Metastable Nanocrystalline Zirconia in Light of the Nucleation Theory

Article pubs.acs.org/JPCC

Metastable Nanocrystalline Zirconia in Light of the Nucleation Theory Helfried Naf̈ e* Institut für Materialwissenschaft, Universität Stuttgart, Heisenbergstraße 3, 70569 Stuttgart, Germany

Devendraprakash Gautam Tyndall National Institute Lee Maltings, University College Cork, Dyke Parade, Cork, Ireland ABSTRACT: It is demonstrated that the theoretical foundation for the existence of metastable nonmonoclinic zirconia due to nanocrystallinity contradicts the fundamental aspects of the classical nucleation theory. As a consequence, the stabilization of the thermodynamically less stable zirconia modifications cannot be related to metastability. The experimental findings suggest that nonmonoclinic zirconia at room temperature results from chemical reactions, the products of which slightly deviate from pure monoclinic zirconia in terms of composition and, hence, in terms of structure.

1. INTRODUCTION Fifty years ago, when Garvie1 described the existence of tetragonal zirconia at room temperature, birth was given to metastable tetragonal zirconia. According to Garvie, the lowtemperature tetragonal modification, even though it is thermodynamically less stable in comparison with the monoclinic phase, occurs because of the stabilizing effect of the surface energy arising from an extremely small crystallite size. Since then, tetragonal zirconia has been one of the examples of metastability in materials science. Subsequently Garvie’s reports1,2 on the topic have altogether been cited almost 1700 times which indicates how welcome they have been in the literature, mostly as a justification and confirmation of other authors’ findings and interpretations and mainly with regard to zirconia but beyond that as well (cf. refs 3−6). It was Volmer7 who pointed out that there is hardly something comparable to the phenomenon of metastability regarding the intricacy of the topic. As evidence, he invoked the length of time elapsed between the first scientific report on a metastability-related experiment in history and the comprehensive understanding of the observations.a Besides, he reminded that Ostwald, who rendered the field a great service by publishing the first methodizing overview of previous literature and, ultimately, by coining the term metastability, failed to recognize the true relevance of Gibbs’ contributions to the subject. In view of the wide variety of experimental difficulties in the field due to diverse influencing factors, Volmer considered the long-lasting lack of a guiding principle to be the main reason for the confusion in understanding. It was his declared aim to deliver such a guiding principle by means of his © 2016 American Chemical Society

overview of the nucleation theory comprehensively dealt with in the book “Kinetics of Phase Formation”.7 Not without regret Volmer recalled that there had already been such a guiding principle in the literature beforehand, namely the theory of capillarity by Gibbs9 originally published about 50 years prior to Volmer’s book. Gibbs’ ideas, however, remained unknown until Volmer10 discovered that his own thoughts were largely identical with what had been brought about by Gibbs much earlier. The varied history in connection with metastability should be remembered when in the following the question is raised as to whether metastable tetragonal zirconia really exists and proves a size effect in stabilizing a thermodynamically less stable crystalline powder. Similar to what Volmer had stated about metastable and supposed metastable events in history, the hypothesis of metastable tetragonal zirconia likewise was and still is accompanied by the discussion of experimental uncertainties, by doubts and alternative interpretations.

2. OBJECTIONS TO THE EXISTENCE OF METASTABLE ZIRCONIA In the literature the main objection to metastability was and still is that zirconia may exist in the tetragonal or cubic roomtemperature form only due to the influence of impurities. This had already been an issue when the existence of metastable zirconia was postulated for the first time.11 Consequentially, a Received: January 16, 2016 Revised: March 8, 2016 Published: April 26, 2016 10523

