Clathrates of group 14 with alkali metals: An exploration

Article abstract of DOI:10.1006/jssc.2000.8755

The quantitative synthesis of four silicon and germanium compounds with the clathrate-II structure, Cs₈Na₁₆Si₁₃₆ (1), Cs₈Na₁₆Ge₁₃₆ (2), Rb₈Na₁₆Si₁₃₆ (3), and Rb₈Na₁₆Ge₃₆ (4), and their characterizations are reported. The corresponding Si-Si and Ge-Ge distances are determined with high accuracy from extensive single-crystal X-ray diffraction work. The compounds (cubic, space group Fd3m, a=14.7560(4), 15.4805(6), 14.7400(4), and 15.4858(6) A for 1, 2, 3, and 4, respectively) are stoichiometric, metallic, and remarkably stable. No evidence was found for vacancies in the silicon and germanium networks or partial occupancies of the alkali metal sites. The stoichiometry of these completely filled clathrates is consistent with the measured temperature-independent Pauli paramagnetism (χ = 7.2 x 10^-4, 6.5 x 10^-4, 6.9 x 10^-5, and 1.4 x 10^-4 emu/mol for 1, 2, 3, and 4, respectively) and metallic resistivity (ρ₂₉₃ ? 10^-5 Ω-cm). (C) 2000 Academic Press.

Full text of DOI:10.1006/jssc.2000.8755

Journal of Solid State Chemistry 153, 92}105 (2000)
doi:10.1006/jssc.2000.8755, available online at http://www.idealibrary.com on
Clathrates of Group 14 with Alkali Metals: An Exploration
Svilen Bobev and Slavi C. Sevov
Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556-5670
E-mail: ssevov@nd.edu.
Received February 25, 2000; in revised form April 17, 2000; accepted April 20, 2000; published online July 11, 2000
Ever since, semiconducting nanocrystals and porous mater-
The quantitative synthesis of four silicon and germanium ials have been extensively studied. It has been shown by
compounds with the clathrate-II structure, Cs8Na16Si136 (1),
Cs8Na16Ge136 (2), Rb8Na16Si136 (3), and Rb8Na16Ge36 (4), and
their characterizations are reported. The corresponding Si+Si
and Ge+Ge distances are determined with high accuracy from
extensive single-crystal X-ray di4raction work. The compounds
(cubic, space group Fd3m, a ؍ 14.7560(4), 15.4805(6),
14.7400(4), and 15.4858(6) A for 1, 2, 3, and 4, respectively) are
stoichiometric, metallic, and remarkably stable. No evidence
was found for vacancies in the silicon and germanium networks
or partial occupancies of the alkali metal sites. The
stoichiometry of these completely 5lled clathrates is consistent
theoretical calculations (4) and con"rmed by experimental
work (5) that making openings in the semiconducting struc-
tures widens the band gap and causes both valence and
conduction bands to have extrema at the zone center. This
brought to light the idea of making phases of group 14
elements with open framework structures, which are pos-
sible candidates for such optoelectronic applications.
It is not a simple task, however, to realize this idea in the
case of silicon and germanium. They both crystallize in
cubic face-centered diamond-type lattices and form two of
with the measured temperature-independent Pauli paramag- the most stable and rigid covalent crystals known. Possible
netism
(v ؍ 7.2 ؋ 10؊4
,
6.5 ؋ 10؊4
,
6.9 ؋ 10؊5
,
and
graphite modi"cations of Si and Ge are unstable and have
never been experimentally prepared. Other structures can
be achieved under high pressure, where transition from
a four- to six-coordinated state occurs, and the semicon-
ducting diamond-type lattice converts to a metallic b-Sn-
type phase (6). To the best of our knowledge, expanded
structures containing solely Si or Ge do not exist. The only
open framework structures of Si and Ge are the so-called
clathrates*inclusion compounds with open three-dimen-
sional frameworks, made of tetrahedrally coordinated sili-
con or germanium atoms and voids that are occupied by
alkali and alkaline-earth metals.
1.4 ؋ 10؊4 emu/mol for 1, 2, 3, and 4, respectively) and metallic
resistivity (q293+10؊5 X-cm). ( 2000 Academic Press
INTRODUCTION
The electronic revolution has brought great changes in
every aspect of today's life. Undoubtedly, these changes
were possible because the Si- and Ge-based electronic devi-
ces allowed miniaturization, functional integration, and low
cost. However, the relatively small and indirect band gaps of
the bulk Si and Ge make them unsuitable for many other
potential applications. The dipole forbidden optical
transition across the indirect energy gap hinders the light-
emitting e$ciency, limits large-scale optoelectronic integra-
tion, and prevents the realization of novel concepts. Con-
BACKGROUND
The story of the clathrates begins as early as 1811 when
siderable scienti"c attention has been focused on altering the "rst scienti"c report on a chlorine}ice compound with
the electronic structure of these elements by introducing unidenti"ed nominal composition that had earlier been
heteroatoms into the crystal structure, i.e., by doping them thought to be crystalline chlorine appeared in the literature
with appropriate elements to overcome the low radiative (7). Twelve years later M. Faraday revised the data and
recombination probability (1). Extensive e!orts for band determined the stoichiometry to be Cl (H O) (8). It was
ꢀ
ꢀ
ꢁꢂ
structure engineering have focused on changing the bonding another 148 years before the structure and the correct for-
geometry, i.e., breaking the symmetry or the crystal peri- mula (Cl (H O) ) were determined (9) and the compound
ꢀ
ꢀ
ꢃꢄꢅꢃ
odicity (2). Recent developments in this area have led to was described as a three-dimensional network of fused large
fabrication of structures that are small enough to exploit polyhedra incorporating channels and cages occupied by
quantum con"nement e!ects and to show an increased the &&guest impurities.'' Meanwhile, a large number of similar
radiative rate by emitting light at room temperature (3). compounds were synthesized (e.g., G (H O) , where
ꢆ
ꢀ
ꢇꢈ
92
0022-4596/00 $35.00
Copyright ( 2000 by Academic Press
All rights of reproduction in any form reserved.

