燃料化学学报（中英文）

Variable	Parameter values
A-site elements	Na, K, Ca, Ba, La
B-site elements	Mg, Ti, V, Cr, Mn, Co, Ni, Cu, Ge, Zr, Sn
x	0, 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875, 1
y	0, 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875, 1

Variable	Parameter values
A-site elements	Na, K, Ca, Ba, La
B-site elements	Mg, Ti, V, Cr, Mn, Co, Ni, Cu, Ge, Zr, Sn
x	0, 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875, 1
y	0, 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875, 1

Composition	CLAS performance	Predicted E_ovf/eV
SrFeO_3−δ^[3]	Oxygen carrying capacity was 0.5% at 500 ℃ (0−0.2 atm $p_{{\mathrm{O_2}}} $), the onset temperature for O₂ release was around 400 ℃	2.16 (SrFeO₃)
SrFe_0.25Co_0.75O_3−δ^[3]	Oxygen carrying capacity was 1.3% at 500 ℃ (0−0.2 atm $p_{{\mathrm{O_2}}} $), the onset temperature for O₂ release was around 290 ℃	1.64 (SrFe_0.25Co_0.75O₃)
Sr_0.8Ca_0.2Fe_0.4Co_0.6O_3−δ^[7]	Oxygen carrying capacity was 1.11% at 450 ℃ (0−0.2 atm $p_{{\mathrm{O_2}}} $)	1.77 (Sr_0.75Ca_0.25Fe_0.375Co_0.625O₃)
Sr_0.76Ca_0.24FeO_3−δ^[33]	Oxygen carrying capacity was 1.2% at 500 ℃ (0.05−0.2 atm $p_{{\mathrm{O_2}}} $)	2.24 (Sr_0.75Ca_0.25FeO₃)
Sr_0.75Ba_0.25FeO_3−δ^[9]	Oxygen carrying capacity was 0.73% at 400−600 ℃ (0.2 atm $p_{{\mathrm{O_2}}} $)	2.06 (Sr_0.75Ba_0.25FeO₃)

Composition	CLAS performance	Predicted E_ovf/eV
SrFeO_3−δ^[3]	Oxygen carrying capacity was 0.5% at 500 ℃ (0−0.2 atm $p_{{\mathrm{O_2}}} $), the onset temperature for O₂ release was around 400 ℃	2.16 (SrFeO₃)
SrFe_0.25Co_0.75O_3−δ^[3]	Oxygen carrying capacity was 1.3% at 500 ℃ (0−0.2 atm $p_{{\mathrm{O_2}}} $), the onset temperature for O₂ release was around 290 ℃	1.64 (SrFe_0.25Co_0.75O₃)
Sr_0.8Ca_0.2Fe_0.4Co_0.6O_3−δ^[7]	Oxygen carrying capacity was 1.11% at 450 ℃ (0−0.2 atm $p_{{\mathrm{O_2}}} $)	1.77 (Sr_0.75Ca_0.25Fe_0.375Co_0.625O₃)
Sr_0.76Ca_0.24FeO_3−δ^[33]	Oxygen carrying capacity was 1.2% at 500 ℃ (0.05−0.2 atm $p_{{\mathrm{O_2}}} $)	2.24 (Sr_0.75Ca_0.25FeO₃)
Sr_0.75Ba_0.25FeO_3−δ^[9]	Oxygen carrying capacity was 0.73% at 400−600 ℃ (0.2 atm $p_{{\mathrm{O_2}}} $)	2.06 (Sr_0.75Ba_0.25FeO₃)

使用图神经网络高通量筛选用于低温化学链空气分离的Sr_xA_1−xFe_yB_1−yO₃钙钛矿

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赵杰 ¹ , 董长青 ¹^,²^,^* , 薛俊杰 ¹ , 胡笑颖 ¹ , 张俊姣 ³

燃料化学学报（中英文） | 2026,54(7): 20250302-1423-20250302-1429

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燃料化学学报（中英文） 2026 , 54 (7) : 20250302-1423 -20250302-1429

