《复合材料 Composites》课程教学资源（学习资料）第五章陶瓷基复合材料_Crystallography of the tetragonal-to-monoclinic phase.pdf_大学文库

Phase transitions Vol. 78, Nos. 7-8, September 2005, 539-545 Taylor franci Crystallography of the tetragonal-to-monoclinic phase transformation in ceria-zirconia N. NAVRUZ Faculty of Science, Department of Physics, Ankara University, Tandogan 06100 Ankara, Turkey (Received 18 August 2004: in final form 25 April 2005) a detailed understanding of the transformation toughening process in zirconia- containing ceramics requires the application of the crystallographic theory of martensitic transformation. Therefore, the crystallographic analysis of the tetragonal-to-monoclinic transformation in ceria-zirconia was performed by using both the infinitesimal deformation approach and Wechsler-Lieberman- Read phenomenological crystallographic theory. All crystallographic parameters such as the habit plane orientation, orientation relationship between the parent and product phases, the direction of the total shape deformation, the amount of the lattice invariant strain. etc. were calculated. The results obtained from the infinitesimal deformation approach were in agreement with those calculated from phenomenological crystallographic theory and also with experimental Keywords: Martensitic transformation; Crystallographic theory; Zirconia-based ceramics PACS numbers: 81. 30Kf: 61.50Ks 1. Introduction Martensitic transformation from the tetragonal(o) to monoclinic (m) phase in the zirconia system has been the subject of great interest in recent years [1-3]. The t-m transformation occurring in the ceria-stabilized polycrystalline tetragonal zirconia is martensitic in nature[4-9]. The transformation may be either stress-induced, or may occur thermally on cooling to below the Ms temperature. The t-> m transforma tion is technologically important because it is the source of both transformation toughening and significant transformation plasticity [10, 11] in ceria-zirconia and other zirconia-containing ceramics In the case of the t to m transformation in partially stabilized zirconia there are three possible, simple correspondences that depend on which monoclinic axis is derived from the unique c, axis of the tetragonal parent phase. The tetragonal ct axis can become the am, bm or cm axis of the monoclinic phase, hence the three Fax:+90312 223 2395. Tel:+903122126720 Email: navruz@science. ankara. edu. tr Phase Transitions IsSN 0141-1594 print/ISSN 1029-0338 online o 2005 Taylor Francis http://www.tandf.co.uk/journals DOl:10.108001411590500158770

Phase Transitions, Vol. 78, Nos. 7–8, September 2005, 539–545 Crystallography of the tetragonal-to-monoclinic phase transformation in ceria-zirconia N. NAVRUZ* Faculty of Science, Department of Physics, Ankara University, Tandogan, 06100 Ankara, Turkey (Received 18 August 2004; in final form 25 April 2005) A detailed understanding of the transformation toughening process in zirconiacontaining ceramics requires the application of the crystallographic theory of martensitic transformation. Therefore, the crystallographic analysis of the tetragonal-to-monoclinic transformation in ceria-zirconia was performed by using both the infinitesimal deformation approach and Wechsler–Lieberman– Read phenomenological crystallographic theory. All crystallographic parameters such as the habit plane orientation, orientation relationship between the parent and product phases, the direction of the total shape deformation, the amount of the lattice invariant strain, etc. were calculated. The results obtained from the infinitesimal deformation approach were in agreement with those calculated from phenomenological crystallographic theory and also with experimental observations. Keywords: Martensitic transformation; Crystallographic theory; Zirconia-based ceramics PACS numbers: 81.30 Kf; 61.50 Ks 1. Introduction Martensitic transformation from the tetragonal (t) to monoclinic (m) phase in the zirconia system has been the subject of great interest in recent years [1–3]. The t!m transformation occurring in the ceria-stabilized polycrystalline tetragonal zirconia is martensitic in nature [4–9]. The transformation may be either stress-induced, or may occur athermally on cooling to below the Ms temperature. The t ! m transformation is technologically important because it is the source of both transformation toughening and significant transformation plasticity [10, 11] in ceria-zirconia and other zirconia-containing ceramics. In the case of the t to m transformation in partially stabilized zirconia there are three possible, simple correspondences that depend on which monoclinic axis is derived from the unique ct axis of the tetragonal parent phase. The tetragonal ct axis can become the am, bm or cm axis of the monoclinic phase, hence the three *Fax: þ90 312 223 2395. Tel.: þ90 312 212 6720. Email: navruz@science.ankara.edu.tr Phase Transitions ISSN 0141-1594 print/ISSN 1029-0338 online # 2005 Taylor & Francis http://www.tandf.co.uk/journals DOI: 10.1080/01411590500158770

