Sb distribution and its consequences in solid solution members of the thermoelectric materials K2Bi8−xSbxSe13

Journal of Alloys and Compounds 388 (2002) 36–42

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Bi / Sb distribution and its consequences in solid solution members of the thermoelectric materials K 2 Bi 82x Sb x Se 13 q a,b a a, Theodora Kyratsi , Duck-Young Chung , Mercouri G. Kanatzidis * a

Department of Chemistry, Michigan State University, East Lansing, MI 48824 -1322, USA Department of Physics, Aristotle University of Thessaloniki, 54006 Thessaloniki, Greece

b

Received 5 October 2001; accepted 26 November 2001

Abstract In an effort to understand the nature of mass fluctuations introduced when b-K 2 Bi 8 Se 13 is alloyed with K 2 Sb 8 Se 13 we determined the detailed crystal structures of two solid solutions of the type K 2 Bi 82x Sb x Se 13 with x54.0 and x52.4. The structure is that of b-K 2 Bi 8 Se 13 which is a promising thermoelectric material with low thermal conductivity. The single crystal structures of K 1.49 Bi 4.72 Sb 3.79 Se 13 and K 1.49 Bi 5.55 Sb 2.97 Se 13 were determined and the Bi / Sb distribution in the structures was examined.  2002 Elsevier Science B.V. All rights reserved. Keywords: Thermoelectrics; Crystal structure; X-ray diffraction

1. Introduction Our investigations of ternary and quaternary compounds of bismuth chalcogenides [1] have shown that several multinary compounds containing alkali metals present promising thermoelectric properties. Alkali metals tend to create structural complexity in the crystal that can lead to complex electronic structure. Additionally, they reside between layers or in tunnels created by covalent frameworks and because they are ionically interacting with the framework, they tend to ‘rattle’ in the respective cages as revealed by their high thermal displacement parameters [2–4]. The structure of b-K 2 Bi 8 Se 13 [5] presents several rare characteristics that include two different interconnected types of Bi / Se blocks, K ions positionally and compositionally disordered with Bi or other K atoms over the same crystallographic sites, and loosely bound K atoms in tunnels. These features seem to be responsible for the low thermal conductivity of this compound (|1.3 W/ m?K). Doping studies [6] on b-K 2 Bi 8 Se 13 have shown that its ZT (for a definition of ZT see Ref. [1]) can be substantially improved, mainly by raising the power factor. A wellknown way to further reduce the thermal conductivity of q

This paper is dedicated to Professor Hugo (Fritz) Franzen. *Corresponding author. Tel.: 11-517-355-9715x174; fax: 11-517353-1793. E-mail address: [email protected] (M.G. Kanatzidis).

materials is to generate solid solutions with other isostructural compounds. In this case a random mass fluctuation is introduced in the crystal lattice that can strongly scatter acoustic phonons. In this work, b-K 2 Bi 8 Se 13 was alloyed with its isostructural K 2 Sb 8 Se 13 analog [5] to produce a series of compounds with the formula K 2 Bi 82x Sb x Se 13 . The Sb / Bi substitution was performed in order to generate extensive mass fluctuations in the lattice of K 2 Bi 8 Se 13 . Our main interest was to study the Bi / Sb distribution in the structure through single crystal X-ray diffraction analysis of selected crystals of K 2 Bi 82x Sb x Se 13 , and to determine whether the K 2 Bi 82x Sb x Se 13 system actually forms solid solutions. A true solid solution would exhibit a random distribution of Sb over all Bi atom sites. Interestingly, as we have discovered in this work, the Bi / Sb distribution is in fact non-uniform and the various metal sites in the structure are disproportionally affected.

