Synthesis, Crystallographic Studies, and Characterization of K 2 Bi 8 Se 13 x S x Solid Solutions

Synthesis, Crystallographic Studies, and Characterization of K 2 Bi 8 Se 13 x S x Solid Solutions Theodora Kyratsi and Mercouri G. Kanatzidis* East Lansing, Michigan / USA, Department of Chemistry and Center for Fundamental Materials Research, Michigan State University Received June 26 th, 2003. Dedicated to Professor Bernt Krebs on the Occasion of his 65th Birthday Abstract. The detailed crystal structures of selected members of solid solutions of the thermoelectric compounds K 2 Bi 8 Se 13 x S x with x 4, x 6andx 10 were determined. The purpose of this study was to understand the nature of Se/S mass fluctuations introduced when β-k 2 Bi 8 Se 13 is alloyed with isostructural K 2 Bi 8 S 13. The details of the K/Bi disorder and Se/S distribution are examined. Lattice parameters, semiconducting band gaps and melting points are reported as function of x. Keywords: Bismuth; Selenium; Chalcogenides; Thermoelectric properties Synthese, kristallographische Untersuchung und Charakterisierung fester Lösungen von K 2 Bi 8 Se 13 x S x Inhaltsübersicht. Die Kristallstrukturen von ausgewählten Proben der festen Lösungen der thermoelektrischen Verbindungen K 2 Bi 8 Se 13 x S x mit x 4, x 6 und x 10 wurden bestimmt. Das Ziel dieser Studie war, die Art der Se/S-Masseschwankungen zu verstehen, wenn β-k 2 Bi 8 Se 13 mit isostrukturellem K 2 Bi 8 S 13 legiert wird. Die Details der K/Bi-Fehlordnung und der Se/S-Verteilung wurdenuntersucht. Gitterparameter, Halbleiterbandlücke und Schmelzpunkte werden in Abhängigkeit von x mitgeteilt. Introduction Ternary and quaternary compounds of bismuth chalcogenides [1] studies have shown that several multinary compounds containing alkali metals present promising thermoelectric properties. A promising material is β-k 2 Bi 8 Se 13 [2] because it possesses low thermal conductivity and relatively high power factor (defined as S 2 σ, σ is the electrical conductivity and S is the thermoelectric power). Doping studies on β-k 2 Bi 8 Se 13 have shown that the performance figure of merit can be substantially improved, mainly by raising the power factor [3]. Next is to explore whether additional improvements can be made by reducing the thermal conductivity by introducing structural disorder through K 2 Bi 8 Se 13-x S x solid solutions. All state-of-the-art thermoelectric materials are solid solutions between isostructural compounds (e.g. Bi 2-x Sb x Te 3,Bi 2 Te 3-x Se x etc). This is typically done in order to introduce mass fluctuation, which greatly reduces the thermal conductivity of the materials. Alloying K 2 Bi 8 Se 13 with other isostructural compounds, K 2 Sb 8 Se 13, has been * Professor Dr. Mercouri G. Kanatzidis Department of Chemistry and Center for Fundamental Materials Research Michigan State University East Lansing, MI 48824 / USA Fax: Int-517-353-1793 E-mail: kanatzid@cem.msu.edu done and K 2 Bi 8-x Sb x Se 13 solid solutions [4] were studied with respect to their thermoelectric properties. Interestingly, from crystallographic studies we learned that the Bi/Sb distribution in the structure was non-uniform [5] and that the various metal sites in the structure were disproportionally affected. We also learned that a substantial reduction in lattice thermal conductivity is achieved. In this work, we focused on the Se sites of the structure and we synthesized the series of K 2 Bi 8 Se 13-x S x solid solutions. The Se/S substitution was studied in detail to determine how the K 2 Bi 8 Se 13-x S x system forms solid solutions, e.g. does it exhibit a random or selective distribution of S atoms over the Se atom sites. Lattice parameters, energy band gaps and melting points and their systematical variations are reported as function of x. Measurements of charge transport properties and thermal conductivities are in progress in order to study the potential of these materials for thermoelectric applications and will be reported elsewhere. Experimental Section Reagents Chemicals were used in this work were generously provided by Tellurex Inc. as obtained: bismuth chunks (99.999 %); selenium shots (99.999 %). Potassium chunks (98 % Aldrich Chemical Co., Inc., Milwaukee, WI), sulfur flowers (Columbus Chemical Industries, Inc, PO Box 8, Columbus, WI 53925). 2222 2003 WILEY-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim DOI: 10.1002/zaac.200300213 Z. Anorg. Allg. Chem. 2003, 629, 2222 2228

