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Duparchy et al. Energy Mater. 2025, 5, 500134 https://dx.doi.org/10.20517/energymater.2025.51 Page 3 of 21

Although Mg (Si,Sn)-based materials feature attractive TE properties and technological advances have been
2
made, its stability remains a major drawback for thermoelectric devices which need to operate at high
[26]
temperatures. Skomedal et al. studied the material stability at high temperature in air, showing the high
sensitivity of the material to oxidation. A further well-known challenge is that the Mg stoichiometry in the
Mg (Si,Sn) solid solutions is difficult to control . Mg content can decrease compared to the target
[27]
2
stoichiometry as Mg has a lower melting point and a higher vapor pressure than the other elements
involved and thus evaporates easily. This impacts the intrinsic Mg point defect densities and thereby the
charge carrier concentration and the functional properties of the material [28,29] . The use of excess Mg in the
synthesis process (nominal starting composition Mg (Si,Sn)) is usually chosen as a strategy to counteract
2+δ
the change in functional properties [30-33] . However, Sankhla et al. studied the effect of heat treatment on
[34]
the stability of material synthesized with excess Mg and demonstrated that changes in transport properties
(decrease in carrier concentration) are linked to Mg loss. Recently, Duparchy et al. investigated room
[27]
temperature stability in air of n- and p-type Mg (Si,Sn) solid solutions, demonstrating that the p-type
2
material which had been synthesized without Mg excess is stable over time while the n-type degrades. This
was traced back to the diffusion of loosely bound Mg in Sn-rich phases via Mg vacancies, leading to
subsequent Mg oxidation at the surface and causing gradual changes in the integral material properties.
[35]
Ghosh et al. showed that the dominant Mg diffusion path is through grain boundaries and Sankhla
et al. developed a microscopic understanding for Mg loss and determined degradation kinetics.
[36]
From these experimental results and first-principles calculations on defect densities [37,38] , it is clear that
Mg (Si,Sn) exhibits a finite solubility range with respect to Mg, with compositions between Mg 2(1+δ1) (Si,Sn)
2
and Mg 2(1+δ2) (Si,Sn) (δ < δ ) being in principle feasible. Here, Mg 2(1+δ1) (Si,Sn) and Mg 2(1+δ2) (Si,Sn) represent
2
1
Mg-poor and Mg-rich thermodynamic states, which represent the lower and upper solubility limit,
respectively, and differ by the concentration of intrinsic point defects. This finite width of presumable line
phase is typical for TE materials and is, e.g., observed for BiTe and Mg Sb 2 [39-42] , with phase widths δ -δ <
3
1
2
0.001. The intrinsic defects with the lowest defect formation energies in Mg (Si,Sn) are Mg-related: Mg
2
[38]
interstitials ( ) and Mg vacancies ( ) . Mg interstitials (Mg on the interstitial position) will be the
dominant defect under Mg-rich conditions, contributing electrons [27,38] . In Mg-poor samples, Mg vacancies
will become more abundant, potentially with defect densities larger than Mg interstitials, acting as acceptor
defects, compensating electrons. Hence, it is important to differentiate between: (i) excess Mg which refers
to an non-soluble content of elemental Mg in the material, (ii) loosely bound Mg which is part of the crystal
lattice but can be removed from it by changing the concentration of point defects and (iii) tightly bound Mg
which refers to Mg that is bound in the crystal lattice of Mg-depleted Mg (Si,Sn) material and cannot be
2
removed from it without initiating decomposition of the compound into its elemental constituents. Tightly
bound Mg is very stable, while Sankhla et al. proved that loosely bound Mg is lost before the material
[36]
starts to decompose and thus the fastest and most important material degradation mechanism. Hence, long-
term stability requires the suppression of this loosely bound Mg from the material.

This might in principle be done by impeding Mg diffusion , avoiding Mg loss by the use of coatings , or
[43]
[44]
[27]
potentially most easily by eliminating the loose Mg source. Duparchy et al. also demonstrated that p-type
materials, which are synthesized without excess Mg and presumably Mg-poor after synthesis [45,46] , remain
stable over years.

This study aims to overcome the fundamental origin of the instability of n-type Mg X by the synthesis of
2
Mg-poor samples. We report for the first time, thermoelectric properties and microstructural analysis of
optimized n-type Mg-poor Mg Si Sn solid solutions. We find that - compared to the usually employed
0.3
0.7
2-δ
Mg-rich material - larger amounts of Sb dopant are required to increase the carrier concentration in