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Page 12 of 20 Hamawandi et al. Energy Mater. 2025, 5, 500065 https://dx.doi.org/10.20517/energymater.2024.204

compounds exhibit the most significant changes in distance within the fourth coordination shell, where the
Sb-Sb interatomic distance (in the c-axis direction) expands from 4.64 to 4.70 Å, and the Bi-Bi distance
increases from 4.76 to 4.81 Å as the temperature rises from 10 to 300 K [Figure 7A and C].

Temperature dependencies of the MSRD factors for the nearest Sb (Bi)-Te, Sb (Bi)-Sb (Bi), and Te-Te atom
pairs in Sb Te and Bi Te are plotted in Figure 8, together with corresponding fits from the correlated
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2
2
3
Einstein model and estimated effective force constants. Note that data points at 300 K were excluded from
the fitting procedure due to potential errors associated with the small amplitude of the experimental EXAFS
spectra. The temperature dependence curves in both materials exhibit pronounced steepness that suggests
relatively weak bonding between Sb, Bi, and Te atoms. Throughout all temperatures, the MSRD factor for
the first coordination shell (M-Te2) consistently remains lower than that of the second coordination shell
(M-Te1). Additionally, there is a notable distinction in the temperature dependencies of MSRD(M-Te2) and
MSRD(M-Te1) [Figure 8D and G], arising from the fact that weak vdW forces connect two adjacent Te2
layers. At the same time, Te1 atoms are situated between two Sb (Bi) layers [Figure 8A]. The bond between
M-Te2 is predominantly covalent, whereas the M-Te1 bond exhibits a combination of covalent and ionic
[25]
characteristics .

In Sb Te , the strength of the Sb-Te2 bond [f(r1 Sb-Te2 ) = 24.2 ± 1.4 N/m] in the first coordination shell is
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2
notably larger than that of the Sb-Te1 bond [f(r2 Sb-Te1 ) = 14.8 ± 0.6 N/m] in the second shell. The
corresponding Einstein temperatures 116.9 ± 3.4 K and 91.3 ± 1.8 K are smaller than those (151 ± 2.4 K and
[44]
129.1 ± 3.4 K) reported for microcrystalline Sb Te . Notably, the Sb interactions with the Te2 from the
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3
second quintile exhibit a similar strength [f(r5 Sb-Te2 ) = 23.0 ± 1.8 N/m] as those within the first coordination
shell. At the same time, the MSRD factor for the Sb-Te2 atom pair in the fifth coordination shell (r5 Sb-Te2 ) is
the largest at 10 K due to increased static disorder [Figure 8A]. Within the layers of Sb Te , the interactions
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3
involving the nearest Sb-Sb and Te-Te atom pairs are comparable: f(r3 Sb-Sb ) = 18.6 ± 0.7 N/m and

f(r4 Te-Te ) = 18.5 ± 0.7 N/m, r e s p e c t i v e l y . A c r o s s t h e v d W g a p , t h e T e 2 - T e 2 b o n d s t r e n g t h
[f(r3 Te2-Te2 ) = 17.4 ± 0.8 N/m] is slightly lower. The corresponding Einstein temperature for the third
coordination shell (Sb-Sb) is 103.7 ± 1.9 K, which is very close to that of microcrystalline Sb Te
2
3
[44]
(109.7 ± 2.2 K) .
In Bi Te , the effective force constant for the first [f(r1 Bi-Te2 ) = 25.7 ± 1.4 N/m] and second
2
3
[f(r2 Bi-Te1 ) = 14.5 ± 0.4 N/m] c o o r d i n a t i o n s h e l l s a r e c l o s e t o t h o s e o b s e r v e d i n Sb T e 3

2
[f(r1 Sb-Te2 ) = 24.2 ± 1.4 N/m and f(r2 Sb-Te1 ) = 14.8 ± 0.6 N/m]. Within the layers of Bi Te , interactions
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involving the nearest Bi-Bi atom pairs [f(r3 ) = 17.4 ± 0.5 N/m] are close to those between Te-Te atom
Bi-Bi
pairs [f(r4 Te-Te ) = 18.1 ± 1.1 N/m]. The interactions between Te2 atoms across the vdW gap of Bi Te
2
3
[f(r3 Te2-Te2 ) = 16.1 ± 0.6 N/m] are lower. The corresponding Einstein temperatures for the first two
coordination shells (106.7 ± 2.9 K and 80.3 ± 1.6 K) are smaller than those determined for microcrystalline
Bi Te (143.4 ± 2.3 K and 122.1 ± 2.7 K ). However, for the third coordination shell (Bi-Bi), the Einstein
[44]
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2
[44]
temperature of 76.5 ± 1.1 K coincides with that (77.7 ± 2.1 K) reported earlier .
Thus, we have demonstrated that the analysis of temperature-dependent X-ray absorption spectra based on
atomistic simulations such as RMC method gives an access to local interatomic interactions described by
effective force constants, which, in turn, affect how phonons propagate through the lattice. A lower force
constant usually results in softer bonds and lower phonon frequencies, leading to lower κ, which is desirable
for TEs . According to interatomic force constants reported in [Figure 8D and G], the large differences in
[53]
the temperature dependencies of MSRD(Sb/Bi-Te2) and MSRD(Sb/Bi-Te1) and related force constants
indicate high anisotropy of the κ in Bi Te and Sb Te in the directions along and across the QLs in their
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3
2
3