N. Nowruz Table 4. The crystallographic parameters obtained from the application of the ID approach to the 1-m transformation in ZrO2-12 mole% Ceo Solutions LCB-1 LCB-2 Amount of Lis,g 0.0027 0.0027 Habit plane, h [0.3009,0.9536,0] [0.9958.0.0914,0] Total shape deformation [0.9999,0.0152,0] [0.2243.0.9745,0 Magnitude, m 0.1640 164 0.08° 8.73 8.87° [00l1^[010 0.08° 8.87° (010A(100 0.04° (001tA0010)m 0.07° Axial strain (% [00 4.94 0.24 1.46 [00lL 0.00 3. Conclusion a detailed crystallographic analysis of the tetragonal-to-monoclinic transformation has been performed on the basis of phenomenological crystallographic theory and the infinitesimal deformation approach in ceria-zirconia. Agreement between WLR theory and the ID approach is found to be excellent. As can be seen in tables 2 and 4, the differences are very small in both solutions. The orientation of the habit plane differs by only 0.07, the direction of the total shape deformation makes an angle of 0. 2. The difference in the orientation relationships is at most 0.01. There is no difference between the ID approach and WLR theory in the amount of LIs The difference in the axial strain is at most 0.05%. Therefore. the calculations certainly indicate that the ID analysis gives almost the same results as WlR theory Moreover, the orientation of the habit plane calculated from WLR theory is only 0.9 from(130) for LCB-I and 0. 1 from(11 1 0)t for LCB-2 The difference between WLR theory and experimental observation [15] in the orien relationships is at most 0. 2. The orientation relationships obtained from the ID approach differ from the exact rational relationships reported [15] by less than 0.20. The predicted habit plane orientation makes an angle of 0.9 with(130) for LCB-I and is only 0.050 from(11 1 0), for LCB-2 References [F.R. Chien, F.. Ubic, V Prakash and A H. Heuer, Stress-induced martensitic transforma tion and ferroelastic deformation adjacent microhardness indents in tetragonal zirconia ingle crystal. Acta Metall. 46 2151-2171(1998) 2 G. Xin, Low temperature st of cubic zirconia. Phys. Stat Sol. (a)177191-201( and R. Oberacker, Tetragonal-to-monoclinic phase transformation in CeOz-stabilized zirconia under multiaxial loading. J. Eur. Ceram Soc 22841-849(2002)3. Conclusion A detailed crystallographic analysis of the tetragonal-to-monoclinic transformation has been performed on the basis of phenomenological crystallographic theory and the infinitesimal deformation approach in ceria-zirconia. Agreement between WLR theory and the ID approach is found to be excellent. As can be seen in tables 2 and 4, the differences are very small in both solutions. The orientation of the habit plane differs by only 0.07 ; the direction of the total shape deformation makes an angle of 0.2 . The difference in the orientation relationships is at most 0.01 . There is no difference between the ID approach and WLR theory in the amount of LIS. The difference in the axial strain is at most 0.05%. Therefore, the calculations certainly indicate that the ID analysis gives almost the same results as WLR theory. Moreover, the orientation of the habit plane calculated from WLR theory is only 0.9 from (130)t for LCB-1 and 0.1 from (11 1 0)t for LCB-2. The difference between WLR theory and experimental observation [15] in the orientation relationships is at most 0.2 . The orientation relationships obtained from the ID approach differ from the exact rational relationships reported [15] by less than 0.2 . The predicted habit plane orientation makes an angle of 0.9 with (130)t for LCB-1 and is only 0.05 from (11 1 0)t for LCB-2. References [1] F.R. Chien, F.J. Ubic, V. Prakash and A.H. Heuer, Stress-induced martensitic transforma￾tion and ferroelastic deformation adjacent microhardness indents in tetragonal zirconia single crystal. Acta. Metall. 46 2151–2171 (1998). [2] G. Xin, Low temperature stability of cubic zirconia. Phys. Stat. Sol. (a) 177 191–201 (2000). [3] G. Rauchs, T. Fett, D. Munz and R. Oberacker, Tetragonal-to-monoclinic phase transformation in CeO2-stabilized zirconia under multiaxial loading. J. Eur. Ceram. Soc. 22 841–849 (2002). Table 4. The crystallographic parameters obtained from the application of the ID approach to the t!m transformation in ZrO2-12 mole% CeO2. Solutions LCB-1 LCB-2 Amount of LIS, g 0.0027 0.0027 Habit plane, h [0.3009, 0.9536, 0] [0.9958, 0.0914, 0] Total shape deformation Direction, d [0.9999, 0.0152, 0] [0.2243, 0.9745, 0] Magnitude, m 0.1640 0.1642 Orientation relationship [100]t^[001]m 0.08 8.73 [010]t^[100]m 8.87 0.19 [001]t^[010]m 0.08 0.08 (100)t^(001)m 8.87 0.21 (010)t^(100)m 0.04 8.73 (001)t^(010)m 0.07 0.07 Axial strain (%) [100]t 4.94 3.67 [010]t 0.24 1.46 [001]t 0.00 0.00 544 N. Navruz