《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 zirconia-generation

Availableonlineatwww.sciencedirect.com SCIENCE Acta materialia ELSEVIER Acta Materialia 52(2004)5709-5721 Martensitic transformation in zirconia Part Il martensite wth Sylvain deville gerard Guenin, Jerome Chevalier Associate Research Unit 5510, Materials Science Department, National Institute of Applied Science(GEMPPM-INSA), Bat B Received 13 July 2004: received in revised form 23 August 2004: accepted 26 August 2004 Available online 25 September 2004 Abstract Though the martensitic transformation in zirconia has been the object of a very large number of studies for the last decades, qualitative and quantitative observations of the formation and growth of relief induced by low temperature treatments has hardly ever been reported. In the first part of the study(Martensitic transformation in zirconia, Part D), we have demonstrated the excellent agreement between the atomic force microscopy quantitative observations and the outputs of the calculations derived from the phe- nomenological theory of martensitic transformation. The intermediate stages of transformation were nonetheless not considered In this second part, the growth mechanisms of monoclinic phase resulting from the martensitic transformation in ceria-stabilized conia(10 mol% CeO2)are investigated. Surface transformation is induced by aging treatments in water vapor at 413 K. The obser- vations are rationalized by the recent analysis proposed for the crystallographic ABCl correspondence choice, where the c, axis transforms to the cm axis. Three growth modes are observed and interpreted in terms of transformation strains accommodation is the largest. The influence of grain boundary paths on the surface relief features is demonstrated. Overall, our results strong, stains Microcracks formation is observed, explaining grain pop-out where the crystallographic disorientation between two adjacent grains port the non-existence of a critical grain size for low temperature transformation, confirmed by the classical thermodynamics theory applied to this particular case. o 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Zirconia; Martensite transformation; Atomic force microscopy; Microcracks 1. Introduction phenomenon is know as aging, and has been widely investigated for its detrimental consequences on the long Martensitic transformations occur in a number of term performance of zirconia components. Several con metal alloys but also minerals and ceramics like zirconia clusions were drawn from the experimental observa- 2 ] In order to stabilize zirconia and retain it in its tions, performed mostly by tEm, sEM and XRD. metastable tetragonal structure at ambient temperature, among which the existence of a critical grain size was it is possible alloying it with various oxides, among observed, size varying from 0. 1 to 0.5 um in the case which yttria(Y2O3) and ceria(CeO2). If the metastable of 3Y-TZP [5, 6]. This existence of a critical grain size tetragonal structure is indeed retained at ambient tem- was demonstrated by the application of the classical perature, the transformation can however occur during thermodynamics theory [7, 8]. Moreover, it was argued low temperature treatment in water vapor [3, 4]. This the transformation was very different in the case ofY TZP and Ce-TZP, because of the respective trivalent Corresponding author. Tel: +334 7243 63 57; fax: +33 4 72 4385 and quadrivalent nature of the stabilizE ing specie, leading to a different oxygen vacancies concentration []. As a E-mail address: sylvain. deville(ainsa-lyon fr(S. Deville) consequence, the aging sensitivity of these two materials 1359-6454/$30.00 C 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi: 10. 1016/j.actamat. 2004.08.03

Martensitic transformation in zirconia Part II. Martensite growth Sylvain Deville *, Ge´rard Gue´nin, Je´roˆme Chevalier Associate Research Unit 5510, Materials Science Department, National Institute of Applied Science (GEMPPM-INSA), Baˆt B. Pascal, 20 av. A. Einstein, 69621 Villeurbanne Cedex, France Received 13 July 2004; received in revised form 23 August 2004; accepted 26 August 2004 Available online 25 September 2004 Abstract Though the martensitic transformation in zirconia has been the object of a very large number of studies for the last decades, qualitative and quantitative observations of the formation and growth of relief induced by low temperature treatments has hardly ever been reported. In the first part of the study (Martensitic transformation in zirconia, Part I), we have demonstrated the excellent agreement between the atomic force microscopy quantitative observations and the outputs of the calculations derived from the phe￾nomenological theory of martensitic transformation. The intermediate stages of transformation were nonetheless not considered. In this second part, the growth mechanisms of monoclinic phase resulting from the martensitic transformation in ceria-stabilized zir￾conia (10 mol% CeO2) are investigated. Surface transformation is induced by aging treatments in water vapor at 413 K. The obser￾vations are rationalized by the recent analysis proposed for the crystallographic ABC1 correspondence choice, where the ct axis transforms to the cm axis. Three growth modes are observed and interpreted in terms of transformation strains accommodation. Microcracks formation is observed, explaining grain pop-out where the crystallographic disorientation between two adjacent grains is the largest. The influence of grain boundary paths on the surface relief features is demonstrated. Overall, our results strongly sup￾port the non-existence of a critical grain size for low temperature transformation, confirmed by the classical thermodynamics theory applied to this particular case.
2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Zirconia; Martensite transformation; Atomic force microscopy; Microcracks 1. Introduction Martensitic transformations occur in a number of metal alloys but also minerals and ceramics like zirconia [1,2]. In order to stabilize zirconia and retain it in its metastable tetragonal structure at ambient temperature, it is possible alloying it with various oxides, among which yttria (Y2O3) and ceria (CeO2). If the metastable tetragonal structure is indeed retained at ambient tem￾perature, the transformation can however occur during low temperature treatment in water vapor [3,4]. This phenomenon is know as aging, and has been widely investigated for its detrimental consequences on the long term performance of zirconia components. Several con￾clusions were drawn from the experimental observa￾tions, performed mostly by TEM, SEM and XRD, among which the existence of a critical grain size was observed, size varying from 0.1 to 0.5 lm in the case of 3Y–TZP [5,6]. This existence of a critical grain size was demonstrated by the application of the classical thermodynamics theory [7,8]. Moreover, it was argued the transformation was very different in the case of Y– TZP and Ce–TZP, because of the respective trivalent and quadrivalent nature of the stabilizing specie, leading to a different oxygen vacancies concentration [4]. As a consequence, the aging sensitivity of these two materials 1359-6454/$30.00
2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2004.08.036 * Corresponding author. Tel.: +33 4 72 43 63 57; fax: +33 4 72 43 85 28. E-mail address: sylvain.deville@insa-lyon.fr (S. Deville). Acta Materialia 52 (2004) 5709–5721 www.actamat-journals.com

