Ji
Wu
a,
Stevin S.
Pramana
a,
Stephen J.
Skinner
a,
John A.
Kilner
ab and
Andrew P.
Horsfield
*a
aDepartment of Materials, Imperial College London, SW7 2AZ, London, UK. E-mail: a.horsfield@imperial.ac.uk; Tel: +44 (0)20 7594 6753
bHydrogen Production Division, International Institute for Carbon-Neutral Energy Research (I2CNER), Motooka 744, Nishi-Ku, Fukuoka 819-0395, Japan
First published on 16th October 2015
La2NiO4+δ (LNO214) is a potential intermediate temperature solid oxide fuel cell (IT-SOFC) cathode material which belongs to the Ruddlesden–Popper (RP) structure series An+1BnO3n+1. There is interest in this material as it offers a way to avoid Sr segregation and associated degradation, as LNO214 can take in oxygen interstitials and become catalytically active without A-site doping. While the bulk ionic conduction mechanisms are well studied, its surface structure and chemistry are still a matter of debate. Recent experimental studies (both with and without dopants) reveal that it has a La-terminated surface and a highly Ni deficient surface layer. These results disagree with previous computer simulations, and undermine the conventional explanation for the oxygen reduction process at the surface. In this work we evaluate the thermodynamic stability of La2NiO4+δ at IT-SOFC operation temperatures. We find that the decomposition of La2NiO4+δ to produce La2O3 and higher order RP phases is indeed thermodynamically favourable. A hypothesis for the formation mechanism of the La-terminated and Ni deficient surface based on partial decomposition and surface passivation is proposed and evaluated.
There are only two sets of simulations of LNO214 surfaces performed so far10,11 to the best of the authors' knowledge. Read et al.10 suggested that LNO surfaces should terminate with Ni due to its lower surface energy. Zhou et al.11 studied the oxygen adsorption mechanism based on the La2NiO4 surface proposed in Read's work. However, the recent surface characterisation of similar RP structured materials, including La2NiO4+δ, La2−xSrxNiO4+δ (LSNO) and PrLaNiO4+δ (PLNO), has revealed that these surfaces terminate with purely A-site cations (La, Sr, and Pr);12–14 no Ni was found in the low energy ion scattering (LEIS) spectra of the surfaces within the detection limit. The Ni:
La(Sr) ratio was also found to be far from stoichiometry down to a depth of about 7 nm.12 A similar absence of Ni and Ni
:
La non-stoichiometry was obtained in LNO.14 These results suggest that the conventional oxygen reduction mechanism which requires oxygen atoms to adsorb onto surface Ni sites might not be possible.
In this study, we provide an explanation for the Ni absence on La2NiO4 surfaces by evaluating the thermodynamic stabilities of a set of related phases over a range of temperatures and oxygen partial pressures. The calculations are based on the existing experimental thermodynamic data for relevant materials.15,16 Based on our calculations, a hypothesis explaining the absence of Ni on LNO surfaces is proposed and discussed. We find that it is thermodynamically advantageous for La2NiO4 to form a combination of La2O3 (containing no Ni, and presumed to appear at the surface) and higher order RP phases (Lan+1NinO3n+1 where n = 2 or 3).
![]() | (1) |
![]() | (2) |
![]() | (3) |
For ease of comparison, all reactions were normalised to consume half a mole of oxygen gas and produce one mole of La2O3.
The change in Gibbs free energy of the above reactions at different temperatures and oxygen partial pressures can be written as:
![]() | (4) |
![]() | (5) |
![]() | (6) |
The standard molar Gibbs formation energy, ΔG0(T), of a compound phase can be expressed as:
ΔG0(T) = G(T) − HSER = a + bT + cT![]() | (7) |
a (J mol−1) | b (J mol−1 K−1) | c (J mol−1 K−1) | d 2 (J mol−1 K−2) | d −1 (J K mol−1) | Ref. | |
---|---|---|---|---|---|---|
La2NiO4 | −2![]() ![]() |
1035.849 | −178.04 | −0.007089 | 1![]() ![]() |
16 |
La3Ni2O7 | −3![]() ![]() |
1781.990 | −301.86 | −0.01712 | 1![]() ![]() |
16 |
La4Ni3O10 | −4![]() ![]() |
2368.174 | −405.25 | −0.0326 | 2![]() ![]() |
16 |
LaNiO3 | −1![]() ![]() |
696.185 | −118.12 | −0.0096 | 648![]() |
16 |
La2O3 | −1![]() ![]() |
674.72 | −118 | −0.008 | 620![]() |
17 |
The chemical potential of oxygen is given by18,19
![]() | (8) |
![]() | (9) |
![]() | (10) |
The constants A, B, C, D, E, F, G, and H are given in Table 2, and are obtained from the NIST chemical data handbook.19 The temperature coefficient t is , where T is the temperature in Kelvin. The unit of
is kJ mol−1, where RT stands for room temperature (298.15 K), and the unit of
is J mol−1 K−1.
