Shape-Dependent Compressibility of TiO2 Anatase Nanoparticles

J. Phys. Chem. C 2008, 112, 9627–9631

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Shape-Dependent Compressibility of TiO2 Anatase Nanoparticles Seung-won Park,† Jung-tak Jang,† Jinwoo Cheon,†,* Hyun-Hwi Lee,‡ Dong Ryeol Lee,‡ and Yongjae Lee§,* Departments of Chemistry and Earth System Sciences, Yonsei UniVersity, Seoul 120749, Korea, and Pohang Accelerator Laboratory, Pohang UniVersity of Science and Technology (POSTECH), Pohang, 790784, Korea ReceiVed: February 21, 2008; ReVised Manuscript ReceiVed: April 9, 2008

We measured the size- and shape-dependent compressibility of the TiO2 anatase nanoparticles using monochromatic synchrotron X-ray powder diffraction and high-pressure diamond-anvil cell techniques. Compared to the bulk anatase sample, the rice-shaped (3.8 × 5.0 nm) and the rod-shaped (3.5 × 21.0 nm) anatase nanoparticles exhibit reduced and enhanced bulk modulus, respectively, ranging between 204(8) and 319(20) GPa. The Williamson-Hall plot analysis of the measured diffraction data from the bulk sample shows that the pressure-dependent increase of the microscopic strain is isotropic, whereas the Strokes-Wilson profile analyses on the two resolved Bragg peaks from the anatase nanoparticles reveal anisotropic distribution and evolution of the relative strain. This might be attributed to the higher c-axial compressibility and also to the higher population contrast of the hard TiO6 and soft O6 octahedra in the nanoparticle samples compared to the bulk sample. Introduction Nanocrystalline solids are generally defined as materials that are less than 100 nm in size in at least one dimension. This gives large surface-to-volume ratios and modifications to the elastic, as well as the electronic, properties observed in the corresponding bulk state.1–8 For example, the melting temperature of CdS is significantly decreased with decreasing particle size.2 The compressibility of alumina and nickel is inversely proportional with particle size.4,5 The pressure where CdSe converts from the wurtzite-type to the rock salt-type increases with decreasing particle size.6,7 Tunability of the particle size thus gives rise to various functional nanomaterials and their unique applications. Recently, controlling the shape of the nanoparticles also became feasible; hence, tailoring the properties as a function of the nanoparticle shape is widely investigated.9,10 Among these, several synthetic methods of generating various TiO2 nanoparticles both in size and shape have been developed.11 In nature, TiO2 occurs in four different crystalline forms—rutile, anatase, brookite, and a dense phase such as R-PbO2-type TiO2.12 They differ in the assemblages and subsequent arrangements of the TiO6 octahedra (Figure 1); hence, fundamental properties such as density, stability, elasticity, and electronic and optical properties are found to be different. Among these, rutile is the thermodynamically most stable phase at ambient conditions, whereas anatase and brookite are stable at low temperature.13–15 Major technological applications of these materials include pigments, plastics, cosmetics, electronics, and catalytic industries. Notably, the anatase phase has been used in photocatalysts, dye-sensitized solar cells, gas sensors, and biomedicine.16–22 Functional anatase nanoparticles, tuned either in particle size or shape, have enhanced photocatalytic effect and larger band gap energy than in bulk state.23,24 Pressure is another means to control the size and shape of a * Corresponding authors e-mail: (Y. L.) [email protected]; (J. C.) [email protected]. † Department of Chemistry, Yonsei University. ‡ Pohang University of Science and Technology. § Department of Earth System Sciences, Yonsei University.