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 for

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 transformation 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 parameters 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 invariantplane 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 deformation 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

Tetragonal-1o-monoclinie phase transformation in ceria-zirconia 541 Table 1. The lattice parameters of the monoclinic and tetragonal phases in ZrO2-12 mole% CeO2 [15]. b(nm) B(deg) Monoclinic 0.5203 0.5217 0.5128 0.5224 evaluating T and factoring it into R, B and P. These methods differ mathematically and are commonly referred to as different theories, but they rest on the same physical assum ptions and so, of course, yield identical results The lattice deformation can be expressed in terms of the lattice parameters of the parent and product phases by an appropriate choice of the lattice correspondence In general, the lattice deformation alone does not give rise to the invariant-plane condition and both the rigid-body rotation and the lattice-invariant deformation (such as slip or twinning)are required to take place in the product phase, so as to minimize the elastic strain energy On applying the crystallographic theory to the t-m transformation in ceria- zirconia, (101) [101] shear is considered as the lattice-invariant strain and the lattice deformation is chosen from the lattice correspondence(LCB) between unit cells of the tetragonal and monoclinic lattices. The lattice deformation matrix, B, for LCB-I can be written as Cm am sin(90-B)0 0=cos(90-6)0 where at, Ct, and am, bm, Cm are the lattice parameters of the tetragonal and monoclinic phases, respectively, and B is the monoclinic angle. The lattice param eters of the parent and product phases for ZrO2-12 mole% CeO2 [15] are given in table 1. The procedure for obtaining crystallographic parameters has been thoroughly described by WLR. Exactly following WLR, all crystallographic param- eters such as the habit plane orientation, the amount of Lis, the direction of the total shape deformation, etc. have been calculated for the t-m transformation in ZrO-12 mole% CeO,. Table 2 summarizes the results of numerical calculation of crystallographic parameters for LCB-l and LCB-2 In the ID theory, all solutions can be expressed in simple and analytical forms Moreover, since the ID approach assumes that the absolute magnitude of each distortion component is much smaller than unity, the successive occurrence of defor mations can be expressed by the addition of matrices with no attention paid to the order of occurrence of the deformations. The id theory has been applied successfully to the discussion of the crystallography of various martensites [20-22] Equation (I)in the ID analysis becomes T=R+B+P

evaluating T and factoring it into R, B and P. These methods differ mathematically and are commonly referred to as different theories, but they rest on the same physical assumptions and so, of course, yield identical results. The lattice deformation can be expressed in terms of the lattice parameters of the parent and product phases by an appropriate choice of the lattice correspondence. In general, the lattice deformation alone does not give rise to the invariant-plane condition and both the rigid-body rotation and the lattice-invariant deformation (such as slip or twinning) are required to take place in the product phase, so as to minimize the elastic strain energy. On applying the crystallographic theory to the t!m transformation in ceriazirconia, (101)t [101]t shear is considered as the lattice-invariant strain and the lattice deformation is chosen from the lattice correspondence (LCB) between unit cells of the tetragonal and monoclinic lattices. The lattice deformation matrix, B, for LCB-1 can be written as B ¼ cm at am at sinð90 Þ 0 0 am at cosð90 Þ 0 0 0 bm ct 0 B BBB BB@ 1 C CCC CCA ð2Þ where at, ct, and am, bm, cm are the lattice parameters of the tetragonal and monoclinic phases, respectively, and is the monoclinic angle. The lattice parameters of the parent and product phases for ZrO2-12 mole% CeO2 [15] are given in table 1. The procedure for obtaining crystallographic parameters has been thoroughly described by WLR. Exactly following WLR, all crystallographic parameters such as the habit plane orientation, the amount of LIS, the direction of the total shape deformation, etc. have been calculated for the t!m transformation in ZrO2-12 mole% CeO2. Table 2 summarizes the results of numerical calculation of crystallographic parameters for LCB-1 and LCB-2. In the ID theory, all solutions can be expressed in simple and analytical forms. Moreover, since the ID approach assumes that the absolute magnitude of each distortion component is much smaller than unity, the successive occurrence of deformations can be expressed by the addition of matrices with no attention paid to the order of occurrence of the deformations. The ID theory has been applied successfully to the discussion of the crystallography of various martensites [20–22]. Equation (1) in the ID analysis becomes T ¼ R þ B þ P: ð3Þ Table 1. The lattice parameters of the monoclinic and tetragonal phases in ZrO2-12 mole% CeO2 [15]. Phase a (nm) b (nm) c (nm) (deg) Monoclinic 0.5203 0.5217 0.5388 81.09 Tetragonal 0.5128 0.5224 Tetragonal-to-monoclinic phase transformation in ceria-zirconia 541