DOI: 10.1021/acs.jpcc.6b00512 J. Phys. Chem. C 2016, 120, 10523−10529

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The Journal of Physical Chemistry C

and, thus, has been verified many times, which concerns both the role of precipitation out of aqueous solutions25−28 and the role of sodium incorporation29−31 into the zirconia lattice. The so-called base-hot-water treatment32−34 as one of the preferred synthesis routes might even represent the implementation of a mixed approach. Quite a number of the examples mentioned above as arguments against metastability had already been known when Garvie put forward his ideas, some of the issues have been addressed in the course of the past 40 years. Among them was the discussion of problems with the interpretation of data on extremely fine-grained ceramic powders: viz. (i) interference may occur of possible surface energy effects with strain in the polydomain structure of most of the powder particles,35 and (ii) grain size variation by ball milling may be interfered with energy entry into the powder36 through which a size effect is difficult to be separated out from the overall energetic situation. Despite all of these facets of an opposing view on the existence of metastable zirconia, Garvie’s interpretation has been and still is considered to be a well-founded piece of scientific insight. The most important reason for that might be that Garvie corroborated his experimental resultsb by additionally providing a theoretical foundation. Up to the present this foundation has apparently functioned as a guiding principle in Volmer’s sense. That means it has served in the community as a higher-ranking argument in order to abstract from all experimentally justified reservations, which ultimately resulted in ignoring them completely. The problem, however, is that the theoretical foundation given by Garvie lacks any scientific value, which ever since has been overlooked in the literature. This will be demonstrated in the following.

number of subsequent studies concentrated on the role of impurities. Clark and Reynolds12 showed that the tetragonal crystals formed upon thermal treatment of dried ZrOCl2·H2O and Zr(OH)4·H2O convert very slowly and irreversibly to the monoclinic modification at about 600 °C and, thus, significantly below the temperature of the reverse process. In accordance with these observations, Cyprès, Wollast, and Raucq13 found that zirconia is tetragonal at room temperature only if the lattice is stabilized by foreign ions. The authors convincingly demonstrated by thermogravimetric analysis that the stabilization may be caused by either OH− or SO42− provided that the zirconia precipitated out of an aqueous solution with Zr(OH)4 or Zr(SO4)2 as solutes. In regard to Zr(SO4)2·4H2O, Clabaugh and Gilchrist14 noticed an extraordinarily slow process of decomposition with the result that SO3 still evolved at a temperature as high as 650 °C. Cyprès, Wollast, and Raucq saw the same behavior on their samples. Not until the temperature reached a value higher than 800 °C the crystalline powder stopped losing weight, and only then, when the crystals proved to be weight-invariant and pure, they were purely monoclinic. Therefore, the authors concluded that the only stable modification of zirconia is the monoclinic one at room temperature. Somewhat later, Clearfield15 independently came to a similar conclusion with regard to the role of agglomerates formed by adsorption of water at the grain surfaces of the zirconia crystals, which is why he designated his room temperature phase as crystalline hydrous zirconia. Its structure was found to be cubic. Boganov, Rudenko, and Makarov16 confirmed the aforementioned findings of Cyprès, Wollast, and Raucq13 by an X-ray diffraction study of the behavior of differently prepared zirconia samples. If the precursor was Zr(OH)4, the oxide resulting from thermal decomposition of the hydroxide at about 400 °C exhibited a cubic structure. Subsequently, upon slowly heating the sample up to 800 °C, it became tetragonal and, eventually, monoclinic. If the oxide stemmed from a nonaqueous synthesis route, it was and always remained monoclinic in the same temperature interval. Likewise, the results of Krauth and Meyer17 gave evidence that nothing else than the monoclinic modification emerges if pure zirconia is the starting material of their preparation technique, i.e., plasma spraying. The technique implies an extremely rapid quenching from a melt produced in a plasma torch. In contrast, if other oxides were added to zirconia as feedstock, the sprayed layers contained the tetragonal form of zirconia. Another impurity that proved to stabilize nonmonoclinic zirconia at room temperature is sodium. Sodium, even at small amounts, is incorporated into the zirconia lattice and induces it to become cubic without any relationship to metastability. This was first suggested by Nishizawa et al.18 and was later impressively confirmed by Fagherazzi and co-workers19−22 on the basis of X-ray and neutron diffraction studies. In the meantime, Näfe and Karpukhina23 have shown that Namodified cubic zirconia is a thermodynamically stable compound of its own, the existence of which reproducibly depends on the temperature and the chemical potential of sodium oxide in the surroundings. The same is also true for hafnia as a chemical twin to zirconia.24 In recent times the employment of different zirconia polymorphs has gained particular relevance in catalysis, which is why the interest in the preparation of nonmonoclinic zirconia is nowadays not only limited to academia. That means the insight described above has variously been put into practice