S. Deville et al. Acta Materialia 52(2004)5709-5721 was expected to be very different. Finally, microcracking ence ABCI was demonstrated. For this correspondence, was observed in the surroundings of transformed grains, it was shown the characteristics of the habit planes and and related to the volume and shear components of the transformation matrix allow a complete accommoda transformation. However, no direct observation and tion of transformation strains by a surface uplift outside clear interpretation of the microcracks formation has of the free surface. Minimal residual stresses should be been reported. The observation of martensite formed expected in that case. a particular interest of this anal during aging treatment is very appealing in regards of ysis relies in the interpretation of martensitic variants the lack of validation of the various theories, for several arrangement in the volume of the material from the reasons. The transformation is occurring at surface so experimental observations of relief features at the that it may be observed straightaway, and the influence surface of a free surface on the transformation can potentially On the other hand, if the martensitic phenomeno- be assessed. Moreover, the transformation is propagat- logical theory was successfully applied, it is worth ing step by step when performing several aging treat- remembering the theory does only describe the trans- ment in autoclave, so that intermediate stages of the formation in mathematical terms, and by no means ransformation should be observed. Then, the less stable in physical terms. No informations on the chemical parts(from an energetical point of view) of the surface mechanism of transformation are brought by the the- are the first one to transform: the transformation ory. If the spatial arrangement was well understood not triggered by the experimental observations, like in terms of transformation strain accommodation grains transforming under the beam during TEM obser the remaining questions were thus: how are these vations. Finally, the sample geometry has no effect on arrangements formed? How do they grow and how he transformation behavior, as opposed to thin foils fast? where the very low thickness induces some peculiar fea In this study, this approach is applied to investigate tures. It should therefore be possible determining some and analyze the nucleation and growth of martensite of the factors affecting the stability in ceria stabilized zirconia and subsequent consequences Considering the scale at which the transformation like microcracking. It is shown how the combination of occurring, very few qualitative and quantitative reports AFM observations and of the outputs of the phenome- of transformation induced relief can be found in the lit nological analysis can provide new insights on both the erature. Considering the dilatational(0.04)and shear physical and the chemical mechanisms of the transfor- (0.16)components of the transformation, this dearth mation, with particular attention being paid on the of experimental observations is not surprising; modifica- influence of the free surface on the variants growth tions of the surface relief occur below the micrometer modes. AFM observations were performed at different range, typically from 10 to 100 nm for a zirconia poly- steps of the aging treatment in order to follow locally crystal of typical grain size(0.5-3 um). In absence of the transformation at the surface of the sample with experimental validation of the relief features, the predic tions of transformation induced relief rely on the valid ity and relevance f the phenomenological theory [9, 10] of martensite transfor- 2. Experimental methods mation. Validation of these predictions requires precise quantitative measurements of martensite relief. The ef- Ceria stabilized zirconia (Ce-TZP) materials were fect of free surface on the transformation local charas processed by classical powder processing route, using teristics relies mostly so far on the outputs of Zirconia Sales Ltd powders, with uniaxial pressing and calculations [11-13]. Preliminary reports [14-16] have sintering at 1823 K for 2 h Residual porosity was neg- nonetheless drawn the attention of the potentialities of- ligible Samples were mirror polished with standard dia fered by atomic force microscopy(AFM), technique mond based products. offering a vertical resolution below the nanometer range The martensitic transformation was induced by a AFM allows straightforward observations of trans- thermal treatment in water vapor autoclave. This kind formed surfaces of bulk samples. The observation of of treatment is known to induce the tetragonal to mond partial transformation of the grains [16] already ques- clinic phase transformation in zirconia [3, 18, 19].Hence, tioned the existence of a critical size for the transforma these treatments were conducted in autoclave at 413K tion. The technique has just been applied [17] to in saturated water vapor atmosphere, with a 2 bar pres- investigate the martensitic relief at the end of the trans- sure, inducing phase transformation at the surface of the formation, and compared with the outputs of the crys- samples with time. Thermal treatment steps were tallographic theory of martensitic transformation. An bounded to the thermal activation of the transformation excellent quantitative agreement was found between and the technical limits of the autoclave. These steps he experimental observations and theoretical predic- could have been reduced by several decades if an higher tions. In particular, the peculiar behavior of correspond- treatment temperature had been chosen

was expected to be very different. Finally, microcracking was observed in the surroundings of transformed grains, and related to the volume and shear components of the transformation. However, no direct observation and clear interpretation of the microcracks formation has been reported. The observation of martensite formed during aging treatment is very appealing in regards of the lack of validation of the various theories, for several reasons. The transformation is occurring at surface so that it may be observed straightaway, and the influence of a free surface on the transformation can potentially be assessed. Moreover, the transformation is propagat￾ing step by step when performing several aging treat￾ment in autoclave, so that intermediate stages of the transformation should be observed. Then, the less stable parts (from an energetical point of view) of the surface are the first one to transform; the transformation is not triggered by the experimental observations, like grains transforming under the beam during TEM obser￾vations. Finally, the sample geometry has no effect on the transformation behavior, as opposed to thin foils where the very low thickness induces some peculiar fea￾tures. It should therefore be possible determining some of the factors affecting the stability. Considering the scale at which the transformation is occurring, very few qualitative and quantitative reports of transformation induced relief can be found in the lit￾erature. Considering the dilatational (0.04) and shear (0.16) components of the transformation, this dearth of experimental observations is not surprising; modifica￾tions of the surface relief occur below the micrometer range, typically from 10 to 100 nm for a zirconia poly￾crystal of typical grain size (0.5–3 lm). In absence of experimental validation of the relief features, the predic￾tions of transformation induced relief rely on the valid￾ity and relevance of the outputs of the phenomenological theory [9,10] of martensite transfor￾mation. Validation of these predictions requires precise quantitative measurements of martensite relief. The ef￾fect of free surface on the transformation local charac￾teristics relies mostly so far on the outputs of calculations [11–13]. Preliminary reports [14–16] have nonetheless drawn the attention of the potentialities of￾fered by atomic force microscopy (AFM), technique offering a vertical resolution below the nanometer range. AFM allows straightforward observations of trans￾formed surfaces of bulk samples. The observation of partial transformation of the grains [16] already ques￾tioned the existence of a critical size for the transforma￾tion. The technique has just been applied [17] to investigate the martensitic relief at the end of the trans￾formation, and compared with the outputs of the crys￾tallographic theory of martensitic transformation. An excellent quantitative agreement was found between the experimental observations and theoretical predic￾tions. In particular, the peculiar behavior of correspond￾ence ABC1 was demonstrated. For this correspondence, it was shown the characteristics of the habit planes and transformation matrix allow a complete accommoda￾tion of transformation strains by a surface uplift outside of the free surface. Minimal residual stresses should be expected in that case. A particular interest of this anal￾ysis relies in the interpretation of martensitic variants arrangement in the volume of the material from the experimental observations of relief features at the surface. On the other hand, if the martensitic phenomeno￾logical theory was successfully applied, it is worth remembering the theory does only describe the trans￾formation in mathematical terms, and by no means in physical terms. No informations on the chemical mechanism of transformation are brought by the the￾ory. If the spatial arrangement was well understood, in terms of transformation strain accommodation, the remaining questions were thus: how are these arrangements formed? How do they grow and how fast? In this study, this approach is applied to investigate and analyze the nucleation and growth of martensite in ceria stabilized zirconia and subsequent consequences like microcracking. It is shown how the combination of AFM observations and of the outputs of the phenome￾nological analysis can provide new insights on both the physical and the chemical mechanisms of the transfor￾mation, with particular attention being paid on the influence of the free surface on the variants growth modes. AFM observations were performed at different steps of the aging treatment in order to follow locally the transformation at the surface of the sample with time. 2. Experimental methods Ceria stabilized zirconia (Ce–TZP) materials were processed by classical powder processing route, using Zirconia Sales Ltd powders, with uniaxial pressing and sintering at 1823 K for 2 h. Residual porosity was neg￾ligible. Samples were mirror polished with standard dia￾mond based products. The martensitic transformation was induced by a thermal treatment in water vapor autoclave. This kind of treatment is known to induce the tetragonal to mono￾clinic phase transformation in zirconia [3,18,19]. Hence, these treatments were conducted in autoclave at 413 K, in saturated water vapor atmosphere, with a 2 bar pres￾sure, inducing phase transformation at the surface of the samples with time. Thermal treatment steps were bounded to the thermal activation of the transformation and the technical limits of the autoclave. These steps could have been reduced by several decades if an higher treatment temperature had been chosen. 5710 S. Deville et al. / Acta Materialia 52 (2004) 5709–5721

