Oxygen-Storage Materials BaYMn2O5+δ from the Quantum-Chemical

Article pubs.acs.org/cm

Oxygen-Storage Materials BaYMn2O5+δ from the Quantum-Chemical Point of View Michael Gilleßen,† Marck Lumeij,† Janine George,† Ralf Stoffel,† Teruki Motohashi,‡ Shinichi Kikkawa,‡ and Richard Dronskowski*,† †

Institute of Inorganic Chemistry, RWTH Aachen University, Landoltweg 1, 52056 Aachen, Germany Faculty of Engineering, Hokkaido University, Sapporo 060-8628, Japan

‡

ABSTRACT: The experimentally known perovskite-like materials BaYMn2O5+δ (δ = 0, 0.5, 1) are characterized by a remarkably reversible oxygen-storage capacity at a moderate 500 °C. We try to elucidate the local structures of the vacancy arrangements in these compounds taking place after an oxygen release. This is done for the three compounds with the help of both ab initio totalenergy calculations of density-functional quality and using classical structure rationale. Our results are compared with experimental structure findings. We further calculate oxygen-vacancy formation energies and predict the pathways of the oxygen atoms through the crystal by using NEB (nudged elastic band) calculations. Structure diagrams of the most likely energy pathways for oxygen migration are presented. Finally, thermodynamic considerations of the oxygen intake are carried out based on quasiharmonic phonon calculations and compared with experimental data. The theoretical molar reaction enthalpy for oxidizing BaYMn2O5 to BaYMn2O6 matches the experimental value. KEYWORDS: oxygen-storage material, nudged elastic band, DFT, oxygen hopping pathways, ab initio thermochemistry, BaYMn2O6

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INTRODUCTION So-called Oxygen-Storage Materials (OSMs) are nowadays mostly used in modern three-way catalysts where they detoxify the automobile exhaust gases. Not only in the automotive industry but also in the chemical industry OSMs have attracted major attention mainly because of their ability to regulate the oxygen partial pressure which is the most crucial ingredient for an exact control of redox reactions. The probably best-known and commercially widely used OSM is CeO2−ZrO2.1 Nonetheless, new oxygen-storage materials have recently been developed. For example, Machida et al. have reported the large oxygen-storage capacity of the oxysulfate Pr2O2SO4,2 and Motohashi et al. have presented remarkably reversible oxygen intake and release properties of BaYMn2O5+δ which may absorb more than 3.7 wt % of oxygen.3 This corresponds to exactly one oxygen atom per BaYMn2O6 formula unit. The value of δ in the sum formula varies stepwise between 0 and 1 although only three distinct compositions are known, namely, for δ = 0, 0.5, and 1. The oxygen storage takes place at moderate temperatures (i.e., 500 °C) and is completely reversible even after 100 cycles. At the moment BaYMn2O5+δ is the oxide with the highest oxygen-storage capability. To understand the fundamental processes which take place inside such an OSM, quantumchemical calculations should be performed. Since the role of the vacancies is tremendously important for the ion-conducting application, we will investigate several vacancy arrangements within BaYMn2O5+δ and try to explain their oxygen sitepreference in the proximity of the yttrium atom, as was already suggested from the experimental results.3 Moreover, the oxygen migration within the material will be investigated by calculating © 2012 American Chemical Society

the preferred minimum-energy pathways of the oxygen ions and their corresponding activation barriers. A more comprehensive overview of studies touching upon the oxygen vacancy formation and migration in perovskite-like systems can be found in the literature.4−7 It is not our intention to deal with the rather complex, albeit enormously interesting, magnetic structure of BaYMn2O5+δ since the application temperature of at least 500 °C is far beyond the Néel temperature and therefore irrelevant for this study.

