J. Phys. Chem. B 2000, 104, 3481-3487
3481
Understanding Polymorphic Phase Transformation Behavior during Growth of Nanocrystalline Aggregates: Insights from TiO2 Hengzhong Zhang* and Jillian F. Banfield Department of Geology and Geophysics, UniVersity of WisconsinsMadison, Madison, WI 53706 ReceiVed: February 7, 2000
To understand the impact of particle size on phase stability and phase transformation during growth of nanocrystalline aggregates we conducted experiments using titania (TiO2) samples consisting of nanocrystalline anatase (46.7 wt %, 5.1 nm) and brookite (53.3 wt %, 8.1 nm). Reactions were studied isochronally at reaction times of 2 h in the temperature range 598-1023 K and isothermally at 723, 853, and 973 K by X-ray diffraction (XRD). A numerical deconvolution method was developed to separate overlapping XRD peaks, and an analytical method for determining phase contents of anatase, brookite, and rutile from XRD data was established. Results show that, in contrast to previous studies, anatase in our samples transforms to brookite and/or rutile before brookite transforms to rutile. Thermodynamic and kinetic analyses further support this conclusion. For general titania samples, the transformation sequence among anatase and brookite depends on the initial particle sizes of anatase and brookite, since particle sizes determine the thermodynamic phase stability at ultrafine sizes. These results highlight extremely important size-dependent behavior that may be expected in other nanocrystalline systems where multiple polymorphs are possible.
Introduction Understanding of the factors that control the phase stability, growth, and phase transformation kinetics in nanocrystalline materials is critical to quantification of materials behavior. Our work relies upon the titania (TiO2) model system, which is characterized by several polymorphs (including rutile, anatase, and brookite) that can be crystallized at low temperatures as ultrafine particles in the laboratory (e.g., refs 1, 2) and nature.3 Titania is an important material. Consequently, new understanding of the factors that dictate the sequence of the phase transformations may provide insights into how phase composition, microstructures, and properties of titania-based materials can be manipulated. Under ambient conditions macrocrystalline rutile is thermodynamically stable relative to macrocrystalline anatase or brookite.4 However, thermodynamic stability is particle-size dependent, and at particle diameters below ca. 14 nm, anatase is more stable than rutile.4 This may explain why anatase can be synthesized at ultrafine sizes. If nanometer-diameter titania is heated, crystal growth leads to alteration of phase stabilities and, ultimately, conversion of both anatase and brookite to rutile. However, it is unclear whether brookite transforms to anatase, or vice versa. Ye et al. reported that brookite transforms to anatase and then to rutile.2 On the other hand, calorimetric data 5 for the transformation enthalpies of anatase-to-rutile and brookite-to-rutile suggest that the thermodynamic phase stability for the three polymorphs is rutile > brookite > anatase. Thus, anatase may either transform directly to rutile, or to brookite and then to rutile. In this study we characterized crystal growth and phase transformation of mixtures of anatase and brookite, both isothermally and isochronally, in the temperature range 5981023 K. Thermodynamic and kinetic analyses of the results * Author to whom correspondence should be addressed. E-mail: hzhang@ geology.wisc.edu.
