《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_martensitic transformation in Ce–Y-TZP ceramics

Availableonlineatwww.sciencedirect.com SCIENCE DIRECT Acta materialia ELSEVIER Acta Materialia 54(2006)1289-1295 On the t-m martensitic transformation in Ce-Y-TZP ceramics Y L. Zhang ,X.J. Jin,YH Rong, T.Y. Hsu(Xu Zuyao),, D.Y.Jiang, J.L. Shi School of Materials Science and Engineering, Shanghai Jiao Tong Unicersity, Shanghai 200030, China Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 200050, China Available online 3 January 200Ker 2005 Received 14 October 2005: accepted 25 Octo Abstract The thermoelastic behavior and crystallography of the tetragonal(t)- monoclinic(m)martensitic transformation in Ce-Y-TZP ceramics are investigated by means of in situ transmission electron microscopy(TEM) and Wechsler-Lieberman-Read phenomenolog ical theory. In situ TEM observations show that in Ce-Y-TZP the t/m interface can move freely with the change of thermal stress sup- plied by the beam illumination, whereas this is not found in thermal cycles. Based on the features of reversibility of interface motion, large thermal hysteresis and high critical driving force for Ce-Y-TZP, the t-m transformation is suggested as a semi-thermoelastic one. The habit plane and the lattice correspondence are determined as(130) and [00 1J//[010]m, which is in agreement with the calci lated results of the phenomenological theory. c 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved Keywords: Martensitic phase transformation; Ceramics; TEM; Thermoelastic 1. Introduction knowledge, even the thermoelastic behavior of the trans formation has not been elucidated so far. i.e. is it a ther A variety of zirconia-containing ceramics were much moelastic transformation? investigated at the end of the last century after the claim Some authors suggested that the t-m martensitic of transformation toughening by Garvie in 1975 [1]. In transformation in zirconia-containing ceramics is a ther addition, the shape memory effect (SME) has been moelastic one [6-9, 12]. The evidence is summarized as observed in Mg-PSZ [2](partially stabilized zirconia), Ce- follows. (1)In Y2O3-ZrO2 [6], MgO-Zro2 [7] and MgO- TZP [3, 4](tetragonal zirconia polycrystalline), as well as Y2O3-ZrO2 [8,9] systems, in situ transmission electron in Ce-Y-TZP [4. Recently, it was revealed that &Ce- microscopy (TEM) studies have shown that the monoclinic under a recoverable strain or lete shape memory recovery laths induced by the electron beam could grow and retract d defo ating temperature(above 500C)[5]. This is the best SMe indicating a glissile t/m interface under thermal stresses among reported shape memory ceramics(SMCs) up to (2) In situ X-ray measurements were performed on a now. These properties are associated with the martensitic stressed surface in bulk Mg- PSZ [10, 11]. The materials transformation from tetragonal (t) to monoclinic(m) sym- had a background m phase content of approximately metry in such ceramics [3]. However, in comparison to its 13 vol % and the volume fraction was reversibly engineering applications, less attention has been paid to increased/decreased by 3 vol. during tensile loadi the mechanism of this unique transformation. To our unloading. Using an optical microscope with Nomarski interference. the reversible surface roughness was observed to appear/disappear on loading/unloading corresponding Eonmslpodeg: zutho r.Tel/fax:+862162932435 o the t-m transformation. Heuer et al. [ 12] concluded I@sjtu.edu.cn(T.Y.Hsu(XuZuyao)) that the t-m transformations in zirconia-containing 1359-6454$30.00 C 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved doi:l0.1016 factant2005.10.062

On the t ! m martensitic transformation in Ce–Y-TZP ceramics Y.L. Zhang a , X.J. Jin a , Y.H. Rong a , T.Y. Hsu (Xu Zuyao) a,*, D.Y. Jiang b , J.L. Shi b a School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200030, China b Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 200050, China Received 14 October 2005; accepted 25 October 2005 Available online 3 January 2006 Abstract The thermoelastic behavior and crystallography of the tetragonal (t) ! monoclinic (m) martensitic transformation in Ce–Y-TZP ceramics are investigated by means of in situ transmission electron microscopy (TEM) and Wechsler–Lieberman–Read phenomenolog￾ical theory. In situ TEM observations show that in Ce–Y-TZP the t/m interface can move freely with the change of thermal stress sup￾plied by the beam illumination, whereas this is not found in thermal cycles. Based on the features of reversibility of interface motion, large thermal hysteresis and high critical driving force for Ce–Y-TZP, the t ! m transformation is suggested as a semi-thermoelastic one. The habit plane and the lattice correspondence are determined as (1 3 0)t and [0 0 1]t//[0 1 0]m, which is in agreement with the calcu￾lated results of the phenomenological theory.
