1906 Journal of the American Ceramic Society-Chevalier et al Vol. 92. No 9 ey of a tetragonal particle embedded in an infinite matrix. AGcl AUSE +AUs. When AGr-m becomes negative, the ugh a rather idealized configuration that does not take tetragonal particle is metastable or unstable and may transform grains, this simple analysis provides considerable insight into the AUSE, the addition of Y203 decreases the driving force of l-m factors affecting the transformation of the particle to its mono- transformation, hence its temperature(see yttria-zirconia phase clinic allotrope. The change of total free energy (4Gi-m)for the diagram in Panel A), making possible the retention of meta I-m transformation of the particle can be expressed by stable tetragonal phase in dense bodies at room temperatures. The elastic self-energy AUsE is directly related to the surround- △Gc+△UsE+△Us (1) ing matrix modulus, so having the matrix of a stiffer material such as alumina, increases AUse, stabilizing the tetragonal here AGe(<0 at temperatures below the equilibrium Ms tem- phase. It is also directly influenced by applied or internal perature)is the difference in chemical free energy between the stresses: tensile hydrostatic stress will act to reduce AUsE tetragonal and monoclinic phases. This is dependent on tem- destabilizing the tetragonal phase, whereas hydrostatic pressure perature and composition, implicitly including the oxygen va- favors the retention of the tetragonal phase. One of the con- content. The term AUsE (>0) refers to the change in sequences of these contributions is that the driving force for the strain energy associated with the transformation of par m transformation will not be the same inside the bulk and on This is dependent on the modulus of the surrounding urface(or even for powders). because neither AUSE nor AUs the size and shape of the particle, and the presence of are the same. In particular, there can be configurations at the internal or external stresses. The final term, AUs(>0)is the surface where the volume change of the transformation can be change in energy associated with the formation of new interfaces accommodated by a surface uplift( Panel B). This accommoda when the transformation occurs, for instance, cracks and mono- tion is not possible in the bulk. (The main features of the clinic variants. The particle remains in its tetragonal state tetragonal to monoclinic transformation at the surface and the if the overall thermodynamic driving force AGr-m>0, i.e. if bulk are schematized in Panel B. There is also the possibility Main Features of the Tetragonal to Monoclin inic Transformation in Zirconia Crystallography of the transformation The tetragonal to monoclinic phase transformation in zirconia is martensitic in nature. Even if alternative approaches have been recently developed, it is most often described by the phenomenological theory of martensitic crystallography(PTMC) The reader may refer to the work of Kelly and Rose> or of Deville et al. for a comprehensive description Crystallographic correspondences exist between the parent( tetragonal)and the product(monoclinic) phase, as schematized in Fig. Bl. They can be described by habit planes and directions(shape strain) as summarized in Table Bl. Thr lattice cor dences exist, called ABC, BCA, and CAB, which correspond to a change of the(ar, br c,) lattice axis of the gonal phase changes into(a, b e a,m) and(cm, anm bm), respectively. Each of these lattice correspondences may occur along two different habit planes. This leads to the six different configurations given in Table Bl and schematized in Fig. B2. The configurations depicted in Fig. B2 take into account the fact that four variants may occur for each crystallographic orrespondence(indeed, in the tetragonal symmetry, a, b, -a and -b are crystallographically equivalent). For each, the shear strain associated to the tetragonal to monoclinic(I-m) transformation is around 0. 16 and the volume expansion around 0.05 Parent phase(t) Fig. B1. Schematic illustration of crystallographic correspondences between the tetragonal(parent) and the monoclinic(product) phases during the martensitic (-m transformation f-m, tetragonal to monoclinic
