J. Phys. Chem. 1990, 94, 7889-1893
7889
Computational Studies of Solid Oxidation Catalystst C. Richard A. Catlow,*’tRobert A. Jackson,§ and John M. Thomas**$ Dauy Faraday Laboratory, The Royal Institution, 21 Albemarle Street, London WIX 4BS, England, and Department of Chemistry, University of Keele, Keele, Staffordshire ST5 5BG. England (Received: January 23, 1990; In Final Form: March 29, 1990)
We summarize the role of computational techniques in modeling the defect and electronic properties of oxides that are currently, or may in future be, used as oxidation catalysts. The formation and migration of defects can be accurately modeled, as can the segregation of defects to surfaces. We also demonstrate the ability of modeling techniques to calculate solution and redox energies in doped and oxidized catalysts. Special attention is focused on oxides possessing the rock-salt, perovskite, or pyrochlore structures, and quantitative data are presented on the following systems: (a) MgO doped with Li20 and CaO doped with either N a 2 0 or La203,all three of which are proven oxidation catalysts; (b) SrTiO, and BaTiO, doped with a trivalent cation M3+ (M = La, Nd, Eu, Y, Fe, Mn, or AI); and (c) Y2X2O7 and Gd2X207(X = Zr or Ti).
Introduction Many ternary oxides that function as efficient selective-oxidation catalysts for the conversion of plentiful hydrocarbons such as methane, butane, and propene to more desirable products such as ethene, maleic anhydride, and acrolein, respectively, entail sacrificial loss of oxygen which is removed from these so-called uniform’V2 catalysts, thereby converting them temporarily to nonstoichiometric solids. The gaseous oxygen present as one of the reactants is taken up by the catalyst, thus making good the anion deficiency created by the sacrificial loss. The cycle repeats itself for as long as the catalyst is active. Typical examples of such catalysts, which have been the subject of much recent inv e ~ t i g a t i o nare ~ , ~LiNi02v8 ~ (a catalyst for converting methane to ethene and ethane) and Bi2Mo0?’O (acrolein from propene). However, it is already clear that there may be very many oxides that exhibit this kind of catalytic action. Moreover, there are indications that some particular types of structure seem to favor sacrificial loss-to the appropriate hydrocarbon (or other) reactant-of constitutional oxygen and to sustain the requisite mobility of the corresponding anion. The rock-salt structure (of which NiO, CaO, and MgO are catalytically demonstrated examples7,’lJ2) is one prominent type. PerovskitesI3J4 and pyrochlores15 (general formulas A B 0 3 and A2B2O7, respectively) are others. There is little doubt that certain individual members of these families of catalysts possess a marked tendency to release oxygen from within their bulk and that solid-state diffusion, permitting the flow of oxygen from the gas phase into and through the solid and on to another region of the surface,l is facile. The catalysis of oxidation is, moreover, of considerable fundamental and practical importance; general issues concern, e.g., the complete combustion of methane and carbon monoxide at modest temperatures, while there are particular concerns such as the partial oxidation of hydrocarbons. We are therefore investigating trends in the defect chemistry of solid catalysts that might reveal clues which could lead to the design of more effective, uniform heterogeneous catalysts.16 We outline below the computational methodology and then arrive at estimates of the energetics of formation of certain relevant defects, their segregation at surfaces and of diffusion of oxygen in a number of oxides, many of which are known to be effective as oxidation catalysts. Of the rock-salt oxides recently reported to be catalytically active (in the oxidative coupling of methane, for instance), we focus on C a O and MgO. The presence of small amounts of La203 seemsll to render CaO more selective toward the formation of C2 and higher hydrocarbons. Likewise, relatively small amounts of alkali-metal oxides, especially Li,O, in MgO results in a ‘Dedicated to Professor K . S. Pitzer on the occasion of his 75th birthday. *The Royal Institution. I University of Keele.
