Chapter 2
Thermodynamic Considerations
and Phase Diagrams
As mentioned in section 1.3.4, Zirconia’s physical properties make it ideal as TBC. Unfortunately, pure Zirconia can not be used for such high temperature application because of its polymorphism and particularly because of the large volume expansion associated with the martensitic transformation tetragonal→monoclinic (t→m).
This transformation can be completely suppressed by Zirconia total stabilisation in the cubic form, which yields the so called Fully Stabilized Zirconia (FSZ), or can be prevented for a limited period of time, which depends on the working temperature, in a material known as Partially Stabilized Zirconia (PSZ).
This chapter deals with ZrO2 stabilization by means of different Rare Earth oxides
that will be called dopants: R2O3. As the relevant effects of alloying in ZrO2 are
based on the extent of cation (R3+) substitution the convention of expressing
concentration as atomic percent cation (mole percent of half-formula-unit for sesquioxides) will be adopted.
In particular the ZrO2-rich end in the ZrO2–RO1.5 phase diagram will be analysed
looking for analogies and differences in the stabilizer behaviour of these oxides. Due to strong similarities in doped Zirconia phase diagrams for different Rare Earth oxides, the ZrO2-YO1.5 diagram will be taken as a base line and the
behaviour of the other dopants will be analysed in comparison to this one.
2.1 Metastability in ZrO
2-RO
1.5phase diagram
An equilibrium phase diagram expresses the thermodynamic stable state of the material and it is derived from free-energy difference analysis. In fact, on the equilibrium line between the phases t and m, the free-energy difference ∆Gt-m=Gt-Gm is equal to zero thus t↔m is a reversible transformation. This means that, moving from this equilibrium line, by changing temperature and/or composition, the phase characterized by a lower content of energy will be more stable, hence the phase with a higher content of energy will transform irreversibly into the thermodynamically stable one (Silvestroni, 1992a).
On the other hand, a non-equilibrium phase (∆G>0) can be stabilized by means of an energy barrier ∆G* and it will remain in its state, even if not
thermodynamically favourable, for kinetic reasons. The resulting phase is termed
metastable. In Zirconia-Rare Earth oxides phase diagrams both the stable and
metastable phases are usually represented (Yoshimura, 1988).
The illustration in Fig. 2.1 shows a graphic representation of Gibbs free energy profile between a metastable and a stable phase: the higher the ∆G*, the longer would take for the metastable phase to evolve into the stable state. From now on the metastable phases will be indicated with the name of the corresponding stable phase written in italic and with an apex.
Fig. 2.1: Schematic representation of phase stabilization by increasing the energy barrier (∆G*) in case of ∆Gt-m>0 (Yashima, Kakihana, and Yoshimura, 1996).
In Zirconia based systems a variety of metastable states can be found, their existence is mainly due to:
• Chemical reactions • Slow diffusion of cations • Diffusionless transformations.
The metastable-stable diagrams discussed in this work exclude the influence of chemical reactions because the presence of other species would change the total bulk composition of the solid. Phase transformations due to chemical reactions should be separately treated taking into account also the chemical reactant, for example in ternary systems as ZrO2-RO1.5-H2O.
Slow kinetics is responsible for metastable phases formation under 1200°C. In fact, in this case phase conversion would occur by cation diffusion but this process is strongly affected by temperature and it is negligible below 1200°C. A relationship between the temperature and the time, at which the average cation diffuses through a distance of 3 µm, shows that it takes about 70 and 7 years at 1100°C and 1200°C respectively to travel the 3 µm distance (Fig. 2.2) (Yashima et al., 1996).
This means that, at this temperature, Zirconia can be considered stabilized in its metastable structure because no transformation can occur at a significant rate. Indeed diffusion of cations is so slow that conventional heat treatments are not enough to attain the true equilibrium phase and such an observation is
responsible for the significant discrepancies among the experimental ZrO2-RO1.5
phase diagrams in the literature below 1400°C (Yashima et al., 1996).