provide new insights into the interplay between size and phase stability in these nanocrystalline aggregates. Experimental Section Starting material was powered dry titania gel synthesized by the sol-gel method.3 The phase content of the starting material was determined to be 46.7 ( 0.1% by weight anatase and 53.3 ( 0.1% by weight brookite, and the average particle diameter of anatase and brookite was 5.1 ( 0.0 nm and 8.1 ( 0.6 nm, respectively. Kinetic experiments were done isothermally at 723, 853, and 973 K, and isochronally at reaction times of 2 h in the temperature range 598-1023 K (at 20 or 25 K intervals). Experiments were duplicated using ∼40 mg of sample for each data point. The detailed experimental procedure was reported previously.3 To determine the phase contents and the particle sizes of anatase, brookite, and rutile, all samples were examined by X-ray diffraction (XRD). Diffraction patterns (Figure 1) were collected using a Scintag PADV diffractometer with Cu Ka radiation (35 kV, 40 mA) in the step scanning mode. The scanning 2θ range was 22-34°, the 2θ step size was 0.03°, and the collecting time at each step was 5 s. In the 2θ range chosen, the 100% intensity (101) peak of anatase, 100% intensity (110) peak of rutile, and the 100% intensity (120), 80% intensity (111), and the 90% intensity (121) peaks of brookite appear (ref JCPDS cards No. 21-1272, 21-1276, and 29-1360). Due to the overlap of the anatase (101) peak with the brookite (120) and (111) peaks, a numerical deconvolution technique was used to separate these peaks. The XRD pattern, after baseline subtraction and Lorentz-polarization correction, was fitted by Pearson VII curves. In the fitting it is assumed that peak broadening of brookite (120), (111), and (121) peaks are the same. This is based on prior TEM (transmission electron microscopy) characterization of the morphology of nanocrystalline brookite and the relatively small 2θ range. We also
10.1021/jp000499j CCC: $19.00 © 2000 American Chemical Society Published on Web 03/22/2000
3482 J. Phys. Chem. B, Vol. 104, No. 15, 2000
Zhang and Banfield
Figure 2. Deconvolution of XRD patterns of samples reacted at 648 K for 2 h (a), and samples reacted at 933 K for 2 h (b). Points: experimental.
reasonable because nanocrystalline particles are approximately randomly oriented in the samples. Furthermore, the exponents of the Pearson VII curves for the brookite (120), (111), and (121) peaks are set equal. Figure 2 illustrates examples of deconvolution. Peak broadening is reduced more at 933 K (Figure 2b) than at 648 K (Figure 2a) due to the faster crystal growth at a higher temperature. At 933 K the peaks become narrower, yet the d spacing (the 2θ position) of each peak is fixed. Consequently, the overlap between brookite (111) and (120) peaks and the anatase (101) peak is greatly reduced, compared to samples treated at 648 K. This makes the overlap of brookite (120) and (111) peaks and the anatase (101) peak more evident, as shown by the sudden change in the slope of the experimental intensity-2θ curve at about 2θ ) 25.7°. Positions of peaks (2θ), the full widths at half-maximum (fwhm), as well as the integrated peak intensities can all be obtained by deconvolution. To calculate particle size, instrumental broadening was determined from the fwhms of the (111), (220), and (311) peaks of a standard coarse silicon powder (NBS 640b, now NIST, MD). The phase content of a sample can be calculated from the integrated intensities of the above-mentioned anatase, rutile, and brookite peaks. If a sample contains only anatase and rutile, the weight fraction of rutile (WR) can be calculated from6 Figure 1. XRD patterns of samples reacted in the temperature range 598-1023 K for 2 h (a), and samples reacted at 723 K (b), 853 K (c), and 973 K (d) for different lengths of time.
assume that the intensities of the three peaks are proportional to their intensities in the JCPDS card (No. 29-1360). This is
WR )
AR 0.884AA + AR
(1)
where AA represents the integrated intensity of the anatase (101) peak, and AR the integrated intensity of rutile (110) peak. If brookite is also present in a sample, similar relations can be
Understanding Polymorphic Phase Transformation
J. Phys. Chem. B, Vol. 104, No. 15, 2000 3483
derived:
WA )
kAAA kAAA + AR + kBAB
(2a)
WR )
AR kAAA + AR + kBAB
(2b)
WB )
kBAB kAAA + AR + kBAB
(2c)
where WA and WB represent the weight fraction of anatase and brookite, respectively. AB is the integrated intensity of the brookite (121) peak, and kA and kB are two coefficients to be determined. Sample mass data and integrated XRD intensity data of the following six samples were inserted into eqs 2a-c, generating eight independent equations with three unknown variables, kA, kB and the initial weight fraction of anatase in sample (a): (a). Duplicate samples were formed by heating the starting materials at 598 K for 3 h. These samples contained only anatase and brookite. (b). Two samples formed by mixing different amounts of pure anatase (JM Catalog Co., MA) with a part of the first duplicate of sample (a). (c). Two samples formed by mixing different amounts of pure rutile (obtained by heating the pure anatase at 1423 K for 1 h) with a part of the second duplicate of sample (a). On the basis of eight equations, the coefficients were optimized, kA ) 0.886 and kB ) 2.721. The value of kA agrees well with the previously reported value of 0.884 for eq 1.6 With eq 2, the phase contents in any samples can be calculated. The average particle sizes of anatase, rutile, and brookite were calculated according to the Scherrer equation7 using the fwhm data of each phase after correcting the instrumental broadening. Results and Discussion Isochronal Reactions. Figure 3a shows the phase contents and the particle sizes of samples treated isochronally at 2 h