2. Experimental

2.1. Synthesis and crystal growth 2.1.1. b -K2 Bi8 Se13 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 under a dry nitrogen atmosphere in a Vacuum Atmospheres Dri-Lab glovebox

0925-8388 / 02 / $ – see front matter  2002 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 02 )00211-6

T. Kyratsi et al. / Journal of Alloys and Compounds 388 (2002) 36 – 42

and flame-sealed at a residual pressure of ,10 24 Torr. The mixture was heated to 850 8C over 12 h and kept there for 1 h, followed by cooling to 450 8C and kept there for 48 h, and cooling to 50 8C at a rate of 215 8C / h. The mixture was annealed at 450 8C for 48 h in order to obtain pure b-K 2 Bi 8 Se 13 phase products.

2.1.2. K2 Sb8 Se13 A mixture of potassium metal (0.376 g, 9.6 mmol), antimony (4.686 g, 38.5 mmol) and selenium (4.938 g, 62.5 mmol) was loaded into a silica tube under a dry nitrogen atmosphere in a Vacuum Atmospheres Dri-Lab glovebox and flame-sealed at a residual pressure of ,10 24 Torr. The mixture was heated to 850 8C over 12 h and kept there for 1 h, followed by cooling to 50 8C at a rate of 215 8C / h. Annealing treatment was unnecessary. 2.1.3. K2 Bi82 x Sb x Se13 Mixtures of b-K 2 Bi 8 Se 13 and K 2 Sb 8 Se 13 in various proportions were loaded into a silica tube and flame-sealed at a residual pressure of ,10 24 Torr. The mixtures were heated to 850 8C over 12 h and kept there for 1 h, followed by cooling to 50 8C at a rate of 215 8C / h. Annealing treatment was unnecessary. For example, K 2 Bi 82x Sb x Se 13 (x54) was prepared by mixing 6 g K 2 Bi 8 Se 13 (2.16 mmol) and 4.492 g K 2 Sb 8 Se 13 (2.16 mmol). Crystals of K 2 Bi 82x Sb x Se 13 (x52.4 and 4.0) were grown with a modified Bridgman technique. They recrystallized in a vertical single-zone furnace, with a temperature gradient |15 8C / cm. The material was placed in a rounded bottom silica tube (9 mm OD), and flamesealed under vacuum (,10 24 Torr). The tube was lowered through the temperature gradient profile with a dropping rate of |0.3 cm / h. 2.2. Electron microscopy Quantitative microprobe analyses and crystal imaging 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.

2.3. Single-crystal X-ray crystallography Intensity data were collected at room temperature on a Bruker SMART Platform CCD diffractometer. The individual frames were measured with an omega rotation of 0.38 and an acquisition time of 40 and 50 s for the single crystals obtained from the member for x54.0 (I) and x52.4 (II), respectively, of K 2 Bi 82x Sb x Se 13 . The SMART [7] software was used for the data acquisition and SAINT [8] for data extraction and reduction. An analytical absorp-