Fig. 2.2: Relationship between temperature and time in which the average atom travels through the distance of 3 µm (Yashima et al., 1996).
Diffusionless transformations, often called partitionless transformations, are responsible for metastable phase formation over 1200°C. Cations diffusion is avoided, quenching the solid solution: this mechanism ‘freezes’ the composition of the phase stable at high temperature in a composition-invariant metastable single phase.
It has to be noted that cation diffusion would be possible at such high temperature and the dopant would redistribute between product and parent phases if a slow cooling rate was applied. However, such phase conversion would be drastically slowed down in any case once temperature drops under 1200°C.
The To(k/j) lines have been defined as the limit to such partitionless transformation
and thus they represent the metastable phase boundaries in the ZrO2-RO1.5
binary solid solutions. On these lines, by analogy with the equilibrium phase boundaries, for a certain composition, the Gibbs free energies of parents, k, and products, j, phases are equal: Gk=Gj and, hence, an energy barrier between the two phases can allow their coexistence (section 2.2).
Fig. 2.3: Schematic representation of the crystal structures of monoclinic, tetragonal (t’ and t’’) and cubic phase (fluorite). The arrows denote the Oxygen displacement (Yashima et al., 1996).
2.1.1 Metastable phases due to diffusionless transformations
In the ZrO2-RO1.5 phase diagram the monoclinic and tetragonal solid solutions
are labelled m and t respectively. The cubic Zirconia solid solution is labelled f (fluorite-like) to distinguish it from the cubic Rare Earth oxide structure, which is normally designated as c.
The fluorite-type structure will be taken as a reference, thus the tetragonal and monoclinic structures will be considered as a fluorite phase distorted with tetragonal and monoclinic symmetry respectively (Fig. 2.3) and, then, evaluated considering the extent of such ‘distortion’.
Fig. 2.4: Fluorite-type structure. Two unit cells of the fluorite structure: the cations (white spheres) are arranged to form a face-centred cubic array
The fluorite structure can be viewed as a face-centred cubic array of cations (Zr4+ or R3+), represented by the white spheres in Fig. 2.4 and Fig. 2.5, with the anions (O2-) residing in the tetrahedral sites (red spheres). It has to be noted that, since
aliovalent dopants (R3+) are incorporated into Zirconia, its stabilization in the cubic structure involves anion vacancies, generated for charge compensation, (Li, Chen, and Penner-Hahn, 1994a), (Li, Chen, and Penner-Hahn, 1994c), (Li, Chen, and Penner-Hahn, 1994b). The Rare Earth dopants have larger ionic sizes than Zr4+ and tend to adopt 8-fold coordination with Oxygen within the solid solution, allowing vacancies to associate preferentially with the host cations and relieving the ‘Oxygen crowding’ around them.
Fig. 2.5: Location of the tetrahedral holes in the fluorite structure; on the right top view.
The tetragonal phase can be classified into the three forms: t, t’, t’’ (Yashima, Ishizawa, and Yoshimura, 1993b): the first is a stable phase, the second and third are metastable. In the t-phase and t’-phase the ct-axis is longer than the
af-axis (where the suffix t and f denotes the tetragonal and fluorite cell
respectively) and the Oxygen is displaced alternatively along the ct-axis; for these
phases the tetragonality is expressed by the axial ratio ct/at. The t’’-form is
interpreted as an intermediate phase between cubic and tetragonal phases since its axial ratio is one but, at the same time, the Oxygen is displaced along the ct-axis as in a tetragonal structure (Table 2.1).
ZrO2 Form symmetry Crystal displacementOxygen axial ratio, c/a Tetragonality
f Cubic no 1
t’’ Tetragonal yes 1
t’ Tetragonal yes >1
Table 2.1: Classification of tetragonal and cubic phases in the system ZrO2-RO1.5 (Yashima et al., 1993b).