In order for T to describe the invariant-plane deformation, the following form must be satisfied: Tn ¼ 0 0 Tn 13 0 0 Tn 23 0 0 Tn 33 0 B @ 1 C A n ð7Þ The physical meaning of equation (7) is that no distortion exists on the xn 1 and xn 2 planes. The resultant matrix Tn has six unknown parameters, i.e., g, w1, w2 , w3, and . These six parameters can be solved using the condition of the invariant-plane deformation in equation (7). In other words, there are six simultaneous equations to solve for the six unknowns: Tn 11 ¼ Tn 12 ¼ T n 21 ¼ T n 22 ¼ T n 31 ¼ T n 32 ¼ 0. The explicit forms of these six equations can be obtained from equations (4) and (5) as T n 11 ¼ ð"1 g=2Þcos2 sin cos þ "2 sin2 ¼ 0 T n 12 ¼ ð"1 g=2Þsin cos cos þ cos cos2 w3 cos ðw2 g=2Þsin cos "2 sin cos cos w1 sin sin ¼ 0 T n 21 ¼ ð"1 g=2Þsin cos cos cos sin2 þ w3 cos "2 sin cos cos þ w1 sin sin ¼ 0 ð8Þ T n 22 ¼ ð"1 g=2Þsin2 cos2 þ cos2 sin cos þ "2 cos2 cos2 þ ð"3 þ g=2Þsin2 ¼ 0 T n 31 ¼ ð"1 g=2Þsin cos sin sin sin2 þ w3 sin "2 sin cos sin þð w2 þ g=2Þcos cos w1 sin cos ¼ 0 T n 32 ¼ ð"1 g=2Þsin2 cos sin þ cos sin sin cos þðw2 þ g=2Þsin þ "2 cos2 sin cos þ w1 cos ð"3 þ g=2Þsin cos ¼ 0: These six unknown parameters can thus be found. Therefore, the rotation matrix on the p coordinate system is obtained as Rp ¼ 0 "2 tan "3 "2 tan 0 0 "3 0 0 0 @ 1 A p ð9Þ where tan ¼ { [ 2 4"2("1 þ"3)]1/2}/2"2. Using the numerical values for "1, "2, "3 and given previously, the normal to the habit plane is found to be [0.3009, 0.9536, 0]. All unknown parameters have been solved, and the direction of the total shape deformation, d, and its magnitude, m, can be obtained from the following equations dn ¼ ½Tn 13, T n 23, T n 33n m ¼ ðTn 13Þ 2 þ ðTn 23Þ 2 þ ðT n 33Þ 2 1=2 : ð10Þ Thus, the infinitesimal deformation approach has also been applied successfully to the t!m transformation in ZrO2-12 mole% CeO2 for LCB-1. Exactly the same procedure has been repeated to obtain the crystallographic solutions for LCB-2. Two sets of solutions are listed in table 4. Tetragonal-to-monoclinic phase transformation in ceria-zirconia 543