37

tion correction was performed using face indexing and the program XPREP in the SAINT software package, followed by a semi-empirical absorption correction based on symmetrically equivalent reflections with the program SADABS [9]. Structural solution and refinements were successfully done using the SHELXTL [10] package of crystallographic programs. The structures were solved with direct methods. After successful assignments of the high electron density peaks as Bi, K, and Se atoms, the thermal parameters and occupancy on each atomic site were examined. For both compounds, (I) and (II), all Se atom sites were fully occupied with reasonable thermal displacement parameters. The refined occupancies of almost all heavy metal sites, initially assigned to Bi atoms, were significantly low indicating that lighter Sb atoms were also involved in these sites. All metal sites, except Sb(8), were refined with mixed Bi and Sb occupancy. The atom Sb(8), which was in a heavily distorted and highly coordinated environment, was found to be quadruply disordered with three adjacent Sb atoms, Sb(18), Sb(28), and Sb(38). Two other sites were found suitable for K atoms (K(1) and K(2)) based on the observed electron densities. These sites also had several electron density peaks located very closely together. Site K(1) was successfully modeled with disorder involving two additional Sb atoms (Sb(11) and Sb(12)). The K(2) site required the inclusion of two other potassium atoms K(21) and K(22). After successive refinements for the positions and occupancies of all atom sites, reasonable thermal parameters and occupancies for all atoms were obtained, as well as very low residual electron densities. Because of the multiple positional disorder in many atom sites only Bi(1) / Sb(1) to Bi(7) / Sb(7) and all Se atoms were refined anisotropically. The final formulae were refined as K 1.49 Bi 4.72 Sb 3.79 Se 13 for (I) and K 1.49 Bi 5.55 Sb 2.97 Se 13 for (II). In both formulae, there were 31 1 extra Sb / Bi ions and a deficiency of K ions compared to the ideal formulae, K 2 Bi 82x Sb x Se 13 . Extra Sb / Bi 31 ions were also observed with SEM / EDS analysis, K 1.94 Bi 5.37 Sb 3.45 Se 13 for (I) and K 1.73 Bi 6.65 Sb 1.43 Se 13 for (II). Despite attempts to find additional K atoms substituting on Sb / Bi atom site in triply and quadruply disordered sites, it was not possible to sustain stable refinement involving a triply disordered model with Bi, Sb, and K atoms. Therefore, we assume that a certain degree of participation of K atom in the metal sites, Bi / Sb(1)–Bi / Sb(7), accounts for the charge neutrality of the structures. In addition, the possibility of the existence of some distributed vacancies over the metal sites cannot be excluded to make up the extra positive charges in the above formulae. The complete data collection parameters, details of the structure solution and refinements for the compounds are given in Table 1. The fractional coordinates and temperature factors (Ueq ) of all atoms with estimated standard deviations are given in Tables 2 and 3.

T. Kyratsi et al. / Journal of Alloys and Compounds 388 (2002) 36 – 42

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Table 1 Summary of crystallographic data and structural analysis for the compounds (I) (x54.0) and (II) (x52.4) of K 2 Sb x Bi 82x Se 13 solid solution Refined formula Formula weight Crystal habit Crystal size, mm 3 Space group ˚ a, A ˚ b, A ˚ c, A b, deg ˚3 Z; V, A Dcalc , g?cm 23 Temp., K ˚ l (Mo Ka), A Absorption coefficient, mm 21 F(000) umin –umax , deg Index ranges Total reflections collected Independent reflections Refinement method Data / restraints / parameters Final R indices [I . 2s (I)] R indices (all data) Largest diff. peak and hole, e?A23 Goodness-of-fit on F 2

K 1.49 Bi 4.72 Sb 3.79 Se 13 2531.95 Black needle 0.15030.02630.012 P2 1 /m (No. 11) 17.3910(13) 4.1539(3) 18.4237(14) 90.3300(10) 2; 1330.91(17) 6.318 293(2) 0.71069 52.864 2110 3.23–30.44 223#h#24, 25#k#5, 225#l #26 17 640 4305 [R(int)50.0719] Full-matrix least-squares on F 2 4305 / 0 / 151 R 1 50.0363, w R 2 50.0801 R 1 50.0514, w R 2 50.0848 1.756 and 22.824 0.989

3. Results and discussion A detailed single crystal crystallographic analysis was performed on the solid solution K 2 Bi 82x Sb x Se 13 members

K 1.49 Bi 5.55 Sb 2.97 Se 13 2604.52 Black needle 0.03030.00630.004 P2 1 /m (No. 11) 17.418(3) 4.1741(7) 18.419(3) 90.481(2) 2; 1339.1(4) 6.459 293(2) 0.71069 57.128 2164 3.21–23.29 219#h#19, 24#k#4, 220#l #20 11 329 2246 [R(int)50.0391] Full-matrix least-squares on F 2 2246 / 0 / 151 R 1 50.0219, w R 2 50.0570 R 1 50.0278, w R 2 50.0592 1.668 and 21.098 1.095

with x54.0 (I) and 2.4 (II). The purpose of this analysis was to examine if these materials are true solid solutions, i.e. random Sb atom distribution over all Bi sites versus preferential substitution of atomic sites by Sb atoms in the

Fig. 1. The crystal structure of K 2 Bi 82x Sb x Se 13 (x54.0 and 2.4) with atom labeling.

