Structural Phase Transition and Related Thermoelectric Properties in Sn Doped AgBiSe 2

: AgBiSe 2 , which exhibits complex structural phase transition behavior, has recently been considered as a potential thermoelectric material due to its intrinsically low thermal conductivity. In this work, we investigate the crystal structure of Sn-doped AgBiSe 2 through powder X-ray diffraction and differential scanning calorimetry measurements. A stable cubic Ag 1 − x /2 Bi 1 − x /2 Sn x Se 2 phase can be obtained at room temperature when the value of x is larger than 0.2. In addition, the thermoelectric properties of Ag 1 − x /2 Bi 1 − x /2 Sn x Se 2 ( x = 0.2, 0.25, 0.3, 0.35) are investigated, revealing that Ag 1 − x /2 Bi 1 − x /2 Sn x Se 2 compounds are intrinsic semiconductors with a low lattice thermal conductivity. This work provides new insights into the crystal structure adjustment of AgBiSe 2 and shows that Ag 1 − x /2 Bi 1 − x /2 Sn x Se 2 is a potentially lead-free thermoelectric material candidate. microstructure and energy-dispersive spectroscopy (EDS) mapping of Ag 0.90 Bi 0.90 Sn 0.20 Se 2 sample were out using a Zeiss Sigma 500 ﬁeld emission scanning electron mi-croscopy (SEM).


Introduction
As devices that can convert heat and electricity, thermoelectric devices have received significant attention and have become a research hotspot in recent years [1][2][3]. The thermoelectric properties of materials can be evaluated by using the dimensionless quantity ZT. The value of ZT can be calculated with the formula S 2 σT/(к ele + к latt ), where S, σ, T, к ele , and к latt are the Seebeck coefficient, electrical conductivity, temperature, electronic thermal conductivity, and lattice thermal conductivity, respectively. Accordingly, semiconductors with low lattice thermal conductivities have been widely studied and show excellent thermoelectric performance. These semiconductors include Zintl phases [4,5], fast ion conductors [6,7], complex oxides [8,9], and chalcogenides [10].
Ternary chalcogenides with the I-V-VI 2 formula (I = Cu, Ag; V = As, Sb, Bi; VI = S, Se, Te) have an intrinsically ultra-low lattice thermal conductivity due to their unique crystal structures [11][12][13]. For example, due to the anharmonicity caused by the repulsion between neighboring chalcogen ions and lone-pair electrons, the lattice thermal conductivity of CuSbS 2 is only about 0.5 W·m −1 ·K −1 at 627 K [14]. In AgSbSe 2 and AgSbTe 2 , the mixing of Ag and Sb atoms can lead to a further decline in lattice thermal conductivity [15][16][17][18]. I-V-VI 2 compounds have a wide range of structural diversity. The crystal structure of Cu-containing compounds such as CuSbS 2 and CuSbSe 2 can be viewed as the stacking of [CuSb(S/Se) 2 ] layers in an AĀAĀ-type sequence along the c axis direction [19,20]. AgSbSe 2 and AgSbTe 2 crystallize in the cubic space group Fm3m with disordered Ag and Sb cations [21], while AgBiVI 2 (VI = S, Se, Te) compounds exhibit complex temperaturedependent phase transition behavior [22][23][24][25].