CLATHRATES OF GROUP 14 WITH ALKALI METALS
93
TABLE 1
Up-to-Date List of Silicon, Germanium, and Tin Clathrate Compounds with Alkali (A) or Alkaline Earth (AE) Metals and Group 13
(Tr) or Group 12 (E) Elements (See Text)
A}¹t
Na Si (10), K Si (11), K Ge (11), K Sn (11), Rb Sn
(21), K
ꢁꢄꢈ(ꢀ) ꢈꢄꢇ(ꢀ) ꢇꢇꢄꢂ(ꢁ)
[1(x(23] (16,23) Cs Na Si (27), Cs Na Ge
ꢁꢈ ꢁꢉꢈ ꢁꢈ ꢁꢉꢈ
Cs
Sn
(21), Cs Sn (43)
ꢆ
ꢇꢈ
ꢆ
ꢇꢈ
ꢆ
ꢇꢈ
ꢆ
ꢇꢈ
ꢆ
ꢇꢇꢄꢈ(ꢁ)
ꢆ
ꢇꢈ
Na Si
[3(x(11] (10), Na Ge
(22), Na Si
(27),
V
ꢁꢉꢈ
V
ꢁꢉꢈ
V
ꢁꢉꢈ
ꢆ
ꢆ
Rb Na Si ,? Rb Na Ge
?
ꢆ
ꢁꢈ ꢁꢉꢈ
ꢆ
ꢁꢈ ꢁꢉꢈ
AE}¹t
A}¹r}Si
A}¹r}Ge
(hp)Ba Si (29), Na Ba Si (28)
ꢆ
ꢇꢈ
V
ꢀ ꢇꢈ
K Al Si (48), Na Ga Si (48), K In Si (48), K Ga Si (48), K Ga Si (51), Rb Ga Si (49)
ꢆ
ꢀꢉ ꢀꢉ
ꢆ
ꢀꢉ ꢀꢉ
ꢆ
ꢁꢆ ꢀꢆ
ꢆ
ꢁꢇ ꢉꢀ
ꢆ
ꢆ
ꢉꢆ
ꢆ
ꢆ ꢉꢆ
K Ga Ge (48), Na Ga Ge (48), K In Ge (48), K Al Ge (45), Rb Al Ge (58), Rb In Ge (46), Rb Ga Ge (49),
ꢆ
ꢀꢉ ꢀꢉ
Cs Ga Ge (59), Cs In Ge (61), K In Ge (46)
ꢉꢆ ꢉꢆ ꢉꢆ
K Ga Sn (48), K In Sn (48), K Al Sn (48), K Ga Sn (51), K Al Sn (45), Rb Al Sn (58), Rb Ga Sn (49),
ꢀꢉ ꢀꢉ ꢀꢉ ꢀꢉ ꢀꢉ ꢀꢉ ꢉꢆ ꢉꢆ ꢉꢆ ꢉꢆ
Cs Ga Sn (59)
ꢉꢆ
Cs Zn Sn (42)
ꢇꢀ
Ba Ga Si (52), Ba Al Si (52), Sr Al Si (52), Sr Ga Si (52)
ꢁꢈ ꢉꢂ ꢁꢈ ꢉꢂ ꢁꢈ ꢉꢂ ꢁꢈ ꢉꢂ
Ba Ga Ge (52), Ba Al Ge (52), Sr Ga Ge (52), Ba In Ge (53)
ꢁꢈ ꢉꢂ ꢁꢈ ꢉꢂ ꢁꢈ ꢉꢂ ꢁꢈ ꢉꢂ
ꢆ
ꢁꢈ ꢉꢂ
ꢆ
ꢁꢈ ꢉꢂ
ꢆ
ꢆ
ꢉꢆ
ꢆ
ꢆ
ꢉꢆ
ꢆ
ꢆ
ꢉꢆ
ꢆ
ꢆ
ꢉꢆ
ꢆ
ꢆ
ꢆ
ꢆ
ꢆ ꢆ
A}¹r}Sn
ꢆ
ꢆ
ꢆ
ꢆ
ꢆ
ꢆ
ꢆ
ꢆ
ꢆ
ꢆ
ꢆ
ꢆ
ꢆ
A}E}Sn
ꢆ
ꢇ
AE}¹r}Si
AE}¹r}Ge
AE}E}Ge
AE}¹M}Si
AE}¹r}Sn
Other
ꢆ
ꢆ
ꢆ
ꢆ
ꢆ
ꢆ
ꢆ
ꢆ
Ba Cd Ge (53), Ba Zn Ge (53)
ꢆ
ꢆ
ꢉꢆ
ꢆ
ꢆ
ꢉꢆ
Ba ¹M Si
, [¹M"Au, Ag, Cu] (57)
ꢆ
V
ꢇꢈ\V
b-Ba Ga Sn (50), Ba Ga Sn
(26)
ꢆ
ꢁꢈ ꢉꢂ
ꢉꢆ
ꢆ
ꢉꢀ ꢁꢂꢇ
X R Ge [X"Cl, Br, I; R"P, As, Sb] (54), I +I Ge
, [x"8/3] (56), I P
Sn (55), I As
Sn (55), Ba Cu
P
(60)
ꢆ
ꢆ
ꢆ
V
ꢇꢈ\V
ꢆ ꢁꢊꢄꢉ(ꢀ) ꢀꢇ
ꢆ
ꢁꢊꢄꢉ(ꢀ) ꢀꢇ ꢆ ꢁꢈ ꢉꢂ
Note. Italics represent the clathrate-II phases. References in parentheses.