The existence of the t’’-form clarifies the conflict in the literature about the presence of a mixed field (tetragonal+cubic) at the phase boundary between the tetragonal and cubic regions in ZrO2-RO1.5 compositionally homogeneous
samples, obtained by rapid quenching of their melt (Yoshimura, Yashima, Noma, and Somiya, 1990).
Phase analysis, conducted by Noma et al. using X-ray diffraction on samples containing 10-13 mol% YO1.5 reveals, in fact, the presence of a mixture of
tetragonal and cubic phases (Noma, Yoshimura, Somiya, Kato, Shibata and Seto, 1988), whereas, according to electron diffraction analysis, carried out by Zhou et al., an analogue sample is characterized by a tetragonal single phase (Zhou, Lei , and Sakuma, 1991).
The cubic phase ‘seen’ by Noma et al. and ‘disappeared’ in the study of Zhou et
al. is nowadays interpreted as t’’ phase, namely a structure with a cubic lattice
but with the Oxygen atom arrangement typical of a tetragonal phase.
Fig. 2.6: Relationship between Y content and the volume fraction of
t’-ZrO2 in the rapidly quenched ZrO2-YO1.5 (Yashima et al., 1993b).
Yashima et al. studied this behaviour on samples containing Erbia. The X-ray diffraction pattern of a powder form ZrO2 containing 14 mol% ErO1.5 showed that
the {400}-type reflection profile does not split into (004) and (400) ones (see Chapter 4), thus it should be interpreted as a cubic structure. On the other hand electron diffraction analysis put in evidence a (112) reflection, which is forbidden for the ideal fluorite-type structure. Also in this case the samples structure has been interpreted as t’’ phase and the (112) reflection has been attributed to the Oxygen ions displacement. As a result, the ‘tetragonal+cubic mixed field’ has to be interpreted as a region in which t’ and t’’ phases coexist. Indeed a de-convolution of the {400} reflection shows that the samples analysed by Yashima
et al. contain both t’ and t’’ forms with a higher percentage of t’’ (Yashima et al.,
1993b). The t’/t’’ phase region has been also observed in ZrO2-YO1.5 samples
and is even clearer in samples containing 12 mol% ErO1.5 (Yashima, Ishizawa,
against YO1.5 content and shows that the first decreases (and the t’’ phase
increases) when the second is increased.
In order to identify the position in the phase diagram of the To(f/t’’) and of the To(t’’/t’)
lines, the cubic-to-tetragonal phase transition has been investigated both at room and high temperature. Studies conducted at room temperature indicate that the t’ lattice parameters vary when the YO1.5 content increases, in particular the at–axis
increases and ct–axis decreases until they eventually reach a similar value when
the YO1.5 is about 14 mol% (Fig. 2.7).
Fig. 2.7:Relationship between YO1.5 content and t'-ZrO2 lattice
parameters at room temperature (Yoshimura et al., 1990).
Neutron-diffraction studies, conducted to calculate the Oxygen displacement as a function of the Yttria content at room temperature, have indicated that, increasing the YO1.5 content, the Oxygen displacement decreases and then is no longer
displaced above 20 mol% YO1.5 (Fig. 2.8). Consequently such composition is
interpreted to be the t’’-f phase boundary at room temperature (Yashima, M., Sasaki, S., Kakihana, M., Yamaguchi, Y., Arashi, H., Yoshimura, M., 1994).
Summarizing: at room temperature, with increasing Yttria content, the displacement of Oxygen ions in the unit cells decreases, so that the intensity of the (112) reflections and the tetragonality of the t’-ZrO2 decrease. At 14 mol%
YO1.5, tetragonality becomes 1, but the displacement of Oxygen ions is not
reduced to zero. Thus, samples with YO1.5 content between 16 and 18 mol% are
in the t’’-form (Yashima et al., 1993b), while sample with YO1.5 content between
10 and 16% are in the t’+t’’ region.