3. GARVIE’S THEORETICAL FOUNDATION The arguments that Garvie1,2 brought forward in order to demonstrate that tetragonal zirconia be metastable are based on conventional considerations of the thermodynamic stability of an arbitrary substance. If this substance consists of small particles and if, for the sake of exactness, the surface of the particles is included into the set of relevant state variables, the molar Gibbs free energy Gi of the substance i is composed of two additive contributions: Gi = μ°i + σiSA *

(1)

where μ°*i is the standard molar Gibbs free energy of i in its state of pure substance, σi is the Gibbs free energy of the surface per unit area, briefly the surface tension, and SA is the surface area of 1 mol of particles i. The standard state of pure substance means that the particles are coarse-grained for which the product between σi and SA can be neglected in comparison with μ*i° . According to Garvie, there must be a particle size, corresponding to a definite particle surface area, at which the two zirconia polymorphs with monoclinic (subscript m) and tetragonal (subscript t) structure coexist. At that point the molar Gibbs free energies Gm and Gt are identical and the differently sloped straight lines describing Gm and Gt as a function of the particle surface cross each other as illustrated in Figure 1. The slopes of the lines are assumed to be due to different values for σm and σt. In this way, left from the crossing point, where coarse-grained particles prevail, the condition Gm < Gt is fulfilled while right from it, i.e. in the range of extremely small particles with a large surface area, the opposite is true. As 10524


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the compound C with the thermodynamic stabilities of P1 and P2 differing from each other in their states of pure substance. That under the circumstances specified above, P1 or P2 may be generated as a phase of its own cannot be explained by applying conventional criteria of coexistence to these two phases alone. Therefore, the nucleation theory has been put forward, by means of which the phenomenon of metastability finds a conclusive interpretation. In the classical nucleation theory,38 the Gibbs free energy change Δg is examined as resulting from the change in the proportions of the new phase and the mother phase when the former is still in its embryonic state and the embryos have an extremely small size. Δg is the thermodynamic consequence of the dynamic interplay of formation and dissolution of the nuclei of the new phase, with the magnitude of Δg being considered as a function of the size of the aggregates of nuclei relative to the state of the pure mother phase. By transferring these ideas to the solution introduced above, out of which the phases P1 and P2 are expected to precipitate, the following components must be regarded as determining the energetic situation of the system: (i) the mother phase consisting of solvent molecules S; (ii) the dissolved species C representing the solutes of the mother phase; (iii) the nuclei of P1 and P2 symbolized by N1 and N2. Because of agglomeration and dissolution of the nuclei they build up aggregates, i.e., A1 and A2, of variable size. For simplicity, these aggregates are approximated as a sphere so that the surface areas of the aggregates can easily be described as a function of their radii r. On account of the abnormally large surface-to-volume ratio, the product of the surface tension and surface area noticeably contributes to the total Gibbs free energy. With the mole numbers nk of all relevant species being the extensive state variables and the pertaining chemical potentials μk being the conjugate intensive variables of the system, it holds for Δg under isobaric and isothermal conditions:

Figure 1. Schematic diagram representing the Gibbs free energy of monoclinic (m) and tetragonal (t) zirconia as a function of the surface area of a powder of fine-grained crystals (according to Garvie1).