? This work.
G"Ar, Kr, Xe, H S, Cl , CH , and G (H O)
ꢀꢇ ꢁꢉꢈ
or tures reported, the vast majority of them being clathrate-I
where G"H S, CO , CHCl , n-propane, (Table 1). So far, there are no clathrates of carbon or lead
ꢀ
ꢀ
ꢇ
ꢀ ꢀ ꢉ
ꢀ
G G (H O)
ꢁꢈ ꢆ
ꢀ
ꢁꢉꢈ
nitromethane, cyclopentane, etc.) and were called gas and known. For carbon, the reason is most likely its tendency
liquid hydrates (double hydrates) or often referred to as for strong n-bonding and the possibility of forming poly-
type I and type II clathrates, respectively. Almost a decade hedra of even larger sizes such as the fullerene-like C and
ꢈꢂ
later, in 1965, the "rst clathrate compounds of Si with the alkali-metal-doped A C (15). For lead, perhaps the
ꢉ ꢈꢂ
sodium were synthesized by &&controlled thermal decompo- more pronounced metallic properties prevent the formation
sition of the Zintl phase NaSi'' and were structurally charac- of localized covalent bonds as required for the clathrates.
terized (10). These compounds were Na Si and Na Si
with the latter reported to be a nonstoichiometric phase di!er much. When normalized, their ideal (completely "lled)
with metal content varying between 3 and 11. The discovery chemical formulas are AX
of the silicon clathrates also stimulated more interest in and -II, respectively. Structurally, however, they are notice-
,
The stoichiometries of the two types of clathrates do not
ꢆ ꢇꢈ
V ꢁꢉꢈ
and AX
, for clathrates-I
ꢃꢄꢅꢃ
ꢃꢄꢈꢅ
compounds of C, Ge, Sn, and Pb with alkali metals. E!orts ably di!erent.
in this direction led to the discovery (1969) of the "rst
The prototypes of the clathrate-I structure are the gas
germanium and tin clathrates of type I, K Ge and hydrates with stoichiometry G (H O) , where G"Ar, Kr,
ꢆ
ꢇꢈ ꢆ ꢀ ꢇꢈ
K Sn , synthesized by direct fusion from pure elements Xe, H S, Cl , CH , etc. Clathrate-I phases crystallize in
ꢆ
ꢇꢈ
ꢀ
ꢀ
ꢇ
(11). Since then, much experimental and theoretical work primitive cubic lattices (space group Pm3n, No. 223). The 46
has been devoted to the clathrates of group 14 with alkali/ clathrand atoms (oxygens from the water in this case) are all
alkaline earth metals. By 1991 5 binary and 17 ternary tetrahedrally coordinated and their arrangement in the unit
phases with clathrate-I structure and only
stoichiometric clathrate-II phases were reported (12). The- sizes: one is a 20-atom pentagonal dodecahedron [5 ], and
ꢁꢀ ꢀ
3
non- cell is such that one can de"ne two polyhedra of di!erent
ꢁꢀ
oretical calculations done in the late 1980s revealed that the other is a 24-atom tetrakaidecahedron [5 6 ] (the
ꢁꢀ ꢀ
hypothetical carbon modi"cations with clathrate structures symbol [5 6 ] denotes a polyhedron with 12 pentagonal
would have only about 0.07}0.09 eV less cohesive energy and 2 hexagonal faces). The guest atoms or molecules can be
per atom than the diamond phase (13). Later, when ab initio encapsulated into these cages if their sizes are comparable to
DFT planewave pseudopotenial methods were used, similar the size of the available empty space. Another feature of this
results were obtained for Si and Ge; i.e., Si and Ge clathrates structure is that the tetrakaidecahedra create a system of
are slightly less stable by about 0.07 and 0.05 eV per atom, three mutually perpendicular &&channels'' by sharing com-
respectively, relative to bulk pure elements (14). Thus, clath- mon hexagonal faces. Three pairs of channels enclose the
rates made of group 14 elements started to attract greater smaller dodecahedra and separate them from each other, as
attention, and in the past 9 years the number of composi- shown in Fig. 1. It is important to note that there are eight
tions with clathrate-type structures has increased by a factor cages per formula unit, two smaller and six larger, and
of 2. There are now more than 50 phases with such struc- therefore the clathrate-I formula can be written as

94
BOBEV AND SEVOV
FIG. 1. (a) Building units of the clathrate-I structure, the 20-atom pentagonal dodecahedron [5ꢁꢀ] with 12 pentagonal faces and the tetrakaidecahedra
[5ꢁꢀ6ꢀ] with 12 pentagonal and 2 hexagonal faces; (b) clathrate-I layer; (c) polyhedral representation of the clathrate-I unit cell. The shaded polyhedra are
the pentagonal dodecahedra, enclosed between the three mutually perpendicular channels of tetrakaidecahedra that share their hexagonal faces.