AgBiSe 2 compound exists in three polymorphs: a disordered cubic phase, an ordered hexagonal phase, and a rhombohedral phase. Their structures are shown in Figure 1. As an n-type semiconductor with poor electrical conductivity, the thermoelectric properties of AgBiSe 2 can be enhanced by increasing the charge carrier concentration via doping In, Nb, or Ge at Ag sites [26][27][28] or by doping halogen elements at Se sites [29]. Both experimental and density functional theory calculation results indicate that p-type hexagonal AgBiSe 2 can potentially be used in room-temperature thermoelectric applications [30,31]. Additionally, the phase transition temperatures of AgBi 1−x Sb x Se 2 are determined by the doping concentration of Sb [32,33]. Very recently, Br-doped cubic (AgBiSe2) 0.7 (PbSe) 0.3 phase has been proved to be potential material with fine thermoelectric properties in the range from 300 to 800 K [34]. The stable cubic AgBiSe 2 phase may potentially exhibit excellent thermoelectric properties due to its intrinsic crystal structures and related electronic structures. The high symmetry can result in energy band degeneracy, and thus lead to high power factor, while the material with disordered atoms usually exhibits ultra-low lattice thermal conductivity [35]. Accordingly, further investigation into methods for achieving a stable cubic AgBiSe 2 phase and enhancing its thermoelectric properties are of great interest. doping In, Nb, or Ge at Ag sites [26][27][28] or by doping halogen elements at Se sites [29]. Both experimental and density functional theory calculation results indicate that p-type hexagonal AgBiSe2 can potentially be used in room-temperature thermoelectric applications [30,31]. Additionally, the phase transition temperatures of AgBi1−xSbxSe2 are determined by the doping concentration of Sb [32,33]. Very recently, Br-doped cubic (Ag-BiSe2)0.7(PbSe)0.3 phase has been proved to be potential material with fine thermoelectric properties in the range from 300 to 800 K [34]. The stable cubic AgBiSe2 phase may potentially exhibit excellent thermoelectric properties due to its intrinsic crystal structures and related electronic structures. The high symmetry can result in energy band degeneracy, and thus lead to high power factor, while the material with disordered atoms usually exhibits ultra-low lattice thermal conductivity [35]. Accordingly, further investigation into methods for achieving a stable cubic AgBiSe2 phase and enhancing its thermoelectric properties are of great interest. Inspired by the research on (AgBiSe2)1−x(PbSe)x, we focus on another IV-A metal and find that a stabilized room-temperature cubic AgBiSe2 phase can also be achieved via Sn substitution. In previous studies, both AgSbSe2 and PbSe have cubic crystal structures, so it is not hard to understand the phase transition behavior in (Ag-BiSe2)1−x(AgSbSe2)x and (AgBiSe2)1−x(PbSe)x solid solutions [32][33][34]. Herein, although the crystal structure of SnSe is not cubic [36], the solid solution between SnSe and AgBiSe2 has a cubic structure at room temperature. Such a finding indicates that in-depth studies on structural phase transition and its related physical properties are needed. In addition, in this work the thermoelectric properties were also investigated, and the results indicate that Ag1−x/2Bi1−x/2SnxSe2 is a potentially lead-free thermoelectric material with ultra-low lattice thermal conductivity.

Materials and Methods
Ag1−x/2Bi1−x/2SnxSe2 samples were prepared via high-temperature solid-state reactions. Stoichiometric amounts of Ag (Alfa, 99.9%), Bi (Aladdin, 99.999%), Sn (Alfa, 99.99%), and Se (Alfa, 99.99%) were cut into small pieces and weighed in an argon-filled glovebox. The elements were mixed and loaded into evacuated silica tubes. The tubes were then heated to 1273 K at a rate of 80 K/h and homogenized at this temperature for 20 h using a programmable furnace. Finally, the tubes were slowly cooled down to room temperature over 20 h. The synthesized ingots were ground into fine powders for use in further measurements.
Powder X-ray diffraction (PXRD) patterns of Ag1−x/2Bi1−x/2SnxSe2 were measured with a step size of 0.02° by using a Bruker D8 Advance X-ray powder diffractometer at room temperature and Cu Kα radiation. Rietveld refinements of AgBiSe2, Ag0.975Bi0.975Sn0.05Se2, and Ag0.95Bi0.95Sn0.10Se2 were performed using Fullprof [37]. Differential scanning calo- Inspired by the research on (AgBiSe2) 1−x (PbSe) x , we focus on another IV-A metal and find that a stabilized room-temperature cubic AgBiSe 2 phase can also be achieved via Sn substitution. In previous studies, both AgSbSe 2 and PbSe have cubic crystal structures, so it is not hard to understand the phase transition behavior in (AgBiSe 2 ) 1−x (AgSbSe 2 ) x and (AgBiSe 2 ) 1−x (PbSe) x solid solutions [32][33][34]. Herein, although the crystal structure of SnSe is not cubic [36], the solid solution between SnSe and AgBiSe 2 has a cubic structure at room temperature. Such a finding indicates that in-depth studies on structural phase transition and its related physical properties are needed. In addition, in this work the thermoelectric properties were also investigated, and the results indicate that Ag 1−x/2 Bi 1−x/2 Sn x Se 2 is a potentially lead-free thermoelectric material with ultra-low lattice thermal conductivity.