This high temperature cubic-tetragonal phase transition has been investigated by Yashima et al. using high temperature X-ray diffraction on rapidly quenched samples containing 12 and 14 mol% ErO1.5. Their experiments indicated that the
transition point is located in the vicinity of the cubic phase solubility limit. In particular the t’-form change occurs around 1390°C and between 900 and
1200°C, in ZrO2-12 mol.% ErO1.5 and ZrO2-14 mol.% ErO1.5 samples respectively
(Yashima et al., 1993), (Yashima et al., 1993b).
Fig. 2.8: Oxygen displacement as a function of Yttria content in ZrO2-YO1.5 solid solution. Unfortunately, due to the very small intensity of the (112) reflection in the X-ray diffraction over 1200°C, they were unable to distinguish whether the sample after
t’ change was t’’-ZrO2 or f-ZrO2. This feature is represented in the phase diagram
by the different suffix added to the name of the To line: To(f/t’) or To(t’’/t’). However
Yashima et al. believe that the t’ effectively changes first into t’’ before transforming into cubic symmetry at higher temperatures (Yashima et al., 1993b). A schematic Gibbs free energy-dopant content diagram can be utilized to summarize the phase stability and formation of the tetragonal phase (Fig. 2.9).
When a sample is quenched from a cubic single-phase region at a high temperature, the cubic phase with composition X higher than X0 is stable, where
X0 is the minimum composition at which the free energy of t’'-ZrO2 is equal to that
of cubic ZrO2. On the other hand, the cubic ZrO2 with composition X lower than
X0 transforms into t’’-ZrO2. The t’’-ZrO2, in turn, partially changes into t'-ZrO2 at a
lower composition than X0’, at which the free energy of t'-ZrO2, is equal to that of
t’’-ZrO2. This diagram also put in evidence the existence of an energy barrier
between t'- and t’’-ZrO2 {Yashima, Ishizawa, et al. 1993 #124} and the existence
of two lines (T0t’/t’’ and T0t’’/f) near the (t+f)/f phase boundary (Yashima et al.,
1993a).
It has to be noted, however, that discrepancies are found in literature about the nature of the cubic-to-t’ phase transformation as the position of the To(f/t) line,
sometimes, has been assumed to be located around the centre of the (tetragonal+cubic) two-phase field (Fig. 2.10).
Fig. 2.10: Schematic ZrO2-RO1.5 phase diagram (Sheu, Tien, and Chen, 1992).
2.2 The ZrO
2-Y
2O
3phase diagram
In this section the main features of the ZrO2-rich end of the metastable-stable
ZrO2-YO1.5 phase diagram will be analysed. Since the TBCs deposition
processes yield metastable states due to cation-diffusionless transformations, as a starting point, the metastable phase diagram in Fig. 2.11 will be examined. Unfortunately the exact position of the metastable phase boundaries is to some extent uncertain, this is highlighted by the adoption of a dotted line in Fig. 2.11 (Yashima et al., 1996).
The high temperature cubic phase with G composition transforms into the t”-form below or at the To(f/t’’) line while the rapid cooling of E compositions allows t’
formation at or below the To(f/t’) or To(t’’/t’). The final structure of the TBC with D
composition will be monoclinic as its rapid cooling is subject to two different cation-diffusionless transformations: first f→t’ and then t→m.
In section 2.1 it has been emphasized that not only the free energy difference between two phases, ∆G, but also the energy barrier, ∆G*, during a
transformation is a fundamental theory for justifying phase changes in Zirconia systems. As already said, such principles explain the two-form coexistence region which can also be observed between the tetragonal and monoclinic phases (region A in Fig. 2.11), and between t’ and t” forms (region B in Fig. 2.11) (Yoshimura et al., 1990). The presence of these regions is shown in Fig. 2.11 and in Fig. 2.12 with the overlapping of horizontal phase segments at the bottom of the diagram; in Fig. 2.11 they are also highlighted in yellow.