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 transformation 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

Tetragonal-10-monoclinic phase transformation in ceria-zirconia [4XY. Chen, X H. Zheng, H.S. Fang, H Z. Shi, X F. Wang and H.M. Chen, The study of martensitic transformation and nanoscale surface relief in zirconia. j Mater. Sci. Lett 21415418(2002) S]G M. Wolten, Diffusionless phase transformation in zirconia and hafnia. J. Am. Ceram Soc.46418-422(1963) [6J.E. Bailey, Monoclinic-tetragonal transformation and associated twinning in thin films of zirconia. Proc. Roy. Soc. A 279 395-412(1964) [7G. K. Bansal and A H. Heuer, On a martensitic phase transformation in zirconia(ZrO2)-L Metallographic evidence. Acta Metall. 20 1281-1289(1972) [8E.C. Subbarao, H.S. Maiti and K.K. Srivastava, Martensitic transformation in zirconia. Phys. Stat Sol. (a)219-39(1974) 9S.T. Buljan, H.A. McKinstry and V.s. Stubican, Optical and X-ray single crystal studies f the monoclinic 2 tetragonal transition in J. Am. Ceram. Soc. 59 351-354 (1976 [0 P.E. Reyes-Morel and l.w. Chen, Transformation plasticity of CeO2-stabilized tetragonal zirconia polycrystals: I. Stress assistance and autocatalysis. J. Am. Ceram. Soc. 71 43-353(1988) [1]G. Rauchs, T. Fett and D. Munz, R-curve behaviour of 9Ce-TZP ceramics Eng Fract Mech.69389401(2002) [12] W.M. Riven, W L. Fraser and S.w. Kennedy, The martensite crystallography of tetragonal zirconia, in Advances in Ceramics, edited by A.H. Heuer and L w. Hobbs Vol. 3(The American Ceramic Society, Columbus, OH, 1981), pp. 82-97 [3]GR. Hugo and B.C. Muddle, Tetragonal to monoclinic transformation in ceria-zirconia, in Mater. Sci. Forum, edited by B. C Muddle, Vol 56-58(Trans. Tech Pub., Switzerland, 1990),pp.357-362 [14]GR. Hugo, B.C. Muddle and R H.J. Hannink, Ceramic developments in Mater Sci. Forum, edited by CC Sorell and B. Ben Nissan, Vol. 34-36(Trans. Tech. Pub Switzerland, 1988), pp. 165-169 [5]GR. Hugo and B.C. Muddle, Application of the crystallographic theory to the tetragonal to monoclinic transformation in ceria-zirconia, in Proc. ICOMAT-92 International Conference on Martensitic Transformations(Monterey Institute, USA 1993),pp.665-670 []A F. Acton, M. Bevis, A.G. Crocker and N D H. Ross, Transformation strain in lattices Proc.Roy.Soc.A320101-103(1970) [17 M.S. Wechsler, D.S. Lieberman and T.A. Read, On the theory of the formation of martensite.Trans. AIME 197 1503-1515(1953 rapny of martensitic transformations Acta Metall. 2 224-232(195 [9T Mura, T. Mori and M. Kato, The elastic field caused by elipsoidal inclusion and the application to martensite formation. J. Mech. Phy 24305-318(1976) [20N. Navruz, Crystallography of cubic to orthorhombic mart ansformation based on the infinitesimal deformation approach in the alloy Aucu Trans.7610291035 [21]N. Navruz, Crystallographic analysis of cubic to orthorhombic martensitic transforma tion for the formation of the oxide plates in tantalum. J. Mater. Sci. Lett. 22 17-19 222 N. Navruz, Application of the infinitesimal deformation approach to the tetragona to-monoclinic transformation in Mgo-partially stabilized zirconia. Phil. Mag. Lett 8415-20(2004)

