Solid-state thermoelectric (TE) technology, which can directly convert temperature gradients into electricity and vice versa, allows waste heat recovery and refrigeration [1][2][3][4]. Without moving parts, TE devices require little maintenance and can be readily integrated with other energy conversion devices [5,6]. The energy efficiency of TE devices is limited by the dimensionless figure of merit zT = S 2 σT/(κe+κL) of TE materials. In this equation, S represents the Seebeck coefficient, σ is the electrical conductivity, T represents the absolute temperature, κe is the electronic thermal conductivity, and κL is the lattice thermal conductivity. The product of S 2 σ is called power factor (PF). Currently, several strategies have been employed to enhance the performance of TE materials, including chemical doping, [7][8][9][10] nanostructuring [11][12][13][14], alloy scattering [15,16], resonant energy level doping [17], convergence of electronic bands [18,19], phonon engineering [20,21], and the exploration of new materials [22,23].
Environmentally friendly TE materials composed of earth-abundant and non-toxic elements have attracted growing interest recently [24][25][26][27]. Among these, higher manganese silicides (HMSs) stand out with promising TE performance for intermediate-temperature energy conversion. HMSs are p-type TE materials with Nowotny chimney ladder (NCL) phases, characterized by a tetragonal Mn sublattice (chimney) and a Si sublattice (ladder) [28,29]. The periodicities of the two sublattices along the c-axis are usually incommensurate, where the compound can be expressed as MnSiγ with a non-integer incommensurate c-axis ratio γ=cMn/cSi. The crystal structures of several members in the HMS family, i.e. Mn4Si7, Mn11Si19, Mn15Si25 and Mn27Si47, have been reported [28][29][30][31]. These phases have a similar a-axis but different c-axis ranging from 17.5 to 117.9 Å.
Recent advancements on HMSs have focused on reducing the thermal conductivity (κ) through heavy element substitution and nanostructuring while enhancing the PF via chemical doping [32][33][34][35][36]. Chen et al. [37] utilized inelastic neutron scattering measurements and first-principles calculations to investigate the phonon dispersions in HMS. They identified several low-energy optical phonon modes, including a distinctive polarization associated with the twisting of Si ladders inside the Mn chimneys. Scattering of acoustic phonons with this low-lying optical polarization contribute to the intrinsically low κ of HMS.
Additionally, a two-channel model of both propagons and diffusons was proposed to explain their low and anisotropic thermal conductivity. Chen et al. [38] substituted Mn with the heavier element rhenium (Re) to enhance point defect scattering, resulting in a lattice thermal conductivity 30% lower than that of pure HMS at 723 K. Similarly, Zhou et al. [39] and Luo et al. [40] demonstrated that SiGe additions and Al doping, respectively, introduced defects that enhanced phonon scattering and suppressed the thermal conductivity.
Additionally, Al doping improved the electrical conductivity by increasing the carrier concentration, which in turn enhanced the PF. Recently, Chauhan et al. [41] co-substituted V and Fe elements at the Mn sites in HMS, achieving charge compensation and enhancing lattice anharmonicity. The charge compensation led to an optimized charge carrier concentration and an improved PF, while the structural modulation-induced anharmonicity resulted in a reduced lattice thermal conductivity. Yu et al. [42] showed that the TE properties of HMS are enhanced through isoelectronic anion and cation co-doping combined with embedded quantum dot techniques. The PF was improved due to band structure modification and charge transfer effects.
Additionally, increased phonon scattering from point defects and nanoprecipitates significantly lowers lattice thermal conductivity, leading to an enhanced zT.
Beyond doping and nanostructuring, grain boundary engineering has emerged as an effective strategy for enhancing the performance of TE materials [43,44]. Modified grain boundary structures can further suppress phonon thermal transport while maintaining electrical performance through the introduction of defects, such as segregated secondary phases, strain fields, pores, or dislocations [45][46][47][48][49][50].
In addition, the incorporation of secondary phases, such as metallic nanoparticles, at grain boundaries can induce a carrier filtering effect, which enhances the Seebeck coefficient by preferentially scattering lowenergy carriers and effectively increasing the density-of-states (DOS) effective mass [51,52]. Despite these advances, there is a lack of studies applying grain boundary engineering, particularly through in situ methods, to enhance the thermoelectric performance of HMS.