Materials and Methods
Ag 1−x/2 Bi 1−x/2 Sn x Se 2 samples were prepared via high-temperature solid-state reactions. Stoichiometric amounts of Ag (Alfa, 99.9%), Bi (Aladdin, 99.999%), Sn (Alfa, 99.99%), and Se (Alfa, 99.99%) were cut into small pieces and weighed in an argon-filled glovebox. The elements were mixed and loaded into evacuated silica tubes. The tubes were then heated to 1273 K at a rate of 80 K/h and homogenized at this temperature for 20 h using a programmable furnace. Finally, the tubes were slowly cooled down to room temperature over 20 h. The synthesized ingots were ground into fine powders for use in further measurements.
Powder X-ray diffraction (PXRD) patterns of Ag 1−x/2 Bi 1−x/2 Sn x Se 2 were measured with a step size of 0.02 • by using a Bruker D8 Advance X-ray powder diffractometer at room temperature and Cu Kα radiation. Rietveld refinements of AgBiSe 2 , Ag 0.975 Bi 0.975 Sn 0.05 Se 2 , and Ag 0.95 Bi 0.95 Sn 0.10 Se 2 were performed using Fullprof [37]. Differential scanning calorimetry (DSC) measurements were performed on the polycrystalline powders of Ag 1−x/2 Bi 1−x/2 Sn x Se 2 (35-45 mg) using a NETZSCH STA 449 F3. DSC measurements were taken over a temperature range of 350 K to 650 K. The heating rate was 10 K/min. The microstructure and energy-dispersive spectroscopy (EDS) mapping of Ag 0.90 Bi 0.90 Sn 0.20 Se 2 sample were carried out using a Zeiss Sigma 500 field emission scanning electron microscopy (SEM). Ag 1−x/2 Bi 1−x/2 Sn x Se 2 (x = 0.2, 0.25, 0.3, 0.35) powders were sintered into pellets with high relative densities by using a LABOX-325 spark plasma sintering instrument (Dr. Sinter Land). An axial compressive stress of 40 MPa was applied at 773 K for 7 min under 10 Pa. The Seebeck coefficients and electrical conductivity values at temperatures of 300 K to 773 K were measured using a NETZSCH SBA 458 instrument with a temperature gradient of 4 K across~8.25 mm. Thermal conductivity was calculated using the standard formula κ = C p Dρ, where C p is the specific heat calculated by the Dulong-Petit law, D is the thermal diffusivity measured using the laser flash method (NETZSCH LFA 457), and ρ is the measured mass density.

Results and Discussion
Theoretical diffraction patterns for hexagonal, rhombohedral, and cubic AgBiSe 2 are shown in Figure   Ag1−x/2Bi1−x/2SnxSe2 (x = 0.2, 0.25, 0.3, 0.35) powders were sintered into pellets with high relative densities by using a LABOX-325 spark plasma sintering instrument (Dr. Sinter Land). An axial compressive stress of 40 MPa was applied at 773 K for 7 min under 10 Pa. The Seebeck coefficients and electrical conductivity values at temperatures of 300 K to 773 K were measured using a NETZSCH SBA 458 instrument with a temperature gradient of 4 K across ~8.25 mm. Thermal conductivity was calculated using the standard formula κ = CpDρ, where Cp is the specific heat calculated by the Dulong-Petit law, D is the thermal diffusivity measured using the laser flash method (NETZSCH LFA 457), and ρ is the measured mass density.

Results and Discussion
Theoretical diffraction patterns for hexagonal, rhombohedral, and cubic AgBiSe2 are shown in Figure    As shown in Figure 2c, the lattice parameters determined from the experimental PXRD patterns increase linearly with increasing Sn concentration. This is consistent with Vegard's law. In general, variations in the lattice parameter of chalcogenide semiconductors can be explained by ionic radius differences between the intrinsic and doped elements. Since the ionic radius of Sn 2+ is difficult to define [38], the increased lattice parameter cannot be directly explained by comparing ionic radii. However, a cubic SnSe phase which crystallizes in a rock salt structure may potentially help understand this change in lattice parameter [39]. The Sn-Se bonding distance in cubic SnSe is about 2.995 Å, much longer than the Ag/Bi-Se distance of 2.916 Å in cubic AgBiSe 2 . Thus, the ionic radius of Sn 2+ in the rock salt structure should be larger than the average ionic radius between Ag + and Bi 3+ .