in the temperature range 598-1023 K. The results indicate that the initial process involves the transformation of anatase in the starting material to brookite without formation of rutile (the brookite content increased from its initial 53.3% to 66.5% at 598 K). This is followed by a reaction of brookite to anatase at 623 K, and then by conversion of anatase to brookite and subsequently to rutile at higher temperatures. Rutile rapidly increases in abundance as temperature increases above 850 K. The initial particle sizes of brookite and anatase in the starting materials are 8.1 and 5.1 nm, respectively. Upon heating, particles of brookite and anatase coarsen; however, the particle sizes of the two phases remain close in all experiments conducted at temperatures below 850 K. The particle size should be determined both by particle coarsening and by phase transformation. Since phase transformation is relatively slow at temperatures below 850 K (Figure 3a), the overall effects of the factors that govern the coarsening rates (such as particle packing and surface energies) should be similar for both phases. At temperatures above 850 K, the particle size of brookite is smaller than that of anatase. This can be attributed to the conversion of larger brookite particles to rutile in the same sample. In a sample, the sizes of all particles of one phase are not uniform (each phase has a particle size distribution). Most particles have diameters close to the average particle size. Only those brookite particles whose diameters are larger than a certain
value can transform to rutile (see later thermodynamic analysis). If the particle size is less than that value, brookite is more thermodynamically stable than rutile. Now that larger brookite particles have transformed to rutile in a sample, the average particle size of the remaining brookite became smaller. The particle size of rutile increases rapidly at temperatures above 850 K, which may imply rutile coarsens faster than anatase and brookite, and/or two or more brookite or anatase particles may transform to form one rutile particle. Isothermal Experiments. Figure 3b shows the phase contents and the particle sizes in samples reacted at 723 K. Rutile formation was not detected. Again, results indicate transformation of anatase to brookite. The slopes of the particle size vs time curves are very close for anatase and brookite, further supporting the similarity in the coarsening behavior of the two phases. The particle size of brookite is almost constant at ∼2 nm larger than that of anatase over the whole reaction period. At 853 K, rutile forms (Figure 3c). When the amount of rutile is small (at time less than ∼5 h), the transformation from anatase to brookite can be observed readily. At longer reaction times, the change in the content of anatase is minor, but the content of brookite decreases with the increase in the amount of rutile. This directly indicates the transformation from anatase to brookite and then from brookite to rutile. The particle size of brookite becomes smaller than that of anatase at longer reaction times, which again can be interpreted to indicate transformation of larger brookite crystals to rutile. At 973 K (Figure 3d), the contents of both brookite and anatase decrease with the increase in the amount of rutile. The decrease in the content of anatase is greater than that of brookite at time less than 20 min, which can be attributed to the transformation of anatase to both brookite and rutile. At longer reaction time, both anatase and brookite transform to rutile. The particle size of brookite becomes far smaller than that of anatase, again suggesting the transformation of larger brookite particles to rutile. Thermodynamic and Kinetic Analyses. The above isothermal and isochronal experiments all indicate that at higher temperatures (above 623 K), anatase transforms to brookite and/ or rutile, and then brookite transforms to rutile. At lower temperatures (below 623 K), the transformation between anatase and brookite may be reversible. We consider this to be a consequence of the dependence of thermodynamic stability on particle size, noting that polymorph growth rates differ, causing changes in relative stability during thermal treatments. The following thermodynamic and kinetic analyses are developed to improve our understanding of this phenomena. Complete thermodynamic data for anatase and rutile are available from the JANAF tables.8 No data are available for brookite. However, the enthalpies of the transformation from anatase to rutile and from brookite to rutile have been determined by Mitsuhashi and Kleppa to be -3.26 and -0.71 kJ mol-1, respectively, at 971 K by solution calorimetry.5 In their work, anatase and brookite samples were precipitated in solution and treated hydrothermally at 430 °C and 1 kbar for 24 and 48 h, respectively. One would expect that such hydrothermally treated samples would be rather coarse. Furthermore, 0.1-0.2 mm size single crystals of anatase were also used in their work. Thus, it can be reasonably assumed that their determined enthalpies are for macroscopic-size anatase and brookite phases. An early reported value of the enthalpy of the transformation from anatase to rutile is -6.67 kJ mol-1at 968 K.9 Particle size of the samples was not specified. If the particle sizes in ref 9 were macroscopic, whereas those in ref 5 were
3484 J. Phys. Chem. B, Vol. 104, No. 15, 2000
Zhang and Banfield
Figure 3. Phase contents and particle sizes of samples reacted in the temperature range 598-1023 K for 2 h (a), and samples reacted at 723 K (b), 853 K (c), and 973 K (d) for different lengths of time. Square: anatase; circle: brookite; triangle: rutile; lines are calculated from the kinetic model (see text). Error bar shows the deviation from the average of two parallel samples.
