ARTICLE pubs.acs.org/JPCA
Cation Environment of BaCeO3-Based Protonic Conductors II: New Computational Models Antonio Cammarata,†,‡ Antonio Emanuele,‡ Antonino Martorana,† and Dario Duca*,† †
Dipartimento di Chimica Inorganica e Analitica “Stanislao Cannizzaro” dell’Universita di Palermo, viale delle Scienze Ed. 17, I-90128 Palermo, Sicily ‡ Dipartimento di Scienze Fisiche e Astronomiche dell’Universita di Palermo, via Archirafi 36, I-90123 Palermo, Sicily ABSTRACT: Quantum chemical calculations have been carried out to simulate Y-doped BaCeO3 derivatives. Hartree-Fock energy functional was used to study octahedral site environments embedded in a Pmcn orthorhombic framework, showing local arrangement characterized by Ce-O-Ce, Ce-O-Y, and Y-O-Y (Z-O-Ξ) configurations and including or not hydrogen close to the moieties encompassing those configurations. The latter are, in fact, representative of - and, in our modeling approach, were treated as - local arrangements that could be found in Y:BaCeO3-doped materials. The geometrical optimizations performed on the structural models and a detailed orbital analysis of these systems allowed us to confirm and deepen new interpretations, concerning experimental findings already reported in the literature. In particular, the bimodal distribution characterizing the Y-O first coordination shell, found by EXAFS analysis, could be attributed to a local clustering of Y atoms showing characteristic Y-O-Y arrangements. Moreover, the local charge analysis, characterizing the models containing or not hydrogen atoms, showed that the moving protons are able to dynamically change the properties of their near environment, in any case, leaving unaltered the global protonic conduction features of the material, irrespective of the kind of cation in a given Z-O-Ξ moiety.
’ INTRODUCTION Hydrated perovskite-type ABO3 oxide materials are often characterized by protonic conduction properties, drawing, for this, great interest connected to their possible technological applications in the field of membrane reactors, hydrogen sensors, batteries and fuel cells.1,2 Much research efforts were thus addressed to understand the elementary processes implied in protonic phenomena related to these materials, mostly to improve stability and efficiency of practical devices, working at temperatures ranging inbetween 600-1100 K. To generate protonic conduction in given perovskite materials, hydrogen atoms must be incorporated into the corresponding material structures. This is usually accomplished by a two-step procedure. In the first, stated amounts of tetravalent B centers are substituted by trivalent species. The formation of one oxygen vacancy per couple of doping cations introduced in the solid matrix is in this way produced. In the second, water vapor is steamed on the doped material to produce structural O-H groups, having acidic properties. In the following, the dissociative water adsorption process producing acidic centers (i.e., mobile protons) is schematically represented by using the Kr€ oger-Vink notation: X • H2 OðgÞ þ V •• O þ OO / 2OHO
ð1Þ
Protons are in this way introduced into the host matrix, while hydrogen diffusion, occurring through adjacent oxygen atoms,3 may arise.4,5 The mechanism of protonic conduction is as a consequence strongly influenced by local distortions, affecting r 2011 American Chemical Society
the proton environment and namely involving doped B-sites.6 For this, the study of the local environments surrounding the doped sites becomes of basis importance in rationalizing local conduction details.4 Yttrium-doped barium cerate (Y:BaCeO3) is generally considered as a reference compound for the perovskite-type proton conductors. The effects of yttrium centers on the barium cerate Pmcn structure7 after water adsorption were studied by neutron diffraction.7,8 Although the studies aimed at the characterization of the longrange average structures of the perovskite-type protonic conductors are common in literature, the local arrangements of the different environments characterizing the same materials have not been thoroughly investigated up to now. However, X-ray absorption (XAS) studies on the octahedral environments of barium cerate materials, involving yttrium,9,10 indium,11 and gadolinium12 as dopants, recently shed light on particular features of these compounds. As an example, it has been shown that the Y3þ cations induce distortions in the surrounding oxygen atoms; these modifications are still present at 750 K. Therefore, they can be related to the peculiar interactions of the yttrium atoms with the barium cerate host matrix. Moreover, Kreuer pointed out that nonhomogeneity of the oxygen network can hinder proton mobility2 and actually, at liquid nitrogen temperature, the XANES region of the Received: July 26, 2010 Revised: January 10, 2011 Published: February 11, 2011 1676
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Figure 1. Z|Ξ:Ba12Ce22O61H2 ODSM fragment: Ba, Ce, O, and H centers are blue, purple, red, and pink; Ξ and Z sites (Z|Ξ = Ce|Ce, Y|Y, and Ce|Y) inside the central octahedral moieties are green. Unprotonated and protonated systems (see text) were modeled starting from the pictured fragment. At variance with the unprotonated systems (exactly corresponding to the illustrated fragment), in the protonated ones, the H atom on the right was removed and placed close to the O center, bridging Z and Ξ atoms (O4, in Figures 2 and 3).
