Thermoelectric Characteristics of β-Ag₂Se_1+x Prepared via a Combined Rapid Mechano-Thermal Approach

Abstract

This study investigates the thermoelectric properties of Se-rich β-Ag₂Se synthesized via a mechanochemical method followed by spark plasma sintering (SPS) in less than 30 min of the total reaction time. Importantly, only a short 10 min milling process followed by appropriate SPS was enough to produce single-phase Ag₂Se_1+x samples with varying selenium content (where x = 0, 0.01, 0.02, 0.04). The introduction of excess selenium significantly influenced the thermoelectric performance, optimizing the carrier concentration during synthesis and resulting in substantial thermoelectric improvements. The sample with nominal composition Ag₂Se_1.01 exhibited a high dimensionless figure-of-merit (ZT) >0.9 at 385 K, which is nearly six times higher than the reference sample (β-Ag₂Se). Our findings bring valuable insight into the technology of optimization of thermoelectric characteristics of Se-rich β-Ag₂Se, highlighting its potential for applications in thermoelectric devices. The study demonstrates the energetically efficient and environmental advantage of our mechanochemical route to produce Se-rich β-Ag₂Se, providing a solvent-free and commercially viable alternative synthesis for energy (thermoelectric and solar energy).

1. Introduction

In the quest for environmentally friendly and efficient thermoelectric (TE) materials capable of harnessing waste heat for clean electricity generation, the attention has shifted towards materials facilitating the direct conversion of heat to electricity and vice versa without generating excessive noise and emissions [1].

To achieve widespread utilization of TE materials, it is crucial that they exhibit high performance and cost-effectiveness. The energy conversion efficiency of TE materials is quantified by the dimensionless figure-of-merit ZT:

$$\mathrm{Z}\mathrm{T}={\displaystyle \frac{S^2}{\rho \lambda }},$$

(1)

where S is the Seebeck coefficient, ρ is the electrical resistivity, λ is the thermal conductivity and T is the absolute temperature [2]. The figure-of-merit ZT directly influences the efficiency of TE devices like thermoelectric generators (TEGs) and heat pumps [3,4,5,6]. Higher ZT values are desired, and materials of interest for TE applications are expected to have a figure-of-merit ZT of at least one [7].

Ag₂Se exists in two main structural phases, each with distinct physical properties that significantly influence its applicability in energy conversion technologies. At low temperatures (LT) below 407 K, Ag₂Se crystallizes in the orthorhombic β-phase (space group P2₁2₁2₁), which is a semiconductor. This phase is characterized by a highly ordered crystal lattice, exhibiting low electrical resistivity, relatively high Seebeck coefficients, and low lattice thermal conductivity. These attributes make the β-phase highly suitable for thermoelectric applications, particularly in the conversion of waste heat into [8,9]. Above 407 K, Ag₂Se undergoes a first-order phase transition to the cubic α-phase (space group Im$\overline{3}$m) [10,11]. The α-phase is characterized as a superionic conductor, where silver ions exhibit high mobility within the lattice, leading to significantly increased ionic conductivity. While this property is advantageous for certain applications, such as solid-state electrolytes, it results in reduced thermoelectric performance due to higher electrical resistivity and altered thermal conductivity in the α-phase. Consequently, the β-phase of Ag₂Se is the primary focus for thermoelectric applications because its semiconducting behavior and stable structure support the optimized interplay of electrical and thermal properties necessary for achieving high ZT values [12,13]. The dominance of the β-phase at low temperatures aligns with the overarching goal of thermoelectric materials to efficiently convert waste heat into electricity in operational environments typically below the α-to-β phase transition temperature.

