CRYSTAL GROWTH & DESIGN
Growth Thermodynamics of Nanoscaled r-Alumina Crystallites
2009 VOL. 9, NO. 4 1692–1697
Rung-Je Yang, Pei-Ching Yu, Chih-Cheng Chen, and Fu-Su Yen* Department of Resources Engineering, National Cheng Kung UniVersity, No. 1 UniVersity Road, Tainan, Taiwan 70101, ROC, and Department of Mechanical Engineering, Far East UniVersity, No. 49, Jhonghua Road, Shinshih Township, Tainan County 744 Taiwan, ROC ReceiVed April 6, 2008; ReVised Manuscript ReceiVed January 18, 2009
ABSTRACT: The growth thermodynamics of nanoscaled R-Al2O3 crystallites after its formation from θ-Al2O3 phase transition by thermal treatment was examined. The crystallite growth characterized with quantized size increments can be performed through coalescence processes. The R-Al2O3 nuclei with sizes 17-20 nm (dcR) coalesced to form R-crystallites of sizes 45-50 nm (dp), then by coalescence of which the stable R-crystallites (ds) with minimum sizes 75-80 nm were obtained. Coalescence of the ds crystallites leads to formation of the crystallites with vermicular growth. A growth thermodynamic model describing the three-staged size growth was proposed. It provides well-coincided calculations with the data observed. The surface free energy of θ-Al2O3, which is being reported for the first time, is 2.16 J/m2. Introduction The natural R-Al2O3 or corundum known by man has possibly been over 7000 years.1 In 1875, the pure synthetic alumina was prepared by thermal decomposition of aluminum salts and by calcining bauxite with soda.1 The beginning in the modern aluminum industry for producing corundum or R-Al2O3 started in 1895 at Gardanne, France, using the Bayer process. However, it is noted that in more than one century, neither the growth mechanism nor the basic thermodynamic data of R-Al2O3 has been well-documented so far (Table 1). In the past decades, three specific crystallite sizes were reported for the R-Al2O3 crystallites obtained by calcinations of boehmite through θ- to R-Al2O3 phase transformation. This has been one of the major routes to produce R-Al2O3 powders. However, the R-Al2O3 crystallites in the powder system normally show the finger or vermicular morphology with sizes larger than 100 nm. This is the largest size noted in this study, by which the R-Al2O3 particles of several nanometer to micrometer sizes are formed. These vermicular structures are composed of differentiable segments with sizes smaller than 100 nm. The “fingerlike” branches with a width in the range of 60 to 100 nm2 or 75 to 100 nm3,4 and would be accompanied with isolated R-Al2O3 particles having sizes smaller than 100 nm2 or 250 to 500 nm3,4 in diameter. Furthermore, the isolated R-Al2O3 crystallites appeared when the formation of R-Al2O3 was low.5 Besides the R-crystallites with vermicular growth of sizes >100 nm and the isolated one of dc. Since the θ- to R-Al2O3 phase transformation is achieved by the nucleation and growth mechanism, in which crystallite growth proceeds consequently after nucleation stage, the presence of three subsequent sizes for R-Al2O3 crystallites with sizes ∼17-20, 45-50, and 75-100 nm are presumably related to the growth processes. Furthermore, the thermodynamic relationships among the three categories of R-Al2O3 crystallites can be made. Table 1 compiles the volume25 and the surface free energies26-30 of aluminas reported previously. Data of θ-Al2O3, including theoretical calculations or empirical results, have not been reported so far. In this study, the growth behavior of the three R-Al2O3 crystallite sizes observed during R-Al2O3 phase formation was examined thermodynamically. A boehmitederived θ-Al2O3 powder of mean crystallite size ∼20 nm was used as the starting material. Examinations were performed using the TEM and XRD techniques. A thermodynamic model for interpreting the presence of the three sizes and the quantized size growth phenomena of R-Al2O3 crystallites was proposed. Experimental Section Sample Preparations. (1) θ-Al2O3:A θ-Al2O3 powder of crystallite size ∼20 nm (XRD-Scherrer formula) prepared by calcinations of boehmite (Al2O3 content >99.9 wt % on dried base, Remet Chemical Corp., USA) was used as the starting material. To reduce the degree of particle agglomeration, we converted the the powder into slurries by mixing with D. I. water and mechanically stirred accompanied by pH adjustment with HNO3 for dispersion. After stirring, the θ-slurry
