Influence of Nucleation Rate on the Yield of ZnO Nanocrystals

Mar 10, 2010 - Almost as soon as he started college, Morteza Khaledi knew he wanted to be a professor. And he quickly... SCIENCE CONCENTRATES ...
0 downloads 0 Views 381KB Size
Download PDF
J. Phys. Chem. C 2010, 114, 5721–5726

5721

Influence of Nucleation Rate on the Yield of ZnO Nanocrystals Prepared by Chemical Vapor Synthesis Moazzam Ali and Markus Winterer* Nanoparticle Process Technology and Center for Nanointegration Duisburg-Essen (CeNide), UniVersity Duisburg-Essen, Duisburg 47057, Germany ReceiVed: August 5, 2009; ReVised Manuscript ReceiVed: January 11, 2010

ZnO nanocrystals were synthesized by chemical vapor synthesis from two different precursorssdiethylzinc and bis(2,2,6,6-tetramethyl-3,5-heptanedionate)zincsat different temperatures in a tubular hot wall reactor. It is observed that the yield of ZnO nanocrystals is temperature dependent, and it decreases with increasing reactor temperature for both precursors. The nucleation rate was calculated by classical nucleation theory and was correlated with the experimental yield of ZnO nanocrystals. Introduction Chemical vapor synthesis (CVS) is a method for the continuous production of nanomaterials. Therefore, a scale-up of the process is possible. CVS has been used for the production of different types of nanomaterialssTiO2,1,2 SiC,3 ZnO,4 CuO,5 and W.6 By CVS, not only doped nanomaterials7,8 but also core/ shell nanomaterials9 can be produced. In CVS, nucleation and growth of particles take place in the gas phase. Typically, an irreversible decomposition reaction of precursor vapors at the beginning of a CVS reactor generates a “chemical supersaturation” of primary growth species and, if the degree of supersaturation is high enough, nucleation occurs. These primary growth species (“monomers”) can also participate in the growth of the particles by condensation or surface reaction rather than further homogeneous nucleation. Once stable nuclei are generated, they coagulate and then coalesce, forming bigger particles depending on the temperature profile in the reactor. These elementary steps of CVS are shown in Figure 1. We have observed that, in CVS, nucleation is temperature dependent and it plays a detrimental role in the yield of ZnO nanocrystals. According to classical nucleation theory, the change in free energy by the formation of a spherical nucleus of radius r from primary growth species (assuming monomers) is given by10

1 1 4 ∆G ) 4πr2σ + πr3 RT ln 3 VM S

()

(1)

where σ is the surface energy of the material, VM the molar volume of the material, R the universal gas constant, T the absolute temperature, and S the saturation ratio. The saturation ratio is defined as the ratio of partial pressure of the growth species or monomers (p) to the equilibrium vapor pressure (ps) of a particle of radius r

S)

p ps

(2)

The first term on the right-hand side of eq 1 is due to the appearance of the surface of the nucleus and increases continu* Corresponding author. E-mail: [email protected]. Phone: +49-203-379-4446. Fax: +49-203-379-4453.

Figure 1. Schematic representation of different elementary processes in a hot wall chemical vapor synthesis reactor during particle formation and growth.

ously on increasing the size of the nucleus (Figure 2). The second term is due to the volume change by formation of the nucleus and its value is negative for S > 1 and continueously decreasing with increasing radius of the nucleus at a constant temperature. The overall effect on ∆G is that it passes through a maximum (Figure 2), which corresponds to a nucleus of critical radius r*. The free energy at r ) r*, called critical free energy (∆G*), is the energy barrier for the nucleation process. The value of r* is obtained by differentiating eq 1 with respect to r, and its value is given by

r* )

2σVM RT ln(S)

(3)

and the corresponding value of the critical free energy (∆G*) is given by

∆G* )

16πσ3VM2 3(RT ln(S))2

(4)

In a supersaturated vapor of monomers (S > 1), random collisions generate nuclei of different radii. Nuclei larger than r* are likely to grow, and smaller nuclei are likely to shrink. Therefore, the rate of formation of nuclei with radii greater than

10.1021/jp907544g  2010 American Chemical Society Published on Web 03/10/2010

5722

J. Phys. Chem. C, Vol. 114, No. 13, 2010

Ali and Winterer

Figure 2. Change in free energy due to nucleation as a function of particle radius.