Studies and Characterization of K 2 Bi 8 Se 13 x S x Solid Solutions Synthesis All manipulations were carried out under a dry nitrogen atmosphere in a Vacuum Atmospheres Dri-Lab glovebox. β-k 2 Bi 8 Se 13. A mixture of potassium metal (0.282 g. 7.2 mmol), bismuth (6.021 g, 28.8 mmol) and selenium (3.697 g, 46.8 mmol) was loaded into a silica tube and subsequently flame-sealed at a residual pressure of <10 4 Torr. The mixture was heated to 850 C over 12 h and kept there for 1 h, followed by cooling to 450 C and kept there for 48 h and cooling at 50 C atarateof 15 C/h. K 2 Bi 8 S 13 : A mixture of potassium metal (0.361 g. 9.2 mmol), bismuth (7.7154 g. 36.9 mmol) and sulfur (1.9238 g. 60.0 mmol) was loaded into quartz tubes and subsequently flame-sealed at a residual pressure of <10 4 Torr. The mixture was heated to 850 C over 12 h and kept there for 1 h, followed by cooling to 50 C ata rate of 15 C/h. K 2 Bi 8 Se 13-x S x solid solutions: A mixture of potassium metal, bismuth, selenium and sulfur was loaded into quartz tubes and subsequently flame-sealed at a residual pressure of <10 4 Torr. For example K 2 Bi 8 Se 13-x S x (x 6) was prepared by mixing 0.313 g K (8.0 mmol), 6.7004 g Bi (32.2 mmol), 2.2152 g Se (28.1 mmol) and 0.7711 g S (24.0 mmol). The mixture was heated to 850 C over 12 h and kept there for 1 h, followed by cooling to 50 C atarate of 15 C/h. The members with x<4 were annealed at 500 C for 48 h. Electron Microscopy Quantitative microprobe analyses of the compounds were performed with a JEOL JSM-35C scanning electron microscope (SEM) equipped with a Tracor Northern energy-dispersive spectroscopy (EDS) detector. Data were acquired using an accelerating voltage of 20 kv and a 1 min accumulation time. Differential Thermal analysis Differential thermal analysis (DTA) was performed with a computer-controlled Shimadzu DTA-50 thermal analyzer. The ground single crystals ( 30 mg total mass) were sealed in quartz ampoules under vacuum. A quartz ampoule containing alumina of equal mass was sealed and placed on the reference side of the detector. The samples were heated to 850 C at 10 C/min and then isothermed for 5 min followed by cooling at 10 C/min to room temperature and repeated the cycle. The DTA sample was examined by powder X-ray diffraction after the experiment. Infrared and Solid State UV/Vis Spectroscopy Optical diffuse reflectance measurements were carried out on finely ground samples at room temperature. The spectra were recorded, in the infrared region (6000-400 cm 1 ), with the use of a Nicolet MAGNA-IR 750 Spectrometer equipped with a diffuse reflectance attachment from Spectra-Tech. Inc. In the 200-2500 nm region, optical diffuse reflectance measurements were also performed at room temperature in a Shimadzu UV-3101 PC double-beam, doublemonochromator spectrophotometer, equipped with an integrating sphere. The measurement of diffuse reflectivity can be used to obtain values for the band gap [1 2, 4] by using Kubelka-Munk [6] theory. Powder X-ray Diffraction The solid solutions were examined by X-ray powder diffraction to assess phase purity, for identification and determination of the lattice parameters. Powder patterns were obtained using a Rigaku Rotaflex powder X-ray diffractometer with Ni-filtered Cu Ka radiation operating at 45 kv and 100 ma. The data were collected at a rate of 2 /min. The purity of phases for the solid solutions was confirmed by comparison of the X-ray powder pattern to the calculated one from single crystal data for β-k 2 Bi 8 Se 13 using Cerius 2 software. The lattice parameters were determined using the experimental powder diffraction patterns and were refined with the program U-Fit [7]. Single-crystal X-ray Crystallography Intensity data from single crystals of selected members of K 2 Bi 8 Se 13-x S x solid solutions were collected at room temperature on a Bruker SMART Platform CCD diffractometer. The individual frames were measured with an omega rotation of 0.3 deg and an acquisition time of 60 sec for the single crystal obtained from the