S. Deville et al Acta Materialia 52(2004)5709-5721 AFM experiments were carried out with a D3100 how obtaining a stack of four variants of corre nanoscope from Digital Instruments Inc, using oxide spondence ABCI was possible and energetically sta sharpened silicon nitride probes(Nanosensor, CONT-R ble, since all interfaces (inside and outside of the model)in contact mode, with an average scanning speed arrangement) between tetragonal and monoclinic of 10 um s. Since the I-m phase transformation is phases were habit planes of the same type. All the accompanied by a large strain, surface relief is modified transformation strain is accommodated by this con by the formation of monoclinic phase. The vertical res- figuration. Fig. 1(a) provides such an observation, olution of AFM allows following very precisely the with its evolution as a function of the aging treat- transformation induced relief. ment time. Treatments steps of 20 h at 413 K in autoclave were performed between each image. The progressive transformation of the inner tetragonal 3. Experimental results part of the arrangement is clearly observed. Thi behavior is interpreted in Fig. 1(b), with the progres 3. Variants growth modes sive growth of variants, toward the inside of the grain. The potential future habit planes are symbol Three different modes of variants growth are experi ized by the dashed line, the transformation strain mentally observed for the correspondence ABCl, lead- being constant along these planes. Hence, the vari- ing to a fourfold symmetry final arrangement. These ants can grow until the transformation is completed three modes will be, respectively, referred to as internal without being restrained by any transformation in growth, external growth and needle growth duced stresses. The way the primary variants can grow to form the initial fourfold symmetry arrange- 3.1.1. Internal growth ment will be discussed later, in regards of the other This first mode of transformation is related to the variants growth mode. This mode will be called"in partial transformation, reported in [17]. It was shown ternal growth, in regards of its peculiar features Fig. 1.(a) Observation of partial transform and internal growth. Aging steps of 20 h. Horizo tal scale: I um/div, vertical scale: 250 nm/div (b) nterpretation of the arrangement observed in(a). The vertical scale is not respected for clarity. The dashed lines represent the location of the inner habit planes before transformation

AFM experiments were carried out with a D3100 nanoscope from Digital Instruments Inc., using oxide sharpened silicon nitride probes (Nanosensor, CONT-R model) in contact mode, with an average scanning speed of 10 lm s
1 . Since the t–m phase transformation is accompanied by a large strain, surface relief is modified by the formation of monoclinic phase. The vertical res￾olution of AFM allows following very precisely the transformation induced relief. 3. Experimental results 3.1. Variants growth modes Three different modes of variants growth are experi￾mentally observed for the correspondence ABC1, lead￾ing to a fourfold symmetry final arrangement. These three modes will be, respectively, referred to as internal growth, external growth and needle growth. 3.1.1. Internal growth This first mode of transformation is related to the partial transformation, reported in [17]. It was shown how obtaining a stack of four variants of corre￾spondence ABC1 was possible and energetically sta￾ble, since all interfaces (inside and outside of the arrangement) between tetragonal and monoclinic phases were habit planes of the same type. All the transformation strain is accommodated by this con- figuration. Fig. 1(a) provides such an observation, with its evolution as a function of the aging treat￾ment time. Treatments steps of 20 h at 413 K in autoclave were performed between each image. The progressive transformation of the inner tetragonal part of the arrangement is clearly observed. This behavior is interpreted in Fig. 1(b), with the progres￾sive growth of variants, toward the inside of the grain. The potential future habit planes are symbol￾ized by the dashed line, the transformation strain being constant along these planes. Hence, the vari￾ants can grow until the transformation is completed, without being restrained by any transformation in￾duced stresses. The way the primary variants can grow to form the initial fourfold symmetry arrange￾ment will be discussed later, in regards of the other variants growth mode. This mode will be called ‘‘in￾ternal growth’’, in regards of its peculiar features. Fig. 1. (a) Observation of partial transformation and internal growth. Aging steps of 20 h. Horizontal scale: 1 lm/div, vertical scale: 250 nm/div. (b) Interpretation of the arrangement observed in (a). The vertical scale is not respected for clarity. The dashed lines represent the location of the inner habit planes before transformation. S. Deville et al. / Acta Materialia 52 (2004) 5709–5721 5711

S. Deville et al. Acta Materialia 52(2004)5709-5721 3.1.2. External growth surface, with the formation of a fully accommodated set This mode is the opposite of the first one. In this case of opposed variants, of fairly small size. The following (Fig. 2(a)), the transformation starts undoubtedly at the bservations show the progressive growth of the vari- y Fig. 2.(a)Observation of external growth. Aging steps of 20 h. Horizontal scale: I um/div, vertical scale: 250 nm/div(b) Interpretation of the rangement observed in(a). The position of the junction plane remains constant along the transformation. The vertical scale is not respected for clarity. The dashed lines represent the location of the habit planes at the previous transformation stage

3.1.2. External growth This mode is the opposite of the first one. In this case (Fig. 2(a)), the transformation starts undoubtedly at the surface, with the formation of a fully accommodated set of opposed variants, of fairly small size. The following observations show the progressive growth of the vari￾Fig. 2. (a) Observation of external growth. Aging steps of 20 h. Horizontal scale: 1 lm/div, vertical scale: 250 nm/div. (b) Interpretation of the arrangement observed in (a). The position of the junction plane remains constant along the transformation. The vertical scale is not respected for clarity. The dashed lines represent the location of the habit planes at the previous transformation stage. 5712 S. Deville et al. / Acta Materialia 52 (2004) 5709–5721

S. Deville et al Acta Materialia 52(2004)5709-5721 ants, the trace of the junction plane being in a constant transformation completion of the grain cannot proceed location. This behavior is well understood considering anymore, until an external event can provide supple the variants progressively grow into the volume of the mentary stresses to overcome the energy barrier opposed mple, while the junction plane remains in the same to transformation completion. The remaining untrans position(Fig. 2(b). All the transformation strain is formed part is transformed very rapidly. The grain goes again accommodated; the variants are at equilibrium from very partial transformation to transformation during all the growth steps. More complex arrange- completion during the last treatment step ments, like the so-called"L-arrangement[17 can be Though no statistical analysis was performed on the obtained by this mode, as shown in the last micrographs different growth modes, it seems from our experimental f Fig. 2(a). Since the variants grow in a direction op- observations the internal growth mode is the first mod posed to the junction plane, this mode will be called"ex- activated, after an apparent initial incubation period of ternal growth about 60 h, during which no surface transformation at all seemed to be observed. The external growth mode 3.1.3. Needle growth follows, and finally the isolated needle growth appears The last growth mode observed in these experiments Hence, the controlling factors of each growth mode corresponds to the transformation sequence observed in must be different Fig. 3. Again, transformation is very likely nucleating at the surface. An isolated martensite needle is formed and 3. 2. Variants growth kinetics grows in size. As soon as it is formed, it begins to gener ate opposite stresses(back stresses) in the surrounding sing experimental ob ons like in Figs. I(a). matrix, opposing continued transformation of the initial 2(a) and 3, the size of eac nt can be measured as variant. Since no complementary variants that could a function of their age, so the kinetic of variants accommodate the transformation strain are observe growth are obtained for every growth mode. These in the first steps, the back stresses are building up as kinetics are given, respectively, in Figs. 4-6. The width the variant thickens, until the formation of a second is normalized to the width of the fully transformed var variant is triggered by the shear components of the back ants for comparison between the three modes. Growth stresses. This second variant will again grow in size and speeds in each case were measured before normalization the formation of a third variant with this last Differences are observed between the three modes configuration, the added stresses are so high that the though similarities are also found. The simplest case is Fig 3. Observation of consecutive isolated needles growth. Aging steps of 20 h