2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Martensitic phase transformation; Ceramics; TEM; Thermoelastic 1. Introduction A variety of zirconia-containing ceramics were much investigated at the end of the last century after the claim of transformation toughening by Garvie in 1975 [1]. In addition, the shape memory effect (SME) has been observed in Mg-PSZ [2] (partially stabilized zirconia), Ce￾TZP [3,4] (tetragonal zirconia polycrystalline), as well as in Ce–Y-TZP [4]. Recently, it was revealed that 8Ce– 0.50Y-TZP exhibits a complete shape memory recovery under a recoverable strain of 1.2% at a relatively high oper￾ating temperature (above 500 C) [5]. This is the best SME among reported shape memory ceramics (SMCs) up to now. These properties are associated with the martensitic transformation from tetragonal (t) to monoclinic (m) sym￾metry in such ceramics [3]. However, in comparison to its engineering applications, less attention has been paid to the mechanism of this unique transformation. To our knowledge, even the thermoelastic behavior of the trans￾formation has not been elucidated so far, i.e., is it a ther￾moelastic transformation? Some authors suggested that the t ! m martensitic transformation in zirconia-containing ceramics is a ther￾moelastic one [6–9,12]. The evidence is summarized as follows. (1) In Y2O3–ZrO2 [6], MgO–ZrO2 [7] and MgO– Y2O3–ZrO2 [8,9] systems, in situ transmission electron microscopy (TEM) studies have shown that the monoclinic laths induced by the electron beam could grow and retract following the same path when focusing and defocusing, indicating a glissile t/m interface under thermal stresses. (2) In situ X-ray measurements were performed on a stressed surface in bulk Mg-PSZ [10,11]. The materials had a background m phase content of approximately 13 vol.%, and the volume fraction was reversibly increased/decreased by
3 vol.% during tensile loading/ unloading. Using an optical microscope with Nomarski interference, the reversible surface roughness was observed to appear/disappear on loading/unloading corresponding to the t ! m transformation. Heuer et al. [12] concluded that the t ! m transformations in zirconia-containing 1359-6454/$30.00
2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2005.10.062 * Corresponding author. Tel./fax: +86 21 62932435. E-mail address: zyxu@sjtu.edu.cn (T.Y. Hsu (Xu Zuyao)). www.actamat-journals.com Acta Materialia 54 (2006) 1289–1295

al / Acta m ceramics are thermoelastic transformations, mainly based of 10 and deposited with carbon. These thin foils were on the tem observation mentioned above and X-ray then suitable for tEM observation measurements(3) When Sme behavior in some zirconia formed using containing ceramics was discovered, Reyes-Morel et al. an H-800 instrument with an attached heater. The temper 3]attributed it to the thermoelasticity in 12Ce-TZP ature of the foil could be increased up to 800C. By care- Here it should be noted that the monoclinic laths are fully adjusting current and illumination conditions of the thermal stress-induced martensite resulting from the illumi- electron beam, the local thermomechanical stress generated nation by the electron beam rather than the thermally by beam heating is expected to induce t-m martensitic induced martensite of the in situ TEM experiments men- transformations tioned above. Nevertheless it is well known that a transfor- mation can traditionally be defined as a thermoelastic 3. Crystallographic calculation process if the interface can adjust its position freely with a change of temperature. In addition, no in situ TEM The crystallography of the t-m transformation in observations for CeOy-ZrO, ceramics have been reported Ce-Y-TZP is calculated on the basis of the Wechsler- so far. Hence, for zirconia-containing ceramics, the results Lieberman-Read (WLR) theory [26]. The WLR theor in the literature have not provided convincing evidence for can be expressed in terms of (3 x 3)matrices as follow the thermoelastic nature, and the nature of the transforma- F= rBS tion in the newly developed ternary Ce-Y-TZP SMC