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Page 6 of 35    Martin-Gonzalez et al. Energy Mater. 2025, 5, 500121  https://dx.doi.org/10.20517/energymater.2025.32

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               system, Tan et al. reported an even lower lattice thermal conductivity of κ  = 0.5 W·m ·K  and a higher zT
                                                                              p
               of 2.5 at 923 K . This multi-scale, or all-size phonon scattering center inclusion is now a widely used
                            [32]
               approach to reduce κ . Around that period and since then, many more examples of successful hierarchical
                                 p
               nanostructuring emerged in the literature, with nanocomposites characterized by multi-scale phonon
               scattering centers of different nature and sizes (see Figure 2A).
               Such nanostructuring was also able to raise interest for materials that were not traditionally considered good
               TEs due to their high  κ , such as the abundant Si. It was realized early on that Si in the form of
                                     p
               nanowires [40-42] , superlattices [43,44] , porous media [31,45] , and combinations of those could result in two orders of
               magnitude reduction in κ , reaching values close to or even below the amorphous limit. For example, a
                                      p
                                              [31]
               porous SiGe nanocrystalline material  provided scattering of phonons due to alloying, pore scattering and
               boundary scattering, together with reduced heat capacity because of porosity, which resulted in thermal
               conductivities of κ  = 0.5 Wm K .
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                              p
               Another highly discussed material is SnSe. Initial reports for the TE performance of the pristine single
               crystal p-type material indicated a zT value of 2.6 , sharply peaking at high temperatures due to strong
                                                          [18]
               bond anharmonicity, resulting in ultra-low thermal conductivities. This was a new zT record at the time.
               The corresponding n-type performance reached a zT of 2.2 . Many subsequent studies on polycrystalline
                                                                  [46]
               samples, on the other hand, reported values consistently below unity (although one would have expected
               that nanostructuring would reduce the thermal conductivity even lower). Later on, another study has,
               however, treated the samples in a specific way to remove the localized oxygen trapped around the grain
               boundaries. This resulted in another zT record of 3.1 [see Figure 1] [12,33] , and better average zT over
               temperature overall, indicating that the trapped oxygen was hurting the performance in two ways:
               increasing the thermal conductivity across the grain boundaries, and reducing the electronic conductivity.
               In other examples, local lattice distortions - such as rattling atoms in skutterudites or strain fields in half-
               Heuslers - reduce κ  by 15%-30% without significantly altering σ . Recent work on Cd-doped-AgSbTe
                                                                        [47]
                                p
                                                                                                         2
               nanocomposites demonstrates zT > 2.5 via strain-induced phonon localization, validated by transmission
                                       [14]
               electron microscopy (TEM) .
               Although initially bottom-up nanostructuring demonstrations were targeted, nowadays top-down
               approaches, such as mechanical alloying and high-energy ball milling followed by hot pressing sintering or
               spark plasma sintering (SPS), are widely used to synthesize nanoparticle powders and bulk-size TE
               materials. This is now widely applied across material families. In this way, the zT values of the different
               materials were gradually doubled and sometimes even tripled compared to their pristine values. For
               example, the abundant and non-toxic family of silicides also raised significant interest due to their ability to
               be nanostructured and extensive studies on these materials exist (Mg Si [48,49] , metal silicides including
                                                                              2
               CrSi , CoSi , TiSi , VSi , and YbSi ). Nanostructuring methods can produce nanoscale precipitates
                                      [52]
                   [50]
                                                 [53]
                           [51]
                                                 2
                   2
                          2
                                 2
                                      2
               located within larger grain formations in the Si matrix, which reduces κ  drastically, as another example of a
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               successful hierarchically nanostructured geometry. Moreover advances in MnSi  (higher manganese
                                                                                       1.7
               silicide) have demonstrated a zT of 0.8 at 800 K, outperforming CrSi  and CoSi . This improvement stems
                                                                                   2
                                                                          2
                                                                                                      [54]
               from intrinsic vacancy engineering, which enhances phonon scattering while maintaining hole mobility .
               Nanostructuring, thus, is a proven strategy that over the past two decades has increased the nominal zT
               values of the most prominent TEs to the range between 1-2 and sometimes even higher (see Figure 1).
               There is still some fascinating work to be done to fully understand the effect of nanostructuring on phonon
               scattering and to create materials that can eliminate most of the phonon contribution to the thermal
               conductivity (we discuss below an example of a three-dimensional (3D) network material  which
                                                                                                  [55]
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