a consequence, Garvie inferred that the tetragonal modification is more stable than the monoclinic one provided that the particle size is below a critical value. In other words, the small crystallite size stabilizes the otherwise less-stable tetragonal phase, which is supposed to provide an explanation for the occurrence of metastable tetragonal zirconia. As threshold particle size a value of about 30 nm was estimated.1 Later, Garvie2 refined his theoretical analysis insofar as eq 1 was brought into a mathematical form by means of which the Gibbs free energy gi of what Garvie calls a microcrystal was expressed as a function of the radius of that microcrystal. By assuming a spherical geometry, Garvie suggested the definition 4 gi = πr 3μ Vi ° + 4πr 2σi * (2) 3 where μV*i° denotes the same quantity as μ*i° but now referred to a unit volume of the microcrystal. Based on the same way of thinking as discussed above, the point of coexistence of the monoclinic and tetragonal modification of the microcrystal under consideration is defined by the critical radius rc that is obtained from equating gm and gt according to eq 2: σ − σt rc = −3 Vm° μ m − μ Vt ° (3) * * rc corresponds to a specific particle surface area. It is the radius of those particles whose surface area SAc defines the abscissa of the crossing point of the two straight lines in Figure 1.

(Δg )p , T = (g (nS , nC , nN1 , nN2))p , T − (g (nS , nC°))p , T

(4)

where nC° is the total number of moles of all sorts of solute species in the system, implying that nC° = nC + nN1 + nN2. From Euler’s homogeneous function theorem (cf. ref 39) and with taking the surfaces of the aggregates A1 and A2 as additional state variables into account, it follows for the two contributions to Δg: (g (nS , nC , nN1 , nN2))p , T = nSμS + nCμC + nN1μ N1 2 2 + nN2μ N2 + 4π (σP1σP2rA1 + σP2rA2 )

(5)

and

4. METASTABILITY AND POLYMORPHISM According to Ostwald,37 metastability characterizes the state of persistent stability of a system that in the course of a phase transition may exist in several stable states, implying that one of them may be comparatively more stable than the one under consideration. In the context of first-order phase transitions that Ostwald exclusively had in view when he coined the term, a prominent example of the manifestation of metastability is the spontaneous precipitation of either phase P1 or phase P2 out of one and the same supersaturated liquid solution of dissolved species of C in the arbitrary solvent S, with C representing the compound that may exist either in modification P1 or in modification P2. In other words, P1 and P2 are polymorphs of

(g (nS , nC°))p , T = nSμS + nC°μC

(6)

In a spherical aggregate, the number of nuclei assembling the aggregate is determined by the ratio between the volume of the sphere and the volume of each nucleus. Therefore, and in view of eqs 5 and 6, eq 4 can be rewritten as follows: 4 3 1 2 πσP2rA1 (μ − μC ) + 4πσP1σP2rA1 3 VN1 Ν1 4 3 1 2 (μ − μC ) + 4πσP2σP2rA2 + πσP2rA2 3 VN2 Ν2

(Δg )p , T =

10525

(7)


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The Journal of Physical Chemistry C The objective of the energetic considerations is to specify the state at which the whole system is in thermodynamic equilibrium. The condition for that is (dg (nS , nC , nN1 , nN2))p , T , nS , nC° = 0

(8)

where the constancy of nS and n°C means that the only change of the system is (i) due to the formation/decomposition of N1 or N2 at the expense/in favor of each other or (ii) due to the formation/decomposition of N1 and/or N2 at the expense/in favor of the dissolved species C. Mathematically, the above constraints have the consequence that the differentials dnN1 and dnN2 that result from applying condition (8) to eqs 5 and 6 are independent variables. This is likewise true for the differentials drA1 and drA2 that come into play if condition (8) is applied to eq 7 and the number of nuclei is expressed as a function of the equilibrium values rA1 * and rA2 * for the radii of the respective aggregates of nuclei:

Figure 2. Change of the Gibbs free energy Δg relative to the maximum value Δgmax as a function of the radii rA1 and rA2 of the aggregates of nuclei of two polymorphic substances dissolved in a liquid mother * , rA2 * : equilibrium values of the radii; curve shape calculated phase (rA1 according to eq 11).

