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J. Phys. Chem. C 2009, 113, 5376–5380
Morphological Stability of Pyrite FeS2 Nanocrystals in Water A. S. Barnard*,† and S. P. Russo‡ School of Chemistry, The UniVersity of Melbourne, ParkVille, 3010, Australia and Applied Physics, School of Applied Sciences, RMIT UniVersity, Melbourne, 3001, Australia ReceiVed: October 22, 2008; ReVised Manuscript ReceiVed: January 29, 2009
By replicating biological processes, it is hoped that many nanomaterials may be tailored for specific applications, but a detailed knowledge of the underlying mechanisms is imperative. A perfect example of this synergy is the similarity between the intracellular biomineralization of single nanocrystals of the nonmagnetic mineral iron pyrite in multicellular magnetotactic bacterium, and the solvo-thermal synthesis of iron sulfide nanoparticles in the laboratory. Although both processes occur in aqueous solutions, the relationship between the morphological stability of the individual nanocrystals and the chemistry of the nanoparticle-water interface is still largely unknown. In the present work, we use a theoretical model capable of describing the stability of nanocrystals as a function of size, shape, temperature, and chemical environment, and use it to examine the morphological stability of pyrite nanocrystals exposed to water, or formed during biomineralization. 1. Introduction Interest in metal sulfide materials has increased in recent years, owing to their wide range of physical, electronic, and chemical properties, which make them candidate materials for technological applications including solar cells,1-3 solid state batteries,4 and catalysis. The pyrite polymorph of iron disulfide (FeS2) is receiving particular attention, as it shows promise for solar energy conversion devices in both photoelectro-chemical and photovoltaic solar cells5 and solid state solar cells6 due to it is favorable solid state properties.2,3,7-9 In general, a variety of methods are used to produce polycrystalline and single-crystal pyrite, including metal organic chemical vapor deposition MOCVD10 or by mixing ironpentacarbonyl and sulfur or hydrogen sulfide in an organic solvent.11 Moreover, 1-D FeS2 nanostructures have been successfully prepared,12 via a solvothermal process at 130 °C in ethylenediamine; akin to a hydrothermal process in water. In this case, the morphology of the particles was controlled by varying the solvent, although the final nanorods were nonuniform in length.12-14 In parallel to the laboratory synthesis of pyrite nanostructures, there has also been considerable work on the biomineralization of magnetosomes, which are intracellular, iron-rich, membraneenclosed magnetic particles that allow magnetotactic bacteria to orient in the earth’s geomagnetic field. Magnetosomes produced by proteobacteria are iron oxide nanoparticles (such as ferrimagnetic magentite, Fe3O4), whereas iron sulfide nanoparticle (such as greigite, Fe3S4, ferrimagnetic greigite, and nonmagnetic pyrite, FeS2) are produced by sulfate-reducing subset of the proteobacteria.15,16 Greigite magnetotactic bacteria appear to be unique to marine systems, and thrive under strongly reducing conditions where the concentration of hydrogen sulfide is relatively high.17 But little ecological information is available concerning their distribution, population structure, or geochemical significance.18 As greigite magnetotactic bacteria die and lyse, dissolved Fe and S in the cells provide reactive surfaces * To whom correspondence should be addressed. amanda.barnard@ unimelb.edu.au. † School of Chemistry, The University of Melbourne. ‡ Applied Physics, School of Applied Sciences, RMIT University. E-mail:
[email protected].
