5912 Chem. Mater. 2010, 22, 5912–5917 DOI:10.1021/cm1018822
Defects, Dopants, and Protons in LaNbO4 Glenn C. Mather,*,† Craig A.J. Fisher,‡,§ and M. Saiful Islam‡ †
Instituto de Cer amica y Vidrio, CSIC, Cantoblanco, 28049 Madrid, Spain, and ‡Department of Chemistry, University of Bath, Bath BA2 7AY, United Kingdom. §Now at the Nanostructures Research Laboratory, Japan Fine Ceramics Center, 2-4-1 Mutsuno, Atsuta-ku, Nagoya, Japan Received July 7, 2010. Revised Manuscript Received September 15, 2010
Simulation methods have been used to investigate the energetics of defect formation, dopant solution, water incorporation, and defect clustering in the high-temperature proton conductor LaNbO4. The interatomic potential model successfully reproduces the observed tetragonal scheelite-type structure of LaNbO4. Formation of an oxygen vacancy, required for protonation, is accompanied by significant local relaxation leading to an [Nb2O7]4- group. The most favorable dopant solution energies are found for Ca2þ and Sr2þ on the La site. Dopant-vacancy association is predicted to occur for a wide range of divalent dopants on the La site and tetravalent dopants on the Nb site. Dopantproton association is also predicted to occur for the range of dopants studied. The lowest M/ - OH• binding energy is found for Ca, which is commonly used in compositions displaying the highest proton conductivities so far reported in the LaNbO4 system.
1. Introduction Proton transport as the principal electrical conduction mechanism in oxides at elevated temperatures is a relatively rare phenomenon which may be exploited in electrochemical devices for the production, separation or oxidation of hydrogen.1-4 Solid oxide fuel cells with proton-conducting electrolytes (protonic ceramic fuel cells, PCFCs) operate within an intermediate temperature range (400-800 C), converting hydrogen without the need for either noblemetal catalysts or fuel recirculation at the anode.5 High levels of proton transport in oxides may also be exploited as hydrogen and humidity sensors,6-9 and in chemical reactors for various important industrial reactions, such as ammonia generation,10 and the partial oxidation11 and reforming12 of methane. Mixed protonic-electronic con*To whom correspondence should be addressed. E-mail:
[email protected].
(1) Iwahara, H.; Asakura, Y.; Katahira, K.; Tanaka, M. Solid State Ionics 2004, 168, 299. (2) Norby, T. Solid State Ionics 1999, 125, 1. (3) Bonanos, N. Solid State Ionics 1992, 53-56, 967. (4) Kreuer, K. D. Ann. Rev. Mater. Res. 2003, 33, 333; Malavasi, L.; Fisher, C. A. J.; Islam, M. S. Chem. Soc. Rev. 2010, in press (DOI: 10.1039/B915141A). (5) Coors, W. G. J. Power Sources 2003, 118, 150. (6) Matsumoto, H.; Suzuki, T.; Iwahara, H. Solid State Ionics 1999, 116, 99. (7) Iwahara, H.; Uchida, H.; Ogaki, K.; Nagato, H. J. Electrochem. Soc. 1991, 138, 295. (8) De Schutter, F.; Vangrunderbeek, J.; Luyten, J.; Kosacki, I.; Van Landschoot, R.; Schram, J.; Schoonman, J. Solid State Ionics 1992, 57, 77. (9) Hassen, M. A.; Clarke, A. G.; Swetnam, M. A.; Kumar, R. V.; Fray, D. J. Sens. Actuators 2000, B 69, 138. (10) Marnellos, G.; Stoukides, M. Science 1998, 282, 98. (11) Asano, K.; Hibino, T.; Iwahara, H. J. Electrochem. Soc. 1995, 142, 3241. (12) Hibino, T.; Hamakawa, S.; Suzuki, T.; Iwahara, H. J. Appl. Electrochem. 1994, 24, 126.