XAS pattern is consistent with local structure changes, with respect to the dry sample, that are associated with the preferential insertion of hydroxyl groups in the vicinity of the doped B-sites. A strong dopant-hydroxyl interaction was also observed using quasi-elastic neutron-scattering experiments on Yb-doped strontium cerate.13 As already stated, computational analyses could be useful in discriminating between structural and electronic factors, influencing perovskite-type oxides’ properties. In fact, several computational works appeared in literature, characterizing dopant selectivity,14,15 chemistry environment of the defects14,16,17 as well as proton mobility.18,19 Both cluster and periodic-boundary-condition (PBC) approaches were, respectively, employed to model local defects and to reproduce crystalline structures.14,19-21 In this work, BaCeO3 and Y:BaCeO3 clusters, also embedding H atoms in the perovskite framework, have been studied by quantum-chemistry (QC) approaches. In the frame of this paradigm, geometric optimizations were performed on large fragments cut from neutron-scattering refined structures whose space groups belonged to the orthorhombic (Pmcn) systems.7 To describe yttrium-doped barium cerate materials, the rearrangements of the atomic centers surrounding the Y atoms in yttrium-doped barium cerate materials was recently attributed to a random sustitution of Ce with Y atoms,9,10 provided that a clear evidence of dopant clustering could not be demonstrated. In the following, the representation having just Ce atoms in the cation coordination shell of yttrium will be denominated octahedron singlesubstitution model (OSSM). In particular, the OSSM local arrangements should be able to account for the peculiar axial distortions, which caused the experimentally determined local anisotropy found for the Y-O bond distances, both in orthorhombic10 and not orthorhombic systems.22 CMDjpcA_6381 indeed modeled the OSSM BaCeO3 configuration by QC method,23 finding, however, only one Y-O distance, against the bimodal distribution singled out by the experiments.9,10,12 Conversely, the computational findings
above suggested that the bimodal distribution could be actually related to a peculiar clustering of yttrium atoms.23 Starting from these results and in the aim to better characterize the title systems, we here propose new models able to explain the Y-O distance anisotropy and related conduction properties, own of perovskite materials. These models involve the substitution of two Ce atoms, both belonging to vicinal octahedra, with two Y atoms. In the following, this modeling representation will be denominated octahedron double-substitution model (ODSM). In the next section (Models and Computational Details), methodologies and modeling details concerning three different ODSMs, having Ce-Ce, Ce-Y, and Y-Y neighboring octahedron centers, are presented, while in the Results and Discussion section, findings and outcomes arising from the application of a cluster approach23,24 on the three models are detailed. Local electronic investigations, including Mulliken charge analysis25,26 (M-ca) and partial density of states27 (P-DOS) in the frame of the C-squared population analysis28 (C-SPA), are also reported and discussed.
’ MODELS AND COMPUTATIONAL DETAILS The two-octahedra ODSM cluster-systems employed in this work, and shown in Figure 1, were cut, so to optimize computational needs and findings’ reliability, from an orthorhombic Pmcn structure resolved by neutron-scattering experiments.29 The symmetry of the fragments assured absence of dipole moment on the resulting systems, which were consistently studied as singlet states. When the formal charges of the atoms are those of the crystalline structures, the chosen stoichiometry Z|Ξ:Ba12Ce22O61H2, with Z|Ξ representing the vicinal pairs Ce|Ce, Y|Y, and Ce|Y, is characterized by a fragment charge equal to 0 only for Ξ = Z = Ce. Even so, only the Ce|Y:ODSM (with the notation Z|Ξ:ODSM, a model is singled out in which the octahedral vicinal atom pair is set by Z and Ξ) structure was calculated fixing its charge at -1. To the Y|Y:ODSM model was conversely 1677
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Figure 2. Details on the optimized atoms embedded in the ODSM fragment of Figure 1. Octahedral central atom pairs (Z|Ξ = Ce|Ce, Ce|Y, and Y|Y) represent the zeros of the parallel numberings, individuating Ba (1-4) and O (1-11) atoms. For convenience, the atom sets {O1, O2, O7, O8} and {O5, O6, O10, O11} along the text are also called neighboring (with respect to the O4 center) vertical and horizontal oxygens, respectively.
attributed charge 0, as already done in a preceding study on Y2: Ba8Ce25O62 fragment.23 The Z|Ξ:Ba12Ce22O61H2 fragments show both oxygen and cerium dangling atoms. The presence of the latter was a necessary choice that allowed us (i) to avoid the introduction of spurious cutoff atoms and (ii) to preserve the lowest formal charge in the fragment, without losing consistency in the computational results. Following a computational protocol already employed for studying perovskites,23 the optimizations were performed just on the coordinates of a bulk moiety, namely, the Z|ΞBa4O11 moiety of Figure 2 embedded in the ODSM fragments and including Z and Ξ vicinal centers, whereas the remaining coordinates were kept fixed to those values setting the external atom cage (externalframe) of the starting Pmcn29 fragment cuts, shown in Figure 1. Unprotonated and protonated systems were considered. The former were modeled by optimizing Z|Ξ: Ba12Ce22O61H2 fragments, as that reported in Figure 1, while in the latter, one of the external hydrogen atoms, present in the previously optimized Z|Ξ: Ba12Ce22O61H2 fragments, was put close to the O4 center of the Z|ΞO11 inner octahedra (for details, see caption of Figure 1) and then relaxed by final calculations, including the coordinate optimization of the Z|ΞBa4O11 moieties. As