10644
J. Phys. Chem. B 1999, 103, 10644-10650
Study of Surface Segregation of Antimony on SnO2 Surfaces by Computer Simulation Techniques Ben Slater,*,†,‡ C. Richard A. Catlow,† David H. Gay,†,‡ David E. Williams,‡ and Vincent Dusastre‡ The Royal Institution, 21 Albemarle Street, London W1X 4BS, U.K., and Chemistry Department, UniVersity College London, 20 Gordon St, London WC1H OAJ, U.K. ReceiVed: February 5, 1999; In Final Form: August 16, 1999
We have carried out a computational bulk and surface study of the behavior of Sb(III) and Sb(V) ions on the (110) and (001) surfaces of SnO2. In addition, we have also examined the behavior of the Sn(II) and oxygen vacancy complex in the bulk and surface. These calculations suggest that Sb(III) is associated with in-plane surface oxygen species, while Sb(V) is subsumed below bridging oxygen ions in a more bulk-like environment. In addition, we find two possible Sn(II)/Ovacancy complex sites for the (110) surface: one is associated with a bridging oxygen vacancy, and the most favorable arrangement is associated with an in-plane subsurface oxygen vacancy. These calculations indicate not only the most favorable complex sites but also predict the surface segregation and defect energies. The theoretically derived sites are in complete agreement with the experimental data reported recently and proposed models for sensor activity.1,2
Introduction Tin (IV) dioxide (SnO2) is a semiconducting material of considerable technological importance with many applications, especially for combustible and toxic gas detection, thin film coatings, and sensor devices.1 The basis of the sensor application is the modification of the conductivity of the metal oxide by adsorption of gases from the atmosphere, a complex phenomenon that is still to be fully understood. The conductivity of the material may be enhanced by introducing carriers into SnO2 either by antimony doping or by oxygen deficiency. Indeed, the material shows high quasimetallic electrical conductivity but retains good optical transparency in the visible region.3 These properties can be used for applications in solar energy conversion devices and in photogalvanic cells.4 Mixed oxides of tin and antimony have also been developed as selective catalysts for the oxidation and ammoxidation of alkenes, notably propylene to acrolein and acrylonitrile.5,6 Structural studies7 indicate that the solubility of antimony cations in the rutile phase of SnO2 is limited to a Sb/Sn ratio of around 5%. Model calculations compared with infrared reflectance measurements for various Sb doping levels suggested that, for doping levels > 1 at. %, the sample might be covered with a reduced carrier concentration surface layer.8 It has been observed9 that polycrystalline materials with a 4% Sb/Sn composition show both the presence of antimony (III) ions at surfaces or grain boundaries in sites with a large electric field gradient at the antimony nucleus, together with bulk antimony (V) ions in octahedral bulk lattice sites. Dramatic surface enrichment in antimony has been reported10 to depend on bulk composition, calcination period, and temperature. We have recently shown2 that Sb segregation to the surface as Sb(III) in Sn1-xSbxO2(x ) 0.005, 0.05), controllable by thermal treatment, strongly alters the effect of water vapor † ‡
The Royal Institution. University College London.