Noteworthy advancements in this domain include the work of Mi et al., which achieved the highest figure-of-merit ZT of 0.96 at T = 401 K through the implementation of excess selenium in Ag₂Se [14]. Mi et al. achieved this by preparing Se-rich β-Ag₂Se using high-temperature annealing followed by controlled cooling, emphasizing compositional tuning and phase stability to enhance thermoelectric properties. Chen et al. further contributed by preparing the LT orthorhombic phase β-Ag₂Se, characterized by high porosity and attained a maximum ZT of 0.9 at T = 390 K [15]. Their unique approach involved the fabrication of porous β-Ag₂Se through a melting and sintering process, leveraging enhanced phonon scattering properties of the porous structure to reduce thermal conductivity. Building on this, Jood et al. successfully suppressed the metastable structure of Ag₂Se using a slight excess of selenium, resulting in the highest ZT of 1.0 at T = 375 K [16]. This underscores the potential of selenium excess as a strategy for enhancing TE properties, warranting further in-depth studies for the development of an economical and effective preparation method.

Furthermore, the combination of silver (Ag) and selenium (Se) presents significant advantages regarding lower toxicity. This differs from the combinations of silver with tellurium (Te) or bismuth (Bi). Additionally, Ag₂Se is a promising and stable thermoelectric (TE) material, maintaining its stability even at 300 K [15]. Additionally, this material is cheaper to produce by omitting rare and expensive Te and replacing it with Se [17]. Ferhat et al. recently identified Ag₂Se as a promising candidate for TE applications in TE coolers and sensor devices [18]. This is attributed to the unique characteristics of the low-temperature modification of Ag₂Se, which exhibits unusually low lattice thermal conductivity (λ_L~0.5 W·m⁻¹·K⁻¹), coupled with low electrical resistivity (ρ~5.10⁻⁶ Ω·m) and a relatively high Seebeck coefficient (S~−150 μV·K⁻¹ at 300 K) [19]. Given recent discoveries of significant positive volume magnetoresistance [20] and thin-film behavior [21] in Ag₂Se, it becomes imperative to undertake a detailed exploration of this system for TE applications at LTs as well [18].

In the broader context of the preparation of Ag₂Se-based compounds, the pursuit of enhanced performance and efficient synthesis methods remains a driving force. Conventional approaches to synthesizing Ag₂Se have drawbacks such as low yield, multiple steps, and long processing periods, contributing to elevated production costs and environmental impact [22]. Additionally, traditional melting–annealing–sintering processes for Ag₂Se are time-consuming and energy-intensive [23]. These limitations highlight the need for more efficient and environmentally friendly synthesis approaches for Ag₂Se and related materials. The present research challenges these conventional methods by introducing a novel approach to the preparation of Ag₂Se-based compounds. The data from various studies emphasize the importance of developing rapid, cost-effective, and less toxic synthesis methods to overcome the cons associated with the conventional synthesis routes of Ag₂Se [24].

A novel approach to the preparation of Ag₂Se-based compounds involves utilizing single-source molecular precursors for the synthesis of Ag₂Se nanocrystals, as demonstrated in one study [25]. Another study highlighted the successful synthesis of binary Ag₂Se and composite Ag⁰:Ag₂Se through an ambient aqueous-solution-based approach without high-temperature heating or the use of organic solvents [26]. Additionally, a unique method involving the nanostructuring of g-Se with silver nanoparticles led to the formation of fine nanowires of trigonal selenium within the glass matrix, enhancing various physical properties effectively [27].

Drawing upon prior research, the transport properties of Ag₂Se demonstrate a significant sensitivity to synthetic methods, composition variations, and resulting defects [16]. For example, Huang et al. [28] employed multiple methods (melting, melting with spark plasma sintering (SPS), and mechanical alloying with SPS) to prepare Ag₂Se bulk materials, resulting in imperfections such as nanosized Ag- or Se-rich precipitates, micropores with Se-aggregated interfaces, and large voids. These imperfections have the potential to impact thermoelectric performance, uniformity, and reproducibility.

The thermoelectric performance of β-Ag₂Se prepared by conventional methods has been widely studied, with ZT values ranging from 0.8 to 1.0 in the 300–400 K range. For instance, Huang et al. reported ZT values of up to 0.9 using melting and spark plasma sintering [28], while Jood et al. achieved a ZT of 1.0 at 375 K by introducing selenium excess to stabilize the matrix [16].Other studies highlight how crystallographic orientation [13] and porosity control [29] significantly influence performance.

