Thermoelectric Performance of Non-Stoichiometric Permingeatite Cu3+mSbSe4

Non-stoichiometric permingeatites Cu3+mSbSe4 (−0.04 ≤ m ≤ −0.02) were synthesized, and their thermoelectric properties were examined depending on the Cu deficiency. Phase analysis by X-ray diffraction revealed no detection of secondary phases. Due to Cu deficiency, the lattice parameters of tetragonal permingeatite decreased compared to the stoichiometric permingeatite, resulting in a = 0.5654–0.5654 nm and c = 1.1253–1.1254 nm, with a decrease in the c/a ratio in the range of 1.9901–1.9903. Electrical conductivity exhibited typical semiconductor behavior of increasing conductivity with temperature, and above 423 K, the electrical conductivity of all samples exceeded that of stoichiometric permingeatite; Cu2.96SbSe4 exhibited a maximum of 9.8 × 103 Sm−1 at 623 K. The Seebeck coefficient decreased due to Cu deficiency, showing p-type semiconductor behavior similar to stoichiometric permingeatite, with majority carriers being holes. Thermal conductivity showed negative temperature dependence, and both electronic and lattice thermal conductivities increased due to Cu deficiency. Despite the decrease in the Seebeck coefficient due to Cu deficiency, the electrical conductivity increased, resulting in an increase in the power factor (especially a great increase at high temperatures), with Cu2.97SbSe4 exhibiting the highest value of 0.72 mWm−1K−2 at 573 K. As the carrier concentration increased due to Cu deficiency, the thermal conductivity increased, but the increase in power factor was significant, with Cu2.98SbSe4 recording a maximum dimensionless figure-of-merit of 0.50 at 523 K. This value was approximately 28% higher than that (0.39) of stoichiometric Cu3SbSe4.

Research efforts are underway to maximize the power factor by controlling carrier concentration through doping, which involves partially substituting certain elements Materials 2024, 17, 4345 2 of 11 into the Cu/Sb/Se sites of permingeatite, while simultaneously reducing the thermal conductivity through lattice scattering [16][17][18].Doping the Cu site requires lowering the Cu chemical potential, which can lead to an increase in the formation of Cu vacancies.These vacancies negate the effects of intentional dopants like Mg or Zn, possibly contributing to the challenges in achieving n-type doping in Cu 3 SbSe 4 [2].However, there are few reports on non-stoichiometric studies regarding the adjustment in Cu content.Control of chemical composition in stoichiometry can influence the physical properties of semiconductors [19].According to Wei et al. [20], Cu-deficient permingeatite Cu 3-x SbSe 4 (0 ≤ x ≤ 0.075) could increase charge carriers (holes), leading to an increase in electrical conductivity.Kwak and Kim [19] also found the changes in thermoelectric properties through Cu content adjustment in tetrahedrite (Cu 12+m Sb 4 S 13 ; −0.04 ≤ m ≤ 0.04); excess Cu reduced the thermal conductivity due to additional phonon scattering, while Cu deficiencies (vacancies) provided additional charge carriers, improving electrical properties.They achieved a maximum ZT value of 0.91 at 723 K for Cu 11.9 Sb 4 S 13 (improved from a ZT of 0.86 for stoichiometric tetrahedrite).In this study, Cu-deficient permingeatites and Cu 3+m SbSe 4 (−0.04 ≤ m ≤ −0.02) were prepared to investigate the influence of non-stoichiometry on the thermoelectric performance.

Experimental Procedure
Non-stoichiometric Cu 3+m SbSe 4 (m = −0.02,−0.03, and −0.04) were synthesized via mechanical alloying (MA) using elemental powders of Cu, Sb, and Se with high-purity (99.9-99.999%).MA was conducted at 350 rpm for 12 h in an Ar atmosphere within the stainless-steel container.The synthetic powder was then subjected to hot pressing (HP) at 573 K for 2 h under 70 MPa in a vacuum.The optimal process conditions of MA−HP for permingeatite were determined in our previous studies [15,16].
The phases and lattice parameters of the synthesized specimens were analyzed using X-ray diffraction with Cu Kα radiation (D8-Advance, Bruker, Billerica, MA, USA) and Rietveld refinement (TOPAS, Bruker).The microstructure of the sintered pellets was observed using the backscattered electron mode of a scanning electron microscope (Quanta400, FEI, Lausanne, Switzerland).The Hall coefficient, carrier concentration, and carrier mobility were evaluated at room temperature using the Hall effect measurement instrument (Keithley 7065).Electrical conductivity and Seebeck coefficient were measured using the ZEM-3 system (Advance Riko, Yokohama, Japan).The thermal diffusivity was evaluated using a TC-9000H equipment (Advance Riko), and then the thermal conductivity was assessed using the measured density of the specimen and theoretical specific heat (0.32 Jg −1 K −1 ) [21].Power factor and ZT values were calculated based on the above thermoelectric parameters obtained in the temperature range of 323-623 K. Comparison was made with the thermoelectric characteristics of stoichiometric Cu 3 SbSe 4 prepared using the same process [21].