T. Kyratsi et al. / Journal of Alloys and Compounds 388 (2002) 36 – 42

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Table 2 4 ˚ 2 310 3 ), and occupancies for K 2 Sb x Bi 82x Se 13 (I) (x54.0) Atomic coordinates (310 ), equivalent isotropic displacement parameters (A

Bi(1) Sb(1) Bi(2) Sb(2) Bi(3) Sb(3) Bi(4) Sb(4) Bi(5) Sb(5) Bi(6) Sb(6) Bi(7) Sb(7) M(8): Sb(8) Sb(18) Sb(28) Sb(38) K(1) Sb(11) Sb(12) K(2) K(21) K(22) Se(1) Se(2) Se(3) Se(4) Se(5) Se(6) Se(7) Se(8) Se(9) Se(10) Se(11) Se(12) Se(13)

x

y

z

U(eq)

Occupancy

4187(1) 4187(1) 6738(1) 6738(1) 8268(1) 8268(1) 3952(1) 3952(1) 1965(1) 1965(1) 5144(1) 5144(1) 259(1) 259(1) 22320(4) 21989(4) 21978(2) 22166(6) 2505(3) 7698(2) 7940(3) 10 218(2) 9678(10) 9710(30) 4829(1) 3975(1) 3063(1) 21079(1) 3095(1) 2714(1) 5423(1) 6334(1) 8665(1) 9238(1) 772(1) 7766(1) 1080(1)

7500 7500 22500 22500 27500 27500 22500 22500 27500 27500 2500 2500 212 500 212 500 217 500 217 500 217 500 217 500 27500 212 500 212 500 212 500 212 500 212 500 2500 7500 2500 212 500 27500 22500 2500 22500 27500 212 500 27500 27500 212 500

789(1) 789(1) 1239(1) 1239(1) 2197(1) 2197(1) 4772(1) 4772(1) 4532(1) 4532(1) 2501(1) 2501(1) 3880(1) 3880(1) 3276(4) 3106(3) 3299(1) 3486(4) 2341(3) 21999(1) 22186(3) 21541(2) 21728(9) 21370(30) 4045(1) 2238(1) 594(1) 2773(1) 5577(1) 3742(1) 928(1) 2642(1) 21617(1) 93(1) 3216(1) 1483(1) 5377(1)

20(1) 20(1) 19(1) 19(1) 18(1) 18(1) 24(1) 24(1) 21(1) 21(1) 20(1) 20(1) 25(1) 25(1) 21(1) 21(1) 21(1) 21(1) 17(1) 17(1) 17(1) 20(1) 20(1) 20(1) 22(1) 19(1) 25(1) 25(1) 22(1) 23(1) 17(1) 19(1) 25(1) 23(1) 28(1) 24(1) 28(1)

0.646(6) 0.354(6) 0.540(6) 0.460(6) 0.488(6) 0.512(6) 0.912(7) 0.088(7) 0.662(6) 0.338(6) 0.919(7) 0.081(7) 0.554(7) 0.446(7) 0.18 0.21 0.47 0.13 0.49 0.33 0.17 0.78 0.17 0.05 1 1 1 1 1 1 1 1 1 1 1 1 1

structure. The gross structural model is the same as in b-K 2 Bi 8 Se 13 , with slightly smaller unit cell parameters as expected from the smaller Sb atoms involved. 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 3D framework, which creates the needle-like crystal morphology, with tunnels filled with K 1 cations (Fig. 1). The eight different metal atom sites in the lattice were examined for Bi / Sb occupancy. The structures of both (I) and (II) exhibit the same atomic arrangements and disordering behavior. The heavy metal sites (M(1)–(7)) in the NaCland Bi 2 Te 3 -type units with Bi / Sb mixed occupancy are in slightly distorted octahedral coordination environment. M(3), M(2), and M(7) sites seem to be the most preferred sites of Sb substitution. These sites are all highly distorted from the regular octahedral geometry with M–Se distances ˚ ranging from 2.711(1) to 3.221(1) A.