ultrafine, the value determined in ref 5 would be more negative (rather than less negative) than that determined in ref 9 because
of the excess enthalpy associated with the abundant surface area of ultrafine particles. The discrepancy between the two values
Understanding Polymorphic Phase Transformation
J. Phys. Chem. B, Vol. 104, No. 15, 2000 3485 that, at particle size less than 11 nm, anatase is the most stable phase; for particles sizes between 11 and 35 nm, brookite is the most stable phase; while for particles sizes greater than 35 nm, rutile is the most stable phase. The stability of anatase and rutile reverses at 16 nm, which agrees reasonably with our previous thermodynamic analysis (14 nm).4 The above results show that for equally sized titania particles, nanocrystalline anatase can transform to brookite and then brookite transforms to rutile. Our experimental results coincide with this thermodynamic analysis. According to the experimental results, we can suppose the transformation sequence among the three phases of titania to be k1
Figure 4. Variation of enthalpies of anatase, brookite, and rutile with particle size.
may be due to incomplete dissolution of samples in the calorimetry.5 In the present work, we take the enthalpy date reported in ref 5. Since entropy contribution to the free energy is minor for anatase and rutile (ref JANAF tables in ref 8), the calorimetry results suggest that the thermodynamic phase stability for macrocrystalline phases is in the order of rutile > brookite > anatase.5 To analyze the phase stability at nanometer sizes, the surface enthalpy data of the three phases are needed. Averaged surface enthalpies of anatase and rutile are4 1.34 and 1.93 J m-2, respectively, based on results of atomistic simulation.10 These theoretically predicted values are rather consistent with the values (0.5-1.7 J m-2) determined by differential scanning calorimetry.11 Since surface free energy is roughly proportional to the product of bulk modulus times the third root of density (eq 11 of ref 4), the surface enthalpy of brookite can be estimated to be 1.66 J m-2 from the interpolation between the data of anatase and rutile, using property data of titania in ref 12. Therefore, the enthalpy of one titania phase relative to that of the rutile phase of infinite size is
H - H(rutile, ∞ size) ) H(titania, ∞ size) - H (rutile, ∞ size) + Amh ) H(titania, ∞ size) H(rutile, ∞ size) + 6
M h (3) DF
where H represents enthalpy, Am the molar surface area of titania that has the particle diameter D and density F. M is the molecular weight of titania (79.9 × 10-3 kg mol-1) and h is the surface enthalpy. Inserting values of H(titania, ∞ size) - H(rutile, ∞ size),5 the values of surface enthalpy stated above, as well as the molecular weight and density data from ref 12 into eq 3, we get the enthalpies (kJ mol-1)
HR - H(rutile, ∞ size) )
217.76 D
(4a)
HA - H(rutile, ∞ size) ) 3.26 +
165.01 D
(4b)
HB - H(rutile, ∞ size) ) 0.71 +
192.55 D
(4c)
where the subscripts R, A, and B stand for rutile, anatase, and brookite, respectively. The particle size D in above equations is in nanometers. Figure 4 illustrates the variation of the enthalpies of the three phases with the particle size. It is seen
k2
A 98 B 98 R
(5)
This consists of two consecutive reactions (A f B and B f R).13 Alternatively, the transformation can also be k1
k2
A 98 B 98 R k3
A 98 R
(6)
