High-throughput screening of phosphide compounds for potassium-ion conductive cathode application
0 Abstract
Cathode materials are crucial in potassium (K) batteries, directly impacting their performance and lifespan. In this study, we used a combination of geometrical-topological (GT) analysis, bond valence site energy (BVSE), Kinetic Monte Carlo (KMC), and first-principles calculations to screen potential cathode materials for K-ion batteries among inorganic phosphides. Through GT analysis, we screened 143 K- and P-containing compounds and identified 30 with two- or three-dimensional K-ion migration pathways. BVSE further narrowed down 13 compounds with K-ion migration energies below 1 eV. KMC simulations of ionic conductivity led to the selection of K3Cu3P2 for detailed first-principles calculations. It was demonstrated that K3Cu3P2 possesses a reversible capacity of 72.47 mAh·g-1, minimal volume change (1.47%), and a charge compensation mechanism involving Cu and P. Its low migration energy barrier contributes to a high ionic diffusion coefficient and conductivity of 1.87 × 10-3 S·cm-1 at 25 °C, making K3Cu3P2 a promising candidate for stable and efficient K-ion diffusion in cathode applications.
Keywords
INTRODUCTION
Fossil fuels, including oil, gas, and coal, remain the dominant global energy source. However, their overuse has raised significant environmental and energy security concerns. To promote sustainable development, there is increasing momentum toward transitioning to clean energy sources such as solar, wind, and nuclear power, which can reduce greenhouse gas emissions and improve energy efficiency[1-5]. The development of electric vehicles and renewable energy technologies has garnered significant societal interest, with high-performance energy storage systems playing a key role in optimizing the use of clean energy[6-8]. Among these technologies, rechargeable batteries, particularly lithium (Li)-ion batteries, are seen as a critical solution for meeting diverse energy needs[9]. However, the limited lithium reserves pose a significant challenge[10-17]. As the demand for rechargeable batteries grows, there is an urgent need to develop sustainable alternatives that offer comparable performance to Li-ion batteries.
Compared to Li-ion batteries, sodium-ion batteries offer advantages such as greater abundance and lower cost[18]. However, their higher electrode potential [-2.71 V vs. standard hydrogen electrode (SHE)] leads to lower energy density and reduced energy storage performance[19-21]. Potassium (K), which shares similar physicochemical properties with lithium, is also abundant (2.09 wt%) and has a standard electrode potential (-2.93 V vs. SHE) close to that of lithium (-3.04 V vs. SHE). This similarity enables K-ion batteries to achieve high operating voltages and energy densities[22]. Replacing expensive materials such as lithium, cobalt, and copper, commonly used in Li-ion batteries, with more affordable and abundant alternatives such as potassium, iron, and aluminum can significantly lower costs while improving safety[23]. However, the larger ionic radius of potassium results in slower ion kinetics during the charging and discharging process, negatively impacting the electrochemical cycle performance and rate capability of K-ion batteries. Therefore, developing electrode materials that facilitate efficient and reversible K-ion transport is crucial[24-31]. High-throughput screening methods have emerged powerfully for accelerating the discovery and design of new materials[32,33]. K2CdO2, as a potential solid electrolyte, was selected from potassium oxides[34]. A topological quantum material, K2MnS2[35], was identified to be the most promising cathode for K-ion batteries.