使用图神经网络高通量筛选用于低温化学链空气分离的Sr_xA_1−xFe_yB_1−yO₃钙钛矿

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赵杰¹, 董长青¹^,²^,^*, 薛俊杰¹, 胡笑颖¹, 张俊姣³

作者信息

¹华北电力大学新能源学院生物质发电成套设备国家工程实验室(华北电力大学), 北京 102206

²华北电力大学新能源学院新能源电力系统全国重点实验室(华北电力大学), 北京 102206

³华北电力大学能源动力与机械工程学院, 北京 102206

通讯作者:

董长青

High-throughput screening of Sr_xA_1−xFe_yB_1−yO₃ perovskites for low-temperature chemical looping air separation using graph neural networks

Jie ZHAO¹, Changqing DONG¹^,²^,^*, Junjie XUE¹, Xiaoying HU¹, Junjiao ZHANG³

Affiliations

¹National Engineering Laboratory for Biomass Power Generation Equipment (NCEPU), School of New Energy, North China Electric Power University, Beijing 102206, China

²New Energy Generation National Engineering Research Center (NCEPU), School of New Energy, North China Electric Power University, Beijing 102206, China

³School of Energy Power and Mechanical Engineering, North China Electric Power University, Beijing 102206, China

Corresponding Author:

E-mail: dongcq@ncepu.edu.cn

出版时间: 2026-07-10 doi: 10.1016/S1872-5813(26)60680-9

文章导航

摘要

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低温化学链空气分离（CLAS）是一种很有前景的富氧气流生产技术。它利用固体载氧体的氧化还原特性选择性地捕获和释放空气中的氧气。氧空位形成能（E_ovf）可用于评估氧化物释放氧的难易程度。本研究通过热力学计算确定了CLAS载氧体的E_ovf适用范围<2.3 eV，训练了一个图神经网络（GNN）并用于预测E_ovf。通过GNN模型预测E_ovf，筛选了3649种Sr_xA_1−xFe_yB_1−yO₃钙钛矿成分。结果表明，A位Ba和Ca离子的掺杂以及B位Co离子的掺杂可以有效降低钙钛矿结构的E_ovf。通过对已知CLAS材料的重新发现，验证了使用E_ovf方法筛选CLAS氧载体的可行性。这些结果表明了图神经网络预测氧空位形成能在加速CLAS载氧体材料发现中的有效性。

关键词

化学链空气分离 / 氧空位形成能 / 图神经网络 / 材料发现

Abstract

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Low-temperature Chemical Looping Air Separation (CLAS) is a promising technology for producing oxygen-enriched gas streams. It utilizes the redox properties of solid oxygen carriers to selectively capture and release oxygen from the air. Oxygen vacancy formation energy (E_ovf) can be used to evaluate the ease of oxygen release by the oxides. In this study, the applicable range of E_ovf for CLAS oxygen carriers was determined to be <2.3 eV using the thermodynamic calculations. A graph neural network (GNN) was trained and used to predict the E_ovf. By predicting E_ovf with the GNN model, a screening from the 3649 compositions of Sr_xA_1−xFe_yB_1−yO₃ perovskites was conducted to discover the CLAS oxygen carriers. The prediction results indicate that the doping of Ba and Ca ions at the A site and Co ions at the B-site can effectively reduce the E_ovf of the perovskite structure. The feasibility of screening the CLAS oxygen carriers using the E_ovf method was validated through the rediscovery some known materials. These results support the effectiveness of GNNs in accelerating the discovery of CLAS oxygen carriers.