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RESULTS AND DISCUSSION Oxygen Vacancy Arrangement. The structure of BaYMn2O5+δ can be described as a doubled perovskite. For δ = 1 the Ba and Y ions are coordinated by 12 and the Mn ions by 6 oxygen atoms each. In an idealized unit cell with the perovskite structure one would have Ba or alternating Y in the center of that cube. On the cube’s corners one would find 8 manganese-centered corner-sharing MnO6-octahedra. In Figure 1 this simple cubic perovskite cell with a central yttrium atom is marked in red. This cell needs to be doubled to reach the full sum formula with an equal amount of barium and yttrium. In the gray unit cell which is also shown there are two specific oxygen atoms in every yttrium and barium layer, respectively. Being able to distinguish the oxygen atoms will be important to perform the calculations, especially when it comes to taking oxygen atoms out of the structure. Received: February 28, 2012 Revised: April 27, 2012 Published: May 3, 2012 1910

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The applied density-functional approach nicely reproduces the structural properties of BaYMn2O6. As a good oxygenstorage material the compound series is capable of losing and storing oxygen atoms, structurally spoken. Therefore, a series of calculations has been carried out to examine how the most stable structure would look like if one or two oxygen atoms were to be removed. In a first step, taking out one oxygen atom, we would end up in the formula BaYMn2O5.5. All different possibilities of oxygen vacancies have been calculated. The different positions are subdivided into three groups, depending on the layer they reside in. Table 2 gives an overview of these Table 2. Comparison of the VASP Total Energies for the Different Assumed Oxygen Vacancies of BaYMn2O5.5 Plus Vacancy Formation Energies ΔEf for One O Atom Per Cell

Figure 1. Unit cell of BaYMn2O6 in a gray box; additionally, a perovskite cell in a red box is shown, which is doubled along the c axis. A cut-out of the corner-connected network built up of purple octahedra, i.e., oxygen-coordinated manganese atoms, is also depicted.

vacancy layer

VASP energy (eV/cell)

ΔEf (eV/cell)

Ba layer Mn layer Y layer

−147.05 −147.38 −147.69

3.36 3.03 2.72

results and shows that the total energy calculated for an oxygen void adopts the lowest value (last row in the table) in the Y layer. Additionally, we show the oxygen vacancy formation energies ΔEf that have been calculated according to the simple formula 1 ΔEf = 2E(BaYMn2O5.5) + E(O2 ) − 2E(BaYMn2O6 ) 2 based on the calculated total energy of solid α-oxygen. This is explained in more detail in the energetics section. The results for ΔEf are close to the values calculated by others (e.g., Kotomin et al.5). For an extended study concerning this topic on similar perovskite-like systems we recommend an Article by Mastrikov et al.6 Coming back to the structural alternatives, the lattice parameters for the most stable structure are depicted in Table 1. As alluded to already, the accuracy of the calculations are also satisfactory for BaYMn2O5.5 for which oxygen has been taken out of the fully occupied BaYMn2O6. While the structure distorts a little, as seen from the deviations of the angles, the lattice parameters a and b enlarge both in the calculation as well as in the experiment. In the next step one more oxygen is taken out of the cell to generate BaYMn2O5. Therefore all possible combinations of two oxygen vacancies have been computed. The results are shown in Table 3. The lowest vacancy formation energy results when both vacancies are located in the Y layer (last row in the table). The second oxygen to be expelled from BaYMn2O5.5 is also the last left in the Y layer.

Yttrium, manganese, and barium have an alternating layered arrangement, the layers being occupied by either one of the two atomic sorts. As a consequence of this and the different ionic sizes, the “octahedra” in the real crystal, as they are shown in Figure 1, are tilted. The yttrium layer is in the middle of the two manganese layers, and they are between two barium layers. Thus, the yttrium layer corresponds to an approximate mirror plane perpendicular to the c axis of the structure. Please note that, for reasons of clarity, most of the oxygen atoms have been depicted in a somewhat transparent manner, and only those which are on the corners of the two octahedra are plotted in full mode. The comparison between the experimental and the calculated structural parameters gives the following results. The experimental structure of BaYMn2O6 we used is characterized by an antiferromagnetic ordering of the spins on the manganese atoms. Although the non-spin-polarized calculations already reproduce the structural results well, we show the results for the most stable antiferromagnetic structure. Nonetheless, this is not of any importance for energetic comparisons made in the sequel. The calculated lattice parameters are very close to the experimental ones, as given in Table 1. The deviations are minimal and can be ascribed to this particular method’s typical overestimation (GGA, see below) of the lattice parameters.