also needs further investigation where F is the shape deformation, B the Bain strain, S the The crystallography of t-m martensitic transforma- simple shear and R the rigid body rotation. tions has been evaluated by a phenomenological theory The inputs required by the phenomenological theory are for many zirconia-containing ceramics [15-23]. The agree- the crystal structures, the lattice parameters of the parent ment between the experimental results and theoretical pre- and product phases, the lattice correspondence (Lc) diction demonstrates that the theory can be applied to between the two structures, and the elements of lattice make reliable, quantitative predictions for the martensitic invariant shear(LIS). In the case of the t-m transforma- transformation in these ceramic systems [24] The shape tion in zirconia-containing ceramics, there are three possi strain associated with the t-m transformation, being ble LCs denoted as LCA, LCB and LCC, which depend on extremely difficult to measure experimentally, is the key the axis of the monoclinic structure being parallel to the issue in understanding transformation toughening and unique c axis of the parent tetragonal phase. This simpl the SME in zirconia-containing ceramics. Thus, the calcu- notation was extended to provide a more comprehensive lation of the shape strain via the phenomenological theory system describing the different LCs between tetragonal is useful and provides an insight into the nature of this and monoclinic zirconia by Hayakawa et al. [15-17]. To transformation allow the different variants of a single correspondence to In the present work, the microstructural evolution is be identified and labeled, they assumed that the two crys studied by means of in situ TEM observations for both tallographically equivalent a, axes are distinguishable from thermal stress-induced and thermally induced martensitic one another and arbitrarily denoted by the axes at and bt transformations in order to investigate the nature of the for example, the notation CAB means that at, b. and ct t-m martensitic transformation in Ce-Y-TZP SMC. become cm, am and bm, respectively The phenomenological theory is applied, and some features of this transformation are discussed 2. Experimental The materials studied here were ternary TZP ceramics with two different Y2O3 contents, i.e., &Ce-0.25Y-TZP (8 mol% CeOx-025 mol% Y2O3-ZrO2) and &Ce-0.50Y TZP Superfine powders were prepared by co-precipitation 51. The composite powders were afterwards compacte into biscuits by uniaxial compression at 200 MPa, and then the biscuits were sintered at 1500 oC for 6 h. The m. values for bulk specimens were measured using an LK-02 dilatometer Discs of 50 um x 3 mm diameter were cut from bulk specimens, then glued on a molybdenum ring with ethoxy- line resin, which served as a supporting skeleton protecting the foils from breakage during manipulation. The well- Fig. 1. Thermally induced martensite(a)and selected area diffraction glued specimens were further ion-thinned at a small angle pattern(b)for 8Ce-0.25Y-TZP

ceramics are thermoelastic transformations, mainly based on the TEM observation mentioned above and X-ray measurements. (3) When SME behavior in some zirconia￾containing ceramics was discovered, Reyes-Morel et al. [3] attributed it to the thermoelasticity in 12Ce-TZP. Here it should be noted that the monoclinic laths are thermal stress-induced martensite resulting from the illumi￾nation by the electron beam rather than the thermally induced martensite of the in situ TEM experiments men￾tioned above. Nevertheless, it is well known that a transfor￾mation can traditionally be defined as a thermoelastic process if the interface can adjust its position freely with a change of temperature. In addition, no in situ TEM observations for CeO2–ZrO2 ceramics have been reported so far. Hence, for zirconia-containing ceramics, the results in the literature have not provided convincing evidence for the thermoelastic nature, and the nature of the transforma￾tion in the newly developed ternary Ce–Y-TZP SMC also needs further investigation. The