Y L Zhang et al. Acta Materialia 54(2006)1289-1295 1291 The bright-field image in Fig. I(a)shows an thermally transformed grain in &Ce-0.25Y-TZP, and the indexed selected area difiraction pattern(Fig. 1(b) indicates that [0Ol] and(010) are parallel with [0 1O]m and (100) respectively. This reorientation relationship is called OR B2 [18, 19], i.e., (001)m(100) [100 m[o 101. The crystallog raphy of the martensitic transformation appears to be much different due to the addition of 0.25%Y,O3. Therefore, the lattice correspondence LCB and the CAB notation of Fig. 2. Schematic of Bain strain Hayakawa et al. in Ce-Y-TZP can be identified. The lattice parameters listed in Table I were extracted from X-ray dif- Table 2 fraction profiles by the least squares method. These values Calculated crystallographic results for the t-m martensitic are comparable with those reported for similar zirconia ceramIcs[9] with difference of±0.7%and<0.5° A standard orthogonal coordinate f illustrated in Fig. 2 0.000038 is established here to facilitate the calculations because the hree axes are not equal in tetragonal phase. From the Habit plane, N (0.3100,-0.9507,0) above information, the Bain matrix under the f base, fB/, Shape deformation matrix, F 0477-0.16150.0001 can be calculated as 00156709971-00003 00 1/am 0 Cm cosB\/00 1 0.00010.0003 100 010八(00 Cm sinB/(010 ever LIS system is selected, i.e., the magnitude of shape 00 cm sin B/a, 0 0 strain is insensitive to the Lis system 0 Cm cos B/a, am/at 0 The calculated results are shown in Table 2. One of the eigenvalues is equal to l, and the other two are larger and 0 bm/ct/ smaller than 1, respectively, satisfying the (1) distortion and no rotation of the invariant plane. The cal culated habit plane is(0. 3100, 0.9507, O)t for 8Ce-05Y where the first matrix on the right-hand side stands for the TZP. Meanwhile our TEM investigation shows the habit LC CAB plane for thermal stress-induced martensite is(130)t, the No experimental results have been obtained so far indi- details of which will be published elsewhere. The difference cating that the special LIS system occurs in zirconia-con- is only 1.05, which demonstrates that both the thermal aining ceramics [24]. For LCB, the match between bm stress-induced and athermal martensitic transformation and c axes is good. As a consequence, the Bain strain(plus obey the same crystallography and Wlr theory is suitable the rotation R) is an invariant plane strain. This means that to deal with the martensitic transformation in ternary the required LIS is very small. Hugo et al. [18, 19]even sug- Ce-Y-TZP ceramics gested that this small mismatch could be elastically accom- modated. and thus the lis is not needed. Therefore. as 4. In situ tem observations assumed in other studies of Ce-TZP [18, 19]. Y-TZP [15- 17] and Mg-PSZ [20, 22]. it is convenient to select a LIS sys- As measured by dilatometry, &Ce-0.50Y-TZP and 8Ce- tem of (10 It for Ce-Y-TZP. In fact, our calculated 0. 25Y-TZP exhibit Ms temperatures of -17 and 109C, results confirm that the solutions of the magnitude of sim- respectively, and therefore different microstructures are ple shear and shape strain remain almost invariant which- expected. Some tetragonal grains are present in &Ce- Table l Lattice constants of ZrO containing ceramics at room temperature Composition I Phase Lattice constant c(nm) 8Ce-0.50YTZP Tetragonal 0.51926 0.51946 Monoclinic 8Ce-025Y-TZP 0.51150 0.52099 12Ce-TZP 0.5217 0.5224 0.5203 0.5338 From Ref [19]The bright-field image in Fig. 1(a) shows an athermally transformed grain in 8Ce–0.25Y-TZP, and the indexed selected area diffraction pattern (Fig. 1(b)) indicates that [0 0 1]t and (010)t are parallel