New members of the homologous series Am[M6Se8]m [M5+nSe9+n]: The quaternary phases A1-xM′3-xBi11+xSe20 and A1+xM′3-2xBi7+xSe14 (A = K, Rb, Cs; M′ = Sn, Pb)

Article abstract of DOI:10.1021/ic010285w

The compounds A_1+xM′_3-2xBi_7+xSe₁₄ and A_1-xM′_3-xBi_11+xSe₂₀ (A = K, Rb, Cs; M′ = Sn, Pb) were discovered from reactions involving A₂Se, Bi₂Se₃, M′, and Se at 760 °C. The single-crystal structures reveal that A_1+xM′_3-2xBi_7+xSe₁₄ are isostructural to K_2.5Bi_8.5Se₁₄ whereas A_1-xM′_3-xBi_11+xSe₂₀ adopt a new structure type. Both compound types belong to the homologous series A_m[M₆Se₈]_m [M_5+nSe_9+n] (M = di- and trivalent metal), whose characteristics are three-dimensional anionic frameworks with tunnels filled with alkali ions. The building units are derived from different sections of the NACI lattice, perpendicular to the [111] (NaCl¹¹¹-type) and [100] (NaCl¹⁰⁰-type) directions, respectively, with dimensions and shapes defined by m and n. The structures of A_1+xM′_3-2xBi_7+xSe₁₄ (m = 2, n = 3) and A_1-xM′_3-xBi_11+xSe₂₀ (m = 1, n = 3) exhibit the same type of stepshaped NACl¹¹¹-type layer but differ in the size of the NaCl¹⁰⁰-type unit. In both structures, the Bi and Sn (Pb) atoms are extensively disordered over the metal sites of the chalcogenide network. The physicochemical and charge transport properties of A_1+xM′_3-2xBi_7+xSe₁₄ and A_1-xM′_3-xBi_11+xSe₂₀ (A = K, Rb, Cs; M′ = Sn, Pb) are reported.

Full text of DOI:10.1021/ic010285w

6204
Inorg. Chem. 2001, 40, 6204-6211
New Members of the Homologous Series Am[M6Se8]m[M5+nSe9+n]: The Quaternary Phases
A1-xM′3-xBi11+xSe20 and A1+xM′3-2xBi7+xSe14 (A ) K, Rb, Cs; M′ ) Sn, Pb)
Antje Mrotzek, Lykourgos Iordanidis, and Mercouri G. Kanatzidis*
Department of Chemistry and Center for Fundamental Materials Research, Michigan State University,
East Lansing, Michigan 48824
ReceiVed March 15, 2001
The compounds A1+xM′3-2xBi7+xSe14 and A1-xM′3-xBi11+xSe20 (A ) K, Rb, Cs; M′ ) Sn, Pb) were discovered
from reactions involving A2Se, Bi2Se3, M′, and Se at 760 °C. The single-crystal structures reveal that
A1+xM′3-2xBi7+xSe14 are isostructural to K2.5Bi8.5Se14 whereas A1-xM′3-xBi11+xSe20 adopt a new structure type.
Both compound types belong to the homologous series Am[M6Se8]m[M5+nSe9+n] (M ) di- and trivalent metal),
whose characteristics are three-dimensional anionic frameworks with tunnels filled with alkali ions. The building
units are derived from different sections of the NaCl lattice, perpendicular to the [111] (NaCl111-type) and [100]
(NaCl100-type) directions, respectively, with dimensions and shapes defined by m and n. The structures of
A1+xM′3-2xBi7+xSe14 (m ) 2, n ) 3) and A1-xM′3-xBi11+xSe20 (m ) 1, n ) 3) exhibit the same type of step-
shaped NaCl111-type layer but differ in the size of the NaCl100-type unit. In both structures, the Bi and Sn (Pb)
atoms are extensively disordered over the metal sites of the chalcogenide network. The physicochemical and
charge transport properties of A1+xM′3-2xBi7+xSe14 and A1-xM′3-xBi11+xSe20 (A ) K, Rb, Cs; M′ ) Sn, Pb) are
reported.
6,7
Introduction
â-K2Bi8Se13 show that these exploratory investigations can
lead to promising thermoelectric materials with promising
There is currently strong interest in developing new physi-
cochemical concepts in designing materials with superior
thermoelectric properties.1-3 Our approach, which has been
outlined in detail elsewhere,4 is focused on complex quaternary
and ternary bismuth chalcogenides with “derivatized” Bi2Te3-
type frameworks. The derivatization is brought about through
the incorporation of alkali metals. The strategy aims to exploit
the beneficial effects of structural complexity and mass fluctua-
tion phonon scattering on the thermopower and thermal
properties. Therefore, we expanded our investigations to qua-
ternary systems to further explore the effects of structural
complexity and mass fluctuation on the physical properties. The
investigation of the systems A/Pb/Bi/Se (A ) K, Rb, Cs, Sr,
Ba, Eu) led to the compounds K1.25Pb3.5Bi7.25Se15,8 RbPbBi3-
Se6, R- and â-CsPbBi3Se6,9 Sr2Pb2Bi6Se13,6 Ba3Pb3Bi6Se15,10
Ba3PbBi6Se13,11 and Eu2Pb2Bi6Se13.6 These phases exhibit an
impressive structural diversity that is characterized by modular
construction achieved by combining fragments excised out of
the Bi2Te3 and NaCl lattices. K1.25Pb3.5Bi7.25Se15 shows promis-
ing thermoelectric properties and belongs to a broad class of
quaternary solids with the general formula A1+xM′4-2xM′′7+xSe15
(A ) K, Rb; M′ ) Pb, Sn; M′′ ) Bi, Sb).8
5,6
conductivity, respectively.4 The examples of CsBi4Te6 and
(1) (a) Slack, G. A. In CRC Handbook of Thermoelectrics; Rowe, D. M.,
Ed.; CRC Press: Boca Raton, 1995; pp 407-440. (b) Slack, G. A. In
Solid State Physics; Ehrenreich, H., Seitz, F., Turnbull, D., Eds.;
Academic: New York, 1997; Vol. 34, p 1. (c) Sales, B. C. Mater.
Res. Bull. 1998, 23, 15-21. (d) Sales, B. C.; Mandrus, D.; Chakou-
makos, B. C.; Keppens, V.; Thompson, J. R.; Phys. ReV. B 1997, 56,
15081-15089. (e) Tritt, T. M. Science 1996, 272, 1276-1277.
(2) (a) Tritt, T. M., Kanatzidis, M. G., Mahan, G. D., Lyon, H. B., Eds.
Thermoelectric Materials 1998sThe Next Generation Materials for
Small-Scale Refrigeration and Power Applications. Mater. Res. Soc.
Symp. Proc. 1998, Vol. 545, see papers in this volume. (b) Tritt, T.
M., Kanatzidis, M. G., Lyon, H. B., Mahan, G. D., Eds. Thermoelectric
MaterialssNew Directions and Approaches. Mater. Res. Soc. Symp.