Interestingly both crystals were found to have only two sites, Bi / Sb(4) and Bi / Sb(6), where Bi atoms decidedly dominate (.90%), leading to the least distorted octahedral coordination. These sites appear to be the least impervious to Sb substitution. The M–Se distances for Bi / Sb(4) and Bi / Sb(6) are in the range of 2.861(1)–3.032(1) and ˚ for compound (I) and 2.865(2)– 2.901(1)–2.945(1) A ˚ for compound (II), 3.040(2) and 2.895(2)–2.961(2) A respectively (Table 4, Fig. 1). The M(8) site (or Sb(8) site) serves as a connecting point between the NaCl-type and the Bi 2 Te 3 -type blocks. Unlike in b-K 2 Bi 8 Se 13 where the corresponding site is occupied by both Bi and K atoms, the Sb(8) site almost exclusively appears to be occupied with Sb regardless of x. In this site Sb atoms are disordered over four slightly different positions. These are Sb(8), Sb(18), Sb(28) and Sb(38), which are apart from each other at distances in the ˚ for (I) and 0.565(9)– range of 0.596(6)–0.767(10) A

T. Kyratsi et al. / Journal of Alloys and Compounds 388 (2002) 36 – 42

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Table 3 ˚ 2 310 3 ), and occupancies for K 2 Sb x Bi 82x Se 13 (II) (x52.4) Atomic coordinates (310 4 ), equivalent isotropic displacement parameters (A

Bi(1) Sb(1) Bi(2) Sb(2) Bi(3) Sb(3) Bi(4) Sb(4) Bi(5) Sb(5) Bi(6) Sb(6) Bi(7) Sb(7) M(8): Sb(8) Sb(18) Sb(28) Sb(38) K(1) Sb(11) Sb(12) K(2) K(21) K(22) Se(1) Se(2) Se(3) Se(4) Se(5) Se(6) Se(7) Se(8) Se(9) Se(10) Se(11) Se(12) Se(13)

x

y

z

U(eq)

Occupancy

4189(1) 4189(1) 6739(1) 6739(1) 8271(1) 8271(1) 3945(1) 3945(1) 1958(1) 1958(1) 5149(1) 5149(1) 260(1) 260(1) 22318(5) 22025(4) 21989(2) 22160(5) 2519(4) 7669(2) 7917(3) 10 208(2) 9719(9) 9684(12) 4828(1) 3984(1) 3061(1) 21102(1) 3097(1) 2712(1) 5426(1) 6340(1) 8666(1) 9250(1) 766(1) 7772(1) 1082(1)

7500 7500 22500 22500 27500 27500 22500 22500 27500 27500 2500 2500 212 500 212 500 217 500 217 500 217 500 217 500 27500 212 500 212 500 212 500 212 500 212 500 2500 7500 2500 212 500 27500 22500 2500 22500 27500 212 500 27500 27500 212 500

784(1) 784(1) 1236(1) 1236(1) 2191(1) 2191(1) 4768(1) 4768(1) 4519(1) 4519(1) 2510(1) 2510(1) 3882(1) 3882(1) 3252(7) 3123(3) 3309(2) 3447(3) 2313(4) 22010(2) 22175(3) 21548(2) 21686(8) 21369(12 4049(1) 2248(1) 584(1) 2769(1) 5578(1) 3728(1) 926(1) 2654(1) 21627(1) 100(1) 3219(1) 1482(1) 5364(1)