[4] X.Y. Chen, X.H. Zheng, H.S. Fang, H.Z. Shi, X.F. Wang and H.M. Chen, The study of martensitic transformation and nanoscale surface relief in zirconia. J. Mater. Sci. Lett. 21 415–418 (2002). [5] G.M. Wolten, Diffusionless phase transformation in zirconia and hafnia. J. Am. Ceram. Soc. 46 418–422 (1963). [6] J.E. Bailey, Monoclinic-tetragonal transformation and associated twinning in thin films of zirconia. Proc. Roy. Soc. A 279 395–412 (1964). [7] G.K. Bansal and A.H. Heuer, On a martensitic phase transformation in zirconia (ZrO2) – I. Metallographic evidence. Acta. Metall. 20 1281–1289 (1972). [8] E.C. Subbarao, H.S. Maiti and K.K. Srivastava, Martensitic transformation in zirconia. Phys. Stat. Sol. (a) 21 9–39 (1974). [9] S.T. Buljan, H.A. McKinstry and V.S. Stubican, Optical and X-ray single crystal studies of the monoclinic ! tetragonal transition in ZrO2. J. Am. Ceram. Soc. 59 351–354 (1976). [10] P.E. Reyes-Morel and I.W. Chen, Transformation plasticity of CeO2-stabilized tetragonal zirconia polycrystals: I. Stress assistance and autocatalysis. J. Am. Ceram. Soc. 71 343–353 (1988). [11] G. Rauchs, T. Fett and D. Munz, R-curve behaviour of 9Ce-TZP ceramics. Eng. Fract. Mech. 69 389–401 (2002). [12] W.M. Kriven, W.L. Fraser and S.W. Kennedy, The martensite crystallography of tetragonal zirconia, in Advances in Ceramics, edited by A.H. Heuer and L.W. Hobbs, Vol. 3 (The American Ceramic Society, Columbus, OH, 1981), pp. 82–97. [13] G.R. Hugo and B.C. Muddle, Tetragonal to monoclinic transformation in ceria-zirconia, in Mater. Sci. Forum, edited by B.C. Muddle, Vol. 56–58 (Trans. Tech. Pub., Switzerland, 1990), pp. 357–362. [14] G.R. Hugo, B.C. Muddle and R.H.J. Hannink, Ceramic developments in Mater. Sci. Forum, edited by C.C Sorell and B. Ben Nissan, Vol. 34–36 (Trans. Tech. Pub., Switzerland, 1988), pp. 165–169. [15] G.R. Hugo and B.C. Muddle, Application of the crystallographic theory to the tetragonal to monoclinic transformation in ceria-zirconia, in Proc. ICOMAT-92, International Conference on Martensitic Transformations (Monterey Institute, USA, 1993), pp. 665–670. [16] A.F. Acton, M. Bevis, A.G. Crocker and N.D.H. Ross, Transformation strain in lattices. Proc. Roy. Soc. A 320 101–103 (1970). [17] M.S. Wechsler, D.S. Lieberman and T.A. Read, On the theory of the formation of martensite. Trans. AIME 197 1503–1515 (1953). [18] J.S. Bowles and J.K. Mackenzie, The crystallography of martensitic transformations, Acta Metall. 2 224–232 (1954). [19] T. Mura, T. Mori and M. Kato, The elastic field caused by a general elipsoidal inclusion and the application to martensite formation. J. Mech. Phys. Solids 24 305–318 (1976). [20] N. Navruz, Crystallography of cubic to orthorhombic martensitic transformation based on the infinitesimal deformation approach in the alloy AuCu. Phas. Trans. 76 1029–1035 (2003a). [21] N. Navruz, Crystallographic analysis of cubic to orthorhombic martensitic transformation for the formation of the oxide plates in tantalum. J. Mater. Sci. Lett. 22 17–19 (2003b). [22] N. Navruz, Application of the infinitesimal deformation approach to the tetragonalto-monoclinic transformation in MgO-partially stabilized zirconia. Phil. Mag. Lett. 84 15–20 (2004). Tetragonal-to-monoclinic phase transformation in ceria-zirconia 545

《复合材料 Composites》课程教学资源（学习资料）第五章 陶瓷基复合材料_Crystallography of the tetragonal-to-monoclinic phase

《复合材料 Composites》课程教学资源（学习资料）第五章陶瓷基复合材料_Crystallography of the tetragonal-to-monoclinic phase