Recently, several silicon phosphides have emerged as promising candidates for solid electrolytes. For example, Li8SiP4 and Li2SiP2, which are based on SiP4 tetrahedral building blocks, have shown potential applicability[36]. The ionic conductivity of Li8SiP4 ranges from 1.15 × 10-6 S·cm-1 at 0 °C to 1.2 × 10-4 S·cm-1 at 75 °C, with an activation energy of 0.49 eV. Li2SiP2[36] exhibits a conductivity of 6.6 × 10-6 S·cm-1 at 75 °C. Meanwhile, LiSi2P3, which adopts a diorite structure, demonstrates favorable ion transport properties with a low activation energy of 0.07 eV[37]. Additionally, HT-NaSi2P3 exhibits a high total conductivity of up to 4 × 10-4 S·cm-1 at 25 °C, featuring the largest supertetrahedral entities (T5)[38]. For K-ion conductors, KSi2P3 displays an ionic conductivity of 1.6 × 10-4 S·cm-1 at 25 °C with an average activation energy of 0.20 eV[39,40]. These findings suggest that phosphides, particularly silicon-based phosphides, are promising candidates for K-ion conductors and warrant further exploration for future applications.
In this study, we performed a high-throughput screening of all phosphide compounds in the Inorganic Crystal Structure Database (ICSD; version 2022/2) for the first time (Schemed in Figure 1)[41]. Initially, we used the geometrical-topological (GT) approach to screen K- and P-containing compounds. Next, we applied the bond valence site energy (BVSE) method to analyze the locations of mobile ions and roughly estimate the migration barriers. This process identified 13 promising K-ion conductors with low migration barriers, which were then selected for further evaluation through Kinetic Monte Carlo (KMC) simulations. Finally, we used density functional theory (DFT) to model charge-discharge products and simulate half-cells, focusing on the most promising compound, K3Cu3P2.
Figure 1. Workflow for screening promising potassium-ion conductors.
MATERIALS AND METHODS
GT approach
The cationic conductivity of inorganic compounds is largely governed by the presence of a continuous network of channels and voids within the crystal structure, which facilitate cation migration. In the Voronoi partition approach, the crystal space is divided into two dual subspaces: atoms and voids. To analyze cation migration pathways, the vertices and edges of Voronoi polyhedra are treated as elementary voids and channels, based on key criteria derived from known solid electrolytes. The construction of the graph and polyhedral representations of the void space, as well as the subsequent analysis of their GT characteristics, is implemented in the ToposPro software package[42]. This GT approach has been successfully applied to predict suitable cathode and electrolyte materials for various cations, including Li+[43], Na+[44], and Zn2+[45].
To assess the geometric criteria for cation migration, we computed the radii of the elementary channels
BVSE calculations
The BVSE approach[48], implemented in the GUI version of the softBV program[49,50], has become a widely adopted tool in crystal chemistry for investigating ionic migration pathways. This method is based on the principle of maintaining local bond strength equilibrium, which is essential for understanding ion movement within a crystal lattice. By considering the Coulombic repulsion between the migrating ion and the ions in the crystal framework, the migration energy barriers for the ions are calculated[51]. The migration energy landscape for K+ was computed using a Cube.file with a resolution of 0.1 and an automatically determined screening factor (f)[52].
To evaluate the dimensionality of the migration map, we determined the migration barrier energy (Em). The most promising candidates for KMC simulations and DFT calculations were selected based on the criterion that Em < 1 eV and the material should exhibit 2D or 3D ionic conductivity. This criterion is important because, although 1D ionic conductors can exhibit high conductivity under certain conditions, their sensitivity to defects and interfaces limits their practical applications.
KMC simulations
Ionic conductivities and diffusion coefficients were calculated using KMC simulations. For this purpose, supercells with volumes exceeding 10,000 Å3 were simulated for 1 to 10 million KMC steps at 300 K. The KMC algorithm, implemented in the command-line version of softBV, utilizes approximate site and migration energies derived from BVSE analysis. The results were averaged over five different configurations to ensure statistical reliability. The unit cells were relaxed using the softBV force field. The ionic diffusion coefficient is a key performance indicator for cathode materials. Compounds with high ionic diffusion coefficients are characterized by continuous ion transport channels and low migration barriers[53,54].