Table 1. Comparison of Experimental and Calculated Lattice Parameters of BaYMn2O6, BaYMn2O5.5, and BaYMn2O58 BaYMn2O6

BaYMn2O5.5

BaYMn2O5

cell parameter

measured9

calculated

measured10

calculated

measured11

calculated

a (Å) b (Å) c (Å) α (deg) β (deg) γ (deg) V (Å3)

5.51974(8) 5.51379(8) 7.60319(10) 90.017(2) 90.280(1) 90.106(1) 231.397

5.558 5.558 7.654 89.70 90.30 91.81 236.31

5.559 5.559 7.640 90.41 88.45 94.49 235.28

5.63 5.63 7.64 90.06 89.94 95.73 241.53

5.542 5.542 7.654 90 90 90 235.08

5.60 5.60 7.54 90.00 90.00 90.00 236.36

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Table 3. Comparison of the Vacancy Formation Energies ΔEf for the Different Assumed Second Oxygen Vacancies of BaYMn2O5 1st vacancy layer +

2nd vacancy layer

ΔEf (eV/cell)

Ba layer Mn layer Mn layer Ba layer Y layer

Ba layer 2nd Mn layer Y layer Y layer Y layer

4.07 4.20 3.75 3.15 2.48

Interestingly enough, the same result is also found experimentally. Looking back at Figure 1 that means that the Y layer in the depicted structure is emptied of its two oxygen atoms to become BaYMn2O5. The most stable structural parameters are compared with the measured ones in Table 1. The deviations between the measured and the quantumchemically calculated results are similarly small, once again. In the experiment the cell undergoes an expansion when going from BaYMn2O6 to BaYMn2O5.5. That means that taking one oxygen atom out increases the volume by about 1.6%. When going from BaYMn2O5.5 to BaYMn2O5 the volume of the cell then decreases, but only by 0.5%. It is useful for an application that the volume differences are exceptionally small because this structural indifference translates into a higher structural stability. Looking at the unit cell used (see the gray frame in Figure 1), a vacancy concentration of 8% results when one oxygen atom per cell is taken out. The corresponding composition is BaYMn2O5.5. As said before, a total-energy calculation reproduces the experimental result that the most favorable vacant lattice position is located in the Y layer (see Table 2). In a computer experiment we have the possibility to check what would happen for a nonstoichiometric, not yet experimentally known (but well imaginable) intermediate state, for example BaYMn2O6−δ which loses less than one oxygen atom. Surely there exist transitional states with δ < 0.5. Even for small amounts of oxygen deficiency it is interesting to know whether the preferred layer for a vacancy will be still the same. With the help of a 2 × 2 × 1 supercell with eight formula units the location of the oxygen void in the yttrium layer can be reproduced for a vacancy concentration of about 2%. The choice for the vacancy to be located rests in the simple third rule of Pauling.12 It links the decreasing stability of edgesharing, or even more so, face-sharing polyhedra with an increasing charge of the coordinated ion and a decrease in its coordination number. Barium and yttrium have the same coordination number since they are both surrounded by 12 oxygen atoms each. Because yttrium is more strongly charged (Y3+ compared to Ba2+), the system tries to eliminate the facesharing cuboctahedra in the yttrium layer rather than in the barium layer. Figure 2 exemplifies how these face-sharing yttrium-coordinating cuboctahedra of oxygen atoms look like. For reasons of clarity all other atoms which do not belong to the cuboctahedra have been left out; thus only the yttrium and the coordinating oxygen atoms are shown. Pauling’s third rule is related to the electrostatic repulsion of cations. With face-sharing polyhedra the system is forced into a corset, so to speak. The distance between the cations is determined by that corset, and it is smaller than in a system where the coordinating polyhedra only share corners. A comparison of the Y−Y distances is not straightforward because the lattice parameters vary from system to system.

Figure 2. Two yttrium atoms in the cell cuboctahedrally coordinated by 12 oxygen atoms each. Four of the atoms belong to both coordination spheres and generate a square (marked in red) which is shared by the two cuboctahedra. The Y layer is plotted in light yellow.