upon the surface-catalyzed combustion rate of carbon monoxide and upon the elevated-temperature electrical conductivity. We suggested that the surface defect states which mediate both the electrical behavior and the surface-catalyzed combustion are best formulated as an association complex of an oxygen vacancy with Sn(II) or Sb(III) and were then able to propose a simple model which unifies the interpretation of the behavior of SnO2 as both a gas sensor and a combustion catalyst. We postulated that a correct formulation of the “absorbed oxgyen” surface species mediating the electrical response is an oxygen molecule trapped in or on a surface oxygen vacancy; that the combustion reaction proceeds partly through these species and partly through lattice oxygen at the surface; that water competes with oxygen for the surface vacancies, blocking this route; and that the binding energy of water to the Sb(III)Vo surface defect complex is less than that to the Sn(II)Vo complex. One objective of the present paper is to begin to address these postulates using computational methods. Since the oxidation state of Sb at the surface has only been deduced indirectly, another objective is to calculate the relative stability of the different Sb states both on the surface and in the bulk. It is well established that atomistic computer modeling techniques can play a major role in developing models for the surface structure of oxides.11 Previous theoretical and computational studies of SnO2 have been mainly confined to the bulk properties of the oxide, where it was predicted12 that the anion vacancy is the dominant type of defect in non-stoichiometric SnO2-x and that a good proportion of dopants are in interstitial sites; in addition, these calculations showed that doping with pentavalent species such as Sb2O5 results in good n-type conductivity. Thus, in the present work, we have simulated the surface properties of stoichiometric SnO2 (rutile structured) with special emphasis on the surface defect chemistry of antimony dopants. In particular, the effects of segregation of both the dopant and point defects to the surface have been investigated. Modeling of the system is facilitated by the observation13 that
10.1021/jp9905528 CCC: $18.00 © 1999 American Chemical Society Published on Web 11/12/1999
Surface Segregation of Antimony on SnO2 Surfaces both the oxygen and tin species remain fully ionic at the surfaces in their formal valence states of -2 and +4, respectively. The relative stability of the perfect surfaces of SnO2 have previously been investigated atomistically by Mulheran et al.14 and Allan et al.15 The electronic structure of the stoichiometric and reduced (110) faces have been investigated by the cluster approach16 and more recently by periodic DFT methods by Gillan et al.17-19 Both cluster and periodic approaches yielded similar results with respect to the reduced surface, where Sn(II) species are formed, albeit where the electron density is considered to be highly asymmetric, as in the case of SnO. We have therefore used modeling techniques first to study the stability of a number of surfaces of the oxide assuming an ionic model and second to calculate the segregation energies of overall charge neutral defects (Sb5+/Sb3+) and defect clusters. Moreover, we have also made a detailed examination of the optimal siting of defect clusters by comparing site substitution and interstitial locations of Sb dopants. Our paper provides therefore a detailed computational study of the phenomenon of Sb segregation in the material which, with the experimental study already published,2 can be related to the application of the material in sensors and other devices. Background All surface calculations were undertaken using the atomistic simulation program MARVIN,20 performing energy minimization calculations which allow us to predict equilibrium surface structures. In addition, one can also determine crystal morphology and examine the influence of solvents/sorbates on the whole morphology or surface structure using static or dynamic techniques. The main feature of MARVIN that distinguishes it from several other surface modeling techniques is that it calculates the long-range electrostatic potential using a 2-D (twodimensional) Ewald sum.21,22 A specified number of layers are considered where the structure is suitably oriented to terminate with the required free surface. The surface structure can be relaxed fully by optimizing the ion positions within the 2D cell (defined by fixed surface vectors) in order to minimize the total energy of the system. This energy can then be used in conjunction with the bulk energy per unit cell to deduce the relative stability of clean and contaminated surfaces. The segregation energy can be expressed as the difference between the total energy of a defect complex at the surface and the total energy of the complex in the lower, bulk-like region of the surface. Repeat layers of the initial cell are chosen to have no dipole moment, ensuring finite surface electrostatic potential and a conditionally convergent surface energy. The interionic potentials employed are based on the shell model23 in which an ion is modeled by a core connected by a harmonic spring to a massless shell in order to describe dipolar electronic effects. The potential parameters used for SnO2 were those developed by Freeman and Catlow.12 Since Sb is a dilute impurity in this study, potential parameters for Sb were simply rescaled based on the relative ionic radii of Sb3+ and Sb5+ 24 and are given in Table 1. These Sb3+ and Sb5+ potentials are approximate; however, the validity of these potentials relies on the assertion, borne out of bulk calculations, that the electrostatic contribution dominates the total energy. The repulsion parameters are not of primary importance, provided they reasonably describe the relative ionic radii of the ions. Thus, we expect these parameters correctly to describe the qualitative behavior of the dopants and, in addition, that the relatiVe total surface defect energies will be predicted with reasonable accuracy.