19(1) 19(1) 19(1) 19(1) 19(1) 19(1) 23(1) 23(1) 20(1) 20(1) 20(1) 20(1) 23(1) 23(1) 14(1) 14(1) 14(1) 14(1) 11(1) 11(1) 11(1) 11(1) 11(1) 11(1) 22(1) 21(1) 25(1) 27(1) 23(1) 22(1) 18(1) 21(1) 28(1) 24(1) 27(1) 23(1) 28(1)

0.805(8) 0.195(8) 0.701(7) 0.299(7) 0.640(7) 0.360(7) 0.939(8) 0.061(8) 0.820(8) 0.180(8) 0.921(8) 0.079(8) 0.720(8) 0.280(8) 0.14 0.26 0.39 0.21 0.49 0.34 0.17 0.67 0.20 0.14 1 1 1 1 1 1 1 1 1 1 1 1 1

U(eq) is defined as one third of the trace of the orthogonalized Uij tensor.

˚ for (II). However, because of this extensive 0.644(7) A spread of the disorder on this site the presence of K in this location cannot be excluded. The M(8) (i.e. Sb(8)) sites in the structure therefore are the most hospitable for Sb ions even at very small values of x. Another hospitable site for Sb ions is the K(1) site which is found mixed occupied with heavier Sb(11) and Sb(12) atoms. This site also serves to connect the NaCl-type blocks to Bi 2 Te 3 -type blocks. There is one other triply disordered site in the structure contains K(2), K(12) and K(22) and is located inside the tunnel made by connecting building blocks. The implications of this crystallographic analysis are that true solid solutions in this system do not exist due to the large number of different metal sites in the structure. The local environments (e.g. size and coordination number) presented by these sites have a strong influence on the type of atoms that are attracted to those sites. This makes it very difficult to create materials with a totally random

distribution of Bi and Sb atoms, in sharp contrast to the well known solid solution system Bi 22x Sbx Te 3 . The reason for being able to prepare true solid solutions in the latter case is the existence of only one crystallographic metal site in the structure. Nevertheless, the presence of extensive Bi / Sb and K / Bi / Sb randomness on some metal sites in the structure of b-K 2 Bi 8 Se 13 is still expected to give K 2 Bi 82x Sb x Se 13 members with lower thermal conductivity than the pure b-K 2 Bi 8 Se 13 phase. Another important insight gleaned from the refinement of the structure of these solid solutions is the uniqueness of the M(8) and K(1) sites. In pristine b-K 2 Bi 8 Se 13 these sites are mixed occupied with K and Bi atoms. As mentioned above, the sites serve as a connection point between the NaCl-type and the Bi 2 Te 3 -type blocks. The latter blocks are covalently bound Bi / Se fragments that are responsible for the semiconducting properties of the material. When K is occupying these connection points, an

T. Kyratsi et al. / Journal of Alloys and Compounds 388 (2002) 36 – 42 Table 4 ˚ for the compound (x54.0) (I) and The selective atomic distances (A) (x52.4) (II) of K 2 Sb x Bi 82x Se 13 solid solution (I) Bi(1)–Se(2) Bi(1)–Se(3) Bi(1)–Se(7) Bi(1)–Se(7) Bi(2)–Se(8) Bi(2)–Se(12) Bi(2)–Se(7) Bi(3)–Se(9) Bi(3)–Se(10) Bi(3)–Se(3) Bi(3)–Se(12) Bi(4)–Se(6) Bi(4)–Se(1) Bi(4)–Se(5) Bi(4)–Se(1) Bi(5)–Se(5) Bi(5)–Se(6) Bi(5)–Se(13) Bi(5)–Se(11) Bi(6)–Se(1) Bi(6)–Se(7) Bi(6)–Se(8) Bi(6)–Se(2) Bi(7)–Se(4) Bi(7)–Se(11) Bi(7)–Se(13) Sb(18)–Se(4) Sb(18)–Se(12) Sb(28)–Se(4) Sb(28)–Se(13) Sb(38)–Se(13) K(1)–Se(9) K(1)–Se(2) K(1)–Se(6) K(1)–Se(3) K(1)–Se(11) Sb(11)–Se(9) Sb(11)–Se(3) Sb(12)–Se(9) Sb(12)–Se(11) K(2)–Se(9) K(2)–Se(4) K(2)–Se(10) K(2)–Se(12) K(2)–Se(11) K(21)–Se(9) K(21)–Se(11) K(21)–Se(10) K(21)–Se(4) K(22)–Se(9) K(22)–Se(10) K(22)–Se(11) K(22)–Se(10)