for further microbial19 and chemical transformations, eventually leading to pyrite formation. Although pyrite formation is known to be the end point of the reductive portion of the sulfur cycle, it is not always observed.18 It is desirable to develop a more complete understanding of the formation of pyrite during biomineralization, as it may play a significant role in marine iron and sulfur cycling in coastal areas. This in turn has general implications for the coupling of iron sulfides with prebiotic organic systems in the early development of life, and possible constraints on the use of greigite as a biomarker in Earth and planetary sciences.20 If tailor-made, environmentally friendly, pyrite FeS2 nanocrystals and nanorods are to be reliably exploited in future devices, it is desirable to be able to predict the equilibrium shape of FeS2 under various conditions and to gain some appreciation of the metastability of kinetically driven shapes with respect to possible morphological transformations. In so doing, it is impossible to ignore other obvious differences between mineralization and biomineralization processes, including the presence of water and varying sulfur concentrations. Investigations of this type are ideal problems for theoretical modeling, where the shape-stability as a function of size, temperature, or chemistry concentrations may be systemically tested.21 To investigate part of this complex multiparameter problem, we examine the relationship between size, shape, temperature, and the coverage of adsorbed water on the surfaces, to determine how these fundamental characteristics are influenced by the local chemical environment. 2. Theoretical Method A shape-dependent thermodynamic model based on a geometric summation of the Gibbs free energy22 has been successfully used to examine the shape of water on titania in the past,23 as well as (adsorbate free) zirconia,24 ceria,21 and cadmium sulfide,25 and performs very well in comparison with experiment. A truncated version of the model has been used here that is applicable specifically to isolated, defect-free structures in the range ∼3-100 nm, as described in ref 26. In this version, the total free energy G is described in terms of the specific surface
10.1021/jp809377s CCC: $40.75 2009 American Chemical Society Published on Web 03/13/2009
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free energies γi, for facets i, weighted by the factors fi (such that ∑i fi ) 1):
G ) ∆f Go +
(
)[ ∑
∑
2 f σy Pex i i i M q 1+ F B0〈R〉 B0
]
fiγ iy (1)
i
where M is the molar mass, F is the density, and the volume dilation induced by the isotropic surface stresses σi (taken from the trace of the surface stress tensor) and external pressure Pex is included using the Laplace-Young formalism, as defined in ref 26. In all cases, we have assumed atmospheric external pressure and have used the bulk modulus B0 ) 154.89 GPa, which we have previously calculated and has been shown to be in good agreement with the corresponding experimental values.27 The surface formation energy, γi, can be further defined in terms of the chemical potential or concentration of any molecule y. The specific surface energies were calculated from the energy per stoichiometric unit of bulk pyrite µFeS2, and the total energy of the surface slabs Ei(NFeS2) using the expressions:
γ iy )
1 n (E (N ) - NFeS2 µFeS2) E 2Ai i FeS2 A′i y,i
(2)
where Ai is the explicit area of the slab in orientation i, and NFeS2 is the number of FeS2 formula units in the (stoichiometric) supercell, as described by Gong and Selloni.28 In the latter term Ey, i is the chemisorption energy of molecule y on facet i, n is the number of adsorbed y molecules in surface a unit cell, and A′i is the area of one surface of i. The value of Ey, i is describe in terms of the chemical potential of y, µy:
Ey,i ) Ei(NFeS2, Ny) - Ei(NFeS2, 0) - Ny µy
(3)
weighted by Ny the total number of adsorbates per unit Ai included in the calculation of Ei(NFeS2, Ny). The chemical potential µy is described by the following:
µy ⇒ µy(P, T) ) Ey +
( )
hνy PexV + kBTln 2 kBT
(4)
where kB is Boltzmann’s constant, T is the temperature, νy is the sum of the vibrational frequencies of y in the reservoir, and V is the quantum volume,
(
h2 V) 2πmy kBT
)
2 3
(5)
which includes my the atomic mass of y. In our study, y ) H2O, and µH2O has been calculated with results to liquid water, by taking EH2O as the energy per H2O molecule in supercell containing 31 water molecules (density ) 1 g cm3), where the internal parameters have been optimized using ab initio molecular dynamics at 300 K until the system equilibrated. 2.1. Computational Parameterization. An advantage of this methodology is that the parameterization may be performed from first principles. In the present work, we have calculated the temperaturesand sulfur saturationsdependent surface ener-
Figure 1. Specific surface energies of formation for stoichiometric pyrite FeS2 {100}, {111}, {110}, and {210} surfaces, as a function of the chemical potential of a 50% monolayer concentration of adsorbed water.