DFT calculations
All DFT calculations[55] were performed using the projected augmented wave (PAW) method[56], implemented in the Vienna Ab initio Simulation Package (VASP)[57,58]. The Perdew-Burke-Ernzerhof (PBE) functional in the generalized gradient approximation (GGA)[59] was used to describe the exchange-correlation interactions. Structural optimization was carried out using the conjugate gradient method, with convergence thresholds of 10-5 eV for energy and 0.03 eV/Å for interatomic forces. A plane-wave energy cutoff of 520 eV was employed. To correct the self-interaction error and account for strong correlation effects in localized electrons, Hubbard U corrections were applied, with a U value of 5.2 eV for Cu[60]. The Ewald summation method[61] was used to screen the system during the K-ion charging process, leading to the generation of various configurations.
The formation energy diagram was constructed to identify the configuration with the lowest energy at different optimized concentrations. Stable intermediate phases were identified as those on the convex hull, while other compounds were classified as metastable or unstable. The energy above the hull (Ehull) for stable intermediate phases was calculated, and the maximum potassium removal capacity was determined for those phases with Ehull < 0.1 eV/atom, providing the reversible capacity of the candidate cathode materials. Ionic migration barriers for K+ ions were calculated using the nudged elastic band (NEB) method[62], with input files generated via the PATHFINDER script (https://pathfinder.batterymaterials.info).
Compounds containing electrochemically active transition metals (Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Nb, Mo, W) were considered as promising cathode materials. The theoretical capacity (in mAh·g-1) was calculated using[63]:
where n is the number of electrons transferred per formula unit, M is the molar mass of the compound, and F is the Faraday constant. The electronic band gap Eg was taken from the Materials Project (https://materialsproject.org). The average voltage profile for each cathode reaction was determined using[64]:
where EKx1 and EKx2 are the DFT energies of the cathode at K concentrations x1 and x2, respectively. EK is the total energy of a K atom in metallic potassium (Im
Ab initio molecular dynamics (AIMD) simulations were performed in the NVT ensemble for 50 ps with a time step of 1.0 fs[65]. A Nosé-Hoover thermostat was employed to control the system temperature. All AIMD simulations were carried out using a (2 × 2 × 1) supercell derived from the relaxed primitive unit cell, containing 96 atoms. The diffusion coefficient of K ions was modeled using the Arrhenius equation:
where D is the diffusion coefficient, D0 is the prefactor of diffusion, kB is the Boltzmann constant, Ea is the activation energy, and T is the temperature. The ionic conductivity was calculated from the extrapolated diffusion coefficient[66] using:
where cK is the concentration of K ions, qK denotes the charge state of K ions, and e refers to the elementary charge.
RESULTS AND DISCUSSION
GT and BVSE analysis
For 143 compounds, the migration map was constructed using the criterion rchan(min). Of these, the diffusion of K ions was predicted to be two-dimensional (2D) for nine compounds and three-dimensional (3D) for 21 compounds [Supplementary Table 1]. The compounds were classified based on their framework types, with frameworks grouped according to the same space group and similar chemical compositions. Previous studies[67] have shown that when the energy barrier Em exceeds 1 eV, the diffusion of K ions is significantly hindered, although it may be overcome at elevated temperatures. In contrast, when the migration barrier Em is less than 1 eV, the ion migration process becomes relatively facile.