However, traditional synthesis methods face challenges such as high energy consumption, long processing times, and defect formation, which can degrade transport properties [18,28]. Newer approaches, such as nanostructuring and solution-based techniques, have shown promise in improving Seebeck coefficients and reducing thermal conductivity [26]. The rapid mechanochemical synthesis employed in this study stands out by enabling the precise control of selenium excess, resulting in a high ZT of 0.94 at 385 K. While the direct comparison with the conventional methods is difficult due to the novelty of this approach, our results align with general trends observed in the literature, demonstrating its potential for superior thermoelectric performance.

Jood et al.’s identification of a metastable phase in nominally stoichiometric Ag₂Se, which is believed to negatively impact transport properties, prompted successful interventions [16]. They prevented the formation of this metastable phase and stabilized the matrix by introducing a slight excess of anions (Se and S). This intervention resulted in achieving high mobility (2510 cm²·V⁻¹·s⁻¹ at 300 K, low lattice thermal conductivity (0.2 W·m⁻¹·K⁻¹ at RT), and a high ZT (≈1.0 over 300–375 K) in anion-rich compositions. These findings underscore the complexity of Ag₂Se in comparison to previously described aspects and emphasize the need for a detailed exploration of this system for TE applications at LTs [18].

In this study, Se-doped polycrystalline Ag₂Se featuring fine grains was synthesized using mechanochemical synthesis followed by the SPS treatment under relatively mild conditions. This research focuses on an in-depth exploration of the thermoelectric properties, with particular attention given to elucidating the impact of the Se substitution on the enhancement of thermoelectric characteristics. The initial results of measuring the thermoelectric properties of the β-Ag₂Se material were recently published, and this extended study builds upon them by focusing on the preparation of Se-rich β-Ag₂Se [30]. The results from this study presented herein not only showcase the efficiency of the rapid synthesis approach but also underscore the superior thermoelectric properties exhibited by the Se-rich β-Ag₂Se, positioning it as a noteworthy candidate for applications in waste heat recovery and energy harvesting [31].

The purpose of this work is to develop and evaluate the aforementioned scalable, solvent-free, and energy-efficient approach for producing selenium-rich β-Ag₂Se by fine-tuning selenium content. Then, we analyze its effects on microstructure and carrier concentration. Overall, this study aims to optimize the material’s thermoelectric properties and demonstrate its potential for achieving high ZT values.

2. Results and Discussion

2.1. Phase Composition and Microstructure Analysis

The structural aspects of milled samples and samples after SPS treatment with the chemical composition of Ag₂Se_1+x (x = 0, 0.01, 0.02, 0.04) were characterized using powder pXRD analysis. The pXRD analysis of milled samples confirmed the presence of the orthorhombic phase of β-Ag₂Se after 10 min of milling. In Figure 1a, the pXRD patterns of the powder samples after mechanochemical synthesis are depicted. The quantitative phase analysis confirmed that all milled Ag₂Se_1+x samples exhibited varying phase compositions, with the main phase being the orthorhombic β-Ag₂Se (space group P2₁2₁2₁, a = 4.333 Å, b = 7.062 Å, c = 7.761 Å), (see

Table 1. Representation of individual phases and lattice parameters in the Ag₂Se_1+x series before and after SPS as calculated from quantitative Rietveld analysis.