Results and Discussion
Figure 1 shows the X-ray diffraction patterns of non-stoichiometric Cu 3+m SbSe 4 produced via MA−HP.All diffraction peaks matched the standard diffraction data of tetragonal permingeatite (PDF# 01-085-0003), and no secondary phase was identified.However, Kumar et al. [22] observed the presence of small amounts of secondary phases in the diffraction peaks between 30 • and 60 • for the Cu 2.96 SbSe 4 sample prepared using vacuum melting, followed by pulverizing and spark plasma sintering.This indicates that the preparation method combining MA and HP in this study is a practical and effective way for the synthesis of non-stoichiometric permingeatite compounds.Compared to the lattice constants of stoichiometric Cu 3 SbSe 4 (a = 0.5661 nm and c = 1.1280 nm), both a-and c-axes were reduced due to Cu deficiency (a = 0.5654-0.5655nm and c = 1.1253-1.1254nm).Additionally, the tetragonality (c/a ratio) of the lattice decreased from 1.9926 to 1.9901-1.9903.Wei et al. [20] reported decreases in lattice constants of Cu 3-x SbSe 4 (x = 0-0.075)from a = 0.5655 nm and c = 1.1253 nm to a = 0.5651 nm and c = 1.1248 nm due to a decrease (deficiency) in Cu content; however, when x is 0.075, the XRD diffraction peaks shift to lower angles, and no further reduction in lattice constants is observed.Kwak and Kim [19] discovered that for non-stoichiometric cubic tetrahedrite Cu 12+m Sb 4 S 13 (−0.3≤ m ≤ 0.3), the lattice constant decreased from a = 1.0350 nm (at m = 0) to a = 1.0338 nm for Cu-poor tetrahedrites at m = −0.3,while increased to a = 1.0384 nm for Cu-rich tetrahedrites at m = 0. Wei et al. [20] reported decreases in lattice constants of Cu3-xSbSe4 (x = 0-0.075)from 0.5655 nm and c = 1.1253 nm to a = 0.5651 nm and c = 1.1248 nm due to a decrease (d ciency) in Cu content; however, when x is 0.075, the XRD diffraction peaks shift to lo angles, and no further reduction in lattice constants is observed.Kwak and Kim [19] covered that for non-stoichiometric cubic tetrahedrite Cu12+mSb4S13 (-0.3 ≤ m ≤ 0.3), the tice constant decreased from a = 1.0350 nm (at m = 0) to a = 1.0338 nm for Cu-poor te hedrites at m = -0.3,while increased to a = 1.0384 nm for Cu-rich tetrahedrites at m = 0 Figure 2 displays microstructures of Cu-deficient permingeatite observed using sc ning electron microscopy.They contained some porosity, but significant changes in crostructure due to Cu vacancies were not observed.Compared to the theoretical den (5.86 gcm -3 ) of Cu3SbSe4 with stoichiometric composition [23], the relative densities o specimens were in the range of 96.5-98.1%,as shown in Table 1.All MA−HP specim exhibited a well-crystallized morphology with an average crystallite size of 78 nm.major fracture mode for Cu-deficient permingeatite was intergranular fracture, whic common for materials with fine grains.Wei et al. [20] also discovered the same morph ogy as our fractured specimens but found that Cu-content-modified grain growth in n stoichiometric samples with Cu deficiency results in larger grain sizes compared to s chiometric samples.However, in this study, no significant change in grain size due to deficiency was observed.Figure 2 displays microstructures of Cu-deficient permingeatite observed using scanning electron microscopy.They contained some porosity, but significant changes in microstructure due to Cu vacancies were not observed.Compared to the theoretical density (5.86 gcm −3 ) of Cu 3 SbSe 4 with stoichiometric composition [23], the relative densities of all specimens were in the range of 96.5-98.1%,as shown in Table 1.All MA−HP specimens exhibited a well-crystallized morphology with an average crystallite size of 78 nm.The major fracture mode for Cu-deficient permingeatite was intergranular fracture, which is common for materials with fine grains.Wei et al. [20] also discovered the same morphology as our fractured specimens but found that Cu-content-modified grain growth in non-stoichiometric samples with Cu deficiency results in larger grain sizes compared to stoichiometric samples.However, in this study, no significant change in grain size due to Cu deficiency was observed.