solid both in microscopic and atomistic scale and, hence, can give rise to corresponding property changes. To form a basis of pressure-dependent property tunability of various functional nanoparticles, we have investigated two shape-contrasting anatase nanoparticles along with a bulk sample using monochromatic synchrotron X-ray and a diamond-anvil cell. We report here that the compressibilities of the anatase nanoparticles vary in a range, and the microscopic strain also evolves in different manners compared to that of a bulk sample (Tables 1 and 2). Experimental Section Preparation of Anatase Nanoparticles. Bulk TiO2 anatase with an average particle size of about 100∼300 nm was purchased from Sigma-Aldrich. The nominally 99.8% pure anatase powder consisted mostly of anatase, but a trace amount of a rutile phase was detected from the laboratory X-ray powder diffraction (XRD) pattern; the strongest peak of anatase is about 35 times more intense than that of rutile. The anatase nanoparticles were synthesized by a high-temperature colloidal method after a slight modification from the previously reported procedure.25 TiCl4 (0.5 mmol), oleic acid (1 mmol), and oleylamine (6 mmol) were heated to 275 °C under an argon atmosphere. After 5 min, the reaction mixture was quenched to roomtemperature using toluene. The resulting anatase nanoparticles were separated into different shapes by a size-selective precipitation method. Figure 2 illustrates the size and shape contrasts of the resulting anatase nanoparticles along with that of the bulk sample used in this study. Compared to the scanning electron microscopy (SEM) image of the “sphere-shaped” bulk anatase particles (100∼300 nm, Figure 2a), the transmission electron microscopy (TEM) images of the as-synthesized nanoparticles are characterized as elongated “rod-shapes” (3.5 × 21.0 nm, Figure 2b) and “rice-shapes” (3.8 × 5.0 nm, Figure 2c), respectively. Specifically, the rod-shaped anatase nanoparticles are found to be grown along the [100] direction to show an interplanar distance of ∼1.9 Å, whereas the rice-shaped anatase nanoparticles show preferential growth along the [001] direction

10.1021/jp801555a CCC: $40.75  2008 American Chemical Society Published on Web 06/10/2008

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Figure 1. Illustrative crystal structures of TiO2 polymorphs: (a) anatase (tetragonal, a ) 3.785 Å, c ) 9.513 Å), (b) rutile (tetragonal, a ) 4.593 Å, c ) 2.959 Å), and (c) brookite (orthorhombic, a ) 9.181 Å, b ) 5.455 Å, c ) 5.142 Å).

TABLE 1: Normalized Lattice Parameters and Unit Cell Volume of the TiO2 Anatase Samples As a Function of Pressure

TABLE 2: The Full Width at Half-maximum Values of the (200) and (101) Reflections of the TiO2 Anatase Samples As a Function of Pressure

sample

P (GPa)

a/a0

c/c0

V/V0

sample

P (GPa)

fwhm (200)

fwhm (101)

bulk

0.0001 0.84 1.98 3.10 3.83 4.82 6.69 0.0001 0.84 1.84 2.82 3.70 4.69 5.70 6.98 7.87 9.17 0.0001 0.84 1.70 3.11 4.54 6.56 7.87 9.16

1.0000 0.9992 0.9984 0.9971 0.9972 0.9964 0.9957 1.0000 0.9993 0.9984 0.9975 0.9973 0.9981 0.9988 0.9982 0.9996 0.9966 1.0000 0.9980 0.9982 0.9964 0.9962 0.9967 0.9966 0.9957

1.0000 0.9970 0.9947 0.9903 0.9901 0.9875 0.9847 1.0000 0.9993 0.9991 0.9965 0.9876 0.9801 0.9758 0.9738 0.9617 0.9662 1.0000 1.0043 0.9960 1.0009 0.9948 0.9827 0.9825 0.9841

1.0000 0.9955 0.9914 0.9847 0.9846 0.9804 0.9763 1.0000 0.9979 0.9959 0.9914 0.9822 0.9764 0.9734 0.9704 0.9610 0.9596 1.0000 1.0003 0.9923 0.9938 0.9873 0.9762 0.9758 0.9756

bulk

0.0001 0.84 1.98 3.10 3.83 4.82 6.69 0.0001 0.84 1.84 2.82 3.70 4.69 5.70 6.98 7.87 9.17 0.0001 0.84 1.70 3.11 4.54 6.56 7.87 9.16