energy of a tetragonal particle embedded in an infinite matrix. Although a rather idealized configuration that does not take into account the presence of a free surface or irregular shapes grains, this simple analysis provides considerable insight into the factors affecting the transformation of the particle to its monoclinic allotrope. The change of total free energy (DGtm) for the tm transformation of the particle can be expressed by DGtm ¼ DGc þ DUSE þ DUS (1) where DGc (o0 at temperatures below the equilibrium MS temperature) is the difference in chemical free energy between the tetragonal and monoclinic phases. This is dependent on temperature and composition, implicitly including the oxygen vacancy content. The term DUSE (40) refers to the change in elastic strain energy associated with the transformation of particles. This is dependent on the modulus of the surrounding matrix, the size and shape of the particle, and the presence of internal or external stresses. The final term, DUS (40) is the change in energy associated with the formation of new interfaces when the transformation occurs, for instance, cracks and monoclinic variants. The particle remains in its tetragonal state if the overall thermodynamic driving force DGtm40, i.e. if jDGcj < DUSE þ DUS. When DGtm becomes negative, the tetragonal particle is metastable or unstable and may transform into its monoclinic state. By decreasing jDGcj and increasing DUSE, the addition of Y2O3 decreases the driving force of tm transformation, hence its temperature (see yttria–zirconia phase diagram in Panel A), making possible the retention of metastable tetragonal phase in dense bodies at room temperatures. The elastic self-energy DUSE is directly related to the surrounding matrix modulus, so having the matrix of a stiffer material, such as alumina, increases DUSE, stabilizing the tetragonal phase. It is also directly influenced by applied or internal stresses: tensile hydrostatic stress will act to reduce DUSE, destabilizing the tetragonal phase, whereas hydrostatic pressure favors the retention of the tetragonal phase. One of the consequences of these contributions is that the driving force for the tm transformation will not be the same inside the bulk and on its surface (or even for powders), because neither DUSE nor DUS are the same. In particular, there can be configurations at the surface where the volume change of the transformation can be accommodated by a surface uplift (Panel B). This accommodation is not possible in the bulk. (The main features of the tetragonal to monoclinic transformation at the surface and the bulk are schematized in Panel B.) There is also the possibility Panel B. Main Features of the Tetragonal to Monoclinic Transformation in Zirconia Crystallography of the transformation. The tetragonal to monoclinic phase transformation in zirconia is martensitic in nature. Even if alternative approaches29 have been recently developed, it is most often described by the phenomenological theory of martensitic crystallography (PTMC). The reader may refer to the work of Kelly and Rose30 or of Deville et al. 31 for a comprehensive description. Crystallographic correspondences exist between the parent (tetragonal) and the product (monoclinic) phase, as schematized in Fig. B1. They can be described by habit planes and directions (shape strain) as summarized in Table B1.31 Three possible lattice correspondences exist, called ABC, BCA, and CAB, which correspond to a change of the (at, bt, ct) lattice axis of the tetragonal phase changes into (am, bm, cm), (bm, cm, am) and (cm, am, bm), respectively. Each of these lattice correspondences may occur along two different habit planes. This leads to the six different configurations given in Table B1 and schematized in Fig. B2. The configurations depicted in Fig. B2 take into account the fact that four variants may occur for each crystallographic correspondence (indeed, in the tetragonal symmetry, a, b, –a and –b are crystallographically equivalent). For each, the shear strain associated to the tetragonal to monoclinic (t–m) transformation is around 0.16 and the volume expansion around 0.05. Fig. B1. Schematic illustration of crystallographic correspondences between the tetragonal (parent) and the monoclinic (product) phases during the martensitic tm transformation. tm, tetragonal to monoclinic. 1906 Journal of the American Ceramic Society—Chevalier et al. Vol. 92, No. 9