member for x 4(I), 60 sec for the member x 6(II) and 30 sec for the member x 10 (III). The SMART software [8] was used for the data acquisition and SAINT [9] for data extraction and reduction.an analytical absorption correction was performed using the program XPREP in SAINT program package, followed by a semi-empirical absorption correction based on symmetrically equivalent reflections with the program SADABS. Structural solution and refinements were done successfully using the SHELXTL [10] package of crystallographic programs. The structures were solved with direct methods. After successful assignment of the high electron density peaks as Bi, K, and Se atoms, the displacement parameters and occupancy on each atomic site was examined. The refined occupancies of all chalcogenide sites which were first assigned to only Se atoms were low, indicating that lighter S atoms were definitely involved in these sites. The opposite was done for the S-rich x 10 member i.e. all sites initially were assigned to S atoms.thus, all these sites were refined with mixed Se and S occupancy. The refined occupancies of almost all heavy metal sites were assigned to Bi atoms. All K sites were successfully modeled with a disorder involving two additional Bi atoms. After successive refinements of the positions and occupancies of all atom sites, reasonable displacement parameters and occupancies were obtained, as well as very low residual electron densities. Because of the multiple positional disorder in many atom sites only Bi(1) to Bi(7) and all chalcogenide sites were anisotropically refined. The final formulae were refined as K 2.05 Bi 7.95 Se 8.89 S 4.11 for (I), K 2.02 Bi 7.99 Se 6.96 S 6.04 for (II) and K 2.03 Bi 7.98 Se 2.97 S 10.03 for (III). The complete data collection parameters and details of the structure solution and refinements for the compounds are given in Table 1. The fractional coordinates and displacement parameters (U eq ) of all atoms with estimated standard deviations are given in Tables 2, 3 and 4. Selective atomic distances are given in Table 5. Results and Discussion Synthesis and thermal analysis K 2 Bi 8 Se 13-x S x solid solutions were prepared by reacting stoichiometric combinations of potassium metal, bismuth, Z. Anorg. Allg. Chem. 2003, 629, 2222 2228 zaac.wiley-vch.de 2003 WILEY-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim 2223

T. Kyratsi, M. G. Kanatzidis Table 1 Summary of Crystallographic Data and Structural Analysis for the compound (I) (x 4.0), (II) (x 6) and s (III) (x 10) of K 2 Bi 8 Se 13-x S x solid solution. a) refined formula K 2.05 Bi 7.97 Se 8.89 S 4.11 K 2.02 Bi 7.99 Se 6.96 S 6.04 K 2.03 Bi 7.98 Se 2.97 S 10.03 formula weight 2582.30 2492.17 2306.96 crystal habit black needle black needle black needle crystal size, mm 3 0.120 x 0.014 x 0.004 0.081 x 0.025 x 0.040 0.610 x 0.040 x 0.030 space group P2 1 /m (No. 11) P2 1 /m (No. 11) P2 1 /m (No. 11) a, Å 17.343(5) 17.2527(34) 16.998(3) b, Å 4.1544(11) 4.1357(8) 4.0834(8) c, Å 18.324(5) 18.2007(36) 17.957(4) β, deg 90.214(5) 90.0850(32) 90.218(4) Z; V, Å 3 2; 1320.3(6) 2; 1298.66(12) 2; 1246.4(4) D calc, gcm 3 6.496 6.373 6.139 temp, K 293(2) 293(2) 293(2) λ(mo K α ), Å 0.71073 0.71073 0.71073 absorption coefficient, mm 1 65.792 64.489 61.659 F(000) 2140 2070 1925 θ min θ max, deg 3.23 30.20 3.25 30.22 3.40 30.16 index ranges 24 h 24, 5 k 5, 24 l 25 24 h 24, 5 k 5, 25 l 25 23 h 21, 5 k 5, 24 l 22 total reflections collected 13105 14662 8938 independent reflections 4170 [R(int) 0.0806] 4105 [R(int) 0.0509] 3871 [R(int) 0.0430] refinement method full-matrix full-matrix full-matrix least-squares on F 2 least-squares on F 2 least-squares on F 2 data / restraints / parameters 4170 / 3/ 170 4105/ 3/ 170 3871/ 3/ 170 final R indices R 1 0.0489 R 1 0.0313, R 1 0.0421 [I>2σ(I)] wr 2 0.0987 wr 2 0.0648 wr 2 0.1001 R indices (all data) R 1 0.1192 R 1 0.0491, R 1 0.0572 wr 2 0.1244 wr 2 0.0692 wr 2 0.1075 largest diff. peak and hole, ea 3 4.019 and 4.214 1.905 and 2.614 1.668 and 1.098 goodness-of-fit on F 2 0.989 0.932 0.968 R 1 Σ F o F c /Σ F o wr 2 {Σ[w(F o 2 F c 2 ) 2 ]/Σ[w(F o 2 ) 2 ]} 1/2 a) Further details of the crystal structure investigations may be obtained from the Fachinformationszentrum Karlsruhe, D-76344 