J. Phys. Chem. B, Vol. 103, No. 48, 1999 10645 TABLE 1: Potential Parameters cation charge (e)
4.0
anion charge (e)
-2.0
shell charge spring constant (eV/Å2) shell charge spring constant (eV/Å2)
1.58 2037.8 -2.47 23.09
Short-Range Parameters V(r) ) A exp(-r/F) - C/r6 interaction
Å/eV
F/Å
C/eV Å6
O2--Sn4+ O2--O2O2--Sb5+ O2--Sb3+ O2--Sn2+
1056.8 15123.6 965.8 1111.0 1316.9
0.3683 0.2230 0.3683 0.3683 0.3683
0.0 28.43 0.0 0.0 0.0
TABLE 2: Bulk Defect Energies for Isolated Sn/Sb Dopants and O2- Vacancies defect
energy/eV
Sn2+ impurity Sb3+ impurity Sn4+ vacancy Sb5+ impurity O2- vacancy
65.93 37.60 87.34 -52.36 19.17
A. Perfect Bulk, Defective Bulk, and Perfect Surface Calculations. A bulk, constant pressure relaxation with atomistic code GULP25 (version 1.2) using the potential parameters reported in Table 1 gave the lattice parameters a ) b ) 4.707 Å and c ) 3.310 Å and the internal coordinate u ) 0.3055. These values differ from those reported by Freeman et al. and Mulheran et al., both in the lattice parameter and the internal coordinate, by less than 1%. The lattice properties are particularly sensitive to the short-range potential cutoff used, and having compared a range of cutoffs we found 7.0 Å to be the most appropriate. We verified that these parameters are associated with a true minimum by inspection of the phonon properties which revealed no negative frequencies. The coordinates, elastic constants, and dielectric constants have been deposited with the journal. To compare fully with the results of Mulheran et al., we have considered a variety of quantities including total energy, structural properties, and residual strain. The structure reported here is slightly lower in energy and gives a superior c/a ratio but does exhibit fractionally more strain (less than 10-7eV/Å) than that obtained by Mulheran. The elimination of residual strain in the unit cell is crucial in producing unrelaxed surfaces. Surfaces with significant residual strains may give rise to misleading surface energies, where the surface has relaxed too severely for comparison with the original bulk energy. The lattice parameters described above give rise to the bulk model with the least strain and best overall structural properties. It should be noted that it was necessary to reduce the symmetry to P1 to obtain the least overall strain. Ideally, one would like to carry out the calculations in the original space group of the material considered (in this case P42/mnm), but we considered it was most important to eliminate strain from the model in order to calculate a consistent set of planar surface energies, since we found the hierarchy of the faces to be strongly affected by the strains present in the bulk. Using the Mott-Littleton26 approximation within the GULP program, we computed the bulk defect energies for Sn2+, Sn4+, Sb3+, and Sb5+ impurities, interstitials, and vacancies. We also calculated the energetic cost of creating an O2- vacancy, and the derived values are shown in Table 2. In addition, to estimate the enthalpic cost of surface segregation, the defect energies for Sn2+VO pairs, Sb5+/Sb3+ pairs, and 2Sb3+VO trios were calculated and are given in Table 3. The defect energies reported in Table 2 are in excellent
10646 J. Phys. Chem. B, Vol. 103, No. 48, 1999
Slater et al.