Sample	Individual Phases (mol.%)			Lattice Parameters for Ag2Se1+x Phase (Å)
	Ag2Se	Ag	Se	a	b	c
Ag2Se1.00	93.0	7.0	0.0	4.3352 ± 0.0002	7.0675 ± 0.0003	7.7723 ± 0.0003
Ag2Se1.01	99.1	0.6	0.3	4.3347 ± 0.0001	7.0673 ± 0.0002	7.7725 ± 0.0002
Ag2Se1.02	73.5	13.0	13.4	4.3350 ± 0.0001	7.0675 ± 0.0002	7.7726 ± 0.0002
Ag2Se1.04	73.2	10.4	16.4	4.3350 ± 0.0001	7.0674 ± 0.0002	7.7723 ± 0.0002
Ag2Se1.00 SPS	100	0.0	0.0	4.3367 ± 0.0003	7.0695 ± 0.0004	7.7742 ± 0.0004
Ag2Se1.01 SPS	100	0.0	0.0	4.3356 ± 0.0002	7.0676 ± 0.0003	7.7697 ± 0.0003
Ag2Se1.02 SPS	100	0.0	0.0	4.3356 ± 0.0002	7.0678 ± 0.0003	7.7704 ± 0.0003
Ag2Se1.04 SPS	100	0.0	0.0	4.3346 ± 0.0002	7.0663 ± 0.0003	7.7680 ± 0.0003

). The pXRD analysis of milled mixtures indicates that the slight excess of Se provides a material with a composition close to that of stoichiometric β-Ag₂Se. By altering the composition through milling, i.e., adding Se, the chemical composition improved, and in the Ag₂Se_1.01 sample, the β-Ag₂Se phase is the most dominant, approaching the stoichiometric composition of the pure β-Ag₂Se phase. This might be explained by the lower purity of the used Se compared to Ag or the volatility of some selenium chemical species. An additional amount of Se, however, hinders the formation of β-Ag₂Se during the 10 min milling period as more elemental Ag is found in the mixtures. Achieving proximity to the stoichiometric composition by adding Se to the matrix is therefore essential to optimize the final chemical composition, which leads to enhanced thermoelectric properties as discussed further.

The phase composition of the investigated Ag₂Se_1+x series after SPS was modified in favor of the pure orthorhombic β-Ag₂Se phase as confirmed by the Rietveld refinement (see the results for the selected sample with x = 0.01 in Figure 1b). This finding further supports the short milling time required to homogenize the input mixture, even if no full conversion is observed in all cases after the milling process. The total reaction time needed to obtain a phase of pure material was less than 30 min. After SPS treatment, the amount of elemental Ag in the stoichiometric mixture Ag₂Se_1+x (x = 0) was so small that it could not be practically quantified. As there were no visible reflections of Se after the SPS process (x = 0.02, 0.04), it was assumed all Se atoms had been incorporated into the crystal structure of the compound. All Se-rich samples comply with the phase pure orthorhombic phase β-Ag₂Se. This is in accordance with previously observed results of Mi et al. [14] and the phase diagram of the Ag-Se system [32]. HT-pXRD patterns were measured to detect a phase transition to the cubic phase α-Ag₂Se, which took place at 400 K (Figure 1c). A transitional state was captured at 403 K where both phases were present, suggesting that the phase transformation was not as fast and needed more energy. The results of the HT-pXRD measurement correspond well with the measured TE data.

This investigation, emphasizing the chemical composition and structure of the Ag₂Se_1+x series, harmonizes with and reinforces prior research delving into analogous materials. Several seminal studies [14,22,33,34] have investigated the crystal structures of Ag₂Se and its derivatives with varying selenium concentrations, shedding light on the intricate interplay between composition, structure, and TE properties. In line with these investigations, Mi et al. focused on the thermoelectric properties of the Ag₂Se_1+x series prepared via annealing at high temperatures, particularly highlighting the crystallographic characterization of the samples. Mi et al. observed that all Ag₂Se_1+x series samples crystallize with the orthorhombic structure further corroborating our findings from the pXRD analysis of the mechanochemically synthesized Ag₂Se_1+x series [14].

Figure 2 illustrates the microstructural evolution of β-Ag₂Se_1+x (x = 0, 0.01, 0.02, 0.04) captured via SEM. SEM images (a)–(d) show the samples after mechanochemical synthesis, highlighting the initial morphology. After mechanochemical synthesis, the samples exhibited similar morphologies, with the exception of x = 0, where two distinct morphologies were observed: rod-like and spherical, consistent with the prior findings detailed in previous study [30]. The morphologies of samples with x = 0.01, 0.02, and 0.04 are similar, characterized by the absence of rod-like particles.