Figure 3. Schematic representation of the chemical vapor synthesis setup (P, pressure gauge; IR, infrared lamp; T, thermocouple).

or equal to r* is an important parameter in CVS. This rate is defined as the nucleation rate and is given by

dNn ∆G* ) A exp dt kT

(

)

(5)

where Nn is the molar concentration of nuclei, k is Boltzmann’s constant, and A is the pre-exponential factor. The exponential term is the probability of the formation of critical nuclei. According to Friedlander,11 A is given by

(

2σ A) πMNA

)( ) 1/2

p 2 VM kT NA

system, a hot wall reactor, and a particle collector. For the synthesis of ZnO nanocrystals from DEZ (liquid at room temperature), a bubbler filled with DEZ (Strem, 95%) was used as a precursor delivery system and the bubbler was placed in an oil bath to control its temperature.12 The temperature of the oil bath was maintained at 288 K for all syntheses. Helium (Air liquide 5.0) was used as a carrier gas for DEZ, and its flow was controlled by a mass flow controller. For the synthesis of ZnO nanocrystals from ZnTMHD (solid at room temperature), the vapor of the ZnTMHD precursor was generated by sublimation of ZnTMHD at 483 K and the vapor was transported to the reactor by the controlled flow of helium (carrier gas).13 Oxygen (Air liquide 4.5) was used as the oxygen source, and it was added just before the reactor to prevent preliminary oxidation of the precursors. A ceramic tube with an inner diameter of 19 mm was used as a reactor vessel for both precursors. After the synthesis of ZnO nanocrystals in the reactor vessel, particles were transported by the gas stream to the particle collector, where they were separated from the gas stream by thermophoresis. In thermophoresis, particles move toward a cold surface in a temperature gradient. We used an infrared lamp as a hot surface (≈800 K) and water-cooled stainless steel walls as a cold surface (≈293 K) to generate the temperature gradient. The absolute pressure of the system was measured by a Baratron gauge and controlled using a butterfly valve. ZnO nanocrystals from DEZ and ZnTMHD were synthesized in the temperature ranges 773-1273 and 873-1773 K, respectively. For DEZ, oxygen and helium flow rates were 1000 and 50 sccm, respectively, with a system pressure of 2000 Pa. For ZnTMHD, oxygen and helium gas flow rates were 5000 and 400 sccm, respectively, with a system pressure of 105 Pa. The molar yield was calculated from the ratio of moles of ZnO powder collected and moles of precursor consumed during the synthesis. Experimentally, the molar yield, Yexp, of ZnO nanoparticles was determined by

Yexp

(6)

where NA is Avogadro’s number and M is the molar mass of the monomer. Experimentally, we observed that the yield of ZnO nanocrystals synthesized by CVS from two different precursorss diethlzinc (DEZ)12 and bis(2,2,6,6-tetramethyl-3,5-heptanedionate)zinc (ZnTMHD)13sdecreases with increasing synthesis temperature. In this report, we study the influence of the hot wall temperature on the nucleation rate and hence on the yield of ZnO nanocrystals. Nanocrystalline ZnO is a material of commercial interest for decades. Commercially, it is used as an activator in rubber, pigment in paints, to improve the heat resistance of polymers and as an ultraviolet absorber in cosmetics. The large surface to volume ratio of nanocrystalline ZnO makes it a good material for gas sensing as well as in catalysis.14,15 Recent applications of nanocrystalline ZnO in solar cells, electroluminescent devices, and field effect transistors16-18 make it a versatile material. Experimental Procedures Figure 3 shows the schematic representation of the synthesis setup. The synthesis setup consists of a precursor delivery

mZnO M ) · 100 mpre Mpre

(7)