Eggenstein-Leopoldshafen, Germany (fax: ( 49)7247-808-666; email: crysdata@fiz-karlsruhe.de) on quoting numbers CSD-413248, CSD-413249 and CSD-413250. selenium and sulfur, at 850 C. The solid solutions with higher sulfur content (x 4) were formed easily as pure phases. For x < 4 an annealing step at 500 C for 48 h was required in order to achieve pure products, and to avoid an impurity with the K 2.5 Bi 8.5 Se 14 -type structure [11] (>20 %). This behavior is similar to that of β-k 2 Bi 8 Se 13 that also requires an annealing treatment. Differential thermal analysis shows one endothermic peak during heating that corresponds to melting followed by a sharp exothermic peak which is due to crystallization, Figure 1a. The melting points of β-k 2 Bi 8 Se 13 and K 2 Bi 8 S 13 were measured to be 700 and 710 C, respectively. All solid solution members showed similar melting points, see Figure 1b, while mild eutectic is observed. Structural description A detailed single crystal crystallographic analysis was performed on the solid solution K 2 Bi 8 Se 13-x S x members with x 4(I), 6 (II) and 10 (III) in order to examine the distribution of Se/S atoms in the structure. The structural model is the same as β-k 2 Bi 8 Se 13, with smaller cell parameters due to smaller S atoms involved, see Table 1. In this structure type, Bi 2 Te 3 -type rods are arranged side by side to form layers perpendicular to the c-axis.then infinite rods of NaCl-type connect the layers to build a 3-D framework, which creates the needle-like crystal morphology, with tunnels filled with K cations, see Figure 2. All three members of the solid solutions exhibit the same atomic arrangements and disordering behavior. The coordination environment of the heavy metal atoms (Bi(1)-Bi(7)) in the NaCl- and Bi 2 Te 3 -type units are distorted octahedral with reasonable thermal parameters. Their Bi-Q distances vary from 2.634(3) to 3.200(3) Å (Q S, Se). Bi(8)/K(3) and K(1)/Bi(9) sites that serve as the connecting points between the two different type blocks (NaCland Bi 2 Te 3 -type) are disordered with K and Bi atoms. The Bi(8)/K(3) site is occupied by 53 % for K for all members of the series studied here, while the occupancies of Bi(9)/ K(1) differed for different members. The K atom fraction on the Bi(9)/K(1) site occupancy increases systematically from 65 % to 67 % and 72 % when the S concentration increases from x 4 to 6 and 10 respectively. For the end members the K occupancy in these positions is 62 % and 80 % for the Se-end [2] and S-end [12] member, respectively. Even though the K(2) site is similar to that of Bi(8)/K(3) and Bi(9)/K(1) in the K 2 Bi 8 Se 13 -end member structure this site involves only K atoms. However, in the solid solutions this site required the inclusion of two Bi atoms (Bi(21) and Bi(22)) for successful modeling of the X-ray data and also to achieve charge balance. The occupancy of Bi on the K(2) site increases in going from the Se-end member to S-end member going from 13 %, 18 % and 23 % Bi contribution when x is 4, 6 and 10, respectively. The K 2 Bi 8 S 13 -end member also has 20 % Bi involved in the same site [12]. The local coordination environment of this site is tricapped trigonal 2224 2003 WILEY-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim zaac.wiley-vch.de Z. Anorg. Allg. Chem. 2003, 629, 2222 2228

Studies and Characterization of K 2 Bi 8 Se 13 x S x Solid Solutions Table 2 Atomic coordinates (x 10 4 ), equivalent isotropic displacement parameters (Å 2 x10 3 ), and occupancies for the compound (I) (x 4) of K 2 Bi 8 Se 13-x S x solid solution x y z U(eq) Occ Bi(1) 5818(1) 1/4 9214(1) 21(1) 1 Bi(2) 6722(1) 3/4 11237(1) 21(1) 1 Bi(3) 8281(1) 1/4 9798(1) 20(1) 1 Bi(4) 6067(1) 1/4 15219(1) 26(1) 1 Bi(5) 8039(1) 3/4 15462(1) 21(1) 1 Bi(6) 5125(1) 1/4 12510(1) 23(1) 1 Bi(7) 10070(1) 1/4 16130(1) 23(1) 1 Se(1) 4820(2) 1/4 14050(2) 21(1) 0.812(19) S(1) 4820(2) 1/4 14050(2) 21(1) 0.188(19) Se(7) 6036(2) 1/4 7751(2) 25(1) 0.66(2) S(7) 6036(2) 1/4 7751(2) 25(1) 0.34(2) Se(3) 6934(2) 3/4 9424(2) 22(1) 0.731(19) S(3) 6934(2) 3/4 9424(2) 22(1) 0.269(19) Se(4) 11074(3) 1/4 17250(3) 27(2) 0.41(2) S(4) 11074(3) 1/4 17250(3) 27(2) 0.59(2) Se(5) 6901(2) 3/4 14416(2) 23(1) 0.63(2) S(5) 6901(2) 3/4 14416(2) 23(1) 0.37(2) Se(6) 