In general, the results obtained from the GT analysis and the BVSE method are consistent, and the migration map of the same dimensionality is obtained [Figure 2]. When considering all channels with rchan > rchan (min) for the construction of the migration map, an exception is found in K4CdP2[68], where the BVSE method predicts 2D migration, while the GT analysis indicates 3D migration. This compound exemplifies how geometrically accessible migration channels can still exhibit high energy barriers for diffusion. For instance, the channels responsible for migration along the [001] direction are sufficiently wide (with rchan = 3.49 Å) but are surrounded by Cd2+ cations [Figure 3]. The migration of K+ ions through these channels is hindered by repulsion between K+ and Cd2+ ions, a finding corroborated by the BVSE analysis. Another channel, which is also deemed inaccessible for migration according to BVSE, has two Cd2+ cations in its environment and a smaller radius (rchan = 3.08 Å), but it does not significantly affect the overall 2D conductivity [Figure 3]. In the cases of K4ZnP2[69] and K5AuP2[70], the channels surrounded by pure cation environments - Zn and Au, respectively - have high migration energies (1.50 eV), which limits the diffusion to 2D conductivity [Supplementary Table 1]. However, in K4BeP2[71] and K3Cu3P2[72], the channels surrounded by Be and Cu, respectively, exhibit much lower migration barriers (0.57-0.73 eV) and play a crucial role in facilitating conductivity, as indicated by the BVSE analysis [Supplementary Table 1].
Figure 2. The crystal structures of K3InP2, showing the 3D potassium ionic migration map from GT approach (left) and BVSE calculation (right). Hereafter ZA designates centers of elementary voids in the GT analysis. 3D: Three-dimensional; GT: geometrical-topological; BVSE: bond valence site energy.
Figure 3. Crystal structures of K4CdP2, illustrating the 3D potassium ionic migration map (left) from the GT approach and the 2D migration map (right) derived from BVSE calculations. The relevant regions of the migration maps are highlighted in green. The elementary channels that are inaccessible to K+ migration due to surrounding Cd2+ cations are highlighted in red. 3D: Three-dimensional; GT: geometrical-topological; 2D: two-dimensional; BVSE: bond valence site energy.
Thirteen compounds with migration energy barriers lower than 1 eV were selected for KMC simulations at room temperature [Supplementary Table 2]. Compounds containing electrochemically active elements were considered as potential cathode materials [Table 1]. The KMC results indicate that K2AuP[73], K2CuP[68] and K3Cu3P2 exhibit moderate diffusion coefficients of approximately 1 × 10-14 cm2·s-1, similar to the well-known lithium cathode material LiFePO4[74] (10-14-10-15 cm2·s-1). Based on these results, K2AuP, K2CuP and K3Cu3P2 were identified as the most promising candidates for cathode materials.
13 most promising K-/P-containing compounds after GT and BVSE analysis
| Formula | ICSD code | Space group | Migration map (GT/BVSE) | Em | σ (S·cm-1) | D (cm2·s-1) | Cg (mAh/g) | Eg (eV) |
| K2AuP | 300201 | Cmcm | 3/3 | 0.45 | 7.01 × 10-9 | 6.29 × 10-14 | 175.12 | 0.95 |
| K2CuP | 61082 | Cmcm | 3/3 | 0.68 | 1.38 × 10-9 | 1.18 × 10-14 | 310.41 | 1.14 |
| K3Cu3P2 | 12163 | R | 3/3 | 0.73 | 2.47 × 10-9 | 1.89 × 10-14 | 217.42 | 1.29 |
| KMnP | 89593 | P4/nmm | 2/2 | 0.45 | 2.34 × 10-11 | 5.25 × 10-16 | 214.43 | 0 |
| K4CdP2 | 61084 | C2/m | 3/2 | 0.32 | 2.77 × 10-16 | 2.81 × 10-21 | 324.18 | 0.82 |
| K3InP2 | 300141 | Ibam | 3/3 | 0.48 | 1.06 × 10-3 | 1.08 × 10-8 | SE* | 0.79 |
| K3AlP2 | 300130 | P | 3/3 | 0.58 | 1.01 × 10-5 | 6.61 × 10-11 | SE | 0.70 |