Subsequently, SEM images (e)–(h) show the samples after SPS with EDX values included. The sintering process induced significant changes in the microstructure. Observable changes include variations in grain boundaries and the appearance of porosity, which is indicative of structural reorganization during the sintering process. While the crystal structure remained unchanged, the process led to a tighter arrangement of individual powder particles, facilitating the formation of well-defined crystal grains. These observations align with the literature, which highlights that reorganization is inherent to the sintering process [35]. Additionally, the observed porosity and fracture surfaces were evident in the sample’s morphology, and they are of critical importance for the thermoelectric (TE) properties of β-Ag₂Se. These features can significantly affect electrical transport properties by potentially suppressing activated charge carriers.

Furthermore, the EDX analysis after SPS confirms a close 2:1 ratio of Ag to Se, which is consistent with the expected stoichiometry of the main β-Ag₂Se phase in the system. EDX analysis reveals that elements Ag and Se are homogeneously distributed in all samples, further confirming findings from pXRD analysis for β-Ag₂Se preparation through the combined mechano-thermal method.

2.2. Thermoelectric Properties

The temperature dependence of electrical resistivity (ρ), Seebeck coefficient (S), thermal conductivity (λ), and the figure-of-merit ZT is illustrated for the Ag₂Se_1+x series in the temperature range of 5–440 K in Figure 3. All four parameters clearly indicate a distinct phase transition from the orthorhombic to the cubic phase at around 400 K, which is consistent with the literature [36,37]. Discrepancies in the curves measuring thermoelectric properties at low and high temperatures can be attributed to the use of different instruments.

Electrical resistivity as a function of temperature is shown in Figure 3a. The Ag₂Se_1.00 sample consistently exhibits lower resistivity values compared to the other samples (x = 0.01, 0.02, 0.04). At low temperatures, the resistivity of all samples shows an initial increase as temperature decreases, reaching a maximum at 55–73 K. This behavior corresponds to the semiconductor nature of the materials, where carrier mobility decreases with decreasing temperature. Samples undergo a transition to a metallic character below this maximum with resistivity decreasing and eventually saturating at temperatures below 10 K. This temperature-dependent trend is characteristic of the Ag₂Se system and aligns with the previous study [38].

In the temperature range of 150–375 K, electrical resistivity (ρ) decreases with increasing temperature, which is typical for semiconductors, as the thermal excitation of carriers dominates over scattering effects [14,16,39]. The higher resistivity of samples observed is attributed to a lower concentration of free electrons caused by the changing Se content [40,41]. For example, Jood et al. reported that the electron concentration for stoichiometric Ag₂Se was approximately 6 × 10¹⁸ cm⁻³ [16], decreasing to 4 × 10¹⁸ cm⁻³ in Ag₂Se_1.01 and remaining stable for higher excess Se contents.

The temperature dependence of the Seebeck coefficient (S) is shown in Figure 3b. Negative values across the entire temperature range confirm the n-type semiconductor nature of all samples. The absolute values of S are higher for samples (x = 0.01, 0.02, 0.04) between 20 K and 300 K. The observed increase in the Seebeck coefficient for the selected samples correlates with the reduced carrier concentration due to selenium content variation. Concurrently, the reduction in thermal conductivity is attributed to enhanced phonon scattering caused by the changing selenium content. These effects synergistically contribute to the improved ZT value observed in the Ag₂Se_1.01 sample with peak ZT of 0.94 at 385 K.

The thermal conductivity (λ) data are presented in Figure 3c. Thermal conductivity is generally low across the whole temperature range, which is a key feature for thermoelectric materials. For stoichiometric Ag₂Se_1.00, λ is higher due to a significant electronic contribution to heat transport. At LTs, the lattice contribution dominates, and a pronounced phononic peak at around 10 K is observed, which is typical for crystalline materials. This peak correlates with the Se content, where a lower carrier concentration in Se- modified samples reduces phonon scattering and results in higher lattice thermal conductivity.