7282(2) 1/4 16261(2) 22(1) 0.747(19) S(6) 7282(2) 1/4 16261(2) 22(1) 0.253(19) Se(2) 5416(2) 1/4 10920(2) 18(1) 0.664(19) S(2) 5416(2) 1/4 10920(2) 18(1) 0.336(19) Se(8) 6302(2) 3/4 12663(2) 19(1) 0.702(18) S(8) 6302(2) 3/4 12663(2) 19(1) 0.298(18) Se(9) 8678(3) 1/4 8376(3) 26(2) 0.251(19) S(9) 8678(3) 1/4 8376(3) 26(2) 0.749(19) Se(10) 9271(2) 3/4 10107(2) 24(1) 0.93(2) S(10) 9271(2) 3/4 10107(2) 24(1) 0.07(2) Se(11) 9211(2) 3/4 16785(2) 24(1) 0.786(19) S(11) 9211(2) 3/4 16785(2) 24(1) 0.214(19) Se(12) 7773(2) 1/4 11475(2) 25(1) 0.89(2) S(12) 7773(2) 1/4 11475(2) 25(1) 0.11(2) Se(13) 11064(2) 3/4 15362(2) 28(1) 0.68(2) S(13) 11064(2) 3/4 15362(2) 28(1) 0.32(2) Bi(8) 8039(4) 1/4 13280(10) 21(2) 0.32(4) K(3) 7676(12) 1/4 13256(9) 29(3) 0.526(13) Bi(81) 8044(6) 1/4 13100(20) 21(4) 0.16(4) Bi(9) 7930(9) 3/4 7832(7) 21(3) 0.177(15) K(1) 7496(9) 3/4 7700(8) 33(3) 0.654(13) Bi(91) 7730(8) 3/4 7992(8) 15(3) 0.167(16) K(2) 10199(6) 3/4 18422(5) 40(2) 0.870(11) Bi(21) 9700(17) 3/4 18220(40) 22(9) 0.07(3) Bi(22) 9630(30) 3/4 18410(50) 30(11) 0.06(3) U(eq) is defined as one third of the trace of the orthogonalized Uij tensor. Table 3 Atomic coordinates (x 10 4 ), equivalent isotropic displacement parameters (Å 2 x10 3 ), and occupancies for the compound (II) (x 6) of K 2 Bi 8 Se 13-x S x solid solution x y z U(eq) Occ Bi(1) 5816(1) 1/4 782(1) 22(1) 1 Bi(2) 6718(1) 3/4 1237(1) 21(1) 1 Bi(3) 8278(1) 1/4 205(1) 20(1) 1 Bi(4) 6069(1) 1/4 4786(1) 26(1) 1 Bi(5) 8042(1) 3/4 4546(1) 21(1) 1 Bi(6) 4879(1) 3/4 2510(1) 24(1) 1 Bi(7) 10076(1) 1/4 3871(1) 24(1) 1 Se(1) 5187(1) 3/4 4053(1) 24(1) 0.722(10) S(1) 5187(1) 3/4 4053(1) 24(1) 0.278(10) Se(2) 4582(1) 3/4 925(1) 19(1) 0.476(10) S(2) 4582(1) 3/4 925(1) 19(1) 0.524(10) Se(3) 6929(1) 3/4 579(1) 24(1) 0.617(10) S(3) 6929(1) 3/4 579(1) 24(1) 0.383(10) Se(4) 11073(1) 1/4 2758(1) 27(1) 0.286(9) S(4) 11073(1) 1/4 2758(1) 27(1) 0.714(9) Se(5) 6908(1) 1/4 5586(1) 24(1) 0.438(10) S(5) 6908(1) 1/4 5586(1) 24(1) 0.562(10) Se(6) 7282(1) 1/4 3744(1) 23(1) 0.591(9) S(6) 7282(1) 1/4 3744(1) 23(1) 0.409(9) Se(7) 6036(1) 1/4 2240(1) 22(1) 0.430(9) S(7) 6036(1) 1/4 2240(1) 22(1) 0.570(9) Se(8) 6296(1) 3/4 2663(1) 21(1) 0.562(9) S(8) 6296(1) 3/4 2663(1) 21(1) 0.438(9) Se(9) 11320(2) 3/4 1628(1) 28(1) 0.169(9) S(9) 11320(2) 3/4 1628(1) 28(1) 0.831(9) Se(10) 9270(1) 3/4 107(1) 23(1) 0.817(9) S(10) 9270(1) 3/4 107(1) 23(1) 0.183(9) Se(11) 9220(1) 3/4 3216(1) 26(1) 0.649(9) S(11) 9220(1) 3/4 3216(1) 26(1) 0.351(9) Se(12) 7770(1) 1/4 1476(1) 24(1) 0.756(9) S(12) 7770(1) 1/4 1476(1) 24(1) 0.244(9) Se(13) 8933(1) 1/4 5366(1) 27(1) 0.449(10) S(13) 8933(1) 1/4 5366(1) 27(1) 0.551(10) Bi(8) 8035(2) 1/4 3301(5) 22(1) 0.275(18) Bi(81) 8034(2) 1/4 3127(7) 23(1) 0.215(17) K(3) 7675(5) 1/4 3278(4) 28(2) 0.520(11) K(1) 12505(4) 1/4 2339(3) 34(1) 0.673(10) Bi(9) 12270(3) 1/4 2019(3) 24(1) 0.191(7) Bi(91) 12052(5) 1/4 2186(4) 21(2) 0.132(6) K(2) 9804(3) 1/4 1576(2) 35(1) 0.827(9) Bi(21) 10309(3) 1/4 1765(6) 24(2) 0.114(6) Bi(22) 10350(6) 1/4 1502(13) 30(4) 0.062(6) U(eq) is defined as one third of the trace of the orthogonalized Uij tensor. prismatic involving 9 chalcogen atoms. This increase of Bi occupancy in this K(2) site is due to the decrease in cage size as one moves from K 2 Bi 8 Se 13 to K 2 Bi 8 S 13 and the unit cell becomes smaller. The smaller the cage size, favors the small Bi 3 ions. All chalcogenide sites were mixed occupied by Se and S. Q(4) and Q(9) sites seem to have somewhat more preference to the S atoms, while Q(10), Q(11) and Q(12) to the Se atoms. All these sites are involved in the K(2) coordination environment while Q(4) and Q(9) are sited between this and the other K/Bi disordered sites. The remaining sites do not seem to have any preference to the atoms involved. In general the present study shows that the K 2 Bi 8 Se 13-x S x solid solutions have a nearly random Se/S distribution. This is not what was observed in solid solutions of the type K 2 Bi 8-x Sb x Se 13. The local environment of the heavy metal sites (e.g. size and coordination number) has strong influence on the type of atoms that are attracted to those sites. This makes it difficult to create materials with a totally random Bi/Sb distribution. The K/Bi substitution is expected to have a noticeable impact in the