With one vacancy the volume of the cell clearly increases, and with a second vacancy the volume decreases, but just a little. The increase is accompanied and may be explained by an increasing Y−Y distance. This Y−Y distance decreases again for BaYMn2O5, but this is only because the whole structure is emptied of oxygen atoms, so the cell volume gets smaller. It is only meaningful to do a comparison with an alternate structure in which the oxygen vacancy would lie in the Ba layer. Table 4 Table 4. Average Y−Y and Ba−Ba Distances (Å) in the Three Compounds BaYMn2O6, BaYMn2O5.5, and BaYMn2O5 with Two Possible Vacancy Arrangements for the Latter Two average Y−Y distance compound BaYMn2O6 BaYMn2O5.5 BaYMn2O5

vacancy in Ba layer

vacancy in Y layer

3.887 (no vacancy) 3.815 3.903 3.817 3.864

average Ba−Ba distance vacancy in Ba layer

vacancy in Y layer

3.878 (no vacancy) 3.810 3.898 3.813 3.864

depicts the development of the Y−Y and the Ba−Ba distances for the two possible vacancy arrangements. In the hypothetical compound, with oxygen vacancies in the Ba layer, the Y−Y distances and also the Ba−Ba distances are shorter than in the energetically more stable compound with the vacancy in the Y layer. We note the fact that the ceramic high-temperature superconductor YBa2Cu3O7−x also adopts a similar perovskite-like structure in which the oxygen vacancies rest in the Y layer, not in the Ba layers,13 just like for the BaYMn2O5+δ series. Oxygen Pathways. For simulating the diffusion pathways of the oxygen atom, we have chosen a nonmagnetic theoretical description. This is important to save precious CPU time because the NEB (nudged elastic band) calculations had to be carried out with a 2 × 2 × 1 supercell. We have taken into account almost all possible atomic migrations. These include the oxygen migration within the Y layer, within the Mn layer (along the x and y directions) and from the Mn layer into the Y and the Ba layers. We only set aside the migrations within the Ba layer because a vacancy inside this layer has already been determined as being very unstable. 1912

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Table 5 presents five different values of energy barriers as a result of our NEB calculations, and we note that just the Table 5. Oxygen Pathways and the Corresponding Activation Energies (eV) oxygen pathway (from → to)

energy barrier

Y layer → Mn layer Mn layer → Y layer Mn layer → Mn layer Mn layer ← Mn layer Ba layer → Mn layer Y layer → Y layer

0.18 0.70 0.78 0.96 0.90 1.37

minimum energy is needed to overcome the barrier between an Y layer and a Mn layer. Thus, an activation energy of 0.18 eV is required when oxygen moves to an energetically lower site inside the Mn layer, and the energy difference between the two states is 0.52 eV. This path is the first entry in the table. The other pathways have a much higher energy barrier with up to one order of magnitude larger values for a hopping between two Y layer positions. The table suggests that the smallest energy is needed when an oxygen atom leaves the yttrium layer, and it resembles the fact that this layer is the first to be emptied when we go from the fully occupied compound BaYMn2O6 to the compound BaYMn2O5.5 with one fewer O atom. The energy graph for the most favorable pathway can be seen in Figure 3.

Figure 4. Octahedral oxygen coordination at the start (top left) and the end (top right) of the most favorable oxygen pathway. At the bottom seven images of the NEB calculation for the oxygen pathway from the Mn to the Y layer are depicted, whose energy path is shown in Figure 3.

atoms. In the picture on the right the oxygen is positioned in an octahedron, made up of two barium, two yttrium, and two manganese atoms. The seven images (intermediate steps) making up the pathway are depicted in the structural sketches at the bottom in Figure 4. These diagrams only show the triangle of two yttrium atoms and one manganese atom (ΔYYMn) through which the oxygen atom has to pass. Please note that a new viewing angle has been chosen with respect to the former diagrams to simultaneously see the triangle and the oxygen migration. We notice that the ΔYYMn triangle opens like a gate (image 1−2). Since the differences are not easy visible to the naked eye, the respective sizes of the triangle areas (AΔ) are also given. The size of the area first increases from 5.97 Å2 (image 1) to 6.28 Å2 (image 3). This is when the system’s total energy is at a maximum (see Figure 3). During the transition state the two (see Figure 4) manganese atoms from the upmost octahedron shift apart from each other (in our picture between image 3 and image 4), thereby stretching this octahedron. Subsequently the ΔYYMn triangle “closes” and also twists a little. The geometry found in this transition state resembles very much the “critical triangle” as introduced by Kilner and Brook three decades ago.14 Energetics. Up to now, we have presented the structural differences concerning the oxygen loss. Looking at the oxygenstorage properties it is most fruitful to also consider the energetic development. The experiment suggests that the oxygen-absorbing reaction is significantly accelerated by selfheating. This would mean a speed-up of the reaction through exothermic oxygen intake. In the sequel we will concentrate on the energetical part which may nonetheless influence the kinetics. We can theoretically estimate the magnitude of exothermic heat upon oxygen intake (δ = 0 → 1) by comparing the compounds’ Gibbs free energies G and enthalpies H as obtained from density-functional total-energy calculations in combination with the simulation of lattice dynamics. The Gibbs free energy was approximated by the Helmholtz free energy A, which is composed of the electronic ground-state energy E0 and the vibrational free energy Aph:

Figure 3. Energy profile for the most favorable oxygen pathway from the Mn to the Y layer. At the start (image 1) there is an oxygen atom in the Y layer and at the end (image 7) the oxygen is in the Mn layer. The dotted line should only guide the eye.