At HTs, thermal conductivity becomes weakly temperature-dependent, with the electronic contribution playing a more prominent role. In the range of 300–450 K, the λ values exhibit only minor variations around the phase transition. However, the slight increase in λ near 380–400 K should be regarded with caution, as it is challenging to measure thermal conductivity precisely in the vicinity of a phase transition.

The temperature dependence of the figure-of-merit (ZT) is shown in Figure 3d. For all samples, ZT increases with temperature, reaching a maximum just before the phase transition at approximately 385 K. Beyond this transition, ZT values drop sharply, decreasing by a factor of ~2. The maximum ZT of 0.94 is achieved for the Ag₂Se_1.01 sample at 385 K, highlighting its optimized balance of thermoelectric properties. Se-modified samples show consistent trends, with their ZT values peaking at the same temperature, further emphasizing the influence of phase transitions on thermoelectric performance. This behavior underscores the significance of fine-tuning the composition of Ag₂Se_1+x to optimize the thermoelectric properties, particularly around the phase transition temperature.

The observed ZT peak near 385 K in the samples can be attributed to a combination of factors that influence the material’s thermal and electrical properties. As the temperature approaches the orthorhombic-to-cubic phase transition, several phenomena occur that enhance the thermoelectric performance. Firstly, the reduction in thermal conductivity is a critical factor contributing to enhanced ZT. As the temperature nears the phase transition, the lattice thermal conductivity continues to drop while the electronic contribution remains stable, thus reducing the total thermal conductivity [42]. Secondly, the optimized carrier concentration and mobility in the Ag₂Se_1+x system are pivotal in achieving high thermoelectric performance. Tuning the selenium amount in the Ag₂Se_1+x system leads to a reduction in the concentration of free electrons, which optimizes carrier mobility. This balance between carrier concentration and mobility results in an increased Seebeck coefficient, particularly near the phase transition, without a significant rise in electrical resistivity [43,44].

Furthermore, the temperature-induced enhancements associated with the orthorhombic phase contribute to improved thermoelectric performance. The orthorhombic phase has more inherent semiconducting properties than the cubic phase, making it better suited for thermoelectric applications. As the material approaches the phase transition, it exhibits enhanced electronic properties, including a higher Seebeck coefficient and more stable electrical resistivity [45,46]. This transition not only influences the electronic structure but also affects the overall thermoelectric efficiency, as the material’s response to temperature changes becomes more favorable for thermoelectric generation.

These factors together contribute to the observed ZT peak near 385 K just before the phase transition to the cubic phase. Once the phase transition occurs, the material undergoes structural changes that disrupt the favorable balance of thermal and electrical properties, leading to a sharp decrease in ZT. This behavior underscores the importance of optimizing the composition of Ag₂Se_1+x around the phase transition to achieve the best thermoelectric performance.

The observed trends are consistent with previous research, confirming the potential of this system for thermoelectric applications [7,9,31,33].

3. Materials and Methods

3.1. Mechanochemical Synthesis

Se-rich samples of β-Ag₂Se_1+x (x = 0, 0.01, 0.02, 0.04) were prepared from the following elements: Ag (99.9%, 125 µm, Thermo Fisher Scientific Chemicals, Waltham, MA, USA) and Se (99.5%, 74 µm, Aldrich, Darmstadt, Germany). The simple mechanochemical synthesis of β-Ag₂Se_1+x was carried out by milling in a laboratory planetary mill PULVERISETTE 6 classic line (Fritsch, Idar-Oberstein, Germany), following Equations (2)–(5):

2 Ag (s) + 1.00 Se (s) → Ag₂Se_1.00 (s)

(2)

2 Ag (s) + 1.01 Se (s) → Ag₂Se_1.01 (s)

(3)

2 Ag (s) + 1.02 Se (s) → Ag₂Se_1.02 (s)

(4)

2 Ag (s) + 1.04 Se (s) → Ag₂Se_1.04 (s)

(5)

and under the milling conditions specified in

Table 2. Conditions for the mechanochemical synthesis of β-Ag₂Se.