pubs.acs.org/cm
ductors are of use as hydrogen-separation membranes13 and, as recently demonstrated, for wireless electrochemical promotion of catalysis.14 The highest proton conductivities known for the solid state are exhibited by Ba- and Sr-based perovskites; these compounds are basic in character, and tend to be unstable in acidic gases such as CO2. Research into alternative high-temperature proton conductors which are not based on Ba or Sr has mostly focused on phosphates, such as LaPO4 and CePO4,15-17 and gallates,18 which are formed of tetrahedral XO4 (X =P, Ga) structural units. More recently, rare-earth orthoniobates and orthotantalates with tetrahedral moieties have been reported by Haugsrud and Norby19,20 as proton-conducting systems with better stability and moderate levels of proton transport. In this study, we focus on lanthanum orthoniobate (LaNbO4), which, on acceptor doping with Ca or Sr, exhibits the highest proton conductivity of the orthoniobate/ orthotantalate series, ∼1 10-3 Scm-1, in wet reducing conditions at 800 C. At temperatures above 500 C, where useful levels of proton conductivity are achieved, LaNbO4 adopts the tetragonal scheelite-type structure; below 500 C, a transition to the fergusonite structure with monoclinic symmetry occurs. (13) Norby, T.; Larring, Y. Solid State Ionics 2000, 136-137, 139. (14) Poulidi, D.; Mather, G. C.; Metcalfe, I. S. Solid State Ionics 2007, 178, 675. (15) Norby, T.; Christiansen, N. Solid State Ionics 1995, 77, 240. (16) Kitamura, N.; Amezawa, K.; Tomii, Y.; Hanada, T.; Yamamoto, N.; Omata, T.; Otsuka-Yao-Matsuo J. Electrochem. Soc. 2005, 152, A488. (17) G omez del Moral, E.; Fagg, D. P.; Chinarro, E.; Abrantes, J. C. C.; Jurado, J. R.; Mather, G. C. Ceram. Int. 2009, 35, 1481. (18) Li, S.; Sch€ onberger, F.; Salter, P. Chem. Commun. 2003, 21, 2694. (19) Haugsrud, R.; Norby, T. Nat. Mater. 2006, 5, 193. (20) Haugsrud, R.; Norby, T. Solid State Ionics 2006, 177, 1129.
Published on Web 10/06/2010
r 2010 American Chemical Society
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In addition to proton transport, LaNbO4 displays a number of other enticing properties. The phase transition to the monoclinic polymorph is associated with stress-induced ferroelasticity,21 of interest for novel energy-absorbing applications.22 The ferroelasticity of the monoclinic polymorph has been correlated to excellent dielectric microwave properties, as recently reported.23 The multifunctionality of LaNbO4 extends to photoluminescence, as it emits light with blue and ultraviolet wavelengths on excitation by ultraviolet and X-ray radiation, respectively.24,25 However, rather little is known of the defect properties of LaNbO4 on the microscopic level. Computer simulation techniques are highly informative in probing the defect properties of materials on the atomic scale, as previous successful studies of ceramic oxide-ion and proton conductors have demonstrated.26-30 In this paper, we employ atomistic simulation, first to reproduce the high-temperature structure of LaNbO4, and then to study the defect and dopant behavior. Using these techniques, we investigate the energetic and mechanistic features of intrinsic defects, dopant and proton incorporation, and defect association. 