previously done,23 periodic boundary conditions were not applied. The imposition of artificial replicas of the local ODSM structure on adjacent supercells and all over the 3-D crystal framework, also causing cooperative physical effects difficult to be individualized and eventually rationalized, was in this way avoided. The Gaussian03 (G03) suite of programs30 was employed to perform the calculations in the frame of the Hartree-Fock (HF) paradigm.26 This option was mainly determined by considering previous results on similar systems, showing that the local description of the geometrical and charge characteristics of perovskite systems are exhaustively captured by ECP basis sets (see below) in the frame of the HF paradigm.23 Geometry optimizations were carried out with the SCF component of the calculation performed by a linear search method, followed, if needed, by a quadratic minimum search method,31 using the G03 standard convergency criteria. The O atoms belonging to the blocked external frame and to the inner octahedra were treated by 3-21G32 and 6-31þG(d,p)33 basis sets, respectively. The latter was also used for the H atoms, irrespective of considering protonated or unprotonated models. The CRENBL ECP,34 the SBKJC VDZ ECP,35 and the Stuttgart RSC 1997 ECP36 pseudopotentials were consistently employed for the Ba, Ce, and Y atoms. The choice of the pseudopotentials above was driven by the results pointed out
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using a comparative analysis performed on preceding QC findings concerning similar perovskite systems, treated at different level of basis-sets and pseudopotentials.23 In particular, the use of unbalanced basis sets was driven by the intrinsic availability of the latter, with respect to the atomic centers involved, and by the heuristic results so far observed for analogous perovskite systems, using the same basis set scheme.23 Moreover, error cancellations were expected when calculating relative values of physical parameters (such as optimized energies, distances, and atomic charges) for the systems whose geometries were optimized at the same level of theory, using the same basis sets and constraints. The HF application in the investigation of the BaCeO3 derivatives deserves some final explanations. To study large solidstate systems by the cluster approach, it is indeed possible to use other functionals, also taking into consideration DFT procedures26 and ONIOM methods,37 either or not involving molecular mechanics (MM). QC/QC ONIOM strategies, treating the model-level moiety by DFT B3LYP hybrid functional,38 resulted however in unsuitable mimicking title systems,23 while easyaccessible parametrization for Y(III) and Ce(IV) centers either in semiempirical or in MM environments (namely, in PM639 or in UFF40) to design, respectively, either QC/QC or QC/MM ONIOM alternative schemes, is to the best of our knowledge still not available. As an example, our efforts to optimize, by HF/ UFF approaches, stoichiometric no-doped systems, as large as Ba69Ce36O141, were systematically biased by convergency problems; unless the already optimized Ce|Ce:Ba12Ce22O61 fragment was not introduced as model-level in the HF/UFF procedure. The structural results of the model level were in this case almost undistinguishable with respect to those obtained for the same fragment in the framework of the HF paradigm. Due to this and to the seeming inadequacy of the DFT results,23 we opted for using HF methods to analyze the title systems. An orbital analysis was finally performed through the inspection of P-DOSs,27 obtained by the application of the C-SPA procedure.28 The whole orbital analysis approach (C-SPA/P-DOS), when applied on perovskite materials, has already been extensively discussed in a previous work,23 hence, it will not be detailed here. It is stressed that the results corresponding to the C-SPA/ P-DOS applications show them to be quite appropriate in discriminating peculiar and complex features, characterizing the BaCeO3 derivatives.
’ RESULTS AND DISCUSSION In this section, the discussion on the computational findings is managed according to the presence of the proton (or its absence) inside the Z|ΞO11 inner octahedra framework, characterized by the presence of Ξ and Z octahedral cations in the ODSM fragments. In a starting section, the unprotonated and protonated Z|Ξ:ODSM fragments are discussed, considering their structural properties, while the electronic analysis of the same fragments is illustrated in a separated ending section. Structural Properties. The Z|Ξ:Ba12Ce22O61H2 starting moieties were cut out of a Pmcn orthorhombic network,29 then optimized as explained in Models and Computational Details. The choice to consider Ce|Ce: Y|Y: and Ce|Y:ODSM systems is related to their representation ability, which concerns different environments, characterizing Y-doped BaCeO3 materials. Unprotonated Fragments. The experimental structure parameters used to start the calculation on the Z|Ξ:Ba12Ce22O61H2 fragments were determined at room temperature by neutron 1678
