Toward General Design of Mn-Based Layered Oxide Cathodes for Sodium-Ion Batteries: From Thermodynamic Principles to Entropy Engineering
Abstract
1. Introduction
2. Thermodynamic Foundations and Phase Design Criteria
2.1. Crystal Structure Foundation and Stacking Mechanism

2.2. Thermodynamic Criteria for Phase Stability
2.2.1. Common Criteria and Phase Stability Boundary
2.2.2. High-Entropy Strategy and Configuration Entropy Stabilization Effect
2.2.3. Multidimensional Thermodynamic Descriptor
3. Elemental Chemistry and Multielement Synergy
3.1. Structure–Activity Relationships of Transition Metal Elements
3.2. Multielement Synergy to Suppress Unfavorable Phase Transformation
3.3. Cocktail Effect for Multifunctional Integration
3.4. Elemental Doping for Modulating Lattice Oxygen Redox Activity
4. Toward Rational Design: A Paradigm Shift in Materials Optimization
4.1. Structural Design Based on Electronic Potential
4.2. Prediction Model for High-Entropy Materials
4.3. The Biphasic Synergy Model as a Method for Designing Highly Stable Cathode Materials
4.4. Defect Engineering
5. Design of Layered Oxides Based on Machine Learning
5.1. Machine Learning for Rational Exploration of High-Dimensional Compositional Space
5.2. High-Throughput Screening and Discovery of New Materials
5.3. The Development of Machine Learning for Sodium-Ion Batteries
6. Synthesis Optimization: Bridging the Gap Between Theory and Experiment
6.1. Based on the Optimized Synthesis Method
6.1.1. High-Temperature Solid-Phase Method
6.1.2. Sol–Gel Method
6.1.3. Coprecipitation Method
6.1.4. Comparison Between Sol–Gel Method and Co-Precipitation Method
6.2. Synthesis Optimization Based on Calcination Conditions
6.3. Synthetic Optimization Method Based on Local Concentration
7. Summary and Outlook
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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| Materials | Sodium Content | Phase | Reference |
|---|---|---|---|
| Na2/3Ni1/3Mn2/3O2 | 0.67 | P2 | [24] |
| Na0.696Ni0.329Mn0.671O2 | 0.696 | P2 | [24] |
| Na0.67Mn0.45Ni0.22Co0.33O2 | 0.67 | P2 | [25] |
| Na0.67Mn0.55Ni0.21Co0.24O2 | 0.67 | P2 | [26] |
| Na0.67Mn0.45Ni0.18Co0.24Ti0.1Mg0.03O2 | 0.67 | P2 | [26] |
| Na0.67Mn0.45Ni0.18Co0.18Ti0.1Mg0.03Al0.04Fe0.02O2 | 0.67 | P2 | [26] |
| Na0.67Mn0.8Fe0.1Ni0.1O2 | 0.67 | P2 | [27] |
| Na0.67Mn0.8Fe0.1Mg0.1O2 | 0.67 | P2 | [27] |
| Na2/3Mn1/2Ni1/6Co1/3O2 | 0.67 | P2 | [14] |
| Na0.7Ni0.2Mn0.6Cu0.15Ti0.05O2 | 0.7 | P2 | [28] |
| Na0.67Li0.1Mn0.62Fe0.18Cu0.09Sm0.01O2 | 0.67 | P2 | [29] |
| Na0.67Zn0.05Ni0.15Fe0.20Mn0.60O1.95F0.05 | 0.67 | P2 | [30] |
| Na0.67Ni0.15Fe0.20Mn0.65O2 | 0.67 | P2 | [30] |
| Na0.85Li0.08Mg0.04Ni0.22Al(B)0.04Mn0.62O2 | 0.85 | P2 | [31] |
| Na0.70Ni0.20Cu0.15Mn0.575Ti0.075O2 | 0.7 | P2 | [32] |