In this work, we investigate the TE properties of Ru-doped HMS with in situ formed nanostructures, prepared via melt-quenching followed by annealing. This method facilitates the formation of MnSi precipitates and pores with a wide size distribution near grain boundaries. The obtained sample shows a glass-like thermal conductivity, distinct from the samples prepared by solid-state reaction. A two-channel model incorporating contributions from propagons and diffusons is employed to understand this low thermal conductivity. Furthermore, quench-annealing process enhances electrical conductivity above 200 K while the Seebeck coefficient remains nearly unchanged due to the enhanced DOS effective mass. As a result, the quench-annealed sample demonstrates a 33% enhancement in zT at 300 K, owing to the enhanced PF and reduced lattice thermal conductivity. This study highlights the potential of grain boundary engineering for controlling heat conduction in thermoelectric materials.
The starting materials are Mn (purity, 99.95%), Ru (purity, 99.9%) and Si (purity, 99.999%) powders. Three HMS samples were synthesized by either melt-quenching or solid-state reaction (SSR), followed by cold-pressing and annealing. For the melt-quenching synthesis, powders with a nominal chemical composition of Mn0.95Ru0.05Si1.78 were weighed and hand-ground with an agate mortar and pestle for 1 hour. The powder was then sealed in an evacuated quartz tube and sintered at 900 °C for 30 hours to obtain a pure phase. Next, the materials were melted at 1250 °C for 10 hours and quenched in water. The resulting ingot was ground into fine powder, cold-pressed under a maximum non-hydrostatic pressure of about 3 GPa [53], and then annealed at 1000 °C for 48 hours in a vacuum-sealed quartz tube. For comparison, undoped HMS (MnSi1.78) and Ru-doped HMS (Mn0.95Ru0.05Si1.78) were prepared by the SSR method at 900 °C for 48 hours in a vacuum. The obtained powders were cold pressed and annealed at 1100 o C for 15 hours in a vacuum-sealed quartz tube using a similar method.
The crystal structure of the samples was investigated by X-ray diffraction (XRD) with a Phillip X'pert diffractometer and the Cu Kα radiation. The samples' morphology and chemical compositions were analyzed using a TESCAN Vega3 SBH scanning electron microscope (SEM) with an energy-dispersive Xray (EDS) spectrometer. The density was measured by the Archimedes method. The resistivity was measured in the temperature range between 5 K and 823 K using the van der Pauw method on samples with a diameter of about 3 mm and a thickness of 0.2 mm. The Seebeck coefficient was measured in the temperature range 80-823 K with home-built setups. The thermal conductivity was measured using the steady-state method on rectangular specimens sized 0.5 × 0.5 × 2.5 mm in the temperature range of approximately 5 K to 300 K [54,55]. All three transport properties were measured along the direction perpendicular to the cold-pressing force. The Hall carrier concentration (pH) and Hall mobility (μH) were measured using a Quantum Design physical property measurement system (PPMS) with a magnetic field sweeping between ±2 T. The specific heat (Cp) of the samples from 2 to 300 K was also measured with the PPMS. to the lower angle indicates the expansion of the lattice constants, which corresponds to lattice expansion due to Ru doping with a larger atomic radius. For the quenched (QH) and quench-annealed (QA) Ru-HMS samples, the XRD analysis reveals notable changes before and after annealing. Prior to annealing, no MnSi phase is detected in the sample. However, after annealing, the emergence of MnSi is evident, accompanied by a shift in the XRD peaks to higher angles, as shown in Figure 1(c). This shift suggests a reduction in lattice constants (Figure 1(d)), indicating that the lattice contracts upon annealing. This contraction is likely due to the formation of MnSi, which depletes Mn from HMS matrix and subtly shrinking the lattice. In addition, it is noted that the lattice constants of the Ru-HMS-SSR and Ru-HMS-QA samples are nearly identical, suggesting a similar Ru concentration in the solid solution. Figure 2(a) and (b) show SEM images of the fractured surface of the Ru-doped HMS sample after quench-annealing. Some nanosized precipitates can be found on the surface of grains and exhibit an average size of about 160 nm. Based on the XRD results, these nanoprecipitates can be attributed to the metallic phase MnSi. Furthermore, pores are clearly observed in the polished samples, as shown in Figure 2(c) and (d). Some of these pores are approximately 1-10 micrometers in size, while others are smaller, measuring around 50-300 nm. Additional SEM images can be found in the Supplementary Material. The calculated size distribution of nanopores is illustrated in Figure 2 (e). The pores have an average size of 290 nm. In contrast, such nanopores are not readily observed in the samples prepared by solid-state reaction followed by cold pressing [53]. Additionally, a few micrometer-sized secondary phases are visible in the sample, as indicated by the white arrows in Figure 2(f). EDS analysis indicates that the atomic ratio of Mn to Si in these secondary phases is approximately 1:1 (see Supplementary Material), consistent with the composition of MnSi. Figure 2(g-i) shows the EDS elemental maps of Mn, Si, and Ru. The mapping confirms that the secondary phases are enriched in Mn and deficient in Si relative to the matrix (MnSi1.75), further supporting the formation of MnSi. These impurity phases are typically located near grain boundaries.