Temperature (K) | 100–700 | 700–2000 | 2000–6000 |
---|---|---|---|
A (kJ mol−1 K−1) | 31.32234 | 30.03235 | 20.91111 |
B (kJ mol−1 K−2) | −20.23531 | 8.772972 | 10.72071 |
C (kJ mol−1 K−3) | 57.86644 | −3.988133 | −2.020498 |
D (kJ mol−1 K−4) | −36.50624 | 0.788313 | 0.146449 |
E (kJ K mol−1) | −0.007374 | −0.741599 | 9.245722 |
F (kJ mol−1) | −8.903471 | −11.32468 | 5.337651 |
G (kJ mol−1) | 246.7945 | 236.1663 | 237.6185 |
H (kJ mol−1) | 0.0 | 0.0 | 0.0 |
The Gibbs free energy of selected decomposition reactions can now be calculated at various temperatures and oxygen partial pressures based on thermodynamic equations and associated constants given above.
It is important to note that the lanthanum nickelates are not stoichiometric when operating as a cathode under SOFC working conditions, where oxygen partial pressure is equal to or more than 0.2 bar. La2NiO4 is usually oxygen rich, while the higher order La3Ni2O7 and La4Ni3O10 are oxygen deficient. In this study, the thermodynamic equation constants of the compounds used are fitted as stoichiometric phases based on thermal measurements on real, non-stoichiometric phases.15–17 To provide a better prediction under experimental conditions, the error due to this difference should be estimated. For example, the Gibbs free energy of formation of the non-stoichiometric La2NiO4+δ is given as:
![]() | (11) |
To determine the uncertainty in the experimental value, we need the stoichiometric Gibbs free energy of formation to compare with. The formation free energy of stoichiometric La2NiO4 is given by:
ΔGLa2NiO4(T, pO2) = μLa2NiO4 − (2μLa + μNi + 2μO2) | (12) |
The difference between the experimental ΔGLa2NiO4+δ and ideal ΔGLa2NiO4 is then:
![]() | (13) |
Similarly, for the higher order La3Ni2O7 and La4Ni3O10, there is:
![]() | (14) |
![]() | (15) |
The differences in the chemical potential of respective LNO RP compounds can be estimated using their DFT calculated ground state energies, assuming a small free energy change due to entropy. The chemical potential of oxygen gas can be calculated using data from the NIST chemical database.19 The defect structures selected for DFT calculation are La2NiO4.25, La3Ni2O6.75 and La4Ni3O9.5. These non-stoichiometries are selected to represent extreme cases observed in experiments. The energy differences between these defect structures and their respective ideal structures are used to plot the Gibbs free energies of reaction when defect species are involved.
Taking the reaction between La2NiO4.25 and La3Ni2O7 as an example, for the overall reaction, we have:
4La2NiO4.25 → 2La3Ni2O7 + La2O3 | (16) |
Its Gibbs free energy of reaction will be:
![]() | (17) |
The other three defect reactions considered are:
![]() | (18) |
![]() | (19) |
![]() | (20) |
Free energy changes of these reactions are then plotted together with their respective ideal reactions.
