Size-Dependent Bandgap of Nanogoethite - The Journal of Physical

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Size-Dependent Bandgap of Nanogoethite Hengzhong Zhang,*,† Meredith Bayne,† Sandra Fernando,† Benjamin Legg,† Mengqiang Zhu,‡ R. Lee Penn,§ and Jillian F. Banfield†,‡ †

Department of Earth and Planetary Science, University of California, Berkeley, California 94720, United States Earth Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States § Department of Chemistry, University of Minnesota
Twin Cities, Minneapolis, Minnesota 55455, United States ‡

ABSTRACT: Rod-shaped goethite nanoparticles with average particle sizes (equivalent spherical diameters) of between ∼9 and 38 nm were synthesized via reaction of ferric nitrate with potassium/sodium hydroxide in aqueous solutions. We deconvoluted the UV
vis spectra into individual absorption bands for each of the nanogoethite samples and determined the particle size dependence for each band. As the particle size decreases, the charge transfer band is slightly red-shifted, whereas five other bands, including the electron pair transition that determines the absorption edge, are blue-shifted. Spectra were also used to determine bandgap energies as a function of particle size via Tauc
Mott plots. Over different photon energy ranges, nanogoethite appears to exhibit direct bandgap (2.5
3.1 eV) and indirect bandgap (1.6
2.1 eV) behaviors. The bandgap widens as particle size decreases, an effect that can be described by the Kayanuma equation, from which the reduced mass of an exciton in nanogoethite was found to be ∼3
4% the mass of a rest electron. The existence of an indirect bandgap at relatively lower energy as compared to the direct bandgap and altered redox properties due to shifts and opening of the bandgap as particle size decreases may partially explain size-dependent chemical and photochemical reactivity of goethite.

’ INTRODUCTION Goethite (α-FeOOH) is a semiconductor (bandgap 2.10
2.50 eV1,2). It is abundant at and near Earth’s surface and forms as nanoparticles as the result of mineral weathering and neutralization of acid mine drainage. During nucleation, crystal growth, and aggregation, nanogoethite particles can adsorb oxyanions, toxic metal cations, and organic molecules. In sunlight, nanogoethite can photochemically oxidize adsorbed organic molecules, leading to its reductive dissolution.3 The goethite band positions and bandgap determine the generation of electrons and holes and, thus, the chemical/photochemical redox behavior. Usually, the bandgap of semiconductor nanomaterials (such as nano-CdSe4 and ZnS5) increases with decreasing particle size due to quantum size effects.6 For example, goethite nanorods have shorter UV
vis absorption wavelengths than do micrometer-scale rods,3 implying a blue-shift in the bandgap. In contrast, it was also reported that the bandgap of a nanogoethite is smaller than that of bulk goethite.7 To investigate this apparent inconsistency, we systematically explored the particle size dependence of the bandgap of goethite. The size-dependence of the goethite bandgap predicts the sizedependence of its reactivity in the environment3,8 and is also relevant for technical applications (e.g., lithium battery electrodes and solar energy devices9,10). ’ EXPERIMENTAL SECTION Syntheses of Nanogoethite. The 8.7 nm goethite nanoparticles (size obtained from Rietveld analysis, as described below) were synthesized using the method in ref 11. Eighteen milliliters r 2011 American Chemical Society

of 2 M Fe(NO3)3 3 9H2O was mixed with 70 mL of 1 M NaOH, and then with 70 mL of deionized (DI) water. The reacted mixture was aged at room temperature for 49 days. The suspension was centrifuged to separate the precipitates from the solution. Precipitates were redispersed in DI water to remove salts and then recovered by centrifugation. The centrifugation/ washing cycle was repeated six times. The final product was dried at 40 °C overnight. The 10.1 nm goethite sample was synthesized as follows. Five milliliters of 5 M KOH was mixed with 250 mL of 0.1 M Fe(NO3)3 3 9H2O in a beaker under magnetic stirring. The mixture was aged at 60 °C for 70 h. Next, the cooled mixture was centrifuged and washed, as above, and the product was dried at 80 °C for 4 h, then at 50 °C for 2 h. The 16.6 nm goethite sample was synthesized by reacting 30 mL of 0.5 M Fe(NO3)3 3 9H2O with 125 mL of 2.5 M KOH, followed by aging at 60 °C for 100 h.11 The aged suspension was treated by repeated centrifugation/washing and then dried at 40 °C overnight to obtain the final product. The 26.8 nm and the 38.2 nm goethite samples were synthesized by reacting 20 mL of 5 M KOH with 200 mL of 0.1 M Fe(NO3)3 3 9H2O, followed by aging at 40 °C for 42 or 72 h, respectively. The aged suspensions were centrifuged, washed, and dried as above. Received: June 2, 2011 Revised: August 5, 2011 Published: August 09, 2011 17704