2. Simulation Methodology Comprehensive reviews of the atomistic simulation techniques incorporated in the General Utility Lattice Program (GULP) are available elsewhere.31,32 In brief, the simulation involves calculation of the potential energy of the system in terms of atomic coordinates, with ionic interactions described as ionic pairwise potentials. The Born model was used, in which the potential energy is partitioned into long-range Coulombic terms and short-range terms approximating Pauli repulsion and dispersive energies. The short-range pair potentials (up to 15 A˚) were specified in the Buckingham form, ! r Cij φij ¼ Aij exp - 6 ð1Þ Fij r where parameters Aij, Fij, and Cij are specific to each ion-ion interaction. Electronic polarizibilities of the ions were taken into account using the shell model developed by Dick and Overhauser.33 Charged defects such as oxygen vacancies or aliovalent dopants cause significant perturbation of the surrounding lattice. The energy of such a defect relative to the perfect, energy-minimized lattice was calculated using a two-region (Mott-Littleton) approach,34 with the lattice partitioned into inner and outer spherical regions centered on an individual defect or defect cluster. Ions in the inner region (>1500 atoms) were relaxed explicitly, (21) Takei, H.; Tunekawa, S. J. Cryst. Growth 1977, 38, 55. (22) Virkar, A. V.; Jue, J. F.; Smith, P.; Metha, K.; Prettyman, K. Phase Transitions 1991, 35, 27. (23) Kim, D.-W.; Kwon, D.-K.; Yoon, S. H.; Hong, K. S. J. Am. Ceram. Soc. 2006, 89, 3861. (24) Blasse, G.; Brixner, L. H. Chem. Phys. Lett. 1977, 38, 55. (25) Hsiao, Y. J.; Fang, T. H.; Chang, Y. S.; Chang, Y. H.; Liu, C. H.; Ji, L. W.; Jywe, W. Y. J. Lumin. 2007, 126, 866. (26) Mather, G. C.; Islam, M. S. Chem. Mater. 2005, 17, 1736. (27) Fisher, C. A. J.; Islam, M. S. J. Mater. Chem. 2005, 15, 3200. (28) Mather, G. C.; Islam, M. S.; Figueiredo, F. M. Adv. Funct. Mater. 2007, 17, 905. (29) Islam, M. S.; Slater, P. R. Mater. Res. Soc. Bull. 2009, 34, 935. (30) Stokes, S. J.; Islam. M. S. J. Mater. Chem. 2010, 20, 6258. (31) Gale, J. D. J. Chem. Soc., Faraday Trans. 1997, 97, 33. (32) Catlow, C. R. A. In Cheetham, A. K.; Day, P., Eds.; Solid State Chemistry: Techniques; Clarendon Press: Oxford, U.K., 1987. (33) Dick, B. G.; Overhauser, A. W. Phys. Rev. 1958, 112, 90. (34) Mott, N. F.; Littleton, M. J. Trans. Faraday Soc. 1938, 34, 485.
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Figure 1. Crystal structure of scheelite-type LaNbO4 showing NbO4 tetrahedra. Table 1. Interatomic Potentials for LaNbO4 (i) Buckingham Potentials (cutoff = 15 A˚) interaction
A (eV)
F (eV)
C (eV A˚6)
La3þ 3 3 3 O2Nb5þ 3 3 3 O2O2- 3 3 3 O2-
1545.21 1286.9583 22764.36
0.359 0.371525 0.149
0.00 0.00 27.89
(ii) Shell Modelb species
Y (e)
k (eV A˚-2)
Nb5þ O2-
-4.596 -2.758
5916.77 30.211
b
Y and k are the shell charge and harmonic force constant, respectively.
whereas the remainder of the crystal, where the defect forces are relatively weak, were treated by more approximate quasicontinuum methods.
3. Results and Discussion 3.1. Crystal Structure and Intrinsic Atomic Defects. The tetragonal, high-temperature structure of LaNbO4, shown in Figure 1, is isostructural with scheelite (CaWO4), with the Nb5þ cations residing in undistorted NbO4 tetrahedra.35 To model the crystal structure, initial sets of potential parameters were taken from the literature36,37 and fitted to the reported scheelite-type structure of LaNbO4 under constant pressure conditions. Phonon densities of states were also calculated to confirm the structure was stable. The final potential parameters and calculated structural parameters are listed in Tables 1 and 2, respectively. The agreement with unit-cell parameters and bond lengths obtained from neutron diffraction35 is very good (Table 2). The calculated dielectric constants, although not reproducing the experimental values reported for LaNbO4 exactly,23 are on the same order of magnitude. Given the uncertainties typically associated with dielectric-constant measurements, and the approximations (35) David, W. I. F. Mater. Res. Bull. 1983, 18, 749. (36) Khan, M. S.; Islam, M. S.; Bates, D. R. J. Phys. Chem. B 1998, 102, 3099. (37) Donnerberg, H.; Exner, M.; Catlow, C. R. A. Phys. Rev. B 1993, 47, 14.