Key words

chemical looping air separation / oxygen vacancy formation energy / graph neural network / material discovery

引用本文

赵杰, 董长青, 薛俊杰, 胡笑颖, 张俊姣. 使用图神经网络高通量筛选用于低温化学链空气分离的Sr_xA_1−xFe_yB_1−yO₃钙钛矿. 燃料化学学报（中英文）, 2026 , 54 (7) : 20250302-1423 -20250302-1429 . DOI: 10.1016/S1872-5813(26)60680-9

Jie ZHAO, Changqing DONG, Junjie XUE, Xiaoying HU, Junjiao ZHANG. High-throughput screening of Sr_xA_1−xFe_yB_1−yO₃ perovskites for low-temperature chemical looping air separation using graph neural networks[J]. Journal of Fuel Chemistry and Technology, 2026 , 54 (7) : 20250302-1423 -20250302-1429 . DOI: 10.1016/S1872-5813(26)60680-9

正文

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Chemical looping air separation (CLAS) is an attractive technology for industrial applications, owing to its high efficiency, low energy consumption, and the potential to integrate with thermoelectric power generation cycles to reduce CO₂ emissions^[1−3]. CLAS operates using oxide-based oxygen carriers that can reversibly absorb and release O₂ in response to changes in the oxygen partial pressure or temperature. As shown in Figure 1, when the oxygen partial pressure is low, the lattice oxygen in the oxide is released in the form of gaseous oxygen, accompanied by the reduction of the oxide. Subsequently, the reduced oxide can be regenerated in air or oxygen-rich stream. Repeating this process in a cyclic manner enables a continuous air separation and oxygen production.

Perovskite materials possess superior oxygen transport capabilities, high chemical stability, and tunable redox properties, which render them ideal oxygen-carrier candidates for chemical looping (CL) processes^[1,4−6]. SrFeO_3−δ with a perovskite structure has been studied for low-temperature CLAS reactions (400−650 °C) due to its excellent oxygen release and absorption capabilities^[2,7]. The perovskite structure of SrFeO_3−δ provides the possibility of doping substitution atoms at the A-site or B-site to further regulate and enhance the material´s redox properties^[7−8]. For instance, the doping of A-site with Ba^[9] or Ca^[8,10] and B-site with Co^[11−12] of SrFeO₃ has demonstrated an enhanced CLAS performance. However, the search for optimal doping elements and concentrations still relies largely on conventional heuristics and trial-and-error methods.

Oxygen vacancy formation energy (E_ovf) can be used to evaluate the redox performance of CLAS materials^[13−15]. Oxygen carrier materials with lower E_ovf are more likely to release lattice oxygen and have a better performance in low-temperature CLAS^[16−17]. Density functional theory (DFT) method is commonly used to calculate the E_ovf of oxides in crystal structures^[18−19]. The E_ovf can be calculated through Equation (1):

$ \begin{matrix}{E}_{{\mathrm{ovf}}}={E}_{{\mathrm{def}}}-{E}_{{\mathrm{perf}}}+{\mu }_{{\mathrm{O}}} \end{matrix} $

(1)

where

$ {E}_{{\mathrm{def}}} $

is the total energy of the supercell with an O vacancy,

$ {E}_{{\mathrm{perf}}} $

is the total energy of the pristine supercell,

$ {\mu }_{{\mathrm{O}}} $

is the O chemical potential. However, calculating the E_ovf using DFT is expensive and time-consuming.

Machine learning methods have been researched for rapid prediction of E_ovf. Linear models based on DFT descriptors such as band gap and formation energy can predict E_ovf with a mean absolute error (MAE) of 0.39 eV, without the need to construct a supercell with an oxygen vacancy^[20−21]. The unified atomistic line graph neural network force-field (ALIGNN-FF), trained with formation energy data of the defect-free crystals, can be directly applied to predict the E_ovf with an MAE of 0.87 eV^[22−23]. The defect graph neural network (dGNN) model, trained with E_ovf data calculated by DFT, predicts the E_ovf of oxides (containing elements present in the training set) with an MAE of 0.52 eV^[14].

In this study, an ALIGNN model was trained using a curated dataset of E_ovf and used for the prediction of E_ovf. The range of E_ovf suitable for CLAS oxygen carriers was estimated using thermodynamic calculations. High-throughput screening for CLAS was performed on 3649 Sr_xA_1−xFe_yB_1−yO₃ perovskites through stability judgment and E_ovf prediction. The feasibility of the E_ovf method for screening CLAS oxygen carriers was confirmed through materials rediscovery.