crystallography of t ! m martensitic transforma￾tions has been evaluated by a phenomenological theory for many zirconia-containing ceramics [15–23]. The agree￾ment between the experimental results and theoretical pre￾diction demonstrates that the theory can be applied to make reliable, quantitative predictions for the martensitic transformation in these ceramic systems [24]. The shape strain associated with the t ! m transformation, being extremely difficult to measure experimentally, is the key issue in understanding transformation toughening and the SME in zirconia-containing ceramics. Thus, the calcu￾lation of the shape strain via the phenomenological theory is useful and provides an insight into the nature of this transformation. In the present work, the microstructural evolution is studied by means of in situ TEM observations for both thermal stress-induced and thermally induced martensitic transformations in order to investigate the nature of the t ! m martensitic transformation in Ce–Y-TZP SMC. The phenomenological theory is applied, and some features of this transformation are discussed. 2. Experimental The materials studied here were ternary TZP ceramics with two different Y2O3 contents, i.e., 8Ce–0.25Y-TZP (8 mol% CeO2–0.25 mol% Y2O3–ZrO2) and 8Ce–0.50Y￾TZP. Superfine powders were prepared by co-precipitation [25]. The composite powders were afterwards compacted into biscuits by uniaxial compression at 200 MPa, and then the biscuits were sintered at 1500 C for 6 h. The Ms values for bulk specimens were measured using an LK-02 dilatometer. Discs of 50 lm · 3 mm diameter were cut from bulk specimens, then glued on a molybdenum ring with ethoxy￾line resin, which served as a supporting skeleton protecting the foils from breakage during manipulation. The well￾glued specimens were further ion-thinned at a small angle of 10 and deposited with carbon. These thin foils were then suitable for TEM observations. In situ observations and analyses were performed using an H-800 instrument with an attached heater. The temper￾ature of the foil could be increased up to 800 C. By care￾fully adjusting current and illumination conditions of the electron beam, the local thermomechanical stress generated by beam heating is expected to induce t ! m martensitic transformations. 3. Crystallographic calculation The crystallography of the t ! m transformation in Ce–Y-TZP is calculated on the basis of the Wechsler– Lieberman–Read (WLR) theory [26]. The WLR theory can be expressed in terms of (3 · 3) matrices as follows: F ¼ RBS; where F is the shape deformation, B the Bain strain, S the simple shear and R the rigid body rotation. The inputs required by the phenomenological theory are the crystal structures, the lattice parameters of the parent and product phases, the lattice correspondence (LC) between the two structures, and the elements of lattice invariant shear (LIS). In the case of the t ! m transforma￾tion in zirconia-containing ceramics, there are three possi￾ble LCs denoted as LCA, LCB and LCC, which depend on the axis of the monoclinic structure being parallel to the unique c axis of the parent tetragonal phase. This simple notation was extended to provide a more comprehensive system describing the different LCs between tetragonal and monoclinic zirconia by Hayakawa et al. [15–17]. To allow the different variants of a single correspondence to be identified and labeled, they assumed that the two crys￾tallographically equivalent at axes are distinguishable from one another and arbitrarily denoted by the axes at and bt; for example, the notation CAB means that at, bt and ct become cm, am and bm, respectively. Fig. 1. Thermally induced martensite (a) and selected area diffraction pattern (b) for 8Ce–0.25Y-TZP. 1290 Y.L. Zhang et al. / Acta Materialia 54 (2006) 1289–1295

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