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The Journal of Physical Chemistry C The synthesized samples were kept in glass vials and stored in a refrigerator for further sample characterization and UV
vis measurements. X-ray Diffraction Characterization. X-ray diffraction (XRD) was used to identify the phases present in the synthesized samples. A small amount of a sample was ground in ∼0.5 mL of acetone in a mortar with a pestle. The suspension was then immediately dripped onto a low X-ray scattering background quartz plate. During drying, the powders dispersed evenly on the plate. The plate was loaded into the sample holder of an X-ray diffractometer (PANalytical X’Pert PRO) operated at 40 kV and 40 mA with a Co Kα radiation X-ray source (wavelength 1.7903 Å). XRD patterns were collected in the 2θ range of 20
90° with a scanning rate of 1°/min. The phases of the synthesized samples were identified using a vendor-developed program (X’Pert HighScore Plus, v. 2.0, PANalytical, Inc.) via searching and matching the XRD peaks against the ICDD2 database.12 For derivation of the average particle sizes of the samples, Rietveld analyses were performed using the program Maud.13 Beforehand, the instrumental peak broadening of the diffractometer as a function of 2θ was determined using bulk Y2O3 powders.13 Using the θ-dependent peak broadening obtained from the Rietveld fitting, the average particle sizes (see below) of goethite samples were obtained along with the root-mean-square microstrains (see ref 14). The size determined using Rietveld analysis was then used to identify each goethite sample (e.g., the 10.1 nm goethite sample). Transmission Electron Microscope (TEM) Characterization. A few grains of goethite nanoparticles were dispersed in DI water under ultrasonic agitation. A single drop of the resulting suspension was placed on a 3 mm copper TEM grid coated with holey carbon film (SPI Supplies) and allowed to air-dry. The grid was examined using an FEI Tecnai F30 FEG TEM operated at 300 kV for high-resolution imaging. Calibrated images were collected using a Gatan charge-coupled device (CCD) camera and Gatan Digital Micrograph software (version 3.8.2). Samples were also examined at lower resolution using a Philips CM200 transmission electron microscope operated at 200 kV. UV
Vis Spectra Measurement. UV
vis spectra of the synthesized nanogoethite samples were measured using an Agilent 8453 UV
vis spectroscopy system. DI water in a UV
vis quartz cell (light length 1 cm; volume 4 mL) was used as the blank. For a sample run, a few grains of a nanogoethite sample were ground in a mortar and then dispersed in a 10 mL vial with DI water. The vial was capped and ultrasonicated in a water bath for 1 h. About 0.5 mL of the dispersed suspension was transferred to the quartz cell using a pipet and then diluted to ∼2/3 of the cell volume using DI water. UV
vis spectra of the sample were collected with a blank run right before each sample run. The appropriate quantity of the sample in the quartz cell was chosen via incremental addition of the suspension into the cell, when the maximum in the absorption curve was observed to be in the absorbance range of ∼1
2 au (90
99% absorption). Ideally, the UV
vis absorption should scale with the concentration of the nanoparticles in the aqueous suspension; that is, the absorption follows the Lambert
Beer law. Two goethite samples (8.7 and 16.6 nm) were used to examine this relationship in the UV
vis determination. A certain mass of the goethite (m = 2.7 and 1.5 mg, respectively, for the 8.7 and 16.6 nm goethite) was dispersed in 10 mL of DI water under ultrasonication for 1 h. 1.8 mL of DI water was added into the quartz cell. Next, 0.2 mL of ultrasonicated goethite suspension was added to the cell, followed