electronic properties of these systems given the large differences in the nature of K- Q vs Bi-Q bonding. The former is ionic in nature and is likely to contribute to carrier scattering from the hard K ions, whereas the latter is covalent and is expected to facilitate carrier transport [13]. The K/Bi disorder on the different crystallographic sites is also expected to affect the charge-transport properties by creating additional energy levels in the gap [13]. Lattice parameters The lattice parameters of selected members of K 2 Bi 8 Se 13-x S x solid solutions were determined using the experimental X-ray powder diffraction patterns and were refined with the program U-Fit, see Table 6. Since smaller atoms substitute Se when x increases, the powder pattern peaks shift to higher 2θ angles (Figure 3a) and smaller unit cell volume is expected.the composition dependence of the unit cell volumes is shown in Figure 3b, where the volume decreases with the introduction of S in the structure. The data seem to follow Vegard s law, which is typical behavior for solid solutions. Z. Anorg. Allg. Chem. 2003, 629, 2222 2228 zaac.wiley-vch.de 2003 WILEY-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim 2225

T. Kyratsi, M. G. Kanatzidis Table 4 Atomic coordinates (x 10 4 ), equivalent isotropic displacement parameters (Å 2 x10 3 ), and occupancies for the compound (III) (x 10) of K 2 Bi 8 Se 13-x S x solid solution x y z U(eq) Occ Bi(1) 5820(1) 1/4 9222(1) 21(1) 1 Bi(2) 6718(1) 3/4 11237(1) 20(1) 1 Bi(3) 8277(1) 1/4 9793(1) 21(1) 1 Bi(4) 6068(1) 1/4 5217(1) 25(1) 1 Bi(5) 8051(1) 3/4 5445(1) 21(1) 1 Bi(6) 4876(1) 3/4 7476(1) 23(1) 1 Bi(7) 10084(1) 1/4 6134(1) 24(1) 1 S(3) 6923(2) 3/4 9418(2) 24(1) 0.758(13) Se(3) 6923(2) 3/4 9418(2) 24(1) 0.242(13) S(12) 7768(1) 1/4 11477(2) 26(1) 0.591(12) Se(12) 7768(1) 1/4 11477(2) 26(1) 0.409(12) S(7) 6021(2) 1/4 7768(2) 23(1) 0.830(13) Se(7) 6021(2) 1/4 7768(2) 23(1) 0.170(13) S(2) 5412(2) 1/4 10938(2) 22(1) 0.812(14) Se(2) 5412(2) 1/4 10938(2) 22(1) 0.188(14) S(5) 6911(2) 3/4 4425(2) 25(1) 0.859(13) Se(5) 6911(2) 3/4 4425(2) 25(1) 0.141(13) S(8) 6301(2) 3/4 12654(2) 23(1) 0.768(12) Se(8) 6301(2) 3/4 12654(2) 23(1) 0.232(12) S(4) 11076(2) 1/4 7248(2) 27(1) 0.900(12) Se(4) 11076(2) 1/4 7248(2) 27(1) 0.100(12) S(13) 8916(2) 1/4 4620(2) 27(1) 0.887(14) Se(13) 8916(2) 1/4 4620(2) 27(1) 0.113(14) S(1) 5197(2) 3/4 5946(2) 24(1) 0.693(13) Se(1) 5197(2) 3/4 5946(2) 24(1) 0.307(13) S(10) 9263(1) 3/4 10114(1) 24(1) 0.533(12) Se(10) 9263(1) 3/4 10114(1) 24(1) 0.467(12) S(11) 9233(2) 3/4 6787(2) 27(1) 0.677(13) Se(11) 9233(2) 3/4 6787(2) 27(1) 0.323(13) S(6) 7287(2) 1/4 6238(2) 24(1) 0.766(13) Se(6) 7287(2) 1/4 6238(2) 24(1) 0.234(13) S(9) 8691(2) 1/4 8372(2) 27(1) 0.956(13) Se(9) 8691(2) 1/4 8372(2) 27(1) 0.044(13) Bi(8) 8005(2) 1/4 3296(5) 21(1) 0.264(15) K(3) 7661(7) 1/4 3272(5) 31(2) 0.536(12) Bi(81) 8011(2) 1/4 3094(6) 20(1) 0.221(14) Bi(9) 7724(4) 3/4 7982(5) 23(2) 0.154(7) K(1) 7493(4) 3/4 7648(4) 31(1) 0.723(11) Bi(91) 7937(6) 3/4 7788(5) 20(2) 0.115(7) K(2) 10203(4) 3/4 8433(3) 37(2) 0.765(10) Bi(21) 9707(3) 3/4 8244(5) 26(2) 0.154(6) Bi(22) 9657(5) 3/4 8542(9) 24(3) 0.077(6) U(eq) is defined as one third of the trace of the orthogonalized Uij tensor. Table 5 The Selective Atomic Distances /Å for the Compound (x 4) (I), (x 6) (II) and (x 10) (III) (I) (II) (III) Bi(1)-Q(7) 2.709(4) Bi(1)-Q(7) 2.681(2) Bi(1)-Q(7) 2.634(3) Bi(1)-Q(3) 2.865(2) Bi(1)-Q(3) 2.8464(12) Bi(1)-Q(3) 2.7939(19) Bi(1)-Q(2) 2.991(3) Bi(1)-Q(2) 2.9796(14) Bi(1)-Q(2) 2.938(2) Bi(2)-Q(8) 2.716(3) Bi(2)-Q(8) 2.6958(18) Bi(2)-Q(8) 2.645(3) Bi(2)-Q(12) 2.797(2) Bi(2)-Q(12) 2.7858(11) Bi(2)-Q(12) 2.7450(17) Bi(3)-Q(9) 2.698(5) Bi(3)-Q(9) 2.680(3) Bi(2)-Q(2) 3.061(2) Bi(3)-Q(10) 2.752(2) Bi(3)-Q(10) 2.7440(10) Bi(3)-Q(9) 2.650(4) Bi(3)-Q(12) 3.200(3) Bi(3)-Q(12) 3.1823(17) Bi(3)-Q(10) 2.7025(15) Bi(4)-Q(6) 2.837(4) Bi(4)-Q(6) 2.8265(18) Bi(3)-Q(3) 3.147(2) Bi(4)-Q(5) 2.930(3) Bi(4)-Q(5) 2.9129(15) Bi(4)-Q(6) 2.763(3) Bi(4)-Q(1) 3.039(4) Bi(4)-Q(1) 3.0295(16) Bi(4)-Q(1) 2.8440(19) Bi(5)-Q(5) 2.746(4) Bi(5)-Q(5) 2.725(2) Bi(4)-Q(5) 2.875(2) Bi(5)-Q(6) 2.863(2) Bi(5)-Q(6) 2.8502(12) Bi(4)-Q(1) 2.990(3) Bi(5)-Q(11) 3.159(4) Bi(5)-Q(11) 3.1633(18) Bi(5)-Q(5) 2.662(3) Bi(6)-Q(1) 2.872(3) Bi(6)-Q(1) 2.8575(16) Bi(5)-Q(6) 