where mZnO is the mass of ZnO nanoparticles collected, mpre is the mass of precursor used during the synthesis, M is the molar mass of ZnO, and Mpre is the molar mass of the precursor. Typical masses of ZnO nanoparticles collected during 30 min of synthesis were in the range 0.25-1.6 g, depending on the reactor temperature. The particle size mentioned in this report represents the crystallite size, which was determined by Rietveld refinement of X-ray diffraction data using the program MAUD.19 The details of Rietveld refinement are discussed elsewhere.12 Results and Discussion The nucleation rate, dNn/dt (mol · m-3 · s-1), is defined as the number of stable nuclei formed per unit time per unit volume, which can be converted into a molar yield (Y) of the material by

dNn f∆V dt Y) 100 dn dt

(8)

Yield of ZnO Nanocrystals

J. Phys. Chem. C, Vol. 114, No. 13, 2010 5723

where dn/dt is the rate of precursor flow (mol · s-1), ∆V is the volume inside the reactor where nucleation takes place, and f is the number of ZnO monomers present in one nucleus. ∆V can be expressed by

∆V )

∆nRT pt

(9)

where ∆n is the number of moles of gases present in the volume element ∆V and pt is the total pressure in the reactor. Assuming an average size of nuclei equal to r, the value for f can be expressed as

f)

4πr3NA 3VM

(10)

In order to determine the molar yield by eq 8, we made the following simplifying assumptions: • The reactor consists of an isothermal hot wall. The Reynolds number for the processes considered here is of the order of 200 assuming that the excess oxygen behaves as an ideal gas and dominates the gas dynamics. Accordingly, the thermal and mass Peclet numbers are of a similar magnitude as the Reynolds number and, therefore, thermal and mass transport are both dominated by convection (not diffusion) and the flow can be considered as a plug flow.20 The error introduced by the assumption of an axially isothermal reactor should be of systematic nature, since we compare the temperature dependence while leaving other parameters constant. It could be the reason for the overestimation of the yield at low temperatures where the model predicts a more peaked curve for both precursors (Figure 4). The deviations could be accounted for in a more complete description of the process including the complete temperature field and loss terms using computational fluid dynamics simulations, as has recently been performed by Reuge et al.21 for ZnO tetrapod production from elemental zinc. • The loss of material by particle evaporation and by diffusional transport toward the reactor wall is neglected. ZnO nanoparticles can suffer material loss due to evaporation, enhanced by the Kelvin effect. Typically, the evaporated species are scavenged by other particles. Therefore, the loss of material by particle evaporation is neglected. According to the argument above, diffusional transport toward the reactor wall is even less likely for particles as their diffusion coefficient is about 3 orders of magnitude smaller compared to ZnO monomers which itself is about 2 orders of magnitude smaller than the oxygen diffusion coefficient. • ZnO is not reacting with water vapor which is a byproduct of the formation reactions. It is known that water vapor can enhance the transport of ZnO through the vapor phase.22 The source for water is the hydrogen in the precursor ligands. It would additionally enhance the water vapor pressure at high temperatures. Since a temperature gradient is required for chemical vapor transport, we neglect it. • The collection efficiency of the particle collector is ideal (100%) and independent of particle size. Thermophoresis in the molecular regime (applicable to our particles) is nearly independent of particle size. A lower

Figure 4. Influence of reactor temperature on the experimental molar yield of ZnO nanocrystals (shown by black diamonds) synthesized from (a) DEZ and (b) ZnTMHD. Black lines represent fitting of experimental molar yield by eq 7.