with [0 1 0]m and (1 0 0)m, respectively. This reorientation relationship is called OR￾B2 [18,19], i.e., (0 0 1)mi(1 0 0)t[1 0 0]mi[0 1 0]t. The crystallog￾raphy of the martensitic transformation appears to be much different due to the addition of 0.25% Y2O3. Therefore, the lattice correspondence LCB and the CAB notation of Hayakawa et al. in Ce–Y-TZP can be identified. The lattice parameters listed in Table 1 were extracted from X-ray dif￾fraction profiles by the least squares method. These values are comparable with those reported for similar zirconia ceramics [19] with difference of ±0.7% and <0.5. A standard orthogonal coordinate f illustrated in Fig. 2 is established here to facilitate the calculations, because the three axes are not equal in tetragonal phase. From the above information, the Bain matrix under the f base, fBf, can be calculated as fBf ¼ 001 100 010 0 B@ 1 CA am 0 cm cos b 0 bm 0 0 0 cm sin b 0 B@ 1 CA 001 100 010 0 B@ 1 CA 1 at 0 0 0 ct 0 0 0 ct 0 B@ 1 CA 1 ¼ cm sin b=at 0 0 cm cos b=at am=at 0 0 0 bm=ct 0 B@ 1 CA; ð1Þ where the first matrix on the right-hand side stands for the LC CAB. No experimental results have been obtained so far indi￾cating that the special LIS system occurs in zirconia-con￾taining ceramics [24]. For LCB, the match between bm and ct axes is good. As a consequence, the Bain strain (plus the rotation R) is an invariant plane strain. This means that the required LIS is very small. Hugo et al. [18,19] even sug￾gested that this small mismatch could be elastically accom￾modated, and thus the LIS is not needed. Therefore, as assumed in other studies of Ce-TZP [18,19], Y-TZP [15– 17] and Mg-PSZ [20,22], it is convenient to select a LIS sys￾tem of ð101Þ½1 0
1 t for Ce–Y-TZP. In fact, our calculated results confirm that the solutions of the magnitude of sim￾ple shear and shape strain remain almost invariant which￾ever LIS system is selected, i.e., the magnitude of shape strain is insensitive to the LIS system. The calculated results are shown in Table 2. One of the eigenvalues is equal to 1, and the other two are larger and smaller than 1, respectively, satisfying the condition of no distortion and no rotation of the invariant plane. The cal￾culated habit plane is (0.3100, 0.9507, 0)t for 8Ce–0.5Y￾TZP. Meanwhile, our TEM investigation shows the habit plane for thermal stress-induced martensite is (1 3 0)t, the details of which will be published elsewhere. The difference is only 1.05, which demonstrates that both the thermal stress-induced and athermal martensitic transformation obey the same crystallography and WLR theory is suitable to deal with the martensitic transformation in ternary Ce–Y-TZP ceramics. 4. In situ TEM observations As measured by dilatometry, 8Ce–0.50Y-TZP and 8Ce– 0.25Y-TZP exhibit Ms temperatures of 17 and 109 C, respectively, and therefore different microstructures are expected. Some tetragonal grains are present in 8Ce– Table 1 Lattice constants of ZrO2-containing ceramics at room temperature Composition Phase Lattice constant a (nm) b (nm) c (nm) b () 8Ce–0.50Y-TZP Tetragonal 0.51222 0.51926 0.51946 81.10 Monoclinic 0.51814 0.53731 8Ce–0.25Y-TZP Tetragonal 0.51150 0.52099 0.52098 80.66 Monoclinic 0.51666 0.53597 12Ce-TZPa Tetragonal 0.5128 0.5217 0.5224 81.09 Monoclinic 0.5203 0.5338 a From Ref. [19]. Fig. 2. Schematic of Bain strain. Table 2 Calculated crystallographic results for the t ! m martensitic transformation Item Value Shear amount, g 0.000038 Characteristic value, k2 1, 1.2176, 0.9007 Habit plane, N (0.3100, 0.9507, 0) Shape deformation matrix, F 1:0477 0:1615 0:0001 0:01567 0:9971 0:0003 0:0001 0:0003 1 0 B@ 1 CA Y.L. Zhang et al. / Acta Materialia 54 (2006) 1289–1295 1291