2.810(2) Bi(6)-Q(8) 2.925(3) Bi(6)-Q(8) 2.9090(13) Bi(5)-Q(13) 2.922(2) Bi(6)-Q(7) 2.931(3) Bi(6)-Q(7) 2.9167(15) Bi(5)-Q(11) 3.132(3) Bi(6)-Q(2) 2.959(3) Bi(6)-Q(2) 2.9298(18) Bi(6)-Q(1) 2.804(3) Bi(7)-Q(4) 2.686(5) Bi(7)-Q(4) 2.660(2) Bi(6)-Q(8) 2.867(2) Bi(7)-Q(11) 2.827(2) Bi(7)-Q(11) 2.8057(12) Bi(6)-Q(7) 2.867(2) Bi(7)-Q(13) 3.047(3) Bi(7)-Q(13) 3.0205(15) Bi(6)-Q(2) 2.891(3) Bi(8)-Q(4) 2.763(8) Bi(8)-Q(4) 2.760(4) Bi(7)-Q(4) 2.612(4) Bi(8)-Q(13) 2.929(17) Bi(8)-Q(13) 2.879(9) Bi(7)-Q(11) 2.7652(19) Bi(81)-Q(4) 2.659(12) Bi(81)-Q(4) 2.664(4) Bi(7)-Q(13) 2.985(2) Bi(9)-Q(9) 2.642(7) Bi(9)-Q(9) 2.733(3) Bi(8)-Q(4) 2.753(5) Bi(9)-Q(11) 2.94(2) Bi(9)-Q(3) 2.961(7) K(3)-Q(4) 3.109(9) K(1)-Q(9) 3.168(13) K(1)-Q(9) 3.184(6) K(3)-Q(5) 3.178(8) K(1)-Q(7) 3.276(12) K(1)-Q(7) 3.262(5) Bi(81)-Q(4) 2.639(4) K(1)-Q(3) 3.310(14) K(1)-Q(6) 3.308(5) Bi(81)-Q(12) 2.931(11) Bi(91)-Q(9) 2.739(8) Bi(91)-Q(9) 2.628(3) K(1)-Q(9) 3.160(6) Bi(91)-Q(3) 2.969(18) Bi(91)-Q(11) 2.884(10) K(1)-Q(7) 3.238(6) K(2)-Q(4) 3.354(8) K(2)-Q(4) 3.344(4) K(1)-Q(6) 3.271(6) K(2)-Q(9) 3.359(9) K(2)-Q(9) 3.336(4) Bi(9)-Q(9) 2.712(5) K(2)-Q(11) 3.448(11) K(2)-Q(11) 3.428(5) Bi(91)-Q(9) 2.628(4) Bi(21)-Q(11) 2.75(6) Bi(21)-Q(11) 2.764(11) Bi(91)-Q(11) 2.850(12) Bi(21)-Q(9) 3.15(3) Bi(21)-Q(9) 2.717(4) K(2)-Q(4) 3.304(5) Bi(22)-Q(9) 2.65(3) Bi(22)-Q(9) 2.671(7) K(2)-Q(9) 3.284(6) Bi(22)-Q(11) 3.06(9) Bi(22)-Q(11) 3.21(2) Bi(21)-Q(9) 2.684(4) Bi(22)-Q(10) 3.18(10) Bi(22)-Q(10) 3.00(2) Bi(22)-Q(9) 2.637(6) Energy gap dependence on concentration The energy gaps, E g, of the end-members and solid solutions were determined optically at room temperature using mid and near infrared spectroscopy. The energy gaps were clearly observable as well-defined and abrupt changes in the absorption coefficient. Band gaps of 0.59 and 0.97 ev were obtained for K 2 Bi 8 Se 13 and K 2 Bi 8 S 13, respectively. Figure 4a shows the absorption spectra of the member x 6 with a band gap of 0.64 ev. The incorporation of S in the K 2 Bi 8 Se 13, which is smaller and possesses lower energy atomic orbitals than Se, should lead to wider energy gap by raising the conduction bands and lowering the valence band. This is consistent with the experimental data where the band gaps increase with increasing x values, see Figure 4b. The band gap variation of the solid solutions shows a quadratic dependence [14] on the composition x, which is common in many semiconducting solid solutions: E g z E g,s (1-z) E g,se b z (1-z) E g,se and E g,s are the band gaps for Se- and S-end members, respectively and the fraction z x/13. The factor b, known as bowing factor, is characteristic of a particular solid solution series. Studies on other systems [15] show that the bowing factor is related to the band structure deformation due to the unit cell volume change, the difference in electronegativity of the substituted atoms, the difference of the anioncation bond lengths. The bowing factor here is b 0.44 ev. In our case the K/Bi disorder is also involved [13] in the band gap formation thus in the bowing factor. This behavior is very different from the observed variation in the K 2 Bi 8-x Sb x Se 13 solid solution series where the trend in band gaps showed an anomalous minimum at low Sb concentrations. This is associated with the strong preference of Sb to substitute for specific K-containing sites in the structure essentially avoiding the formation of a solid solution phase. Such strong preferences are not observed in the K 2 Bi 8 Se 13-x S x materials. Conclusions Solid solutions of the type K 2 Bi 8 Se 13-x S x have the β- K 2 Bi 8 Se 13 structure type with same atomic arrangements and disordering behavior. The Se/S distribution was studied 2226 2003 WILEY-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim zaac.wiley-vch.de Z. Anorg. Allg. Chem. 2003, 629, 2222 2228

