrO2 are then isostructural. Fig. 5 gives the evolution of the tetragonal phase as a function of the fluence for Xe (400 keV) ions. At high flu￾ence, a saturation effect is also observed. Because the sizes of the domains associated with the tetragonal phase do not evolve versus the fluence, it is reasonable to assume that the Fig. 4. Evolution of the Kubelka–Munk function DF(R) as a function of the photon energy for different samples of pure zirconia irradiated by 400 Xe ions at different fluences at room temperature (5 · 1015 cm2 squares, 1016 cm2 triangle). The peak near 2.55 eV is identified with Fa color centers [20]. 98 D. Simeone et al. / Nucl. Instr. and Meth. in Phys. Res. B 250 (2006) 95–100