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Seo et al. Energy Mater. 2025, 5, 500123 https://dx.doi.org/10.20517/energymater.2025.38 Page 7 of 18

b 1
A3 4h 0.85(1)/0.15 0.36278(6) 0.36182(4) / 0.0074(4)
2
b
A4 4g 0.91(1)/0.09 0.28930(8) 0.10239(4) 0 0.0118(4)
b
A5 2a 0.91(1)/0.09 0 0 0 0.0108(6)
1
Zn1 4h 0.23(1) 0.1049(3) 0.10319(16) / 0.020(2)
2
Zn2 4g 1 0.22122(6) 0.45436(3) 0 0.0087(2)
Zn3 4g 1 0.38005(6) 0.26102(3) 0 0.0095(2)
1
Sb1 4h 1 0.19403(3) 0.00335(2) / 0.0069(1)
2
1
Sb2 4h 1 0.37734(3) 0.19475(2) / 0.0066(1)
2
Sb3 4g 1 0.04017(3) 0.14758(2) 0 0.0049(1)
Sb4 4g 1 0.19053(3) 0.33315(2) 0 0.0042(1)
1
Sb5 2c 1 0 / 0 0.0051(2)
2
Ca Yb Zn Sb
7.72(2) 1.28 4.45(2) 9
b 1
A1 4h 0.86(1)/0.14 0.0615(1) 0.4089(1) / 0.0075(2)
2
b 1
A2 4h 0.87(1)/0.13 0.1226(1) 0.2391(1) / 2 0.0103(2)
b 1
A3 4h 0.81(1)/0.19 0.3634(1) 0.3619(1) / 0.0088(2)
2
b
A4 4g 0.88(1)/0.12 0.2896(1) 0.1022(1) 0 0.0123(2)
b
A5 2a 0.88(1)/0.12 0 0 0 0.0100(3)
1
Zn1 4h 0.23(1) 0.1054(3) 0.1035(2) / 2 0.023(2)
Zn2 4g 1 0.2214(1) 0.4543(1) 0 0.0097(1)
Zn3 4g 1 0.3807(1) 0.2609(1) 0 0.0104(2)
1
Sb1 4h 1 0.1940(1) 0.0034(1) / 0.0077(1)
2
1
Sb2 4h 1 0.3779(1) 0.1946(1) / 2 0.0078(1)
Sb3 4g 1 0.0407(1) 0.1475(1) 0 0.0060(1)
Sb4 4g 1 0.1909(1) 0.3331(1) 0 0.0055(1)
1
Sb5 2c 1 0 / 0 0.0062(1)
2
a b
U corresponds to one-third of the trace of the orthogonalized U tensor; A = Ca in Ca Zn Sb ; Ca/Yb mixed-site in the three quaternary compounds.
eq ij 9 4.48(2) 9

All relativistic effects were incorporated using a scalar relativistic approximation, except for spin-orbit coupling. The potential inside each Wigner-Seitz (WS)

sphere was treated as spherically symmetric , and a combined correction was applied to account for the overlapping regions. Empty spheres were
[28]
automatically included, and the space was filled with overlapping WS atomic spheres . The WS sphere radii were automatically calculated to optimize the
[28]
overlapping potential's approximation to the full potential. The WS radii used for the two models are as follows: Ca, 1.891-2.158 Å; Zn, 1.335-1.504 Å; Sb,

1.631-1.911 Å for Ca Zn Sb ; Ca, 1.891-2.158 Å; Yb, 1.975-2.040 Å; Zn, 1.335-1.504 Å; Cu, 1.465 Å; Sb, 1.631-1.911 Å for Ca YbZn Cu Sb . The used basis sets
0.5
9
4.5
9
9
8
4
were 4s, 4p and 3d orbitals for Ca, 6s, 6p and 5d orbitals for Yb, 4s, 4p and 3d orbitals for Zn, 4s, 4p and 3d orbitals for Cu, 5s, 5p, 5d and 4f orbitals for Sb. The