0.5655 nm and c = 1.1253 nm to a = 0.5651 nm and c = 1.1248 nm due to a decrease (deficiency) in Cu content; however, when x is 0.075, the XRD diffraction peaks shift to lower angles, and no further reduction in lattice constants is observed.Kwak and Kim [19] discovered that for non-stoichiometric cubic tetrahedrite Cu12+mSb4S13 (-0.3 ≤ m ≤ 0.3), the lattice constant decreased from a = 1.0350 nm (at m = 0) to a = 1.0338 nm for Cu-poor tetrahedrites at m = -0.3,while increased to a = 1.0384 nm for Cu-rich tetrahedrites at m = 0.3.Figure 2 displays microstructures of Cu-deficient permingeatite observed using scanning electron microscopy.They contained some porosity, but significant changes in microstructure due to Cu vacancies were not observed.Compared to the theoretical density (5.86 gcm -3 ) of Cu3SbSe4 with stoichiometric composition [23], the relative densities of all specimens were in the range of 96.5-98.1%,as shown in Table 1.All MA−HP specimens exhibited a well-crystallized morphology with an average crystallite size of 78 nm.The major fracture mode for Cu-deficient permingeatite was intergranular fracture, which is common for materials with fine grains.Wei et al. [20] also discovered the same morphology as our fractured specimens but found that Cu-content-modified grain growth in nonstoichiometric samples with Cu deficiency results in larger grain sizes compared to stoichiometric samples.However, in this study, no significant change in grain size due to Cu deficiency was observed.Figure 3 shows the electrical conductivity of Cu 3+m SbSe 4 .As the Cu deficiency increased, the electrical conductivity increased.Compared to Cu 3 SbSe 4 , the electrical conductivity was higher at temperatures above 423 K.The nondegenerate nature of the electrical transport was not affected by the Cu deficiencies.In the temperature range of 323-623 K, the electrical conductivity increased from (4.2-4.5)× 10 3 Sm −1 for Cu 3 SbSe 4 [16] to (6.3-9.8)× 10 3 Sm −1 for Cu 2.96 SbSe 4 .This was because the Cu deficiency increased the charge carrier (hole) concentration.It is well understood that even minor deviations from stoichiometric chemical composition can influence the physical properties of semiconductors.Specifically, deficiencies in Cu can introduce extra holes, thereby increasing carrier concentration and enhancing electrical conductivity [24,25].According to Kwak and Kim [19], as the Cu deficiency increased in Cu 12+m Sb 4 S 13 (−0.3≤ m ≤ 0.3), the hole concentration increased, leading to an increase in electrical conductivity, while the excess Cu contributed to lowering the carrier concentration.Xia et al. [26] also found in Cu 1−x InTe 2 (0 ≤ x ≤ 0.10) that the Cu deficiency increased the carrier concentration from 2 × 10 18 to 3 × 10 18 cm −3 and decreased the mobility from 100 to 40 cm −2 V −1 s −1 .Figure 3 shows the electrical conductivity of Cu3+mSbSe4.As the Cu deficiency increased, the electrical conductivity increased.Compared to Cu3SbSe4, the electrical conductivity was higher at temperatures above 423 K.The nondegenerate nature of the electrical transport was not affected by the Cu deficiencies.In the temperature range of 323-623 K, the electrical conductivity increased from (4.2-4.5)× 10 3 Sm -1 for Cu3SbSe4 [16] to (6.3-9.8)× 10 3 Sm -1 for Cu2.96SbSe4.This was because the Cu deficiency increased the charge carrier (hole) concentration.It is well understood that even minor deviations from stoichiometric chemical composition can influence the physical properties of semiconductors.Specifically, deficiencies in Cu can introduce extra holes, thereby increasing carrier concentration and enhancing electrical conductivity [24,25].According to Kwak and Kim [19], as the Cu deficiency increased in Cu12+mSb4S13 (-0.3 ≤ m ≤ 0.3), the hole concentration increased, leading to an increase in electrical conductivity, while the excess Cu contributed to lowering the carrier concentration.Xia et al. [26] also found in Cu1−xInTe2 (0 ≤ x ≤ 0.10) that the Cu deficiency increased the carrier concentration from 2 × 10 18 to 3 × 10 18 cm -3 and decreased the mobility from 100 to 40 cm -2 V -1 s -1 .As shown in Table 1, the Cu deficiency in permingeatite increased the carrier concentration from 5.2 × 10 18 to (7.9-9.6)× 10 18 cm -3 while decreasing the mobility from 505 to 210-410 cm -2 V -1 s -1 .The carrier concentration increased with greater Cu deficiency, which was consistent with the observed changes in lattice constants with varying Cu deficiencies.Since both carrier concentration and lattice constants reflect the extent of artificially introduced Cu deficiencies, it can be concluded that Cu deficiencies have been intentionally introduced and have influenced the structure and properties of the permingeatite compounds.The carrier mobility in the non-stoichiometric samples was lower compared to As shown in Table 1, the Cu deficiency in permingeatite increased the carrier concentration from 5.2 × 10 18 to (7.9-9.6)× 10 18 cm −3 while decreasing the mobility from 505 to 210-410 cm −2 V −1 s −1 .The carrier concentration increased with greater Cu deficiency, which was consistent with the observed changes in lattice constants with varying Cu deficiencies.Since both carrier concentration and lattice constants reflect the extent of artificially introduced Cu deficiencies, it can be concluded that Cu deficiencies have been intentionally introduced and have influenced the structure and properties of the permingeatite compounds.The carrier mobility in the non-stoichiometric samples was lower compared to the stoichiometric sample.This suggests that point defects resulting from Cu deficiencies affect the carrier scattering mechanism.Generally, as the carrier concentration increases, the mobility decreases.However, in the case of the specimen with m = −0.04, the mobility increased despite the increase in carrier concentration.Although we cannot provide a definitive explanation for this, changes in lattice parameters (an increase in the c/a axial ratio) and an increase in sintering density (relative density) may be contributing factors.Do et al. [2] found that a single Cu vacancy in the unit cell does not significantly alter the band structure; energy states near the valence band maxima remain largely unaffected, and there is only a small splitting of the conduction band minima.This suggests that the frequently observed p-type behavior in as-prepared permingeatite can be attributed to native Cu vacancies.This has been experimentally confirmed by Wei et al. [20], who controlled the hole concentration by adjusting the Cu deficiency.
