Materials Science and Engineering A 438–440 (2006) 399–402
The size dependence of structural stability in nano-sized ZrO2 particles Y.L. Zhang a , X.J. Jin a,∗ , Y.H. Rong a , T.Y. Hsu (Xu Zuyao) a , D.Y. Jiang b , J.L. Shi b a
School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200030, China b Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 200050, China Received 13 June 2005; received in revised form 17 January 2006; accepted 14 March 2006
Abstract The stable or metastable phase was found to be dependent on the size of ZrO2 nano particles. Amorphous hydrated ZrO2 powders prepared by precipitation were annealed at 1300 ◦ C and maintained for different length of time followed by being quenched in ambient. The average particle size and phases were determined by X-ray diffraction cross-checked by transmission electron microscopy. The powders were found composed of monoclinic (m) phase when the particle size (d) is larger than 31 nm, whereas tetragonal (t) phase remains stable at room temperature when particle size is less than 14 nm. The mixture of the t and m phases is observed when average particle size locates between 14 and 31 nm. Thermodynamic calculation indicates that the surface free energy difference between tetragonal and monoclinic phases surpasses the volume chemical free energy difference between two phases at room temperature when the particle size of zirconia decreases below 13 nm. The lower surface energy of tetragonal phase results in the stability of tetragonal structure at room temperature, while tetragonal phase is normally stable at high temperature for coarse ceramics. The experimental results are in good agreement with theoretical prediction. © 2006 Elsevier B.V. All rights reserved. Keywords: ZrO2 ; Nano particles; Surface free energy; Excess volume
1. Introduction The polymorphic nature of pure zirconia (ZrO2 ) has received much attention for the scientific interest and potential engineering application [1]. It is well known that at about 1170 ◦ C, a martensitic transformation from tetragonal to monoclinic symmetry takes place in ambient. Tetragonal phase, which is normally stable at high temperature for coarse grain ceramics has been observed stable or metastable at room temperature (RT) [2]. In 1929, Ruff and Ebert [3] first prepared the metastable tetragonal (t) phase at RT by igniting zirconium salts. Cypres et al. [4] obtained the metastable t phase via heating Zr(OH)4 and suggested that small amounts (0.75 wt.%) of bound OH groups in solid solution were responsible for stabilization of t phase at RT. Mazdiyasni et al. [5] found that the metastable t phase prepared by thermal decomposition of zirconium alkoxides may convert to monoclinic (m) phase upon heating the oxide above 400 ◦ C. By heating the precipitated and calcinated samples at various temperatures up to 1000 ◦ C, Garvie [6] manufactured the zirconia particles with
∗
Corresponding author. E-mail address:
[email protected] (X.J. Jin).
0921-5093/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2006.03.109
different sizes and observed the phase fields of t, t + m, and m with increased grain size, respectively. He argued that the grain size governed the appearance of the t phase because of lower surface energy of t phase at RT than that of m phase, and the critical grain size was calculated as 30 nm, above which the metastable t phase could not exist at RT. Mitsuhashi et al. [7] claimed that the domain boundaries in a particle inhibited the t → m transformation and the existence of a single-domain t-ZrO2 was explained by the absence of an active nucleation site. Similar conclusion also was drawn by Chen and Chiao [8], who investigated the t → m transformation in ZrO2 particles deposited on a Cu matrix by internal oxidation method and proposed a nucleation statistics model [9]. Recently, the stabilization of the high-temperature phase, as a general phenomenon in nano-sized materials, has attracted much attention. For example, the ␥-Fe (FCC) particles with fcc structure is found at RT when the size of particles is less than 50 nm, while ␥-Fe in normal coarse grains will transform into ␣-Fe with bcc structure at 912 ◦ C [10]. Stabilization of high temperature phase has been found to be correlated with grain sizes rather than extrinsic factors such as impurity. Nevertheless, some problems still remain unclear for the structural stabilization in ZrO2 as well as some alloys: (1) In the experiments mentioned above, ZrO2 particles are fabricated through heating amorphous precursors at
400
Y.L. Zhang et al. / Materials Science and Engineering A 438–440 (2006) 399–402
relatively low temperature, and the complicated process of crystallization is involved. However, here it cannot be determined that the resultant m-ZrO2 at RT is formed via t → m transformation or crystallization directly. The intrinsic reasons for high temperature structural stability at RT in nano-sized ZrO2 is thus obscure. (2) The critical grain size for stabilization of t-ZrO2 need to be identified, analogous to a new model suggested for pure metals [11–13]. (3) The coexistence of t and m phases is found in ZrO2 as similar as Fe and Co [14,15], which means a t + m phase field at RT. This phenomenon is suggested to result from the size distribution, i.e. there is grain size distribution in one batch of samples, implying that the grain sizes of m-ZrO2 are absolutely larger than that of t-ZrO2 at RT. In this paper, the size dependent phase stability of ZrO2 is explored experimentally and theoretically associated with t → m transformation by taking consideration of ‘excess volume’ of an interface [17,18].