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Figure 1. XRD patterns (thick color lines) and the Rietveld fits (thin black lines) of goethite nanoparticles of different sizes. Calculated XRD pattern of bulk goethite is shown for identification of diffraction planes. The minor peak at 28.1° (h) in the 10.1 nm sample is due to the presence of minor hematite; the intense sharp peak at 65.1° (q) in the 8.7 nm sample came from the XRD quartz plate.

by well mixing and UV
vis determination. The addition of the goethite to the cell was repeated seven times, yielding goethite nanoparticle concentration of 0.2n/(0.2n + 1.8)  m/10 (mg/ mL) in the cell, where n is the number of addition of goethite suspension to the cell.

’ RESULTS AND DISCUSSION Sample Characterization. Figure 1 shows XRD patterns of the synthesized samples, with comparisons to the calculated XRD pattern of bulk goethite (indexing based on the Pnma space group). Results show that all of the samples are goethite, with the exception of the 10.1 nm sample, which contained 2.8% weight hematite. From the Rietveld fittings of the XRD patterns (Figure 1), the average particle sizes of the five samples are 8.7, 10.1, 16.6, 26.8, and 38.2 nm. The average microstrain of all samples is 2.4  10
4; the average goodness of fit is 2.9, close to 2.0 for a near perfect fitting. Some of the fitted peaks (e.g., 210) deviate significantly from the experimental data, possibly because goethite nanoparticles are nonspherical (as assumed in the Rietveld program). The average particle sizes can be considered as the equivalent diameters of spherical goethite nanoparticles. TEM images (Figure 2) show that goethite nanoparticles are indeed nonspherical in all of the samples. Observations show that the XRD determined sizes based on the Rietveld analysis are close to the shorter dimensions (i.e., the diameters) of the nanorods. The nanorods are highly aggregated side-by-side, making it hard to identify boundaries of individual particles for analysis of particle size distribution. Visual inspection shows that most particles resemble each other, although the aspect ratio (length to diameter) varies from ∼5 to 15 for all particles in a sample. UV
Vis Spectra and Bandgap. Figure 3a shows UV
vis spectra of the nanogoethite samples. Both the absorption onset and the peak positions are blue-shifted as the particle size decreases. With increasing particle size, the background of the absorption curves increases due to contributions from scattering from larger nanoparticles (e.g., Rayleigh scattering). The scattering 17705

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Figure 2. TEM images showing aggregation of goethite nanorods in (a,b) 10.1 nm sample, (c) 8.7 nm sample, (d) 16.6 nm sample, (e) 26.8 nm sample, and (f) 38.2 nm sample. Image (b) is a closer and high-resolution view of the 10.1 nm sample.

contribution was largely subtracted using a regression that fits linearly in the ∼800
1100 nm wavelength range,15 producing the result shown in Figure 4. Figure 3b shows the scattering-corrected UV
vis spectra of 16.6 nm goethite as a function of the nanoparticle concentration. It is seen that the absorption increases with increasing nanoparticle concentration. The absorption at the prominent absorption peak at 293 nm wavelength is plotted versus the concentration in Figure 3c. Figure 3d shows a similar plot for the 8.7 nm goethite. The results demonstrate that the scattering-corrected absorption follows the Lambert
Beer law (linear relationship between absorbance and concentration) very well. This indicates that nanoparticle aggregation (that causes some degree of scattering) does not change the size-dependence of the spectra after correction for the scattering (Figure 4); otherwise, there would be appreciable

deviations from the Lambert
Beer law in the plots shown in Figure 3c and d. The goethite UV
vis spectra result from three types of electronic transitions: (1) ligand field (Fe d
d) transitions, (2) interactions between magnetically coupled Fe(III) ions, and (3) O(2p) f Fe(3d) charge transfer.1 For bulk goethite, the band positions and the corresponding transitions were reported in refs 16 and17 and summarized in ref 1. These include the charge transfer 6T1u f 2t2g at ∼250 nm and the electron pair transition (EPT) 2(6A1) f 2(4T1)(4G) at ∼480 nm that primarily determines the absorption edge position (i.e., the optical bandgap). Because of overlapping of various transitions, direct determination of the band positions in the UV
vis spectra (Figure 3) is difficult. Thus, we fitted the UV
vis spectra (after calibration of the scattering, above) using Gaussian peak functions 17706