DSC measurements were performed for Ag 1−x/2 Bi 1−x/2 Sn x Se 2 (x = 0, 0.05, 0.10, 0.15, 0.20, 0.25, 0.30) in order to understand the polymorph change at room temperature. The results are shown in Figure 3. For pristine AgBiSe 2 , one small peak at about 500 K indicates the phase transition from a hexagonal to a rhombohedral phase, while the sharp peak at 586 K represents the transformation to a cubic phase. For Sn-containing materials, the temperature corresponding to the sharp endothermic peak decreases with increasing Sn concentrations. Therefore, the thermal energy required to overcome the potential energy between the hexagonal and cubic phases also decreases. For Ag 0.925 Bi 0.925 Sn 0.15 Se 2 , a small and flat endothermic peak at about 520 K indicates the existence of the hexagonal phase, consistent with the prior discussion of PXRD data. The finding is interesting since neither AgBiSe 2 nor SnSe has a cubic structure at room temperature. Accordingly, in order to understand the phenomenon, detailed analysis of the crystal structures for Ag-V-Se (V = As, Sb, Bi) compounds was performed. As shown in Figure 2c, the lattice parameters determined from the experimental PXRD patterns increase linearly with increasing Sn concentration. This is consistent with Vegard's law. In general, variations in the lattice parameter of chalcogenide semiconductors can be explained by ionic radius differences between the intrinsic and doped elements. Since the ionic radius of Sn 2+ is difficult to define [38], the increased lattice parameter cannot be directly explained by comparing ionic radii. However, a cubic SnSe phase which crystallizes in a rock salt structure may potentially help understand this change in lattice parameter [39]. The Sn-Se bonding distance in cubic SnSe is about 2.995 Å , much longer than the Ag/Bi-Se distance of 2.916 Å in cubic AgBiSe2. Thus, the ionic radius of Sn 2+ in the rock salt structure should be larger than the average ionic radius between Ag + and Bi 3+ .
DSC measurements were performed for Ag1−x/2Bi1−x/2SnxSe2 (x = 0, 0.05, 0.10, 0.15, 0.20, 0.25, 0.30) in order to understand the polymorph change at room temperature. The results are shown in Figure 3. For pristine AgBiSe2, one small peak at about 500 K indicates the phase transition from a hexagonal to a rhombohedral phase, while the sharp peak at 586 K represents the transformation to a cubic phase. For Sn-containing materials, the temperature corresponding to the sharp endothermic peak decreases with increasing Sn concentrations. Therefore, the thermal energy required to overcome the potential energy between the hexagonal and cubic phases also decreases. For Ag0.925Bi0.925Sn0.15Se2, a small and flat endothermic peak at about 520 K indicates the existence of the hexagonal phase, consistent with the prior discussion of PXRD data. The finding is interesting since neither AgBiSe2 nor SnSe has a cubic structure at room temperature. Accordingly, in order to understand the phenomenon, detailed analysis of the crystal structures for Ag-V-Se (V = As, Sb, Bi) compounds was performed. AgBiSe2 shows multiple crystal phase transitions with increasing temperature, transforming from ordered hexagonal P3 ̅ m1 to rhombohedral R3 ̅ mR and then to the disordered rock salt structure [21]. AgSbSe2 is a cubic phase material with mixed Ag and Sb atoms [21], while AgAsSe2 crystallizes in the rhombohedral space group R3 ̅ mH [40]. Although these compounds crystallize in different space groups, their crystal structures are very similar, as shown in Figure 4. It is clear that the difference between Ag-Se and AgBiSe 2 shows multiple crystal phase transitions with increasing temperature, transforming from ordered hexagonal P3m1 to rhombohedral R3mR and then to the disordered rock salt structure [21]. AgSbSe 2 is a cubic phase material with mixed Ag and Sb atoms [21], while AgAsSe 2 crystallizes in the rhombohedral space group R3mH [40]. Although these compounds crystallize in different space groups, their crystal structures are very similar, as shown in Figure 