All density functional theory calculations in this work have been performed using the CRYSTAL09 software package,20,21 based on the expansion of the crystalline orbitals as a linear combination of a local basis set consisting of atom-centered Gaussian orbitals. The basis sets used for Ni and O atoms are triple-valence all-electron basis sets. A Ni atom is described by a 28–411d(41) contraction (one s, four sp, -and two d shells). An O atom is described by an 8–411d(1) contraction (one s, three sp, and one d shells). The most diffuse sp(d) exponents are αNi = 0.6144(0.411) bohrs−2 and αO = 0.1843(0.6) bohrs−2.21 The La core electrons are described by using a pseudopotential, which is adapted from Dolg et al.'s quasirelativistic La pseudopotential.22 The La valence electron basis functions are 411p(411)d(311)f(11) contracted sets (three s, three p, three d and two f shells) with the most diffuse exponent being αLa = 0.15 bohrs−2 for each s, p, d and f shell.23 A ”ghost” atom is used to describe La vacancy by removing all but the two most diffuse contractions of each original La s, p, d and f shell. These basis sets ensure that we have an accurate description of electron density at the La vacancy site.
The B3LYP hybrid-exchange electron density functional,24 implemented in the CRYSTAL09 package, is used to approximate electron exchange and correlation. This hybrid functional is expected to give a reliable description of solid oxide systems such as the LNO-RP family oxides.23,25,26 Numerical integration of the exchange and correlation potentials and energy functional is performed on an atom-centered grid of points. The XXLGRID option implemented in CRYSTAL09 was used for all calculations, which consisted of a pruned grid consisting of 99 radial points and 5 subintervals with (146, 302, 590, 1454 and 590) angular points.21 The cutoff threshold parameters of direct summation of the Coulomb and exchange series are set to be 7, 7, 7, 7 and 14 as described in the CRYSTAL09 manual.21 A Pack–Monkhorst mesh with a shrinking factor of 8 was chosen for reciprocal space sampling of La2NiO4. For larger La3Ni2O7 and La4Ni3O10 systems, the shrinking factor used is 4. The structures selected as the initial input for DFT simulation are taken from Skinner's4 (La2NiO4) and Ling's27 (La3Ni2O7 and La4Ni3O10) neutron diffraction studies. The supercells used in the calculations are the respective minimum conventional crystallographic cells of La2NiO4 (28 atoms), La3Ni2O7 (24 atoms) and La4Ni3O10 (34 atoms). We computed the La vacancy migration barrier height using a (2 × 1 × 1) supercell of the conventional La2NiO4 lattice. This defective supercell contains 55 atoms. One of the La atoms is replaced by the La “ghost” atom mentioned above. Charge neutrality is maintained by promoting three Ni2+ atoms to Ni3+. The La vacancy migration energy is evaluated using the Distinguished Reaction Coordinate (DRC) method implemented in the CRYSTAL09 package. A full description of the DRC method and its robustness has been given by Rimola et al. and will not be detailed here.28
According to Fig. 1, the decomposition of La2NiO4 into higher order RP La–Ni–O materials is thermodynamically favourable up to about 1400 K at 0.2 bar oxygen partial pressure (atmospheric pressure of oxygen). La3Ni2O7 is the energetically favourable phase below 1000 K, while La4Ni3O10 will be more favourable above 1000 K. LaNiO3 is never the preferred phase over the entire temperature range considered. These results show that LNO would start to decompose when it is in contact with air even at room temperature. The decompositions will also take place at the designated IT-SOFC operation temperature (600–800 °C). We suspect that the decomposition products La2O3 and La3Ni2O7 will form a layered structure on top of the bulk La2NiO4. Taking the (001) surface as an example, there are two possible stacking orders, La3Ni2O7–La2O3–La2NiO4 and La2O3–La3Ni2O7–La2NiO4, with both being ordered from the surface to the bulk. The latter one is predicted to be the favourable stacking order. The first stacking order contains a large lattice mismatch between La2O3 and the two La–Ni–O RP phases, while the second one only contains one such large mismatch and one very small interfacial strain between the two La–Ni–O RP phases. The lattice mismatch between La3Ni2O7 and La2NiO4 is only about 1% at the (001) interface.4,27,29 This predicted stacking order is consistent with Druce et al.'s secondary ion mass spectrometry (SIMS) – low energy ion scattering (LEIS) depth profiling of polycrystalline La2NiO4. Druce's depth profile also showed a La enriched – Ni enriched – stoichiometric layered structure from the surface to the bulk of the crystal.14 The peak Ni:
La ratio they observed in the Ni enriched region is about 2
:
3, which agrees with the Ni
:
La ratio in our predicted sub-surface La3Ni2O7 layer.