ꢁ
ꢂ
G G X , where X denotes the clathrand element (group 14 Clearly, the molecules in this case are larger than the &&guest
ꢀ ꢈ ꢇꢈ
element or water molecule), and G and G stand for the species'' in the clathrate-I structures. The framework-build-
ꢁ
ꢂ
ꢁꢀ ꢁꢀ ꢀ
atoms/molecules occupying the [5 ] and [5 6 ] poly- ing atoms are again four-bonded in a nearly ideal tetrahed-
hedra, respectively. ral environment and also form two di!erent polyhedra. The
Clathrate-II crystallizes in the face-centered Fd3m cubic key di!erence is that here, in addition to the pentagonal
ꢁꢀ
space group (No. 227). The parent compounds of this type dodecahedron [5 ], the second-type polyhedra are built of
ꢁꢀ ꢇ
are the liquid and double hydrates G (H O)
and 28 atoms, hexakaidecahedra [5 6 ], that have 12 pentag-
ꢀꢇ
ꢀ
ꢁꢉꢈ
ꢀ
G G (H O) , respectively, where G"H S, CO , n-pro- onal and 4 hexagonal faces (Fig. 2). They are linked to each
ꢁꢈ ꢆ
ꢀ
ꢁꢉꢈ
ꢀ
pane, nitromethane, cyclopentane, tetrachloromethane, etc. other by their hexagonal faces, forming a diamond-like
FIG. 2. (a) Building units of the clathrate-II structure, the 20-atom pentagonal dodecahedron [5ꢁꢀ] with 12 pentagonal faces and the hexa-
kaidecahedra [5ꢁꢀ6ꢇ] with 12 pentagonal and 4 hexagonal faces; (b) clathrate-II layer; (c) polyhedral representation of the clathrate-II unit cell. The shaded
polyhedra are the pentagonal dodecahedra that are linked together. The hexakaidecahedra share their 4 hexagonal faces forming a diamond-like
structure.

CLATHRATES OF GROUP 14 WITH ALKALI METALS
95
structure. The smaller pentagonal dodecahedra are not iso- transfers its valence electron to the ¹t (¹t"Tetrel, i.e.,
lated as in the clathrate-I structure but are rather linked group 14 element) network to become a cation. Each Tt, on
through common faces to form layers. The latter are stacked the other hand, is bonded to four other Tt atoms and is
in an ABC sequence typical of cubic close packing, as shown therefore neutral. Thus, the clathrate-I phase with ideal
in Fig. 2. The ratio of smaller to larger cavities in clathrate- stoichiometry 8 : 46 should be a conductor because of the
II is 16 : 8 and therefore the formula can be written as eight extra electrons per formula from the eight alkali meta-
ꢁ
ꢂ
G G X
.
ls. Nevertheless, as mentioned above, property measure-
ꢁꢈ ꢆ ꢁꢉꢈ
An analogy can also be drawn between the zeolites and ments suggest that the clathrate-I phases can be
the clathrates*the latter often being referred to as &&zeolites diamagnetic and semiconducting instead of metallic. For
without oxygen'' or &&oxygen-free zeolites'' (14). Because of a long time A Tt compounds were considered examples of
the many ways of linking SiO tetrahedra in the zeolites the metal-to-insulator Mott transition (17). However, the
via the rather #exible Si}O}Si angle, there are a great explanation for these properties is the formation of defects
ꢆ
ꢇꢈ
ꢇꢋꢀ
variety of zeolite structures, both naturally occurring and in the four-bonded Tt network (18}20). A missing Tt atom
ꢇꢈ
experimentally synthesized. Formal removal of the oxygen, will leave the four neighboring atoms with incomplete val-
i.e., replacement of the X}O}X bonding (X"Al, Si, Ge) ence shells; i.e., four extra electrons will be needed to com-
with direct X}X bonds while preserving the tetrahedral plete their octet con"gurations with lone pairs. Two
coordination, and appropriate &&rescaling'' of the unit cell vacancies per formula will translate to 2;(!4)"!8 nega-
would result in the formation of isomorphous open frame- tive charges, and this equals the number of donated elec-
works. The bond energy of Si}Si or Ge}Ge is such that trons by the eight alkali metals. Thus, the compound
stretching the bonds and bending the angles are no longer becomes electronically balanced and provides a nice agree-
favorable, and as a result, there are only two types of silicon ment between experimental data and theory. Only more
or germanium clathrates, clathrate-I and clathrate-II, recent single-crystal work on clathrate-I compounds in the
known thus far. Their structures are analogous with the binary Rb}Sn and pseudo-binary (K,Cs)}Sn systems has
structures of the melanophlogite and zeolite ZSM-39 (MTN shown that indeed one of the framework sites is partially
or Dodecasil 3C), respectively. Another very important dif- occupied, and the stoichiometry A Sn ᮀ represents the
ꢆ
ꢇꢇ ꢀ
ference between the zeolites and the clathrates is that there correct and electronically balanced formula for a Zintl com-
are zeolite structures that are stable upon removal of the pound with two Sn vacancies (ᮀ) per formula (21). Another
atoms or molecules occupying the channels and cages, way to balance the &&extra'' charges from the alkali metals is
whereas the clathrate structures collapse upon removal of to substitute Tt atoms from the network with an electron-
the alkali metals.