Studies and Characterization of K 2 Bi 8 Se 13 x S x Solid Solutions Figure 1 (a) Typical DTA of x 10 member (b) Melting points of K 2 Bi 8 Se 13-x S x solid solutions versus x. Figure 3 (a) Powder X-ray diffraction for β-k 2 Bi 8 Se 13 and K 2 Bi 8 S 13. The shift of the peaks is clear especially at higher 2θ angles for K 2 Bi 8 S 13.(b) Unit cell volume in Å 3 of K 2 Bi 8 Se 13-x S x solid solutions versus x. Table 6 Refined unit cell parameters for K 2 Bi 8 Se 13-x S x solid solutions. x a/å b/å c/å β/deg V/Å 3 0 17.581 4.2311 18.521 90.464 1377.7 4 17.356 4.1823 18.365 90.341 1333.0 6 17.300 4.1752 18.269 90.228 1319.3 8 17.131 4.1433 18.112 90.372 1285.5 10 17.084 4.1320 18.014 90.430 1271.6 13 16.941 4.0949 17.842 90.505 1237.6 Figure 2 Structure of K 2 Bi 8 Se 13-x S x solid solutions. for several numbers in detail and the formation of true solid solutions was observed. This is in contrast to the K 2 Bi 8-x Sb x Se 13 solid solutions where the Bi/Sb distribution Z. Anorg. Allg. Chem. 2003, 629, 2222 2228 zaac.wiley-vch.de 2003 WILEY-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim 2227

T. Kyratsi, M. G. Kanatzidis increase with x following a common quadratic variation while the lattice parameters follow Vegard s law. Measurements of charge transport properties and thermal conductivities are in progress and will be reported elsewhere. Acknowledgments. Financial support from the Office of Naval Research (Contract No. N00014-02-1-0867) and ONR-DARPA is gratefully acknowledged. The work made use of the SEM facilities of the Center for Electron Optics at Michigan State University. MGK thanks the Alexander von Humboldt Foundation for a fellowship. Figure 4 (a) Absorption spectrum of K 2 Bi 8 Se 13-x S x for x 6. The band gap is 0.64 ev. (b) Variation of band gap in K 2 Bi 8 Se 13-x S x solid solutions versus is non-uniform particularly at low x. The smaller unit cell size of the solid solutions reduce the size of the tunnels that host the K ions in the original structure allowing Bi atoms to be involved on these sites. At the same time the K fraction rises on a different site (Bi(9)/K(1)) that compensates electronically and maintain charge balance. This situation represents an excellent example of well defined anti site K, Bi defects and could cause profound changes in the electric properties of the solid solutions by creating additional energy levels in the gap. The band gaps of the solid solutions References [1] (a) M. G. Kanatzidis, Semiconductors and Semimetals, 2000, 69, p. 51 (b) D.-Y. Chung, L. Iordanidis, K.-S. Choi, M. G. Kanatzidis, Bull. Kor. Chem. Soc. 1998, 19, 1283. [2] D.-Y. Chung, K.-S. Choi, L. Iordanidis, J. L. Schindler, P. M. Brazis, C. R. Kannewurf, B. Chen, S. Hu, C. Uher, M. G. Kanatzidis, Chem. Mater. 1997, 9, 3060. [3] P. W. Brazis, M. Rocci-Lane, J. R. Ireland, D.-Y. Chung, M. G. Kanatzidis, C. R. Kannewurf, Proceedings of the 18 th International Conference on Thermoelectrics, 619 (1999). [4] Th. Kyratsi, J. S. Dyck, W. Chen, D.-Y. Chung, C. Uher, K. M. Paraskevopoulos, M. G. Kanatzidis, J. Appl. Phys. 2002, 92, 965. [5] Th. Kyratsi, D.-Y. Chung, M. G. Kanatzidis, J. Alloys Compds. 2002, 338, 36. [6] (a) W. W. Wendlandt, H. G. Hecht, Reflectance Spectroscopy; Interscience Publishers: New York, 1966; (b) G. Kortüm, Reflectance Spectroscopy; Springer-Verlag, New York, 1969; (c) S. P. Tandon, J. P. Gupta, Phys. Status Solidi 1970, 38, 363. [7] M. Evain, U-Fit: A cell parameter refinement program, Institut des Materiaux de Nantes, Nantes, France (1992). [8] SMART: 1994, Siemens Analytical X-ray Systems, Inc., Madison, Wisconsin 53719 USA. [9] SAINT: Version 4, 1994-1996, Siemens Analytical Xray Systems, Inc., Madison, Wisconsin 53719 USA. [10] SHELXTL: Version 5, 1994, G. M. Sheldrick, Siemens Analytical X-ray Systems, Inc., Madison, Wisconsin 53719 USA. [11] K 2.5 Bi 8.5 Se 14 can be easily form by the direct combination of the elements while attempts to form the S analogue (K 2.5 Bi 8.5 S 14 ) were not successful. [12] M. G. Kanatzidis, T. J. McCarthy, T. A. Tanzer, L.-H. Chen, L. Iordanidis, T. Hogan, C. R. Kannewurf, C. Uher, B. Chen, Chem. Mat. 1996, 8, 1465. [13] D. Bilc, S. D. Mahanti, M. G. Kanatzidis, P. Larson, submitted for publication. [14] J. A. Van Vechten, T. K. Bergstresser, Phys.Rev.B1970, 1, 3351. [15] (a) M. Ferhat, F. Bechstedt, Phys. Rev. B 2002, 65, 075213; (b) Y.-M. Yu, S. Nam, B. O, K.-S. Lee, Y. D. Choi, J. Lee, P. Y. Yu, Applied Surface Science 2001, 182, 159; (c) R. Venugopal, B. K. Reddy, D. R. Reddy, Opt. Mat. 2001, 17, 483. 2228 2003 WILEY-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim zaac.wiley-vch.de Z. Anorg. Allg. Chem. 2003, 629, 2222 2228