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Figure 3. Measured UV
vis spectra of nanogoethite of different sizes (a); background-subtracted UV
vis spectra (b) and Lambert
Beer plot (c) of 16.6 nm goethite, and (d) Lambert
Beer plot of 8.7 nm goethite. Absorbances in (c) and (d) are those measured at 293 and 278 nm wavelength, respectively. The concentration refers to the quantity (mg) of goethite nanoparticles in a unit volume (mL) of aqueous suspension.

(Figure 4). The first peak in these fittings may correspond to the 1T2u f 2t2g charge transfer. However, the obtained band positions (190 or 200 nm) for this transfer are less certain due to lack of data below 200 nm. The fitted band positions of the next six transitions were assigned in reference to ref 1 and with consideration of systematic changes with the particle size, as shown in Figure 5 (from 6T1u f 2t2g to 6A1 f 4T2(4G); the latter could not be obtained for the 8.7 nm sample, see Figure 4a). The last fitted peak (650.4, 662.9, and 694.0 nm in Figure 4c
4e, respectively) in bigger nanoparticles can be considered as a further calibration to the background (see above) due to scattering at larger sizes. Figure 5 shows that, except for the 6T1u f 2t2g transition, the band positions of other five transitions decrease with the decreasing particle size (i.e., are blueshifted). The quantum confinement at nano sizes accounts primarily for the blueshift.4,6 The lattice contraction at nano sizes (e.g., in nano-TiO2; ref 14) may also contribute to the effect, as atoms vibrate faster at shorter atomic distances and hence light absorption moves to higher wavenumber or higher photon energy. The red-shift in the charge transfer band (6T1u f 2t2g) may arise from shortening of the Fe
O bonds. In smaller particles, the Fe
O octahedra are compressed due to

higher surface stress.14 This results in shorter Fe
O bonds, which should facilitate the O(2p) f Fe(3d) charge transfer and hence cause the red-shift. Generally, the Tauc
Mott (TM) plot is used to determine the bandgap of semiconductor materials.15 In a TM plot, the (AE)α is plotted against E, where A represents the UV
vis absorbance, E the photon energy, and α = 2 or 1/2 for direct or indirect bandgap, respectively. Extrapolation of the linear section of the TM plot to (AE)α = 0 to intercept the E axis defines the optical bandgap. Figure 6a and b shows the TM plots of nanogoethite for the cases of direct and indirect bandgap, respectively. In these plots, the absorbances are those corrected for the scattering (Figure 4). The obtained bandgap as a function of particle size is illustrated in Figure 7. The bandgap of bulk goethite is 2.50 eV.2 The direct bandgap of nanogoethite approaches this value as the particles size increases (Figure 7), suggesting that nanogoethite is a direct bandgap material. This is supported by the presence of linear sections in the TM plot in Figure 6a in the photon energy range of ∼2.7
3.4 eV. However, Figure 6b shows that nanogoethite also contains a significant amount of indirect bandgap structure, 17707

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Figure 4. Background subtracted UV
vis spectra of goethite nanoparticles of average sizes (a) 8.7 nm, (b) 10.1 nm, (c) 16.6 nm, (d) 26.8 nm, and (e) 38.2 nm. Absorption components are from peak fitting using Gaussian distribution line profiles.