poorer element, from group 13 or 12, for example. This idea
According to Table 1, so far there are seven binary or has been widely used in the past 10}15 years to make new
pseudo-binary compounds between alkali metals and group ternary phases with the clathrate-I structure. The ideal
14 elements with the clathrate-I structure: Na Si
,
stoichiometries will be A ¹r ¹t
and A E ¹t
ꢆ ꢇ ꢇꢀ
and [AE] E ¹t , where A"alkali,
ꢆ ꢆ ꢉꢆ
or
ꢆ ꢇꢈ
ꢆ
ꢆ
ꢉꢆ
K Si , K Ge , K Sn , Cs Sn , Rb Sn
ꢆ ꢇꢈ ꢇꢈ ꢇꢈ ꢇꢈ
Cs Sn
ꢁꢄꢈ(ꢀ) ꢈꢄꢇ(ꢀ) ꢇꢇꢄꢂ(ꢁ)
, and [AE] ¹r ¹t
ꢆ
ꢆ
ꢆ
ꢆ
ꢇꢇꢄꢈ(ꢁ)
ꢆ
ꢁꢈ ꢉꢂ
K
. The phase Na Si was initially rec- AE"alkaline earth, ¹r(Triel)"group 13, and E"group
ꢆ ꢇꢈ
ognized from a X-ray powder di!raction pattern (10). Based 12 elements. The existence of many of these compositions
on structure re"nement and bulk elemental analysis and their compliance with the Zintl concept have been
(Na: Si+1 : 6), the stoichiometry was determined to be proven (Table 1). Nonetheless, there are many controversial
8 : 46 (1 : 5.75), in agreement with the ideal stoichiometric results such as A ¹r ¹t , A ¹r ¹t
,
and
ꢆ
ꢀꢉ ꢀꢉ
ꢆ
ꢁꢈ ꢉꢂ
ratio and the measured metallic-like electric resistivity with
\ꢀ \ꢉ
A
[AE] ¹t that neither "t into the above-mentioned
ꢆ\V
V
ꢇꢈ
room temperature values on the order of 10 }10 )-cm. scheme nor ful"ll the Zintl requirements.
Recently, the ideal stoichiometry for Na Si was con"rmed
ꢆ ꢇꢈ
by Rietveld analysis and Si NMR work (16). The "rst are the compounds with the clathrate-II type structure.
Even more complicated and di$cult for interpretation
ꢀꢊ
single-crystal re"nements of the clathrate-I structure were Until recently, only the nonstoichiometric Na Si
and
V ꢁꢉꢈ
done on data collected with a Weissenberg camera for Na Ge
potassium compounds with Si, Ge, and Sn and were also (10,22). Initially, for Na Si , the sodium content x was
re"ned as 8 : 46 (11). The latter led to a con#ict with the reported to vary between 3 and 11, but later the range of the
phases were known in the binary A}¹t systems
V
ꢁꢉꢈ
V ꢁꢉꢈ
reported
semiconducting
\ꢁ
properties
of
K Ge
domain compositions was broadened to lower (x"1) and
ꢆ
ꢇꢈ
(o +10 )-cm), a compound that had been thought to higher (x"23) concentrations (16,23). There have been
ꢀꢊꢉ
be isoelectronic with Na Si . The accuracy of the speculations that this nonstoichiometric phase also under-
ꢆ ꢇꢈ
stoichiometry and the structure determination have been goes insulator-to-metal Mott transition at x+10 (22}24).
