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Page 14 of 18 Seo et al. Energy Mater. 2025, 5, 500123 https://dx.doi.org/10.20517/energymater.2025.38

Table 4. QVAL and volume of the five cationic sites in Ca Zn Sb 9
9
4.5
Atom (Wyckoff site) Ca1 (4h) Ca2 (4h) Ca3 (4h) Ca4 (4g) Ca5 (2a)
QVAL 1.800 2.279 2.336 2.312 2.215
3
Volume (Å ) 50.82 57.80 63.72 62.29 73.17

Table 5. Hall effect measurement results for the three title compounds
3
20
2
Compound Carrier concentration n (× 10 carriers/cm ) Mobility η (cm /V·s)
[19]
Ca Zn Sb 9 0.607 48.966
4.5
9
Ca YbZn Sb 9 0.663 47.705
4.5
8
Ca YbZn Cu Sb 0.700 28.864
8 4.4 0.1 9
Ca YbZn 4.35 Cu 0.15 Sb 9 1.264 23.755
8

Figure 7. For four compounds in the Ca YbZn 4.5-y Cu Sb (0 ≤ y ≤ 0.15) system, temperature-dependent (A) electrical conductivity σ and
9
y
8
(B) Seebeck coefficient S are plotted over the range of 323 to 861 K. Corresponding data for the ternary Ca Zn Sb 9 [19] compound are
4.5
9
presented for comparison.
those of σ. In general, the correlation between S, the carrier concentration, and the effective mass can be
expressed by = , where k = the Boltzmann constant, e = the charge of electron, h = the Planck
B
constant, n = the carrier concentration, and m = the effective mass . Therefore, according to this equation,
*
[6]
the effective masses of our title compounds can be evaluated as follows: 0.74, 0.80, 0.82, and 0.96 m for
e
Ca Zn Sb , Ca YbZn Sb , Ca YbZn Cu Sb , and Ca YbZn Cu Sb , respectively. In addition, the
4.5
8
4.4
9
0.15
4.35
8
0.1
9
9
8
4.5
9
9
effective mass and mobility are inversely proportional to each other, but those hardly affect S directly.
Therefore, this kind of observation implied the possibility of multiple electronic bands or nonparabolic
band effects, which could influence the TE properties of the title compounds. In addition,
2
Supplementary Figure 4A displays the results for the power factor (PF), which was computed using PF = S σ.
Figure 8A shows the temperature-dependent thermal conductivity κ of the title compounds with
tot
minimum κ values of 0.57, 0.82, 0.76, 0.70, and 1.00 W/mK for Ca Zn Sb 9 [19] , Ca YbZn Sb ,
9
8
4.5
9
4.5
tot
Ca YbZn Cu Sb , Ca YbZn Cu Sb , and Ca YbZn Cu Sb , respectively. Typically, the κ is delineated
0.15
tot
9
0.1
9
4.45
0.05
9
8
4.4
8
8
4.35
as the sum of the electronic contribution κ and the lattice contribution κ . Given that the κ value is
elec
elec
latt
determined through the application of the Wiedemann-Franz law (κ = LσT; , where L is
elec
-8
in 10 WΩK and S in μ/K), the determination of the term κ involves the subtraction of the κ from the κ tot
elec
latt
value (κ = κ - κ ) .
[32]
latt
elec
tot