gies for the {100}, {111}, {110}, and {210} surfaces using Density Functional Theory (DFT) within the GeneralizedGradient Approximation (GGA) with the Perdew and Wang (PW91)29 exchange-correlation functional, implemented via the Vienna Ab initio Simulation Package (VASP).30,31 We have used the Linear Tetrahedron Method (LTM) and ultrasoft, gradientcorrected Vanderbilt-type pseudopotentials (US-PP)32,33 for both the initial structural relaxations and reconstructions, and the final static (single point) calculations required for the determination of the specific surface free energies and surface stress tensors. The electronic relaxation technique used here is an efficient matrix-diagonalization routine based on a sequential band-byband residual minimization method of single-electron energies,34,35 with direct inversion in the iterative subspace, whereas the ionic relaxation involves minimization of the Hellmann-Feynman forces, to an energy convergence of 10-4 eV. In each case, a two-dimensional slab was generated, surrounded by 15 Å of vacuum space perpendicular to the crystallographic plane of interest (i), and the surface structure and internal parameters were fully reconstructed and relaxed prior to the calculation of the energy and stress. This methodology is consistent with our previous study of stoichiometric pyrite nanocrystals and nanorods at T ) 0 K,27 and produced the set of results shown in Figure 1, where the specific surface free energy is given as a function of µH2O. In this case, the results are shown for 50% monolayer coverage. It is important to point out that, although a detailed description of the surface structure is beyond the scope of the present work, the configuration of the water molecule on the {111} and {110} surfaces differed substantially from the {100} and {210} surfaces. In all cases, the water molecule was positioned adjacent to under-coordinated bridging sulfur atoms in the terminal atomic layer of a prerelaxed surface slab, and the upper layers and molecules re-relaxed to find the equilibrium adsorption configuration. In the former cases, this converged to a vertically aligned water molecule with the oxygen chemisorbed and the SsO bond perpendicular to the surface. In the latter cases, the water molecule became inverted, with under-coordinated bridging sulfur atom interacting with the H atoms. This configuration persisted following perturbation and re-running the calculation beginning with a different initial configuration. Although this configuration indicates a preference for physisorption, which is not well-described by DFT, calculations of the change in the core electrostatic potential indicate that some charge transfer is still occurring, so this (physisorption) configuration has been
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Figure 2. A collection of shapes for pyrite FeS2 nanocrystals, formed using limited combinations of crystallographic forms: (a) cube, (b) octahedron, (c) pyritohedron, (d) rhombic dodecahedron, (e) truncated cube, (f) truncated octahedron, and (g) truncated pyritohedron. {100} facets are shown in red, {111} facets in green, {110} facets in blue, and {210} facets in gray (color online).
used in the surface free energy calculations. In general, this is now a topic of ongoing investigations. 3. Discussion of Results In our previous work,27 we showed that the equilibrium shape of pyrite nanocrystals consists of {100} and {111} facets, but no {110} and {210} facets, which is consistent with the morphology predicted by the Wulff construction for pyrite macro-crystals. For stoichiometric particles under ∼20 nm (at 0 K), the equilibrium morphology occupies the cuboctahedron T truncated-cube shape-continuum. However, it is possible that other shapes (which are often observed macroscopically) may be thermodynamically stable in the presence of water, or at higher temperatures. To investigate this issue, a collection of possible shapes have been considered, by including only limited subsets of crystallographic forms, as shown in Figure 2. Among these shapes are the perfect closed forms of the cube (Figure 2a), octahedron (Figure 2b), pyritohedron (Figure 2c), and dodecahedron (Figure 2d), enclosed entirely by {100}, {111}, {210}, and {110} surfaces, respectively. In addition to this, we have included a truncated cube enclosed by {100} and {111} facets (Figure 2e), a truncated octahedron enclosed by {111} and {210} facets (Figure 2f), and a truncated pyritohedron enclosed by {210} and {110} facets (Figure 2g). On the basis of the stoichiometric surface energies at 0 K, the energetic ordering of the shapes in the absence of water (calculated using eq 1) follows: truncated cube < cube < truncated octahedron < octahedron < truncated pyritohedron < pyritohedron < dodecahedron, as shown in Figure 3. Note that these shapes have not been defined by a truncation in an arbitrary plane along the normal of the minority facets, but rather by limiting the subset of facet i included in each shape. Hence they are special cases of a minimum energy geometry, which represent kinetic morphologies where growth in the alternate directions is maximized. By modeling the relative stability of these shapes over a given range of temperatures and water concentrations, we receive information concerning growth resulting from thermodynamic considerations, overall thermodynamic stability, and the stability of shapes resulting from known (prescribed) kinetic growth considerations.
Figure 3. Free energy of formation for pyrite FeS2 nanocrystals with a variety of shapes, with respect to bulk pyrite, as a function of the average diameter 〈D〉.