⎛ r* ⎞ * drA1 0 = ⎜ A1 (μ Ν1 − μC ) + 2σP1⎟rA1 ⎝ VN1 ⎠ ⎛ r* ⎞ * drA2 + ⎜ A2 (μ Ν2 − μC ) + 2σP2⎟rA2 ⎝ VN2 ⎠

(9)

Independence means that in the most general case both of the variables drA1 and drA2 can simultaneously never be equal to zero. Therefore, the sum of additive terms in eq 9 is equal to zero only if each of the summands is separately equal to zero. In this way, two relationships can be derived which characterize the case of thermodynamic equilibrium between all species of the system: μ Ν1 − μC = −

2σP1 V * N1 rA1

μ Ν2 − μC = −

2σP2 V * N2 rA2

heterophase fluctuations.38 Randomly, the nuclei arise, persist for a while, agglomerate together or dissolve partly or completely, and vanish again, with the result that the proportions of N1 and N2 permanently change without precipitation taking place. Nevertheless, there is a small but nonvanishing probability for the formation of aggregates larger than rA1 * and rA2 * . Such aggregates have a much stronger tendency to grow to macroscopic crystals, which means that once they are present to a certain extent, the phase transition ultimately gets completed. It is known from practice that if the solute exists in various polymorphic modifications, only one of them precipitates from the solution. It is also known that there is no other way to control the result of the precipitation process than by inoculation of the solution or by seeding, i.e., by immersion of seed crystals of P1 or P2 in the solution. According to Volmer and Weber,10 the adsorption of nuclei at the respective surfaces of a seed crystal with subsequent growth of the surfaces is energetically much more favored than the formation of a totally new aggregate of nuclei out of the mother phase without seeds.

(10)

The shape of each of these relationships is the same as if only one sort of nuclei was present in the solution.7,38,40 By virtue of eq 10, the expression for Δg according to eq 7 changes as follows: ⎛ ⎛ 2 rA1 ⎞ 2 rA2 ⎞ 2 2 (Δg )p , T = 4πrA1 σP1⎜1 − σP2⎜1 − ⎟ + 4πrA2 ⎟ * * ⎠ 3 rA1 ⎠ 3 rA2 ⎝ ⎝ (11)

5. REACTIONS LEADING TO NONMONOCLINIC ZIRCONIA The aforementioned facts significantly contrast with those that Garvie took as a basis for his theoretical description. The first aspect of contrast, even though it is quite a formal but nevertheless a fundamental one, concerns the nature of the process that is under consideration. While metastability has a bearing on phase transition, Garvie referred to that phenomenon in order to explain the outcome of a chemical reaction. With regard to the possible role of sodium as an impurity the experiments that Garvie1 interpreted as yielding nonmonoclinic zirconia have to be understood as the result of an equilibrium reaction between monoclinic (m) and cubic (c) zirconia in the presence of small amounts of sodium oxide:

Equation 11 describes a two-dimensional surface in a threedimensional system of coordinates, represented by rA1, rA2, and Δg. Such a surface is exemplarily illustrated in Figure 2. It becomes apparent that the equilibrium point Δg(r*A1,r*A2) is identical with the maximum of the function Δg(rA1,rA2). That the system under consideration is in equilibrium and, thus, is in its most stable state although the Gibbs free energy runs through a maximum rather than a minimum is the characteristic feature of any metastable system. It is the essence of metastability. Even though the state at the maximum and all states within the radius intervals 0 ≤ rA1 ≤ r*A1 and 0 ≤ rA2 ≤ r*A2 are thermodynamically less favorable than the states far beyond r*A1 and rA2 * , the supersaturated solution together with the aggregates of solid nuclei of type N1 and N2 may persist for an unlimited period of time. Either types of nuclei together with the solution represent a system in which dynamic processes of growth and decay continuously proceed as a consequence of