as the TM plot for indirect bandgap also presents linear sections in the photon energy range of ∼2.1
2.6 eV. The indirect bandgap may arise from band bending/shifting due to crystal structure truncation and hence atomic structure distortion on nanoparticle surfaces. The variation of the bandgap with the crystal size can be described by the Kayanuma equation (when in the SI

units):18 Egap, nano ¼ Egap, bulk þ

¼ Egap, bulk þ 17708

p2 π 2 1:786e2
0:248ERy
2 2μR ð4πε0 εr ÞR p2 π 2 1:786e2 0:248μe4

2 2μR ð4πε0 εr ÞR 2ð4πε0 εr Þ2 p2

ð1Þ

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where Egap,nano and Egap,bulk represent the bandgap of nano- and bulk crystals, respectively; R is the radius of the nanocrystal; μ and ERy are, respectively, the reduced mass and Rydberg energy of an exciton (a bound electron
hole pair) in the crystal; e is the electron charge (1.602  10
19 C); p is the reduced Plank constant (1.055  10
34 JS); ε0 is the vacuum permittivity (8.854  10
12 J
1 C2 m
1); and εr is the relative dielectric constant of the crystal (εr = 11.70 for goethite at 20 °C; ref 19). After known quantities were inserted in the above equation, the equation can be written in the following form when the bandgap is in electronvolts, the particle size (diameter, D) in nanometers, and the reduced mass in kilograms: Egap, nano ¼ Egap, bulk þ  1028 μ

1:37  10
30 0:44
2:7
D μD2 ð2Þ

Equation 2 shows that size affects the bandgap in proportion to 1/D2 or 1/D, which means that the short dimension (diameter) should have a much larger influence (due to quantum confinement)

Figure 5. Absorption band positions of goethite nanoparticles as a function of particle size. Assignment of the band to the electronic transition/origin is shown on the top left panel (see text).

than the long dimension (length) for goethite nanorods. Thus, the observed change of the spectra (Figure 3a) in different samples is mainly due to the change in the size (determined from Rietveld analysis) rather than the variation in the aspect ratio. This is further supported by the good fitting (below) of the bandgap as a function of the particle size using eq 2 (otherwise, significant deviation of the data from the equation would be expected). Fitting eq 2 to the data shown in Figure 7 generates: Egap,bulk = 2.50 ( 0.02 (standard error) eV and μ = (2.67 ( 0.17)  10
32 kg (∼2.9% mass of a rest electron) for the case of direct bandgap, and Egap,bulk = 1.64 ( 0.03 eV and μ = (3.77 ( 0.42)  10
32 kg (∼4.1% mass of a rest electron) for the case of indirect bandgap. The small reduced mass may indicate that the excitons diffuse quickly in goethite nanoparticles. For direct bandgap, the deduced bandgap of bulk crystal (2.50 eV) is consistent with the value in ref 2 (2.50 eV) and slightly higher than the value in ref 1 (2.10 eV). In the particle size range studied, the direct bandgap ranges from ∼2.5 to 3.1 eV, corresponding to the light

Figure 7. Variation of the bandgap of goethite nanoparticles with the average size. The lines are the fits to the Kayanuma equation (see text).

Figure 6. Tauc
Mott plot for (a) direct and (b) indirect bandgap of goethite nanoparticles. The intercept of a dotted line with the horizontal axis defines the value of the bandgap. 17709

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The Journal of Physical Chemistry C wavelength range of ∼400
500 nm for the 6A1f4E,4A1 transition and the 2(6A1)f2(4T1) EPT (Figure 5). Thus, these two transitions determine primarily the UV
vis absorption edge, that is, the optical bandgap. The indirect bandgap is smaller than the direct bandgap (Figure 7), similar to the result for nanohematite.15 If the indirect bandgap results primarily from the surface atoms, the smaller indirect bandgap may indicate that goethite nanoparticles (with a higher fraction of atoms residing at the surface) can make better use of solar light for catalytic reactions as compared to larger crystals, provided enough phonons (lattice vibrations) are available to assist the indirect electron transition from the valence band (VB) to the conduction band (CB). The increase in widening of the direct/indirect bandgap at small sizes may result from a shift up in the CB and a shift down in the VB, increasing the reduction and oxidation capabilities. These predictions are consistent with the report that goethite nanorods have higher and persistent chemical/photochemical reactivity than microrods.3 Using X-ray absorption spectra (XAS) and X-ray emission spectra (XES), Gilbert et al. deduced that the bandgap of a 6 nm goethite (∼2.0 eV) is smaller than that of bulk goethite,7 in contrast to the results from the present work. This inconsistency may arise because the XAS/XES method probes mainly the charger transfer transition whose band energy decreases with decreasing particle size (Figure 5), as well as transitions other than the absorption edge-determining ones (e.g., the EPT).