which consists of two consecutive reactions and one competition reaction (A f R). In the above reactions, k is a kinetic constant for its corresponding reaction. In fact, case (5) is a special case of (6) when k3 f 0. It is known that the transformation from nanocrystalline anatase to rutile is governed by interface nucleation and/or surface nucleation, and the derived kinetic equations involve the particle size term.14,15 Anatase and brookite have a polytypic rather than polymorphic structural relationship (see ref 16) and their interconversion simply involves displacement of atoms into adjacent sites on two of four Ti planes.17 For simplicity, we assume that all reactions are first-order with respect to the weight fraction, and as such the kinetic equations in integrated forms for case (6) can be derived using a method similar to that in ref 13:
WA ) WA0 exp[-(k1 + k3)t] WB ) WA0
(7a)
k1
{exp[- (k1 + k3)t] k2 - (k1 + k3) exp(- k2t)} + WB0 exp(- k2t) (7b) WR ) WA0 + WB0 - WA - WB
(7c)
where WA0 and WB0 are the initial weight fractions of anatase and brookite in the starting material, and t is the time. We attempted to fit eqs 7a-c to the experimental data in Figures 3b-d (see Figure 3). Although the fits are far from perfect (probably because of the fact that no particle size effect has been taken into account), the presumed kinetic model based on the supposed transformation sequence can indeed describe the observed tendency of the variation of the phase contents with time. Assuming k3 ) 0, the variation of the weight percent with temperature in Figure 3a can also be reproduced reasonably using the following kinetic constants (h-1) obtained from parameter optimization:
(
k1 ) 1.18 exp -
1433 T
(
k2 ) 3.48 × 108 exp -
)
(8a)
19701 T
)
(8b)
3486 J. Phys. Chem. B, Vol. 104, No. 15, 2000
Zhang and Banfield
Figure 6. Enthalpies of anatase (square), brookite (circle), and rutile (triangle) calculated from eq 4 for samples of Ye el at. 2 reacted nonisothermally at the rate 25 K min-1.
where T is the absolute temperature. The above constants show that the activation energy for the A f B transformation (11.9 kJ mol-1) is much lower than that for the B f R transformation (163.8 kJ mol-1), while the frequency factor of the latter is much higher than that of the former. This means the transformation from anatase to brookite can be achieved at lower temperatures, whereas that from brookite to rutile requires higher temperatures. Furthermore, once the B f R transformation starts, it can proceed rapidly (because the frequency factor is large). Such kinetic considerations agree quite well with experimental results shown in Figure 3a and also with predictions made on the basis of the atomic details of the transformation mechanisms.16, 17 Ye at al. studied the sequence of phase transformation in nanocrystalline brookite-rich samples (brookite 40.8%, 15.5 nm; anatase 32.7%, 22.7 nm; and rutile 26.5%, 27.2 nm).2 Their conclusion that brookite transforms to anatase and then to rutile seemingly contradicts our present conclusion. However, this distinct difference can be explained by the differences in the thermodynamic stabilities of phases (considering their sizes) present in the starting materials. It is seen from Figure 5 that the enthalpy of anatase is higher than that of brookite in our starting materials, thus during the heat treatment, less stable anatase transforms to brookite. For the isochronal experiment (Figure 5a) the enthalpy of rutile becomes the lowest at temperatures above ∼850 K, thus transformation from brookite (or anatase) to rutile becomes very rapid (Figure 3a). Conversely, on the basis of size information reported for the starting materials of Ye et al., we calculated that the enthalpy of brookite is higher than that of anatase (Figure 6). Thus, during their nonisothermal heat treatment, less stable brookite can transform to anatase and then further to rutile. Conclusions
Figure 5. Enthalpies of anatase (square), brookite (circle), and rutile (triangle) calculated from eq 4 using particle size data in Figure 3 for samples reacted isochronally at 2 h (a), or isothermally at 723 K (b), 853 K (c), and 973 K (d).