Proc. 1997, Vol. 478, see papers in this volume.
Recently we also described K1-xSn4-xBi11+xSe21,12 K1-xSn5-x
-
Bi11+xSe22,13 and K1+xSn4-2xBi7+xSe15,8 which have structures
(6) (a) Kanatzidis, M. G.; Chung, D.-Y.; Iordanidis, L.; Choi, K.-S.; Brazis,
P.; Rocci, M.; Hogan, T.; Kannewurf, C. Mater. Res. Soc. Symp. Proc.
1998, 545, 233-246. (b) Bravis, P. W.; Rocci-Lane, M. A.; Ireland,
J. R.; Chung, D.-Y.; Kanatzidis, M. G.; Kannewurf, C. R. Proc. XVIIIth
Int. Conf. Thermoelectrics (ITC ’99), Baltimore, 1999, 619-622.
(7) (a) Kanatzidis, M. G.; McCarthy, T. J.; Tanzer, T. A.; Chen, L.-H.;
Iordanidis, L.; Hogan, T.; Kannewurf, C. R.; Uher, C.; Chen, B. Chem.
Mater. 1996, 8, 1465-1474. (b) Chen, B.; Uher, C.; Iordanidis, L.;
Kanatzidis, M. G. Chem. Mater. 1997, 9, 1655-1658.
(8) Choi, K.-S.; Chung, D.-Y.; Mrotzek, A.; Brazis, P.; Kannewurf, C.
R.; Uher, C.; Chen, W.; Hogan, T.; Kanatzidis, M. G. Chem. Mater.
2001, 13, 756-764.
(9) Chung, D.-Y.; Iordanidis, L.; Rangan, K. K.; Brazis, P. W.; Kannewurf,
C. R.; Kanatzidis, M. G. Chem. Mater. 1999, 11, 1352-1362.
(10) Iordanidis, L.; Kanatzidis, M. G. To be published.
(3) CRC Handbook of Thermoelectrics; Rowe, D. M., Ed.; CRC Press:
Boca Raton, 1995. (b) Hicks, L. D.; Dresselhaus, M. S. Phys. ReV. B
1993, 47, 12727-12731. (c) Hicks, L. D.; Dresselhaus, M. S. Phys.
ReV. B 1993, 47, 16631-16634. (d) Hicks, L. D.; Harmann, T. C.;
Dresselhaus, M. S. Appl. Phys. Lett. 1993, 63, 3230-3232. (e) Broido,
D. A.; Reinecke, T. L. Appl. Phys. Lett. 1995, 67, 1170-1171. (f)
Sofo, J. O.; Mahan, G. D. Appl. Phys. Lett. 1994, 65, 2690-2692.
(4) (a) Kanatzidis, M. G.; DiSalvo, F. J. ONR Q. ReV. 1996, 27, 14-22.
(b) Chung, D.-Y.; Iordanidis, L.; Choi, K.-S.; Kanatzidis, M. G. Bull.
Korean Chem. Soc. 1998, 19, 1283-1293. (c) Kanatzidis, M. G.
Semicond. Semimet. 2001, 69, 51-100.
(11) (a) Wang, Y.-C.; DiSalvo, F. J. Chem. Mater. 2000, 12, 1011-1017.
(b) Iordanidis, L.; Bravis, P. W.; Kannewurf, C. R.; Kanatzidis, M.
G. Mater. Res. Soc. Symp. Proc. 1998, 545, 189-196.
(12) Mrotzek, A.; Chung, D.-Y.; Hogan, T.; Kanatzidis, M. G. J. Mater.
Chem. 2000, 10, 1667-1672.
(5) Chung, D.-Y.; Hogan, T.; Brazis, P. W.; Rocci-Lane, M.; Kannewurf,
C. R.; Bastea, M.; Uher, C.; Kanatzidis, M. G. Science 2000, 287,
1024-1027.
(13) Mrotzek, A.; Chung, D.-Y.; Ghelani, N.; Hogan, T.; Kanatzidis, M.
G. Chem. Eur. J. 2001, 7, 1915-1926.
10.1021/ic010285w CCC: $20.00 © 2001 American Chemical Society
Published on Web 10/26/2001

New Members of the Series Am[M6Se8]m[M5+nSe9+n
]
Inorganic Chemistry, Vol. 40, No. 24, 2001 6205
further cooled to 50 °C in 11 h. The product consisted of a silvery
chunk with needles growing across its surface. Rb1-xSn3-xBi11+xSe20
is the major phase with a second minor unidentified phase. Pure material
can be made as follows: A mixture of 0.014 g (0.056 mmol) of Rb2-
Se, 0.500 g (0.763 mmol) of Bi2Se3, 0.026 g (0.219 mmol) of Sn, and
0.017 g (0.215 mmol) of Se was transferred into a carbon-coated silica
tube. The tube was placed under the flame of a natural gas-oxygen
torch until the mixture melted, and then the tube was removed from
the flame and allowed to solidify. A quantitative microprobe analysis
with a SEM/EDS system performed on different crystals gave the
following average composition: Rb0.7Sn3.2Bi11.5Se20.
Physical Measurements. Electron Microscopy. Quantitative micro-
probe analyses of the compounds were performed with a JEOL JSM-
35C SEM equipped with a Tracor Northern EDS detector. Data were
acquired using an accelerating voltage of 25 kV and a 60 s accumulation
time. The quantitative microprobe analyses have a standard deviation
of about 2-5%.
closely related to each other and to those of â-K2Bi8Se13 and
K2.5Bi8.5Se14.14 They are all members of a newly identified grand
12
homologous series Am[M6Se8]m[M5+nSe9+n
]
(M ) di- and
trivalent metal) in both a compositional and structural sense.
Their structures are composed of [M5+nSe9+n] (NaCl111-type)
and [M6Se8]m (NaCl100-type) units15 of variable dimensions
defined by n and m, which link to produce anionic frameworks
with alkali metal (Am) filled tunnels. The existence of the
homologous series was recognized after these compounds were
discovered and structurally characterized. The series however
has predictive properties, and here we describe several new
members that in fact were targeted for synthesis based on the
general formula Am[M6Se8]m[M5+nSe9+n] with m ) 2, n ) 3
and m )1, n ) 3. We report on the crystal structure and charge
transport properties of K1+xSn3-2xBi7+xSe14, K1+xPb3-2xBi7+xSe14,
Cs1+xSn3-2xBi7+xSe14, Cs1+xPb3-2xBi7+xSe14, K1-xSn3-xBi11+xSe20,
K1-xPb3-xBi11+xSe20, Rb1-xSn3-xBi11+xSe20, Rb1-xPb3-xBi11+xSe20,
Cs1-xSn3-xBi11+xSe20, and Cs1-xPb3-xBi11+xSe20 and discuss
their relationship to the known members of the Am[M6Se8]m-
[M5+nSe9+n] series.
Differential Thermal Analysis. Differential thermal analysis (DTA)
was performed with a computer-controlled Shimadzu DTA-50 thermal
analyzer as described earlier.12 The samples were heated to 900 °C at
10 °C/min and kept at this temperature (isothermed) for 5 min followed
by cooling at -10 °C/min to 50 °C.