Volume of the Milling Chamber:	250 mL
Material of Milling Chamber and Medium:	WC
Loading of Milling Chamber:	50 balls (⌀ 10 mm)
Ball-to-Powder Ratio (BPR):	73:1
Total Mass of Input Reactants:	5 g
Milling Atmosphere:	Ar
Addition:	Methanol (<1 mL)
Rotation Speed:	550 rpm
Milling Time:	10 min

.

3.2. Pellets for the Measurements of Thermoelectric Properties

Ultimately, the powders from mechanochemical synthesis were subjected to the spark plasma sintering (SPS) process within a graphite die, with a sintering temperature of 723 K, a holding time of 15 min, and an applied pressure of 80 MPa, resulting in the formation of pellets (Ø 10 mm). To remove the excess graphite layer remaining on the surface after SPS, the pellets were polished. To facilitate further measurements, the polished pellet was divided into smaller geometrically appropriate parts using a diamond wire saw. All analyses were performed on the parts originating from a single pellet. The sample’s mass was determined using analytical balances, and dimensions were obtained through multiple measurements using a calibrated digital caliper. The theoretical density, determined based on lattice parameters obtained from the ICSD database (Inorganic Crystal Structure Database), was calculated to be 8.23 g·cm⁻³. The density of the prepared tablets was calculated from geometric dimensions and sample mass. However, the experimental density values of all samples were approximately 15% lower than the theoretical density. This discrepancy arose due to several factors, including residual porosity within the pellets caused by the SPS process, microstructural inhomogeneity, and surface effects or residual impurities. Despite this discrepancy, the experimental densities are sufficient to support the high thermoelectric performance demonstrated by the samples, indicating that the remaining porosity or inhomogeneity does not negatively impact the key transport properties. The studied series with the chemical composition Ag₂Se_1+x and calculated pellet densities are given in

Table 3. Calculated densities of the pellets with the mixture composition β-Ag₂Se_1+x.

Sample Composition	Experimental Density of Pellet (g·cm−3)	Experimental Density of Pellet (%)
Ag2Se1.00	7.07	86.1
Ag2Se1.01	6.94	84.4
Ag2Se1.02	6.71	81.6
Ag2Se1.04	6.95	84.6

.

3.3. Characterization Techniques

The phase purity of β-Ag₂Se_1+x was checked by powder X-ray diffraction acquired on powder Bruker D8 Advance diffractometer with CuKα radiation equipped with a Lynxeye XE-T detector. Phase transition occurring around 404 K was further studied using powder X-ray diffraction (pXRD) measurements performed in Bragg–Brentano geometry using a Cu lamp and strip D/teX detector by Rigaku Ultima IV type II (Tokyo, Japan). The sample was placed in a standard holder in the high-temperature chamber HTK 1200N (Anton Paar, Graz, Austria) in an oxygen atmosphere. The chamber was heated to 423 K and then cooled back to room temperature. During this process, the temperature change was controlled at a constant rate, and the goniometer was rotated at a speed of 0.02 degrees per minute (θ/min).

A scanning electron microscopy (SEM) investigation was conducted employing the MIRA3 FE-SEM microscope (TESCAN, Brno, Czech Republic), which was fitted with an energy-dispersive X-ray (EDX) detector (Oxford Instruments, Abingdon, UK) for EDX analysis.

To measure the TE properties below 300 K, a commercial apparatus called the Physical Property Measurement System (PPMS) from Quantum Design (San Diego, CA, USA) was utilized. For concurrent measurements of electrical resistivity, ρ, Seebeck coefficient, S, and thermal conductivity, λ, the Thermal Transport Option (TTO) sample holder was employed.