Crystal Growth & Design, Vol. 9, No. 4, 2009 1693 was microwave dried and ground in an agate mortar with a pestle till finer than 200 mesh (74 µm). (2) θ- to R-Al2O3 transformation: To investigate the R-Al2O3 growth, the dried powder samples for examining the θ- to R-phase transformation and R-Al2O3 size growth were obtained by further thermal treating to scheduled temperatures and then quench to room temperature. The temperature range of θ- to R-Al2O3 transformation was determined from DTA (Differential thermal analysis) using a heating rate of 10 °C/min in air atmosphere. Characterizations. Crystalline phase identifications, R-phase formation and the R-crystallite size measurements during θ- to R-phase transformation processing were performed using XRD powder methods (Rigaku, Japan) with Ni-filtered CuKR radiation. For phase identification, the samples were scanned from (2θ )) 80-20° at a scanning rate of 4°/min. The mean crystallite sizes of R-Al2O3 in the samples were calculated by the XRD-Scherrer formula31 (crystallite size ) 0.9λ/ Bcos θ, where λ ) 1.5405 Å, B ) the width at the half-peak height (WHPH) in radians, and θ ) the Bragg angle). The reflection peak (012)R of R-Al2O3 was applied. The scanning rate was 0.5°/min and 2θ was 24.5-34.5°. The instrument peak width was calibrated using a well-crystallized silicon powder. Data calculations were assisted by a software, XRD Pattern Processing and Identification, Jade for Windows, Version 5.0, developed by Materials Data Inc. The fraction of R-Al2O3 formation in the samples was determined by quantitative XRD powder methods using CaF2 as the internal standard. The integrated intensities of the (012) reflection for R-Al2O3 and the (111) reflection for the CaF2 internal standard (10 wt %) were measured. The values of R-Al2O3 contents then derived by the ratio comparing to an R-Al2O3-CaF2 calibration curve. The range of investigation was 1.5-97 wt %. The morphology and microstructure of the R-Al2O3 crystallites were examined with a transmission electron microscope (TEM, JEOL AEM3010, and Tecnai FEG-TEM). Finally, thermodynamic descriptions and calculations for the relationships among three categories of R-Al2O3 were proposed in this study.
Results and Discussion Crystallite Size of r-Al2O3 during Phase Transformation. Figure 1 illustrates the three step quantized size growth of R-Al2O3 crystallite after the crystallites were formed. The subsequent size dimensions were 17-20 nm (critical size for R-phase formation7), 45-50 nm (primary size7), and 70-80 nm. Both the crystallite size growth from 17-20 to 45-50 nm and from 45-50 to 70-80 nm display the independence of the amount of R-Al2O3 formation, implying that the crystallite growth can be performed through coalescence of pre-existing crystallites.8,9 Figure 2 shows the detailed examinations using HR-TEM techniques on the typical R-crystallites of sizes ∼50 and ∼100 nm. Both are composed of several domains, which are well-matched with each other (images a and b in Figure 2), being of single-crystal. The former is formed by crystallite coalescence of 15-20 nm R-crystallites, while the latter is built up by ∼50 nm R-crystallites. Assuming that the particles are approximately spherical, calculation on the numbers needed to form a particle of ∼50 nm in diameter (dp) is about 25, if R-nuclei of ∼17-20 nm are engaged. Similarly, crystallite with sizes ∼70-80 nm will be formed by coalescence of 4-5 preexisting crystallites of ∼45-50 nm. Vermicular structure (>100 nm) can also be found for the R-crystallites with sizes larger than 80 nm (images c and d in Figure 1). The vermicular R-crystallite is assembled by connection of R-Al2O3 crystallites with sizes 75-100 nm. Since lowering the surface energies can be an urgent necessity that must be succeeded for a small particle, coalescing R-crystallites of critical size to form that of primary size, or coalescence of 17-20 nm R-crystallites to form R-crystallites of size ∼45-50 nm can be considered as undertaking a necessity. Furthermore, the coalescence process to reduce the surface energy for the powder system will become inferior because of the increase in numbers of crystallite
1694 Crystal Growth & Design, Vol. 9, No. 4, 2009
Yang et al.