| Na0.70Ni0.20Cu0.15Mn(0.65−x)TixO2 | 0.7 | P2 | [32] |
| Na0.70Ni0.20Cu0.15Mn0.65O2 | 0.7 | P2 | [32] |
| NaMn4.58Al18Ni2.58O2 | 1 | P2 | [33] |
| NaNi1/3Fe1/3Mn1/3O2 | 1 | O3 | [34] |
| NaxLi0.05Ni0.45Mn0.25Mg0.05Ti0.25O2 | 0.7–0.95 | O3 | [35] |
| Na0.85Mn0.45Ni0.25Li0.05Cu0.1Ti0.15O2 | 1 | O3 | [36] |
| Na0.98Ca0.01Ni0.33Fe0.33Mn0.315Sn0.015O2 | 0.98 | O3 | [37] |
| NaNi0.475Mn0.475Mo0.05O2 | 1 | O3 | [38] |
| Na(Ni0.4Cu0.1Mn0.4Ti0.1)0.92Fe0.08O2 | 1 | O3 | [39] |
| Na0.9Mn1/2Fe1/3Cu1/6O2 | 0.9 | O3 | [40] |
| NaNi0.35Fe0.2Mn0.3Ti0.1Sb0.05O2 | 1 | O3 | [41] |
| NaNi0.305Fe0.33Mn0.33Ce0.025O2 | 1 | O3 | [41] |
| Na0.95Li0.07Sn0.01Ni0.22Fe0.2Mn0.5O2 | 0.95 | O3 | [42] |
| NaLi1/3Mn2/3O2 | 1 | O3 | [43] |
| NaNi0.3Mn0.52Mo0.03Cu0.1Ti0.05O2 | 1 | P2/O3 | [44] |
| NaLi0.05Fe0.04Al0.01Ni0.4Mn0.4Ti0.1O2 | 1 | O3 | [45] |
| NaxLi0.05Mn0.55Ni0.3Cu0.075Mg0.025O2 | 0.7–1 | P2/O3 | [46] |
| Descriptor Symbol | Implication | Definition and Computational Logic |
|---|---|---|
| Sodium Concentration | The content of sodium ions in the material phase | |
| TM Ionic Potential | The electrostatic interaction strength between the transition metal (TM) cation and oxygen anion. It is calculated as the ratio of the effective charge of the TM ion () to its ionic radius (): . | |
| TM Mixing Entropy | The configurational entropy of the transition metal layer. It quantifies the disorder introduced by multiple TM elements and is calculated using the Boltzmann equation, , where is the molar fraction of the ith element and R is the gas constant. | |
| Cationic Potential | A composite descriptor representing the overall electrostatic field of all cations. It is typically defined as the weighted average of the ionic potentials of all cations in the lattice, used to predict structural stability and phase formation. | |
| TM Ionization Energy | The energy required to remove an electron from the transition metal ion (oxidation potential). It reflects redox activity and is usually defined as the first ionization energy of the isolated gaseous atom, often used as a proxy for Fermi level alignment. | |
| TM Radius | The ionic radius of the transition metal cation. It is a critical geometric parameter that influences the TM–O bond length and the lattice volume; values are typically taken from Shannon’s empirical tables for specific coordination numbers (e.g., octahedral sites). |
| Materials | Method | Specific Method | Reference |
|---|---|---|---|
| Na1−xLixNi0.5Mn0.5O2 | Doping | Li doped alkali metal layer | [95] |
| Na0.67Mn0.55Ni0.25Ti0.2−xLixO2 | Doping | Li-doped transitional metal layer | [97] |
| Nax[Ni0.6Co0.2Mn0.2]O2 | Synthetic method | Using co-precipitation with hydroxides | [98] |