Infrared Spectroscopy. Diffuse reflectance spectra were recorded
in the region 6000-400 cm-1 with the use of a Nicolet MAGNA-IR
750 spectrometer equipped with a collector diffuse reflectance accessory
from Spectra-Tech, Inc. Band gaps were obtained as described
elsewhere.7
Charge Transport Measurements. Room temperature conductivity
measurements were performed in the usual four-probe geometry. The
Seebeck coefficient was measured between 300 and 400 K by using a
SB-100 Seebeck effect measurement system, MMR Technologies, Inc.
Powder X-ray Diffraction. Powder patterns of all starting materials
and products were obtained using a CPS 120 INEL X-ray powder
diffractometer equipped with a position-sensitive detector and graphite-
monochromated Cu KR radiation. The purity and homogeneity were
confirmed by comparing the X-ray powder diffraction pattern to that
calculated from single-crystal data using the CERIUS2 software.16
Experimental Section
Synthesis. All manipulations were carried out under a dry nitrogen
atmosphere in a Vacuum Atmospheres Dri-Lab glovebox. The starting
material Bi2Se3 was obtained by reaction of stoichiometric amounts of
the elements (99.999% purity) in evacuated quartz glass ampules at
800 °C for 3 days. The alkali selenide A2Se (A ) K, Rb, Cs) was
prepared by stoichiometric reaction of alkali metal and selenium in
liquid ammonia.
A1+xM′3-2xBi7+xSe14 (A ) K, Cs; M′ ) Sn, Pb). A mixture of A2-
Se (1 mmol), M′ (7 mmol), Se (7 mmol), and Bi2Se3 (7 mmol) was
loaded in a carbon-coated quartz tube (9 mm diameter) and sealed at
a residual pressure of <10-4 Torr. The starting materials were heated
within 24 h to 800 °C and kept there for 24 h, followed by slow cooling
to 50 °C at a rate of 0.5 °C/min. A silver, shiny, polycrystalline ingot
of pure A1+xM′3-2xBi7+xSe14 was obtained after washing any impurities
with dimethylformamide (DMF), methanol, and diethyl ether. A
quantitative microprobe analysis with a SEM/EDS system performed
Single-Crystal X-ray Crystallography. Single crystals of K1.40Sn2.20
-
Bi7.40Se14, K0.70Sn2.70Bi11.30Se20, Rb0.36Sn2.36Bi11.64Se20, and Cs0.46Sn2.46
-
Bi11.54Se20 were mounted on the tip of a glass fiber. The intensity data
were collected on a Bruker SMART Platform CCD diffractometer with
graphite-monochromatized Mo KR radiation and the SMART software17
for data acquisition. The extraction and reduction of the data were
performed with the program SAINT.18 The observed systematic
absences led in each case to the space group P21/m. For the data sets
of K1.40Sn2.20Bi7.40Se14, K0.70Sn2.70Bi11.30Se20, and Cs0.46Sn2.46Bi11.54Se20
an analytical absorption correction was performed using the program
XPREP19 followed by a semiempirical absorption correction based on
symmetrically equivalent reflections with the program SADABS.20 Only
on different crystals gave the following average compositions: K1.8
Sn2.1Bi7.8Se14, K1.6Pb2.3Bi8.0Se14, Cs1.1Sn1.9Bi7.9Se14, and Cs1.0Sn2.7Bi7.6
Se14, respectively.
-
-
A1-xM′3-xBi11+xSe20 (A ) K, Rb, Cs; M′ ) Sn, Pb). A mixture of
A2Se (1 mmol), M′ (3 mmol), Se (3 mmol), and Bi2Se3 (5.5 mmol)
was loaded in a carbon-coated quartz tube (9 mm diameter) and sealed
at a residual pressure of <10-4 Torr. The starting materials were heated
within 12 h to 800 °C and kept there for 24 h, followed by slow cooling
to 400 °C at a rate of 0.1 °C/min and then to 50 °C in 10 h. A silver,
shiny, polycrystalline ingot of A1-xM′3-xBi11+xSe20 was obtained after
washing any impurities with dimethylformamide (DMF), methanol, and
diethyl ether. A quantitative microprobe analysis with a SEM/EDS
system performed on different crystals gave the following average
compositions: K0.9Sn2.7Bi10.9Se20, K0.7Pb2.8Bi11.1Se20, Rb1.0Pb3.5Bi11.4Se20,
Cs0.8Sn3.1Bi11.3Se20, and Cs0.7Pb3.5Bi10.6Se20, respectively.
a semiempirical absorption correction was done for Rb0.36Sn2.36Bi11.64
-
Se20. The crystal structures were solved with direct methods (SHELXS-
9719) and refined using the SHELXTL package of crystallographic
programs.19
K1.40Sn2.20Bi7.40Se14. Twenty-seven crystallographically indepen-
dent positions (Bi1-8, Sn1-2, Se1-14 and K1-3) were found situated
1
3
on mirror planes (y ) /4 and /4). The structure refinement revealed
unusually high thermal displacement parameters for the Bi2, Bi5-7
sites which introduced a disorder model with mixed Bi/Sn occupancies
in the same crystallographic site. The refinement resulted in 14% Sn
in the Bi2 site, 13% Sn in the Bi5 site, 16% Sn in the Bi6 site, and
17% in the Bi7 site. High thermal displacement parameters of the
Sn1-2 sites indicated less electron density than calculated. This led to
Rb1-xSn3-xBi11+xSe20. Initially the compound was synthesized the
following way: A mixture of 0.040 g (0.160 mmol) of Rb2Se, 0.734 g
(1.118 mmol) of Bi2Se3, 0.038 g (0.320 mmol) of Sn, and 0.025 g
(0.317 mmol) of Se was transferred into a carbon coated silica tube,
which was flame-sealed under vacuum. The tube was heated to 760
°C in 24 h, kept at 760 °C for 3 days, cooled to 450 °C in 60 h, and
(14) Chung, D.-Y.; Choi, K.-S.; Iordanidis, L.; Schindler, J. L.; Brazis, P.
W.; Kannewurf, C. R.; Chen, B.; Hu, S.; Uher, C.; Kanatzidis, M. G.
Chem. Mater. 1997, 9, 3060-3071.
(16) CERIUS2, version 1.6; Molecular Simulations, Inc.: Cambridge,
England, 1994.
(17) SMART; Siemens Analytical X-ray Systems Inc.: Madison, WI, 1996.
(18) SAINT V-4; Siemens Analytical X-ray Systems Inc.: Madison, WI,
1994-1996.
(19) Sheldrick, G. M. SHELXTL V-5; Siemens Analytical X-ray Systems
Inc.: Madison, WI, 1994.
(15) (a) NaCl111 is meant to indicate that this fragment derives from cutting
the NaCl lattice perpendicular to the [111] direction. NaCl100 refers
to a section of the NaCl lattice derived from a cut perpendicular to
the [100] direction. (b) In a previous publication,13 we addressed the
(NaCl111) and (NaCl100) fragments as Bi2Te3-type and NaCl-type,
respectively. We now realize this may be inadequate for large values
of n.