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The Journal of Physical Chemistry A powder diffraction (NPD).29 Relevant relaxed distances and angles obtained after optimizations are reported in Table 1. Concerning the Ce|Ce systems (i.e., Z = Ξ = Ce), the three oxygen atom sets {1, 3, 2, 4}, {1, 5, 2, 6}, {4, 6, 3, 5} individualize three different crossing planes that include into their intersection the central cerium atom, both before and after the calculations. In each of these planes, two couples of oxygen atoms, together with the cerium atom, single out two incident lines, making two opposite-to-the-vertex pair of angles. The same holds true for the three sets {4, 10, 9, 11}, {7, 10, 8, 11}, {7, 4, 8, 9} of oxygen centers. This result shows that the calculated atomic arrangements of the central clusters fit, as previously reported,23 into the average long-range structure experimentally determined by diffraction analysis, without introducing large distortion. Inspecting Table 1, we see that, despite the presence of two short values (dZO9 = dΞ-O3 = 212 pm), the calculated Ce-O distances are in agreement with the experimental ones. As a matter of fact, molecular dynamics simulations performed on Y:BaZrO3 perovskites also show a characteristic local anisotropy around the zirconium centers.41 However, the shortest ZrO distances, isolated at 3K and corresponding to the Ce-O ones present in the title Y:BaCeO3 derivatives, already disappear at 77K. As a consequence, the distance anisotropy, characterizing the surrounding environments of the zirconium centers, is removed.41 The shortest distances characterizing different perovskite materials and, namely, Y:BaCeO3 derivatives, could hence disappear because of the occurrence of thermal motions. In the present case, this fact could contribute to the reproduction of the found experimental dCe-O values. The Ba-Ce distances are arranged according to a bimodal distribution centered at around 368 and 382 pm. The first set of distances is characterized by the presence of the Ba1-Z and Ba4-Ξ interactions, while the second one is characterized by the remaining six Ba-Ce interactions. Both of the average values and their relative weights (i.e., 1:3) are in very good agreement with the corresponding parameters found by the EXAFS experiments (see footnote c in Table 1). As mentioned in the preceding sections, also the Y-O distances, present in the Y:BaCeO3 materials, experimentally showed distinctive bimodal distributions.9 In order to find a possible origin of this feature, we already proposed a Y-doped model23 in which two clustered yttrium atoms were bound to each other by one bridge oxygen center. The present model is actually characterized by the same Y-O-Y moiety but, in addition, shows larger local details around the octahedral yttrium centers; hence, it can be considered, as already stated, an extension of the former model. In the present model both the octahedral centers of the Z|Ξ: Ba12Ce22O61H2 fragment were yttrium atoms (i.e., Z = Ξ = Y), while the inner Z|ΞBa4O11 moiety was optimized inside a surrounding rigid cage as that already employed for the Ce|Ce: ODSM system (see Models and Computational Details). Relevant distances are shown in Table 1. Three characteristic Y-O distances can be recognized, at ca. 217, 228, and 234 pm. These distance values show relative weight of 1:6, 3:6 and 2:6, respectively. As argued for the shortest Ce-O distance, found in the Ce|Ce:Ba12Ce22O61H2 fragment, the short and the medium YO distances characterizing the Y|Y:Ba12Ce22O61H2 fragment, due to thermal motion, could together contribute to defining the weight of the shorter Y-O distance of the experimentally found bimodal distribution. In this case, the calculated average distances (225 and 234 pm) as well as their relative weights (4:6 and 2:6) would result in
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Table 1. Relevant Geometric Parameters Characterizing the Z|ΞBa4O11 Environment of the Unprotonated Orthorhombic Pmcn Y:BaCeO3 Calculated Models distancesa/pm
Ce|Ceb
Y|Yb
Ce|Yb
dBa1-Z
382
369
378
dBa2-Z
383
382
382
dBa3-Z
375
365
376
dBa4-Z
370
358
362
ÆdBa-Zæc dBa1-Ξ
378 365
368 354
374 359
dBa2-Ξ
380
372
375
dBa3-Ξ
391
374
393
dBa4-Ξ
377
367
368
ÆdBa-Ξæc
378
367
374
dBa-Z|Ξd
378
368
374
dZ-O4
226
229
222
dZ-O7 dZ-O8
226 224
233 229
229 224
dZ-O9
212
217
214
dZ-O10
228
228
230
dZ-O11
227
235
224
ÆdZ-Oæc
224
228
224
dΞ-O1
224
234
229
dΞ-O2
224
228
227
dΞ-O3 dΞ-O4
212 227
216 228
223 231
dΞ-O5
228
226
228
dΞ-O6
227
233
229
ÆdΞ-Oæc
224
227
228
dZ|Ξ-Od
224
228
226
a
The reported atomic labeling is coherent with that of Figure 2. b Geometric parameters that characterize the Z|Ξ:Ba12Ce22O61H2 fragments, being Z|Ξ = Ce|Ce, Y|Y, and Ce|Y. c Average values calculated on homonym distance parameters. The corresponding averaged EXAFS values10 resulted in the following: dBa-CeEXAFS = 381 pm, dBa-YEXAFS = 375 pm, dCe-OEXAFS = 227 pm, and dY-OEXAFS = 226 pm. It is here to be recalled that the dY-OEXAFS and dBa-CeEXAFS values are separately averaged on couples of distances (223 and 233 pm and 371 and 384 pm, respectively), characterizing bimodal dY-O and dBa-Ce distributions.10,23 d Average values calculated on the distance parameters involving, separately, either Ba or O atoms and both the Z and Ξ centers. The corresponding averaged NPD values29 resulted in the following: dBa-Z|ΞNPD = 381 pm and dZ|Ξ-ONPD = 224 pm. It is, in passing, recalled that the NPD crystallographic analysis cannot distinguish between yttrium and cerium atoms .22,23
excellent agreement with the EXAFS findings (see footnote c in Table 1). The Ba-Y distances are spread in the range 354382 pm, showing a mean value of 368 pm. The slight disagreement with the experimental values (see footnotes c and d of Table 1) can be explained by taking into account the geometric and stoichiometric characteristics of the Z|Ξ:Ba12Ce22O61H2 fragments (see Figures 1 and 2). In fact, in the analysis of the Y|Y: ODSM system, only the four central Ba atoms are considered in evaluating the average Ba-Y distance, whereas, a more correct evaluation should at least involve the consideration of the two sets of four Ba atoms at the left and at the right side of the Z and Ξ centers, respectively. These are in-between Ce and Y atoms and are fixed in the Y|Y:ODSM fragment. For this reason, the characteristics of the Ba-Y distances will be deepened and reexamined considering the following Ce|Y:ODSM fragment. 1679