ꢀꢉ
questioned ever since. The formal electronic structure can Later, it was shown by Na NMR that the transition can
be derived from the Zintl}Klemm}Busmann concept; name- occur, even at x(9 (25). The same authors also suggested
ꢀꢉ
ly, each alkali metal atom is merely an electron donor and that the large Na Knight shifts and broad NMR peaks for

96
BOBEV AND SEVOV
Na Si
at x(9 can be attributed to localized alkali metal dently, a higher "gure of merit can be expected for
V ꢁꢉꢈ
electrons. Also, the Na Si
structure was re"ned from X- material with low lattice thermal conductivity. Si and
V ꢁꢉꢈ
ray powder di!raction with the aid of the Rietveld method Ge clathrates are considered promising candidates for
to determine the distribution of the sodium atoms within thermoelectric applications since their relatively large unit
the two available alkali metal sites, i.e., the centers of the cells with &&voids and rattlers inside them'' are important
pentagonal dodecahedra and the hexakaidecahedra (16,23). prerequisites for scattering of the heat-carrying phonons
It was concluded that, for x48, the Na atoms occupy and thereby for low phonon-contributed thermal lattice
ꢁꢀ ꢇ
preferably the larger [5 6 ] cage. Unlike clathrate-I, sub- conductivity. All this interest has led to the search for
stitution of the ¹t atoms with triel and other elements has reliable and reproducible ways for the synthesis of all clath-
not led to as many ternary compounds. Only the structure rates in high yields and with de"ned stoichiometry. Here, we
of Ba Ga Sn
ꢁꢈ ꢉꢀ ꢁꢂꢇ
disorder of Sn and Ga on all crystallographic sites (26). The clathrate-II family, Cs Na Si
ꢁꢈ ꢁꢉꢈ
(3), and Rb Na Ge
ꢁꢈ ꢁꢉꢈ
, where x"32$1.4, and no indication for tal structural characterization, and magnetic and transport
has been reported but with extensive report the direct synthesis of four new members of the
(1), Cs Na Ge (2),
ꢆ
ꢆ
ꢁꢈ ꢁꢉꢈ
structure re"nement has given the composition Rb Na Si
ꢁꢈ ꢁꢉꢈ
(4), their single-crys-
ꢆ
ꢆ
Ba Ga Sn
ꢁꢈ
V
ꢁꢉꢈ\V
potassium content, although the reaction mixture includes properties.
K, Ba, Ga, and Sn. The re"nement indicates that the Ba
cations occupy only the smaller cages while the larger ones
remain empty. No elemental analysis, resistivity, or mag-
netic measurements have been done to prove the authors'
EXPERIMENTAL
Synthesis. All manipulations were performed inside a ni-
trogen-"lled glove box with the moisture level below
1 ppm (vol). The starting materials were Na (Alfa, ingot,
99.9% metal basis), Cs (Acros, 99.95%), Rb (Alfa, 99.8%
metal basis), Si (Alfa, lump, 99.9999% metal basis), and Ge
(Acros, powder, 99.999%). The sodium surface was cleaned
with a scalpel immediately before use. The four compounds
were synthesized from reactions loaded with the exact
stoichiometric ratio 8 : 16 : 136 and intended to yield clath-
rate-II phases. The mixtures were loaded in niobium con-
tainers that were subsequently arc-welded in an Ar-"lled
chamber. The prepared &&reaction vessels'' were then sealed
conclusion that the compound is electronically balanced
and belongs to the Zintl phases. Until very recently, there
was no unequivocal structure determination for compounds
with the clathrate-II structure. The "rst well-re"ned struc-
tures and reproducible direct syntheses were reported for
the stoichiometric and completely "lled silicon and germa-
nium clathrate-II compounds Cs Na Si
and
ꢆ
ꢁꢈ ꢁꢉꢈ
Cs Na Ge
ꢁꢈ ꢁꢉꢈ
(27).
ꢆ
The interest in clathrates jumped abruptly even higher
after the unexpected discovery of superconductivity in the
clathrate-I compounds Ba Na Si and Ba Si (28,29). It
W
V ꢇꢈ
ꢆ ꢇꢈ
was unprecedented because no other examples of supercon-
\ꢃ
in fused silica jackets under vacuum at ca. 10 mm Hg
ꢉ
ductivity were known for phases with covalent sp bonding.
(below discharge). The reactions were carried out at 6503C
for 3 weeks. At higher temperatures Si and Ge readily react
with Nb, forming the stable phases NbSi and NbGe , and
More recent research showed that the silicon clathrates
have low compressibility and therefore are considered po-
tential superhard materials (30). In addition, it was hy-
pothesized that variable physical properties such as the
Seebeck coe$cient or thermopower (S) and the electrical (p)
and thermal (j) conductivities may be tuned by altering the
guest atoms in the cages. This brought new motivation for
clathrate studies as potential thermoelectric materials. The
stability of the clathrates, the fact that they conduct electric-
ity relatively well, and the possibility of &&rattling'' guest
cations in the cavities bring the clathrates closer to the
ultimate thermoelectric PGEC (&&phonon-glass and an elec-
tron crystal'') material, a concept introduced by Slack in
1979 (31). To increase the "gure of merit Z¹, an empirical
coe$cient that measures the thermoelectric performance
ꢀ
ꢀ
this causes leaks of alkali metals into the silica container. At
6503C neither Si nor Ge melts, and therefore, more time was
needed to ensure better di!usion of the alkali metals into the
silicon and germanium for this inhomogeneous system (32).