The transformation sequence among the three titania polymorphs anatase, brookite, and rutile is size dependent, because the energies of the three polymorphs are sufficiently close that they can be reversed by small differences in surface energy. If particle sizes of the three nanocrystalline phases are equal, anatase is most thermodynamically stable at sizes less than 11 nm, brookite is most stable for crystal sizes between 11 and 35 nm, and rutile is most stable at sizes greater than 35 nm. However, crystal sizes of anatase and brookite in synthesized products may be unequal, and this can alter the direction of the initial transformation (e.g., the present work vs that of Ye et al.2). Our analyses resolve the previous (apparent) contradiction.
Understanding Polymorphic Phase Transformation In our samples, anatase transforms to brookite and/or rutile, and then brookite further transforms to rutile. The activation energy of the anatase to brookite transformation is small (11.9 kJ mol-1), thus the transformation can proceed at lower temperatures. The activation energy of the brookite to rutile transformation is higher (163.8 kJ mol-1), thus the transformation proceeds rapidly only at higher temperatures. Many compounds (especially oxides and oxyhydroxides) crystallize as multiple polymorphs at low temperatures. Some evidence for the size-dependent stability of some of these phases is accumulating (e.g., ultrafine γ-Al2O3 f R-Al2O3 18). Because initial crystal sizes and polymorph growth rates vary considerably, complex phase transformation sequences, analogous to those reported here, may occur in these systems. The analyses provided here provide a basis for understanding such phenomena.
Acknowledgment. Thanks are extended to Brian L. Bischoff, who synthesized the raw materials. Financial support for this study was provided by National Science Foundation Grants EAR-9508171 and EAR-9814333.
J. Phys. Chem. B, Vol. 104, No. 15, 2000 3487 References and Notes (1) Bokhimi, Morales, A.; Novaro, O.; Lopez, T.; Sanchez, E.; Gomez, R. J. Mater. Res. 1995, 10, 2788. (2) Ye, X. S.; Sha, J.; Jiao, Z. K.; Zhang, L. D. NanoStructured Materials 1997, 8, 919. (3) Banfield, J. F.; Bischoff, B. L.; Anderson, M. A. Chem. Geol. 1993, 110, 211. (4) Zhang, H.; Banfield, J. F. J. Mater. Chem. 1998, 8, 2073. (5) Mitsuhashi, T.; Kleppa, O. J. J. Am. Ceram. Soc. 1979, 62, 356. (6) Gribb, A. A.; Banfield, J. F. Am. Mineral. 1997, 82, 717. (7) Jenkins, R.; Snyder, R. L. Introduction to X-ray Powder Diffractometry; John Wiley & Sons: New York, 1996; p 90. (8) Chase, M. W.; Davies, C. A.; Downey, J. R.; Frurip, D. J.; McDonald, R. A.; Syverud, A. N. J. Phy. Chem. Ref. Data 1985, 14 (Suppl. 1), 1680-1681. (9) Navrotsky, A.; Kleppa, O. J. J. Am. Ceram. Soc. 1967, 50, 626. (10) Oliver, P. M.; Watson, G. W.; Kelsey, E. T.; Parker, S. C. J. Mater. Chem. 1997, 7, 563. (11) Terwilliger, C. D.; Chiang, Y. M. J. Am. Ceram. Soc. 1995, 78, 2045. (12) Kim, D. W.; Enomoto, N.; Nakagawa, Z. J. Am. Ceram. Soc. 1996, 79, 1095. (13) Boudart, M. Kinetics of Chemical Processes; Butterworth-Heinemann: Boston, 1991; p 63. (14) Zhang, H.; Banfield, J. F. Am. Mineral. 1999, 84, 528. (15) Zhang, H.; Banfield, J. F. J. Mater. Res. 2000, 15, 437. (16) Banfield, J. F.; Verblen, D. R. Am. Mineral. 1992, 77, 545. (17) Penn, R. L.; Banfield, J. F. Am. Mineral. 1998, 83, 1077. (18) McHale, J. M.; Auroux, A.; Perrotta, A. J.; Navrotsky, A. Science 1997, 277, 788.