0.0748 0.0824 0.0906 0.0966 0.1013 0.1147 0.1375 0.8867 0.8829 0.9091 0.9134 0.8819 0.9639 1.0332 0.9690 1.0294 1.0462 1.2827 1.4096 1.3890 1.3181 1.4009 1.5273 1.5705 1.5559

0.07573 0.08032 0.08439 0.08293 0.09214 0.10278 0.11718 1.0389 1.0474 1.0553 1.0814 1.0433 1.0489 1.0406 1.0416 1.0405 1.0428 1.3213 1.3534 1.3299 1.3404 1.2173 1.3490 1.3503 1.3464

rod

rice

to show an interplanar distance of ∼2.4 Å by the high resolution TEM (HRTEM) analyses (Figure 2, panels d and e). High-Pressure Synchrotron X-ray Powder Diffraction Experiment. High-pressure monochromatic synchrotron XRD measurements were performed using a Merrill-Bassett-type diamond-anvil cell and an imaging plate detector at 5A-HFMS beamline at the Pohang Accelerator Laboratory (PAL). Each powder sample was loaded into a 250 µm diameter × 150 µm thick sample chamber in a preindented stainless steel gasket, along with a few small ruby chips as a pressure gauge. A mixture of 16:3:1 v/v of methanol/ethanol/water was used as a hydrostatic pressure transmitting fluid (hydrostatic up to ∼10 GPa). The pressure at the sample was measured by detecting the shift in the R1 fluorescence line of the included ruby chips. The sample pressure was gradually increased up to 9 GPa. The sample was equilibrated for about 10 min at each measured pressure. An 18 keV synchrotron X-ray beam of 200 µm in diameter was provided by a sagitally focusing monochromator and mirrors. Each diffraction data was measured for 1 min on a MAR345 imaging plate, and the data were processed after detector calibration against LaB6 standard data using the Fit2d suite of programs.26 The peak positions and shapes, including full width at half-maximum (fwhm), at each measured pressure were derived from individual profile fitting methods using the CMPR suite of programs.27

rod

rice

Results and Discussion The monochromatic synchrotron XRD patterns measured from the three anatase samples clearly show the differences in the peak width and intensity (Figure 3). The Bragg peaks from the bulk anatase particles are characterized by well-separated, sharp, and intense peaks compared to those from the nanoparticles. The observed particle-size broadening effect from the nanoparticles is more pronounced in the rice-shaped sample than in the rod-shaped sample. Close examination of the Bragg peaks from the nanoparticle samples reveals that the broadening of the peaks is also dependent on the Miller indices, in particular, (200) versus (004). This, coupled with the increasing overlapping between the neighboring Bragg peaks under pressure, made us use an individual profile fitting procedure to derive the pressure-dependent evolution of the peak shape and positions. Figure 4 shows the pressure-dependent variations of the normalized unit cell lengths (a/a0, c/c0) and volume (V/V0) of the bulk anatase and the rod-shaped and rice-shaped anatase nanoparticles. In all cases, the c-axis length is found to be more compressible than the a-axis length. The “fast” decrease in the c-axis length compared to the a-axis length in anatase has been interpreted in terms of the difference in the directional population of the “hard” occupied (TiO6) and “soft” empty (O6) oxygen octahedra and their tendency to attain closer packing upon

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J. Phys. Chem. C, Vol. 112, No. 26, 2008 9629

Figure 2. TiO2 anatase samples used in the high-pressure experiment. (a) SEM image of the bulk TiO2 (100∼300 nm, sphere-shaped), (b) TEM images of the synthesized rod-shaped TiO2 nanoparticles (3.5 nm width and 21.0 nm length), (c) the rice-shaped TiO2 nanoparticles (3.8 nm width and 5.0 nm length). HRTEM images of (d) the rod-shaped TiO2 nanoparticles and (e) the rice-shaped TiO2 nanoparticles. The insets are the fast Fourier transformation (FFT) images on the respective nanoparticles.