(20) SADABS V-4; Siemens Analytical X-ray Systems Inc.: Madison, WI,
1994-1996.

6206 Inorganic Chemistry, Vol. 40, No. 24, 2001
Mrotzek et al.
Table 1. Summary of Crystallographic Data and Structural Analysis
chemical formula
fw
space group (No.)
a, Å
b, Å
c, Å
K1.40Sn2.20Bi7.40Se14
2967.75
P21/m
17.402(2)
4.2054(6)
21.227(3)
109.524(2)
2; 1464.1(4)
6.732
K0.70Sn2.70Bi11.30Se20
4288.51
P21/m
16.139(2)
4.1470(5)
17.009(2)
116.881(2)
1, 1015.4(2)
7,013
Rb0.36Sn2.36Bi11.64Se20
4322.60
P21/m
16.038(2)
4.1540(6)
17.028(3)
116.517(2)
1, 1015.1(3)
7.071
Cs0.46Sn2.46Bi11.54Se20
4343.95
P21/m
16.100(3)
4.1360(8)
17.077(3)
116.79(3)
1, 1015.1(3)
7.106
â, deg
Z; V, Å3
Dcalcd, g cm-3
temp, °C
25
25
27
25
λ(Mo KR), Å
µ(Mo KR), cm-1
R1/wR2,a %
0.71073
63.734
3.56/6.40
0.71073
68.385
3.20/5.39
0.71073
70.021
5.40/14.68
0.71073
69.633
5.26/11.19
2
2
a R1 ) ∑||Fo| - |Fc||/∑|Fo|, wR2 ) {∑[w(Fo - Fc2)2]/∑[w(Fo )2]}1/2
.
Table 2. Fractional Atomic Coordinates (y ) 0.25) and Equivalent
Table 3. Fractional Atomic Coordinates (y ) 0.25) and Equivalent
Atomic Displacement Parameter (Ueq) Values in 10-3 Å2 for
Atomic Displacement Parameter (Ueq) Values in 10-3 Å2 for
K1.40Sn2.20Bi7.40Se14 with Estimated Standard Deviations in
K0.70Sn2.70Bi11.30Se20 with Estimated Standard Deviations in
Parentheses
Parentheses
a
a
x
z
occupancy
Ueq
x
z
occupancy
Ueq
Bi1
Bi2/Sn2′
Bi3
0.09141(3)
0.71973(3)
0.47670(3)
0.33756(3)
0.08145(3)
0.12573(3)
0.88949(3)
0.66445(2)
0.82947(8)
0.8678(9)
0.98618(3)
0.06218(3)
0.90710(3)
0.13971(3)
0.72984(3)
0.38501(3)
0.42845(3)
0.48219(3)
0.78941(8)
0.8089(9)
1
19.8(1)
18.4(1)
18.0(1)
20.1(1)
16.6(1)
15.1(1)
15.3(1)
18.8(1)
37.5(4)
37.5
Bi1
0.61134(5) 0.08257(4)
1
22.0(1)
21.2(2)
18.7(2)
22.5(2)
27.1(2)
21.7(2)
38.4(5)
135(11)
20.4(3)
21.0(4)
19.8(3)
20.3(3)
36.9(4)
21.5(4)
17.2(3)
22.6(4)
18.1(3)
20.0(3)
0.862(1)/0.138
1
1
0.870(1)/0.130
0.841(1)/0.159
0.829(1)/0.171
1
0.771(1)
0.229
0.830(1)
0.170
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Bi2/Sn2′ 0.14917(5) 0.73635(4) 0.960(5)/0.040
Bi3/Sn3′ 0.08980(5) 0.45083(4) 0.962(5)/0.038
Bi4/Sn4′ 0.67808(5) 0.36766(4) 0.973(5)/0.027
Bi5/Sn5′ 0.18244(6) 0.24181(4) 0.766(5)/0.234
Bi6/Sn6′ 0.89378(5) 0.00127(4) 0.885(5)/0.115
Sn1/Bi1′ 0.59625(9) 0.78650(8) 0.896(5)/0.104
Bi4
Bi5/Sn5′
Bi6/Sn6′
Bi7/Sn7′
Bi8
Sn1
K1
Sn2
K2
K3
Se1
Se2
Se3
Se4
Se5
Se6
Se7
Se8
Se9
K1
0.490(1)
0.502(1)
0.35(1)
Se1
Se2
Se3
Se4
Se5
Se6
Se7
Se8
Se9
Se10
0.4186(1)
0.8178(1)
0.9429(1)
0.2850(1)
0.4950(1)
0.3514(1)
0.8856(1)
0.6905(1)
0.9741(1)
0.2343(1)
0.04448(9)
0.1391(1)
0.67410(9)
0.50409(9)
0.3323(1)
0.77551(9)
0.40700(9)
0.6822(1)
0.88813(9)
0.10949(9)
1
1
1
1
1
1
1
1
1
1
0.34162(8)
0.336(1)
0.5778(2)
0.69010(7)
0.721(1)
0.6441(2)
31.3(4)
31.3
37.2(9)
18.6(3)
26.1(4)
15.3(3)
19.9(3)
18.8(3)
19.0(3)
23.0(3)
19.9(3)
19.5(3)
29.3(4)
20.4(3)
15.4(3)
21.8(3)
20.5(3)
0.01824(7)
0.78769(8)
0.40080(7)
0.17055(8)
0.63385(7)
0.54799(7)
0.28434(8)
0.02976(7)
0.81127(7)
0.57368(9)
0.77947(7)
0.99300(7)
0.21553(7)
0.42291(7)
0.08557(6)
0.93938(8)
0.01565(6)
0.87413(7)
0.15803(6)
0.80265(6)
0.24668(7)
0.25356(7)
0.29345(7)
0.34801(7)
0.63749(7)
0.58576(6)
0.55302(7)
0.49053(7)
a Ueq is defined as one-third of the trace of the orthogonalized Uij
tensor.
Table 4. Fractional Atomic Coordinates and Equivalent Atomic
Displacement Parameter (Ueq) Values in 10-3 Å2 for
Rb0.36Sn2.36Bi11.64Se20 with Estimated Standard Deviations in
Parentheses
Se10
Se11
Se12
Se13
Se14
a
x
y
z
occupancy
Ueq
a Ueq is defined as one-third of the trace of the orthogonalized Uij
tensor.
Bi1
Bi2
Bi3
Bi4
0.61199(5)
0.25 0.08172(5)
1
1
1
1
21.0(2)
20.0(2)
17.2(2)
21.8(2)
0.85144(5) -0.25 0.26356(5)
0.09208(5) -0.75 0.45219(5)
0.32303(5) -0.25 0.63387(5)
a disorder model with mixed Sn/K occupancies in the Sn1-2 sites.