September 2009 The Tetragonal-Monoclinic Transformation in Zirconia Table B1. Crystallographic Features of the Tetragonal-Monoclinic Martensitic Transformation in Zirconia correspondence shear Shape amplitude ABC I 0.0344 -0.9537 0.0026 0.1640 0.1556 0.0518 0.0055 0.0028 0.3005 0.1640 ABC 2 0.0344 0.0915 0.1597 0.1640 0.1556 0.0518 0.0171 0.0007 -0.9956 0.0373 BCA I (1)010J 0.0344 0.0034 0.0030 0.1761 0.1683 0.0518 0.1751 0.9193 0.0186 BCA 2 (1l)o 0.0344 0.0168 0.0004 0.176l 0.1683 0.0518 0.9996 0.0558 0.0241 0.1670 CAB I [00.0027 0.3006 0.1640 0.164 0.1556 0.0518 0.9537 0.0026 0.0001 0.0002 CAB 2 (101)[o 0.0027 0.9958 -0.0373 0.1640 0.1556 0.0518 0.0915 0.1597 0.000 iput parameters: I-phase: a, =5.128 A, C,=5.224 A; m-phase: am=5.203 A, bm=5.217 A, c,=5.388 A, Bm,=98.91. Expression in the lattice axis system of the tragonal parent phase ' Expression in the orthogonal axis system bounded to the tetragonal lattice axis system ABC1 ABC2 BCA2 CAB1 ACt Fig B2. Self-accommodating variant pairs deduced from the different lattice correspondences with the effect of t-m transformation on a surface Features of the transformation at the surface Recently, atomic force microscopy(AFM) brought new insights into the transformation induced relief. A typical example of surface uplift associated to the onset of transformation in a ceria-stabilized zirconia is given in Fig. B3. The relief exhibit fourfold symmetry, with a set of four variants. This indicates that the free surfaces where the observations are done are nearly perpendicular to the craxis. Among the six possible configurations of Fig. B2, only ABCI and BCA2 present the most mportant shape strain along the craxis. In the case of BCA2, however, a significant strain takes place along the braxis to which would lead to important internal stresses. Therefore ABCI is the most likely to occur in practice at the surface, because all the volume increase associated to the transformation is relaxed through a surface uplift. In other words, for such configuration
Features of the transformation at the surface Recently, atomic force microscopy (AFM) brought new insights into the transformation induced relief. A typical example of surface uplift associated to the onset of transformation in a ceria-stabilized zirconia is given in Fig. B3. The relief exhibits fourfold symmetry, with a set of four variants. This indicates that the free surfaces where the observations are done are nearly perpendicular to the ct-axis. Among the six possible configurations of Fig. B2, only ABC1 and BCA2 present the most important shape strain along the ct-axis. In the case of BCA2, however, a significant strain takes place along the bt-axis too, which would lead to important internal stresses. Therefore ABC1 is the most likely to occur in practice at the surface, because all the volume increase associated to the transformation is relaxed through a surface uplift. In other words, for such configuration Fig. B2. Self-accommodating variant pairs deduced from the different lattice correspondences with the effect of tm transformation on a surface perpendicular to the junction plane.31 tm, tetragonal to monoclinic. Table B1. Crystallographic Features of the Tetragonal–Monoclinic Martensitic Transformation in Zirconia31 Lattice correspondence Lattice invariant shearw Magnitude of g Habit plane normalz Shape strainz Shape strain amplitude Shear component Volume change ABC 1 011 ð Þ 011 0.0344 0:9537 0:0055 0:3005 2 4 3 5 0:0026 0:0028 0:1640 2 4 3 5 0.1640 0.1556 0.0518 ABC 2 011 ð Þ 011 0.0344 0:0915 0:0171 0:9956 2 4 3 5 0:1597 0:0007 0:0373 2 4 3 5 0.1640 0.1556 0.0518 BCA 1 110 ð Þ 110 0.0344 0:0034 0:3935 0:9193 2 4 3 5 0:0030 0:1751 0:0186 2 4 3 5 0.1761 0.1683 0.0518 BCA 2 110 ð Þ 110 0.0344 0:0168 0:9996 0:0241 2 4 3 5 0:0004 0:0558 0:1670 2 4 3 5 0.1761 0.1683 0.0518 CAB 1 ð Þ 101 101 0.0027 0:3006 0:9537 0:0001 2 4 3 5 0:1640 0:0026 0:0002 2 4 3 5 0.1640 0.1556 0.0518 CAB 2 101 ð Þ 101 0.0027 0:9958 0:0915 0:0003 2 4 3 5 0:0373 0:1597 0:0001 2 4 3 5 0.1640 0.1556 0.0518 Input parameters: t-phase: at 5 5.128 A˚ , ct 5 5.224 A˚ ; m-phase: am 5 5.203 A˚ , bm 5 5.217 A˚ , cm 5 5.388 A˚ , bm 5 98.911. w Expression in the lattice axis system of the tetragonal parent phase. z Expression in the orthogonal axis system bounded to the tetragonal lattice axis system. September 2009 The Tetragonal-Monoclinic Transformation in Zirconia 1907