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Table 2. Calculated and Experimental Properties of LaNbO4
Table 3. Frenkel and Schottky Disorder
Unit Cell Parameters (A˚)
type
param
expa
calcd
difference
a c
5.4009 11.6741
5.4347 11.6890
0.0338 0.0149
Bond Lengths (A˚) bond
exp
calcd
difference
La-O 4 La-O 4 Nb-O 4
2.5052 2.5209 1.8628
2.4493 2.5151 1.9657
-0.0559 -0.0058 0.1029
Dielectric Constants param
expb
calcd
ε0 ε¥
19.3
11 3
Elastic Constants (GPa)
a
param
calcd
c11 c33 c12 c13 c16 c44 c66
237 160 117 73 -18 39 68
See ref 35. b See ref 23
of the model, the calculated value is satisfactory. The difference is unlikely to have a drastic effect on the calculated properties or energies, particularly the relative energies and overall trends. The calculated elastic constants are also listed in Table 2, although to the best of our knowledge, no experimentally determined elastic properties for high-temperature LaNbO4 have yet been reported. Intrinsic defects in an ionic solid, including Frenkeland Schottky-type disorder, can give rise to intrinsic diffusion of ions. However, such point defects are difficult to study experimentally on the atomic scale. Simulation techniques enable these defects to be examined with atomic resolution, and thus provide a useful probe of intrinsic defect behavior. In this study, the energies of isolated intrinsic defects such as vacancies and interstitials were calculated, from which the enthalpies of the various Frenkel and Schottky disorder types were determined. The calculation of the latter also required calculation of the lattice energies of La2O3,36 Nb2O5,38 and LaNbO4. The resulting defect energies are listed in Table 3. The most favorable intrinsic disorder type in LaNbO4 is the O Frenkel defect (Table 3), although its magnitude indicates that a negligible concentration of such species will be present. The La Frenkel defect requires substantially more energy, whereas the energy of the Nb Frenkel defect could not be determined because of the inability of the structure to accommodate Nb5þ interstitial ions with their high charge. (38) Baetzold, R. C. Phys. Rev. B 1993, 48, 5789.
defect equation
energy (eV/defect)
000
LaLa f La••• i þ VLa OO f O00i þ V•• O 000 00000 LaLa þ NbNb þ 4OO f VLa þ VNb •• þ 4VO þ LaNbO4 000 La Schottky-type 2LaLa þ 3OO f 2VLa þ 3V•• O þ La2O3 00000 Nb Schottky-type 2NbLa þ 5OO f 2VNb þ 5V•• O þ Nb2O5
La Frenkel O Frenkel Schottky
7.45 3.53 5.60 4.08 6.62
The arrangement of Nb-O4 tetrahedra around an oxygen vacancy is shown schematically in Figure 2. Significant relaxation of Nb-O4 tetrahedra about the oxygen vacancy results in the formation of an [Nb2O7]4- group (Figure 2b), with two tetrahedra corner-sharing an oxygen. This is facilitated by rotation of the nearer of the two [NbO4]3tetrahedra in the [Nb2O7]4- group to the vacancy defect center with respect to the perfect structure. We note that condensation of two or three Nb-O4 units around a doubly ionized oxygen vacancy forming an [Nb2O7]4- or [Nb3O11]7group has been reported recently by Kuwabara et al. based on DFT calculations.39 Given the similarity of the double-tetrahedral units we find here to those which form in the La1-xBa1þxGaO4-x/2 ionic conductor,40 we conjecture that oxide-ion transport in LaNbO4 also involves the breaking and reforming of the [Nb2O7]4- units in a cooperative “cogwheel-type” process, as in the gallate. Further examination of this process, for example, by molecular dynamics, while beyond the scope of the present study, needs to be undertaken. 