1　Methodology

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1.1　Machine learning

The charge-neutral E_ovf dataset^[14,24] utilized in this article was based on DFT-computed data using the Generalized Gradient Approximation (GGA) with Hubbard U correction. The dataset comprises 48 cationic elements, 102 space groups, 901 compounds, 2329 distinct oxygen vacancy structures, 9342 oxygen sites (see Section S1 in Supplemental Information). The distribution of elements in the dataset is shown in Figure 2(a).

The Atomistic Line Graph Neural Network (ALIGNN) demonstrated superior performance over other graph neural networks in multiple atomistic prediction tasks by incorporating bond angle information^[23,25]. As shown in Figure 2(b), the ALIGNN was trained to predict the E_ovf at all oxygen sites within the crystal structures. Details on the ALIGNN can be found in the related paper^[23,25]. In brief, each node in the atomistic graph is assigned 9 input node features based on its atomic species: electronegativity, group number, covalent radius, valence electrons, first ionization energy, electron affinity, block and atomic volume. The inter-atomic bond distances are used as edge features with a radial basis function up to a cut-off of 8 Å. A periodic 12-nearest-neighbor graph construction was used. This atomistic graph is then used for constructing the corresponding line graph using interatomic bond-distances as nodes and bond-angles as edge features. The dataset was partitioned into training, validation, and test sets at a ratio of 80∶10∶10, and an ALIGNN model was trained to predict the E_ovf.

1.2　Thermodynamic calculations

The E_ovf predicted by the ALIGNN corresponds to the zero-temperature limit. Therefore, thermodynamic calculations are required to determine the range of E_ovf values that are suitable for various chemical looping applications. In light of the comparable E_ovf across distinct sites in the ideal perovskite structure^[14,26], it is reasonable to assume that the properties of oxygen vacancies have a degree of similarity among these sites. At a specified temperature T, the Gibbs free energy for the formation of oxygen vacancies in the crystalline structure is expressed as follows^[27]：

$ \Delta G=n*{h}_{{\mathrm{ovf}}}-T{\Delta S}_{{\mathrm{cf}}} $

(2)

where n represents the number of vacancies, h_ovf denotes the formation enthalpy per defect (including contributions from vibrational enthalpy and entropy for each defect), and ΔS_cf is the configurational entropy. Assuming a total number of N atoms in the system (where N ≫ n), the structural entropy is derived via Stirling’s approximation as follows^[27]：

$ {\Delta S}_{{\mathrm{cf}}}={k}_{{\mathrm{B}}}\times n \times (\ln N-\ln n)$

(3)

In the context of solids within the zero-temperature limit, the volume change is negligible, and thus the h_ovf can be reasonably approximated by the E_ovf^[28]. The chemical potential Δμ is introduced to determine the Gibbs free energy of oxygen vacancy formation under the relevant thermodynamic constraints^[14]：

$ \Delta G=n \times \left({E}_{{\mathrm{ovf}}}+{\Delta }\mu \right)-T\times {k}_{{\mathrm{B}}}\times n \times (\ln N-\ln n)$

(4)

when the system reaches equilibrium, the condition

$ \Delta G=0 $

leads to the following expression for the dimensionless oxygen vacancy concentration：

$ {c}_{v}=\frac{n}{N}={{\mathrm{e}}}^{-\left({E}_{{\mathrm{ovf}}}+{\Delta }\mu \right)/\left({k}_{{\mathrm{B}}}T\right)} $

(5)

Given a specific oxygen vacancy concentration, the corresponding Δμ at the thermodynamic constraints can be determined by inverting the above expression^[14]. By comparing the Δμ curves corresponding to different E_ovf values on the Ellingham diagram, the applicable ranges of E_ovf for different chemical looping applications can be identified^[13−14].