ants, the trace of the junction plane being in a constant location. This behavior is well understood considering the variants progressively grow into the volume of the sample, while the junction plane remains in the same position (Fig. 2(b)). All the transformation strain is again accommodated; the variants are at equilibrium during all the growth steps. More complex arrange￾ments, like the so-called ‘‘L-arrangement’’ [17] can be obtained by this mode, as shown in the last micrographs of Fig. 2(a). Since the variants grow in a direction op￾posed to the junction plane, this mode will be called ‘‘ex￾ternal growth’’. 3.1.3. Needle growth The last growth mode observed in these experiments corresponds to the transformation sequence observed in Fig. 3. Again, transformation is very likely nucleating at the surface. An isolated martensite needle is formed and grows in size. As soon as it is formed, it begins to gener￾ate opposite stresses (back stresses) in the surrounding matrix, opposing continued transformation of the initial variant. Since no complementary variants that could accommodate the transformation strain are observed in the first steps, the back stresses are building up as the variant thickens, until the formation of a second variant is triggered by the shear components of the back stresses. This second variant will again grow in size and trigger the formation of a third variant. With this last configuration, the added stresses are so high that the transformation completion of the grain cannot proceed anymore, until an external event can provide supple￾mentary stresses to overcome the energy barrier opposed to transformation completion. The remaining untrans￾formed part is transformed very rapidly. The grain goes from very partial transformation to transformation completion during the last treatment step. Though no statistical analysis was performed on the different growth modes, it seems from our experimental observations the internal growth mode is the first mode activated, after an apparent initial incubation period of about 60 h, during which no surface transformation at all seemed to be observed. The external growth mode follows, and finally the isolated needle growth appears. Hence, the controlling factors of each growth mode must be different. 3.2. Variants growth kinetics Using experimental observations like in Figs. 1(a), 2(a) and 3, the size of each variant can be measured as a function of their age, so that the kinetic of variants growth are obtained for every growth mode. These kinetics are given, respectively, in Figs. 4–6. The width is normalized to the width of the fully transformed var￾iants for comparison between the three modes. Growth speeds in each case were measured before normalization. Differences are observed between the three modes, though similarities are also found. The simplest case is Fig. 3. Observation of consecutive isolated needles growth. Aging steps of 20 h. S. Deville et al. / Acta Materialia 52 (2004) 5709–5721 5713

S. Deville et al Acta Materialia 52(2004)5709-5721 that of external growth(Fig. 5). The width increase of the variants is proportional to the treatment time: the growth rate is thus constant. As far as the internal growth is concerned(Fig. 4), transformation occurs in two stages. In the first one, the variants width increases rapidly, and then approaches a lower and nearly con- stant growth rate, until transformation completion. A more complex behavior is observed needle growth mode untransformed volume (Fig. 6); transformation occurs in three stages. The first 0 two stages are similar to that of internal growth, with a age(hrs)at 140C progressive decrease of the growth kinetics. A third stage is finally observed with a very fast growth speed Fig. 4. Normalized variant width as a function of its age, internal to complete the transformation. growth mode The distinction between these three stages is based on of growth ven in Table 1 and can be discussed on the basis of strain accommodation arguments. For the three modes, the initial growth rate very similar(Il nm/h at 413 K), and must be therefore elated to a similar mechanism. It is therefore proposed to correspond to the unconstrained growth. At the very beginning of transformation, the magnitude of transfor mation induced stress due to non-accommodation(for needle growth)is so low that the variants are free to grow at a similar speed than in the case of a nearly tses fect accommodation demonstrated for the two ot modes(internal and external growth). However, as these back stresses are building up very rapidly in the regions of misfit as the variant thickens, the growth rate falls age(hrs)at 140C down very rapidly. This corresponds to the steady rate Fig. 5. Normalized variant width as a function of its age, external of growth(stage ID), where the growth rate is smaller than 3 nm/h and continuously decreasing with aging time. The growth rate of stage II of the internal growth is similarly low, but must be related to a different phe nomenon. In this case. it has been shown the transfor mation strains were continuously accommodated during the transformation. No induced stresses will act to slow down the transformation. Considering the pro posed analysis (Fig. I(b)), the progressive diminution age Il stage Ill of the size of the inner untransformed part is likely to 04 decrease the driving force for transformation, so that the overall growth rate decreases. By using the model 02 proposed for the volumic arrangement of the variants [17. it was possible calculating the remaining volume of untransformed tetragonal phase by using the 304050 remen its of the apparent traces of habit planes at sur- face. The estimation of the remaining untransformed Fig. 6. Normalized variant width as a function of its age, isolated volume(also normalized) is plotted on the same graph needle growth The correlation between the variants growth speed and Growth rate of martensite variants for the different growth modes Growth rate(nm/hatl40°)±1 Initial rate(stage D) Steady rate(stage n) Burst rate(stage In External growth