3.2. Dopant-Ion Substitution and Dopant-Vacancy Association. Increasing the dopant content in LaNbO4 beyond that which has been achieved to date (∼2 at %)41 is likely to be an important strategy for improving its proton conductivity. With this in mind, we have calculated the relative incorporation energies of a variety of dopant species for different charge-compensation mechanisms. Although the prediction of the solubility limit of a particular dopant is a much more demanding task, the relative energies provide useful information about trends in dopant solubility between different species. The relative energetics of dopant incorporation were assessed for a range of both divalent and tetravalent dopants on the La and Nb sites, respectively. Formation of oxygen vacancies was found to be the most energetically favorable compensation mechanism according to 1 1 1 •• = MO þ La La þ OO f MLa þ La2 O3 þ VO 2 2 2
ð2Þ
and 1 1 1 •• = MO2 þ Nb Nb þ OO f MNb þ Nb2 O5 þ VO 2 2 2
ð3Þ
(39) Kuwabara, A.; Haugsrud, R.; Stlen, S.; Norby, T. Phys. Chem. Chem. Phys. 2009, 11, 5550. (40) Kendrick, E.; Kendrick, J.; Knight, K. S.; Islam, M. S.; Slater, P. R. Nat. Mater. 2007, 6, 871. (41) Mokkelbost, T.; Kaus, I.; Haugsrud, R.; Norby, T.; Grande, T.; Einasrud, M.-A. J. Am. Ceram. Soc. 2008, 91, 879.
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Figure 2. Arrangement of selected NbO4 tetrahedra in (a) the ideal LaNbO4 structure and (b) in the neighborhood of an oxygen vacancy (indicated with a square), showing the formation of an [Nb2O7]4- group (blue).
where M represents the aliovalent dopant. The interatomic potentials for the dopant cations were taken from studies of the corresponding binary metal oxides.42-46 The energies of the above reactions were then evaluated by combining the corresponding defect- and lattice-energy terms. The calculated solution energies as a function of ionic radius for LaNbO4 are plotted in panels a and b in Figure 3 for substitution on the La and Nb sites, respectively. Two main points emerge from these results. First, the most favorable dopants for substitution on the La site are Ca2þ and Sr2þ. These dopants are associated with the highest proton conductivity reported to date for LaNbO4.19,20 That these dopants exhibit the lowest solution energies may be rationalized in terms of their similar size47 to the host cation: 1.12 A˚ for Ca2þ and 1.26 A˚ for Sr2þ in 8-fold coordination compared with 1.16 A˚ for La3þ. The high solution energies of other divalent dopants with ionic radii much larger or smaller than La implies that lattice strain due to ion-size mismatch plays a significant role in determining dopant solubility. A similar phenomenon has been observed in fluorite- and perovskite-based ion conductors. Second, the solution energy associated with doping on the Nb site also shows a strong dependence on ionic radii, with the dopants Ti4þ (IVrTi4þ = 0.42 A˚),47 Sn4þ (0.55 A˚), and Zr4þ (0.59 A˚), of similar ionic radii to the host Nb5þ cation (0.48 A˚), showing the lowest solution energies. Extrinsic oxygen vacancies formed on doping with subvalent cations can be trapped by the dopant, as is well documented,48 leading to defect clustering and to higher activation energies for oxide-ion conductivity. The effects of defect clustering are important in oxide-ion-conducting perovskite systems, but have not been studied in the LaNbO4 system. Whereas trapping of oxide-ion vacancies is evidently disadvantageous for applications involving oxide-ion (42) Lewis, G. V.; Catlow, C. R. A. J. Phys. C, Solid State Phys. 1985, 18, 1149. (43) Cherry, M.; Islam, M. S.; Catlow, C. R. A. J. Solid State Chem. 1995, 119, 125. (44) Freeman, G. M.; Catlow, C.R.A. J. Solid State Chem. 1990, 85, 65. (45) Cherry, M.; Islam, M. S.; Gale, J. D.; Catlow, C. R. A. J. Phys. Chem. 1995, 99, 14614. (46) Dwivedi, A.; Cormack, A. N. Philos. Mag., A 1990, 61, 1. (47) Shannon, R. D. Acta Crystallogr., Sect. A 1976, 32, 751. (48) Kilner, J. A. Solid State Ionics 2000, 129, 13.
