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

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 E was taken from the Materials Project (https://
g
materialsproject.org). The average voltage profile for each cathode reaction was determined using :
[64]

(2)

where E and E are the DFT energies of the cathode at K concentrations x and x , respectively. E is the
Kx2
Kx1
2
K
1
total energy of a K atom in metallic potassium (Im3m).
Ab initio molecular dynamics (AIMD) simulations were performed in the NVT ensemble for 50 ps with a
time step of 1.0 fs . A Nosé-Hoover thermostat was employed to control the system temperature. All
[65]
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:

(3)

where D is the diffusion coefficient, D is the prefactor of diffusion, k is the Boltzmann constant, E is the
B
0
a
activation energy, and T is the temperature. The ionic conductivity was calculated from the extrapolated
diffusion coefficient using:
[66]
(4)

where c is the concentration of K ions, q denotes the charge state of K ions, and e refers to the elementary
K
K
charge.

RESULTS AND DISCUSSION
GT and BVSE analysis
For 143 compounds, the migration map was constructed using the criterion r (min). Of these, the
chan
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 have shown that when the energy barrier E exceeds 1 eV, the diffusion of K ions is
[67]
m
significantly hindered, although it may be overcome at elevated temperatures. In contrast, when the
migration barrier E is less than 1 eV, the ion migration process becomes relatively facile.
m
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 r >
chan
r (min) for the construction of the migration map, an exception is found in K CdP , where the BVSE
[68]
chan
2
4
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