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The Journal of Physical Chemistry A The latter system, built by substituting one Ce atom of the inner octahedra with one Y atom (i.e., Z = Ce, Ξ = Y), mimics local arrangements of the border zone characterizing Y-doped sites. As usual, a partial geometric optimization was performed to study the local changes induced on the structure. The starting geometry was unchanged with respect to those of the previous calculations. Significant calculated distances are reported in Table 1. The average ÆdCe-Oæ value (224 pm) is the same as that we already found for the Ce|Ce:ODSM system but with a larger spread of the value. Moreover, the first oxygen coordination shell of the Y atoms resulted in more expansion than that characterizing the Ce atoms, present in the other inner octahedron of the same fragment. In particular, the Y-O distances are distributed in a range varying from 223 to 231 pm, while the average distance is equal to 228 pm. However, the Y-O distance spread does not allow one to single out an unambiguous bimodal distribution, as conversely suggested by the EXAFS data collected on the Y:BaCeO3 systems.9 It conversely has to be stressed that the interesting geometric property already observed for the Ce|Ce:ODSM fragment, regarding the pair of opposite-to-thevertex angles, is still holding in the Ce|Y:ODSM system. Finally, the EXAFS Ba-Ce distances are better reproduced by the Ce|Ce:ODSM than the Ce|Y:ODSM system. This result, as previously discussed, has to be connected to the Z|Ξ:ODSMs here studied, hence to the fact that the Ce|Ce:ODSM fragment are, for statistical reasons, more suitable than the Ce|Y:ODSM fragment for analyzing the Ba-Ce distances. On the contrary, as before prefigured in discussing the Y|Y:ODSM fragment, the Ba-Y distances, as evaluated by the Ce|Y:ODSM fragment, are well arranged in a wide range according to a single distribution centered around 374 pm, in agreement with the single Ba-Y distance found by EXAFS experiments on Y:BaCeO3 materials. Protonated Fragments. Suitably modified Z|Ξ:ODSM fragments were also employed to analyze the effects of the proton on the environment of the octahedral centers. In these structures, one of the two hydrogen atoms was removed from the original position and placed close to the O4 center. The H-O4 distance (dH-O4), H-O4-Ξ angle (aH-O4-Ξ) and H-O4-Ξ-O2 dihedral angle (DH-O4-Ξ-O2) were set (in starting the optimization) to 95 pm, 80.0, and 45.0, irrespective of the Z|Ξ:ODSM protonated system considered. Relevant distances and angles obtained after the optimizations, also including the hydrogen coordinate relaxation, are reported in Table 2. The analysis of the latter shows that the proton when included in the inner octahedra environment of the Z|Ξ:ODSM fragments modifies to some extent the starting local geometric arrangements (i.e., those of the unprotonated fragments). In particular, the values of the Z-O and Ξ-O distances of the Ce|Ce: systems were changed, especially along the Z-O4-Ξ moiety. Indeed, the Z-O4 and Ξ -O4 distances increased, whereas the opposite ones, that is, the Z-O9 and Ξ-O3 distances, similar to the ZO8 and Ξ-O5 distances, decreased. As a result, the volume of the Z|ΞO11 inner octahedra in the Ce|Ce: fragment was almost unchanged, in agreement with analogous behaviors that have been observed in studying single octahedron models of protonated BaCeO3 fragments.41 Also, the Ba-Z and Ba-Ξ distances increased, in this way, expanding the surrounding barium coordination shell, characterizing the Ce|Ce:ODSM system. The main structural distortions discussed above for the Ce|Ce:ODSM system also affect the protonated Y|Y: and Ce|Y:ODSM systems. However, in the Ce|Y:ODSM fragment, the octahedral volume remains, like for the Ce|Ce: one, unchanged while in the Y|Y:
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Table 2. Relevant Geometric Parameters Characterizing the Z|ΞBa4O11 Environment of the Protonated Orthorhombic Pmcn Y:BaCeO3 Calculated Models distancesa/pm
Ce|Ce
Y|Y
Ce|Y
dBa1-Z
400
394
395
dBa2-Z
405
397
401
dBa3-Z
386
372
387
dBa4-Z
380
370
374
ÆdBa-Zæb dBa1-Ξ
393 384
383 379
389 378
dBa2-Ξ
397
392
394
dBa3-Ξ
405
386
405
dBa4-Ξ
387
380
381
ÆdBa-Ξæb
393
384
389
dBa-Z|Ξc
393
384
389
dZ-O4
240
237
241
dZ-O7 dZ-O8
224 220
230 224
225 221
dZ-O9
204
209
206
dZ-O10
226
227
226
dZ-O11
226
234
223
ÆdZ-Oæb
223
227
224
dΞ-O1
218
231
226
dΞ-O2
223
225
228
dΞ-O3 dΞ-O4
210 240
214 237
213 237
dΞ-O5
218
222
225
dΞ-O6
226
230
228
ÆdΞ-Oæb
222
226
226
dZ|Ξ-Oc
223
226
224
dZ-Hd
248
247
258
dΞ-Hd
244
243
233
dH-O4
95
94
95
a
angles /
Ce|Ce
Y|Y
Ce|Y
aH-O4-Z
83.8
83.4
89.5
aH-O4-Ξ
81.3
82.1
75.8
DH-O4-Ξ-O2
4.9
8.0
8.0
a
For the indexing of distances and angles, see footnotes a and b of Table 1. b Average values calculated on homonym distance parameters. For corresponding experimental parameter references, see footnote c of Table 1. c Average values calculated on the distance parameters involving, separately, either Ba or O atoms and both the Z and Ξ centers. For corresponding experimental parameter references, see footnote d of Table 1. d In the optimizations of the protonated systems, one of the external hydrogen atoms present in the Z|Ξ:Ba12Ce22O61H2 fragment (see Figure 1) is placed close to the O4 center of the Z|ΞO11 moiety (see Figure 2) and relaxed with the latter.
ODSM fragment the distribution of the Y-O distances were centered, as for the homonym unprotonated fragment, around the values found by the EXAFS analysis.9 With respect to this, it has to be stressed that the bimodal distribution, corresponding to the protonated fragments, is characterized by a large spread of the distance values that is also in agreement with the large DebyeWaller factor reported by Longo et al.9 Finally, the a H-O4-Z and a H-O4-Ξ angles as well as the D H-O4-Ξ-O2 dihedral angles are quite similar, irrespective of the considered system. In particular, due to the small dihedral 1680
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Figure 3. Details on the optimized ΞO6H moiety embedded in the protonated ODSM fragments, showing the proton lying onto the plane individuated by the O4, Ξ, and O2 centers; it is to be noticed that the hydrogen atom is pointing to the O2 center. The atomic labeling is coherent with that of Figure 2.