Fig. 1. Grain size and the mole fraction of t and m phases in nano-sized ZrO2 after holding at 1300 ◦ C for different times.
3. Results and discussion 2. Experiments Amorphous hydrated ZrO2 was precipitated from a hot solution of ZrOCl2 ·8H2 O with NH3 , washed by the distilled water, and dried for 48 h at around 100 ◦ C. In order to obtain nano-sized particles with various grain sizes, the as-prepared amorphous powders were heated for different time in a furnace preheated to 1300 ◦ C and then quenched in ambient. The average grain sizes in diameter (d) of the powders were determined from the (1 1 1) peak of X-ray diffraction (Dmax-rC) using the Scherrer formula: d = 0.89λ/B cos θ, where is the wavelength of X-ray (Cu K␣1 ), B is the corrected half-width of diffraction peak and θ is the diffraction angle, respectively. This method is claimed to give a precision of ±10% in the region of 10–100 nm for a related series of samples and an absolute accuracy of ±25% [6]. The grain sizes were also verified by the transmission electron microscopy (TEM, JEM-100CX). The molar fraction of the monoclinic phase, Fm , was determined by the relative intensity relationship of the X-ray diffraction: Fm = [Im (1 1 1) + ¯ ¯ Im (1 1 1)]/[I where Im (1 1 1), m (1 1 1) + It (1 1 1) + Im (1 1 1)], ¯ Im (1 1 1) and It (1 1 1) are the relative peak intensities of the ¯ reflections of m phase and the (1 1 1) reflection (1 1 1) and (1 1 1) of t phase, respectively.
As illustrated in Fig. 1, the mean grain size grows rapidly in the initial stage when heating at 1300 ◦ C, and reaches to the limit after about 30 min. Fig. 2 shows the corresponding X-ray diffractions, indicating that the molar fraction of the tetragonal phase increases as the grain size decreases. As can be seen in Fig. 1, the powders are composed of m phase with the grain size larger than about 31 nm, whereas tetragonal structure remains stable at RT when d < 14 nm. The coexistence of the t and m phases is observed when 14 < d < 31 nm. The boundaries of grain size for t + m phase region, 14 and 31 nm, are comparable to the Garvie’s results [2,6]. However, in his experiments, the upper limit of 30 nm is obtained by heating the precursor at 800 ◦ C, lower than the start temperature of reverse t → m transformation. In contrast, at 1300 ◦ C, only t-ZrO2 remains stable after crystallization, and during cooling the t → m transformation will be triggered in some particles depending on the grain size. As a consequence, all of the m phase in the samples are certain to have undergone t → m transformation. Following Chen et al.’s suggestion [9], in order to survey the stability of t-ZrO2 further, the powders are afterward grinded in an agate mortar and immerged into liquid nitrogen. The molar fractions of m-ZrO2 are found to increase by about 5–10% in
Fig. 2. (a)X-ray patterns of ZrO2 particles with different holding time at 1300 ◦ C and (b) TEM image of ZrO2 holding at 1300 ◦ C for 5 min.
