N. Nowruz Table 2. The crystallographic parameters calculated from WLR theory to the 1-m transformation in ZrO-12 mole ceo. Solutions LCB-I LCB-2 Amount of Lis,g 0.0027 Habit plane, h [0.3006,0.9537,-0.0004[0.9958.0.0915,-0.0013 Total shape deformation [0.999.0.0159,-0.0013][0.2276,0.9737,-0.0003] Magnitude 0.1640 8.72° [010L∧[100 0.19 [00l1^[010 (1001A(001 0.21 (010xA(100m 0.04 8.7 (001tA(010m Axial strain (%) 3.72 0.00 Table 3. The direction cosines aij relating the p system to the n system. x∥/[00 osφ(a1) cos 6 sinφ(a12) Sine sin中(a13) sinφ(a21) os6cosφ(a22) sin ecosφ(a23) 鸡/Dol sin 0(a32) The explicit form of equation(3)on the p coordinate system (xi//1ooJ x2//[010], xi//[001]) for LCB-I can be written as E1-g/28-w3w2-g/2 2+g/2w1e3+g/2 where 81=(cm-a/a,=0.05070, E?=[am cos(90-B)-aat=0.00238 and E3= (bm-CD/c=-000134 and 8=[am sin(90- B)l/a,=0. 15715. The amount of LIS, g, and the components of the rotation matrix, W1, w2, w3, are unknown parameters to be determined later. The total shape deformation matrix TP expressed on the p coordinate system can be converted into T expressed on the xi-x2-x3 ortho- normal coordinate system(n system) by the usual tensor conversion: T=∑∑aT where ai are the direction cosines defined in table 3. With this definition, the normal, h, to the habit plane on the p coordinate system is written as sin e sin sin A cos p, cos g1 6The explicit form of equation (3) on the p coordinate system ðxp 1 ==½100t, xp 2 ==½010t, xp 3 ==½001tÞ for LCB-1 can be written as Tp ¼ "1 g=2 w3 w2 g=2 w3 "2 w1 w2 þ g=2 w1 "3 þ g=2 0 B @ 1 C A p ð4Þ where "1 ¼ (cm at)/at ¼ 0.05070, "2 ¼ [am cos(90
) at]/at ¼ 0.00238 and "3 ¼ (bm ct)/ct ¼ 0.00134 and ¼ [am sin(90
)]/at ¼ 0.15715. The amount of LIS, g, and the components of the rotation matrix, w1, w2, w3, are unknown parameters to be determined later. The total shape deformation matrix Tp expressed on the p coordinate system can be converted into Tn expressed on the xn 1 xn 2 xn 3 ortho￾normal coordinate system (n system) by the usual tensor conversion: T n ij ¼ X 3 k¼1 X 3 l¼1 akialjT p kl ð5Þ where aij are the direction cosines defined in table 3. With this definition, the normal, h, to the habit plane on the p coordinate system is written as h ¼ ½sin sin , sin cos , cos p: ð6Þ Table 2. The crystallographic parameters calculated from WLR theory 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 [0.3006, 0.9537, 0.0004] [0.9958, 0.0915, 0.0013] Total shape deformation Direction, d [0.9999, 0.0159, 0.0013] [0.2276, 0.9737, 0.0003] Magnitude, m 0.1640 0.1640 Orientation relationship [100]t^[001]m 0.09 8.72 [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 8.72 (001)t^(010)m 0.08 0.08 Axial strain (%) [100]t 4.93 3.72 [010]t 0.25 1.46 [001]t 0.00 0.00 Table 3. The direction cosines aij relating the p system to the n system. xn 1 xn 2 xn 3 xp 1 == [100]p cos  (a11) cos sin  (a12) sin sin  (a13) xp 2 == [010]p sin  (a21) cos cos  (a22) sin cos  (a23) xp 3 == [001]p 0 (a31) sin (a32) cos (a33) 542 N. Navruz