0022-3654/90/2094-7889$02.50/0
powerful catalyst for the same reactions of methane. Many oxides belonging to the simple and triply layered perovskite structures are also known to be promising catalysts that function through the involvement of sacrificial oxygen. CaMnO, and CaMn03, (0 -< x 5 0.5) for the conversion of propene to benzene or 2methylpropene to p-xylene,I4 and YBazCu3O6+, (0 I x I 1 .O) for the ammoxidation of toluene to benzonitrile,” are also proven catalysts possessing the simple (though nonstoichiometric) and triple-layer perovskite structures. There have also been reports that certain members of the pyrochlore familyI5*l8(see Figure l), depending upon the precise nature of A and B, are also good selective-oxidation catalysts for the oxidative coupling of methane. With the availability of reliable interatomic potentials and efficient computational techniques based on energy minimization procedures, it is, at the very least, possible to assist interpretation of existing data; there is also the hope of gaining deeper insights that will, in turn, lead to the evolution of new, superior catalysts. Clearly, the role of structural defects and impurities (dissolved or exsolved) both within the bulk and a t the surfaces of solid oxides, as well as the nature of redox reactions leading to formation and migration of electronic defects, is crucial to the proper understandings of the mode of operation. of these novel catalysts.
Outline of Computational Methods Employed The methodologies used in this field and adapted here have been comprehensively described hitherto.19 They are now quite (1) Thomas, J. M. Angew. Chem., Inr. Ed. Engl. 1988, 27, 73. (2) Wells, P. B. Faraday SOC.Discuss. 1989, 87, I . (3) Keller, G. E.; Basin, M . M. J . Catal. 1982, 73, 9. (4) Hinsen, W.; Baerns, M. Chem. Z f g . 1983, 107, 223. (5) Labinger, J. A.; Ott, K. C.; Mehta, S.; Rockstad, H. K.; Zoulman, S. J . Chem. Soc., Chem. Commun. 1982, 543. (6) Otsuka, K.; Suga, K.; Yamanaka, 1. Catal. Lett. 1988, I , 423. (7) Pickering, I. J.; Maddox, P. J.; Thomas, J. M. Angew. Chem. 1989, 101, 828. (8) Ungar, R. K.; Zhang, X.; Lambert, R. M. Appl. Catal. 1988, 42,4. (9) Burrington, J. D.; Grasselli, R. K. Ado. Coral. 1981, 30, 897. (IO) Buttrey, D. J.; Thomas, J. M.; Jefferson, D. A. Philos. Mag. 1986,
53, 897. (1 I ) Chaudhary, V . R.; Choudari, S. T.; Rajut, A. M.; Rad, V. H. J . Chem. SOC.,Chem. Commun. 1989, 1526. (12) Campbell, K . D.; Zhang, H.; Lunsford, J. H. J . Phys. Chem. 1988, 92, 750. (13) Popplemeir, K. R.; Leonowicz, M. E.; Longo, J. M. J . Solid Srare Chem. 1982,44, 89. Pickering, I. J. Ph.D. Thesis, University of London, 1990. (14) Reller, A.; Thomas, J. M.; Jefferson, D. A,; Uppal, M. K. Proc. R. SOC.London 1984, A394, 223. (15) Ashcroft, A. T.; Cheetham, A. K.; Green, M. L. H.; Grey, C. P.; Vernon, P. D. F. J . Chem. Soc., Chem. Commun. 1989, 1667. (16) Pickering, I. J.; Thomas, J. M.; Maddox, P. J. New Deoelopments in Selectioe Oxidation; Centri, G., Trifino, F., Eds.; Elsevier: Amsterdam, 1990; p 453. (17) Andersson, S.; Bovin, J . - 0 . Narure 1989, 340, 1 1 10. (18) Thomas, J. M.; Jones, R. H.; Couves, J. W.; Cheetham, A. K. Work in preparation. (19) Catlow, C. R . A.; Mackrodt, W. C., Eds. Computer Simulation of Solids; Lecture Notes in Physics 166; Springer-Verlag: Berlin, 1982.