The products of both reactions were well-shaped crystals
with triangular faces, typical of compounds with F-centered
cubic lattices, and had a distinctive bluish metallic luster.
The yields were quantitative and the crystals were easily
washed with deionized water and ethyl alcohol and separ-
ated under a microscope from the traces of unreacted dust-
like Si and Ge or eventually NbSi and NbGe .
ꢀ
ꢀ
ꢀ
(¹"temperature and Z"pS /j), one needs material with
X-ray diwraction studies. X-ray powder di!raction pat-
high thermopower and low thermal conductivity. The latter terns were taken on an Enraf-Nonius Guinier camera with
has two components*thermal electronic conductivity that CuKa radiation. Powder patterns of the product, before
ꢁ
is proportional to the electrical conductivity (no more than and after it was washed with water or heated under dynamic
5% of the total j) and lattice thermal conductivity. Clearly, vacuum, did not show any di!erences in the line intensities
since the electrical conductivity and the electronic compon- and positions. The patterns were also used to verify the unit
ent of the thermal conductivity cannot be varied indepen- cell parameters by a least-squares re"nement of the

CLATHRATES OF GROUP 14 WITH ALKALI METALS
97
positions of the lines, calibrated by silicon (NIST) as an important crystallographic parameters and details for the
internal standard. re"nements of the four compounds are summarized in Table 2.
Single-crystal di!raction data were collected on an Enraf- The "nal positional and equivalent isotropic displace-
Nonius CAD-4 di!ractometer with graphite mono- ment parameters and important distances are listed in
chromated MoKa radiation at room temperature. A few Tables 3 and 4, respectively.
crystals were selected from each compound, mounted on
quartz "bers, and checked for singularity. For the best ones,
Property measurements. Magnetic measurements were
0.20;0.20;0.20 mm for Cs Na Si
ꢁꢈ ꢁꢉꢈ
0.20;0.12;0.10 mm for Cs Na Ge
ꢁꢈ ꢁꢉꢈ
0.16;0.12;0.08 mm for Rb Na Si
ꢁꢈ ꢁꢉꢈ
0.08;0.04;0.04 mm for Rb Na Ge
were collected with u}2h scans in one octant for 1, 2, and range 2}10 K. The samples (17 mg of 1, 18 mg of 2, 58 mg of
3 and in a full sphere for 4. The data for 1, 2, and 3 were 3, and 72 mg of 4) were prepared by selecting crystals under
corrected for absorption using the average of three t-scans microscope and subsequently checking their quality by
in each, while the data for 4 were treated with DIFABS powder XRD.
(2h "903), carried out on a Quantum Design MPMS SQUID mag-
ꢆ
ꢄ!ꢅ
(2h "1003), netometer at a "eld of 3 T over a temperature range of
ꢆ
ꢄ!ꢅ
(2h "503), and 10}270 K. Tests for superconductivity were also per-
ꢆ
ꢆ
ꢄ!ꢅ
(2h "503), data formed at a "eld of 0.1 or 0.3 T in the temperature
ꢁꢈ ꢁꢉꢈ ꢄ!ꢅ
(Xabs) due to the lack of good t-scan re#ections. The
Four-probe resistivity measurements (van der Pauw's
ꢀ
structures were solved and re"ned on F with the aid of the method) were made on single crystals and pellets using
SHELXTL-V 5.1 software package (33). As expected, the a home made set up and Hewlett-Packard 3457A digital
re"nements con"rmed the clathrate-II structure and multimeter. Thin platinum wires (1 lm in diameter) were
stoichiometry (Fd3m space group (No. 227)) without any &&glued'' inline to the surface of the measured material with
partially occupied network sites or disorder for the alkali a silver paste. The crystal or the pellet with the attached
metals sites. Our previous work on 1 and 2 revealed that the probes was then mounted on the top of a chip, which was
re"nements on the data collected for crystals before and then connected to the multimeter with the aid of four
after being treated with water, alcohol, acids, and heat and coaxial wires. Reliable and reproducible data can be ac-
being treated hydrothermally are virtually identical (27) quired within the resistivity range from 100 M) to 100 l).
(within the standard deviation of less than 2.2p). The list of The pellets for the measurements were prepared from
TABLE 2
Selected Crystallographic Parameters for Cs8Na16Si136, Cs8Na16Ge136, Rb8Na16Si136, and Rb8Na16Ge136
Empirical formula
Formula weight
Na CsSi
ꢀ
Na CsGe
ꢀ
Na RbSi
ꢀ
Na RbGe
ꢀ ꢁꢅ
ꢁꢅ
ꢁꢅ
ꢁꢅ
656.42
1412.92
608.98
1365.48
Wavelength (A), MoKa
Crystal system
0.71073
Cubic
Space group, No.
