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Page 8 of 15 Li et al. J. Mater. Inf. 2025, 5, 21 https://dx.doi.org/10.20517/jmi.2024.87

DFT results
We calculated the reversible capacities of K AuP, K CuP and K Cu P . The formation energies and convex
3 2
2
2
3
hull phase diagrams were constructed to elucidate the structural evolution during K-ion insertion and
extraction. Compounds with an energy above the convex hull (E ) exceeding 0.1 eV/atom are considered
hull
thermodynamically unstable [35,80] . As shown in Figure 4, K Cu P exhibits a reversible capacity of
3
3 2
72.47 mAh·g , significantly higher than that of K AuP and K CuP.
-1
2
2
Supplementary Figure 1 reveals that K Cu P possesses a layered structure with the space group R3m, and
3
3 2
we constructed a 3D migration map for K ions. During the charging process, two stable intermediate
compounds, K Cu P (x = 8/3, 2), were selected for analysis [Supplementary Figure 2]. We estimated the
3 2
x
voltage for each reaction by evaluating the slope of the formation energy, revealing two primary voltage
plateaus at 1.37 and 2.76 V, as shown in Figure 5A. Notably, one-third of the K ions are easily
deintercalated, while the remaining ions are more challenging to extract, which influences the overall
[81]
battery capacity. For comparison, the previously reported cathode material K FeP O has a reversible
7
2
2
capacity of 60 mAh·g and a voltage plateau of around 2.7 V. In contrast, K Cu P not only exhibits a higher
-1
3
3 2
reversible capacity but also a more favorable voltage profile, offering superior energy density.
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 K Cu P
x
3 2
(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 K Cu P can maintain excellent reversibility and high
3 2
3
capacity even after multiple charge-discharge cycles.
We performed a comprehensive analysis of the electronic structure of K Cu P (x = 3, 8/3, 2) by examining
3 2
x
the density of states (DOS). K Cu P is identified as a semiconductor, with a significant overlap between the
3 2
3
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 K Cu P further undergo oxidation to Cu , resulting
+
2+
x
3 2
in a rightward shift in the DOS and a filling of the conduction band. This shift enhances the metallic
characteristics of K Cu P [Figure 6]. As an intermediate compound, K Cu P exhibits improved electronic
7/3
x
3 2
3 2
conductivity compared to K Cu P [Supplementary Figure 4]. Furthermore, the increasing DOS near the
3
3 2
Fermi level suggests that the release of potassium atoms further enhances the electronic conductivity of
K Cu P , which in turn improves the high-rate charging performance of the material.
x
3 2
To further investigate the electronic behavior, we conducted Bader charge analysis to calculate the charge
[82]
distribution of each atom in K Cu P . As summarized in Supplementary Table 3, upon the release of 2/3
3 2
x
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
[83]
calculated the migration barriers through the CI-NEB method . 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