0 1990 American Chemical Society
7890
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The Journal of Physical Chemistry, Vol. 94, No. 20, 1990
nn
Catlow et al. TABLE I: Energies of Solution of Alkali-Metal Oxides into Alkaline Earth Oxide Host, with Oxygen Vacancy Compensation (after Catlow et al." and Foot") alkali-metal alkaline earth solution energy." eV, oxide oxide host per M 2 0 dissolved 5.45 Li20 MgO Na20 CaO 3.05 K2O SrO 3.20 1.48 K20 BaO Positive values signify endothermic processes.
TABLE 11: Energies of Oxidation Reactions (Vacancy to Hole) in Alkaline-Earth Oxides Doped with a Monovalent Cation According to (2)O
48f Anion sile
8a Anion site
oxide
oxidation energy per vacancy, eV
oxide
oxidation energy per vacancy, eV
-2.28 -1.72
SrO BaO
-2.95 -1.74
MgO
CaO Figure 1 . (100) projection of the pyrochlore structure A2B207.
standard for the study of defects in ionic and semiionic solids, and there are many applications reported in the recent literature. In studies of the structural and defect properties of solids, energy minimization methods employing effective potentials have proved to be versatile and accurate in modeling a wide range of solid materials. When applied to perfect crystal structures and perfect surfaces, standard summation procedures are used to evaluate the lattice or surface energy; the Ewald technique2' allows accurate summation of the long-range Coulomb terms. The calculated energies are then minimized with respect to atomic coordinates and unit-cell dimensions: Newton-Raphson (Le., second derivative) energy minimization methods are normally employed. Having determined the minimum energy structure, subsequent calculations of the second derivatives of the energy with respect to atomic coordinates provide the information necessary to evaluate elastic, dielectric, and lattice dynamical properties. Standard are available for carrying computer codes ( e g , PLUTOand THBREL) out these applications. In studies of defects and impurities, energy minimization methods are used within the context of the Mott-Littleton m e t h o d ~ l o g y , lin~ -which ~ ~ a region of crystal containing typically 100-500 atoms surrounding the defect is relaxed to equilibrium. Polarization of the more distant regions of the crystal is treated by use of formulations based on continuum dielectric theory. The methods may be adapted to study the structures and energies of surface defect^.^^^^^ Again, we note that generalized computer codes (HADESand CASCADE) are available for undertaking these calculations. In solid-state studies, energy minimization methods summarized above are adequate and appropriate for many problems, including most of those of relevance to the present paper. We should note, however, that molecular dynamics methods which include atomic motion explicitly in the simulation and Monte Carlo techniques which undertake computational statistical mechanics have a valuable role in solid-state simulations. Examples of their application are given in ref 20 and 25. The reliability of the results of simulation studies depends critically on the quality of the interatomic potentials that model the interactions between the atoms in the solid. The potentials we have used to simulate oxides are based on a Born model description of the solid (generally with integral ionic charges) and short-range pair potentials, which, for more covalent materials, are supplemented by explicit bond-bending terms; a shell model26 (20) Catlow. C. R. A. Annu. Rev. Mater. Sci. 1986. 16, 517. (21) Tosi, M. P. Solid State Phys. 1964, 16, 1, (22) Lidiard, A. 8. J . Chem. Soc.. Faraday Trans. 2 1989, 85, 341. (23) Tasker. P. W. In ref. 19. (24) Mackrodt, W. C . J . Chem. Soc., Faraday Trans. 2 1989, 85, 541. ( 2 5 ) Yashonath. S.; Thomas. J . M : Yowak. A . K.: Cheetham, A . K . .Yart~rr1988 3?!
601
"Note that for a given host lattice, energies are independent of dopant.