Y.L. Zhang et al. / Materials Science and Engineering A 438–440 (2006) 399–402
401
Table 1 The parameters used in the calculation of Gibbs free energy of t and m phases by ‘excess volume’ model Structure
a
t-ZrO2 m-ZrO2
˚ [20,21] Lattice constants (A) a
b
c
β
5.074 5.1507
5.2028
5.188 5.3156
99.194
B0 (RT) (GPa)
α0 (×10−5 /K)
E (eV)
19021 18922
3.982719 2.345823
26.2424 26.2024
B0 (RT), α0 and E are bulk modulus, bulk expansion coefficients and cohesive energy, respectively. a The lattice constants of t-ZrO at room temperature (RT) are extrapolated from the experimental results in Refs. [20,21]. 2
the samples of 14 < d < 31 nm after grinding, which is in agreement with Chen’s results. For d < 14 nm, no m-ZrO2 is observed even after cooling in liquid nitrogen. It implies that t phase for particles with average grain size less than 14 nm is thermodynamically stable and extra work done by grinding cannot trigger the t → m transformation. Assuming that the surface energy of t phase is lower than that of the m phase, the Gibbs free energy of the t phase (Gt ) would be lower than that of the m phase (Gm ) for very small particles. To elucidate the relationship between the structural stability and grain size, the Gibbs free energy of t- and m-particles in the equilibrium state are calculated. The nano-crystalline materials can be treated as consist of two components: a crystalline interior part built by atoms in the lattice of crystallites (grains); and an interfacial part comprising atoms in the interfaces or grain boundaries between crystallites. The Gibbs free energy for t and m phases can be expressed as [16]: Gt = (1 − xti )G0t + xti Git ,
i i Gm = (1 − xm )G0m + xm Gim ,
(1) where the subscript stands for t or m phase, xi is the atomic fraction of the interface, G0 and Gi are the Gibbs free energy of crystallites and the interfaces. The two terms in the right hand represent the contribution of the crystalline and interfacial components, respectively. In the calculation, it is not rigorous to directly use the surface energy of bulk materials without taking account of the particularity of the nano-structure. Theoretical calculations [17,18] indicate that the ‘excess volume’ of an interface is the most significant parameter influencing the interfacial energy, which characterizes the extent of the lattice distortion at the interface with respect to the crystallite. The atomic fraction at the interface is: xi =
6δ , (1 + V )d
(2)
where δ is the thickness of the interfacial layer, V is the excess volume. The universal equation of state [19] and the equation of phase equilibria in nano-sized crystal [11] are employed to compute Gi . The Gibbs free energies for t and m phases can be calculated as a function of d at reference temperature (293 K), after putting the parameters listed in Table 1 [20–25] into equations. As can be seen in Fig. 3, the driving force for t → m transformation at 293 K, Gt→m = Gm − Gt , decreases with decreasing the grain size in comparison with the constant for bulk materials. When Gt→m = 0, d = 13 nm, which means
Fig. 3. Calculated Gibbs free energy of t and m phases with respect to nano grain size at 293 K. The inset shows the enlarged region near the grain size of 13 nm.
that in the equilibrium state, the t-ZrO2 with d < 13 nm possesses a lower Gibbs free energy than m-ZrO2 , as shown in Fig. 3. Thus all particles with d < 13 nm will be thermodynamically stable and remain t structure since the uniform t phase is obtained first at 1300 ◦ C in our experiments. The fact that no m-ZrO2 is found in samples with d < 14 nm (Fig. 2) agrees with the calculation. Therefore, the grain size of 13 nm is the thermodynamically critical size for stabilization of t phase. There is a two-phase region for the particles with 14 < d < 31 nm in our experiment and similar phenomena are also found in nano-sized Fe and Co. Some authors suggest that the twophase region is solely attributed to the crystallite size distribution. The fact that the mole fraction of m phase increases for the powder with 14 < d < 31 nm after grinding also verifies that those untransformed t-ZrO2 particles are just metastable rather than stable thermodynamically. Chen et al. [9] demonstrate that the t → m transformation in nano-sized ZrO2 is heterogeneousnucleation-controlled, and the effective defects for heterogeneous nucleation decrease with decreasing grain size. Therefore, for a ZrO2 particles with 14 < d < 31 nm, the grain size may be not the only factor to determine the structural stability, and the transformation behavior is different even in the ZrO2 particles with the same grain size, i.e. the transformation may occur, or may not occur in one given particle, which depends on probability of finding a defect. The presence of pin-hole porosity, hydrostatic strain energy and strong aggregation tendency of nano-crystallites make the problem even more complicated [2].