The formation of nanoprecipitates at grain boundaries has also been reported in other TE materials synthesized via non-equilibrium processing techniques, such as melt-spinning or melt-quenching followed by sintering or annealing [56,57]. These processing methods often produce compositional inhomogeneities or metastable solid solutions that decompose upon subsequent heat treatment, resulting in secondary phase precipitation at energetically favorable sites such as grain boundaries [58]. In our study, MnSi nanoprecipitates formed at the grain boundaries as a result of slight Mn-rich deviation from the stoichiometric composition of HMSs. During annealing, the system enters a two-phase region in the Mn-Si phase diagram, where the HMS phase coexists with MnSi. Local Mn enrichment, particularly at grain boundaries due to segregation and enhanced diffusion, facilitates the nucleation and growth of MnSi precipitates at these interfaces. This precipitation process is also accompanied by the formation of nanopores near the grain boundaries. These pores likely originate from the Kirkendall effect [59], where unequal diffusion rates between Mn and Si during phase separation lead to vacancy supersaturation and eventual void formation. Additionally, the rejection of elements during precipitate formation and local volume contraction may further contribute to porosity. The concurrent presence of MnSi nanoprecipitates and nanopores at grain boundaries plays a critical role in electron and phonon transport in the material.
Ru atoms usually act as electron donors in the HMS when substituting for Mn atoms. Previous studies on Ru-doped HMS suggest that Ru negatively impacts TE performance of p-type HMS by reducing the electrical conductivity [60]. Figure 3(a) demonstrates the temperature dependence of the electrical conductivity of our samples. The n-type Ru substitution significantly decreases the electrical conductivity of p-type HMS at low temperatures. However, at higher temperatures as shown in Figure 3(b), the QA sample exhibits higher electrical conductivity than the other two samples. Figure 3(c) shows the temperature dependence of the Seebeck coefficient. All the samples exhibit the characteristics of p-type conduction. The Seebeck coefficient gradually increases with temperature up to 750 K for all three samples. At low temperatures, the Seebeck coefficient increases linearly with temperature, which can be attributed to its degenerate semiconductor behavior [38,61]. The Ru-doped samples exhibit an increased Seebeck coefficient in comparison to the undoped sample across almost the entire temperature range. Notably, the Ru-HMS-QA and Ru-HMS-SSR samples exhibit nearly identical Seebeck coefficients, while the QA sample shows higher electrical conductivity than the other. This improvement is likely due to improved crystallinity and reduced carrier scattering resulting from the melt-quench-anneal process. Furthermore, the formation of MnSi nanoprecipitates in the QA sample may contribute to an energy filtering effect at the interfaces between HMS and MnSi. Such an effect has been previously reported in HMS systems with embedded nanostructures, where the Seebeck coefficient is preserved or even enhanced despite an increase in carrier concentration [34,42]. These combined mechanisms help explain the improved electrical performance observed in the QA sample.
The PF is shown in Figure 3(d). The quenched Ru-doped HMS achieves a peak PF of 1.62×10 -3 W m -1 K -2 at 756 K. In comparison, the maximum for the undoped HMS is only 1.15×10 -3 W m -1 K -2 at 726 K.
