Y L Zhang et al. Acta Materialia 54(2006)1289-1295 and(2)the nucleation and growth of a tetragonal phase within the monoclinic phase △g(n⑧d+d⑧n), The stored elastic energy generated by the t-m trans- where e is the eigenstrain Ag and d are the magnitude and formation is crucial for the reverse transformation in the unit vector of the simple shear, respectively, and n is the 3Ce-0. 25Y-TZP. The elastic energy is reported to be normal to the habit plane. Thus, the resultant matrices of about 80% of the total energy to form a monoclinic eigenstrain corresponding to LCA, LCB and LCC are nucleus [35]. When a thermal stress-induced monoclinic 00.00090.0013 0.00060.00130.073 lath is not anchored by the grain boundary, the slow for- ward/backward motion of t/m interface(growth/receding 0.06720.0716 00.0009 of martensite) may be observed by careful adjustment of 0.0200 0.0478 the beam intensity. 0.04790.07330 This suggests that the stored energy in the matrix is ben- d 0.00060 eficial for the reverse martensitic transformation being one part of the driving force. In this case, the reverse transforma- tion can occur through the motion of the interface without a nucleation process. Therefore, the forward. backward and respectively, and the trace of the matrix refers to the vol- zero motion of the m/t interface can be manipulated by the ume strain of the transformation. When LCA is chosen the resultant strain is the largest, implying the probability increase,decrease or holding steady of the beam intensity. that Lca would be least in practice, since LCA has the In contrast a burst-like thermal stress-induced transforma- tion usually occurs in 8Ce-050Y-TZP. The martensites are worst mismatch among the three LCs. It is not surprising anchored by grain boundaries and the transformations in that the eigenstrain of LCC is almost the same as that of djacent re tris iggered. Here the reverse transforma- LCB because the values of am and bm are nearly identical tions cannot occur by simply decreasing the beam intensity indicating almost the same stored elastic strain energy. The because the stored energy is relaxed and the nucleation needs calculated magnitudes of LIS are 3.68%, 0.004% and an additional driving force 3.68% corresponding to LCA, LCB and LCC, respectively Similar phenomena are also found during thermal Since the simple shear is needed in the transformation, the cycles. When the foil is heated to 800C using the heater smaller the magnitude, the easier the transformation pro- instead of the electron beam, the majority of the m phase ceeds. Compared to lcC, LCB is therefore preferred be- undergoes an m t reverse transformation through nucle- cause of the smaller magnitude of the LIS, although two ation of the tetragonal phase for both 8Ce-025Y-TZP and LCs have the same resultant strain energy. In other words Ce-0.50Y-TZP. The reverse motion of the t/m interface LCB is the most favorable lc. while lca is unfavorable cannot be observed in several thermal cycles(heat- for the largest resultant strain energy ing cooling). This may be attributed to the homoge- neous stress distribution when using the heater in 6. Conclusions comparison with the local thermal stress generated by the electron beam. For Ce- TZP or Ce-Y-TZP, the thermally The t- m martensitic transformation in 8Ce-0.25Y induced transformations are also generally burst-like TZP and 8Ce-05Y-TZP zirconia-containing ceramics has released and the reverse transformation needs nucleation. The main conclusions are summarized as follows %e-s. 3,5], implying the occurrence of autocatalysis. This means been studied through in situ TEM observations and cI that the stored energy associated with thermal martensite is tallographic calculations by means of the WLR Therefore, the t/m interface of thermally induced martens ite cannot move backward, and an additional driving force (1) In situ tem observations show that the t/m interface has to be applied to trigger the reverse transformation can move freely with the change of thermal stress Moreover, a larger driving force usually implies a more generated by the beam illumination for Ce-Y-TZP, rapid movement of the t/m interface [36]. This is perhaps whereas this does not occur in thermal cycles the reason for not having observed the smooth motion of(2) The t-m transformation is suggested to be a semi- an athermal t/m interface in thermal cycles thermoelastic process rather than a thermoelastic one because there exist a large thermal hysteresis and a 5.3. Lattice correspondences high critical driving force and reversible motion of the t/m interface can occur only under thermal stress The LC most commonly observed in Ce-TZP is LCB, (3)The crystallography of the t-m martensitic trans- with less occurrence of LCC [24]. However, only LCB formation is calculated using the WlR theory. The was observed in Ce-Y-TZP in the present work. In order shape strain is insensitive to the Lis system and the to identify the possibility of three LCs, the crystallography calculated habit plane is(0.3100, 0.9507, O)t, which is calculated by assuming LCB, LCC and LCA. The eigen is in good agreement with the experimental result of strain resulting from a stress-free transformation can be (30)tIn Ce-Y-TZP, only lattice correspondence B expressed as: is found in this workand (2) the nucleation and growth of a tetragonal phase