The material characterized, in as deposited conditions, by a content of Yttria so low that its path, upon cooling, passes across the To(t/m) line is described as
‘transformable’, as in TBC terminology this term refers to the t→m transformation. In practice this means that the stabilizer content has always to be over the value given by the intersection of the To(t/m) curve with the lowest working
temperature (room temperature). Such value, then, characterizes the minimum Yttria addition for the Y-PSZ applications as TBC.
By extension, the maximum stabilizer content, in a partially stabilized Zirconia, can be obtained by intersecting the To(f/t’’) curve with the lowest working
temperature. This composition also represents the minimum stabilizer content required for a fully stabilized Zirconia. Full stabilization usually refers, in fact, to the production of a cubic phase which has to be in thermodynamic equilibrium at the working temperatures and kinetically constrained from transforming at lower temperatures. Because the cubic-tetragonal transformation is not kinetically suppressible for YO1.5 contents lower than ≈20 mol%, retention of the cubic
phase upon cooling requires its composition to be above this percentage.
Fig. 2.11: ZrO2–YO1.5 metastable phase diagram: in yellow the two phase
The composition typically used in thermal barrier coatings for gas turbines is ZrO2-7.6±1 mol% YO1.5 (6–8 wt.% Y2O3), hereto abbreviated as 7YSZ. Such
composition can be assimulated to composition E in Fig. 2.11, thus as-deposited 7YSZ TBCs have a metastable tetragonal single-phase structure supersaturated with Y (t’).
Fig. 2.12: ZrO2-rich end of the ZrO2-YO1.5 metastable-stable
phase diagram (Yashima et al., 1996).
By annealing this composition (indicated as composition 1 in Fig. 2.12) for a long period of time above the eutectoid line (at 1000°C), the metastable tetragonal phase t’ is susceptible to partitioning into the equilibrium assemblage, as its free energy content is higher than that of the completely decomposed state. Thus it transforms into a mixture of Yttria-poor tetragonal phase t and Yttria-rich cubic phase f (t’→t+f). The equilibrium phase composition can be read as the intersection of the isothermal line for the working temperature with the tetragonal and cubic equilibrium phase boundaries: i.e. at the temperature T1 the composition B represents the metastable tetragonal state and TT1 and FT1 the
tetragonal and cubic phases respectively. On cooling from T1 temperature, the TT1 phase should change its composition following the equilibrium boundary t/t+f
and should transform into a mixture of monoclinic and cubic phases at the eutectoid temperature. However, due to the high cooling rate, it will transform directly into an oversaturated monoclinic phase when passing through the To(t/m)
line. This monoclinic phase is also metastable, since its Gibbs free energy is higher than that of a decomposed state of monoclinic + cubic phase. For this reason this metastable monoclinic phase is called m’-phase and could be transformed diffusionlessly into the tetragonal phase by heating above To(t/m).
With an analogue criteria, on cooling from the T1 temperature, the FT1
composition should change its composition following the t+f/f boundary but, due to the high cooling rate, it will transform into t’’ or t’.
2.3 ZrO
2co-doped with Yttria and one Rare Earth oxide
As shown in section 2.2, TBCs ‘non-transformability’ requires selecting a coating composition that yields a metastable t’ structure (as-deposited) and whose Tot/m
temperature is below room temperature. The range of stabilizer content that fulfil such requirements is represented by the shaded area in Fig. 2.13. On the other hand, since the coatings could also undergo partitioning, other points outside the shaded area are equally relevant (red dots in Fig. 2.13). Eventually it is correct to say that our interest is extended to the red dashed region in Fig. 2.13.
Fig. 2.13: Schematic ZrO2-RO1.5 rich region phase diagram.
The aim of this thesis is to analyse the stability of 7YSZ co-doped with a second Rare Earth oxide, hence a preliminary study on the ternary phase diagrams ZrO2-YO1.5-RO1.5 is needed in order to choose, at least theoretically, the amount
of co-dopant that is possible to add to produce a now-transformable TBC. In practice the same kind of analysis conducted so far for binary systems ZrO2-RO1.5 should be carried out on the new three constituents systems.