Figure 1. R-Al2O3 crystallite displays three steps of size growth during its early stage of formation. (a) Size growths show disproportional to the amount of formation. (b) The corresponding XRD patterns of (a). The TEM micrographs show crystallites with sizes (c) ∼17-20, ∼45-50, and 80-100 nm and (d) monodiscrete ∼75-80 nm. (e) R-Al2O3 crystallites with typical vermicular growth occur when the size is larger than ∼100 nm.
involved (Figure 3). The surface energy reduction caused by coalescence of smaller particles will be substituted by larger particles. Figure 3 shows the relationship between the theoretical surface area reductions per unit volume (of the solid) vs the growth of the three characteristic crystallite sizes, assuming the reduction is beginning in the powder system of mean size ∼17 nm. The surface area reduction results from R-crystallite coarsening from diameters 17-20 to 45-50 nm (dcR to dp) (Figure 3, curve a) and then from 45-50 to ∼100 nm (Figure 3, curve b) and then occurrence of the vermicular growth (Figure 3, curve c) are represented by the three curves. It is clear, for each curve, the reduction rate (surface area to diameter) begins to lessen once the diameter of the crystallite coarsens to certain sizes. Or as coalescence of 17-20 nm (dcR) crystallites to form crystallites of sizes around 45-50 nm, the reduction rate falls, so it is lower than that obtained by coalescence of 45-50 nm (dp) crystallite; because of that, coalescence of 45-50 nm (dp) crystallites to form an ∼100 nm sized crystallite then occurs. Thus, the quantity of surface area expense resulted from the coalescence of R-Al2O3 of sizes 17-20 and 45-50 nm that bring about the presence of crystallites 45-50 and 75-100 nm, respectively, can then be related to the effectiveness in reducing the surface energy of the powder system. And it is obvious that the vermicular growth for the R-Al2O3 by connecting segments of 75-100 nm2-4 seems to reflect the necessity of the reducing surface area becoming less significant. Thermodynamic Model. Figure 4 depicts a thermodynamic model for describing nanosized R-Al2O3 crystallite growth. After
the presence of R-Al2O3 nuclei, the crystallite growth process succeeds. The phenomena investigated above show that the R-Al2O3 crystallite growth that is progressed through coalescence mechanism (Figure 2) by three steps is presumably induced by removal of surface area (Figure 3). From the thermodynamic point of view, as the crystallite growth proceeds, in addition to volume (V∆Gv) and surface energies (A∆γ), another positive energy, interfacial energy (designated as Einter), contributed by coalescence process due to the removal of surface area among R-crystallites, occurs. The quantity of interfacial energy herein equals to the total interfacial energy of the total smaller R-Al2O3 crystallites subtracts that of the larger ones formed.32 The interfacial energy may include both the energies required for particle rotation and removal of interfaces among R-crystallites (line 4 of Figure 4). Because the induced positive energy due to the removal of interfacial area of R-Al2O3 nuclei is much larger than the negative volume energies of the crystallite formed by coalescence, the original decreasing tendency in total free energy change then would be turned into an increasing one. As a result, the second critical size (primary size, dp) would occur and the total free energy change could be expressed as eq 3
(
)
d3 1 ∆Gr ) πd3∆Gθ-R + πd2∆γθ-R + 3 πd2cR - πd2 γ1 6 dcR (3)
Growth Thermodynamics of Nanoscaled R-Alumina Crystallites
Crystal Growth & Design, Vol. 9, No. 4, 2009 1695
Figure 2. HRTEM micrographs show R-Al2O3 crystallites of sizes (a) ∼45 and (b) ∼80 nm are formed by coalescence of R-Al2O3 crystallites of ∼15-20 and 45-50 nm, respectively. The corresponding electron diffraction patterns demonstrate that both size crystallites are single crystal.