than ideal collection efficiency is lowering the overall yield independent of the reactor temperature as we force thermophoresis by an independently applied thermal gradient.11 According to a model for simultaneous aerosol nucleation, condensation, and coagulation by Pratsinis,23 the development of the aerosol volume, and therefore the aerosol mass, depends on nucleation and condensation. The half-lives for the decomposition of DEZ and ZnTMHD are orders of magnitude smaller compared to the residence time of gas inside the reactor at temperatures where particle formation is observed. The presence of an excess of oxygen and high reactor temperature further increases the probability of complete decomposition of the precursors. For example, complete decomposition of diethylzinc has already been observed above 673 K.24 Therefore, it is reasonable to assume complete decomposition of the precursors in a very small volume at the beginning of the reactor. Surface growth by reaction of existing nuclei with precursor molecules or intermediates is negligible, since the precursor decomposition reactions are very fast in the regime investigated. Surface growth by condensation of monomers is certainly possible. However, coagulation plays a more important role compared to condensation for fast precursor decomposition rates.23 Therefore, within our simple model, the computation of the molar yield is limited to contributions by nucleation. Small errors made in neglecting condensation are numerically compensated in an overestimated value for the fitting parameter ∆n. From eq 8, it is clear that the molar yield, Y, is temperature dependent as dNn/dt and ∆V are functions of temperature, evident from eqs 5 and 9, respectively. In order to determine the influence of temperature on the nucleation rate, the temperature dependence of A and ∆G* were determined by eqs 6

5724

J. Phys. Chem. C, Vol. 114, No. 13, 2010

Ali and Winterer

TABLE 1: Synthesis and Kinetics Parameters for DEZ and ZnTMHD (See Text) parameters precursor mole fraction total process pressure preexponential constant activation energy residence time critical radius of nucleation amount of substance in nucleation volume

x pt (Pa) ko (s-1) Ea (kJ mol-1) t (s) r (nm) ∆n (mol)

values for DEZ

source

values for ZnTMHD

source

0.0205 2000 2.4 × 1017 217.7 0.02 (at 773 K) 0.17(2) 1.2(4) × 10-8

set in experiment set in experiment Kim et al.25 Kim et al.25 estimated from plug flow fit using eq 8 fit using eq 8

0.003 105 4.2(6) × 108 149.6 0.1 (at 1073 K) 0.37(7) 7(4) × 10-10

set in experiment set in experiment fit using eq 8 by mass spectrometry13 estimated from plug flow fit using eq 8 fit using eq 8

and 4, respectively. Assuming that σ and VM for ZnO are temperature independent, the only parameters in eqs 6 and 4 that depend on temperature are S and p, respectively. The value of p, the partial pressure of the primary growth species (or ZnO monomers), is obtained from the decomposition kinetics of the precursor. Assuming a first order reaction for the formation of the primary growth species (or ZnO monomers) by decomposition of the precursor in an excess of oxygen, p is given by

[

( )}]

{

p ) xpt 1 - exp -kot exp -

Ea RT

(11)

where x is the mole fraction of ZnO monomers produced by complete decomposition of the precursor, ko is the frequency factor, Ea is the activation energy for decomposition of the precursor, and t is the residence time in the hot zone of the reactor. The experimental values of x, pt, ko, Ea, t, and dn/dt for DEZ and ZnTMHD are given in Table 1. For DEZ, the values of ko and Ea are taken from Kim et al.25 There is no report of ko and Ea for ZnTMHD in the vapor phase. Therefore, the decomposition of ZnTMHD at different reactor temperatures was studied by attaching a quadrupole mass spectrometer at the exit of the reactor in order to determine the activation energy Ea.13 The value of ps in eq 2 is given by the Kelvin equation11

{ }

ps ) pbulk exp

2σVM rRT

(12)

where r is the radius of the nucleus. The equilibrium vapor pressure of bulk ZnO (pbulk) at that temperature is given by

{

pbulk ) K · exp -

∆VH RT

}

(13)

where K is a constant and its value is equal to 7.245 × 105 Pa and ∆VH is the enthalpy of bulk ZnO evaporation (134 kJ/mol).26 For all of the calculations, we used a bulk value of σ for ZnO equal to 0.1 J/m2.27 Parts a and b of Figure 4 show the experimental molar yield of ZnO nanocrystals synthesized from DEZ and ZnTMDH, respectively, as well as fits using eq 8. For both of the precursors, the experimental molar yield first increases due to monomer formation according to eq 11 and then decreases with synthesis temperature due to a decrease in supersaturation as the ZnO partial pressure increases. For DEZ, the fitting was performed using r (average size of nuclei) and ∆n as fitting parameters. For ZnTMHD, as the value of ko is not known, ko, r, and ∆n were used as fitting parameters. The values of ko, r, and ∆n obtained after fitting are given in Table 1. For DEZ, the value of r (average size of nuclei) obtained from the fitting is equal to 0.17(2) nm, which is close to the value of ZnO nanocrystals