1.3　High-throughput screening for Sr_xA_1−xFe_yB_1−yO₃

The Sr_xA_1−xFe_yB_1−yO₃ perovskite structures were constructed by substituting A- and/or B-site cations in SrFeO₃ using the pymatgen package^[29]. Table 1 summarizes the dopant types and concentrations investigated in this study. By exhausting all possible combinations of A- and/or B-site dopants in the selected cation network, 3520 perovskite models were constructed. Through a preliminary screening process, some of these combinations were filtered out due to their inability to form stable perovskite phases. Firstly, the total valence of the compositions was examined to determine whether it can be zero (see Section S2 in Supplemental Information). Besides charge neutrality, a modified tolerance factor

$ \tau =\dfrac{{r}_{{\mathrm{O}}}}{{r}_{{\mathrm{B}}}}-{n}_{{\mathrm{A}}}\left({n}_{{\mathrm{A}}}-\dfrac{{r}_{{\mathrm{A}}}/{r}_{{\mathrm{B}}}}{\ln\left({r}_{{\mathrm{A}}}/{r}_{{\mathrm{B}}}\right)}\right) $

^[30] was applied to estimate the stabilities of the perovskite structures, where r_O, r_A, r_B represent the radii of oxygen anion, and the A- and B-site cations (see Table S1 in Supplemental Information). n_A and n_B are the oxidation states of the A- and B-site cations, respectively. The modified tolerance factor (τ) carries more chemical information and exhibits better predictive ability than the classical Goldschmidt tolerance factor^[4,30].

After the initial construction of the doped crystal structures, the fast structure optimization was performed using the ALIGNN-FF^[23] model, for which the model parameters were directly adopted from the literature^[23] and shared publicly. The ALIGNN-FF was developed using both energies and forces for applications, such as, in fast structure optimization. Then, the optimized crystal structures were input into the ALIGNN model which is then trained for E_ovf to predict the E_ovf for each oxygen site. The average of all the E_ovf values for each crystal structure was calculated and used as an indicator to evaluate the redox performance. The process is illustrated in Figure 3.

2　Results and discussion

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2.1　The range of E_ovf for oxygen carrier selection

As shown in Figure 4, the Gibbs free energy of several key reactions is used to distinguish different chemical looping reactions^[13,31]. The data of reactions was from calculations with the FactSage software. For a target oxygen vacancy concentration of [V_O] = 1%, Figure 4 shows the oxygen vacancy formation chemical potential Δμ at various temperatures for different values of E_ovf. It has been shown that the trends of E_ovf across different perovskite oxides remain the same for different extents of oxygen vacancy^[32]. Therefore, it is reasonable to estimate the performance of the oxygen carrier by using E_ovf of the chemical potential corresponding to [V_O] = 1%. From Figure 4, it can be inferred that for CLAS, the suitable E_ovf values should be approximately less than 2.3 eV when the temperature is higher than 500 ℃. Previous studies have indicated that materials with E_ovf less than 2.5 eV are suitable for thermochemical O₂ storage and pumping/separation^[13,15], which is in agreement with the estimated results. Additionally, this estimation method can also be applied to assess the suitability of materials in fields such as chemical looping full oxidation (CLFO), chemical looping with oxygen uncoupling (CLOU), and chemical looping syngas production.

2.2　The training results of the ALIGNN model for predicting E_ovf

The ALIGNN model trained for predicting E_ovf was tested. The oxides in the test set did not exist in the training set or the validation set. As shown in Figure 5, the ALIGNN model achieved a mean absolute error (MAE) of 0.26 eV in predicting the E_ovf values at different oxygen sites of the oxides in the test set, and the coefficient of determination (R²) reached 0.94. The closer the MAE is to 0 and the R² is to 1, the higher the accuracy of the model. This result outperforms the linear model using the DFT descriptors (0.39 eV)^[20−21] and the dGNN model based on a simpler convolutional architecture relative to the ALIGNN (0.52 eV)^[14].

2.3　High-throughput screening of Sr_xA_1−xFe_yB_1−yO₃

The screening results from the 3649 compositions of Sr_xA_1−xFe_yB_1−yO₃ perovskites are presented in Figure 6. Most of the compositions containing ions of Na, K, Mg and Cu were filtered out due to the inability to achieve electrical neutrality. It is noted that the nonstoichiometric cases of perovskites (Sr_xA_1−xFe_yB_1−yO_3−δ) were not considered in the preliminary screening process. The different grids in the Figure 6 may represent the same chemical composition.