The second critical crystal size, dp, can be easily obtained by differentiation of eq 3
dp(nm) )
68(γ1 - ∆γθ-R) 17∆Gθ-R × 10-9 + 6γ1
(4)
where γ1 is the interfacial free energy derived from coalescence of R-Al2O3 nuclei. Continuous heating leads to the size growth of R-crystallite, bringing about the lowering of ∆Gr in eq 3. And finally ∆Gr E 0 will be reached. It is noted the TEM images reveal both the growth of R-Al2O3 with sizes ∼45-50 and ∼75-100 nm is performed by coalescence, and thus the interfacial energy induced by the removal of the interfaces of these particles should inevitably occur. However, these energies induced by forming the latter size can be much smaller. And only that of the former (line 4 in Figure 4) can be of significance. The growth thermodynamic model (Figure 4) consists of three stages of R-Al2O3 crystallite growth. The free energy change of one R-Al2O3 nucleus growth, because its formation from transformation of θ-phase can be described through this thermodynamic model. For a powder system, the total free energy is decreased with the progress of the nucleation and growth process. For a single R-crystallite, the R-Al2O3 crystallites with positive total free energy change, ∆Gr > 0, will behave as thermodynamically metastable during the phase transformation. R-Alumina crystallites need to keep on growing to exceed the size corresponding to point D, ds, that bringing the particles to meet the requirement ∆Gr E 0 to accomplish the phase transformation. Alpha alumina crystallites with sizes smaller and larger than ds could behave
Figure 3. Relationships between the removed surface area per unit volume induced by the crystallite coalescence and the corresponding crystallite size generated during the process of R-Al2O3 growth, assuming that the growth process could be performed through coalescence of a 17 nm crystallite to form spherical particles 50 and 100 nm in diameter. (a) Sremoved ) 88.2 - 1500/d, (b) Sremoved ) 30 1500/d, and (c) Sremoved ) 15 - 1500/d.
as thermodynamically metastable and stable, respectively. Therefore, although R-Al2O3 crystallites with sizes smaller than ds could exist, they would experience phase-retrogression to θ-phase within tens of seconds if appropriate thermal treatment conditions were adopted.9 Furthermore, the related thermodynamic data of θ- to R-Al2O3 phase transformation can be calculated through the Gibbs free energy change and growth characteristics of three crystallite sizes observed.
1696 Crystal Growth & Design, Vol. 9, No. 4, 2009
Yang et al.
Figure 4. Schematic representation for the free energy differences of θ- f R-Al2O3 phase transformation associated with the nucleation and coalescence growth of a spherical R-Al2O3 nucleus with diameter d.
In this study, the value of volume free energy of θ-phase is proposed to lie between that of δ- and R-Al2O3 (volume free energy difference between δ- and R-Al2O3 is -0.225 × 109 J/m3 (Table 1)). As a result, the volume free energy difference of θ- and R-phase (GV(θ-R)) is assumed to be -0.1125 × 109 J/m3. Inserting the value and the critical crystallite size of R-Al2O3 (17 nm) into eq 2 gives the surface free energy difference between θ- and R-Al2O3, ∆γθ-R. Thus, the surface free energy of θ-Al2O3 that has not been reported so far can be 2.16 J/m2 if that of the R-phase is adopted as 2.64 J/m2.29 Subsequently, substituting the volume and the surface free energies of θ- and R-Al2O3 back into eq 1, and letting ∆Gr ) 0, the primary stable crystallite size related to point B in Figure 4 can be obtained as 26 nm. According to the results, θ-Al2O3 crystallites with sizes larger than the primary stable size, being about 30 nm, (because θ- to R-Al2O3 phase transformation can result in a 9.0% volume reduction) might transform to nanosized R-Al2O3 crystallites