Figure 4 represents the Seebeck coefficient of Cu 3+m SbSe 4 .All samples exhibited positive Seebeck coefficient values, which indicate p-type semiconductor behavior.Do et al. [2] modeled permingeatite as a periodic supercell and calculated the formation energies of various defects.They found positive formation energies of vacancies with values increasing from Cu (0.65 eV) to Se (0.94 eV) to Sb (2.13 eV); hence, forming vacancies at any atomic site requires energy.Among these, only Cu vacancies act as acceptors, while Se vacancies do not seem to contribute charge carriers.The results also indicate that the observed p-type behavior in nominally pure Cu 3 SbSe 4 is likely due to the presence of Cu vacancies rather than Se vacancies.In this study, due to the deficiency of Cu, the Seebeck coefficient decreased, resulting from the increase in carrier concentration.Assuming a single parabolic band for carriers near the Fermi level, the Seebeck coefficient for nondegenerate semiconductors can be expressed as a function of the carrier concentration [20].In this case, the Seebeck coefficient is inversely proportional to the carrier concentration.Cu 2.98 SbSe 4 exhibited a Seebeck coefficient ranging from 363 to 322 µVK −1 at temperatures from 323 to 623 K, while Cu 2.96 SbSe 4 exhibited lower values of 192-243 µVK −1 .Stoichiometric Cu 3 SbSe 4 demonstrated 307-348 µVK −1 in the same temperature range [16].Skoug et al. [27] reported 300-400 µVK −1 at 80-623 K for undoped permingeatite.Wei et al. [20] discovered that all samples of Cu 3−x SbSe 4 (0 ≤ x ≤ 0.075) exhibited values higher than 320 µVK −1 at 323-623 K. Kumar et al. [22] observed a decreasing trend in the Seebeck coefficient with increasing temperature and Cu deficiency for all samples of Cu 3−δ SbSe 4 (0 ≤ δ ≤ 0.04) in the range of 300-675 K, with Cu 2.99 SbSe 4 exhibiting a maximum value of 263 µVK −1 at 475 K.
Materials 2024, 17,4345 5 of 11 the stoichiometric sample.This suggests that point defects resulting from Cu deficiencies affect the carrier scattering mechanism.Generally, as the carrier concentration increases, the mobility decreases.However, in the case of the specimen with m = -0.04, the mobility increased despite the increase in carrier concentration.Although we cannot provide a definitive explanation for this, changes in lattice parameters (an increase in the c/a axial ratio) and an increase in sintering density (relative density) may be contributing factors.Do et al. [2] found that a single Cu vacancy in the unit cell does not significantly alter the band structure; energy states near the valence band maxima remain largely unaffected, and there is only a small splitting of the conduction band minima.This suggests that the frequently observed p-type behavior in as-prepared permingeatite can be attributed to native Cu vacancies.This has been experimentally confirmed by Wei et al. [20], who controlled the hole concentration by adjusting the Cu deficiency.