In this work, we focus on comparing the thermoelectric properties of the SSR and QA samples to evaluate the influence of different synthesis methods. Because the QH sample represents an intermediate state, its thermoelectric properties were not characterized in this study and remain a subject for future investigation. We further performed Hall effect measurement on the quench-annealed Ru-doped HMS. As shown in Figure 4(a), the hole concentration is nearly constant across the temperature range, which is characteristic of a degenerate p-type semiconductor [38,61]. The room temperature carrier concentration is larger than that of the undoped HMS sample [62], possibly due to the formation of metallic MnSi phase or some ptype defects introduced during the quench-annealing process. Figure 4(b) presents mobility as a function of inverse temperature, following an approximately T -3/2 dependence. This behavior is indicative of dominant acoustic phonon scattering in degenerate semiconductors at elevated temperatures [60]. The mobility values range from approximately 10 cm² V -1 s -1 at 20 K to about 1 cm² V -1 s -1 at 300 K, which are lower than the undoped sample. To better understand the electrical properties of HMS, we used the measurement data to extract the DOS effective mass using a single parabolic band model [62]. The details of the calculation can be found in the Supplementary Material. The relationship between the Seebeck coefficient and carrier concentration of quench-annealed Ru-HMS at 300 K is shown in Figure 5, alongside the data for other doped HMS samples [38,[63][64][65][66]. Our sample exhibits a higher carrier concentration than the undoped HMS while maintaining a comparable Seebeck coefficient, with an effective mass m * of 12 m0 calculated using the single parabolic band model. This increased effective mass, likely resulting from the energy filtering effect, enables Ru-HMS to maintain a high Seebeck coefficient despite an increased carrier concentration.
The specific heat data for the undoped and Ru-doped HMS samples are plotted in Figure 6(a). A previous study has reported that low-energy optical phonons and low-lying twisting modes contribute to the specific heat of HMS [37]. Accordingly, we employ a model that includes contributions from the electronic specific heat, a Debye term, and an Einstein term to fit the low-temperature specific heat data, using the following equation [67]:
where γ is electronic specific heat coefficient, N is the number of atoms per mole, 𝑘 𝐵 is the Boltzmann constant, 𝑛 𝐸 is the Einstein oscillator strength per mole, and 𝜃 𝐷 and 𝜃 𝐸 are Debye and Einstein temperature, respectively. γ is proportional to the electron DOS at the Fermi level, which is proportional to the electron effective mass 𝑚 * , as shown in the following equation:
where 𝑉 𝑚𝑜𝑙 is the molar volume and 𝑛 𝛾 is the number of electrons per formula unit [19]. Figure 6 (b) and (c) shows Cp/T 3 as a function of T for undoped and Ru-doped HMS samples below 30 K. Although the Debye and Einstein contributions to the specific heat are nearly identical in the undoped and Ru-doped samples, the Ru-doped sample exhibits a higher electronic specific heat. The obtained electronic specific heat coefficient γ of the Ru-doped and undoped HMS are 7.81×10 -5 J g -1 K -2 (8.38×10 -3 J mol -1 K -2 ) and 5.19×10 -5 J g -1 K -2 (5.45×10 -3 J mol -1 K -2 ), respectively. This finding suggests a larger effective mass in the Ru-doped sample, consistent with our Seebeck coefficient analysis. The fitted Einstein temperatures for the undoped and Ru-doped HMS samples are 64 K and 61 K, respectively. Figure 7(a) shows the measured thermal conductivity of the polycrystalline samples, which are compared with an HMS single crystal [37]. The low-temperature 𝜅 peak is largely suppressed in the polycrystal samples. The lattice thermal conductivity 𝜅 𝐿 is calculated by subtracting the electronic contribution from the total thermal conductivity. The electronic thermal conductivity κE in Figure 7(c) is calculated using the Wiedemann-Franz law, 𝜅 𝐸 = 𝐿𝜎𝑇, where L is the Lorenz number. It is noted that the constant Lorentz number L0 = 2.44 × 10 -8 W Ω K -2 failed to accurately represent 𝜅 𝐸 when materials deviate from the degenerate limit [68]. Therefore, a corrected Lorenz number for semiconductors, determined based on the measured Seebeck coefficient is used and provided in Supplementary Material. The corrected Lorentz number for quench-annealed Ru-HMS sample is 1.85×10 -8 W Ω K -2 at 300 K, significantly smaller than L0.