A ternary diagram consists of a triangular base prism with binary diagrams as lateral faces. As an example, a section at a given temperature of the phase diagram for the ZrO2-YO1.5-YbO1.5 system is shown in Fig. 2.14. In order to build
and RO1.5-R’O1.5 diagrams to be available. Therefore, due do the paucity of data
about ternary systems in the literature, as a starting point, the binary phase diagrams have been analysed for all the possible ZrO2-RO1.5 systems.
Fig. 2.14: Schematic ZrO2-YO1.5-YbO1.5 ternaryphase diagram (Rebollo, Gandhi, Levi, 2003). In each binary phase diagram, the relevant points, namely the red dots highlighted in Fig. 2.13, were marked in order to set the boundaries of the area of interest. These points are:
1. the values (in mol%) of the intersections between the 1400°C isotherm line and the boundaries of the tetragonal solid solution + cubic solid solution (fluoride) phase field; these points will be indicated as T1400 and F1400;
2. the temperature of the ZrO2 richer eutectic;
3. the values (in mol%) of the intersections between the metastable line Tof/t’
or Tot’’/t’ and:
a. the 1400°C isotherm line,
b. the eutectic temperature isotherm line, c. the room temperature isotherm line;
4. the values (in mol%) of the intersections between the eutectic isotherm line and the boundaries of the tetragonal solid solution + cubic solid solution (fluoride) phase field; these points will be indicated as EE and FE;
5. the values (wt% or mol%) of the intersections between the metastable line Tot/m and the room temperature isotherm line.
Once all these points were identified in all the diagrams and their coordinates collected, the sets of analogue points were plotted against the dopant atomic number, molecular weight and ionic radius. The aim was to find a trend in such graphs that would have allowed to cover possible ‘gaps’ in the available data
without the necessity of further experimental analysis. Of course, this methodology can only yield indicative results and, as such, has to be considered reliable only as a first approach study.
In the context of this problem, two different groups of dopants can be identified: one involves, in the range of temperature 1000-1500°C, the precipitation of cubic phase (fluoride type) to relieve the supersaturation of t’, whereas the second group tends to give pyroclore (R2Zr2O7) as precipitated phase (Indicated by Py in
the diagrams in Fig. 2.15). The first group include all the Rare Earths except for Lanthanium, Praseodymium and Neodymium that belong to the other group, albeit, for Neodymium, the precipitation of the zirconate occurs only at the lower temperature. Due to the poor knowledge about the thermodynamic of pyroclore precipitation, the study conducted within this work will be limited to the elements belonging to the first group.
In the literature there are many discrepancies about the estimated Rare Earth ionic radii because of the experimental difficulties often encountered when estimating such values (Silvestroni, 1992b). Therefore, the ionic radii used in this work will correspond to the revised values for Rare Earth trivalent ions (R3+) eight-fold coordinated from Shannon (Shannon, 1976).
The presence in literature both of experimental and calculated diagrams will also allow a parallel analysis and, eventually, a comparison between them.
2.4 Calculated phase diagram
The phase diagrams shown in Fig. 2.15 and in Fig. 2.16 are the result of the calculations that Yokokawa et al. reported after studying a range of Zirconia containing systems. Such diagrams are based on evaluated or estimated thermodynamic properties of stoichiometric compounds and solid solution in the ZrO2-RO1.5 systems (Yokokawa, Sakai, Kawada, and Dokiya, 1993).
Fig. 2.15: Calculated phase diagrams for ZrO2-RO1.5 binary
systems (Yokokawa et al., 1993). The ZrO2–YO1.5 system has been
Fig. 2.16: Calculated phase diagrams for ZrO2-ScO1.5 binary systems (Yokokawa et al., 1993). 0 2 4 6 8 10 12 14 16 18 20 0.085 0.09 0.095 0.1 0.105 0.11 Ionic Radius (nm) RO 1. 5 m o l% T1400 F1400 T1400 Sc F1400 Sc
Fig. 2.17: Trend for T1400 and F1400 molar composition versus dopant ionic radius.