4. It is clear that the difference between Ag-Se and V-Se bonding distances plays a major role in determining the crystal structure of Ag-V-Se materials. In order to describe the bonding distance difference simply, the ratios between average Ag-Se and V-Se bonding distances in octahedrons are shown in the figure. The ratios of r avg (Ag-Se)/r avg (V-Se) for AgBiSe 2 , AgSbSe 2 and AgAsSe 2 are 0.95, 1.00, and 1.09, respectively. The ratios affect the Se-As-Se angle directly, and further determine the Crystals 2021, 11, 1016 5 of 10 distortion degree of the octahedral environments. The longer Bi-Se distance in AgBiSe 2 leads to a Se-Bi-Se angle of 87.2 • . In contrast, the shorter As-Se distance of 2.710 Å in AgAsSe 2 results in a larger Se-As-Se angle (92.5 • ). Accordingly, for AgVSe 2 compounds, adjustment of Ag-Se and V-Se distances can change the crystal structure. The Sn-Se bonding distance is longer than the Ag-Se distances but shorter than the Bi-Se distances. In Ag 1−x/2 Bi 1−x/2 Sn x Se 2 , the bonding distance difference between Ag/Sn-Se and Bi/Sn-Se decreases with increasing Sn ratio. So the crystal structure of AgBiSe 2 can be transformed to cubic phase via Sn doping. The Rietveld refinement results of Ag 1−x/2 Bi 1−x/2 Sn x Se 2 (x = 0, 0.05, 0.10) are consistent with the above analysis. As is shown in Figure S1, the Se-Bi-Se angle increases with increasing x value. Considering that these structures are extremely complex, further experimental studies on the crystal structures of metal-doped AgBiVI 2 (VI = S, Se, Te) are still needed. V-Se bonding distances plays a major role in determining the crystal structure of Ag-V-Se materials. In order to describe the bonding distance difference simply, the ratios between average Ag-Se and V-Se bonding distances in octahedrons are shown in the figure. The ratios of ravg(Ag-Se)/ravg(V-Se) for AgBiSe2, AgSbSe2 and AgAsSe2 are 0.95, 1.00, and 1.09, respectively. The ratios affect the Se-As-Se angle directly, and further determine the distortion degree of the octahedral environments. The longer Bi-Se distance in AgBiSe2 leads to a Se-Bi-Se angle of 87.2°. In contrast, the shorter As-Se distance of 2.710 Å in AgAsSe2 results in a larger Se-As-Se angle (92.5°). Accordingly, for AgVSe2 compounds, adjustment of Ag-Se and V-Se distances can change the crystal structure. The Sn-Se bonding distance is longer than the Ag-Se distances but shorter than the Bi-Se distances. In Ag1−x/2Bi1−x/2SnxSe2, the bonding distance difference between Ag/Sn-Se and Bi/Sn-Se decreases with increasing Sn ratio. So the crystal structure of AgBiSe2 can be transformed to cubic phase via Sn doping. The Rietveld refinement results of Ag1−x/2Bi1−x/2SnxSe2 (x = 0, 0.05, 0.10) are consistent with the above analysis. As is shown in Figure S1, the Se-Bi-Se angle increases with increasing x value. Considering that these structures are extremely complex, further experimental studies on the crystal structures of metal-doped AgBiVI2 (VI = S, Se, Te) are still needed. As shown in Figure S2, there is no obvious pore or crack in the cross-sectional image, suggesting high density of the sintered sample. The distribution for all elements is homogeneous, indicating that the material is phase pure. Figure 5 shows the measured temperature-dependent thermoelectric transport properties of Ag1−x/2Bi1−x/2SnxSe2. Tin doping leads to significant changes in both the Seebeck coefficient and electrical conductivity. Due to the phase transition behaviour, both Seebeck coefficient and electrical conductivity of pristine AgBiSe2 do not change monotonically with increasing temperature. Pristine AgBiSe2 is an intrinsic n-type semiconductor with a negative Seebeck coefficient over the entire measured temperature range. The Seebeck coefficients of the Sn-doped materials are positive at room temperature, indicating that the dominating As shown in Figure S2, there is no obvious pore or crack in the cross-sectional image, suggesting high density of the sintered sample. The distribution for all elements is homogeneous, indicating