These predictions agree partly with a long-term decomposition experiment on La2NiO4+δ. In this experiment Gauquelin et al. heated La2NiO4+δ to 1273 K in flowing air for two weeks.30 The characterisation of the heated surface by transmission electron microscopy (TEM) revealed layers of La3Ni2O7 and La4Ni3O10 with thicknesses of about 700 nm. On the (100) surface, both La3Ni2O7 and La4Ni3O10 were found, but only La4Ni3O10 was present on the (001) surface. According to our calculations, La4Ni3O10 should be the most stable phase at 1273 K. The mixed layer of La4Ni3O10 and La3Ni2O7 may be due to incomplete conversion of La3Ni2O7 formed at a lower temperature during the heating process and the previous thermal history.
To form the transformed layers, La needs to move from the bulk to the surface. As there are different diffusion paths for La to the (001) and (100) surfaces we expect different La diffusion rates, and hence different growth rates for the transformed layers at these surfaces. One significant difference between our prediction and that of Gauquelin's experiment is that the other predicted product, La2O3, was not observed in the experiment.30 A surface layer only containing La2NiO4 and its higher order RP counterparts cannot give the La rich region observed by XPS12 and SIMS-LEIS depth profiling14 but rather the opposite (La deficient region30). Burriel et al. reported that the La and Sr rich surface layer is about 7 nm thick in the related La2−xSrxNiO4+δ phase. In Druce's more recent work,14 the La enriched layer is only about 1 nm thick in the depth profile of polycrystalline ceramic La2NiO4. Such a thin layer may be damaged by the destructive Focused Ion Beam (FIB) technique, which was used to cut a suitable lamellar cross-section at the surface for the TEM study in Gauquelin's experiment.
Despite the thermodynamically favoured decomposition process (about −100 kJ mol−1 for La2O3 production at room temperature), La2NiO4 is stable and does not transform into its higher order RP phases completely at room temperature. In the long-term decomposition experiment, only about 700 nm of the surface La2NiO4 was converted into La3Ni2O7 or La4Ni3O10 after two weeks.30 Therefore, there must be a very slow rate determining step or a surface passivation mechanism to prevent complete decomposition of La2NiO4. The three experimental studies mentioned earlier treated the samples differently (1273 K for two weeks (Gauquelin), 723 K for 72 hours (Burriel) and 1273 K for 12 hours (Druce)). A shorter heating time at a lower temperature gives a thinner transformed layer (only a few nanometers) than the high temperature, long-term heated sample (about 700 nm).12,14,30 Heating temperature and duration do have a significant impact on the amount of La2NiO4 transformed. The reactions that result in the formation of the surface oxide layer must therefore include at least one activation process. A strong candidate is the diffusion of La, a process that is necessary for the oxide formation, which will be activated. The diffusion barriers of several possible La diffusion paths are briefly evaluated in the next section. The large difference in the thickness of A-site enriched layers reported by Burriel and Druce, despite having similar thermal treatments, is believed to be mainly due to Sr segregation which only occurs in Burriel's Sr-doped La2−xSrxNiO4+δ. This would lead to a much thicker (7 nm compared to Druce's 1 nm) A-site (La + Sr) enriched region despite a similar thermal history. In addition, Burriel's sample is a single crystal while Druce tested a polycrystalline ceramic sample. The different natures of the samples should also affect the amount of decomposed La2NiO4.
Fig. 2 and 3 clearly show that oxygen partial pressure has a significant impact on the Gibbs free energy of these reactions. According to the graphs, the critical oxygen partial pressure required to allow decomposition varies with temperature. Therefore, the thickness of maximum decomposition layers formed at different temperatures after long heating times will vary with critical oxygen partial pressure. In a controlled low pO2 or high vacuum environment, this maximum transformation thickness can be measured to verify the hypothesis. If this proves to be true, controlling the oxygen partial pressure and the temperature might provide a way to suppress or reverse the decomposition when desired.