Acta Materialia 54(2006)1289-I 0. 25Y-TZP, indicating uncompleted transformation, temperature aided the reverse transformation from mono- whereas no monoclinic phase is found in 8Ce-050Y-TZP clinic to tetragonal. It is reasonable to believe that as a con- at ambient temperature Under illumination by the electron sequence, the induced monoclinic martensites, such as laths beam, the martensitic transformation can be induced in A and B in Fig 3(c), are generated by local thermal stress both 8Ce-05Y-TZP and 8Ce-025Y-TZP. For 8Ce- The continuous growth of martensite plates starting at 0. 25Y-TZP, thermal stress-induced t/m interfaces were the edge is illustrated in Figs. 3(cHe). When focusing the produced and annihilated reversibly. However, the thermal electron beam, the first monoclinic lath A nucleated at stress-induced transformation in 8Ce-050Y-TZP showed a the grain boundary and grew across the grain. The second burst-like characteristic, which was also observed in other lath b then formed rapidly and grew to the same size as the systems [7,8]. The transformed martensite could not move first. The whole process was too rapid to obtain an image irrespective of the intensity of the electron beam. The in between. A further increase in the beam intensity athermal transformation was found to be burst-like for resulted in the formation of the martensite lath c and the measurement of the M, temperatures by dilatomets mw speed(Fig. 3(d). As the transformation proceeded, thickening of the formed laths A and B at a relatively of thermal stress-induced martensite in an isolated grain of martensite laths with different orientations were induced 8Ce-0.25Y-TZP caused by the illumination with the elec- and grew until the grain was eventually full of martensite tron beam. Figs. 3(a) and (b)show that some thermally ( Fig. 3(e)). Above TEM observation indicated that the induced monoclinic martensite is embedded in the tetrago- induced monoclinic lath usually nucleated at the grain nal matrix at room temperature. During illumination, an boundary, resided with high stress. Similar results were also elevated temperature on the surface of the sample and a observed in binary systems [6-8] thermally induced stress due to the thermal expansion After the illumination had been turned off for severa anisotropy [27, 28] are expected to occur. The elevated minutes, the twin structure in the grain shown in c Fig. 3. In situ TEM images for stress-induced t- m martensitic transformation in &Ce-025Y-TZP.(a) Bright-field and (b) dark-field images for thermally induced martensite; (cHe) the formation and growth of the stress-induced martensite at the expense of the thermally induced martensite under continuous electron beam illumination

0.25Y-TZP, indicating uncompleted transformation, whereas no monoclinic phase is found in 8Ce–0.50Y-TZP at ambient temperature. Under illumination by the electron beam, the martensitic transformation can be induced in both 8Ce–0.5Y-TZP and 8Ce–0.25Y-TZP. For 8Ce– 0.25Y-TZP, thermal stress-induced t/m interfaces were produced and annihilated reversibly. However, the thermal stress-induced transformation in 8Ce–0.50Y-TZP showed a burst-like characteristic, which was also observed in other systems [7,8]. The transformed martensite could not move irrespective of the intensity of the electron beam. The athermal transformation was found to be burst-like for the measurement of the Ms temperatures by dilatometry. The sequential images in Fig. 3 demonstrate the growth of thermal stress-induced martensite in an isolated grain of 8Ce–0.25Y-TZP caused by the illumination with the elec￾tron beam. Figs. 3(a) and (b) show that some thermally induced monoclinic martensite is embedded in the tetrago￾nal matrix at room temperature. During illumination, an elevated temperature on the surface of the sample and a thermally induced stress due to the thermal expansion anisotropy [27,28] are expected to occur. The elevated temperature aided the reverse transformation from mono￾clinic to tetragonal. It is reasonable to believe that as a con￾sequence, the induced monoclinic martensites, such as laths A and B in Fig. 3(c), are generated by local thermal stress. The continuous growth of martensite plates starting at the edge is illustrated in Figs. 3(c)–(e). When focusing the electron beam, the first