The energy profile shows a local minimum for image 1, that is, when oxygen is in the Y layer and the corresponding vacancy is located in the Mn layer. As said before, an energy barrier of 0.18 eV has to be overcome to reach a minimum energy at image 7 for which the oxygen is in the Mn layer and the vacancy can be found in the Y layer. Image 7 lies 0.52 eV lower in energy. According to the NEB calculations the easiest way for an oxygen atom to change its position within the crystal is when it starts in a Y layer (or vacancy in the Mn layer, image 1) moving to an Mn layer (or vacancy in the Y layer, image 7). Figure 4 schematically shows structural cut-outs at the start and the end point of the oxygen pathway at the top. Only the hopping oxygen and the coordinating atoms are depicted. At the start (left) oxygen occupies a somewhat compressed, octahedrally coordinated position in which the “octahedron” is built up from four yttrium and two slightly closer manganese 1913

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For the same temperature, the first-principles heat capacities of the two products are Cp1 = 229.9 J mol−1 K−1 (BaYMn2O5.5) and Cp2 = 240.3 J mol−1 K−1 (BaYMn2O6). Because the heat capacities are so similar to each other and we assume the oxidation as being instantaneous, we use the heat capacity of the final product for the remaining thermodynamic calculations. In other words, the heat capacity of the oxides phase is approximated, to a satisfactory accuracy, by the one of BaYMn2O6 (Cptheo(oxide phase) = Cp2). Given the knowledge of the reaction enthalpy and the heat capacity, the temperature change of the oxidation reaction may be expressed as

G(T ) ≈ A(T ) = E0 + A ph (T )

The error made by using this approximation (that is, neglecting the volume expansion of the solid-state materials) lies well below 1 kJ mol−1. The enthalpy was then obtained by the relation H(T ) = G(T ) + TS(T ) = G(T ) − T dG(T )/dT

The thermodynamic potentials of oxygen were calculated by a hybrid ansatz summing up the electronic total energy E0 and the vibrational zero-point energy Aph,0, calculated for solid αoxygen, the literature value of the heat of sublimation ΔHsub,15 database values16 for the temperature-dependent entropy S(T), and the heat capacity Cp(T) of gaseous oxygen, as given in G(O2 ) = E0 + A ph,0 + ΔHsub − TS +

ΔT = ∂Q /Cp ≈ −ΔH /Cp

such that there will be a rise in temperature of ΔT = 899 K in case the heat is absorbed solely by the oxide compound. The results of the measurement presented in Figure 5 reveal that the oxygen content immediately increases when an oxygen

∫ Cp(T ) dT

and H(O2 ) = E0 + A ph,0 + ΔHsub +

∫ Cp(T ) dT

The calculation for solid oxygen converges for the antiferromagnetically arranged paramagnetic oxygen molecules and an equilibrium volume which is only 9% larger than the measured one.17 For taking in one oxygen atom per cell BaYMn2O5 (i.e., δ = 0), which corresponds to one-fourth O2 per formula unit, the reaction reads BaYMn2O5(s) +

1 O2(g) → BaYMn2O5.5(s) 4

(reaction # 1)

The calculated enthalpy of this reaction is an exothermic ΔHR = −101.5 kJ mol−1 at 300 K, and there is no significant change up to a much higher temperature of 1500 K where the enthalpy is ΔHR = −100.1 kJ mol−1. The Gibbs free energy of this reaction, however, gets less exergonic from ΔGR = −105.0 kJ mol−1 at 300 K to ΔGR = −59.7 kJ mol−1 at 1500 K since gaseous O2 is present. Thus, the oxygen intake will still take place at higher temperatures but with a slightly lowered energy gain. In case one more oxygen atom is worked into BaYMn2O5.5 (i.e., δ = 0.5) to form BaYMn2O6, the reaction reads BaYMn2O5.5(s) +

