Origin of Ultralow Thermal Conductivity in n-Type Cubic Bulk AgBiS₂: Soft Ag Vibrations and Local Structural Distortion Induced by the Bi 6s² Lone Pair

Abstract

Crystalline materials with ultralow thermal conductivity are essential for thermal barrier coating and thermoelectric energy conversion. Nontoxic n-type bulk cubic AgBiS 2 exhibits exceptionally low lattice thermal conductivity (κ lat ) of 0.68−0.48 W/m K in the temperature range of 298− 820 K, which is near the theoretical minimum (κ min ). The low κ lat is attributed to soft vibrations of predominantly Ag atoms and significant lattice anharmonicity because of local structural distortions along the [011] direction, arising because of the stereochemical activity of the 6s 2 lone pair of Bi, as suggested by pair distribution function analysis of the synchrotron X-ray scattering data. The low-temperature heat capacity of AgBiS 2 shows a broad hump because of the Ag-induced low-energy Einstein modes as also suggested from phonon dispersion calculated by first-principle density functional theory. Low-energy optical phonons contributed by Ag and Bi strongly scatter heat-carrying acoustic phonons, thereby decreasing the κ lat to a low value. A maximum thermoelectric figure of merit of ∼0.7 is attained at 820 K for bulk spark plasma-sintered n-type AgBiS 2 .

XBi4S7 (X = Mn, Fe): New Cost‐Efficient Layered n‐Type Thermoelectric Sulfides with Ultralow Thermal Conductivity

“…These distortions of the crystal lattice induce highly anharmonic behavior and consequently a large Grüneisen parameter. Similar results have been recently found in Bi/Sb containing complex materials as AgBiS2, [31] AgBi3S5, [32] AgSbSe2, [78] Cu12Sb4S13, [79] K2Bi8Se13, [71] and Sb2Se3. [80] The value of the Debye temperature θD also reflects the thermal conductivity and is defined as follows: [81] & = FeBi4S7 were respectively estimated to ~180 K and ~200 K. These values are slightly low compared with Bi2Se3 (~205 K) [74] and BiCuOSe (~243 K), [70] and in good agreement with the low thermal conductivity in these systems.…”

“…Among this family, numerous efficient p-type materials have been unveiled and optimized as tetrahedrite Cu12Sb4S13 (ZT ~ 0.8 at 700 K), [2][3][4][5][6] colusite Cu26V2Sn6S32 (ZT ~ 0.93 at 675 K), [7][8][9][10] Cu2SnS3 (ZT ~ 0.85 at 723 K), [11,12] bornite Cu5FeS4 (ZT ~ 0.79 at 550 K), [13][14][15][16] Cu2ZnSnS4 (ZT ~ 0.36 at 700 K), [17] stannoidite Cu8Fe3Sn2S12 (ZT ~ 0.35 at 630 K), [18] germanite derivative Cu22Fe8Ge4S32 (ZT ~ 0.17 at 575 K) [19] … Nevertheless, only few n-type sulfide thermoelectrics with moderate figure of merit are available, like Bi2S3 (ZT ~ 0.6 at 675 K), [20][21][22] TiS2 (ZT ~ 0.5 at 700 K), [23][24][25] CuFeS2 (ZT ~ 0.21 at 573 K), [26] Cu4Sn7S16 (ZT ~ 0.21 at 600 K), [27] Cu2CoTi3S8 (ZT ~ 0.2 at 670 K) [28,29] and CuFe2S3 (ZT ~ 0.14 at 700 K). [30] Very recently, Rathore et al obtained a ZT ~ 0.7 at 820 K in the AgBiS2 phase [31] while Tan et al reported an ultralow thermal conductivity and high ZT ~ 1 at 800 K for complex material AgBi3S5 doped with Cl. [32] In such compound, Skoug and Morelli evidenced the relationship between the lone pair electrons of Bi 3+ and the low thermal conductivity.…”

Entropy Engineered Cubic n‐Type AgBiSe2 Alloy with High Thermoelectric Performance in Fully Extended Operating Temperature Range

“…Considering the local structure, the first peak in the G ( r ) data has been selected to represent the chemical bonding of the nearest atom–atom correlation (i.e., Se‐Ag/Bi/Pb). It is found that a shoulder occurs between the G ( r ) and the fitting curves, which demonstrates the local structural distortion, and based on consideration that the cationic off‐centering has been respectably addressed in certain materials with lone‐pair electrons, such as PbTe [ 32 ] and AgBiS 2 , [ 33 ] we attempt to tackle the off‐centering of anions in this study, which potentially could suppress the propagation of acoustic phonons as recently noted. It is suggested that off‐centering of Se atom by 0.118 Å in the [111] direction of x = 0.2 can more appropriately describes the nearest‐neighbor correlation, while another case proposes the off‐centering along the same [111] direction by 0.119 Å for x = 0.3 (Figure S9, Supporting Information), which is similar to (SnTe) 1−2 x (SnSe) x (SnS) x .…”

Slowing down the heat in thermoelectrics

“…The rattling Tl atom leads to low κ lat in TlInTe 2 (~0.4 Wm −1 K −1 at 300 K) 235 and TlSe (~0.78 Wm −1 K −1 at 300 K), 239 which are lower than those of the other 1D Zintl‐type phases such as Ca 5 Al 2 Sb 6 , 255 Ca 3 AlSb 3 , 256 and Sr 3 GaSb 3 257 . Similarly, the Ag rattling atom causes low κ lat in AgBi 3 S 5 (~0.3 Wm −1 K −1 at 300 K), 134 CsAg 5 Te 3 (~0.18 Wm −1 K −1 at 300 K), 287 Tl 2 Ag 12 Se 7 (~0.45 Wm −1 K −1 at 300 K), 259 and AgBiS 2 (~0.68 Wm −1 K −1 at 300 K) 258 …”