monoclinic lath A nucleated at the grain boundary and grew across the grain. The second lath B then formed rapidly and grew to the same size as the first. The whole process was too rapid to obtain an image in between. A further increase in the beam intensity resulted in the formation of the martensite lath C and thickening of the formed laths A and B at a relatively low speed (Fig. 3(d)). As the transformation proceeded, martensite laths with different orientations were induced and grew until the grain was eventually full of martensite (Fig. 3(e)). Above TEM observation indicated that the induced monoclinic lath usually nucleated at the grain boundary, resided with high stress. Similar results were also observed in binary systems [6–8]. After the illumination had been turned off for several minutes, the twin structure in the grain shown in Fig. 3. In situ TEM images for stress-induced t ! m martensitic transformation in 8Ce–0.25Y-TZP. (a) Bright-field and (b) dark-field images for thermally induced martensite; (c)–(e) the formation and growth of the stress-induced martensite at the expense of the thermally induced martensite under continuous electron beam illumination. 1292 Y.L. Zhang et al. / Acta Materialia 54 (2006) 1289–1295

YL Zhang et al. Acta Materialia 54(2006)1289-1295 Fig 4. In situ TEM images for stress-induced martensitic transformation in 8Ce-025Y-TZP. The stress-induced martensite forms(marked by an arrow in (a))and grows(b, c) when focusing the electron beam, shrinks (d, e)and disappears(f) when defocusing the electron beam. Fig 3(e)disappeared, implying the occurrence of a reverse whereas it is a non-thermoelastic transformation when transformation. By carefully controlling the electron beam, none of them is satisfied. A semi-thermoelastic martensitic the reversible motion of the t/m interface in the same grain transformation can be identified if the three criteria are was recorded, as shown in Fig. 4 partially satisfied. When switching the electron beam on again, a new The transformation characteristics of the t-m tran monoclinic lath marked by the arrow in Fig 4(a)was intro- formation in Ce-Y-TZP revealed by the in situ TEM duced, and then continuously grew as shown in Figs. 4(b) observations indicated that the reversibility of the motion ind(c). While defocusing, the lath receded and eventually of the interface and the contribution of the stored energy disappeared(Figs. 4(d)f). These results indicate a for reverse transformation indeed occur in the thermal smooth motion of the t/m interface corresponding to ther- stress-induced martensite. However, the critical driving mal stress resulting from the focusing and defocusing of the force for Ce-Y-TZP is m4000 J/mol and the thermal electron beam hysteresis of 8Ce-0 25Y-TZP is As-Ms=437C [35] These values are orders of magnitude differer IScussIon compared to x10 J/mol and 10C of the corresponding values for a typical thermoelastic transformation [33] 5.1. Semi-thermoelastic feature This means that the t-m martensitic transformation in Ce-Y-TZP only partially satisfies the three criteria Based on previous work [29-34], Hsu and co-workers outlined above. Hence, the t-m martensitic transfor [13, 14] suggested the criteria for the thermoelastic transfor- mation in Ce-Y-TZP is suggested as a semi-thermoelastic mation as follows: (1)a small critical driving force and a transformation small hysteresis;(2) the reversibility of the motion of the interface between martensite and parent phases; and(3) 5.2. Reverse martensitic transformation in Ce-Y-TZP the shape strain is accommodated elastically and the store energy in martensite can contribute a part of the driving It is found that the t- m reverse transformation of our force for the reverse transformation. A transformation is in situ TEM observations may occur through two different thermoelastic when all of these three criteria are satisfied, modes: (1) the receding of the transformed monoclinic lath