The presence of high remaining electron density near these sites
introduced a split model for the Sn1-2 sites with the sum of the
occupancies constrained to be 1 (fully occupied) for a split position.
The refinement resulted in the following occupancies: 77% and 23%
for the Sn1 and K1 site, respectively, 83% and 17% for the Sn2 and
K2 site, respectively. This leads to the general charge balanced formula
Bi5/Sn5′ 0.82202(7) -0.25 0.76185(7) 0.775(3)/0.225 27.6(3)
Bi6/Sn6′ 0.89463(7) -0.75 0.00224(6) 0.686(3)/0.314 21.7(3)
Sn1/Bi1′ 0.6000(1) -0.75 0.7854(1) 0.644(3)/0.356 43.2(4)
Rb1
Se1
Se2
Se3
Se4
Se5
Se6
Se7
Se8
Se9
Se10
0.498(1)
0.4180(2)
0.8197(2)
0.25 0.502(1)
0.25 0.0453(1)
0.25 0.1399(1)
0.182(5)
113(12)
19.1(4)
19.2(4)
17.2(4)
18.8(4)
46.6(8)
20.4(5)
15.2(4)
23.4(5)
20.1(4)
21.1(4)
1
1
1
1
1
1
1
1
1
1
0.0593(1) -0.25 0.3272(1)
0.2878(1) -0.75 0.5060(1)
0.5080(2) -0.25 0.6672(2)
0.6481(2) -0.25 0.2233(1)
0.8851(1) -0.75 0.4068(1)
0.6938(2) -0.75 0.6825(2)
0.0245(1) -0.25 0.1112(1)
0.7644(2) -0.25 0.8907(1)
K
1+xSn3-2xBi7+xSe14 assuming the formal charges of K+, Sn2+, Bi3+
,
and Se2-. After anisotropic refinement the R1 and wR2 values dropped
to 3.6% and 6.4%, respectively. The results of the structure refinements
and other crystallographic data are given in Tables 1, 2, and 6.
K0.70Sn2.70Bi11.30Se20. Eighteen crystallographically independent posi-
tions (Bi1-6, Sn1, Se1-10 and K1) were found situated on mirror
1
3
planes (y ) /4 and /4). The structure refinement revealed relatively
high thermal displacement parameters for the Bi2-6 sites, which
introduced a disorder model with mixed Bi/Sn occupancies for these
sites. The refinement resulted in small but significant amounts (between
2% and 4%) of Sn in the Bi2-4 sites. Sn is accumulated in the Bi5
and Bi6 sites with 23% Sn and 11% Sn, respectively. An unusual
thermal displacement parameter of the Sn1 site indicated higher electron
density in this site which led to a mixed-occupancy model between Sn
a Ueq is defined as one-third of the trace of the orthogonalized Uij
tensor.
and Bi. The refinement converged at 10% Bi in the Sn1 site. The
thermal displacement parameter of the K1 site remained high with 135
Å2 even after the refinement of the occupancy of this site that converged
1
to 0.35(1), i.e., equal to about /3 occupied. This leads to the general

New Members of the Series Am[M6Se8]m[M5+nSe9+n
]
Inorganic Chemistry, Vol. 40, No. 24, 2001 6207
Table 5. Fractional Atomic Coordinates (y ) 0.25) and Equivalent
Atomic Displacement Parameter (Ueq) Values in 10-3 Å2 for
Cs0.46Sn2.46Bi11.54Se20 with Estimated Standard Deviations in
Parentheses
a
x
z
occupancy
Ueq
Bi1
Bi2
Bi3
Bi4
Bi5/Sn5′
Bi6/Sn6′
Sn1
Bi1′
Cs1
Se1
Se2
Se3
Se4
Se5
Se6
Se7
Se8
Se9
Se10
0.61230(6)
0.14887(6)
0.09146(6)
0.67817(6)
0.18104(9)
0.89449(8)
0.6037(2)
0.5850(5)
0.4975(6)
0.4189(2)
0.8192(2)
0.9398(2)
0.2865(2)
0.4934(2)
0.3495(2)
0.8853(2)
0.6915(2)
0.9740(2)
0.2345(2)
0.08062(6)
0.73650(5
0.45149(5)
0.36466(6)
0.23897(9)
0.00216(7)
0.7980(2)
0.7614(4)
0.4985(6)
0.0458(2)
0.1392(1)
0.6723(1)
0.5077(2)
0.3277(4)
0.7768(2)
0.4064(1)
0.6856(2)
0.8884(2)
0.1081(2)
1
1
1
1
16.7(2)
13.7(2)
12.0(2)
18.1(2)
28.6(3)
21.7(2)
21.8(6)
21.8
0.737(2)/0.263
0.830(2)/0.170
0.798(2)
0.202
0.230(7)
91(6)
1
1
1
1
1
1
1
1
1
1
16.0(5)
13.7(5)
13.4(5)
16.0(5)
67.7(2)
17.0(5)
10.6(4)
30.3(7)
18.6(5)
24.4(6)
Figure 1. ORTEP representation of the structure of K1.40Sn2.20Bi7.40
-
Se14 with atom labeling.
a Ueq is defined as one-third of the trace of the orthogonalized Uij
tensor.
charge-balanced formula K1-xSn3-xBi11+xSe20 assuming the formal
charges of K+, Sn2+, Bi3+, and Se2-. After anisotropic refinement the
R1 and wR2 values dropped to 3.2% and 5.4%, respectively. The results
of the structure refinement and other crystallographic data are given in
Tables 1 and 3.
Rb0.36Sn2.36Bi11.64Se20. The structure was refined with the model of
K1-xSn3-xBi11+xSe20 as a starting point. Even though Sn was introduced
in all the bismuth sites, only sites Bi5 through Bi7 contained statistically
significant amounts of Sn. All atoms were refined anisotropically to
the final R values, R1 ) 5.4%, wR2 ) 14.7%. The results of the
structure refinements are given in Table 1. The fractional atomic
coordinates and equivalent isotropic displacement parameters are listed
in Table 4.
Cs0.46Sn2.46Bi11.54Se20. The structure was refined with the model of
K1-xSn3-xBi11+xSe20 as a starting point. Only sites Bi5 through Bi7 and
Figure 2. ORTEP representation of the structure of K0.70Sn2.70Bi11.30
-
Sn1 contained statistically significant amounts of Sn and Bi, respec-
tively. High remaining electron density (8.10 e/Å3) close to the Sn1
site led to a splitting of the mixed occupied site into two distinct
positions. Anisotropic refinement dropped the final R values to R1 )
5.3%, wR2 ) 11.2%. The results of the structure refinements are given
in Table 1. The fractional atomic coordinates and equivalent isotropic
displacement parameters are listed in Table 5. Selected interatomic
distances for all compounds can be found within the Supporting
Information.