| P2-Na0.7MnO2/O3-NaMnO2 | Synthetic method | Change the crystallization cooling rate | [99] |
| Na0.67Ni0.33Mn0.57Sn0.1O2 | Doping | Doping with Sn element | [100] |
| Na0.8Li0.2Fe0.2Mn0.6O2 | Doping | Li doping | [101] |
| Na0.7Ni0.2Cu0.1Fe0.2Mn0.5O2–δ | Doping | Introducing impurities to create local differences in cation potential | [102] |
| Na0.732Ni0.273Mg0.096Mn0.63O2 | Doping | Mg ion doping | [103] |
| Na0.7Mn0.4Ni0.3Cu0.1Fe0.1Ti0.1O1.95F0.1 | Synthetic method | Change the calcination temperature | [104] |
| NaxLi0.05Mn0.55Ni0.3Cu0.075Mg0.025O2 | Doping | - | [46] |
| Na0.85Li0.05Ni0.3Fe0.1Mn0.5Ti0.05O2 | - | - | [105] |
| NaxCu0.1Co0.1Ni0.25Mn0.4Ti0.15O2 | - | Change the sodium ion content | [106] |
| Na0.76Ni0.20Mn0.42Fe0.30Mg0.04Ti0.015Zr0.025O2 | Doping | Mg, Ti, Zr doping | [107] |
| Na0.75Cu0.1Fe0.2Mg0.2Mn0.4Ti0.1O2 | Doping | Forming high-entropy materials by incorporating multiple elements | [108] |
| Na0.8Ni0.23Fe0.34Mn0.43O2 | Doping | Fe, Ni doping | [109] |
| Na0.8Li0.03Mg0.05Ni0.28Fe0.05Mn0.54Ti0.05O2 | Doping | Forming high-entropy materials by incorporating multiple elements | [110] |
| NaxMn0.4Ni0.3Fe0.15Li0.1Ti0.05O2 | Doping | Forming high-entropy materials by incorporating multiple elements | [23] |
| Na0.8Mg0.06Ni0.34Mn0.54Ti0.06O2 | - | - | [111] |
| Na0.76Ni0.33Mn0.48O2 | Synthetic method | Coprecipitation | [112] |
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Dong, L.; Qian, X.-Y.; Xiong, J.; Zhang, Y.-H.; Wang, X.; Ding, J.-Y.; Zhang, F.-J.; Shen, J.-Q.; Zhang, Q.-R.; Sun, Y.-G. Toward General Design of Mn-Based Layered Oxide Cathodes for Sodium-Ion Batteries: From Thermodynamic Principles to Entropy Engineering. Molecules 2026, 31, 836. https://doi.org/10.3390/molecules31050836
Dong L, Qian X-Y, Xiong J, Zhang Y-H, Wang X, Ding J-Y, Zhang F-J, Shen J-Q, Zhang Q-R, Sun Y-G. Toward General Design of Mn-Based Layered Oxide Cathodes for Sodium-Ion Batteries: From Thermodynamic Principles to Entropy Engineering. Molecules. 2026; 31(5):836. https://doi.org/10.3390/molecules31050836
Chicago/Turabian StyleDong, Li, Xiang-Yu Qian, Jian Xiong, Yi-Han Zhang, Xing Wang, Jing-Yi Ding, Fa-Jia Zhang, Jia-Qi Shen, Qi-Rui Zhang, and Yong-Gang Sun. 2026. "Toward General Design of Mn-Based Layered Oxide Cathodes for Sodium-Ion Batteries: From Thermodynamic Principles to Entropy Engineering" Molecules 31, no. 5: 836. https://doi.org/10.3390/molecules31050836
APA StyleDong, L., Qian, X.-Y., Xiong, J., Zhang, Y.-H., Wang, X., Ding, J.-Y., Zhang, F.-J., Shen, J.-Q., Zhang, Q.-R., & Sun, Y.-G. (2026). Toward General Design of Mn-Based Layered Oxide Cathodes for Sodium-Ion Batteries: From Thermodynamic Principles to Entropy Engineering. Molecules, 31(5), 836. https://doi.org/10.3390/molecules31050836