made of only one ZnO monomer estimated from the molar volume of ZnO. On the other hand, for ZnTMHD, the value of r is higher, 0.37(7) nm, which is equal to ZnO nuclei consisting of around nine ZnO monomers. This indicates that when DEZ is used as a precursor under our synthesis condition, each ZnO monomer can act as a stable nucleus, but for ZnTMHD nine ZnO monomers are needed to cluster together to make a stable nucleus. Therefore, the probability of formation of stable nuclei is higher with DEZ compared to ZnTMHD, which leads to higher experimental molar yields of ZnO nanocrystals when DEZ is used as a precursor (compare parts a and b of Figure 4). Velasco et al.28 determined the molecular size of the growth species in atmospheric pressure MOCVD of ZnO from diethylzinc and water from the measured diffusivities to about 0.6 and 0.9 nm at 1023 and 973 °C, respectively, which are of the same order of magnitude as the size of the critical nuclei determined from our model. The parameter ko has only a small influence on the maximum yield, but it changes the shape of the temperature dependence, since it determines the threshold temperature above which particle formation is initiated by precursor decomposition. Changing the value of r by a factor of 0.5 or 2 decreases or increases the maximum yield by almost an order of magnitude. The molar yield varies linearly as a function of the parameter ∆n. The same trend in the molar yield is observed for ZnO nanoparticles synthesized from ZnTMHD precursor. The dependence of p and ps on the reactor temperature is shown in Figure 5a. It can be noticed that the partial pressure of ZnO monomers from DEZ becomes constant above 760 K, as above 760 K all of the DEZ is decomposed and likely converted into ZnO monomers. Similarly, the partial pressure of ZnO monomers from ZnTMHD becomes constant after 1170 K. The influence of the reactor temperature on the equilibrium vapor pressure (ps) of ZnO nanocrystals (r ) 0.18, 0.37, and 1.0 nm) is shown in Figure 5a too, which is determined by eq 12. It can be noticed that ps increases continuously with temperature, indicating a higher volatility at higher temperatures. According to the Kelvin equation, smaller particles have a higher tendency to evaporate as the value of ps is higher for r ) 0.18 nm compared to 0.37 and 1.0 nm, at a particular reactor temperature. The overall effect on S is that it starts to decrease drastically above 760 K for DEZ (Figure 5b) and above 1170 K for ZnTMHD (Figure 5c), which leads to a decrease in the nucleation rate and hence in the yield. Since ZnTMHD is thermally more stable compared to DEZ, it decomposes at a temperature where the vapor pressure of ZnO is higher than for the process window of DEZ, which generates a lower supersaturation and, therefore, a lower yield. Assuming, that inside the reactor, zinc oxide can exist mainly in two different forms, (1) ZnO nanoparticles and (2) very small clusters or monomers (ZnO)n, the yield could be decreased by • condensation of (ZnO)n on the surface of the ZnO nanoparticles

Yield of ZnO Nanocrystals

J. Phys. Chem. C, Vol. 114, No. 13, 2010 5725

Figure 6. Influence of reactor temperature on the crystallite size of ZnO nanocrystals synthesized from DEZ and ZnTMHD precursors. Error bars are smaller than the marker sizes.

Figure 5. Influence of reactor (synthesis) temperature on (a) ZnO monomer partial pressure (p) for DEZ and ZnTMHD precursors and equilibrium vapor pressure of ZnO nanocrystals (ps) of average nuclei radii equal to 0.18, 0.37, and 1.0 nm, (b) saturation ratio for DEZ and (c) saturation ratio for ZnTMHD. The vapor pressures p and ps and the saturation ratio are determined by eqs 11, 12, and 2, respectively.