Figure 3. Calculated solution energies as a function of dopant ionic radius for (a) divalent dopants on the La site (8-fold coordination) and (b) tetravalent dopants on the Nb site (4-fold coordination). Dashed lines are guides for the eye only. Table 4. Calculated Binding Energies of M/-V•• O Pair Clusters and M/-OH•O Proton-Dopant Association Energies in LaNbO4 for Favorable Dopant Species binding energy (eV) dopant cation
dopant radius
M/-V •• O
M/-OH•O
Ca/La Sr/La Ti/Nb Sn/Nb Zr/Nb
1.12 1.26 0.42 0.55 0.59
-0.45 -0.46 -1.10 -0.90 -0.92
-0.18 -0.30 -2.46 -1.30 -1.34
transport, similar phenomena in proton-conducting oxides may have both beneficial and detrimental effects. For proton-conducting electrolytes, high levels of oxide-ion conductivity are undesirable. However, mixed proton and oxide-ion conductivity in ceramic membranes, giving rise to steam permeation, provides a method of direct hydrocarbon reforming in the anode compartment of a PCFC, in addition to having other potential applications.49,50 The energies of defect clusters in LaNbO4 were evaluated based on simple pair clusters (M/-V •• O) of a divalent or tetravalent dopant ion and nearest neighbor oxygen vacancy. The pair-cluster binding energies, shown in Table 4 for the most favorable divalent and tetravalent dopant species, respectively, were calculated according to Ebind ¼ Ecluster - ΣEisolated defects (49) Coors, W. G. J. Electrochem. Soc. 2004, 151, A994. (50) Coors, W. G. Solid State Ionics 2007, 178, 481.
ð4Þ
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Inspection of Table 4 reveals that the pair-defect cluster energies are favorable for all divalent and tetravalent dopants examined. It is expected, therefore, that clustering, with its associated higher oxide-ion migration energies and thus lower oxide-ion diffusion coefficients, may be significant in doped LaNbO4. We note that for the range of divalent and tetravalent dopants examined here, lower binding energies are observed with increasing dopant ion radius. 3.3. Water Incorporation and Dopant-Proton Association. Incorporation of mobile protons in the LaNbO4 structure is understood to involve filling of oxygen vacancies with hydroxyl groups in wet or hydrogen-containing atmospheres, with the second proton attaching itself to a lattice oxygen • •• H2 O þ O O þ VO f 2OH
Table 5. Parameters for the O-H Interaction Morse potential
D (eV)
β (A˚-1)
ro (A˚)
O3 3 3H
7.0525
2.1986
0.9485
A (eV)
F (A˚)
C (eV A˚6)
311.97
0.2500
0
Buckingham potential O3 3 3H
Table 6. Calculated Parameters for H2O Incorporation (EH2O) and O-H Bond Lengths EOH (eV)a
EH2O(eV)
O-H (A˚)
15.16
-0.25
0.982
a
Includes Morse potential.