TABLE 111: Defect and Dopant Solution Energies in La203-Doped CaO (Based on Potentials Taken from Lewis and Catlow") ( a ) Calculated Defect Energies defect
energy, eV
La2+ substitutional at CaZCsite cation vacancy anion vacancy anion interstitial
-18.10 20.49 21.60 -14.26
(b) Lattice Energies energy, eV -127.29 -36.38
La203 CaO
(c) Solution Energies (per mole of Lalo,) impurity solution mode
-
energy, eV
(a) cation vacancy formation reaction 'La203" 3Ca, 2La,, V", 3"CaO" (b) oxygen interstitial formation solution reaction "La203" + 2Ca,, 2La, + 0," 2"CaO"
+
-
+
+ +
2.44 4.07
description of ionic polarizability is normally included. Detailed discussions of the current status of this field are given in ref 27. Moreover, it is clear from the extensive literature of the past IO years on the modeling of oxides that accurate and quantitative results can be obtained from structural, surface, and defect properties using already available interatomic potentials. Results and Discussion (i) Systems Based on Rock-Salt Oxides. Calculations have been performed on the energies of solution of Li20, N a 2 0 , and K 2 0 in the rock-salt oxides MO ( M = Mg, Ca, Sr, and Ba)29330 and also of La203 in CaO. The relevant energies for oxidation of an anion vacancy into an electron hole in the doped divalent oxides have also been calculated, and recently we have calculated the energetics corresponding to the formation of the La3+ substitutional defect and the solution of La203in CaO (see Tables 1-1 11).
( a ) Alkali-Metal Oxides Doped with Low-Valence Ions. The defect structure of these doped oxides was extensively studied in the context of radiation damage phenomena,28well before the importance of the material in catalytic studies was realized. Li20 has limited solubility in MgO; the most straightforward mode of (26) Dick, B. G.; Overhauser, A. W. Phys. Reu. B 1958, 112, 90. (27) Catlow, C. R. A.; Freeman, C . M.; Islam, M.S.; Jackson, R. A.; Leslie, M.; Tomlinson, S. M. Philsos. Mag.A 1988, 58. 123. (28) Abraham, M. M.; Chen, Y.; Boatner. L. A,; Reynolds, R. W. Phys. Rev. Lett. 1916, 37, 849. (29) Catlow, C . R. A,; Foot, J . D.; Colbourn, E. A . J . Phys. Chem. Solids 1988, 49, 1225. (30) Foot, J . D. M.Sc. Thesis, University of Keele, 1989
The Journal of Physical Chemistry, Vol. 94, No. 20, 1990 7891
Computational Studies of Solid Oxidation Catalysts
0
@
M g 2 + ion 0 2 - ion
0 Li'
w
w
Substitutional
0
Oxygen Vacancy
e
0- hole state
Localised,
Figure 3. Two schematic representations of the regular perovskite structure, AB03.
w - w
Figure 2. Defect structure of Li+-doped MgO. In the upper figure, Li+ substitutionals are compensated by oxygen vacancies. In the lower figure the vacancy has been filled by incoming oxygen and localized hole states (shown on sites adjacent to the Li' ions) have been created.
incorporation of Li+ into the MgO matrix is as a substitutional ion at a cation site with compensating oxygen vacancies (Figure 2). This may be represented by using Kroger-Vink notation as "Li20"
-
+ 2MgMgX+ Oox
2LiM;
+ V," + 2"MgO"
(1)
where "Li20" and "MgO" indicate the incoming lithium oxide and the magnesium oxide displaced to the surface and Vo- signifies a doubly charged oxygen vacancy. The results of calculation^^^^^^ of the solution energy corresponding to this reaction are given in Table I, where the calculations for analogous reactions involving other alkali-metal oxides in alkaline earth oxide hosts are also presented. These are of immediate interest in that they show that solution of Li20 in MgO is appreciably endothermic, in line with the observed low solubility. In contrast, NazO and K 2 0 have much lower solution energies in respectively CaO and SrO and are, as we discuss later, candidates for use in the tailoring of oxidation catalysts. To render Li/MgO catalyticallyactive for the oxidation of hydrocarbons, it is necessary to immerse the material in oxygen. In terms of defect chemistry this results in the oxidation vacancies with the consequent creation of hole states. Since the valence band of these materials is constructed from O(2p) orbitals, localized hole states may be described as 0- ions. Thus the oxidation reaction may be written as Vd'
+ 7202
-
00"
+ 2h'
(2)