that the material is phase pure. Figure 5 shows the measured temperature-dependent thermoelectric transport properties of Ag 1−x/2 Bi 1−x/2 Sn x Se 2 . Tin doping leads to significant changes in both the Seebeck coefficient and electrical conductivity. Due to the phase transition behaviour, both Seebeck coefficient and electrical conductivity of pristine AgBiSe 2 do not change monotonically with increasing temperature. Pristine AgBiSe 2 is an intrinsic n-type semiconductor with a negative Seebeck coefficient over the entire measured temperature range. The Seebeck coefficients of the Sn-doped materials are positive at room temperature, indicating that the dominating charge carriers are holes. The room-temperature Seebeck coefficient of Ag 0.90 Bi 0.90 Sn 0.20 Se 2 is about +130 µV/K, while that of Ag 0.875 Bi 0.875 Sn 0.25 Se 2 increases to about +350 µV/K. A similar carrier type transition behaviour has been observed in AgBi 1-x Sb x Se 2 [33,34]. With increasing temperature, the Seebeck coefficients of the Ag 1−x/2 Bi 1−x/2 Sn x Se 2 samples are converted into n-type negative values. The carrier type change from p-type to n-type can be at- The measured total thermal conductivity of Ag1−x/2Bi1−x/2SnxSe2 samples is shown Figure 6a. The room temperature thermal conductivity of Ag1−x/2Bi1−x/2SnxSe2 ranges fro 0.5-0.6 W/m· K, lower than the measured thermal conductivity of pristine AgBiSe2 due the enhanced point defect scattering. It should be noticed that the thermal conductivi of Sn-doped samples is inclined to contain less bipolar contribution due to the coexi ence of holes and electrons. The thermal conductivity contributed from lattice vibrati (κlatt) and bipolar effect (κbip) is calculated by subtracting the electronic thermal condu tivity from total thermal conductivity. The electronic thermal conductivity (κele) is es mated by using the formula κele = LσT, where L, σ, and T are the Lorenz factor, electric conductivity, and absolute temperature, respectively. The Lorenz factors are calculat using a single parabolic band (SPB) model [41]. Considering that Ag1−x/2Bi1−x/2SnxSe2 m doping Sn and the increased phonon-phonon scattering with increasing temperatur Figure 7 presents the calculated ZT values of the Ag1−x/2Bi1−x/2SnxSe2 samples. The final Z values are very low compared with state-of-the-art thermoelectric materials, rangin from 0.06 to 0.14 at 773 K. However, due to the high structural symmetry and low the mal conductivity of these materials, Ag1−x/2Bi1−x/2SnxSe2 can still be viewed as a potenti thermoelectric material candidate.

Conclusions
In summary, the polymorph changes and thermoelectric properties of Sn-dope AgBiSe2 were investigated. The room-temperature crystal structure of Ag1−x/2Bi1−x/2SnxSe was transformed from a hexagonal structure to a disordered cubic structure when th value of x was larger than 0.20. In addition, the carrier type of Ag1−x/2Bi1−x/2SnxSe2 at room temperature was p-type, in contrast to the the n-type conductivity of pristine AgBiSe The electrical conductivity exponentially increased with increasing temperature. Th

Conclusions
In summary, the polymorph changes and thermoelectric properties of Sn-doped AgBiSe 2 were investigated. The room-temperature crystal structure of Ag 1−x/2 Bi 1−x/2 Sn x Se 2 was transformed from a hexagonal structure to a disordered cubic structure when the value of x was larger than 0.20. In addition, the carrier type of Ag 1−x/2 Bi 1−x/2 Sn x Se 2 at room temperature was p-type, in contrast to the the n-type conductivity of pristine AgBiSe 2 . The electrical conductivity exponentially increased with increasing temperature. The thermal conductivity of Ag 1−x/2 Bi 1−x/2 Sn x Se 2 was ultra-low (in the range of 0.4 to 0.8 W/m·K) over the entire measured temperature range. Due to its high structural symmetry and low thermal conductivity, Ag 1−x/2 Bi 1−x/2 Sn x Se 2 is a potentially lead-free thermoelectric material candidate. However, further in-depth investigation into enhancing the power factor of this material will be necessary.