Fig. 3(e) disappeared, implying the occurrence of a reverse transformation. By carefully controlling the electron beam, the reversible motion of the t/m interface in the same grain was recorded, as shown in Fig. 4. When switching the electron beam on again, a new monoclinic lath marked by the arrow in Fig. 4(a) was intro￾duced, and then continuously grew as shown in Figs. 4(b) and (c). While defocusing, the lath receded and eventually disappeared (Figs. 4(d)–(f)). These results indicate a smooth motion of the t/m interface corresponding to ther￾mal stress resulting from the focusing and defocusing of the electron beam. 5. Discussion 5.1. Semi-thermoelastic feature Based on previous work [29–34], Hsu and co-workers [13,14] suggested the criteria for the thermoelastic transfor￾mation as follows: (1) a small critical driving force and a small hysteresis; (2) the reversibility of the motion of the interface between martensite and parent phases; and (3) the shape strain is accommodated elastically and the stored energy in martensite can contribute a part of the driving force for the reverse transformation. A transformation is thermoelastic when all of these three criteria are satisfied, whereas it is a non-thermoelastic transformation when none of them is satisfied. A semi-thermoelastic martensitic transformation can be identified if the three criteria are partially satisfied. The transformation characteristics of the t ! m trans￾formation in Ce–Y-TZP revealed by the in situ TEM observations indicated that the reversibility of the motion of the interface and the contribution of the stored energy for reverse transformation indeed occur in the thermal stress-induced martensite. However, the critical driving force for Ce–Y-TZP is
4000 J/mol and the thermal hysteresis of 8Ce–0.25Y-TZP is As Ms = 437 C [35]. These values are orders of magnitude different when compared to
10 J/mol and
10 C of the corresponding values for a typical thermoelastic transformation [33]. This means that the t ! m martensitic transformation in Ce–Y-TZP only partially satisfies the three criteria outlined above. Hence, the t ! m martensitic transfor￾mation in Ce–Y-TZP is suggested as a semi-thermoelastic transformation. 5.2. Reverse martensitic transformation in Ce–Y-TZP It is found that the t ! m reverse transformation of our in situ TEM observations may occur through two different modes: (1) the receding of the transformed monoclinic lath Fig. 4. In situ TEM images for stress-induced martensitic transformation in 8Ce–0.25Y-TZP. The stress-induced martensite forms (marked by an arrow in (a)) and grows (b,c) when focusing the electron beam, shrinks (d,e) and disappears (f) when defocusing the electron beam. Y.L. Zhang et al. / Acta Materialia 54 (2006) 1289–1295 1293

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 work

and (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

Y L Zhang et al. Acta Materialia 54(2006)1289-1295 Acknowledgment 16 Hayakawa M, Oka M. Acta Metall 1989: 37: 2229 We are grateful for the financial support of this work 1N Hu kawa M, Adachi K, Oka M. Acta Metall 1990: 38: 1753. Muddle bc. Hannink rh. mater Sci Forum 1988- 34- from Emerson Electric Corporation, USA [19] Hugo GR, Muddle BC. Mater Sci Forum 1990: 56-58:357. [20] Kriven WM, Fraser WL, Kennedy Sw. In: Heuer AH, Hobbs Lw References ditors. Advances in ceramics. Science and technology of zirconia, ol. 3. Columbus(OH): American Ceramic Society: 1981. p 82. 21] Bailey JE. Proc R Soc London Ser A 1964: 279: 395 [1]Garvie RC, Hannink RH. Nature 1975: 258: 703 [22] Kelly PM, Ball CJ. J Am Ceram Soc 1986: 69: 259 2]Swain MV. Nature 1986: 332: 234 [23] Choudhry MA, Crocker AG. In: Claussen N, M. Heuer Ah 3]Reyes-Morel PE, Chen IW. J Am Ceram Soc 1988: 71: 343 editors. Advances in ceramics. Science and technology of zirconia, 4]Jiang BH, Tu JB, Hsu(Xu Zuyao)TY, Qi X. Mater Res Soc Symp ol. 12. Columbus(OH): American Ceramic 1984.p.46 Proc1992;246:213 [24] Kelly PM, Wauchope C. Key Eng Mater 1998: 153-154: 97 []Zhang YL, Jin x, Hsu (Xu Zuyao)TY, Zhang YF, Shi JL. Mater Sci [25] Shi JL, Lin Zx, Qian WJ, Yen TS J Eur Ceram Soc 1994: 14: 265 Forum2002;394-395:573 [26]Wechsler MS, Lieberman DS, Read TA. Trans Am Inst Min Eng 6 Mecartney ML, Ruhle M. Acta Metall 1989: 37: 1859 953:197:1503 [7] Hannink RH. Porter JR, Marshall DB. J Am Ceram Soc 1986: 69: cl 16. [27]Schubert H J Am Ceram Soc 1986: 69: 270 8Lee RR. Heuer AH. J Am Ceram Soc 1988: 71: 701 [28]Schmauder S, Schubert H J Am Ceram Soc 1986: 69: 534. 