ð5Þ
The energetics of water incorporation were evaluated using the same methodology as that employed in previous studies of proton-conducting oxides26,51,52 according to EH2 O ¼ 2EOH - EVO•• þ EPT
ð6Þ
where EOH is the energy associated with replacing an O2ion with an OH- group, EV••O is the energy needed to create an oxygen vacancy, and EPT is the energy of the gas-phase reaction O2- þ H2O=2OH-.53,54 A Morse potential was used to model the attractive O-H interaction VðrÞ ¼ Df1 - exp½ - βðr - ro Þg2
ð7Þ
using parameters (Table 5) developed from ab initio quantum mechanical cluster calculations,55 with a point charge representation of the surrounding lattice. The dipole moment of the O-H group was included by placing charges of -1.4263 and þ0.4263 on the O and H species, respectively (to give an overall charge of -1), and the interaction between lattice oxygens and the hydroxyl group was taken into account with an additional Buckingham potential term.56 Table 6 lists the calculated values for EOH, EH2O, and the O-H bond length after relaxation. As with previous studies,26,51 our simulation technique may be used to probe the proton site and investigate the most energetically favorable O-H configuration. After structural relaxation, the proton is oriented toward a neighboring oxygen along an edge of the Nb-O4 tetrahedron, as shown schematically in Figure 4. The equilibrium O-H distance, 0.98 A˚, has not been reported previously for LaNbO4. This value is very similar to that determined by atomistic simulation for the proton-conducting perovskite oxides SrCeO3 (0.986 A˚)26 and BaCeO3 (0.99 A˚).52
(51) Davies, R. A.; Islam, M. S.; Gale, J. D. Solid State Ionics 1999, 126, 323. (52) Gl€ ockner, R.; Islam, M. S.; Norby, T. Solid State Ionics 1999, 122, 145. (53) Wright, K.; Freer, R.; Catlow, C. R. A. Phys. Chem. Miner. 1995, 20, 500. (54) Catlow, C. R. A. J. Phys. Chem. Solids 1977, 28, 1131. (55) Saul, P.; Catlow, C. R. A. Philos. Mag. B 1985, 51, 107. (56) Schr€ oder, K. P.; Sauer, J.; Leslie, M.; Catlow, C. R. A.; Thomas, J. M. Chem. Phys. Lett. 1992, 188, 320.
Figure 4. Orientation of proton (blue) relative to an [NbO4]3- tetrahedron.
Haugsrud and Norby report a hydration enthalpy of approximately -1.2 eV for La0.99Ca0.01NbO4-δ determined from conductivity studies,19,20 which is slightly less negative than better proton conductors such as acceptordoped SrCeO3 and BaCeO3. Our model also gives a negative value of -0.25 eV for the hydration energy, consistent with the exothermic uptake of protons from water in the atmosphere. A possible explanation for the calculated value not being as negative as the measured value is that the former does not include the influence of grain boundaries on the energetics of water absorption. It is worth noting that grain boundaries play an important role in proton absorption and transport in wet atmospheres in the low-temperature range.57,58 Fjeld et al.58 have noted that protons are the major charge carriers in the grain boundaries at 400 C where the monoclinic LaNbO4 polymorph stabilizes, although the grain-boundary conductivity is much lower than that of the grain interior. Similar behavior is likely for the tetragonal form as well. Future simulation studies of protons at grain boundaries in this material could help shed light on this intriguing phenomenon. Because of their net positive charge relative to the lattice, protons may associate with subvalent dopant species, in an analogous manner to dopant-vacancy association, with a concomitant decrease in proton mobility. Protontrapping effects have been observed experimentally59,60 (57) Poulidi, D.; Mather, G. C.; Tabacaru, C. N.; Thursfield, A.; Metcalfe, I. S. Catal. Today 2009, 146, 279. (58) Fjeld, H.; Kepaptsoglou, D. M.; Haugsrud, R.; Norby, T. Solid State Ionics 2010, 181, 104. (59) Karmonik, C.; Udovic, T. J.; Paul, R. L.; Rush, J. J.; Lind, K.; Hempelmann, R. Solid State Ionics 1998, 109, 207. (60) Matzke, Th.; Stimming, U.; Karmonik, Ch.; Soetratmo, M.; Hempelmann, R.; G€ uthoff, F. Solid State Ionics 1996, 86-88, 621.