• diffusion of (ZnO)n toward the reactor wall and subsequent deposition • deposition of (ZnO)n on the cool surface of the thermophoretic collector • loss of (ZnO)n downstream of the reactor lost in the vacuum system. The first path will not contribute to a loss in yield, since the particles are collected; the second path is inefficient as described above. Species like (ZnO)n will behave like (gas) molecules due to their small size. Therefore, most likely, they are lost downstream of the reactor or the collector. A decreasing yield has been observed in spray-pyrolysis of micrometer-sized oxide particles (PbO, Bi2O3, MoO3, and V2O3) with increasing reactor temperature.29,30 There, the decrease in yield was attributed to particle evaporation and diffusional transport of oxide vapors to the reactor walls. The evaporation from the particle surface not only decreases the yield but also causes a decrease in the size of the particles.29 In our experiments, we observed that the particle size increases (as determined by X-ray diffraction) with reactor temperature (Figure 6), indicating a different cause for the decreasing yield. Here, the particles grow mainly by coagulation and coalescence processes. The increase in size of ZnO nanocrystals with temperature is probably due to faster sintering rates at higher

temperatures31 as well as due to scavenging of the evaporated ZnO monomers by other ZnO particles. The small (nano) size of our ZnO particles provides a large surface area per unit reactor volume for scavenging of ZnO monomers instead of diffusional transport toward the reactor wall. The evaporation of ZnO monomers from the surface of ZnO nanocrystals does not play a substantial role in the yield in this temperature regime. However, for ZnTMHD, the size of ZnO nanocrystals starts to decrease at 1773 K which is probably the onset for substantial evaporation of ZnO from the surface of nanocrystals. The yield can be substantially increased when nucleation is first performed at low temperature in a microwave plasma with a high nucleation rate and growth in a hot wall reactor.12 Similarly, Kleinwechter et al. have observed that nucleation of ZnO in high temperature flames is difficult if not impossible but facile in an argon-oxygen plasma.32 Conclusions Two different zinc oxide precursorssdiethylzinc and bis(2, 2,6,6-tetramethyl-3,5-heptanedionate)zincswere used for the chemical vapor synthesis of ZnO nanocrystals. The nucleation rate has a substantial influence on the yield of the material. A decrease in the nucleation rate at higher reactor temperature leads to a decrease in the yield of ZnO nanocrystals independent of the type of precursor used through the non-negligible vapor pressure of ZnO. Therefore, precursors that are more readily decomposed at lower temperatures (DEZ instead of ZnTHMD) or processes which generate a high supersaturation at low temperature (microwave plasma instead of hot wall reactors) are possible solutions to this problem. Acknowledgment. The financial support of the German Research Foundation (DFG) through the Research Training Group: Nanotronics (1240) is gratefully acknowledged. We thank Joachim Brehm for supplying the yield data using ZnTMHD and Hermann Sieger for mass spectrometry of ZnTMHD decomposition. References and Notes (1) Akhtar, M. K.; Xiong, Y.; Pratsinis, S. E. AIChE J. 1991, 37, 1561. (2) Akurati, K. K.; Bhattacharya, S. S.; Winterer, M.; Hahn, H. J. Phys. D: Appl. Phys. 2006, 39, 2248. (3) Klein, S.; Winterer, M.; Hahn, H. Chem. Vap. Deposition 1998, 4, 143.