angle value found for the different Z|Ξ:ODSM systems, we can regard the proton as lying onto the plane individuated by the O4, Ξ, and O2 centers (see Figure 3) and, for this, determining a peculiar directionality able to turn out local perturbations around the same protonic species. Electronic Analysis. To deepen our insight into the electronic properties of the Z|ΞBa4O11 moiety and to analyze the effects of the yttrium centers on its local environment, we performed C-SPA/P-DOS and M-ca. analyses on the calculated Pmcn Z|Ξ: Ba12Ce22O61H2 fragment, hypothesizing that local electronic rearrangements could be related to changes in the protonic conduction. It is here to be underlined that, in the following DOS analysis, the involved “bands” are of cluster species. Hence, their meaning is peculiarly local23 and straightforwardly different with respect to those characterizing, as an example, periodic systems treated by delocalized functions.42 In particular, their use is in the following addressed at evaluating differential properties, characterizing the effects (i) of the dopants in the BaCeO3 fragments and (ii) of the proton in the surrounding environment of the same dopants. Unprotonated and Protonated Fragments. The Z|Ξ:Ba12Ce22O61H2 fragment was clustered to form seven sets of atomic species to analyze simultaneously: (i) the Z|Ξ Ba4O11 moiety, (ii) the Ba4 atomic cluster in-between the central octahedra, (iii) the Z, (iv) cations, (v) the O4 center, and finally, the clusters (vi) Oζ and (vii) Oξ formed by the central octahedral oxygen atoms, except for the O4 center, around the Z and Ξ cation, respectively. The F versus ε curves of Figures 4 and 5 represent the orbital contribution of a given atomic set to the MOs of the Z|Ξ:Ba12Ce22O61H2 fragment, while the abscissa values fit the energy range considered. The involved atomic sets are either those of the systems (i-vii), belonging to the Z|ΞBa4O11 moiety, or that of the whole Z|Ξ:Ba12Ce22O61H2 fragment. It should be, at first, noticed that the eigenvalue ranges individuated by the grouped red bar sets that characterize the Z|Ξ:Ba12Ce22O61H2 fragment peaks are nearly coincident, irrespective of the Z|Ξ:ODSM system, with the P-DOS peak widths of the (i-vii) atomic sets, which belong to the ZΞ|Ba4O11 moiety. The presence of two sharp peaks can be also observed for all the different systems; they are centered at about -39.0 and -20.0 eV. These correspond to MOs almost entirely attributable to the Ba4 cluster and are always present regardless of the considered protonated and unprotonated Z|Ξ:
Figure 4. C-SPA/P-DOS analysis of the Z|Ξ:Ba12Ce22O61H2 fragments when hydrogen is not embedded in the framework, Z|Ξ = Ce| Ce (a), Ce|Y (b), Y|Y (c): orbital contribution of atomic sets included in the Z|ΞBa4O11 moiety to the MOs of the same moiety against energy values (F vs ε). Ba4 group, green line; Z atom, purple line; Ξ atom, blue line; O4 atom, light blue line; Oζ moiety, yellow line; Oξ moiety, red line; Z|Ξ Ba4O11 cluster: black line. The red bars individualize the eigenstates of the whole Z|Ξ:Ba12Ce22O61H2 fragment. The F lines are obtained by a convolution of fixed-width Lorentzian curves centered on the energy bin used in the DOS analysis, being the height proportional to the weight of the AO set contribution in the bin. The black segment on the top inviduates the HOMO-LUMO edge.
ODSM system. Another common feature of the C-SPA curves concerns the Oζ and Oξ orbital contributions, which in any case overlap (see Figures 4 and 5). The findings above show that both of the octahedral sites are electronically similar, hence, anisotropic effects can be excluded for the different model clusters. 1681
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Table 3. Mulliken Charges of Relevant Atomic Centers, Characterizing the Z|ΞBa4O11 Environment of the Unprotonated and Protonated Orthorhombic Pmcn Y:BaCeO3 Calculated Models atomic centera
Ce|Ceb
Y|Yb
Ce|Yb
Ba1
0.2|0.0
0.9|0.1
0.0|-0.1
Ba2
0.1|-0.2
0.1|-0.1
0.2|-0.1
Ba3
0.1|0.0
0.9|0.9
0.7|0.6
Ba4
0.2 | 0.4
1.2|1.0
1.0|0.8
O1
-1.4|-1.4
-1.4|-1.4
-1.4|-1.3
O2
-1.4|-1.4
-1.4|-1.5
-1.4|-1.5
O3 O4
-1.4|-1.4 -1.4|-0.9
-1.5|-1.3 -1.8|-0.9
-1.5|-1.3 -1.6|-0.8
O5
-1.4|-1.3
-1.4|-1.4
-1.4|-1.4
O6
-1.4|-1.3
-1.4|-1.3
-1.4|-1.3
O7
-1.4|-1.4
-1.4|-1.3
-1.4|-1.4
O8
-1.4|-1.4
-1.4|-1.4
-1.4|-1.4
O9
-1.4|-1.3
-1.4|-1.3
-1.4|-1.3
O10
-1.4|-1.3
-1.4|-1.3
-1.4|-1.3
O11 H
-1.4|-1.4 - |0.3
-1.4|-1.4 - |0.4
-1.4|-1.4 - |0.3
a The reported atomic labeling is coherent with that of Figure 2. b The verti-bar employed for the value representation distinguishes between the Mulliken charges of the unprotonated (left) and protonated (right) model.
Figure 5. C-SPA/P-DOS analysis of the Z|Ξ:Ba12Ce22O61H2 fragments when hydrogen is embedded in the framework, Z|Ξ = Ce|Ce (a), Ce|Y (b), Y|Y (c): orbital contribution of atomic sets included in the Z|ΞBa4O11 moiety to the MOs of the same moiety against energy values (F vs ε). Ba4 group, green line; Z atom, purple line; Ξ atom, blue line; O4 atom, light blue line; Oζ moiety, yellow line; Oξ moiety, red line; Z|ΞBa4O11 cluster: black line. The no influential H orbital contribution is not reported. The red bars individuate the eigenstates of the whole Z|Ξ:Ba12Ce22O61H2 fragments. The F lines are obtained by a convolution of fixed-width Lorentzian curves centered on the energy bin used in the DOS analysis, being the height proportional to the weight of the AO set contribution in the bin. The black segment on the top inviduates the HOMO-LUMO edge.