From eq 2, we can see that the final surface free energies (and hence the shape, and the total free energy of formation) is a function of the degree of coverage (or concentration) of adsorbed water on the surface, described by n; whereas from eq 4, we see that the specific surface free energies is a function of the water temperature, described by the chemical potential of water. This makes a graphical comparison of morphologies over a range of sizes rather complicated, so we have chosen to show the relative stability of 35 nm particles for a limited set of adsorption concentrations n (as a function of T), as shown in Figure 4. These results effectively sample 〈n, T〉 space, and could be reproduced for any alternative point in this manifold. From Figure 4a, we can see that at low water (adsorption) concentrations the nanomorphology of pyrite depends very little on the temperature. The formation of octahedral nanocrystals is energetically favorable under at low temperatures, but the formation of truncated cubic shapes are consistently favored over ∼90 K. Even at low temperatures, this is distinctly different from the adsorbate-free case (shown at 0 K in Figure 3), indicating that even a low coverage of water can have an important influence on shape. When the coverage of water is increased to 50% ML coverage (Figure 4b) the cross-over from
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Figure 4. Free energy of formation for 35 nm pyrite FeS2 nanocrystals with a variety of shapes, with respect to bulk pyrite, as a function of the water temperature, with (a) n ) 1/3, (b) n ) 1/2, and (c) n ) 2/3 monolayer (ML) coverages of water on the surfaces. Shapes include (s) cube (Figure 2a), (- - - -) octahedron (Figure 2b), (- - - - -) pyritohedron (Figure 2c), ( · · · · · · · ) rhombic dodecahedron (Figure 2d), (s · s) truncated cube (Figure 2e), (- · - · -) truncated octahedron (Figure 2f), and (- · - · - · ) truncated pyritohedron (Figure 2g).
Figure 5. The shape of 35 nm pyrite FeS2 nanocrystals (characterized by the fraction of surface area occupied by octahedral {111} facets) as a function of temperature, for ML coverages n ) 1/3, 1/2, and 2/3. The transition point indicates the temperature at which the shape is independent of ML coverage.
octahedral to truncated-cubic morphologies shifts to ∼270 K (around zero Celsius), and another cross-over from truncatedcubic to perfect-cubic nanocrystals is introduced at ∼510 K. This crossing in the relative stability is quite shallow, indicating a kinetic (rather then thermodynamics) regime. At still higher concentrations of adsorbed water, the dependence on temperature is substantial (Figure 4c). With a 2/3 ML coverage of water, the octahedral shape is preferred below ∼340 K, the
truncated cube between ∼340 and ∼450 K, and the perfect cubic shape beyond ∼450 K. In general, this is indicative of a smooth morphological transformation with temperature, which can also be described by optimizing the shape (in the octahedron-tocube shape-continuum),27 as shown in Figure 5. As we can see, there is a transition point at 395 K, where the shape is independent of the ML coverage of water. This indicates that the shape observed in pyrite nanocrystals formed in water may be indicative of the water temperature during formation, but that the presence of water (itself) does not promote the formation of alterative shapes such as the dodecahedron, or the characteristic pyritohedron. These results also have implications for attempts to understand the codependent relationship between the stability of nanomaterials and their chemical environment. Just as nanoparticles can affect the environment, so too environmental changes such as exposure to air or water can also have an important impact on the stability of nanomaterials, even after synthesis (or formation). It has been previously shown that ∼3 nm sized particles of the another sulfide (zinc sulfide, synthesized in methanol) exhibits a reversible structural transformation accompanying methanol desorption, and the binding of water to surfaces at room temperature.38 In this case, more detailed characterization of the morphological (shape) changes was not reported. 4. Conclusions Therefore, by using the shape-dependent thermodynamic model, and energetic and elastic parameters calculated from first
5380 J. Phys. Chem. C, Vol. 113, No. 14, 2009 principles, we have examined the morphological stability of pyrite nanocrystals as a function of temperature and concentration of water adsorbed on the surface. Our results indicate that the shape of pyrite nanocrystals, such as those formed during biomineralization, are likely to be affected by the temperature and coverage of water. In particular, we find that irrespective of water concentration on the surface, an increase in water temperature is likely to promote the formation of {100} facets at the expense of {111} facets. While these results are consistent with the formation of nanoscale pyrite biominerals in water at neutral pH,36 such as those where sulfide-producing magnetotactic bacteria are found,37 future work is required to understand the role of water in the phase selectivity between the pyrite and the greigite, which are both observed during biomineralization, and the marcasite phase of FeS2 which, interestingly, is not. Acknowledgment. The authors would also like to acknowledge the use of the Australian Partnership for Advanced Computing National Facility supercomputer center in carrying out this work. References and Notes (1) Ennaoui, A.; Tributsch, H. Sol. Cells 1984, 13, 197. (2) Ennaoui, A.; Fiechter, S.; Goslowsky, H.; Tributsch, H. J. Electrochem. Soc. 1985, 132, 1579. (3) Ennaoui, A.; Fiechter, S.; Jaegermann, W.; Tributsch, H. J. Electrochem. Soc. 1986, 133, 97. (4) Wang, S. S.; Seefurth, R. N. J. Electrochem. Soc. 1987, 134, 530. (5) (a) Tributsch, H. Struct. Bonding (Berlin) 1982, 49, 128. (b) Tributsch, H. In Bockris, J. O., Ed. Modern Aspects of Electrochemistry; Pergamon: Oxford, 1986; Vol. 14,Chap. 4. (6) Bucher, E. Appl. Phys. 1978, 17, 1. (7) Bither, T. A.; Bouchard, R. J.; Cloud, W. H.; Donohue, P. C.; Siemons, W. J. Inorg. Chem. 1968, 7, 2208. (8) Birkholz, M.; Fiechter, S.; Hartmann, A.; Tributsch, H. Phys. ReV. B 1991, 43, 11926.