TABLE 3: Pair and Trio Energies for Sb and Sn Impurities defect
energy/eV
Sn2+VO pair Sb5+/Sb 3+ pair 2Sb3+VO trio
82.39 -15.55 92.88
TABLE 4: Relaxed Surface (SE) and Attachment Energies (AE) of SnO2 Surfaces face
dhkl
Serelaxed/ J m-2
AERelaxed/ eV mol-1
Serelaxed/ J m-2 a
(110) (210) (101) (100) (310) (321) (211) (301) (311) (111) (001) (212) (221) (112)
3.35 2.12 2.64 4.74 (2.37) 1.50 1.21 1.76 1.41 1.35 2.31 3.19 (1.59) 1.27 1.48 1.44
1.401 1.480 1.554 1.648 1.973 1.731 2.135 1.824 2.051 2.209 2.363 2.351 2.280 3.677
-9.689 -54.925 -9.952 -7.095 -104.350 -29.077 -24.733 -43.715 -34.041 -17.816 -8.867 -69.540 -40.298 -88.940
1.380 1.487 1.554 1.664 1.679 1.758 1.821 1.860
a
2.217 2.366
Calculated by Mulheran and Harding.22
agreement with those previously reported,12 and those displayed in Table 3 are comparable with those obtained from related studies.27 The results of the calculations of both surface and attachment energies20 on the clean surface for a number of different surfaces are given in Table 4 in order of relative surface energy. The interplanar spacing (dhkl) is reported since this is the simplest guide to morphological importance of a plane; those with larger interplanar distance generally dominate in the crystal habit. The (100) and (001) faces have a plane of symmetry bisecting the crystal cell, which reduces dhkl for those planes by a factor of 2.28 The data correlates reasonably well with the values calculated by Mulheran and Harding14 who used augmented lattice parameters (a ) 4.699, c ) 3.317, and u ) 0.306), though there are some significant discrepancies. Allan et al.15 also carried out a morphological and systematic surface study of SnO2, and our results show general agreement, though their surface energies are considerably higher than those reported here. In deriving accurate surface energies, it is critical, as noted, that one considers a fully relaxed surface (in this case all total energies are accurate to 1 part in 107 eV) and that the number of free layers and fixed layers gives rise to a convergent surface energy. Allan et al.15 used parameters derived from electron gas calculations, where both the Sn-O and O-O potentials terms used were considerably softer than those used in the present work. The hardness of the potentials used here actually only causes a significant difference with the stepped (211) and (310) faces. In these faces, as in the case of (110), the surface consists of alternate oxygen and tin/oxygen layers. We observe more severe relaxations for the (211) and (310) layers in particular, due primarily to the more repulsive nature of the O-O potential, which causes a corrugation of the oxygen layers. We consider the region size and potential parameters to be responsible for the discrepancies between this and previous work. In actuality, only two surfaces are disputed, the (210) and (310) surfaces. To establish unequivocally whether any anomalous long range electrostatic effects are associated with the fixed region for these two surfaces, we carried out slab calculations where all the constituent ions of the slab are explicitly relaxed. These calculations supported the values shown in Table 4; the largest discrepancy is 0.05 eV.
These relative surface energies do not correlate simply with interplanar distance, in contrast to the majority of ionic and semiionic crystals. Mulheran and Harding used “the surface excess energy” (i.e., the difference between the total surface energy and the bulk energy) compared to the 2D cell area and found a degree of correlation. The small range of surface energies coupled with the rather stable higher index surfaces suggests a complex morphology and that the habit is likely to be extremely sensitive to the presence of defects and impurities. The (110) surface is the most thermodynamically stable and would be expected to feature predominantly in the morphology. The (100) is rather stable, while the surface energy suggests the (001) surface is very unstable. However, when the attachment energies are considered, we find the two planes (110 and 001) are very close in energy, which is in accordance with experimental observations, where the two planes are both observed. Note that the six faces with the lowest surface energies correspond exactly to those observed by experiment.29-34 To the authors knowledge, the remainder of the surfaces have yet to be observed; thus, our calculations explain the experimental observations in terms of both thermodynamic and kinetic stability, in contrast to previous atomistic studies.14,15 B. Segregation Energies. In the following calculations, Sb/ Sn ratios of