(1 − δ)ZrO2 − ε (m) +

ε(1 − δ) δ O2 Na 2O + 2 2

⇌ Zr1 − δNaδO2 − 1.5δ (c) 10526

(12) DOI: 10.1021/acs.jpcc.6b00512 J. Phys. Chem. C 2016, 120, 10523−10529

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supersaturated solution. In the case of equilibrium an energetic discrimination into a more stable and a less stable state is excluded. Suppose the crossing point of the straight lines in Figure 1 would correspond to the equilibrium point Δg(rA1 * ,rA2 *) of Figure 2, the above statement means that the differently sloped curves to the right of the crossing point of Figure 1 do not exist. They have no thermodynamic justification. The conclusion drawn from these curves about the stabilization of the tetragonal modification is untenable. At first glance, eq 7 resulting from the nucleation theory seems to resemble Garvie’s eq 2. However, the similarity is merely superficial because the meaning of both equations is different. In order to find out what the differences are between eqs 2 and 7, the Gibbs free energy of the whole system according to eq 5 is tentatively split into the sum of energetic contributions formally stemming from three subsystems, namely

In other studies the existence of tetragonal (t) zirconia is likewise related to a chemical reaction rather than a phase transition. For instance, tetragonal zirconia may be the result of an imcomplete splitting off water from zirconium hydroxide: [Zr(OH)4 ]aq ⇌ (ZrO2 − δ (OH−)2δ )(t ) + (2 − δ)H 2O (13)

The effect of other anions on the emergence of the tetragonal modification is conceivable according to the same pattern. When authors claimed to have produced metastable tetragonal zirconia by means of gas condensation41 or by evaporation of metallic zirconium,42 it must likewise be suspected that a chemical reaction is the cause rather than a phase transition. The underlying reaction is likely to be a change in the oxygen stoichiometry, which means that the tetragonal modification is the result of an incomplete oxidation of zirconium or zirconium suboxide: ⎛ δ⎞ Zr + ⎜1 − ⎟O2 ⇌ ZrO2 − δ (t) ⎝ 2⎠ ZrO2 − χ +

χ−δ O2 ⇌ ZrO2 − δ (t) 2

(χ > δ )

(g (nS , nC , nN1 , nN2))p , T = (g (nS , nC))p , T + (g (nN1))p , T + (g (nN2))p , T (14)

(15)

Substituting the left-hand side of eq 15 with the right-hand side of eq 5 and making use of the same relationships as before, it is obtained

A similar interpretation may be envisaged in order to understand the emergence of cubic and tetragonal zirconia upon thermal decomposition of zirconium alkoxides,43 i.e., Zr(OR)4 with R being an organic substituent. Again, the process is clearly no phase transition but a chemical reaction. Since olefin and alcohol are split off from the alkoxide44 and since these substances may maintain a reducing oxygen atmosphere in the course of the thermal treatment, an incompletely oxidized oxide according to eq 14 could be the outcome. Alternatively, on account of the relationship between Zr(OH)4 and Zr(OR)4, it is conceivable that the alkoxide decomposes imperfectly and minor amounts of organic residues stabilize the nonmonoclinic structure of zirconia. Both of these hypotheses would agree with the observation of Mazdiyasni, Lynch, and Smith44 that a broad and undefined endothermic reaction over a range of several hundred degrees is discernible from a differential thermal analysis meanwhile the cubic zirconia undergoes transition to the tetragonal and, finally, monoclinic polymorph. If the alkoxide decomposition proceeds via hydrolysis,45 the formation of tetragonal zirconia may be understood as obeying eq 13. The common feature of all reactions the synthesis routes are based on is that they yield a product, the nature of which is not exactly identical with that of pure monoclinic zirconia. On the one hand, the deviation from the normative composition is due to the presence of foreign atoms that are either adsorbed or incorporated into the lattice, on the other hand, a native atom is concerned if the oxygen nonstoichiometry exceeds a tolerable limit. In both cases the imperfect composition induces a deviation from the monoclinic structure.