The electrical resistivity was measured simultaneously with the Seebeck coefficient via the four-terminal and static direct-current method using custom equipment. The sample together with the holder, was placed in a furnace controlled by the Lakeshore 331S temperature controller. A Keithley 2401 source meter served as the source for a gradient heater and a current source for measuring electrical resistivity. Meanwhile, an Agilent 34970A data acquisition unit equipped with a multiplexing card was responsible for scanning the voltages and temperatures across the sample. The thermal conductivity was measured by a laser flash method in a flowing N₂ atmosphere (LFA 467, Netsch, Selb, Germany) in the temperature range of 300–440 K and was obtained as a product of measured thermal diffusivity, heat capacity (using Pyroceram 9606 as a standard) and experimental density.

Low-temperature (LT) and high-temperature (HT) measurements allowed us to observe the temperature dependence of the thermoelectric properties and identify the maximum ZT values at required temperatures.

4. Conclusions

Mechanochemistry, a field gaining increasing prominence in materials science, involves chemical transformations induced by mechanical force. The planetary ball mill employed in this study served as a powerful tool to harness mechanochemical reactions, allowing for the expedited synthesis of Ag₂Se_1+x compounds. The distinctive advantage of this approach lies in its ability to achieve a high degree of mixing and reactivity over a short duration. This led to the formation of finely tuned thermoelectric materials with enhanced properties. It is noteworthy that the accelerated synthesis of Ag₂Se_1+x in a remarkably brief 10 min milling process sets a new benchmark for the synthesis of Ag₂Se-based compounds. The implications of this rapid mechanochemical synthesis are far-reaching, promising to streamline production processes, reduce energy consumption, and open new avenues for the exploration of thermoelectric materials.

This study successfully demonstrated the enhanced thermoelectric properties of β-Ag₂Se synthesized via a rapid mechanochemical approach followed by spark plasma sintering (SPS). The varying amounts of selenium (x = 0, 0.01, 0.02, 0.04) significantly affect the thermoelectric performance by optimizing carrier concentration and reducing the thermal conductivity of the material. The best-performing sample, with the composition of Ag₂Se_1.01, achieved a dimensionless figure-of-merit (ZT) of 0.94 at 385 K. While the ZT value of 0.94 for the Ag₂Se_1.01 sample is high, it does not surpass the best-known values in the literature, such as the ZT of 1.0 achieved by Jood et al. [16] or 0.96 reported by Mi et al. [14]. These higher values were achieved using more time-intensive or complex synthesis techniques, such as the annealing or suppression of metastable phases. Nonetheless, our rapid mechanochemical method combined with SPS demonstrates a competitive ZT value, offering a practical and scalable alternative for the synthesis of this thermoelectric material. The modification of selenium amount has been demonstrated as an effective strategy for tuning the thermoelectric performance of Ag₂Se, consistent with previous research findings.

Phase composition analysis confirms the predominance of the orthorhombic β-Ag₂Se phase, which highlights the effectiveness of the mechanochemical synthesis and subsequent SPS method. The SPS process plays a crucial role in achieving phase purity and transforming the sample into a phase-pure material despite the presence of significant amounts of unreacted precursors in the milled sample. This finding underscores the importance of SPS as a critical technological step in the preparation of high-purity β-Ag₂Se. Microstructural observations through SEM and EDX analyses reveal significant changes in grain boundaries and porosity post-sintering. This contributes to the material’s enhanced thermoelectric characteristics.

The results indicate that the β-Ag₂Se place with the composition closest to the stoichiometric, and only minimal change in the Se content, leads to the best results mainly because of reduced lattice thermal conductivity and improvements in electrical conductivity, thereby achieving a high ZT, which is crucial for the efficient use of thermoelectric materials.

Overall, the results of this work not only confirm the effectiveness of mechanochemical and SPS methods for preparing high-performance β-Ag₂Se materials but also provide a foundation for future research aimed at further improving and applying these materials in the field of thermoelectrics. By demonstrating the benefits of selenium doping and the viability of the synthesis methods used, this study advances our understanding of how to enhance thermoelectric materials for practical and sustainable energy solutions.