Compound | a (Å) | b (Å) | c (Å) | Ref. | |
---|---|---|---|---|---|
La2NiO4 | Expt. | 5.459 | 5.464 | 12.685 | 4 |
Calc. | 5.538(8) | 5.539(3) | 12.752(2) | ||
Error | 1.47% | 1.39% | 0.52% | ||
La3Ni2O7 | Expt. | 5.397 | 5.450 | 20.507 | 27 |
Calc. | 5.435(0) | 5.586(1) | 20.868(3) | ||
Error | 0.70% | 2.49% | 1.76% | ||
La4Ni3O10 | Expt. | 5.413 | 5.462 | 27.960 | 27 |
Calc. | 5.448(3) | 5.570(8) | 28.512(2) | ||
Error | 0.65% | 1.99% | 1.97% |
In Fig. 4 and 5 we can see that all the defective reactions still have negative reaction Gibbs energy in the IT-SOFC working temperature range (873–1073 K). The defective reactions seem to be always favourable even at temperatures beyond 1673 K according to the trend shown in Fig. 4 and 5. However, the assumption of small energy change due to entropy will not hold at temperatures much higher than 1673 K, so the estimated trends based on ground-state DFT calculations should only be used to predict reactions at lower temperature ranges. For the temperature range we are interested in (873–1073 K), these four reactions can give an idea of the order of magnitude of the decomposition Gibbs energies under experimental conditions since the involved phases are some of the extremely defective cases. It is noted that the 214-defect reactions are particularly favourable as shown in the figures (about 100 kJ mol−1 more favourable than ideal reactions). This suggests that a significant amount of energy is required to accommodate the oxygen interstitials in La2NiO4.25 at the ground state (DFT simulation condition). At the ground state (0 K), it is more difficult for the ideal lattice to take in an interstitial oxygen (like defective LNO214) than to lose an oxygen and form a vacancy (like defective LNO327 and LNO4310) due to the contraction of the lattice at a low temperature. This is one of the sources of errors when using DFT simulation to estimate the Gibbs energies of reaction for the defective reactions. At IT-SOFC working temperatures, the energy differences between the defective LNO214 reaction and the defective LNO327 (or LNO4310) reactions should be smaller. The actual Gibbs free energy of reaction will be affected by specific experimental conditions, including temperature, oxygen partial pressure, thermal histories and initial composition of the materials, but they will fall somewhere close to the calculated region where the Gibbs free energy of the decomposition reaction is less than zero. Therefore, the simple conclusion drawn from these estimations is that the decomposition will be favoured at IT-SOFC operation temperatures even for the extremely defective compositions.
As noted earlier, for the LNO214 structure to decompose, La atoms need to diffuse into the surface. As an activation process, this diffusion has an associated activation energy. We have computed the activation energy of two possible diffusion steps (shown in Fig. 6). We obtained a barrier height of 4.31 eV for the rocksalt path, and a height of 4.57 eV for the perovskite path. Although no experimental cation diffusion data for La2NiO4 are available, our calculated value for the perovskite layer (4.57 eV) is comparable to the La diffusion activation energy of 4.98 eV in LaCrO3.31 Compared to the oxygen diffusion activation energy (0.88 eV)5 in single crystal La2NiO4, the La diffusion activation energy is about five times as large. Assuming a simple Arrhenius relationship between the diffusion rate and the diffusion activation energy, we can estimate that the La diffusion rate is at least 3 orders of magnitudes smaller than the O diffusion rate. This might be part of the reason behind the limited decomposition. A more detailed study on the La diffusion during the decomposition reaction is being carried out, and the results will be presented in a future publication.
Some questions remain unclear and cannot be answered with the hypothesis. Although thermodynamically favourable, the decomposition reactions studied were very slow as shown in experiments. The diffusion barrier of La is briefly evaluated and shows a quite high diffusion activation energy. The details of the decomposition reaction kinetics are being studied at the moment. These reaction kinetics will be critical to the evaluation of the long term stability of La2NiO4. Only a few particular decomposition reactions were considered in this study. Therefore, there might be other combinations of stable species. To find out the most stable combinations of phases, a density functional theory (DFT) based full phase diagram of the La–Ni–O system is planned.
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