without via coalescence mechanism if appropriate thermal treatment conditions were employed. Further, inserting dp size (∼50 nm) into eq 4, then γ1 can be obtained. Substituting ∆GV(θ-R), ∆γθ-R, and γ1 back into eq 3, and letting ∆Gr ) 0, the crystallite size for the accomplishment of phase transformation as well as the smallest stable crystallite size caused by coalescence mechanism is about 75 nm. The calculation results coincide well with the smallest stable crystallite size, ∼75-100 nm, reported previously.3-5,9,10 The calculated surface free energy of θ-Al2O3 and the growth characteristic crystallite size during phase transformation were summarized in Table 2. Occurrence of Vermiculated r-Crystallites. The vermiculargrowth caused by the coalescence of two or more R-Al2O3 crystallites would occur once crystallites exceeding the stable crystallite size, ds. It can be because of values of ∆Gr becoming negative (Figure 4, ds) and the surface energy reduction in terms of size growth being insignificant (Figure 3). Therefore, for
Table 2. Characteristic Crystallite Sizes of r-Al2O3 and the Free Surface Energy of θ-Al2O3 Observed and Calculated in This Study dcR (nm) experiment calculation
dB (nm)
17
dp (nm)
ds (nm)
γθa (J/m2)
45-50
75-100 75
2.16
26
a
Assuming that the volume free energy difference between θ- and R-Al2O3 is 0.1125 × 109 J/m3 and the surface free energy of R-Al2O3 is 2.64 J/m2.
R-Al2O3 crystallites with sizes larger than ds, taking coalescence process to reduce surface area are now must no necessity of forming spherical. A spherical particle shows minimum surface area. And the vermicular-like connection of R-Al2O3 will occur. Thus its occurrence can be considered closely related to the thermodynamic state or surface/volume ratio of R-Al2O3 crystallites. Thus, R-Al2O3 crystallites with total free energy difference larger and smaller than zero may coarsen to form near spherical and vermiculated particles, respectively. It may explain why the cross-sectional diameter of the vermiculated R-crystallites observed in previous studies was 75-100 nm. Moreover, it could be clear to interpret the vermicular structure of R-Al2O3 crystallites could be formed through the coalescence process because the vermiculated crystallites are single crystals instead of polycrystalline caused by sintering processes in this study. Conclusions 1. The presence of three subsequent sizes for R-Al2O3 crystallite after forming the R-nuclei (dcR, d ) 17-20 nm) is characterized with quantized size growth. The growth is performed through coalescence of the unstable R-nuclei to form R-crystallites of sizes 45-50 nm (dp) first, then by which the final stable R-Al2O3 crystallite with sizes 75-80 nm (ds) are formed. Normally the three sizes’ crystallites can show discrete
Growth Thermodynamics of Nanoscaled R-Alumina Crystallites
or isolated units. However, the 75-80 nm units would form vermicular structure once the coalescence process proceeds. 2. A proposed thermodynamic model describing the threestaged growth demonstrated to provide well-coincided calculations with the data observed. It is found that both the primary (dp) and smallest stable size (ds) are formed during the phase transformation and the surface free energy of θ-Al2O3 has not been reported so far can be 2.16 J/m2. 3. On the basis of the proposed thermodynamic model, it is supposed that θ-Al2O3 with sizes larger than 30 nm in diameter would transform into stable R-Al2O3 directly without proceeding coalescence growth processes. Acknowledgment. We thank Miss Liang-Chu Wang of National Sun Yat-Sen University for the assistance in TEM examinations. This study was supported by the National Science Council (NSC-96-2221-E-006-122-MY2) and the Ministry of Economic Affairs (96-EC-17-A-08-S1-023) of the Republic of China.