Concerning the Y|Y:ODSM system, we see that for eigenvalues ranging from -16.0 to -5.0 eV, both the yttrium atoms, together with the Ba4 moiety, represent the main contributors to the corresponding MOs range; on the contrary, in the Ce|Ce:
ODSM system, the cerium atoms of the inner octahedra give a smaller contribution to MOs in that energy range. In the latter system, MOs running in the interval included between about 5.0 eV and the HOMO region are entirely attributable to the barium AOs, while in both the systems containing yttrium, the Y and Ba AOs mix together, producing MOs in the same energy range. These last features, together with the characteristic barium peaks, were already observed for eigenvalues in the same energetic region characterizing OSSM fragments.23 The C-SPA of the protonated and unprotonated systems show quite similar behavior. However, a characteristic small peak, caused by the AO contribution of the Ba4 moiety and of the O4 center, can be observed for all the protonated Z|Ξ:ODSM fragment at about -17.5 eV. In fact, the insertion of the hydrogen atom into the Z|ΞO11 inner octahedral environment would seem to modify the orbital contribution of just the Ba4 moiety and the O4 center, producing a MO fingerprint for the protonated systems in the eigenvalue interval ranging in-between -20.0 and -16.0 eV. In passing, it is here recalled that an analogous behavior have been also observed in protonated and unprotonated OSSM structures.41 It was already argued that the substitution of cerium with yttrium atoms in perovskite materials localize an increased electronic density around the Y-doped sites.9 According to the M-ca. procedure, this feature, as shown by Table 3, is captured by the Ce| Y: and Y|Y:ODSM systems, which actually show a decrease toward more negative values of the Mulliken charge on the oxygen atom placed in-between the Z and Ξ centers when at least one of these is an yttrium atom. Table 3 reports the Mulliken charges of the atoms that have mainly modified the C-SPA curves of the protonated with respect to the unprotonated Z|Ξ:Ba12Ce22O61H2 fragments, that is, the O4 atom, and for completeness, the remaining oxygen atoms of the central octahedra, the barium atoms in-between the octahedra, and the hydrogen that characterizes the protonated systems. Interestingly, the analysis of the oxygen environments 1682
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The Journal of Physical Chemistry A characterizing the Z|Ξ:ODSM systems allowed us to fix local charge configurations, which could be related to the occurrence of proton diffusion in the title materials.23 Table 3 clearly points that the different Z|Ξ:ODSM systems are characterized by homogeneous charge behaviors. The unprotonated Ce|Ce:ODSM system, as an example, shows equal values irrespective of the oxygen center considered. A similar situation also holds for the unprotonated Ce|Y: and Y|Y:ODSM systems, besides a characteristic rise of the negative charge values that can be observed for the Z-O-Ξ bridging O4 centers. It is interesting to notice that the average oxygen charge present in the external frame of the BaCeO3 fragments is very close to -1.4 au either in the unprotonated or in the protonated systems and irrespective of the nature of the Z and Ξ centers. That atomic charge is characteristic of the oxygens of the inner octahedra in the Ce|Ce:ODSM system. The observation above, stating the equality among these different sets of oxygen atoms, clearly contribute to validate the here proposed cluster models. Moreover, the distribution of the charges in the barium centers show, as expected, a more isotropic behavior in the system not containing Y atoms. This fact actually reveals the ability of the doping atoms to modify both the local structural properties and the corresponding local electronic environments. The introduction of hydrogen in the central octahedra, corresponding to the formation of the protonated models, apparently produces changes in the charge distribution of the oxygen atoms. In particular, while we can notice a decrease of the absolute value in the O4 atom for all the ODSM systems, the hydrogen charges resulted higher at about 0.1 au in the Y|Y: with respect to the Ce|Y: and Ce|Ce:ODSM systems. Besides the changes on the O4 atoms, the remaining oxygen centers of the fragments are not very affected by the introduction of the hydrogen into the Z|ΞO11 inner octahedra and the average value of the Mulliken charges of the protonated ODSM systems remains quite similar to that of the unprotonated ones. Taking into consideration the charge distributions that characterize the different Z|Ξ:ODSM systems, it is possible to infer hypotheses on the hydrogen diffusion mechanism occurring in the Y-doped BaCeO3 materials. In doing this, we hypothesize that a large amount of diyttrium (clustered) sites are formed in the Y-doped BaCeO3 materials and we assume, as already stated, that the different Z|Ξ:ODSM systems are representative of different local situations in the same materials. The mimicking ability of the Y|Y:ODSM fragment in reproducing the experimental structural evidence concerning the bimodal Y-O distance distribution is, in our opinion, a plausible reason to state the first inference, while the second is supported by the homogeneous oxygen charge behavior, one of the external frames of the different fragments, which is coherent with the local properties of the unprotonated Ce| Ce:ODSM system. The findings reported in Table 3 and, in particular, the relative charge value characterizing the O4 with respect to the neighboring {O5, O6, O10, O11} horizontal and {O1, O2, O7, O8} vertical oxygens, see Figure 2, show that the hydrogen center can diffuse in the bulk being, in any case, favored by the present charge gradients, independently of the considered Z|ΞO11 inner octahedra pairs, that is, Ce|Ce, Ce|Y, and Y|Y. Hence, it is clear that the intraoctahedral diffusions in doped materials should always be allowed, irrespective of the nature of the metallic center inside the octahedron, whereas the interoctahedral diffusions, which clearly are also not prevented by opposite charge gradients, should have lower occurrence probabilities due to the larger distance “jump” needed.43
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It has been reported that local basic phenomena play an important role in driving conductivity in Y-doped BaCeO3 materials.23,44 Taking into consideration the M-ca. results summarized in Table 3, it is clear that the charge gradients, present in the Y-doped BaCeO3 derivatives, are, at variance, not able to strongly affect the hydrogen diffusion. This peculiarity actually would occur because hydrogen species in the bulk diffusion should be able to dynamically change their neighboring environments and the surrounding oxygen properties, yet leaving unchanged the favorable and almost isotropic local charge gradients (see Table 3). Although the latter could be related to the material basic characteristics,44 their reduced influence on the conductivity, in our opinion, does not rule out the fundamental role claimed for the local basicity on the Y-doped BaCeO3 derivative conductivity. To prove this conjecture, it is interesting to point an estimation of the relative protonation energy parameter (η), as defined below: ð1Þ η ¼ ΔEZjCΞ - ECejCe ΔEZ|Ξ and ΔECe|Ce are, in fact, the energy difference occurring between protonated and unprotonated fragments in the Z|Ξ: ODSM and Ce|Ce:ODSM systems, respectively. The η parameter straightforwardly represents a relative estimation of the protonation stability occurring on different sites of the BaCeO3 derivatives. Moreover, because ΔE values are singularly characterized by consistent basis-sets, error cancellation, as inferred in Models and Computational Details, should occur in their, and as a consequence in the η, evaluation. In particular, the η values resulted in 0.0, -147.0, and -178.1 kJ 3 mol-1 for Ce|Ce:, Ce|Y:, and Y|Y:ODSM systems, respectively. This behavior, in agreement with the experimental results, therefore shows (i) that the local basicity increases with increasing the yttrium concentration44 and (ii) that, although all the oxygen sites of the yttrium-doped cerate perovskites are accessible along proton diffusion, hydrogen spends, on the average, a longer time close to yttrium with respect to cerium oxygenated sites.9,10 Both these points, showing a relationship existing between either local basicity or local conductivity and local concentration of yttrium centers, clearly suggest a link between basicity and conductivity in presence of Y-doping BaCeO3 perovskite materials. By using In:, Y:, and Gd:OSSMBaCeO3 protonated fragments, we are now studying proton hopping phenomena by performing unconstrained geometrical optimizations around fixed proton placements.41 In agreement with the inference above, preliminary results on these models show that the protonic transfer occurs always through paths, which lie on planes that contain the proton itself, the oxygen to which at the beginning it is bound, the nearest trivalent or tetravalent cation and another oxygen at about 90 with respect to the first one (see, for example, Figure 3). This typical planar transfer occurs even if the proton, at the first optimization step, occupies an out-of-plane position.