The slight differences in the average E_ovf for the same material, such as Sr_xBa_1−xFe₁Ti₀O₃ and Sr_xBa_1−xFe₁V₀O₃, may be attributed to random errors introduced during the crystal structure optimization process. For the Sr_1−xCa_xFeO₃, it is known that the E_ovf first decreases and then increases with the increase of the Ca²⁺ concentration from 0 to 0.5^[10]. This is consistent with the predictions. In certain compositions, such as Sr_0.125Ba_0.875CoO₃, the doping of the Ba ion at the A-sites also leads to a decrease in E_ovf. The doping of the Co ion at the B-sites shows a pronounced trend of decreasing E_ovf with an increasing concentration. Among all the compositions with a predicted average E_ovf below 2.0 eV, the Co ion is consistently present (see Section S4 in Supplemental Information).

2.4　Rediscovery of low-temperature CLAS materials

Through the screening criterion E_ovf < 2.3 eV, a series of known low-temperature CLAS oxygen carriers were rediscovered, as shown in Table 2. This indicates that the E_ovf can be used to accelerate the material discovery for the low-temperature CLAS process. Still, this method has certain limitations. The E_ovf can be used to assess the ease of oxygen release from the oxides, but it cannot be used to evaluate the material´s re-oxidation extent. For example, although the predicted E_ovf for BaCoO₃ is as low as 1.44 eV, it is difficult to be fully oxidized after oxygen loss, making it unsuitable for low-temperature CLAS^[12].

3　Conclusions

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Based on the graph neural network for predicting the E_ovf, this work proposes a fast method for the screening of low-temperature CLAS oxygen carriers, and conducts a high-throughput screening from the 3649 compositions of Sr_xA_1−xFe_yB_1−yO₃ perovskites. Through the thermodynamic estimation, it was found that the E_ovf value for the CLAS material should be less than 2.3 eV. An the ALIGNN model was trained for the prediction of the E_ovf and the test set shows that the model has a MAE of 0.26 eV. In the high-throughput screening, the doping of the Co ions at the B-site was found to be able to effectively reduce the E_ovf of the perovskite structure. And the doping of specific proportions of Ba and Ca ions at the A site can also contribute to lowering the E_ovf. Under the screening criterion of E_ovf < 2.3 eV, the model rediscovered several previously reported oxygen carriers for the low-temperature CLAS. This work demonstrates that using GNN to predict E_ovf can accelerate the discovery process of CLAS materials. In a broader context, the presented methods may also accelerate the discovery of materials for other related chemical looping applications, such as chemical looping full oxidation and chemical looping syngas production.

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2026年第54卷第7期

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doi: 10.1016/S1872-5813(26)60680-9

接收时间：2025-10-23
首发时间：2026-09-23
出版时间：2026-07-10

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收稿日期：2025-10-23
修回日期：2025-11-21
录用日期：2025-12-14

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¹华北电力大学新能源学院生物质发电成套设备国家工程实验室(华北电力大学), 北京 102206

²华北电力大学新能源学院新能源电力系统全国重点实验室(华北电力大学), 北京 102206

³华北电力大学能源动力与机械工程学院, 北京 102206

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2种不同金属材料的力学参数

科 Family	属数 Number of genus	种数 Number of species	占总种数比例 Percentage of total species (%)	属 Genus	种数 Number of species	占总种数比例 Percentage of total species (%)
鹅膏菌科Amanitaceae	2	11	5.26	鹅膏菌属 Amanita	10	4.78
小菇科 Mycenaceae	2	12	5.74	丝盖伞属 Inocybe	5	2.39
多孔菌科 Polyporaceae	8	14	6.70	蜡蘑属 Laccaria	5	2.39
红菇科 Russulaceae	3	23	11.00	小皮伞属 Marasmius	6	2.87
				小菇属 Mycena	11	5.26
				光柄菇属 Pluteus	5	2.39
				红菇属 Russula	17	8.13
				栓菌属 Trametes	5	2.39

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