Barnard and Russo (9) Ennaoui, A.; Fiechter, S.; Pettenkofer, Ch.; Alonso-Vante, N.; Bu¨ker, K.; Bronold, M.; Ho¨pfner, Ch.; Tributsch, H. Sol. Energy Mater. Sol. Cells 1993, 29, 289. (10) Chatzitheodorou, G.; Fiechter, S.; Kunst, M.; Jaegermann, W.; Tributsch, H. Mater. Res. Bull. 1986, 21, 1481. (11) Chatzitheodorou, G.; Fiechter, S.; Ko¨nenkamp, R.; Kunst, M.; Luck, J.; Tributsch, H. Mater. Res. Bull. 1988, 23, 1261. (12) Xuefeng, Q.; Yi, X.; Yitai, Q. Mater. Lett. 2001, 48, 109. (13) Kar, S.; Chaudhuri, S. Chem. Phys. Lett. 2004, 398, 22. (14) Kar, S.; Chaudhuri, S. Mater. Lett. 2005, 59, 289. (15) DeLong, E. F.; Frankel, R. B.; Bazylinski, D. A. Science 1993, 259, 803. (16) Po´sfai, M.; Dunin-Borkowski, R. E. ReV. Mineral. Geochem. 2006, 61, 679. (17) Bazylinski, D. A Chem. Geol. 1996, 132, 191. (18) Po´sfai, M.; Buseck, P. R.; Bazylinski, D. A.; Frankel, R. B. Science 1998, 280, 880. (19) Schippers, A.; Jorgensen, B. Geochim. Cosmochim. Acta 2002, 66, 85. (20) Rickard, D.; Butler, I. B.; Oldroyd, A. Earth Planet. Sci. Lett. 2001, 189, 85. (21) Barnard, A. S.; Kirkland, A. I. Chem. Mater. 2008, 20, 5460. (22) Barnard, A. S.; Zapol, P. J. Chem. Phys. 2004, 121, 4276. (23) Barnard, A. S.; Zapol, P.; Curtiss, L. A. J. Chem. Theo. Comp. 2005, 1, 107. (24) Barnard, A. S.; Yeredla, R. R.; Xu, H. Nanotech. 2006, 17, 3039. (25) Barnard, A. S.; Xu, H. J. Phys. Chem. C 2007, 111, 18112. (26) Barnard, A. S. J. Phys. Chem. B 2006, 110, 24498. (27) Barnard, A. S.; Russo, S. P. J. Phys. Chem. C 2007, 111, 11742. (28) Gong, X.-Q.; Selloni, A. J. Phys. Chem. B 2005, 109, 19560. (29) Perdew, J.; Wang, Y. Phys. ReV. B 1992, 45, 13244. (30) Kresse, G.; Hafner, J. Phys. ReV. B 1993, 47, RC558. (31) Kresse, G.; Hafner, J. Phys. ReV. B 1996, 54, 11169. (32) Vanderbilt, D. Phys. ReV. B 1990, 41, 7892. (33) Kresse, G.; Hafner, J. J. Phys.: Condens. Matter. 1994, 6, 8245. (34) Kresse, G.; Furthmu¨ller, J. Comput. Mater. Sci. 1996, 6, 15. (35) Wood, D. M.; Zunger, A. J. Phys. A 1985, 18, 1343. (36) Berner, R. A Am. J. Sci. 1967, 265, 773. (37) Bazylinski, D. A.; Frankel, R. B.; Garratt-Reed, A. J.; Mann, S. Biomineralization of Iron Sulfides in Magnetotactic Bacteria from Sulfidic Environments In Iron Biominerals; Frankel, R. B., Blakemore, R. P., Eds.; Plenum: New York, 1990, pp 239. (38) Zhang, H.; Gilbert, B.; Huang, F.; Banfield, J. F. Nature 2003, 424, 1025.
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