1 O2(g) → BaYMn2O6(s) 4

Figure 5. Result of the thermogravimetric (TG) measurement during oxidation of powder BaYMn2O5+δ. In this measurement, temperature, weight, and the differential thermal analysis (DTA) signal of the sample were measured while the gas flow was switched from 5% H2/ 95% Ar (t = 0−3 min) to N2 (3−5 min), and then O2 (beyond 5 min).

stream passes the sample. In addition, the sample temperature sharply rises from about 510 °C to about 610 °C during oxygen intake. The temperature change of ΔTexp = 100 K, however, is much smaller than theoretically predicted because large parts of the reaction heat have been consumed by other partners, that is, the platinum pan and the gaseous oxygen which also increase in temperature. To make a more quantitative assessment, we need to include the role of the platinum pan together with the amount of oxygen in our thermochemical model calculations of the experimental reaction enthalpy: During the TG-DTA experiment, a sample of BaYMn2O5 (40 mg, n(oxide phase) = 0.0961 mmol, Cptheo(oxide phase) = 240.3 J mol−1 K−1) rests on a platinum pan (100 mg, n(Pt) = 0.5126 mmol, Cpexp(Pt) = 28.565 J mol−1 K−1 18) and is oxidized with flowing oxygen gas (125 ± 25 mL min−1 for one minute corresponding to n(O2) = 5.1 ± 1 mmol according to the ideal gas law, Cpexp(O2) = 33.734 J mol−1K−1 18) to yield BaYMn2O6 plus some excess heat. The flow rate is rather inaccurate because of the complexity of the equipment. Taking these data and ΔTexp = 100 K, the excess heat simply results as

(reaction # 2)

Here, we obtain a theoretical reaction enthalpy of ΔHR = −114.9 kJ mol−1 at 300 K which also keeps constant with increasing temperature. The Gibbs free energy of the reaction arrives at ΔGR = −115.6 kJ mol−1 at 300 K and ΔGR = −58.5 kJ mol−1 at 1500 K. Both steps of the oxygen-intake reaction are exergonic. It is reasonable to assume that the excess heat helps in overcoming certain activation barriers (see above section) such that this factor possibly speeds up the reactions. To quantitatively validate the theoretical results another thermogravimetric experiment was conducted in which the temperature change of a BaYMn2O5+δ sample was monitored during the absorption of one oxygen atom per formula unit, namely, going from δ = 0 (BaYMn2O5) to δ = 1 (BaYMn2O6). The experiment took place at a starting temperature of about 500 °C. As written before, the theoretical molar reaction enthalpy for this oxidation is just the sum of the two partial reactions (reaction # 1 and reaction # 2). For a given temperature of 800 K, ΔHRtheo amounts to −216.1 kJ mol−1.

ΔhR exp = ΔT exp[Cpexp(Pt)n(Pt) + Cp theo(oxide phase) n(oxide phase) + Cpexp(O2 )n(O2 )]

which yields ΔhRexp = −21.0 ± 3.4 J. We are certainly aware of the fact that this experimental heat has been calculated by using, 1914

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conducted for the BaYMn2O5+δ powder to quantitatively evaluate the exothermic heat upon oxygen intake of this oxide. A 40 mg sample of BaYMn2O5+δ was placed in a platinum pan (100 mg in weight) and set in a commercial thermobalance (Rigaku, TG8120GH). The sample was heated and kept at T ≈ 500 °C in a 5% H2/95% Ar gas mixture. Then, temperature, weight, and differential thermal analysis (DTA) signal of the sample were monitored while the gas flow was switched from 5% H2/95% Ar to O2 via N2. The gas flow rate was between 100 and 150 mL min−1. The intermediate N2 flow was necessary to prevent an extrinsic thermal contribution due to the combustion reaction between H2 and O2.

among other experimental data, the theoretical heat capacity of the oxide phase, but there is no other choice because Cp(oxide phase) is entirely unknown otherwise. Because ΔhRexp has been produced by oxidizing 0.0961 mmol of BaYMn2O5, the experimental molar reaction enthalpy arrives at ΔHR exp = ΔhR exp/n(oxide phase) = −218.3 ± 35.1 kJ mol−1