References (1) Greville, C. Encyclopaedia Britannica “Corundum ” 7, 11th ed.; Encylopaedia Britanica: Chicago, 1951; p 207. (2) Badker, P. A.; Bailey, J. E. J. Mater. Sci. 1976, 11, 1794. (3) Dynys, F. W.; Halloran, J. W. J. Am. Ceram. Soc. 1982, 65, 442. (4) Hench, L. L.; Ulrich, D. R. Ultrastructure Processing of Ceramics, Glasses and Composites; John Wiley and Sons: New York, 1984; pp 142-151. (5) Wynnyckyj, J. R.; Morris, C. G. Metall. Trans., B 1985, 16, 345. (6) Wen, H.-L.; Chen, Y.-Y.; Yen, F.-S.; Huang, C.-Y. Nanostruct. Mater. 1999, 11, 89. (7) Wen, H.-L.; Yen, F.-S. J. Cryst. Growth 2000, 208, 696. (8) Chang, P.-L.; Yen, F.-S.; Cheng, K.-C.; Wen, H.-L. Nano Letters 2001, 1, 253. (9) Yang, R. J.; Yu, P. C.; Chen, C. C.; Yen F. S. Cryst. Growth Des. 2009, under review.
Crystal Growth & Design, Vol. 9, No. 4, 2009 1697 (10) Yu, P.-C.; Yang, R.-J.; Chang, Y.-T.; Yen, F.-S. J. Am. Ceram. Soc. 2007, 90, 2340. (11) Banfield, J. F.; Navrotsky, A. ReViews in Mineralogy & Geochemistry, Vol. 44: Nanoparticles and the EnVironment; Mineralogical Society of America and Geochemical Society: Washington, D.C., 2001. (12) Penn, R.; Lee; Banfield, J. F. Am. Mineral. 1998, 83, 1077. (13) Penn, R.; Lee Banfield, J. F. Science 1998, 281, 969. (14) Penn, R. Lee.; Oskam, G.; Strathmann, T. J.; Searson, P. C.; Stone, A. T.; Veblen, D. R. J. Phys. Chem. B 2001, 105, 2177. (15) Penn, R. Lee; Stone, A. T.; Veblen, D. R. J. Phys. Chem. B 2001, 105, 4690. (16) Huang, F.; Zhang, H.; Banfield, J. F. Nano Lett. 2003, 3, 373. (17) Lee, W.-H.; Shen, P. J. Cryst. Growth 1999, 205, 169. (18) Shen, P.; Lee, W.-H. Nano Lett. 2001, 1, 707. (19) Kuo, L.-Y.; Shen, P. Mater. Sci. Eng. 2000, A276, 99. (20) Yu, J. G. ; Zhao, X. F.; Liu, S. W.; Li, M.; Mann, S.; NG, D. H. L. Appl. Phys. A: Mater. Sci. Process. 2007, 87, 113. (21) Co¨lfen, H.; Mann, S. Angew. Chem., Int. Ed. 2003, 42, 2350. (22) Givargizov, E. I. Oriented Crystallization on Amorphous Substrate; Plenum Press: New York, 1991. (23) Zhu, H.; Averback, R. S. Mater. Manuf. Process 1996, 11, 905. (24) Teng, M. H.; Marks, L. D.; Johnson, D. L. J. Mater. Res. 1997, 12, 235. (25) Chase, M. W.; Davies, Jr., C. A.; Doweny, J. R.; Fruip, Jr.; McDonalds, R. R.; Syverud, A. N. JANAF Thermochemical Tables; 3rd ed.; American Chemical Society: Washington, D.C., 1986. (26) Kingery, W. D.; Bowen, H. K.; Uhlmann, D. R. Introduction to Ceramics; 2nd ed.; John Wiley & Sons: New York, 1976. (27) Sun, J.; Stirner, T.; Matthews, A. Surf. Coat. Technol. 2006, 201, 4205. (28) Blonski, S.; Garofalini, S. H. Surf. Sci. 1993, 295, 263. (29) McHale, J. M.; Auroux, A.; Perrotta, A. J.; Navrotsky, A. Science 1997, 277, 788. (30) McHale, J. M.; Navrotsky, A.; Perrotta, A. J. J. Phys. Chem. B 1997, 101, 603. (31) Cullity, B. D. Elements of X-ray Diffraction, 2nd ed.; Addison-Wesley: London, 1978. (32) Stokes, R. J.; Evans, D. F. Fundamentals of Interfacial Engineering; Wiley-VCH Publishers: New York, 1997; Chapter 3.
CG800351D