where the hole state, h', is modeled as a substitutional 0-. The calculated for this reaction is reported in Table 11, together with those for the analogous doped oxides. We note that oxidation of the doped materials with hole formation as represented by (2) is exothermic. Thus, except at low oxygen partial pressures, we would expect holes to predominate over vacancies and that oxidation will enhance the solubility of the dopant in the rocksalt-structured host. It is significant that, for the heavier alkali metals dissolved in oxides of the heavier alkaline-earth oxides, there is, overall, an exothermic solution, a fact which suggests that there would be merit in employing BaO rather than MgO or CaO as solid "solvents" for improved catalysts. Calculations have therefore clarified the key energetic terms controlling the formation of 0- hole centers in monovalent doped alkaline-earth oxides. These centers are known to facilitate hdyrogen abstraction in partial oxidation reactions, although to be effective they must have an appreciable concentration at the surface of the oxide. We shall return to the relative energetics of bulk and surface defect species below. It is noteworth; that these 0- centers were first observed in single crystals of MgO that had been heated in air or oxygen.31 Lunsford et al.32have shown
that 0- centers function as H-atom abstractors from methane, there being essentially zero activation energy for this process. (b) Rock-Salt Oxides Doped with Multiply Charged Cations. We focus here on the apparently simple system, CaO doped with La203. Recent work3, has shown that this material is effective in promoting oxidative coupling of simple hydrocarbons. Calculations have allowed us to assess the energetics of solution of La203in CaO and the nature of the predominant defects. The results, collected in Table 111, show that the solution of La203 in CaO is considerably endothermic. The defect energies in Table IIIa are combined with the lattice energies in Table IIIb to give estimates of the energies of the two modes of solution of the impurity, the first involving the creation of cation vacancies and the second oxygen interstitials to compensate the higher charge of the dopant ion. The solubility of the trivalent oxide in the host phase must therefore be limited. Our calculations predict that the predominant defects created by dissolving La203 in CaO will be cation vacancies. Oxygen defects will be minority species, and we therefore conclude that the net flux of oxygen through such a solid will be low. In the light of our computations it is likely that the catalytic activity of this material is associated with exsolved La203,the properties of which may well be modified by interaction with the CaO host. (ii) Systems Based on Perovskites and Pyrochlores. Doping of perovskite-structured (Figure 3) materials, especially BaTiO, and SrTiO,, is routinely undertaken in order to modify their electronic properties. As with the rock-salt-structured oxides, subtle changes in the electronic properties of these solids may drastically alter catalytic activity. However, in the complex oxides considered here, the dominant electronic species is governed by the precise type of the site-substitution operative in the solid. In the case of trivalent ions doped into BaTiO, and SrTi03, three types of dissolution mechanisms are, in principle, possible: first, substitution at the A metal (Ba or Sr) site, which at sufficiently low partial pressure of oxygen will lead to electron compensation and hence to "n-type" conductivity. Second, substitution at the B metal (Ti) site, which at sufficiently high oxygen partial pressure will result in hole compensation and "p-type" conductivity. Third, self-compensation in which the dopant occupies both A and B metal sites in equal proportions with no resulting effect on electronic properties. In Table IV we present results of the calculated energies for the different modes of dissolution of a range of dopants in both SrTi03 and BaTiO,. It is clear that the larger dopant ions preferentially occupy the A sites, whereas smaller ions occupy B sites. This behavior could have been predicted on qualitative grounds, but calculations provide reliable quantitative estimates of the relative energies of the different modes of solution. (31) Abraham, M. M.; Unruh, W. P.;Chen, Y. Phys. Reu. B 1974,9(4), 1842. (32) Ito, T.; Lunsford, J. H. Nature 1985, 314, 721. (33) Chaudhary, V. R.; Choudari, S. T.; Rajut, A. M.; Raul, V. H. Cutal. Lett. 1989, 3, 85.