This is in almost perfect agreement with the value that was calculated from first principles, namely, ΔHRtheo = −216.1 kJ mol−1, but it might be a lucky coincidence because our model to calculate the experimental reaction enthalpy is based on some approximations and simplifications: We first assume that the increase in temperature, measured by a thermocouple under the platinum pan, and the corresponding reaction heat is uniformly distributed over the entire system (oxide + platinum + oxygen). The calculation of the experimental reaction enthalpy then comprises a rather crude estimation of the oxygen amount which carries away the excess heat. That is to say that we do not take the actual oxygen flow into account but assume a fixed amount of oxygen, calculated by multiplying the oxygen flux with the time by which the temperature is restored (see also Figure 5). Especially the overall heat consumption of oxygen might be large and can easily be over- but also underestimated. Nevertheless the experimental observations are, at least semiquantitatively, very well reproduced by these calculations. To improve the quality of our thermochemical measurements, additional experimental efforts are needed in the future.

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CONCLUSION The OSM BaYMn2O5+δ, which has remarkable properties, are characterized by a doubled perovskite structure and, thus, alternating layers of yttrium, barium, and manganese. The ab initio stability calculations upon release of oxygen reproduces the experimental findings for the vacancy position of being situated in the Y layer. In the compound BaYMn2O5 the whole layer is emptied of anions. The energetically easiest way for the oxygen migration is found with the help of an NEB (nudged elastic band) calculation to be from an Y layer to a Mn layer. This hopping path has only a small energy barrier of 0.18 eV. While it has been experimentally stipulated that the oxygen intake reaction is significantly accelerated by self-heating, this finding is affirmed from first-principles thermodynamic considerations which yield exothermic and also exergonic reactions, thereby helping to overcome certain activation barriers. The molar reaction enthalpy of oxidizing BaYMn2O5 to yield BaYMn2O6 has been calculated from first principles, and it arrives at ΔHRtheo = −216.1 kJ mol−1, very close to the experimentally approximated value which is ΔHRexp = −218.3 ± 35.1 kJ mol−1.

THEORETICAL METHODOLOGY

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The total energies and electronic structures of all phases were calculated in the context of density-functional theory. We used the Vienna ab initio Simulation Package (VASP),19−22 together with plane-wave basis sets and the projector augmented wave method.23 The contributions of interelectronic correlation and exchange to the total energies were treated using the generalized-gradient approximation (GGA)24 as parametrized by Perdew, Burke, and Ernzerhof.25 The kinetic energy cutoff of the plane waves was set to 500 eV. For the calculation of saddle points and the minimum energy paths (MEP), the nudged elastic band (NEB) method was applied,26,27 as implemented within VASP. By starting from well-converged initial and final states, a set of seven in-between images was constructed, and these were connected by artificial spring forces. Within the climbing image (CI)−NEB method,28 the image with the highest energy (climbing image) is identified and moved up the potential surface, thereby achieving a maximum energy. The CI−NEB method, if converged, is known to yield a good approximation for the reaction coordinate around the saddle point. Vibrational properties were calculated with the program FROPHO29,30 based on the ab initio force-constant method.31 Hellmann− Feynman forces needed to construct the force constant matrix were obtained by calculations with VASP on 2 × 2 × 2 supercells, which leaves us with 16 formula units, and by shifting all symmetryindependent atoms away from their equilibrium positions by 0.02 Å. The vibrational free energy Aph was directly obtained from the FROPHO post processing. The evaluation of the thermodynamic potentials at finite temperatures is straightforward.32

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would like to thank the high-performance computing centers at RWTH Aachen University and at Forschungszentrum Jülich for providing us with large amounts of CPU time. Additional financial support provided by the RWTH seed fund is gratefully acknowledged. T.M. thanks for the financial support by a Grant-in-Aid for Science Research (Contract No. 22750181) from the Japan Society for the Promotion of Science.

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REFERENCES

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EXPERIMENTAL PROCEDURES

A polycrystalline sample of BaYMn2O5+δ was synthesized with a solidstate reaction route utilizing an oxygen-pressure-controlled encapsulation technique, as described elsewhere.3 The X-ray powder diffraction analysis indicated that the resultant product was essentially of single phase. Thermogravimetric (TG) measurement was 1915

dx.doi.org/10.1021/cm300655y | Chem. Mater. 2012, 24, 1910−1916

Chemistry of Materials

Article

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