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(5) Sartale, S. D.; Sankapal, B. R.; Lux-Steiner, M.; Ennaoui, A. Thin Solid Films 2005, 480, 168. (6) Iwamoto, M.; Abe, T.; Tachibana, Y. J. Mol. Catal. A 2000, 155, 143. (7) Gilbert, B.; Kim, C. S.; Dong, C.-L.; Guo, J.; Nico, P. S.; Shuh, D. K. In X-ray Absorption Fine Structure
XAFS13; Hedman, B., Pianetta, P., Eds.; American Institute of Physics: Melville, NY, 2007; p 721. (8) Cwiertny, D. M.; Handler, R. M.; Schaefer, M. V.; Grassian, V. H.; Scherer, M. M. Geochim. Cosmochim. Acta 2008, 72, 1365. (9) Lou, X.; Wu, X.; Zhang, Y. Electrochem. Commun. 2009, 11, 1696. (10) Gardner, J. M.; Kim, S.; Searson, P. C.; Meyer, G. J. J. Nanomater. 2011, doi: 10.1155/2011/737812. (11) Mazeina, L.; Navrotsky, A. Clays Clay Miner. 2005, 53, 113. (12) Powder Diffraction File ICDD-PDF2; International Center for Diffraction Data: Newton Square, PA, 2003. (13) Lutterotti, L.; Bortolotti, M. IUCr: Compcomm Newsletter 2003, 1, 43. Available at http://www.ing.unitn.it/∼maud/. (14) Zhang, H.; Chen, B.; Banfield, J. F. Phys. Chem. Chem. Phys. 2009, 11, 2553. (15) Chernyshova, I. V.; Ponnurangam, S.; Somasundaran, P. Phys. Chem. Chem. Phys. 2010, 12, 14045. (16) Sherman, D. M.; Waite, T. D. Am. Mineral. 1985, 70, 1262. (17) Scheinost, A. C.; Schulze, D. G.; Schwertmann, U. Clays Clay Miner. 1999, 47, 156. (18) Kayanuma, Y. Phys. Rev. B 1988, 38, 9797. (19) Rosenholtz, J. L.; Smith, D. T. Am. Mineral. 1936, 21, 115.

’ CONCLUSIONS Deconvolution of the electron transitions by fitting of the UV
vis spectra of nanogoethite with particles sizes between ∼9 and 38 nm showed that all bands except for a charge transfer band exhibit blue-shifts as the particle size decreases. Nanogoethite exhibits both direct and indirect bandgap characteristics. The bandgap increases with decreasing particle size, in accordance with the Kayanuma equation. The fitted reduced mass of an exciton is small (∼ 3
4% the mass of a rest electron), suggesting that the mobility of photon-generated electron
hole pairs is high in goethite nanocrystals. At small sizes, the smaller indirect bandgap relative to the direct bandgap as well as the possible shifts up in CB and down in VB predict enhanced photochemical reactivity of nanogoethite. Similar conclusions may be applicable to other nano sized iron oxyhydroxides and iron oxides. ’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT Financial support was provided by the National Science Foundation (Grant no. EAR-0920921) and the U.S. Department of Energy (Grant no. DE-AC02-05CH11231). ’ REFERENCES (1) Cornell, R. M.; Schwertmann, U. The Iron Oxides, 2nd ed.; Wiley-VCH GmbH & Co. KGaA: Weinheim, Germany, 2003. (2) Sherman, D. M. Geochim. Cosmochim. Acta 2005, 69, 3249. (3) Cwiertny, D. M.; Hunter, G. J.; Pettibone, J. M.; Scherer, M. M.; Grassian, V. H. J. Phys. Chem. C 2009, 113, 2175. (4) Li, L.-S.; Hu, J.; Yang, W.; Alivisatos, A. P. Nano Lett. 2001, 1, 349. 17710

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