Figure 4 represents the Seebeck coefficient of Cu3+mSbSe4.All samples exhibited positive Seebeck coefficient values, which indicate p-type semiconductor behavior.Do et al. [2] modeled permingeatite as a periodic supercell and calculated the formation energies of various defects.They found positive formation energies of vacancies with values increasing from Cu (0.65 eV) to Se (0.94 eV) to Sb (2.13 eV); hence, forming vacancies at any atomic site requires energy.Among these, only Cu vacancies act as acceptors, while Se vacancies do not seem to contribute charge carriers.The results also indicate that the observed p-type behavior in nominally pure Cu3SbSe4 is likely due to the presence of Cu vacancies rather than Se vacancies.In this study, due to the deficiency of Cu, the Seebeck coefficient decreased, resulting from the increase in carrier concentration.Assuming a single parabolic band for carriers near the Fermi level, the Seebeck coefficient for nondegenerate semiconductors can be expressed as a function of the carrier concentration [20].In this case, the Seebeck coefficient is inversely proportional to the carrier concentration.Cu2.98SbSe4 exhibited a Seebeck coefficient ranging from 363 to 322 µVK -1 at temperatures from 323 to 623 K, while Cu2.96SbSe4 exhibited lower values of 192-243 µVK -1 .Stoichiometric Cu3SbSe4 demonstrated 307-348 µVK -1 in the same temperature range [16].Skoug et al. [27] reported 300-400 µVK -1 at 80-623 K for undoped permingeatite.Wei et al. [20] discovered that all samples of Cu3−xSbSe4 (0 ≤ x ≤ 0.075) exhibited values higher than 320 µVK -1 at 323-623 K. Kumar et al. [22] observed a decreasing trend in the Seebeck coefficient with increasing temperature and Cu deficiency for all samples of Cu3−δSbSe4 (0 ≤ δ ≤ 0.04) in the range of 300-675 K, with Cu2.99SbSe4 exhibiting a maximum value of 263 µVK - 1 at 475 K.  Figure 5 shows the thermal conductivity of Cu 3+m SbSe 4 .The thermal conductivity values of the non-stoichiometric samples were higher than those of the stoichiometric sample, likely due to the increased carrier concentrations.This leads to enhanced carrier scattering, which results in shorter mean free paths.As the temperature increased in all specimens, the thermal conductivity decreased; no bipolar effect was observed up to 623 K, and phonon−phonon scattering (Umklapp scattering; κ ~T−1 ) predominated.Non-stoichiometric specimens exhibited thermal conductivities of 1.41-1.71Wm −1 K −1 at 323 K and 0.95-0.79Wm −1 K −1 at 623 K, which are higher than those of stoichiometric Cu 3-x SbSe 4 (1.19-0.75Wm −1 K −1 at 323-623 K) [16].According to Wei et al. [20], Cu 3-x SbSe 4 (x = 0-0.075)exhibited a decrease in thermal conductivity with increasing temperature, while as Cu deficiency increased, the thermal conductivity increased from 2.60 Wm −1 K −1 at 323 K for Cu 3 SbSe 4 to 2.77 Wm −1 K −1 at 323 K for Cu 2.975 SbSe 4 .In contrast, Kumar et al. [22] found a decrease in thermal conductivity with increasing Cu deficiency in Cu 3−δ SbSe 4 (δ = 0-0.04)due to more generated defects, ranging from 2.2-1.4Wm −1 K −1 at 300-675 K for Cu 2.99 SbSe 4 to 1.9-1.0Wm −1 K −1 for Cu 2.96 SbSe 4 .According to Kwak and Kim [19], as the Cu content decreased in non-stoichiometric tetrahedrites Cu 12+m Sb 4 S 13 (−0.3≤ m ≤ 0.3), the thermal conductivity increased from 0.54-0.65 at 323-723 K to 0.97-0.98Wm −1 K −1 .In this study, the increase in thermal conductivity in the Cu-deficient permingeatite is interpreted to be dominantly attributed to the increase in carrier concentration rather than the increase in defect concentration.
Materials 2024, 17, 4345 6 of 11 Figure 5 shows the thermal conductivity of Cu3+mSbSe4.The thermal conductivity values of the non-stoichiometric samples were higher than those of the stoichiometric sample, likely due to the increased carrier concentrations.This leads to enhanced carrier scattering, which results in shorter mean free paths.As the temperature increased in all specimens, the thermal conductivity decreased; no bipolar effect was observed up to 623 K, and phonon−phonon scattering (Umklapp scattering; κ ~ T −1 ) predominated.Non-stoichiometric specimens exhibited thermal conductivities of 1.41-1.71Wm −1 K −1 at 323 K and 0.95-0.79Wm −1 K −1 at 623 K, which are higher than those of stoichiometric Cu3-xSbSe4 (1.19-0.75Wm −1 K −1 at 323-623 K) [16].According to Wei et al. [20], Cu3-xSbSe4 (x = 0-0.075)exhibited a decrease in thermal conductivity with increasing temperature, while as Cu deficiency increased, the thermal conductivity increased from 2.60 Wm −1 K −1 at 323 K for Cu3SbSe4 to 2.77 Wm −1 K −1 at 323 K for Cu2.975SbSe4.In contrast, Kumar et al. [22] found a decrease in thermal conductivity with increasing Cu deficiency in Cu3−δSbSe4 (δ = 0-0.04)due to more generated defects, ranging from 2.2-1.4Wm −1 K −1 at 300-675 K for Cu2.99SbSe4 to 1.9-1.0Wm −1 K −1 for Cu2.96SbSe4.According to Kwak and Kim [19], as the Cu content decreased in non-stoichiometric tetrahedrites Cu12+mSb4S13 (-0.3 ≤ m ≤ 0.3), the thermal conductivity increased from 0.54-0.65 at 323-723 K to 0.97-0.98Wm −1 K −1 .In this study, the increase in thermal conductivity in the Cu-deficient permingeatite is interpreted to be dominantly attributed to the increase in carrier concentration rather than the increase in defect concentration.In Figure 6, the electronic and lattice thermal conductivities are shown.The thermal conductivity in Figure 5 is determined by heat transfer due to carriers (electronic thermal conductivity, κE) and phonons (lattice thermal conductivity, κL) [23].In this study, the electronic thermal conductivity was derived using the Wiedemann−Franz law (κE = LσT), where L is the Lorenz number, and the lattice thermal conductivity was calculated using the equation κL = κ − κE [23].As the temperature and Cu deficiency increased, the electronic thermal conductivity increased, as shown in Figure 6a.This was because the temperature and Cu deficiency increased the carrier concentration.From 323 to 623 K, Cu3SbSe4 exhibited κE = 0.02-0.04Wm −1 K −1 , while Cu2.96SbSe4 showed an increased electronic thermal conductivity, κE = 0.03-0.10Wm −1 K −1 .In Figure 6b, Cu3SbSe4 had κL = 1.17-0.71Wm −1 K −1 at 323-623 K, while the lattice thermal conductivity of non-stoichiometric permingeatite increased to κL = 1.38-1.69Wm −1 K −1 at 323 K and κL = 0.73-0.95Wm −1 K −1 at 623 K.In this study, the deficiency of Cu in permingeatite was found to be ineffective in phonon scattering.In Figure 6, the electronic and lattice thermal conductivities are shown.The thermal conductivity in Figure 5 is determined by heat transfer due to carriers (electronic thermal conductivity, κ E ) and phonons (lattice thermal conductivity, κ L ) [23].In this study, the electronic thermal conductivity was derived using the Wiedemann−Franz law (κ E = LσT), where L is the Lorenz number, and the lattice thermal conductivity was calculated using the equation κ L = κ − κ E [23].As the temperature and Cu deficiency increased, the electronic thermal conductivity increased, as shown in Figure 6a.This was because the temperature and Cu deficiency increased the carrier concentration.From 323 to 623 K, Cu 3 SbSe 4 exhibited κ E = 0.02-0.04Wm −1 K −1 , while Cu 2.96 SbSe 4 showed an increased electronic thermal conductivity, κ E = 0.03-0.10Wm −1 K −1 .In Figure 6b, Cu 3 SbSe 4 had κ L = 1.17-0.71Wm −1 K −1 at 323-623 K, while the lattice thermal conductivity of non-stoichiometric permingeatite increased to κ L = 1.38-1.69Wm −1 K −1 at 323 K and κ L = 0.73-0.95Wm −1 K −1 at 623 K.In this study, the deficiency of Cu in permingeatite was found to be ineffective in phonon scattering.Figure 7 represents the Lorenz numbers determined using a simple relationship [1 L = 1.5 + exp(-|α|/116).Non-stoichiometric samples with m ≥ -0.03 exhibited Lorenz nu bers that were similar to or slightly increased compared to the stoichiomet permingeatite, (1.54-1.60)× 10 -8 V 2 K -2 at 323 K and (1.56-1.58)× 10 -8 V 2 K -2 at 623 K, wh the sample with m = -0.04showed increased Lorenz numbers at 323-623 K, ranging fro 1.69 × 10 -8 to 1.62 × 10 -8 V 2 K -2 .The Lorenz number typically ranges from (1.44-2.45)× 1 V 2 K -2 , and higher L values are indicative of degenerate semiconducting or a metallic sta Thus, the Cu vacancies in permingeatite served as more evidence of increased carrier co centration.Figure 7 represents the Lorenz numbers determined using a simple relationship [16], L = 1.5 + exp(−|α|/116).Non-stoichiometric samples with m ≥ −0.03 exhibited Lorenz numbers that were similar to or slightly increased compared to the stoichiometric permingeatite, (1.54-1.60)× 10 −8 V 2 K −2 at 323 K and (1.56-1.58)× 10 −8 V 2 K −2 at 623 K, while the sample with m = -0.04showed increased Lorenz numbers at 323-623 K, ranging from 1.69 × 10 −8 to 1.62 × 10 −8 V 2 K −2 .The Lorenz number typically ranges from (1.44-2.45)× 10 −8 V 2 K −2 , and higher L values are indicative of degenerate semiconducting or a metallic state.Thus, the Cu vacancies in permingeatite served as more evidence of increased carrier concentration.The changes in the power factor of Cu3+mSbSe4 are shown in Figure 8.As the temperature increased, the power factor increased for all specimens, resulting from the temperature dependence of electrical conductivity and the Seebeck coefficient.Although the Seebeck coefficient decreased due to Cu deficiency at a certain temperature (Figure 4), the electrical conductivity increased (Figure 3), resulting in an increase in power factor.For the specimen Cu2.97SbSe4, a maximum power factor of 0.72 mWm −1 K −2 was recorded at 573 K.This value represents an improvement of approximately 53% compared to the power factor of stoichiometric Cu3SbSe4 (0.47 mWm −1 K −2 at 573 K).Wei et al. [20] reported that Cu2.950SbSe4 and Cu2.925SbSe4 achieved power factor values exceeding 60% higher than that of stoichiometric permingeatite, reaching 0.90 mWm −1 K −2 at 523 K.According to Kwak and Kim [19], Cu-poor tetrahedrites in the off-stoichiometric