compression.28 The relative decrease in the c-axis length is most pronounced in the rod-shaped (grown along the a-axis) nanoparticles, with the rice-shaped (grown along the c-axis) one least pronounced, whereas no clear trend is observed in the relative decrease in the a-axis length. This results in the overall volume compressibilities that ranges from the rice-shaped nanoparticles, the bulk particles, and the rod-shaped nanoparticles in an increasing order. In other words, the compressibility of the bulk anatase is tuned in an opposite manner depending on the nanoparticle shape. The volume compressibility was determined using the Birch-Murnaghan equation of state (BM-EoS), which is based upon the assumption that the high-pressure strain of a solid can be expressed as a Taylor series of the Eulerian strain,

f ) [(V0 ⁄ V)2⁄3 - 1] ⁄ 2

(1)

where V0 and V represent the unit-cell volume under ambient and high-pressure conditions, respectively. Expansion in the Eulerian strain yields the following isothermal equation-of-state (eq 2),

P(f) ) 3K0 f(1 + 2f)5⁄2{1 + 3 ⁄ 2(K ′ -4)f + 3 ⁄ 2[K0K ″ + (K ′ -4)(K ′ -3) + 35 ⁄ 9]f 2 + . . .} (2) where K0 represents the bulk modulus, defined as K0 ) -V0(∂P/ ∂V)P)0 ) 1/β, where β is the volume compressibility coefficient, and K′ and K′′ represent the first and second derivatives of the bulk modulus with respect to pressure (K′ ) ∂K0/∂P; K′′ ) ∂2K0/ ∂P2). Because of the limited pressure range investigated and the small volume reduction at the maximum pressure (less than 4%), the P-V data of the anatase samples were fitted using a truncated second-order BM-EoS with K′ fixed at 4. It is interesting to note that the bulk modulus of anatase has been reported in a wide range from the previous experimental

Figure 3. Synchrotron XRD patterns of the TiO2 anatase samples measured at ambient conditions (the wavelength of the beam is 0.6888 Å; asterisks indicate a trace amount of rutile impurity in the bulk sample).

(between 59 and 360 GPa) and theoretical (between 194 and 272 GPa) studies.13,29–32 These discrepancies seem to originate from the different sample status (either single crystal or polycrystalline with different particle sizes and shape) used in the experimental investigations and from the different accounts on the electronic bonding structure assumed in the theoretical calculations. The bulk modulus obtained in our study is 241(11) GPa. Although this value is within the previously reported range, it is larger than those reported from the most recent experimental (190(10) GPa from polycrystalline anatase) and the quantummechanical simulation (∼200 GPa) studies.28 On the other hand, the rod-shaped nanoparticles show a lower value of 204(8) GPa

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Figure 4. Pressure-dependent variations of (a) the normalized lattice parameters and (b) the normalized unit cell volume of the TiO2 anatase samples.

Figure 5. (a) The Williamson-Hall plot of the TiO2 anatase bulk sample and (b) the scaled strain derived from the slopes of the W-H plot.

than the bulk sample, whereas the rice-shaped nanoparticles exhibit a larger value of 319(20) GPa (Figure 4b). It is clear that the nanoparticle shape affects the bulk compressibility. We suspect that this might be partly due to the differences in the relative population of the soft empty oxygen (O6) octahedral units within different (nano)crystallites, as discussed above, and also partly due to the anisotropic distribution of the crystallo-chemical defects, such as oxygen vacancies,33 and their dependence on the particle size and shape. The distribution of such defects might be identified using pressureinduced evolution of microscopic strain. To shed light into the shape-dependent strain distribution and its evolution upon compression, we have employed an individual profile shape analysis method. In the case of the bulk sample where the Bragg peaks are well separated, Williamson-Hall (W-H) plot analysis34 was performed (Figure 5). Williamson-Hall plot analysis is the method that deconvolutes the size- and strain-induced broadening based on the peak width data as a function of 2θ. It can be expressed by the following equation (eq 3).