’ CONCLUSIONS Quantum Chemical calculations have been carried out to simulate unprotonated and protonated Pmcn orthorhombic BaCeO3 derivatives. Geometrical optimizations in the frame of the cluster approach followed by a detailed orbital analysis allowed us to confirm new perspectives already introduced in the interpretation of experimental results concerning the title materials. Namely, a characteristic bimodal Y-O distance distribution found by EXAFS was explained on the basis of local 1683
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The Journal of Physical Chemistry A clustering of yttrium atoms. Starting from the structural findings, based on geometric and electronic considerations, it was possible to self-consistently analyze also the charge distributions characterizing the Y-doped BaCeO3 materials. In particular, the joined analysis of the charge and structure properties of the considered BaCeO3 derivatives let us confirm (i) that the protonic intraoctahedral diffusion is more likely to occur than the interoctahedral one and ii) that the gradients in the local charge density should play a minor role in the same protonic diffusion. The latter conversely could be driven by local basicity changes, related to the presence of doping yttrium centers. Following these results, ab initio geometrical optimizations and classical molecular dynamic simulations are now being performed on Y:BaZrO3 systems. In analyzing these systems, double zirconium substitutions are mostly considered. The study represents the starting points to investigate if yttrium local clustering could occur also in other Y-doped perovskites hence to investigate if this occurrence could be at the basis of the conductivity properties of the same materials.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT Financial support has been provided by the Italian Ministero dell’Universita e della Ricerca (PRIN 2006: Ceramici Protonici per Celle a Combustibile) and by the Universita di Palermo (ex 60%: Ossidi Misti a Base di Cerato di Bario: Sintesi, Caratterizzazione Strutturale e Studio Computazionale del Meccanismo di Conduzione Protonica). Calculations were run on the CCCP Linux cluster, close to the Department of Inorganic and Analytical Chemistry “S. Cannizzaro” of the University of Palermo and on the COMETA HPC cluster, close to the Department of Physics and Astronomy of the University of Palermo. ’ REFERENCES (1) (a) Iwahara, H. Solid State Ionics 1995, 77, 289–298. (b) Bonanos, N.; Knight, K. S.; Ellis, B. Solid State Ionics 1995, 79, 161–170. (c) Tomita, A.; Hibino, T.; Suzuki, M.; Sano, M. J. Mater. Sci. 2004, 39, 2493–2497. (d) Iwahara, H.; Asakura, Y.; Katahira, K.; Tanaka, M. Solid State Ionics 2004, 168, 299–310. (2) Kreuer, K. D. Annu. Rev. Mater. Res. 2003, 33, 333–359. (3) (a) Kreuer, K. D. Chem. Mater. 1996, 8, 610–641. (b) Kreuer, K. D.; Fuchs, A.; Maier, J. Solid State Ionics 1995, 77, 157–162. (4) Islam, M. S. J. Mater. Chem. 2000, 10, 1027–1038. (5) Wakamura, K. J. Phys. Chem. Solids 2005, 66, 133–142. (6) Islam, M. S.; Davies, R. A.; Fisher, C. A. J.; Chadwick, A. V. Solid State Ionics 2001, 145, 333–338. (7) Knight, K. S. Solid State Ionics 1994, 74, 109–117. (8) (a) Knight, K. S.; Soar, M.; Bonanos, N. J. Mater. Chem. 1992, 2, 709–712. (b) Scherban, T.; Villeneuve, R.; Abello, L.; Lucazeau, G. Solid State Ionics 1993, 61, 93–98. (c) Knight, K. S.; Bonanos, N. Solid State Ionics 1995, 77, 189–194. (d) Knight, K. S.; Bonanos, N. Mater. Res. Bull. 1995, 30, 347–356. (e) Melekh, B. T.; Egorov, V. M.; Baikov, Y. M.; Kartenko, N. F.; Filin, Y. N.; Kompan, M. E.; Novak, I. I.; Venus, G. B.; Kulik, V. B. Solid State Ionics 1997, 97, 465–470. (9) Longo, A.; Giannici, F.; Balerna, A.; Ingrao, C.; Deganello, F.; Martorana, A. Chem. Mater. 2006, 18, 5782–5788. (10) Giannici, F.; Longo, A.; Deganello, F.; Balerna, A.; Arico, A. S.; Martorana, A. Solid State Ionics 2007, 178, 587–591.
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