Cu12+mSb4S13 (-0.3 ≤ m ≤ 0.3) exhibited higher power factor values compared to Cu-rich specimens, with a maximum value of 1.08 mWm −1 K −2 at 723 K.The ZT values of Cu3+mSbSe4 are presented in Figure 9.The ZT value is proportional to the operating temperature of a material; however, it is often constrained by the The changes in the power factor of Cu 3+m SbSe 4 are shown in Figure 8.As the temperature increased, the power factor increased for all specimens, resulting from the temperature dependence of electrical conductivity and the Seebeck coefficient.Although the Seebeck coefficient decreased due to Cu deficiency at a certain temperature (Figure 4), the electrical conductivity increased (Figure 3), resulting in an increase in power factor.For the specimen Cu 2.97 SbSe 4 , a maximum power factor of 0.72 mWm −1 K −2 was recorded at 573 K.This value represents an improvement of approximately 53% compared to the power factor of stoichiometric Cu 3 SbSe 4 (0.47 mWm −1 K −2 at 573 K).Wei et al. [20] reported that Cu 2.950 SbSe 4 and Cu 2.925 SbSe 4 achieved power factor values exceeding 60% higher than that of stoichiometric permingeatite, reaching 0.90 mWm −1 K −2 at 523 K.According to Kwak and Kim [19], Cu-poor tetrahedrites in the off-stoichiometric Cu 12+m Sb 4 S 13 (−0.3≤ m ≤ 0.3) exhibited higher power factor values compared to Cu-rich specimens, with a maximum value of 1.08 mWm −1 K −2 at 723 K.The changes in the power factor of Cu3+mSbSe4 are shown in Figure 8.As the temperature increased, the power factor increased for all specimens, resulting from the temperature dependence of electrical conductivity and the Seebeck coefficient.Although the Seebeck coefficient decreased due to Cu deficiency at a certain temperature (Figure 4), the electrical conductivity increased (Figure 3), resulting in an increase in power factor.For the specimen Cu2.97SbSe4, a maximum power factor of 0.72 mWm −1 K −2 was recorded at 573 K.This value represents an improvement of approximately 53% compared to the power factor of stoichiometric Cu3SbSe4 (0.47 mWm −1 K −2 at 573 K).Wei et al. [20] reported that Cu2.950SbSe4 and Cu2.925SbSe4 achieved power factor values exceeding 60% higher than that of stoichiometric permingeatite, reaching 0.90 mWm −1 K −2 at 523 K.According to Kwak and Kim [19], Cu-poor tetrahedrites in the off-stoichiometric Cu12+mSb4S13 (-0.3 ≤ m ≤ 0.3) exhibited higher power factor values compared to Cu-rich specimens, with a maximum value of 1.08 mWm −1 K −2 at 723 K.The ZT values of Cu3+mSbSe4 are presented in Figure 9.The ZT value is proportional to the operating temperature of a material; however, it is often constrained by the The ZT values of Cu 3+m SbSe 4 are presented in Figure 9.The ZT value is proportional to the operating temperature of a material; however, it is often constrained by the maximum temperature achievable during fabrication, which is deemed to have the optimal nominal composition for high performance and stability.The incorporation of Cu deficiency could enhance the thermoelectric performance of permingeatite due to increased carrier concentration.Despite increased thermal conductivity, the rise in power factor was significant; thus, for the samples in the range of −0.03 ≤ m ≤ −0.02, the ZT was improved at high temperatures.The highest ZT of 0.50 was recorded at 523 K for Cu 2.98 SbSe 4 .Wei et al. [20] reported a ZT of 0.20 at 673 K for stoichiometric permingeatite Cu 3 SbSe 4 , whereas non-stoichiometric Cu 2.925 SbSe 4 exhibited a higher ZT of 0.50 at 673 K, suggesting that Cu deficiency helped improve the thermoelectric properties of permingeatite.While their specimens were synthesized using a wet MA process with an alcohol solution as the processing agent in atmosphere gas (95% Ar and 5% H 2 ), our specimens were synthesized using a dry MA process without any processing agent in atmosphere gas (100% Ar).Additionally, the synthesized Cu-deficient powders were sintered using the SPS (spark plasma sintering) process at high temperatures (673 K and 703 K), whereas in our study, they were sintered using the HP process at a lower temperature (573 K).Although the influence of Cu deficiency on the thermoelectric properties of permingeatite may be similar, the differences in the synthesis and sintering processes resulted in variations in the magnitude of this influence (i.e., the values of the thermoelectric properties); the highest thermoelectric performance was reported at 673 K in one study, while in our study, the same performance was recorded at a significantly lower temperature of 523 K, which is 150 K lower.Kwak and Kim [19] obtained a ZT of 0.86 at 723 K for stoichiometric tetrahedrite Cu 12 Sb 4 S 13 ; however, they recorded the highest ZT value of 0.91 at 723 K for non-stoichiometric Cu 11.9 Sb 4 S 13 .Therefore, it has been confirmed that the deficiencies (vacancies) of Cu in p-type Cu-based chalcogenide compounds increase the charge carrier concentration, thereby helping to improve the thermoelectric performance.