that of external growth (Fig. 5). The width increase of the variants is proportional to the treatment time; the growth rate is thus constant. As far as the internal growth is concerned (Fig. 4), transformation occurs in two stages. In the first one, the variants width increases rapidly, and then approaches a lower and nearly con￾stant growth rate, until transformation completion. A more complex behavior is observed needle growth mode (Fig. 6); transformation occurs in three stages. The first two stages are similar to that of internal growth, with a progressive decrease of the growth kinetics. A third stage is finally observed with a very fast growth speed to complete the transformation. The distinction between these three stages is based on the measurements of growth rate, given in Table 1, and can be discussed on the basis of strain accommodation arguments. For the three modes, the initial growth rate is very similar (11 nm/h at 413 K), and must be therefore related to a similar mechanism. It is therefore proposed to correspond to the unconstrained growth. At the very beginning of transformation, the magnitude of transfor￾mation induced stress due to non-accommodation (for needle growth) is so low that the variants are free to grow at a similar speed than in the case of a nearly per￾fect accommodation demonstrated for the two other modes (internal and external growth). However, as these back stresses are building up very rapidly in the regions of misfit as the variant thickens, the growth rate falls down very rapidly. This corresponds to the steady rate of growth (stage II), where the growth rate is smaller than 3 nm/h and continuously decreasing with aging time. The growth rate of stage II of the internal growth is similarly low, but must be related to a different phe￾nomenon. In this case, it has been shown the transfor￾mation strains were continuously accommodated during the transformation. No induced stresses will act to slow down the transformation. Considering the pro￾posed analysis (Fig. 1(b)), the progressive diminution of the size of the inner untransformed part is likely to decrease the driving force for transformation, so that the overall growth rate decreases. By using the model proposed for the volumic arrangement of the variants [17], it was possible calculating the remaining volume of untransformed tetragonal phase by using the meas￾urements of the apparent traces of habit planes at sur￾face. The estimation of the remaining untransformed volume (also normalized) is plotted on the same graph. The correlation between the variants growth speed and 0 0.2 0.4 0.6 0.8 1 0 10 20 30 40 50 60 age (hrs) at 140˚C variant width and untransformed volume (normalised) Stage I Stage II variant width untransformed volume Fig. 4. Normalized variant width as a function of its age, internal growth mode. Stage I 0 0.2 0.4 0.6 0.8 1 0 10 20 30 40 50 60 age (hrs) at 140˚C variant width (normalised) Fig. 5. Normalized variant width as a function of its age, external growth mode. 0 0.2 0.4 0.6 0.8 1 0 10 20 30 40 50 60 70 80 age (hrs) at 140˚C variant width (normalised) stage I stage III stage II Fig. 6. Normalized variant width as a function of its age, isolated needle growth mode. Table 1 Growth rate of martensite variants for the different growth modes Growth rate (nm/h at 140 C) ± 1 Initial rate (stage I) Steady rate (stage II) Burst rate (stage III) Needle growth 11 50 Internal growth 11 <1 – External growth 13 – – 5714 S. Deville et al. / Acta Materialia 52 (2004) 5709–5721

S. Deville et al. Acta Materialia 52(2004 )5709-5721 the remaining volume seems fairly good, supporting the ses are so high that reaching a fourfold configuration proposed interpretation. The underlying physical origin with partial transformation(like the one of Fig. l(a)) of this behavior may be related to the presence of a gra- was not favorable at all. The energy disequilibrium is dient of residual stresses at the surface [20]. The layer too high to allow partial transformation close to the free surface will be more affected by the pres- ence of residual compressive stresses opposed to the 3.3. Grain boundary effects transformation. The stresses can oppose the propaga tion of the habit plane in the near surface layer, in a sim- Several transformation induced relief can be ac- ilar manner to the action of oxide layers in the case of counted for by the presence and path of grain bounda- martensitic transformation in metals. However when ries and will be described now the transformation propagates (internal growth), the The first feature is related to the presence of external surface effects take more and more importance. Though variants, as described in [17], where secondary external ill speculative, this effect could explain the observed variants are observed on the sides of simple variants trend of growth rate. A program is under way in the lab- arrangement. An example of this is given in Fig. 7, with oratory to assess more precisely the role of the surface the corresponding interpretation of the variants residual stresses on the transformation propagation. arrangement below the free surface. The interesting The last trend (stage III) is only observed in the case point to note is the straightforward relationship between of needle growth, and corresponds to an"explosive" the apparent width of variants at the surface and the rowth. It has been shown for this mode that transfor- variants penetration depth below the free surface Vari mation strain is not accommodated and stresses conse- ations of variants width and height at surface will there- quently building up with the needle growth. These fore be directly related to a modification of the stresses will act to slow down the transformation prop- penetration depth, as shown in Fig. 7. Since the trans- agation, their magnitude being so high that the transfor- formation is, at least in the first stages, stopped by the mation is momentarily stopped presence of grain boundaries, it can be assumed the pen The energy necessary to complete the transformation etration depth variations reflects the path of grain was probably brought by an event exterior to the grain. boundaries in the volume of the grain, below the free If a neighboring grain is transforming(as it is the case surface. Triggering the transformation on the other side here), long range stresses can be induced in the sur- of the grain boundary requires additional stresses, which rounding grains. These stresses can overcome the energy are not provided in the first stage of the transformation barrier and trigger the transformation of the comple- The transformation induced relief appears thus as mentary variants all at once, so as to reach a final directly related to the grains boundaries path and shape arrangement where the transformation strains are below the free surface accommodated on the long range. It is worth noticing The second effect related to grain boundaries pres that only a minimum value of the growth rate in this ence has some very important consequences as far as stage can be provided here. Transformation completion the transformation propagation is concerned, and is re- could have occurred at any time during the treatment lated to the formation of microcracks. Fig 8 provides a step. Considering the fact that very large stresses are case where two parts of the surface(a and b) present a accumulated, it seems safe assuming the transformation fourfold symmetry, though with a slight disorientation, completion occurred all at once(explosive or burst while the third part(c)presents a very different orienta- growth), at a speed approaching the sound speed Stres- tion. The approximate grain orientation, deduced from Fig. 7. Observation and interpretation of more complex relief features with secondary external variants. The decrease of the width and height at surface is related to a decrease of the penetration depth of the variants

the remaining volume seems fairly good, supporting the proposed interpretation. The underlying physical origin of this behavior may be related to the presence of a gra￾dient of residual stresses at the surface [20]. The layer close to the free surface will be more affected by the pres￾ence of residual compressive stresses opposed to the transformation. The stresses can oppose the propaga￾tion of the habit plane in the near surface layer, in a sim￾ilar manner to the action of oxide layers in the case of martensitic transformation in metals. However, when the transformation propagates (internal growth), the surface effects take more and more importance. Though still speculative, this effect could explain the observed trend of growth rate. A program is under way in the lab￾oratory to assess more precisely the role of the surface residual stresses on the transformation propagation. The last trend (stage III) is only observed in the case of needle growth, and corresponds to an ‘‘explosive’’ growth. It has been shown for this mode that transfor￾mation strain is not accommodated and stresses conse￾quently building up with the needle growth. These stresses will act to slow down the transformation prop￾agation, their magnitude being so high that the transfor￾mation is momentarily stopped. The energy necessary to complete the transformation was probably brought by an event exterior to the grain. If a neighboring grain is transforming (as it is the case here), long range stresses can be induced in the sur￾rounding grains. These stresses can overcome the energy barrier and trigger the transformation of the comple￾mentary variants all at once, so as to reach a final arrangement where the transformation strains are accommodated on the long range. It is worth noticing that only a minimum value of the growth rate in this stage can be provided here. Transformation completion could have occurred at any time during the treatment step. Considering the fact that very large stresses are accumulated, it seems safe assuming the transformation completion occurred all at once (explosive or burst growth), at a speed approaching the sound speed. Stres￾ses are so high that reaching a fourfold configuration with partial transformation (like the one of Fig. 1(a)) was not favorable at all. The energy disequilibrium is too high to allow partial transformation. 3.3. Grain boundary effects Several transformation induced relief can be ac￾counted for by the presence and path of grain bounda￾ries, and will be described now. The first feature is related to the presence of external variants, as described in [17], where secondary external variants are observed on the sides of simple variants arrangement. An example of this is given in Fig. 7, with the corresponding interpretation of the variants arrangement below the free surface. The interesting point to note is the straightforward relationship between the apparent width of variants at the surface and the variants penetration depth below the free surface. Vari￾ations of variants width and height at surface will there￾fore be directly related to a modification of the penetration depth, as shown in Fig. 7. Since the trans￾formation is, at least in the first stages, stopped by the presence of grain boundaries, it can be assumed the pen￾etration depth variations reflects the path of grain boundaries in the volume of the grain, below the free surface. Triggering the transformation on the other side of the grain boundary requires additional stresses, which are not provided in the first stage of the transformation. The transformation induced relief appears thus as directly related to the grains boundaries path and shape below the free surface. The second effect related to grain boundaries pres￾ence has some very important consequences as far as the transformation propagation is concerned, and is re￾lated to the formation of microcracks. Fig. 8 provides a case where two parts of the surface (a and b) present a fourfold symmetry, though with a slight disorientation, while the third part (c) presents a very different orienta￾tion. The approximate grain orientation, deduced from Fig. 7. Observation and interpretation of more complex relief features with secondary external variants. The decrease of the width and height at surface is related to a decrease of the penetration depth of the variants. S. Deville et al. / Acta Materialia 52 (2004) 5709–5721 5715