Se20 with atom labeling.
resemble a cut out of a Bi2Te3-type layer. Condensation of these
units via one octahedron edge results in a step-shaped layer of
the formula [M5+nSe9+n] (n ) 3). The distorted Bi-octahedra
have interatomic distances ranging from 2.74 to 3.20 Å for K1.40
Sn2.20Bi7.40Se14, 2.74-3.11 Å for K0.70Sn2.70Bi11.30Se20, 2.76-
3.09 Å for Rb0.36Sn2.36Bi11.64Se20, and 2.75-3.08 Å for Cs0.46
Sn2.46Bi11.54Se20. The distances reflect the different extent of
Sn/Bi disorder in the step-shaped layers of these compounds.
While in K1.40Sn2.20Bi7.40Se14 only position Bi2 contains a
considerable amount of Sn (11%), mixed occupancies are found
for Bi3, Bi4 in K0.70Sn2.70Bi11.30Se20, although the fraction of
Sn is small, varying from 2.7% to 4.0% Sn. The fraction of Sn
-
-
Results and Discussion
Structure Description. The quaternary phases A1-xM′3-x
Bi11+xSe20 (A ) K, Rb, Cs; M′ ) Sn, Pb) crystallize in a new
structure type while A1+xM′3-2xBi7+xSe14 adopts the K2.5Bi8.5
-
-
Se14 structure type.14 These compounds belong to the homolo-
gous series Am[M6Se8]m[M5+nSe9+n] (M ) Bi, Sn or Pb) with
n ) 3 and m ) 1 and 2, respectively. Figures 1 and 2 show a
[010] projection of their structures displaying distinct building
units of the NaCl111-type and NaCl100-type, that are derived from
the NaCl lattice as a (111) and a (100) cut, respectively. These
units, which are highlighted in Figure 3, are infinitely long in
the b-direction. They are linked side by side so as to form a
three-dimensional anionic framework with partially alkali filled
tunnels running along the b-axis.
in these sites is negligible in Rb0.36Sn2.36Bi11.64Se20 and Cs0.46
Sn2.46Bi11.54Se20.
-
The two structure types differ in the size of the [M6Se8] units
that link the stepped [M5+nSe9+n] layers (n ) 3) via MSe
interactions (M ) Bi, Sn (Pb)) to a three-dimensional frame-
work. In A1-xM′3-xBi11+xSe20 (A ) K, Rb, Cs; M′ ) Sn, Pb)
these blocks are three M octahedra wide and one octahedron
high and therefore very similar to those found in A1-xM′4-x
-
12
Bi11+xSe21 and K1-xSn5-xBi11+xSe22.13 All metal positions in
this block show mixed Bi/M′ occupancy for A1-xM′4-xBi11+xSe21.
In contrast, in K1+xSn3-2xBi7+xSe14 the corresponding [M6Se8]
units are two M octahedra high in the direction perpendicular
Figure 3 compares both structure types which possess the
same [M8Se12] NaCl111-type unit (see boxed area) that are four
Bi-octahedra thick and two Bi-octahedra high and therefore
to the NaCl111-type layers. Here the outer surface of the NaCl100
-

6208 Inorganic Chemistry, Vol. 40, No. 24, 2001
Table 6. Selected Distances in Å for K1.40Sn2.20Bi7.40Se14
Mrotzek et al.
a
Bi1
Bi4
Bi7
-Se1
2.805(2)
2.9051(9)
3.020(1)
3.122(2)
2.724(2)
2.8734(9)
3.090(1)
3.175(2)
2.731(1)
2.898(1)
3.018(1)
3.221(1)
Bi2
Bi5
Bi8
-Se4 × 2
-Se5
2.8581(9)
2.899(2)
3.0388(9)
3.202(2)
2.929(1)
2.935(1)
2.957(1)
2.961(1)
2.757(2)
2.767(1)
3.223(1)
3.235(1)
Bi3
Bi6
Sn1
-Se5 × 2
-Se6
2.8734(9)
2.880(2)
3.015(2)
3.0525(9)
2.732(1)
2.810(1)
3.152(1)
3.382(2)
0.66(1)
2.814(1)
3.047(2)
3.494(2)
3.570(2)
3.717(1)
0.69(2)
-Se1 × 2
-Se2 × 2
-Se4
-Se3 × 2
-Se3
-Se2
-Se3 × 2
-Se7
-Se12
-Se8
-Se6 × 2
-Se2 × 2
-Se3
-Se4
-Se11 × 2
-Se12 × 2
-Se13
-Se8 × 2
-Se9 × 2
-Se10
-Se9
-K1
-Se13 × 2
-Se12 × 2
-Se12
-Se14 × 2
-Se13 × 2
-Se11
-Se7 × 2
-Se11
-Se2
-Se8 × 2
-Se1 × 2
-Sn2
K1
K3
-Sn1
0.66(1)
3.23(1)
3.28(1)
3.31(1)
3.44(1)
3.49(2)
3.420(3)
3.441(3)
3.466(3)
3.544(3)
3.559(4)
3.573(4)
Sn2
-K2
0.69(2)
K2
-Se1 × 2
-Se7 × 2
-Se8 × 2
-Se11
-Se10 × 2
2.836(2)
3.002(2)
3.499(2)
3.588(2)
3.752(2)
-Se5 × 2
-Se9 × 2
-Se10 × 2
-Se13
3.23(1)
3.25(1)
3.25(1)
3.47(2)
-Se13
-Se9 × 2
-Se6
-Se2
-Se5 × 2
-Se6
3.52(2)
-Se10 × 2
-Se7 × 2
-Se14
-Se14 × 2
-Se11
-Se6
a Because of the mixed Bi/Sn occupancy on several metal sites, these distances represent only average values.
Figure 3. Comparison between two homologues to show close relationship. (A) A larger section of the structure of K1.40Sn2.20Bi7.40Se14 viewed
down the b-axis. (B) The structure of K0.70Sn2.70Bi11.30Se20 viewed down the b-axis. Small white spheres: Se. Large light-gray spheres: K. Middle-
gray spheres: Bi. Dark-gray spheres: Sn. The archetypal NaCl111-type and NaCl100-type building units are highlighted in both structures.
type block shows considerable mixed K/Sn occupancy with
distinct split positions according to the required K-Se and Sn-
Se bond distances. We found 23% in the K1 site and 17% in
the K2 sites that correspond to the Sn1 and Bi6 site, respectively,
in K0.70Sn2.70Bi11.30Se20, see Figure 1. A similar disorder of Bi
and K is reported for the ternary phase K2.5Bi8.5Se14.14 The metal
positions in the interior of the NaCl100-type block exhibit
extensive disorder of Bi and Sn in the same crystallographic
site with 13% Sn in the Bi5 site, 16% Sn in the Bi6 site, and
17% Sn in the Bi7 site. However, the Bi8 site is fully occupied
by Bi.
the tunnel and possibly “rattling” about their crystallographic
site.