7892
The Journal of Physical Chemistry, Vol. 94, No. 20, 1990
TABLE IV: Solution Energies of Trivalent Oxides into SrTi03 and BaTiO, (Assuming Compensation with Hole or Electron States: Based on Potentials in Reference 41 for SrTi03 and Reference 42 for BaTiO,)"
dopant
La3+ Nd" Eu3+
Y'+ Fe3+ Mn'' ~ 1 3 +
solution energy per dopant cation, eV A-site B-site selfsubstn substn compensation (a) BaTiO, -1.20 5.85 0.74 -0.60 4.93 0.58 4.43 0.64 0.02 1.04 3.97 0.92 9.57
9.52 14.92
5.72 5.57 9.55
5.04 4.79 7.35
Nd3+ Eu3'
Y'+ Mn3+ AI'+
3.44 5.72
10.34 8.82
2.67 3.05
4.06 4.78 1 1.92 13.65
7.76 6.54 4.12 4.57
1.69 1.44
3.80 4.89
-
"Reactions for different compensation modes are as follows: A site, + 2AA + 2TiTi 2MA + 2Ti'Ti+ 2 A 0 + 1/202; B site, MzO3 + 2TiTi+ 0, 2M'Ti + vo" + 2Ti02;self-compensation,M 2 0 3 + BaBa + TiTi M'Ba + MITi + BaTiO,. M20,
TABLE V: Oxygen (02-)Frenkel Energies' in Pyrochlore-Structured Oxides (Based on Potentials Taken from Lewis and Catlow") Frenkel Frenkel
oxide Y2Ti207 YZZr207
energy, eV
oxide
4.85
Gd2Ti207 Gd2Zr20i
3.51
TABLE VI: Calculated Seereeation Energies' in Li+-Dowd M defect Li+ 0(Li+O-) complex
energy, eV
5.44 2.38
'By Frenkel energy we mean the energy required to transfer an oxygen (02-)ion from a lattice (480 to a vacant oxygen (8b) site; see Figure I More surprising is the contrast between the behavior of the two alkaline-earth titanates. In SrTi03, unlike the situation that prevails for BaTi03, we find that self-compensation is preferred by almost all the dopants, suggesting that it will be far more difficult to modify the electronic behavior of the material by simple doping. This behavior could not have been predicted on qualitative grounds. The results of the calculations are in line with the limited amount of available experimental data, and they demonstrate the power of the simulation methods in predicting how chemical modifications of complex oxides can influence electronic behavior. Several oxides crystallizing with the pyrwhlore structure (Figure I) are known to act as partial oxidation catalysts. Their crystal structure is based on that of fluorite with ordering of the A (tetravalent) cations, B (trivalent) cations, and the oxygen vacancies. The defect structure of the materials is, however, surprisingly poorly understood. Some of the best inferences have come from calculation^,^^ which show that the basic mode of disorder involves thermal excitation of oxygen ions from the (480 crystallographic sites to vacant (8b) positions (i.e., the oxygen vacancy sites that are ordered in the pyrochlore structure). The results of recent calculations in this laboratoryg5 for four pyrochlores-Gd2Ti207, Y2Ti207,Gd2Zr207,and Y2Zr20,-are given in Table V . As is discussed further below, the oxygen vacancies created on the (480site exhibit high mobility and could certainly have a major influence on the course of oxidative reactions catalyzed by these materials. (iii) Modeling of Surface Defects and Surface Segregation. Several successful modeling studies of defects and impurities on the surfaces of oxides have been reported by Tasker and by Mackrodt and Colbourn; an excellent recent review is available (34) Van Dijk, M. P.; Burgraff, A. J.: Cormack, A . N.; Catlow, C. R. A . Solid Srate Ionics 1985, 17. 159. (35) Catlow, C. R . A . : Wilde, P. Unpublished work
a
segregation energy, eV -0.18
-0.95 -1.70
'Defined as energy of defect at the surface relative to energy at bulk lattice site. Negative value indicates that the surface site is favored. TABLE VII: Oxygen Vacancy Activation Energies in Oxides Crystallizing in the Rock-Salt (RS), Perovskite (PE), and Pyrochlore (PY) Structures
oxide MgO (RS) CaO (RS) SrTiO' (PE) BaTiO, (PE) Y2Ti207(PY) Y J r 2 0 7 (PY) Gd2Ti207 (PY) Gd2Zr207(PY)
(b) SrTi03
La3+
Catlow et al.
