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 freemechanism 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