5726

J. Phys. Chem. C, Vol. 114, No. 13, 2010

(4) Polarz, S.; Roy, A.; Merz, M.; Halm, S.; Schro¨der, D.; Schneider, L.; Bacher, G.; Kruis, F. E.; Driess, M. Small 2005, 5, 540. (5) Nasibulin, A. G.; Richard, O.; Kauppinen, E. I.; Brown, D. P.; Jokiniemi, J. K.; Altman, I. S. Aerosol Sci. Technol. 2002, 36, 899. (6) Magnusson, M. H.; Deppert, K.; Malm, J. O. J. Mater. Res. 2000, 15, 1564. (7) Kennedy, M.; Seggern, H. V.; Winkler, H.; Kolbe, M.; Fischer, R. A.; Xaomao, L.; Benker, A.; Winterer, M.; Hahn, H.; Schmechel, R. J. Appl. Phys. 2001, 89, 1679. (8) Srdic, V. V.; Winterer, M.; Moller, A.; Miehe, G.; Hahn, H. J. Am. Ceram. Soc. 2001, 84, 2771. (9) Ostraat, M. L.; DeBlauwe, J. W.; Green, M. L.; Bell, L. D.; Atwater, H. A.; Flagan, R. C. J. Electrochem. Soc. 2001, 148, 265. (10) McDonald, J. E. Am. J. Phys. 1963, 31, 31. (11) Friedlander, S. K. Smoke, Dust and Haze; Oxford University Press: 2000. (12) Ali, M.; Friedenberger, N.; Spasova, M.; Winterer, M. Chem. Vap. Deposition 2009, 15, 192. (13) Brehm, J. Synthesis und Charakterisierung nanokristalliner transparenter Halbeiteroxide. Ph.D. thesis, Cuvillier Verlag Go¨ttingen, 2005.Brehm, J. U.; Winterer, M.; Hahn, H. J. Appl. Phys. 2006, 100, 064311. (14) Liao, L.; Lu, H. B.; Li, J. C.; He, H.; Wang, D. F.; Fu, D. J.; Liu, C. J. Phys. Chem. C 2007, 111, 1900. (15) Kwak, G.; Yong, K. J. Phys. Chem. C 2008, 112, 3036. (16) Law, M.; Greene, L. E.; Johnson, J. C.; Saykally, R.; Yang, P. Nat. Mater. 2005, 4, 455. (17) Wang, Z. L. J. Phys.: Condens. Matter 2004, 16, R829.

Ali and Winterer (18) Suh, D.; Lee, S. Y.; Hyung, J. H.; Kim, T. H.; Lee, S. K. J. Phys. Chem. C 2008, 112, 1276. (19) Lutterotti, L.; Matthies, S.; Wenk, H. R. IUCr: Newsletter of the CPD 1999, 21, 14 (available at http://www.ing.unitn.it/∼maud/). (20) Jensen, K. F. J. Cryst. Growth 1998, 98, 148. (21) Reuge, N.; Basca, R.; Serp, P.; Caussat, B. J. Phys. Chem. C 2009, 113, 19845. (22) Ntep, J. M.; Barbe, M.; Cohen-Solal, G.; Bailly, F.; Lusson, A.; Triboulet, R. J. Cryst. Growth 1998, 184/185, 1026. (23) Pratsinis, S. E. J. Colloid Interface Sci. 1988, 124, 416. (24) Dumont, H.; Marbeuf, A.; Bouree, J.-E.; Gorochow, O. J. Mater. Chem. 1993, 3 (10), 1075. (25) Kim, Y. S.; Won, Y. S.; Hagelin-Weaver, H.; Omentto, N.; Anderson, T. J. Phys. Chem. A 2008, 112, 4246. (26) Determined by fitting data taken from Figure 2 in Koumoto, K.; Mizuta, S.; Yanagida, H. J. Ceram. Assoc. Jpn. 1980, 88, 1016. (27) Olorunyolemi, T.; Birnboim, A.; Carmel, Y.; Wilson, O. C.; Lloyd, I. K. J. Am. Ceram. Soc. 2002, 85, 1249. (28) Velasco, A.; Mitsuji, H.; Minami, W.; Lee, J. K.; Komiyama, H.; Kim, H. J. J. Cryst. Growth 2008, 310, 3837. (29) Lyons, S. W.; Xiong, Y.; Ward, T. L.; Pratsinis, S. E.; Kodas, T. T. J. Mater. Res. 1992, 7, 3333. (30) Xiong, Y.; Lyons, S. W.; Pratsinis, S. E.; Kodas, T. T. J. Am. Ceram. Soc. 1995, 78, 2490. (31) Tsantilis, S.; Pratsinis, S. E. Langmuir 2004, 20, 5933. (32) Kleinwechter, H.; Janzen, C.; Knipping, J.; Wiggers, H.; Roth, P. J. Mater. Sci. 2002, 37, 4349.

JP907544G