(II) 2.6975(12) 2.8727(10) 2.9995(10) 3.2392(12) 2.6818(13) 2.7756(9) 3.1400(10) 2.7108(14) 2.7270(9) 3.1911(11) 3.2207(14) 2.8616(14) 2.9090(9) 2.9592(9) 3.0319(14) 2.7431(14) 2.8552(9) 3.0208(10) 3.1819(16) 2.9005(12) 2.9400(12) 2.9420(10) 2.9446(9) 2.6949(14) 2.8136(10) 3.0614(10) 2.685(4) 3.018(5) 2.778(2) 2.888(3) 2.812(8) 3.194(4) 3.300(4) 3.332(4) 3.367(5) 3.428(5) 2.761(2) 2.914(3) 2.643(3) 2.945(5) 3.408(3) 3.427(3) 3.467(4) 3.507(4) 3.525(4) 2.731(11) 2.847(17) 3.444(17) 3.743(14) 2.79(4) 2.82(6) 3.49(6) 3.63(5)

Bi(1)–Se(2) Bi(1)–Se(3) Bi(1)–Se(7) Bi(1)–Se(7) Bi(2)–Se(8) Bi(2)–Se(12) Bi(2)–Se(7) Bi(3)–Se(9) Bi(3)–Se(10) Bi(3)–Se(3) Bi(3)–Se(12) Bi(4)–Se(6) Bi(4)–Se(1) Bi(4)–Se(5) Bi(4)–Se(1) Bi(5)–Se(5) Bi(5)–Se(6) Bi(5)–Se(13) Bi(5)–Se(11) Bi(6)–Se(1) Bi(6)–Se(2) Bi(6)–Se(8) Bi(6)–Se(7) Bi(7)–Se(4) Bi(7)–Se(11) Bi(7)–Se(13) Sb(18)–Se(4) Sb(18)–Se(12) Sb(28)–Se(4) Sb(28)–Se(13) Sb(38)–Se(13) K(1)–Se(9) K(1)–Se(2) K(1)–Se(3) K(1)–Se(6) K(1)–Se(11) Sb(11)–Se(9) Sb(11)–Se(3) Sb(12)–Se(9) Sb(12)–Se(11) K(2)–Se(9) K(2)–Se(4) K(2)–Se(10) K(2)–Se(12) K(2)–Se(11) K(21)–Se(9) K(21)–Se(11) K(21)–Se(10) K(21)–Se(4) K(22)–Se(9) K(22)–Se(10) K(22)–Se(11) K(22)–Se(10)

2.7226(15) 2.8878(11) 3.0095(11) 3.2268(15) 2.7088(16) 2.7904(10) 3.1444(11) 2.7386(17) 2.7457(10) 3.1979(12) 3.2097(17) 2.8652(15) 2.9169(11) 2.9666(11) 3.0397(16) 2.7705(16) 2.8689(11) 3.0241(11) 3.1573(17) 2.8948(15) 2.9474(11) 2.9522(11) 2.9606(15) 2.7284(16) 2.8188(11) 3.0821(12) 2.716(5) 3.040(5) 2.785(3) 2.900(5) 2.873(8) 3.189(5) 3.300(5) 3.330(7) 3.354(5) 3.492(6) 2.802(2) 2.929(3) 2.656(4) 3.005(6) 3.404(4) 3.449(3) 3.476(4) 3.519(4) 3.501(4) 2.781(10) 2.939(15) 3.396(15) 3.771(13) 2.777(14) 2.81(2) 3.49(2) 3.633(18)

ionic interaction occurs and the covalent framework is interrupted causing an electronic disconnection between these two types of blocks. On the other hand, when Bi atoms occupy the connection points, the covalent bonding can extend from one block to the next maintaining the electronic communication throughout the structure. There-

