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Page 6 of 15 Li et al. J. Mater. Inf. 2025, 5, 21 https://dx.doi.org/10.20517/jmi.2024.87

Figure 2. The crystal structures of K InP , showing the 3D potassium ionic migration map from GT approach (left) and BVSE calculation
3
2
(right). Hereafter ZA designates centers of elementary voids in the GT analysis. 3D: Three-dimensional; GT: geometrical-topological;
BVSE: bond valence site energy.
instance, the channels responsible for migration along the [001] direction are sufficiently wide (with r =
chan
+
3.49 Å) but are surrounded by Cd cations [Figure 3]. The migration of K ions through these channels is
2+
hindered by repulsion between K and Cd ions, a finding corroborated by the BVSE analysis. Another
+
2+
2+
channel, which is also deemed inaccessible for migration according to BVSE, has two Cd cations in its
environment and a smaller radius (r = 3.08 Å), but it does not significantly affect the overall 2D
chan
conductivity [Figure 3]. In the cases of K ZnP and K AuP , the channels surrounded by pure cation
[70]
[69]
4
2
2
5
environments - Zn and Au, respectively - have high migration energies (1.50 eV), which limits the diffusion
to 2D conductivity [Supplementary Table 1]. However, in K BeP 2 [71] and K Cu P [72] , the channels
3
3 2
4
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].
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
[73]
considered as potential cathode materials [Table 1]. The KMC results indicate that K AuP , K CuP and
[68]
2
2
K Cu P exhibit moderate diffusion coefficients of approximately 1 × 10 cm ·s , similar to the well-known
2 -1
-14
3
3 2
2 -1
-15
[74]
lithium cathode material LiFePO (10 -10 cm ·s ). Based on these results, K AuP, K CuP and K Cu P
-14
2
3 2
3
2
4
were identified as the most promising candidates for cathode materials.
Among all the phosphides considered, K InP exhibits the highest ionic conductivity, approaching
[75]
3
2
1 × 10 S·cm . However, the narrow band gap of K InP (approximately 0.75 eV) facilitates electronic
-1
-3
3
2
conductivity, which can trigger redox reactions, potentially leading to material decomposition and affecting
the long-term performance and lifespan of the battery. Note that the PBE functional exhibits a systematic
underestimation in band gap predictions. According to statistical data , the band gaps calculated using
[76]
PBE are typically 30%-50% lower than experimental values, which is attributed to the limitations of the PBE
functional in describing electronic exchange and correlation energies. To mitigate this issue, the band gap of
K InP could be widened through doping, specifically by replacing In with elements of higher
3
2
electronegativity or different valency. Such doping could enhance its performance as a solid electrolyte
material. Substituting In with elements such as Ga or Al may be particularly effective, as these elements