0 2 4 6 8 10 12 14 16 18 20 22 24 0.085 0.09 0.095 0.1 0.105 0.11 Ionic Radius (nm) R O 1. 5 m o l % Ee Fe Ee Sc Fe Sc
900 950 1000 1050 1100 1150 1200 0.085 0.09 0.095 0.1 0.105 0.11 Ionic Radius (nm) E u te ct ic T em p er at u re ( C ) Eutectic Tempetature Eutectic Temperature Sc
Fig. 2.19: Trend for the eutectic temperature versus dopant ionic radius.
Fig. 2.17 and Fig. 2.18 clearly show that increasing the dopant ionic radius, the width of the t+f field both at 1400°C and at the eutectic temperature is increased. In reality this does not necessarily mean that the overall dimension of the tetragonal+cubic field is enlarging, in fact the eutectic temperature rises for higher values of the dopant ionic radius (Fig. 2.19) reducing the extent of this field.
The ZrO2-YO1.5 diagram fits very well within these trends if placed according to
ionic size (between Holmium and Dysprosium) but it does not if placed according to atomic mass or number (smaller than La). On the other hand, Scandia does not follow the trend in any case.
Calculated phase diagrams do not include metastable regions hence, in this case, no consideration about the behaviour of the diagram relevant points related to metastable phases could have been done.
2.5 Experimental phase diagram
Experimental diagrams describing the following systems were found in the literature: ZrO2-NdO1.5 (Andrievskaya and Lopato, 1995), ZrO2-SmO1.5
(Andrievskaya and Lopato, 1995), ZrO2-EuO1.5 (Andrievskaya and Lopato, 1995),
ZrO2-GdO1.5 (Sobol and Voronko, 2004), ZrO2-DyO1.5 (Pascual and Duran,
1980), ZrO2-YO1.5 (Yashima et al., 1996), ZrO2-ErO1.5 (Yashima et al., 1996) and
ZrO2-YbO1.5 (Gonzalez, Moure, Jurado, and Duran, 1993), ZrO2-ScO1.5 (Yashima
et al., 1996).
Nevertheless, the incomplete and fragmentary data presented in these diagrams did not allow the construction of a satisfactory graph for all the experimental (eight) points in our interest. Besides, even when the information about a relevant point was enough to build a graph, it was not always possible to identify a trend because of the high degree of data scatter between the experimental diagrams. Finally, in the very few cases in which a trend could be found, experimental data did not agree with calculated diagrams. This wide divergence in results can be attributed to the difficulty in the experimental procedure to obtain accurate values
and to the variety of metastable states that may form in Zirconia systems which often lead to contradictions and discrepancies when the same system is studied by different researchers (Yashima et al., 1996).
2.6 High temperature stability
The incoherence of the experimental data severely limited the possibility of using them for our purposes. On the other hand, other studies were found in the literature which were restricted to the evaluation of the metastable phases alone for the ZrO2-RO1.5 systems, instead of analysing the whole phase diagram.
According to these studies (Yashima et al., 1996), (Yoshimura et al., 1990), although the position of the Tot/m curve is uncertain, all ZrO2-RO1.5 systems
(where R is Nd, Sm, Y, Er or Yb) share a metastable t/m boundary with very similar features. For example, all of them have a composition correspondent to the intersection between the Tot/m curve and the room temperature line around
6-7 mol% RO1.5. The same studies reveal that also the Tof/t’ line is independent of
the dopant species except for Sc, in fact in this case both the Tot/m and the Tof/t’
curves are shifted to higher compositions in comparison to the other diagrams. Due to the fact that all the above cited binary systems share a similar metastable phase diagram, the final structure obtained in rapidly quenched ZrO2-RO1.5
systems is independent from the adopted dopant (Yoshimura et al., 1990). Thus the stabilizing effect of oxide additions to Zirconia can be considered invariant (at least in as-deposited conditions) whether Nd, Sm, Y, Er or Yb is adopted.