S. Deville et al. Acta Materialia 52(2004)5709-5721 2um pop-out(arrows). 20 h later(right, height image). The a s between three grains(denoted a, b and c), 3D and height image(left and middle)and grain Fig 8. Formation of microcracks at the grain boundar ows on the first micrograph represent the approximate orientation of the a, and b, axis of the two adjacent grains. Arrows on the other micrographs indicate the microcracks location. Grains a and b have both the cr axis close the free surface normal, while grain c is differently oriented the fourfold symmetry of surface relief, is represented by tion induced relief features. By using the analysis of the arrows on the first micrograph of Fig. 8 the influence of grain boundaries, the presence of micro- At the various interfaces of theses zones, microcracks cracks and the approximate orientation derived from the are revealed by AFM observations. This is illustrated fourfold symmetry, it possible describing the grain the middle micrograph of Fig. 8, in height mode; the boundaries paths(dashed lines ). Three grains(1, 4 and contrast steps reflect the path of microcracks(arrows). 5) presenting a close orientation(c, axis close to free sur If further aging treatment is performed, microcracking face normal) are observed in the middle part. Other is so extensive that grain pop-out occurs, and some part grains (2, 3 and 6) with different orientations are ob- of the surface are taken away, as shown on the right- served in the surroundings. Microcracks are observed hand side micrograph of the figure(arrows), where the at the locations of orientation misfit. It is also worth remaining holes are easily observed. Holes are located noticing grain pop-out occurred where the misfit was where important microcracking was previously the greatest, i.e. between grains 3 and 4 or 4 and 6 observed, and between grains having the largest diori- Grains 3 and 6 do not show any evidence of a fourfold entation relationships symmetry, so that their cr axis must be away from the These observations allow explaining the whole proc free surface normal, and therefore very different of that ess of microcracks formation: (a) transformation occurs in two adjacent grains, but having different crystallo- graphic orientations (b) variants grow until the grain boundary is reached(c) microcracks are formed due to ransformation accommodation misfit at the grain boundary( d)grain pop-out occurs as a consequence of extensive microcracking Finally, if the two adjacent grains present a crystallo- graphic orientation nearly identical, it is possible observ ing transgranular variants running through the grai boundary. This has already been demonstrated in 3Y TZP [16], and is also probably the case here in Fig. 9 for Ce-TZP. The orientation misfit leads to an interrup- tion of the symmetry in the middle of the transformed parts. The estimated grain orientations are given in the figure, along with the grain boundary location(dashed line). The occurrence of low-disorientation grain bound aries is fairly common in ceramics, so that it is a plausi 2 ble explanation for the relief features observed in Fig. 9 All these observations can be used to interpret the Fig. 9. Probable grain boundary of low disorientation, leading to the ransformation behavior at a larger scale, as shown in orientation of the a, and b, axis of the two adjacent grains is plotted on Fig. 10. A partially transformed zone of larger size the micrograph, along with the position of the grain boundary(dashed hown in the figure, with various different transforma

the fourfold symmetry of surface relief, is represented by the arrows on the first micrograph of Fig. 8. At the various interfaces of theses zones, microcracks are revealed by AFM observations. This is illustrated in the middle micrograph of Fig. 8, in height mode; the contrast steps reflect the path of microcracks (arrows). If further aging treatment is performed, microcracking is so extensive that grain pop-out occurs, and some part of the surface are taken away, as shown on the right￾hand side micrograph of the figure (arrows), where the remaining holes are easily observed. Holes are located where important microcracking was previously observed, and between grains having the largest disori￾entation relationships. These observations allow explaining the whole proc￾ess of microcracks formation: (a) transformation occurs in two adjacent grains, but having different crystallo￾graphic orientations (b) variants grow until the grain boundary is reached (c) microcracks are formed due to transformation accommodation misfit at the grain boundary (d) grain pop-out occurs as a consequence of extensive microcracking. Finally, if the two adjacent grains present a crystallo￾graphic orientation nearly identical, it is possible observ￾ing transgranular variants running through the grain boundary. This has already been demonstrated in 3Y– TZP [16], and is also probably the case here in Fig. 9 for Ce–TZP. The orientation misfit leads to an interrup￾tion of the symmetry in the middle of the transformed parts. The estimated grain orientations are given in the figure, along with the grain boundary location (dashed line). The occurrence of low-disorientation grain bound￾aries is fairly common in ceramics, so that it is a plausi￾ble explanation for the relief features observed in Fig. 9. All these observations can be used to interpret the transformation behavior at a larger scale, as shown in Fig. 10. A partially transformed zone of larger size is shown in the figure, with various different transforma￾tion induced relief features. By using the analysis of the influence of grain boundaries, the presence of micro￾cracks and the approximate orientation derived from the fourfold symmetry, it possible describing the grain boundaries paths (dashed lines). Three grains (1, 4 and 5) presenting a close orientation (ct axis close to free sur￾face normal) are observed in the middle part. Other grains (2, 3 and 6) with different orientations are ob￾served in the surroundings. Microcracks are observed at the locations of orientation misfit. It is also worth noticing grain pop-out occurred where the misfit was the greatest, i.e. between grains 3 and 4 or 4 and 6. Grains 3 and 6 do not show any evidence of a fourfold symmetry, so that their ct axis must be away from the free surface normal, and therefore very different of that Fig. 8. Formation of microcracks at the grain boundaries between three grains (denoted a, b and c), 3D and height image (left and middle) and grain pop-out (arrows), 20 h later (right, height image). The arrows on the first micrograph represent the approximate orientation of the at and bt axis of the two adjacent grains. Arrows on the other micrographs indicate the microcracks location. Grains a and b have both the ct axis close the free surface normal, while grain c is differently oriented. Fig. 9. Probable grain boundary of low disorientation, leading to the observed disrupted relief of transgranular variants. The approximate orientation of the at and bt axis of the two adjacent grains is plotted on the micrograph, along with the position of the grain boundary (dashed line). 5716 S. Deville et al. / Acta Materialia 52 (2004) 5709–5721