41

fore, these so-called connection points are crucial in defining the electronic properties of these materials and can potentially serve as ‘valves’ by controlling the K / Bi (or in this case Sb) substitution. The substantial filling of the M(8) and K(1) sites with Sb atoms early in the substitution process (i.e. beginning at small x values in K 2 Bi 82x Sb x Se 13 ) helps to explain why the band gap of these materials first decreases with x (up to |1.5) and then increases at higher x values as would normally be expected 1 [11].

4. Concluding remarks The distribution of Sb atoms in the K 2 Bi 82x Sb x Se 13 series with x54.0 and 2.4 is not uniform as would be expected from a true solid solution. The M(8) and K(1) sites are the most accepting of Sb atoms and these are the sites that serve to join the NaCl-type and the Bi 2 Te 3 -type blocks in the structure. In addition, the M(1), M(2), M(3), and M(7) sites also seem to be highly preferred for Sb substitution. By contrast M(4) and M(6) sites are the least likely to accept Sb atoms and here the Bi atoms decidedly dominate. The observed characteristic disordering behavior involving diverse atoms such as K, Sb and Bi, is representative of these compounds and this property may lead to significant flexibility in compositional changes in the K / Bi / Sb ratio in these systems. It is also responsible for the ease in synthesis of pure solid solutions of K 2 Bi 82x Sb x Se 13 . Finally, the variable selectivity of the metal sites in this structure type for Sb atoms and presumably by other metals as well, may in fact be a property that can be profitably exploited in future experiments aimed at modifying the electronic properties of the materials with greater precision and sophistication.

Acknowledgements Financial support from the Office of Naval Research (Contract No. N00014-01-1-0728) is gratefully acknowledged

References [1] M.G. Kanatzidis, Semiconductors Semimetals 69 (2000) 51. [2] A. Mrotzek, D.-Y. Chung, N. Ghelani, T. Hogan, M.G. Kanatzidis, Chem. Eur. J. 7 (9) (2001) 1915. [3] K.-S. Choi, D.-Y. Chung, A. Mrotzek, P. Brazis, C. Kannewurf, C.

1 Given that energy gaps of the end members K 2 Bi 8 Se 13 and K 2 Sb 8 Se 13 are 0.59 and 0.78 eV, respectively [5], increase on the band gap of the K 2 Bi 82x Sb x Se 13 solid solutions with increasing Sb participation would be expected.

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Uher, W. Chen, T. Hogan, M.G. Kanatzidis, Chem. Mat. 13 (3) (2001) 756. [4] A. Mrotzek, D.-Y. Chung, T. Hogan, M.G. Kanatzidis, J. Mater. Chem. 10 (7) (2000) 1667. [5] 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. 9 (12) (1997) 3060. [6] P.W. Brazis, M. Rocci-Lane, J.R. Ireland, D.-Y. Chung, M.G. Kanatzidis, C.R. Kannewurf, in: Proceedings of the 18th International Conference on Thermoelectrics, 1999, p. 619.

[7] SMART, Siemens Analytical Xray Systems, Inc, Madison, WI, USA, 1994. [8] SAINT: Version 4, Siemens Analytical Xray Systems, Inc, Madison, WI, USA, 1994–1996. ¨ [9] G.M. Sheldrick, University of Gottingen, Germany (in press). [10] G.M. Sheldrick, SHELXTL: Version 5, Siemens Analytical Xray Systems, Inc, Madison, WI, USA, 1994. [11] T. Kyratsi, J.S. Dyck, W. Chen, C. Uher, K.M. Paraskevopoulos, M.G. Kanatzidis (submitted for publication).