activation energy, eV 2.40 2.20 0.65
0.62 0.28 0.71
0.22 0.68
in ref 24. One of the most important features to emerge from their work is the importance of the variation of the defect energy as it penetrates from the surface into the bulk of the crystal-an effect that can give rise to the phenomenon of surface segregation of impurities. We may illustrate this through the results of recent comput a t i o n ~on~ two ~ materials of catalytic relevance: Y3+-dopedT h o 2 and Li+-doped MgO. Thus, in Figure 4 we show the calculated variation of the energy of the oxygen vacancy and Y3+substitutional as a function of the layer depth beneath the ( 11 1 ) surface of a thoria host. In the case of the oxygen vacancy we note that there is a barrier to the penetration of the defect from the surface into the bulk. In contrast, for Y3+ substitution, there is no such barrier; moreover, the impurity has a higher energy at the surface and will preferentially segregate away from the surface region. It is not yet clear what the particular consequences of this spatial variation in the oxygen vacancy are in the context of catalyzed oxidations. It could well mean that the limiting step in the gas-solid reaction is the migration of the bulk oxygen to or from the bulk via the subsurface barrier, but other elementary steps involved in the overall catalytic oxidation need to be considered before firm predictions may be made. The calculations on Li+ and 0- (hole) segregation energies are presented in Table VI. They show that segregation of the (Li'O-) complex, for the existence of which cogent experimental proof already exists.31 The segregated (Li+-O-) complex is very possibly the active site in partial oxidation catalysis by this material. (io) Modeling of Oxygen Migration. We emphasized earlier the central importance of migration of oxygen through the bulk of an oxide catalyst effective in a number of distinct kinds of oxidation. Calculations can greatly enhance our understanding of this problem, and it is now possible routinely to evaluate the activation energies for oxygen defect transport and to compare these values for different materials. Such calculations require that the saddle point for the migration process be identified. In high-symmetry materials this is generally straightforward with the saddle point commonly being located at the point where the migrating ion is midway between the two lattice sites involved in the migration process. For lower symmetry structures, a detailed search of the potential energy surface may be needed. There are several subtle points that await further clarification in computations of this kind. For example, is it legitimate to assume, as we have done, that the valence state or effective charge of an ion remains unchanged as it traverses the saddle point? Moreover, are we reliably guided by trends in activation energies (within a given family of oxides) or should we seek to undertake the more difficult task of computing the absolute rates of migration, making allowance for the operation of a compensation (36) Gorman, A . M.; Catlow, C. R. A. Manuscript in preparation.
The Journal of Physical Chemistry, Vol. 94, No. 20, 1990 1893
Computational Studies of Solid Oxidation Catalysts a
02-
16'9 16.8 16.7
-VACANCY FORMATION; (1 11) Tho RELAXED
L1t I
of key aspects of the defect and electronic properties of solid oxides capable of sustaining heterogeneous catalytic oxidation. Our aim has been to lay the foundations of an approach that, with further refinement, should assist in the development and design of better catalysts. Of the three main categories of structural types considered here, more systematic comparative experimental work on catalysis has already been carried out on rock-salt-based catalysts than those based on perovskites or pyrochlores. Computations lead to some useful predictions, viz., that Na20-doped CaO may be a superior oxidation catalyst than Li,O-doped MgO. Experimental investigations, recently carried bear out this prediction. Calculations also predict that it would be advantageous to employ BaO rather than MgO or C a O as solid "solvents" for improved catalysts, and there is clearly a need for a joint computationalexperimental study based on the favorable energetics of surface segregation of (M+O-) ion pairs, given that both (Li+O-) and (Na'O-) entities f a ~ i l i t a t e ~hydrogen ~ , ~ * abstraction from methane. For the perovskite- and pyrochlore-based catalysts, there is currently a mismatch between those systems that have already been experimentally investigated and those (discussed in this paper) for which computational data are now available. This arises in part because of the present incomplete range of effective potentials required for the computations. However, as the results in Table VI1 show, it is clear that pairs of related materials warrant experimental study to ascertain the role of oxygen migration in the overall catalysis. The results summarized in Figure 4 show how difficult it may be for oxygen to penetrate to the bulk of certain oxide catalysts. While we have incorporated most of the factors likely to influence the various elementary steps involved in the overall catalysis, we recognize that certain subtleties have been omitted. For example, it important to know whether hole states are delocalized or self-trapped as 0- ions on oxygen. Estimates of the relevant energetics can, however, be obtained computational-
5
16.5 16.6 0.5
2.5
3.5
4.5
5.5
6.5
1.5
Plane index P
b
Y3+ SUBSTITUTIONAL; (1 11) T h o 2 RELAXED 26.2
25.0
25.5
r4
t \
1
Y '*sub formation
~
bulk sub formation
I
25.4
1 .o
I
2.0
I
I
3.0
I
I
4.0
I
5.0
I
I
~
ly.28,29.39
There is obviously a need for well-defined, joint computational-experimental studies of selected solid oxide catalysts to be undertaken. Such work is now in progress.