Perspective and Classification of the New Quaternary
Selenides. A1+xM′3-2xBi7+xSe14 and A1-xM′3-xBi11+xSe20 (A )
K, Rb, Cs; M′ ) Sn, Pb) are new members of the homologous
series Am[M6Se8]m[M5+nSe9+n] with n ) 3 and m )2 and m )
1, respectively. The close relationship of K1-xSn3-xBi11+xSe20
to K1-xSn4-xBi11+xSe2112 and K1-xSn5-xBi11+xSe2213 is obvious
from the color scheme depicted in Figure 4. While the NaCl100
-
type block (boxed area) remains the same for all three phases,
the latter two (i.e., n ) 4 and n ) 5) can be easily derived
from K1-xSn3-xBi11+xSe20 by successively adding SnSe equiva-
lents to the [M8Se12] layers. One can also imagine compounds
The tricapped prismatic site within the tunnels is fully
occupied with K, and its ADP is normal in K1.40Sn2.20Bi7.40
-
Se14. In contrast, the corresponding sites in A1-xSn3-xBi11+xSe20
are only partly occupied, see Table 3, and the observed large
ADP of the alkali atoms is caused by positional disorder along
with the formulas K1-xSn2-xBi11+xSe19 (n ) 2) and K1-xSn6-x-
Bi11+xSe23 (n ) 6) that would belong to the series Am[M6Se8]m-
[M5+nSe9+n] for m ) 1. A similar relationship exists between

New Members of the Series Am[M6Se8]m[M5+nSe9+n
]
Inorganic Chemistry, Vol. 40, No. 24, 2001 6209
Figure 4. The homologous series Am[M6Se8]m[M5+nSe9+n]. A member generating scheme illustrating successive additions of MSe units to a M5Se9
layer. Small white spheres: Se. Large light-gray spheres: K. Middle-gray spheres: M. Question marks are meant to indicate predicted but as of
yet undiscovered compositions.
â-K2Bi8Se13,6,7 K1+xSn3-2xBi7+xSe14, and K1+xSn4-2xBi7+xSe15,8
which are successive members. They differ by one SnSe unit
per formula.
products of compositions that differ only by one SnSe per
formula. We attempted to synthesize the two missing members
Rb1+xM′3-2xBi7+xSe14 (M′ ) Sn, Pb) but did not succeed; instead
we obtained Rb1-xM′3-xBi11+xSe20 with an unknown minority
phase.
Charge Transport Properties. Preliminary charge transport
measurements of several members of these phases have been
carried out. The electrical conductivity of the quaternary
selenides described here was measured on polycrystalline ingots
and found to be strongly influenced by the ingot preparation
conditions. If the molten mixture of the starting materials was
quenched, high electrical conductivity, 1700 S/cm, was observed
for K1-xSn3-xBi11+xSe20, and also for Rb1-xSn3-xBi11+xSe20,
1350 S/cm. For a slowly cooled sample of K1-xSn3-xBi11+xSe20
(see description in the Experimental Section) we found the much
lower electrical conductivity of 520 S/cm at room temperature.
For slowly cooled samples, the substitution of K by Cs seems
The scheme of Figure 4 places all known members in the
same context and offers an easy way to predict new phases by
combining known [M6Se8]m blocks and [M5+nSe9+n] layers.
Besides varying n to obtain new compounds it would be worth
exploring if members with m > 2 are also stable. The numerous
compounds discovered in the systems K/Sn/Bi/Se and Rb/Sn/
Bi/Se8,12,13,21 suggest strongly that the A/M′/Bi/Se system may
be “infinitely adaptiVe”.22 In other words, small variations of
the ratio of the starting materials result in new compounds with
gradually evolving structural features. The system seems to
adjust to a new structure type each time the composition changes
rather than form varying mixtures of two or more phases or
form solid solutions. The Am[M6Se8]m[M5+nSe9+n] homology
may capture only a fraction of the total number of phases
possible, as we have observed compositions which do not belong
to the series.23 It is remarkable that we are able to make pure
to decrease the electrical conductivity (370 S/cm for Cs1-xSn3-x
-
Bi11+xSe20) while the Pb analogues K1-xPb3-xBi11+xSe20 (700
S/cm) and Cs1-xPb3-xBi11+xSe20 (690 S/cm) possess higher
electrical conductivity than the Sn compounds. A similar trend
is found for A1+xM′3-2xBi7+xSe14, see Table 7. The room
(21) Iordanidis, L.; Mrotzek, A.; Kanatzidis, M. G. Unpublished results.
(22) (a) Anderson, J. S. J. Chem. Soc., Dalton Trans. 1973, 10, 1107-
1115. (b) Swinnea, J. S.; Steinfink, H. J. Solid State Chem. 1982, 41,
114-123. (c) Mercurio, D.; Parry, B. H.; Frit, B.; Harburn, G.;
Williams, R. P.; Tilley, R. J. D. J. Solid State Chem. 1991, 92, 449-
459.
(23) Mrotzek, A.; Kanatzidis, M. G. Chem. Commun. 2001, 17, 1648-
1649.

6210 Inorganic Chemistry, Vol. 40, No. 24, 2001
Mrotzek et al.
Table 7. Thermoelectric Properties, Band Gaps, and Melting Points
for Members of the Am[M6Se8]m[M5+nSe9+n] Series
σ
S300K
(µV/K)
Eg
(eV)
mp
(°C)
compd
(S/cm)
6,7
â-K2Bi8Se13
250
150
2000
630
200
350
110
1700
520
-200
-100
-45
-32
-48
-56
-70
-16
-68
-49
-25
-46
-69
-91
-52
-43
0.59
0.56
c
0.56
0.40
0.62
0.39
c
0.30
0.55
c
0.54
0.40
c
672
692
689
692
669
716
662
676
676
694
675
667
668
714
673
680
14
K
K
K
2.5Bi8.5Se14
1+xSn3-2xBi7+xSe14
1+xPb3-2xBi7+xSe14
Cs1+xSn3-2xBi7+xSe14
Cs1+xPb3-2xBi7+xSe14
1+xSn4-2xBi7+xSe15
1-xSn3-xBi11+xSe20
K1-xSn3-xBi11+xSe20
1-xPb3-xBi11+xSe20
Rb1-xSn3-xBi11+xSe20
Rb1-xPb3-xBi11+xSe20
Cs1-xSn3-xBi11+xSe20
Cs1-xPb3-xBi11+xSe20
1-xSn4-xBi11+xSe21
1-xSn5-xBi11+xSe22
8
K
K
a
b
a
K
700
a
a
1350
1060
370
690
1800
450
b
Figure 6. Infrared absorption spectrum of K1-xSn3-xBi11+xSe20 obtained
at room temperature. The energy band gap is indicated in the spectrum.
b
12
13
K
K
c
c
a Quenched. b Slowly cooled. c Could not be determined reliably due
to the high absorption from mid gap states.