Materials 2024, 17, 4345 9 of 11 maximum temperature achievable during fabrication, which is deemed to have the optimal nominal composition for high performance and stability.The incorporation of Cu deficiency could enhance the thermoelectric performance of permingeatite due to increased carrier concentration.Despite increased thermal conductivity, the rise in power factor was significant; thus, for the samples in the range of −0.03 ≤ m ≤ −0.02, the ZT was improved at high temperatures.The highest ZT of 0.50 was recorded at 523 K for Cu2.98SbSe4.Wei et al. [20] reported a ZT of 0.20 at 673 K for stoichiometric permingeatite Cu3SbSe4, whereas non-stoichiometric Cu2.925SbSe4 exhibited a higher ZT of 0.50 at 673 K, suggesting that Cu deficiency helped improve the thermoelectric properties of permingeatite.While their specimens were synthesized using a wet MA process with an alcohol solution as the processing agent in atmosphere gas (95% Ar and 5% H2), our specimens were synthesized using a dry MA process without any processing agent in atmosphere gas (100% Ar).Additionally, the synthesized Cu-deficient powders were sintered using the SPS (spark plasma sintering) process at high temperatures (673 K and 703 K), whereas in our study, they were sintered using the HP process at a lower temperature (573 K).Although the influence of Cu deficiency on the thermoelectric properties of permingeatite may be similar, the differences in the synthesis and sintering processes resulted in variations in the magnitude of this influence (i.e., the values of the thermoelectric properties); the highest thermoelectric performance was reported at 673 K in one study, while in our study, the same performance was recorded at a significantly lower temperature of 523 K, which is 150 K lower.Kwak and Kim [19] obtained a ZT of 0.86 at 723 K for stoichiometric tetrahedrite Cu12Sb4S13; however, they recorded the highest ZT value of 0.91 at 723 K for nonstoichiometric Cu11.9Sb4S13.Therefore, it has been confirmed that the deficiencies (vacancies) of Cu in p-type Cu-based chalcogenide compounds increase the charge carrier concentration, thereby helping to improve the thermoelectric performance.

Conclusions
Cu-deficient permingeatites were prepared by mechanical alloying and hot pressing.Phases, lattice parameters, microstructures, charge transport characteristics, and thermoelectric properties were evaluated depending on the extent of Cu deficiency.No secondary phases were observed, and the relative densities of all samples were above 96.5%.Due to Cu deficiency, the lattice constants significantly decreased, and the tetragonality of permingeatite also decreased.Increased carrier (hole) concentration due to Cu deficiency led to a decrease in the Seebeck coefficient.However, the electrical conductivity increased, resulting in a higher power factor, with Cu2.97SbSe4 recording a maximum power factor of

Conclusions
Cu-deficient permingeatites were prepared by mechanical alloying and hot pressing.Phases, lattice parameters, microstructures, charge transport characteristics, and thermoelectric properties were evaluated depending on the extent of Cu deficiency.No secondary phases were observed, and the relative densities of all samples were above 96.5%.Due to Cu deficiency, the lattice constants significantly decreased, and the tetragonality of permingeatite also decreased.Increased carrier (hole) concentration due to Cu deficiency led to a decrease in the Seebeck coefficient.However, the electrical conductivity increased, resulting in a higher power factor, with Cu 2.97 SbSe 4 recording a maximum power factor of 0.72 mWm −1 K −2 at 573 K, which is 53% higher than that of stoichiometric permingeatite at

Figure 1 .
Figure 1.X-ray diffraction patterns of non-stoichiometric permingeatite Cu 3+m SbSe 4 prepared by the MA−HP process.

Table 1 .
Relative densities, lattice parameters, and charge transport characteristics of stoichiometric and non-stoichiometric permingeatites.

Table 1 .
Relative densities, lattice parameters, and charge transport characteristics of stoichiometric and non-stoichiometric permingeatites.