N. Nowruz correspondences A, B or C[12]. Experimental observations have established [13] that both lattice correspondences B (LCB)and C(LCC)can occur for t->m transforma- tion in ZrO -12 mole% CeO, with LCB being much more common. Two distinct rientation relationships have been identified [13, 14 between the m and t phases Expressed in a manner consistent with LCB, these are LCB-2 [001lm/100 [010Jm//00ll [010m/001L [100m go to [010J 001m~9to[00k ie.(100)m/(010 e.(001)m/(100h Two distinct orientation relationships have been observed which differ by a rotation of x9 about a common direction [010lm//001]t The orientation relationship LCB-l appears to be more common than the relationship LCB-2, so that the most equently observed combination is LCB-1 [15. The t-m transformation is important in understanding the mechanism of transformation strengthening and toughening in ceria-zirconia. Hugo and Muddle [15] applied the theory developed by Acton et al. [16] to the t-m transformation in ceria-zirconia. Hugo and Muddle [15] assumed the lattice-invariant strain (Lis) to be accommodated elastically and the elastic accommodation hypothesis was used instead of a Lis in their study. The predicted habit plane and orientation relationships were consistent with those observed experimentally In the present study, a detailed crystallographic analysis of the t-m martensitic transformation with the (101)[101]t LIS system in ZrO2-12 mole% CeO, has been performed by using both the infinitesimal deformation (ID)approach and Wechsler et al. [17(WLR) phenomenological theory. All crystallographic param- eters for LCB-l and LcB-2 obtained from the two theories have been discussed 2. Analysis The phenomenological crystallographic theory based on matrix algebra [17, 181 discusses the crystallographic and morphological aspects of a phase transformation with the assumption that the habit plane between parent and product phases unstrained and unrotated (the invariant-plane criteria). When such an invariant- plane condition is attained, the product phase becomes a plate-like shape and the elastic strain energy associated with the transformation is minimized to be zero [ 19] The phenomenological crystallographic theory considers that the shape change of a region before and after the transformation(the total shape deformation) is brought about by the combination of lattice deformation to change the lattice, rigid-body rotation and lattice-invariant deformation. The basic equation of phenomenological crystallographic theory is T= RBP where T is the total shape deformation, R a rigid-body rotation, B a lattice deforma tion and p a lattice-invariant strain. Several methods have been devised forcorrespondences A, B or C [12]. Experimental observations have established [13] that both lattice correspondences B (LCB) and C (LCC) can occur for t!m transforma￾tion in ZrO2-12 mole% CeO2, with LCB being much more common. Two distinct orientation relationships have been identified [13, 14] between the m and t phases. Expressed in a manner consistent with LCB, these are: Two distinct orientation relationships have been observed which differ by a rotation of
9 about a common direction [010]m//[001]t. The orientation relationship LCB-1 appears to be more common than the relationship LCB-2, so that the most frequently observed combination is LCB-1 [15]. The t!m transformation is important in understanding the mechanism of transformation strengthening and toughening in ceria-zirconia. Hugo and Muddle [15] applied the theory developed by Acton et al. [16] to the t!m transformation in ceria-zirconia. Hugo and Muddle [15] assumed the lattice-invariant strain (LIS) to be accommodated elastically and the elastic accommodation hypothesis was used instead of a LIS in their study. The predicted habit plane and orientation relationships were consistent with those observed experimentally. In the present study, a detailed crystallographic analysis of the t!m martensitic transformation with the (101)t [101]t LIS system in ZrO2-12 mole% CeO2 has been performed by using both the infinitesimal deformation (ID) approach and Wechsler et al. [17] (WLR) phenomenological theory. All crystallographic param￾eters for LCB-1 and LCB-2 obtained from the two theories have been discussed. 2. Analysis The phenomenological crystallographic theory based on matrix algebra [17, 18] discusses the crystallographic and morphological aspects of a phase transformation with the assumption that the habit plane between parent and product phases is unstrained and unrotated (the invariant-plane criteria). When such an invariant￾plane condition is attained, the product phase becomes a plate-like shape and the elastic strain energy associated with the transformation is minimized to be zero [19]. The phenomenological crystallographic theory considers that the shape change of a region before and after the transformation (the total shape deformation) is brought about by the combination of lattice deformation to change the lattice, rigid-body rotation and lattice-invariant deformation. The basic equation of phenomenological crystallographic theory is T ¼ RBP ð1Þ where T is the total shape deformation, R a rigid-body rotation, B a lattice deforma￾tion and P a lattice-invariant strain. Several methods have been devised for LCB-1 LCB-2 [001]m//[100]t [100]m//[010]t [010]m//[001]t [010]m//[001]t [100]m
9 to [010]t [001]m
9 to [100]t i.e. (100)m//(010)t i.e. (001)m//(100)t 540 N. Navruz