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and simulated by both quantum mechanical and atomistic techniques in other proton-conducting oxides.26,51,61 Recent neutron-spin-echo experiments 62 on proton dynamics in hydrated BaZr0.9Y0.1O2.95 indicate that the proton spends an extended time in the vicinity of a dopant Y cation prior to further diffusion. The binding energy associated with a cluster comprised of an OH group and an adjacent dopant cation was calculated as the difference between the sum of the isolated defects and the cluster energy Ebind ¼ EðM= - OH•O Þ - fEðM= Þ þ EðOH•O Þg
ð8Þ
The negative values for the binding energies, shown in Table 4, indicate that M/Nb-OH• and M/La-OH• clusters are likely to form, with the lowest binding energies found for divalent dopants on the La site. The smallest protondopant association energy is expected for Ca2þ. Although proton conductivity in LaNbO4 has not been documented for many different dopants, Ca2þ and Sr2þ are the species which are reported to produce the most appreciable proton transport.19,20 These results indicate that proton mobility is very sensitive to the type of acceptor dopant ion, and may be related to basicity as well as ion-size factors. An analogy may be drawn with the SrCeO3 protonconducting system, in which the Y3þ and Yb3þ dopants most often associated with high proton conductivity were found to have the lowest M/-OH• binding energies.26 The results of both studies suggest the important influence of ion-size mismatch and elastic strain between host and dopant on proton-trapping in solid-state proton conductors. The minimum binding energy should thus occur when the ionic radii of dopant and host are approximately the same. (61) Islam, M. S.; Davies, R. A.; Gale, J. D. Chem. Mater. 2001, 13, 2049. (62) Karlsson, M; Engberg, D.; Bjorketun, M. E.; Matic., A.; Whanstrom, G.; Sundell, P. G.; Berastergui, P.; Ahmed, I.; Falus, P.; Farago, B.; Borjesson, L.; Eriksson, S. Chem. Mater. 2010, 22, 740.
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4. Conclusions Computer modeling techniques have been used to examine the energetics of defects, dopants and clustering in scheelite-type LaNbO4. This study is relevant to the potential applications of LaNbO4, in particular electrochemical devices based on the proton-conducting properties of the doped system. The main results can be summarized as follows. (1) The simulation model successfully reproduces the observed complex scheelite-type LaNbO4 structure. The energies calculated for intrinsic atomic defects are relatively high. The formation of an oxygen vacancy is accompanied by rearrangement of the adjacent [NbO4]3- tetrahedra to form an [Nb2O7]4- unit. (2) Dopant substitution is found to be most favorable for Ca2þ and Sr2þ on the La site; the similar size of these dopants to the host cation indicates the importance of minimizing elastic strain on acceptor doping. Solution on the Nb site is of higher energy but, as for doping on the La site, the most favorable dopants are those of similar ionic radii to Nb, namely Ti4þ, Sn4þ, and Zr4þ. Dopant-vacancy association is predicted to be favorable for simple pair clusters M/La-V •• O. (3) Water dissolution is calculated to be exothermic with an equilibrium O-H distance of 0.98 A˚. Binding energies for M/-OH• pairs are calculated to be favorable for all examined dopants. The weakest association is found for Ca2þ, one of the dopants associated with the highest proton conductivity in LaNbO4. This indicates that elastic strain not only influences dopant incorporation energies but also the proton-trapping energy, which is minimized for dopants with similar ionic radii to the host cation. Acknowledgment. G.C.M. thanks the British Council (program “Marina Bueno” ref EST000785) for a travel and subsistence grant.