On the other hand, this behaviour does not reflect the long term durability of the coatings obtained by different oxides. In fact, these have different effects on the equilibrium phase boundaries of the t+f field which means that the equilibrium tetragonal phase formed by partitioning of the as-deposited structure could pass, upon cooling, through the Tot/m curve making the coating ‘transformable’ and
hence affecting its long term durability. Since such transformation is inevitable in terms of thermodynamics, it is of basic importance to evaluate the ‘kinetic resistance’ to partitioning of each system in order to assess the maximum temperature they can reach before being destabilised.
The relative effect of different trivalent stabilizers on the resistance of TBC materials against partitioning and the resulting monoclinic transformation is summarized in Fig. 2.20. In this picture the phase stability of singly doped binary ZrO2-RO1.5 compositions (circles) and co-doped ZrO2-RO1.5-R’O1.5 compositions
(diamonds) is plotted against the dopant radii. The phase stability is represented by the maximum temperature reachable before significant monoclinic formation is observed, and the shaded areas represent the temperatures where some partitioning is observed without significant monoclinic evolution upon cooling. Co-doped compositions showing no sign of instability at 1500°C (empty diamonds) are not expected to decompose at higher temperatures as they would enter the single phase cubic field.
The phase stability of singly doped Zirconias at constant dopant concentration (7.6%) shows a strong dependence on cation size, being optimal for Yb and Y and declining for both larger and smaller cations.
Fig. 2.20: Relative resistance to de-stabilization in Zirconia based systems, plotted as the temperature of the last heat treatment stage before the onset of substantial monoclinic formation, as a function of ionic size (8-fold coordination). The circles represent singly doped compositions (Y or Rare Earth), while the diamonds represent ternary compositions containing equal proportions of Y and a RE dopant, with the 15.2%YO1.5
composition added for comparison. The empty symbols denote compositions that did not exhibit any signs of partitioining (Levi, 2004).
The reasons for the trend of decreasing stability with ionic size are not immediately evident. In fact, since the decomposition of t’ into the equilibrium tetragonal+cubic forms requires long-range cation diffusion, the diffusion rates should vary inversely with cation size. A larger cation, in fact, is expected to introduce into the host structure a higher distortion level which should reduce the permeability to cation diffusion; such speculation, however, is clearly in contrast with the experimental observations.
According to Rebollo et al., thermodynamic considerations are more consistent with the experimental data than observations solely based on cation motion. Analysing the calculated diagrams shown in Fig. 2.15, they demonstrated that the driving force (namely the free energy difference between parent and produced phases) for the separation of t’ into t+f increases with the width of the corresponding two-phase field (Rebollo, Gandhi, and Levi, 2003) and that the t+f field widens systematically from Y to Nd. The deduction is that the driving force for phase separation may increase with increasing ionic size, justifying the experimental data illustrated in Fig. 2.20. A different approach was adopted to explain the poor resistance to de-stabilization in the ZrO2-ScO1.5 system. In this
case, in fact, instead of using, as for the other ZrO2-RO1.5 systems, the calculated
experimental phase diagram (Fig. 2.21) proposed by Yashima et al. (Yashima et al., 1996)
Fig. 2.21: Metastable-stable phase diagram in the ZrO2-ScO1.5 system
(Yashima, Ishizawa, Fujimori, Kakihana, Yoshimura, 1995).
In this diagram the tetragonal boundary shifts to higher concentrations reducing the driving force for partitioning and then making 7.6 mol% ScSZ essentially insensitive to partitioning (Rebollo, Gandhi, and Levi, 2003). Nevertheless, the concurrent shift in the Tot/m curve makes this composition ‘transformable’ upon
cooling in accordance with the experimental findings about ZrO2-ScO1.5 systems