| K6InP3 | 300147 | P | 3/3 | 0.40 | 4.50 × 10-6 | 3.41 × 10-11 | SE | 0.75 |
| K3P | 25550 | P63/mmc | 3/3 | 0.21 | 1.24 × 10-6 | 9.67 × 10-12 | SE | 0.21 |
| K4P3 | 64625 | Cmcm | 3/3 | 0.77 | 7.33 × 10-7 | 6.18 × 10-12 | SE | 0 |
| KP | 14010 | P212121 | 3/3 | 0.39 | 3.01 × 10-8 | 2.72 × 10-13 | SE | 1.03 |
| K4BeP2 | 300110 | R | 3/3 | 0.57 | 7.63 × 10-8 | 6.04 × 10-13 | SE | 1.14 |
| K3BP2 | 300104 | C2/c | 3/3 | 0.87 | 3.89 × 10-8 | 3.67 × 10-13 | SE | 1.67 |
Among all the phosphides considered, K3InP2[75] exhibits the highest ionic conductivity, approaching
DFT results
We calculated the reversible capacities of K2AuP, K2CuP and K3Cu3P2. The formation energies and convex hull phase diagrams were constructed to elucidate the structural evolution during K-ion insertion and extraction. Compounds with an energy above the convex hull (Ehull) exceeding 0.1 eV/atom are considered thermodynamically unstable[35,80]. As shown in Figure 4, K3Cu3P2 exhibits a reversible capacity of
Figure 4. Formation energies during charge and discharge, along with the energy above the convex hull (Ehull) for different compositions of (A) K2AuP, (B) K2CuP and (C) K3Cu3P2.
Supplementary Figure 1 reveals that K3Cu3P2 possesses a layered structure with the space group R
Figure 5. (A) Calculated voltages and (B) calculated changes in the unit cell volume. The dotted line indicates that this voltage plateau is difficult to achieve with conventional electrolytes.
During the charge/discharge cycles, K-ion insertion and extraction induce structural and volumetric changes in the cathode material. These volume changes can significantly affect the stability of the crystal structure. Large expansions or contractions can cause stress concentration within the lattice, leading to potential cracks or structural failure. As shown in Figure 5B, we analyzed the structural evolution of KxCu3P2 (x = 3, 8/3, 2). After the extraction of one-third of the K ions, the material experienced only a slight volume reduction of 1.47%, with minimal changes in lattice constants and angles, indicating exceptional structural stability [Supplementary Figure 3]. This suggests that K3Cu3P2 can maintain excellent reversibility and high capacity even after multiple charge-discharge cycles.
We performed a comprehensive analysis of the electronic structure of KxCu3P2 (x = 3, 8/3, 2) by examining the density of states (DOS). K3Cu3P2 is identified as a semiconductor, with a significant overlap between the 3d orbitals of Cu and the 3p orbitals of P, indicating a strong covalent interaction between Cu and P atoms. Upon the release of potassium atoms, some Cu+ ions in KxCu3P2 further undergo oxidation to Cu2+, resulting in a rightward shift in the DOS and a filling of the conduction band. This shift enhances the metallic characteristics of KxCu3P2 [Figure 6]. As an intermediate compound, K7/3Cu3P2 exhibits improved electronic conductivity compared to K3Cu3P2 [Supplementary Figure 4]. Furthermore, the increasing DOS near the Fermi level suggests that the release of potassium atoms further enhances the electronic conductivity of
Figure 6. Calculated partial DOS for KxCu3P2 (x = 3, 8/3, 2) with decreasing potassium content. DOS: density of states.
To further investigate the electronic behavior, we conducted Bader charge analysis[82] to calculate the charge distribution of each atom in KxCu3P2. As summarized in Supplementary Table 3, upon the release of 2/3 potassium atoms, the Cu and P atoms lose 0.089 and 0.064 electrons, respectively, which provides additional evidence for the contribution of Cu and P to charge compensation during ion migration.