9]Lee RR. Heuer AH. J Am Ceram Soc 1988: 71: 694 29]Kaufman L, Cohn M. Prog Met Phys 1958: 165. 10JMarshall DB, James MR. J Am Ceram Soc 1986: 69: 215 30] Wayman CM. Mater Sci Forum 1990: 56-58: 1 I1Marshall DB, Swain MV. J Am Ceram Soc 1989: 72: 1530 [1]Ling HC, Owen wS. Acta Metall 1981: 29: 1721 12]Heuer AH, Ruhle M, Marshall DB. J Am Ceram Soc 1990: 73: 1084. [32]Maki T. In: Proceedings of the Ist Japan international SAMPE [13] Guo ZH, Rong YH, Chen SP, Hsu(Xu Zuyao) TY, Hong JM, Zhao symposium 89.p.22 XN. Mater Trans JIM 1999: 40: 193 33] Hsu(Xu Zuyao) TY. Mater Sci Forum 1990: 56-58: 145 14 Hsu (Xu Zuyao) TY. In: Inoue K, Otsuka K, Chen H, editors. 4] Hsu (Xu Zuyao)TY.J Mater Sci Technol 1994: 10: 107. International conference on displacive phase transformations and [35] Zhang YL, Jin XJ, Hsu (Xu Zuyao) TY. J Eur Ceram Soc eir applications in materials engineering. Warrendale(PA): TMS 2003:23:685 1998.p [6] Zhao Y, Zhang JH, Hsu (Xu Zuyao) TY. J Appl Phys 2000: 88 [15] Hayakawa M, Kuntai N, Oka M. Acta Metall 1989: 37: 2223

Acknowledgment We are grateful for the financial support of this work from Emerson Electric Corporation, USA. References [1] Garvie RC, Hannink RH. Nature 1975;258:703. [2] Swain MV. Nature 1986;332:234. [3] Reyes-Morel PE, Chen IW. J Am Ceram Soc 1988;71:343. [4] Jiang BH, Tu JB, Hsu (Xu Zuyao) TY, Qi X. Mater Res Soc Symp Proc 1992;246:213. [5] Zhang YL, Jin XJ, Hsu (Xu Zuyao) TY, Zhang YF, Shi JL. Mater Sci Forum 2002;394–395:573. [6] Mecartney ML, Ru¨hle M. Acta Metall 1989;37:1859. [7] Hannink RH, Porter JR, Marshall DB. J Am Ceram Soc 1986;69:c116. [8] Lee RR, Heuer AH. J Am Ceram Soc 1988;71:701. [9] Lee RR, Heuer AH. J Am Ceram Soc 1988;71:694. [10] Marshall DB, James MR. J Am Ceram Soc 1986;69:215. [11] Marshall DB, Swain MV. J Am Ceram Soc 1989;72:1530. [12] Heuer AH, Ruhle M, Marshall DB. J Am Ceram Soc 1990;73:1084. [13] Guo ZH, Rong YH, Chen SP, Hsu (Xu Zuyao) TY, Hong JM, Zhao XN. Mater Trans JIM 1999;40:193. [14] Hsu (Xu Zuyao) TY. In: Inoue K, Otsuka K, Chen H, editors. International conference on displacive phase transformations and their applications in materials engineering. Warrendale (PA): TMS; 1998. p. 119. [15] Hayakawa M, Kuntani N, Oka M. Acta Metall 1989;37:2223. [16] Hayakawa M, Oka M. Acta Metall 1989;37:2229. [17] Hayakawa M, Adachi K, Oka M. Acta Metall 1990;38:1753. [18] Hugo GR, Muddle BC, Hannink RH. Mater Sci Forum 1988;34– 36:165. [19] Hugo GR, Muddle BC. Mater Sci Forum 1990;56–58:357. [20] Kriven WM, Fraser WL, Kennedy SW. In: Heuer AH, Hobbs LW, editors. Advances in ceramics. Science and technology of zirconia, vol. 3. Columbus (OH): American Ceramic Society; 1981. p. 82. [21] Bailey JE. Proc R Soc London Ser A 1964;279:395. [22] Kelly PM, Ball CJ. J Am Ceram Soc 1986;69:259. [23] Choudhry MA, Crocker AG. In: Claussen N, Ruhle M, Heuer AH, editors. Advances in ceramics. Science and technology of zirconia, vol. 12. Columbus (OH): American Ceramic Society; 1984. p. 46. [24] Kelly PM, Wauchope CJ. Key Eng Mater 1998;153–154:97. [25] Shi JL, Lin ZX, Qian WJ, Yen TS. J Eur Ceram Soc 1994;14:265. [26] Wechsler MS, Lieberman DS, Read TA. Trans Am Inst Min Eng 1953;197:1503. [27] Schubert H. J Am Ceram Soc 1986;69:270. [28] Schmauder S, Schubert H. J Am Ceram Soc 1986;69:534. [29] Kaufman L, Cohn M. Prog Met Phys 1958:165. [30] Wayman CM. Mater Sci Forum 1990;56–58:1. [31] Ling HC, Owen WS. Acta Metall 1981;29:1721. [32] Maki T. In: Proceedings of the 1st Japan international SAMPE symposium; 1989. p. 225. [33] Hsu (Xu Zuyao) TY. Mater Sci Forum 1990;56–58:145. [34] Hsu (Xu Zuyao) TY. J Mater Sci Technol 1994;10:107. [35] Zhang YL, Jin XJ, Hsu (Xu Zuyao) TY. J Eur Ceram Soc 2003;23:685. [36] Zhao Y, Zhang JH, Hsu (Xu Zuyao) TY. J Appl Phys 2000;88: 4022. Y.L. Zhang et al. / Acta Materialia 54 (2006) 1289–1295 1295