402
Y.L. Zhang et al. / Materials Science and Engineering A 438–440 (2006) 399–402
4. Conclusions Structural stability in nano-sized ZrO2 particles was investigated in this letter. Both experimental results and theoretical calculations indicate that the t-ZrO2 particles with d < 14 nm are thermodynamically stable at room temperature, and the ZrO2 particles with 14 < d < 31 nm are metastable possibly due to a kinetic nucleation barrier. Acknowledgement The authors are grateful to the financial support from the National Natural Science Foundation of China under contract no. 59971029. References [1] [2] [3] [4] [5]
B. Basu, Int. Mater. Rev. 50 (2005) 239–256. S. Shukla, S. Seal, Int. Mater. Rev. 50 (2005) 45–64. O. Ruff, F.Z. Ebert, Anorg. Allgem. Chem. 180 (1929) 19–41. R. Cypres, R. Wollast, J. Raucq, Ber. Deut. Keram. Ges. 40 (1963) 527–531. K.S. Mazdiyasni, C.T. Lynch, J.S. Smith, J. Am. Ceram. Soc. 48 (1974) 372–375. [6] R.C. Garvie, J. Phys. Chem. 69 (1965) 1238–1243. [7] T. Mitsuhashi, M. Ichihara, U. Tatsuke, J. Am. Ceram. Soc. 57 (1974) 97–101.
[8] I.W. Chen, Y.H. Chiao, Acta Metall. 31 (1983) 1627–1638. [9] I.W. Chen, Y.H. Chiao, K. Tsuzaki, Acta Metall. 33 (1985) 1847–1859. [10] K. Haneda, Z.X. Zhou, A.H. Morrish, Phys. Rev. B 46 (1992) 13832–13837. [11] Q.P. Meng, Y.H. Rong, T.Y. Hsu (Xu Zuyao), Sci. Chin. Ser. E 45 (2002) 485–494. [12] Q.P. Meng, N. Zhou, Y.H. Rong, S.P. Chen, T.Y. Hsu (Xu Zuyao), Acta Mater. 50 (2002) 4563–4570. [13] Q.P. Meng, Y.H. Rong, T.Y. Hsu (Xu Zuyao), Phys. Rev. B 65 (2002) 174118–174124. [14] C. Kuhrt, L. Schultz, J. Appl. Phys. 73 (1993) 1975–1980. [15] O. Kitakami, H. Sato, Y. Shimada, Phys. Rev. B 56 (1997) 13849– 13854. [16] X. Zu, R. Birringer, U. Herr, H. Gleiter, Phys. Rev. B 35 (1987) 9085–9090. [17] H.J. Fecht, Phys. Rev. Lett. 65 (1990) 610–613; H.J. Fecht, Acta Metall. Mater. 38 (1990) 1927–1932. [18] M. Wagner, Phys. Rev. B 45 (1992) 635–639. [19] P. Vinet, J.R. Smith, J. Ferrante, J.H. Rose, Phys. Rev. B 35 (1987) 1945–1953. [20] S.M. Lang, J. Am. Ceram. Soc. 47 (1964) 641–644. [21] C.J. Howard, R.J. Hill, B.E. Reichert, Acta Crystallogr. B 44 (1988) 116–120. [22] M.V. Nevitt, S.K. Chan, J.Z. Liu, M.H. Grimsditch, Y. Fang, Physica B 150 (1988) 230–233. [23] A.P. Mirgorodsky, M.B. Smirnov, P.E. Quintard, Phys. Rev. B 55 (1997) 19–22. [24] H. Baker, Alloy Phase Diagrams, ASM International, Ohio, USA, 1992. [25] G. Jomard, T. Petit, A. Pasturel, L. Magaud, G. Kresse, J. Hafner, Phys. Rev. B 59 (1999) 4044–4052.