With Ru doping, κE is suppressed by up to 80% at 22 K. κL is calculated using 𝜅 𝐿 = 𝜅 -𝜅 𝐸 , as shown in Figure 7(d). It is noted that the lattice thermal conductivity of the Ru-HMS prepared by SSR remains similar to that of undoped samples. This indicates that enhanced scattering from point defects and lattice distortions by Ru-doping has minimal impact on reducing thermal conductivity. Instead, the reduction of 𝜅 is primarily attributed to decreased electronic thermal conductivity, as illustrated in Figure 7(c). After quenchannealing, 𝜅 𝐿 is reduced as compared to the other two samples.
The quench-annealed sample exhibits a significant suppression of the phonon-related peak in the κ curve, although the peak remains discernible. This behavior is characteristic of a "glass-like" thermal transport regime, commonly observed in disordered crystalline materials where phonon propagation is strongly suppressed due to enhanced scattering events. The resulting monotonic increase in lattice thermal conductivity cannot be explained by a classic phonon transport model. In amorphous or highly disordered materials, diffusons are important heat carriers for which the heat transport is characterized with a diffusivity term instead of MFPs used to describe propagons with longer MFPs than their wavelengths [69].
A two-channel model including the propagon and diffuson contributions to κ has been employed to explain the low κ in materials with disorders and complex structures [37,[70][71][72]. This model is employed here to study the thermal transport in the quench-annealed Ru-HMS sample.
Accounting for the porosity of the polycrystalline sample, the intrinsic thermal conductivity of the solid without porosity (κs) is estimated using the Maxwell-Eucken relation [73,74]:
where f is the porosity and 𝑓 = 1 -𝜌/𝜌 𝑠𝑖𝑛𝑔𝑙𝑒 , where ρ is the sample density and ρsingle is the density of the single crystal. The relative density for the QA sample is about 95% determined by the Archimedes method. Based on the two-channel model, 𝜅 𝑠 = 𝜅 𝑝𝑟 + 𝜅 𝑑𝑖𝑓𝑓 , where κpr and κdiff represent propagon and diffuson thermal conductivities, respectively. The Ioffe-Regel frequency ωIR corresponding to the Ioffe-Regel limit, where the phonon MFP equals the interatomic spacing, divides the phonon DOS into propagon and diffuson regimes. Below ωIR, lattice thermal transport is described using the Callaway model for propagons, while above ωIR, it is modeled using the random walk theory with thermal diffusivity. In HMS, ωIR is calculated to be 24.5 THz (16 meV), as shown by the red line in Figure 8(a). A detailed analysis of the two-channel model can be found in the Supplementary Material. The two-channel model fitting is shown in Figure 8(b). The fitting successfully reproduces the temperature dependence of lattice thermal conductivity of quench-annealed Ru-HMS. The diffuson contribution to κ starts above 50 K and accounts for approximately 60% of the lattice thermal conductivity at 300 K. Figure 9 shows the calculated zT of three samples. In the case of quench-annealed Ru-HMS sample, there is a notable increase in zT of about 33% at 300 K compared to the undoped sample. This enhancement can be attributed to several factors. The quench-annealing process increases the carrier concentration, while the Seebeck coefficient remains unaffected due to the effective mass enhancement. As a result, the PF is improved. Furthermore, the lattice thermal conductivity is suppressed due to increased nanostructure scattering. Consequently, the combination of higher PF and lower lattice thermal conductivity leads to a substantial improvement in the overall zT for the quench-annealed sample.
This study reports suppressed thermal conductivity and enhanced thermoelectric properties in Rudoped HMS with grain boundary nanostructures. The melt-quench-annealing process leads to the formation of MnSi nanoprecipitates and pores near the grain boundaries. As a result, the quench-annealed sample exhibits a weak temperature-dependent thermal conductivity, resembling glass-like thermal transport behavior. A two-channel model incorporating contributions from propagons and diffusons is employed to understand this unusual thermal transport. The diffuson contribution to thermal conductivity begins above 50 K and accounts for approximately 60% of lattice thermal conductivity at 300 K. Furthermore, the quench-annealed Ru-HMS exhibits a higher carrier concentration while maintaining a similar Seebeck coefficient compared to the undoped sample, attributed to its increased effective mass of 12 m0. The PF of the quench-annealed Ru-HMS is significantly higher than that of the undoped sample. Owing to improved