within the monoclinic phase. The stored elastic energy generated by the t ! m trans￾formation is crucial for the reverse transformation in 8Ce–0.25Y-TZP. The elastic energy is reported to be about 80% of the total energy to form a monoclinic nucleus [35]. When a thermal stress-induced monoclinic lath is not anchored by the grain boundary, the slow for￾ward/backward motion of t/m interface (growth/receding of martensite) may be observed by careful adjustment of the beam intensity. This suggests that the stored energy in the matrix is ben￾eficial for the reverse martensitic transformation being one part of the driving force. In this case, the reverse transforma￾tion can occur through the motion of the interface without a nucleation process. Therefore, the forward, backward and zero motion of the m/t interface can be manipulated by the increase, decrease or holding steady of the beam intensity. In contrast, a burst-like thermal stress-induced transforma￾tion usually occurs in 8Ce–0.50Y-TZP. The martensites are anchored by grain boundaries and the transformations in adjacent grain are triggered. Here the reverse transforma￾tions cannot occur by simply decreasing the beam intensity because the stored energy is relaxed and the nucleation needs an additional driving force. Similar phenomena are also found during thermal cycles. When the foil is heated to 800 C using the heater instead of the electron beam, the majority of the m phase undergoes an m ! t reverse transformation through nucle￾ation of the tetragonal phase for both 8Ce–0.25Y-TZP and 8Ce–0.50Y-TZP. The reverse motion of the t/m interface cannot be observed in several thermal cycles (heat￾ing M cooling). This may be attributed to the homoge￾neous stress distribution when using the heater in comparison with the local thermal stress generated by the electron beam. For Ce-TZP or Ce–Y-TZP, the thermally induced transformations are also generally burst-like [3,5], implying the occurrence of autocatalysis. This means that the stored energy associated with thermal martensite is released and the reverse transformation needs nucleation. Therefore, the t/m interface of thermally induced martens￾ite cannot move backward, and an additional driving force has to be applied to trigger the reverse transformation. Moreover, a larger driving force usually implies a more rapid movement of the t/m interface [36]. This is perhaps the reason for not having observed the smooth motion of an athermal t/m interface in thermal cycles. 5.3. Lattice correspondences The LC most commonly observed in Ce-TZP is LCB, with less occurrence of LCC [24]. However, only LCB was observed in Ce–Y-TZP in the present work. In order to identify the possibility of three LCs, the crystallography is calculated by assuming LCB, LCC and LCA. The eigen￾strain resulting from a stress-free transformation can be expressed as: e T ¼ 1 2 Dgðn  d þ d  nÞ; ð2Þ where e T is the eigenstrain, Dg and d are the magnitude and the unit vector of the simple shear, respectively, and n is the normal to the habit plane. Thus, the resultant matrices of eigenstrain corresponding to LCA, LCB and LCC are 0 0:0009 0:0013 0:0672 0:0716 0:0200 0 B@ 1 CA; 0:0006 0:0013 0:0733 0 0:0009 0:0478 0 B@ 1 CA and 0:0479 0:0733 0 0:0006 0 0 0 B@ 1 CA; respectively, and the trace of the matrix refers to the vol￾ume strain of the transformation. When LCA is chosen, the resultant strain is the largest, implying the probability that LCA would be least in practice, since LCA has the worst mismatch among the three LCs. It is not surprising that the eigenstrain of LCC is almost the same as that of LCB because the values of am and bm are nearly identical, indicating almost the same stored elastic strain energy. The calculated magnitudes of LIS are 3.68%, 0.004% and 3.68% corresponding to LCA, LCB and LCC, respectively. Since the simple shear is needed in the transformation, the smaller the magnitude, the easier the transformation pro￾ceeds. Compared to LCC, LCB is therefore preferred be￾cause of the smaller magnitude of the LIS, although two LCs have the same resultant strain energy. In other words, LCB is the most favorable LC, while LCA is unfavorable for the largest resultant strain energy. 6. Conclusions The t ! m martensitic transformation in 8Ce–0.25Y￾TZP and 8Ce–0.5Y-TZP zirconia-containing ceramics has been studied through in situ TEM observations and crys￾tallographic calculations by means of the WLR theory. The main conclusions are summarized as follows: (1) In situ TEM observations show that the t/m interface can move freely with the change of thermal stress generated by the beam illumination for Ce–Y-TZP, whereas this does not occur in thermal cycles. (2) The t ! m transformation is suggested to be a semi￾thermoelastic process rather than a thermoelastic one because there exist a large thermal hysteresis and a high critical driving force and reversible motion of the t/m interface can occur only under thermal stress. (3) The crystallography of the t ! m martensitic trans￾formation is calculated using the WLR theory. The shape strain is insensitive to the LIS system and the calculated habit plane is (0.3100, 0.9507, 0)t, which is in good agreement with the experimental result of (1 3 0)t. In Ce–Y-TZP, only lattice correspondence B is found in this work. 1294 Y.L. Zhang et al. / Acta Materialia 54 (2006) 1289–1295