S. Deville et al Acta Materialia 52(2004)5709-5721 The ABCI correspondence is the more favorable from an energetic point of view. grains likely to have their c, axis close to the surface normal are the first ones to transform [17] 1 For this correspondence, three different modes of var wants growth have been identified, all of which leading to a final fourfold symmetry. In particular, the partial 4 transformation formed by four opposed variants is a stable configuration, since all the transformation strains are accommodated on long range. In this case, the transformation is proceeding progressively to its completion Variants can propagate into the volume by the exter 3 nal growth mode until an obstacle (i.e. grain bound ary)is encountered. Variants then grow from the inside(internal growth). All the variants are thus joining themselves at a grain boundary, at a common origin If isolated single variants are formed (i.e. without a symmetric variant), transformation strains are not Fig. 10. Observation of transformation induced relief in a large portion of the surface. The relief features allow the approximate accommodated, so that very high level of transforma determination of the location of grain boundaries. Deduced grains are tion induced stresses can be obtained locally. Consid numbered, and grain pop-out tions are indicated. Grains 1.4 ering the very large energy disequilibrium, the and 5 present a very low crysta nic disorientation. Dashed lines transformation is brought to its completion quasi-in represent the expected grain bo stantaneously when stimulated by an external(extra grain)event. In this case, the variants growth speed is at least larger of one range of order than for stable of grain 4. The misfit is consequently more important internal or external growth than between grains I and 4 for which crystallographic orientations are very similar The formation of micro- As far as the nucleation of variants leading to the for- cracks that could later grow in size and potentially lead mation of partially transformed grains(Fig. 1(a)is con to critical defects and components failure is here under- cerned, two mechanisms can be considered: stood at a microscopic scale, in terms of crystallographic arguments. A phenomenon occurring at the scale of the Each one of variants is formed after the other (i.e grain has macroscopic consequences. The presence of needle growth mode), by nucleation at the surface microcracks in the transformed zone has previously and propagation into the volume as the variant been demonstrated [21, 22], though the underlying criti grows. As the magnitude of transformation induced cal factors for their formation have never been under stresses increases with the growth of the variants, stood so straightforwardly these stresses can act to trigger the transformation of neighboring complementary variants. Hence, it will very unlikely lead to the partial transformation 4. Discussion configuration, considering the energy disequilibrium and the above mentioned remarks 4 Variants nucleation The four variants composing the final arrangement are formed at the same time so that no intermediate As far as the nucleation of the variants is concerned situation with non-accommodated transformation it is worth resuming the main features of the experimen strains is encountered. The arrangement is stable tal observations at this point from its beginning, so that further growth of the var wants can proceed slowly and at equilibrium An incubation stage seems to be present during the aging induced transformation. No relief is observed Taking into account the partial conclusions pre- during the first 60 h of the aging treatment. Since sented the second mechanism is the more favorable can he AFM scans size is obviously limited, it cannot didate able to explain the experimental observations. In however be ascertained that no variants at all are this case. the variants must be formed all at once and formed at the surface of the sample during this nucleat ate at a common origin point. This analysis stage. draws several consequences concerning the chemical

of grain 4. The misfit is consequently more important than between grains 1 and 4 for which crystallographic orientations are very similar. The formation of micro￾cracks that could later grow in size and potentially lead to critical defects and components failure is here under￾stood at a microscopic scale, in terms of crystallographic arguments. A phenomenon occurring at the scale of the grain has macroscopic consequences. The presence of microcracks in the transformed zone has previously been demonstrated [21,22], though the underlying criti￾cal factors for their formation have never been under￾stood so straightforwardly. 4. Discussion 4.1. Variants nucleation As far as the nucleation of the variants is concerned, it is worth resuming the main features of the experimen￾tal observations at this point. An incubation stage seems to be present during the aging induced transformation. No relief is observed during the first 60 h of the aging treatment. Since the AFM scans size is obviously limited, it cannot however be ascertained that no variants at all are formed at the surface of the sample during this stage. The ABC1 correspondence is the more favorable from an energetic point of view. Grains likely to have their ct axis close to the surface normal are the first ones to transform [17]. For this correspondence, three different modes of var￾iants growth have been identified, all of which leading to a final fourfold symmetry. In particular, the partial transformation formed by four opposed variants is a stable configuration, since all the transformation strains are accommodated on long range. In this case, the transformation is proceeding progressively to its completion. Variants can propagate into the volume by the exter￾nal growth mode until an obstacle (i.e. grain bound￾ary) is encountered. Variants then grow from the inside (internal growth). All the variants are thus joining themselves at a grain boundary, at a common origin. If isolated single variants are formed (i.e. without a symmetric variant), transformation strains are not accommodated, so that very high level of transforma￾tion induced stresses can be obtained locally. Consid￾ering the very large energy disequilibrium, the transformation is brought to its completion quasi-in￾stantaneously when stimulated by an external (extra￾grain) event. In this case, the variants growth speed is at least larger of one range of order than for stable internal or external growth. As far as the nucleation of variants leading to the for￾mation of partially transformed grains (Fig. 1(a)) is con￾cerned, two mechanisms can be considered: Each one of variants is formed after the other (i.e. needle growth mode), by nucleation at the surface and propagation into the volume as the variant grows. As the magnitude of transformation induced stresses increases with the growth of the variants, these stresses can act to trigger the transformation of neighboring complementary variants. Hence, it will very unlikely lead to the partial transformation configuration, considering the energy disequilibrium and the above mentioned remarks. The four variants composing the final arrangement are formed at the same time, so that no intermediate situation with non-accommodated transformation strains is encountered. The arrangement is stable from its beginning, so that further growth of the var￾iants can proceed slowly and at equilibrium. Taking into account the partial conclusions pre￾sented, the second mechanism is the more favorable can￾didate able to explain the experimental observations. In this case, the variants must be formed all at once and nucleate at a common origin point. This analysis draws several consequences concerning the chemical Fig. 10. Observation of transformation induced relief in a large portion of the surface. The relief features allow the approximate determination of the location of grain boundaries. Deduced grains are numbered, and grain pop-out (gp) locations are indicated. Grains 1, 4 and 5 present a very low crystallographic disorientation. Dashed lines represent the expected grain boundaries. S. Deville et al. / Acta Materialia 52 (2004) 5709–5721 5717