Next, we examined the migration behavior of K ions, since migration energy barriers are critical in determining the charge and discharge rates of batteries, especially at high discharge currents, which can lead to rapid capacity fading. We identified two distinct diffusion pathways using the PATHFINDER script, and calculated the migration barriers through the CI-NEB method[83]. Path 1 involves K ion migration within the (001) plane, suggesting a 2D migration mechanism, while Path 2 follows the [001] direction, indicating a 3D migration pathway in Figure 7A. The calculated migration barriers for these two paths are 0.108 and
Figure 7. Illustration of (A) the migration pathways and (B) the calculated migration energy barriers for Path 1 and Path 2 in K3Cu3P2.
To estimate the overall K-ion migration activation energy and diffusion coefficient of the material at room temperature, we conducted AIMD simulations at temperatures ranging from 600 to 1,000 K. As shown in Figure 8A, the migration channel diagram obtained by AIMD is similar to that computed by CI-NEB. The activation energy barrier for K+ migration was found to be 0.11 ± 0.01 eV in Figure 8B, which is in good agreement with the value obtained from the CI-NEB calculations, confirming that the material undergoes minimal structural reorganization or phase transition during ionic migration. Based on the AIMD results, we can analyze the ion diffusion behavior during the charging process. The potassium atoms in K3Cu3P2 are located at K1 and K2 sites, respectively. The diffusion coefficients of both ions were calculated at 600 K
Figure 8. Illustration of (A) migration channel and (B) Arrhenius plot of the logarithm of the diffusivity, log (D), vs. 1000/T for K3Cu3P2.
The corresponding K-ion diffusion coefficient (D) at 300 K is calculated to be approximately 2.17 ×
CONCLUSIONS
In this study, we present a novel approach for screening phosphide compounds as potential cathode materials for K-ion batteries. Using a combination of GT analysis, BVSE calculations, KMC simulations, and DFT calculations, we have identified several promising candidates. The GT analysis revealed 30 previously unreported ionic conductors, while BVSE and KMC simulations highlighted 13 potential K-ion conductors. Among these, K3Cu3P2 emerged as the most promising cathode material, with a diffusion coefficient exceeding 1 × 10-14 cm2·s-1 and a theoretical capacity of 217.42 mAh·g-1. DFT calculations further assessed the thermodynamic stability of K3Cu3P2 by evaluating its formation energy and energy above the convex hull and predicting its reaction voltage platform. It is confirmed by DFT calculations that K3Cu3P2 exhibits a reversible capacity of 72.47 mAh·g-1 and a voltage platform of 2.76 V, outperforming the previously reported K2FeP2O7. Notably, this K3Cu3P2 compound demonstrates excellent structural stability, with a minimal volume change of only 1.47% during charge-discharge cycling. Additionally, K3Cu3P2 benefits from enhanced electronic conductivity, which facilitates high-speed charging. Its low activation energy of 0.11 eV, high diffusion coefficient of 2.17 × 10-8 cm2·s-1, and high conductivity of 1.87 × 10-3 S·cm-1 at 25 °C collectively contribute to improving the battery’s power density. Overall, this study highlights
DECLARATIONS
Authors’ contributions
Methodology, validation, formal analysis and data curation: Li, Y.; Kabanova, N. A.
Investigation, write-review and editing and visualization: Wang, J.; Blatov, V. A.
Availability of data and materials
The data supporting the findings of this study are included in the Supplementary Materials.
Financial support and sponsorship
This work is supported by the National Natural Science Foundation of China (Grant No. 52272307), the National Key Research and Development Program of Intergovernmental Cooperation in Science and Technology (Grant No.2022YFE0141100), and the Fundamental Research Funds for the Central Universities.
Conflicts of interest
All authors declared that there are no conflicts of interest.
Ethical approval and consent to participate
Not applicable.
Consent for publication
Not applicable.
Copyright
© The Author(s) 2025.
Supplementary Materials
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Li, Y.; Kabanova, N. A.; Blatov, V. A.; Wang, J. High-throughput screening of phosphide compounds for potassium-ion conductive cathode application. J. Mater. Inf. 2025, 5, 21. http://dx.doi.org/10.20517/jmi.2024.87
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