4 3 μ Ν1 2 πrA1 + 4πσP1rA1 3 VN1 4 3 μ Ν2 2 = πrA2 + 4πσP2rA2 3 VN2

(g (nN1))p , T = (g (nN2))p , T

(16)

The identity of eqs 2 and 16 means that Garvie concentrated on only a part of the total thermodynamic system and ignored that this system comprises more species than just N1 and N2. Garvie’s approach ignored the involvement of the reservoir of C species in the process of growth and decay with regard to A1 and A2, and it also ignored the nature of the solvent molecules for the energetic status of C. Instead of employing the most general way of expressing the equilibrium condition (8), Garvie defined the equilibrium case by simply equating g(nN1) and g(nN2) and, thus, arrived at the form of eq 3 from eq 16. In addition, by assuming that rA1 = rA2, Garvie’s considerations abstracted from the individual sizes of A1 and A2 although they are the logical consequence of the other individual properties. While one of the inherent features of metastability is that each of the polymorphs if dissolved in a solution has a finite, nonzero probability to precipitate out of that solution, the energetic circumstances as defined by Garvie according to Figure 1 always favor the emergence of only one single sort of the polymorphs. This process is strictly deterministic and cannot be affected by inoculation whereas the nucleation theory requires it to be random and highly sensitive to seeding. In summary, Garvie’s theoretical foundation disregards aspects that are of fundamental significance for the phenomenon of metastability. By this approach, although referring to Gibbs, the sophisticated character of Gibbs’ theory of capillarity is violated. There is a tendency in the literature to generalize Garvie’s considerations and to apply them to other polymorphic materials,3−5,46 implying that the thermodynamic stability of nanocrystalline particles is treated separately from and in contrast to the well-established nucleation theory. The present

6. GARVIE’S REASONING OF METASTABILITY IN THE LIGHT OF THE NUCLEATION THEORY As demonstrated in the previous paragraphs, a metastable solution of two polymorphs is characterized by the fact that the radii of A1 and A2 in general differ from each other because the volumes of the nuclei and the surface tensions of the polymorphs likewise differ. Despite all of these differences, the nucleation theory allows the different nuclei to be described as being in equilibrium with each other and with the 10527


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analysis is to raise the awareness of the conflicting situation involved in such a generalization.

7. CONCLUSIONS The foundation for the existence of metastable nonmonoclinic zirconia given by Garvie contradicts the nucleation theory and, thus, ignores unique aspects of metastability. Therefore, the theoretical approach in order to verify the size effect for stabilization of usually less stable zirconia modifications due to metastability is invalid. Nonmonoclinic zirconia at room temperature is not the outcome of a phase transition but the outcome of various chemical reactions that yield products deviating from the right one due to the presence of foreign atoms or a lack of oxygen with the compositional deviations having structural implications.

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AUTHOR INFORMATION

Corresponding Author

*Phone ++49 711 685 61941; Fax ++49 711 685 51941; e-mail [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS D.G. is very grateful to the Max Planck Society for providing a scholarship. ADDITIONAL NOTES Fahrenheit’s investigations about the freezing of water in evacuated vessels are considered to belong to the first reports on undercooling. They originate from 1724,8 whereas Gibbs’ theoretical interpretation9 was published about 150 years later. b The irony of Garvie’s evidence of tetragonal zirconia is that according to what is known today, his samples must undoubtedly have been Na-modified ZrO2 rather than ZrO2. Therefore, it is no wonder that the structure of what he held in his hands differed from monoclinic. In fact, the highest impurity content of Garvie’s samples was due to sodium. One batch was even prepared by precipitation out of an aqueous ZrO(NO3)2− NaOH solution,1 which nowadays is an established way to synthesize Na-modified ZrO2. The second batch, obtained without deliberate addition of NaOH, had the same high sodium content. The sodium might have originated from the synthesis route widespread at that time with Na2ZrO3 as an intermediate product. a

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Metastable Nanocrystalline Zirconia in Light of the Nucleation Theory

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