6.0
Planeindex P
Figure 4. Variations of dopant and defect energies in the fluoritestructured oxide T h o 2 with degree of penetration from the (1 1 1 ) surface of the oxide. (a) Oxygen vacancy; (b) Y3+substitutional. (The plane index P is the pth plane parallel to the surface (1 11) plane.)
effect between the preexponential terms and activation energies? We believe that, at this stage, calculated estimates of activation energy alone are a sensible step forward. To illustrate the value of such simulations, we present in Table VI1 calculated activation energies for oxygen vacancy migration in the materials discussed (which effects transport of lattice 02-) earlier in this paper, Le., MgO, CaO, SrTi03, BaTi03, and the titanate and zirconate pyrochlores. The variation in the activation energies between the different structure types is marked. In particular, we note the low values for vacancy migration in the pyrochlores, a result with practical consequences for these materials both as oxidation catalysts and as oxygen conductors.
Summary and Conclusions With the aid of a number of specific examples we have shown how computational studies can contribute to our understanding
Acknowledgment. We are grateful to the Science and Engineering Research Council for general support. We also acknowledge many useful discussions with E. A. Colbourn, W. C. Mackrodt, P. W. Tasker, A. M., Stoneham, and I . J. Pickering. We also thank our colleagues A. M. Gorman and P. Wilde for permission to cite results not yet published. Registry No. MgO, 1309-48-4; Li,O, 12057-24-8; CaO, 1305-78-8; N a 2 0 , 13 13-59-3; La203, 131 2-81-8; SrTiO,, 12060-59-2; BaTiO,, 12047-27-7; La, 7439-91-0; Nd, 7440-00-8; Eu, 7440-53-1; Y, 7440-65-5; Fe, 7439-89-6; Mn, 7439-96-5; AI, 7429-90-5; Y2Ti207,12037-02-4; Y2Zr20,, I21 37-5 1-8; Gd2Ti207,12024-89-4; Gd2Zr207, 11073-79-3. (37) Nishimura, M.; Richard, D.;Thomas, J . M.; Waller, D. Manuscript in preparation. See also: Lin, C.-H.;Wang, J.-X.;Lunsford, J. H. J . Cuial. 1988, 1 1 1 , 302. (38) Lunsford, J. H.; Lin, C.-H.; Wang, J.-X.; Campell, K. D. In Microslruciure and Properries of Catalysis; Treacy, M. M. J., Thomas, J. M., White, J . M., Eds.; Materials Research Society Proceedings 1 1 1 ; Materials Research Society: Pittsburgh, PA, 1988; p 305. (39) Torrance, J. B.; Matzger, R. M. Phys. Reu. Leu. 1989, 63, 1515. (40) Lewis, G . V.; Catlow, C. R. A. J . Phys. C 1985, 18, 1149. (41) Jackson, R. A.; Tomlinson, S. M.; Akhtar, M. J. To be published. (42) Lewis, G . V.; Catlow, C. R. A. J . Phys. Chem. Solids 1986,47, 89.