Figure 7. Differential thermogram of Cs1-xSn3-xBi11+xSe20 showing
melting and recrystallization events. Heating/cooling rate of 10 °C/
min.
absolute value of the negative Seebeck coefficient increases from
-45 to -62 µV/K for K1+xSn3-2xBi7+xSe14 and -32 to -52
µV/K for K1+xPb3-2xBi7+xSe14, respectively. The Cs analogues
have slightly higher thermopower at room temperature with -48
Figure 5. Variable-temperature thermoelectric power data of poly-
crystalline ingots of K1+xM‘3-2xBi7+xSe14 and A1-xM‘3-xBi11+xSe20 (A
) K, Rb, Cs; M‘ ) Sn, Pb).
temperature values for slowly cooled K1+xSn3-2xBi7+xSe14 (2000
S/cm), K1+xPb3-2xBi7+xSe14 (630 S/cm), Cs1+xSn3-2xBi7+xSe14
(200 S/cm), and Cs1+xPb3-2xBi7+xSe14 (350 S/cm) are higher
µV/K (Cs1+xSn3-2xBi7+xSe14) and -56 µV/K (Cs1+xPb3-2x-
Bi7+xSe14). Such moderately low values may be reasonable
considering the high electrical conductivity of these sample. In
comparison to the ternary selenide K2.5Bi8.5Se14, the partial
substitution of K and Bi by Sn (Pb) causes a drastic drop in the
thermopower from -100 µV/K at room temperature. As found
for K2.5Bi8.5Se14 its properties are sensitive to the preparation
method; therefore we can expect that the quaternary analogue
would behave similarly.
than the value reported for the isostructural ternary, K2.5Bi8.5
Se14. The former values are comparable to those of quenched
1-xSn3-xBi11+xSe20 and slowly cooled K1-xPb3-xBi11+xSe20.
-
K
The high conductivity of quenched samples is attributed to the
generation of a large number of defects in the structure, whose
exact nature is not known but can be speculated to be M/Se
anti-site defects or Se vacancies.
Table 7 summarizes room temperature values for ther-
mopower, electrical conductivity, band gaps, and melting points
for A1+xM′3-2xBi7+xSe14, A1-xM′3-xBi11+xSe20 (A ) K, Rb, Cs;
M′ ) Sn, Pb), K2.5Bi8.5Se14, â-K2Bi8Se13, K1+xSn4-2xBi7+xSe15,
K1-xSn4-xBi11+xSe21, and K1-xSn5-xBi11+xSe22. All materials are
n-type semiconductors. The thermopower was measured be-
tween 300 and 400 K on oriented polycrystalline aggregates of
Slowly cooled samples of K1-xSn3-xBi11+xSe20 exhibit a
linearly rising absolute Seebeck value from -68 µV/K at 300
K to -107 µV/K at 400 K. However, we observed much lower
thermopower for the quenched sample. The low values starting
from -16 to -28 µV/K correspond to the higher electrical
conductivity observed for this sample, see Table 7. Quenched
Rb1-xSn3-xBi11+xSe20 behaves similarly, exhibiting a low ther-
mopower of -26 µV/K at 300 K that rises to -35 µV/K at 400
A1+xM′3-2xBi7+xSe14 and A1-xM′3-xBi11+xSe20. These com-
K. By comparison, the slowly cooled sample of Cs1-xSn3-x-
pounds possess moderate negative Seebeck coefficients with a
nearly linear dependence, see Table 7 and Figure 5. The negative
values indicate n-type behavior with electrons as the dominant
charge carriers. With rising temperature from 300 to 400 K the
Bi11+xSe20 possesses higher thermopower (-69 µV/K increasing
to -92 µV/K) consistent with its lower electrical conductivity
of 370 S/cm. Substitution of Sn by Pb led analogously to
K1+xPb3-2xBi7+xSe14 to an about 30% reduced thermopower for

New Members of the Series Am[M6Se8]m[M5+nSe9+n
]
Inorganic Chemistry, Vol. 40, No. 24, 2001 6211
Concluding Remarks
K1-xPb3-xBi11+xSe20 (-49 µV/K at 300 K). The thermopower
of Rb1-xSn3-xBi11+xSe20 (-46 µV/K at 300 K) is comparable
to the latter, see Table 7. In contrast, the Pb analogue
Cs1-xPb3-xBi11+xSe20 shows values rising from -91 µV/K at
300 K to -126 µV/K at 400 K, the highest thermopower
observed for any A1-xM′3-xBi11+xSe20 (A ) K, Rb, Cs; M′ )
Sn, Pb).
The exploration of the system A/M′/Bi/Se (A ) K, Rb, Cs;
M′ ) Sn, Pb) reported here and elsewhere8,12,13 leads to the
suggestion that it may be “infinitely adaptive”. The existence
of the grand homologous series Am[M6Se8]m[M5+nSe9+n] that
defines a certain fraction of the possible compounds seems clear
at this stage. The phases A1+xM′3-2xBi7+xSe14 and A1-xM′3-x
-
Energy Gaps and Thermal Properties. The infrared ab-
sorption spectra of A1+xM′3-2xBi7+xSe14 and A1-xM′3-xBi11+xSe20
(A ) K, Rb, Cs; M′ ) Sn, Pb) were recorded at room
temperature in the range 0.1-0.7 eV. The optical band gaps of
Bi11+xSe20 (A ) K, Rb, Cs; M′ ) Sn, Pb) were predicted and
synthesized as new members of this series. All members of the
homologous series are constructed from the basic NaCl111- and
the NaCl100-type modules whose sizes vary according to n and
m. The phases A1+xM′3-2xBi7+xSe14 and A1-xM′3-xBi11+xSe20
are n-type narrow band gap semiconductors with moderate
electrical conductivity and thermopower. The pursuit of new
members of the series continues.
K
1+xSn3-2xBi7+xSe14, Rb1-xSn3-xBi11+xSe20, and Cs1-xPb3-x-
Bi11+xSe20 could not be determined reliably. However, for
K1+xPb3-2xBi7+xSe14, Cs1+xM′3-2xBi7+xSe14, K1-xM′3-xBi11+xSe20,
Rb1-xPb3-xBi11+xSe20, and Cs1-xSn3-xBi11+xSe20 we were able
to observe optical band gaps between ∼0.3 eV (see Figure 6)
and 0.6 eV. The narrow band gaps of these quaternary selenides
are consistent with the observed charge transport behavior
described above.
Acknowledgment. Financial support from the Office of
Naval Research (Grant No. N00014-98-1-0443) and the Deut-
sche Forschungsgemeinschaft is gratefully acknowledged. This
work made use of the SEM facilities of the Center for Advanced
Microscopy at Michigan State University.
According to DTA experiments A1+xSn3-2xBi7+xSe14 and
A1-xSn3-xBi11+xSe20 (A ) K, Rb, Cs) melt and recrystallize
without structural change (the melting points are listed in Table
7), while the analogous lead compounds melt incongruently. A
typical differential thermogram is shown in Figure 7 for
Cs1-xSn3-xBi11+xSe20. The well-defined melting and crystal-
lization events and their close proximity reflect the essentially
congruent melting behavior of the material.
Supporting Information Available: X-ray crystallographic data
for K1.40Sn2.20Bi7.40Se14, K0.70Sn2.70Bi11.30Se20, Rb0.36Sn2.36Bi11.64Se20, and
Cs0.46Sn2.46Bi11.54Se20, in CIF format. This material is available free of
charge via the Internet at http://pubs.acs.org.
IC010285W