S. Deville et al. Acta Materialia 52(2004)5709-5721 mechanism of the transformation, the first one being the neous nucleation). In that case, there is no need nucleation of the transformation in the volume and not to create a new interface between the two phases at the surface. It was believed the transformation was al- so that the transformation is much more favorable ways starting at the surface of the grains. The analysis from an energy point of view. proposed here provides evidences of the contrary, at (2) The second one is related to the approximations least during the first stages of the transformation and made in [17]. The matrix transformation was con this particular growth mode. When different growth siderably simplified by the cancellation of the terms modes are activated (i.e. isolated needle or external having a magnitude smaller than 6/1000. This growth, the nucleation of the variants occurs at the sur hypothesis is valid as far as the configuration of face, and variants propagate into the volume as they la transformation induced relief is concerned. How- er grow in sIze ever, as nearly all the terms of the transformation From the analysis proposed here, it is possible com- matrix are not strictly equal to zero, the abcl cor- pleting the scenario of the transformation [19, 23, 24 respondence does not allow a complete accommo- (a) chemical adsorption of water at the ZrO2 surface dation of the transformation strains. Though of (b)reaction of H,O with 0- on ZrO, surface to form de. some residual stresses are hydroxyl groups(OH)(c)grain boundary diffusion of expected. These second order stresses can act as a (OH) into the inner part(d) annihilation of the oxygen supplementary argument for the continuance of vacancies by(oh)(e) when the oxygen vacancy con the transformation on previously transformed centration is reduced so low that the tetragonal phase parts, adding to the first mentioned argument is no longer stable, t-m transformation occurs at a pref the four opposed variants(f) growth of the opposed var- the current experimental observations. If only the l rential site and leads to the simultaneous formation of The combination of these two effects can rationaliz iants until the surface is reached. This mechanism could orably orientated grains(with respect to the free sur- therefore explain both the incubation time and the ther- face) are transformed during the first stage, mal activation of the transformation observed exper transformation proceeds then by activating less favora mentally, as it would correspond to the time required ble orientation, as shown in Fig. 10. Grains 1, 4 and 5 for the (Oh) for diffusing along the grain boundary. are the first ones to transform, all of them having their This is supported by the strong correlation reported Cr axis close to the free surface normal. Transforma between the thickness of the transformed layer and the tion of grains 2, 3 and 6, grains that are more stable, diffusion distance of (OH)[25]. As further action of was triggered later, their crystallographic orientation the water is required for the transformation to propa- being much less favorable(no fourfold symmetry ob- gate, the observed thermal activation of the transforma- served, i.e. the transformation strains ad odation tion could corresponds to the thermal activation of the is not as good) (OH) diffusion along the grain boundaries. Since the transformation is thermally activated, the thermal treat- 43. Discussion on the thermodynamics modeling of the ment steps could have been shortened by electing an transformation higher temperature. Experiments were nonetheles bounded to the technical limits of the autoclave If a tetragonal grain does not transform all at bserved experimentally, there should not be a 4.2. Factors affecting the growth stage grain size below which transformation is not oc Moreover, some of the growth mechanisms do not re Having discussed the various growth mechanisms quire a nucleation of the transformation in the volume related to the ABCl correspondence, the intrinsic origin i.e. diffusion of species is not necessary. In the case of of the growth mechanism can also be questioned. It has external growth and isolated needle growth, transforma- been proven [17] the ABCI correspondence allows a tion starts at surface(not compulsory at a grain bound complete accommodation of transformation strains, so ary) and then propagates into the volume as the variants that no residual stresses are induced by the transforma- grow in size, so that the grain boundaries do not have tion Continuance of transformation in the surroundings any importance during the first stages. The growth stage of already transformed parts cannot be accounted by can be affected by a change in grain size, since grain these residual stresses. Two effects can account for the boundaries act as obstacles to the transformation but experimental observations the nucleation stage is very little sensitive to the grain 1) The first one arises from the classical nucleation It is worth recalling the end point thermodynamic ap- eory, which demonstrates the continuation of proach of the transformation at this point. The transfor the transformation is much easier where some parts mation has been analyzed in terms of thermodynamic of the crystal have already transformed(heteroge- arguments by several authors [7, 8, 26], and the free

mechanism of the transformation, the first one being the nucleation of the transformation in the volume and not at the surface. It was believed the transformation was al￾ways starting at the surface of the grains. The analysis proposed here provides evidences of the contrary, at least during the first stages of the transformation and this particular growth mode. When different growth modes are activated (i.e. isolated needle or external growth), the nucleation of the variants occurs at the sur￾face, and variants propagate into the volume as they la￾ter grow in size. From the analysis proposed here, it is possible com￾pleting the scenario of the transformation [19,23,24]: (a) chemical adsorption of water at the ZrO2 surface (b) reaction of H2O with O2
on ZrO2 surface to form hydroxyl groups (OH)
(c) grain boundary diffusion of (OH)
into the inner part (d) annihilation of the oxygen vacancies by (OH)
(e) when the oxygen vacancy con￾centration is reduced so low that the tetragonal phase is no longer stable, t–m transformation occurs at a pref￾erential site and leads to the simultaneous formation of the four opposed variants (f) growth of the opposed var￾iants until the surface is reached. This mechanism could therefore explain both the incubation time and the ther￾mal activation of the transformation observed experi￾mentally, as it would correspond to the time required for the (OH)
for diffusing along the grain boundary. This is supported by the strong correlation reported between the thickness of the transformed layer and the diffusion distance of (OH)
[25]. As further action of the water is required for the transformation to propa￾gate, the observed thermal activation of the transforma￾tion could corresponds to the thermal activation of the (OH)
diffusion along the grain boundaries. Since the transformation is thermally activated, the thermal treat￾ment steps could have been shortened by electing an higher temperature. Experiments were nonetheless bounded to the technical limits of the autoclave. 4.2. Factors affecting the growth stage Having discussed the various growth mechanisms related to the ABC1 correspondence, the intrinsic origin of the growth mechanism can also be questioned. It has been proven [17] the ABC1 correspondence allows a complete accommodation of transformation strains, so that no residual stresses are induced by the transforma￾tion. Continuance of transformation in the surroundings of already transformed parts cannot be accounted by these residual stresses. Two effects can account for the experimental observations: (1) The first one arises from the classical nucleation theory, which demonstrates the continuation of the transformation is much easier where some parts of the crystal have already transformed (heteroge￾neous nucleation). In that case, there is no need to create a new interface between the two phases, so that the transformation is much more favorable from an energy point of view. (2) The second one is related to the approximations made in [17]. The matrix transformation was con￾siderably simplified by the cancellation of the terms having a magnitude smaller than 6/1000. This hypothesis is valid as far as the configuration of transformation induced relief is concerned. How￾ever, as nearly all the terms of the transformation matrix are not strictly equal to zero, the ABC1 cor￾respondence does not allow a complete accommo￾dation of the transformation strains. Though of very low magnitude, some residual stresses are expected. These second order stresses can act as a supplementary argument for the continuance of the transformation on previously transformed parts, adding to the first mentioned argument. The combination of these two effects can rationalize the current experimental observations. If only the fav￾orably orientated grains (with respect to the free sur￾face) are transformed during the first stage, transformation proceeds then by activating less favora￾ble orientation, as shown in Fig. 10. Grains 1, 4 and 5 are the first ones to transform, all of them having their ct axis close to the free surface normal. Transforma￾tion of grains 2, 3 and 6, grains that are more stable, was triggered later, their crystallographic orientation being much less favorable (no fourfold symmetry ob￾served, i.e. the transformation strains accommodation is not as good). 4.3. Discussion on the thermodynamics modeling of the transformation If a tetragonal grain does not transform all at once, as observed experimentally, there should not be a critical grain size below which transformation is not occurring. Moreover, some of the growth mechanisms do not re￾quire a nucleation of the transformation in the volume, i.e. diffusion of species is not necessary. In the case of external growth and isolated needle growth, transforma￾tion starts at surface (not compulsory at a grain bound￾ary) and then propagates into the volume as the variants grow in size, so that the grain boundaries do not have any importance during the first stages. The growth stage can be affected by a change in grain size, since grain boundaries act as obstacles to the transformation, but the nucleation stage is very little sensitive to the grain size. It is worth recalling the end point thermodynamic ap￾proach of the transformation at this point. The transfor￾mation has been analyzed in terms of thermodynamic arguments by several authors [7,8,26], and the free 5718 S. Deville et al. / Acta Materialia 52 (2004) 5709–5721