value in the bulk anatase (Figure 5b). As expected, the relative strain in the bulk sample increases with pressure. There is, however, a discontinuity near 4 GPa, and we observe an abrupt increase in the average strain by a factor of ca. 3. The nature of this discontinuity is unclear as there is no apparent structural phase transition seen in this pressure range. It is possible, however, that this might indicate pressure-induced defects such as dislocations or faults or be related to the change in the property of the pressure-transmitting fluid used in this experiment. The freezing pressures of methanol, ethanol, and water are 3.5 GPa, 1.8 GPa, and 0.2 GPa at ambient temperature, respectively.35 In the case of the nanoparticles, most of the Bragg reflections, except for the (101) and (200) peaks, overlap with one another, and this made us use the Strokes-Wilson (S-W) equation instead of the W-H analysis to derive the pressure-induced evolution of the microscopic strain based on the (101) and (200) peaks. The S-W equation can be expressed by the following equation,

(βobs - βinst) cos θ ) λ⁄DV + 4εstr sin θ

(3)

βobs and βinst are the observed and instrumental integral breadth in radian 2θ of a reflection located at 2θ, respectively; str is the weighted average strain; and DV is the volume weighted crystallite size. In our case, we used the fwhm of the peaks instead of using integral breadth, and we also assumed the data measured at 0 GPa to represent βinst in order to simplify the analysis and to extract pressure-induced growth of the relative strain. Figure 5a shows the resulting plot of (βobs-βinst)cos θ against 4(sin θ) and linear fits to the data. The resulting slopes of the W-H plot correspond to the pressure-induced evolution of the microscopic strain normalized to the ambient pressure

εstr )

β 4 tan θ

(4)

where str represents the weighted average strain; β represents the integral breadth in radian 2θ of a reflection located at 2θ. Again, we used fwhm in radian 2θ instead of the integral breadth to simplify the analysis. Figure 6 shows the pressure-dependent changes of the fwhm of the (101) and (200) reflections from the nanoparticle samples as well as from the bulk sample. It appears that the fwhm of the (101) and (200) reflections from the bulk anatase uniformly increases with pressure (Figure 6a), illustrating that the distribution of the microscopic strain and its pressure-induced development is isotropic, as derived from

Compressibility of TiO2 Anatase Nanoparticles

J. Phys. Chem. C, Vol. 112, No. 26, 2008 9631 ratory (R0A-2006-000-10255-0), and the Second Stage of Brain Korea 21 of the Chemistry and the Earth-AtmosphereAstronomy Institute at Yonsei University. Experiments at PAL were supported in part by the Ministry of Science and Technology (MOST) of the Korean Government and by Pohang University of Science and Technology (POSTECH). We thank Sangmi Choi and Hae-gu Park of the Chemistry Department at Yonsei University for the technical assistance during the PAL experiment. References and Notes

Figure 6. Pressure-dependent changes of (a) the fwhm of the (200) and (101) reflections from the TiO2 anatase nanoparticles and (b) their derived weighted average strain (Stokes-Wilson plot).

the W-H analysis (Figure 5). In the case of the rice-shaped and rod-shaped nanoparticles, however, the pressure-dependent increase of the fwhm is not monotonic but is dependent on the Miller indices. In both cases, the fwhm of the (200) reflection increases with pressure, whereas the fwhm of the (101) reflection remains more-or-less constant (Figure 6a). This is clearly seen in the evolution of the derived microscopic strain with pressure, and the slopes of str versus pressure calculated from the (200) reflection are notably larger than those from the (101) reflections, whereas the strain from the (101) reflection appears to be saturated with larger values than that from the (200) reflection in the entire pressure range (Figure 6b). The preferential increase of the microscopic strain associated with the (200) reflections, coupled with the larger overall strain of the (101) reflection, might be related to the observed higher c-axial compressibility and also to the higher contrast in the population of the hard TiO6 and soft O6 octahedra in the nanoparticle samples compared to the bulk sample. The larger str values, as well as the fwhms, of the rice-shaped anatase nanoparticles demonstrate that it is overall more strained than the rod-shaped nanoparticles or the bulk anatase, possibly due to the enhanced spatial restrictions on size and shape control. This might explain the largest bulk modulus of the rice-shaped nanoparticles among the three anatase samples. We encourage further computational studies to reveal the nature of the size- and shape-dependent compression mechanisms. Acknowledgment. This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2006-D00538), the National Research Labo-

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