Fd3m, 227
Unit cell dimensions (A)
Volume (Aꢉ), Z
Density (calculated, g/cmꢉ)
Absorption coe$cient (cm\ꢁ)
Absorption correction
h range (deg)
Limiting indices
Re#ections collected
Independent re#ections
a"14.7560(4)
3212.9(2), 8
2.714
36.06
t-scan
2.39}44.90
04hkl429
3322
a"15.4805(6)
3709.8(2), 8
5.059
290.41
t-scan
2.28}49.95
04hkl433
4864
a"14.7400(4)
3202.5(2), 8
2.526
43.97
t-scan
2.39}24.86
04hkl417
706
a"15.4858(6)
3713.6(2), 8
4.885
296.83
Xabs
2.28}24.99
!164hkl418
1370
680
977
165
188
[R "0.0256]
[R "0.1178]
[R "0.0570]
[R "0.0770]
*ꢁꢂ
*ꢁꢂ
*ꢁꢂ
*ꢁꢂ
Data/restraints/parameters
680/0/15
977/0/15
165/0/15
188/0/15
Goodness-of-"t on Fꢀ
1.202
1.033
1.061
1.103
Final R? indices [I'2p ](%)
R "2.01
R "4.31
R "1.69
R "2.75
'
ꢁ
ꢁ
ꢁ
ꢁ
wR "4.53
wR "8.30
wR "3.91
wR "5.49
ꢀ
ꢀ
ꢀ
ꢀ
R indices [all data] (%)
R "2.31
R "9.24
R "2.06
R "3.09
ꢁ
ꢁ
ꢁ
ꢁ
wR "4.61
wR "9.81
wR "4.08
wR "5.57
ꢀ
ꢀ
ꢀ
ꢀ
Extinction coe$cient
Largest di!. peak (e/Aꢉ)
hole
0.00015(3)
0.00016(2)
0.00005(4)
0.00002(2)
0.773
!0.517
0.0183/1.8215
1.857
!2.019
0.0356/8.7128
0.251
!0.176
0.0000/5.3098
0.784
!0.676
0.0262/1.7491
Weight coe$cient A/B
? R "[+#F "!"F #]/+"F "; wR "+[+w[(F )ꢀ!(F )ꢀ]ꢀ]/[+w(Fꢀ)ꢀ],ꢁꢋꢀ; w"[pꢀ(F )ꢀ#(AP)ꢀ#BP]\ꢁ , where P"[(F )ꢀ #2(F )ꢀ]/3.
ꢁ
ꢃ
#
ꢃ
ꢀ
ꢃ
#
ꢃ
ꢃ
ꢃ
#

98
BOBEV AND SEVOV
TABLE 3
Atomic Coordinates and Equivalent Isotropic Displacement
TABLE 4
Important Distances (A) in Cs8Na16Si136, Cs8Na16Ge136
,
Parameters (Ueq)? for Cs8Na16Si136, Cs8Na16Ge136, Rb8Na16Si136
,
Rb8Na16Si136, and Rb8Na16Ge136
and Rb8Na16Ge136
Cs Na Si
Rb8Na16Si136
Si1 2.3728(7);2
ꢆ
ꢁꢈ ꢁꢉꢈ
Si1}
Si2}
Si1
Si1
Si2
Si1
Si3
Si2
Si1
Si2
Si3
Na
Cs
2.3809(2);2
2.3924(5)
2.3717(2)
2.3717(2);3
2.3584(4)
2.3584(4);4
3.3738(2);12
3.2781(2);6
3.1948(1);2
5.2170(1)
Si1}
Si2}
ꢀ
Atom
Site
x
y
z
;
[A ]
%ꢆ
Si1
Si2
Si1
Si3
Si2
Si1
Si2
Si3
Na
Rb
Si1
Si1
Si2
Rb
2.395(1)
2.3716(7)
2.3716(7);3
2.362(1)
Cs8Na16Si136
Si1
Si2
Si3
Na
Cs
96g
32e
8a
0.06768(1)
x
x
0.37022(1)
0.00664(5)
0.00666(6)
0.0066(1)
0.0187(2)
0.01990(6)
0.21728(2)
x
1/8
0
Si3}
Na}
Si3}
Na}
2.362(1);4
1/8
0
1/8
0
3.3737(4);12
3.2770(4);6
3.1913(1);2
5.2114(7)
16c
8b
3/8
3/8
3/8
Cs8Na16Ge136
6.1175(2)
6.1109(2)
Cs}
Si1
Si1
Si2
Cs
3.9452(2);12
4.0214(3);12
4.0311(4);4
6.3859(2)
Rb}
3.9367(6);12
4.0147(7);12
4.0205(9);4
6.3826(2)
Ge1
Ge2
Ge3
Na
96g
32e
8a
0.06783(2)
x
x
0.37038(3)
0.0110(1)
0.01038(1)
0.0099(2)
0.034(1)
0.21772(3)
x
1/8
0
1/8
0
1/8
0
16c
8b
Cs
3/8
3/8
3/8
0.0344(3)
Cs8Na16Ge136
Rb8Na16Ge136
Ge1}
Ge2}
Ge1 2.4980(4);2
Ge1 2.5033(9)
Ge2 2.4881(5)
Ge1 2.4881(5);3
Ge3 2.4860(7)
Ge2 2.4860(7);4
Ge1 3.5395(3);12
Ge2 3.4437(3);6
Ge3 3.3516(1);2
Ge1}
Ge2}
Ge1 2.4932(8);2
Ge1 2.510(1)
Ge2 2.4911(9)
Ge1 2.4911(9);3
Ge3 2.493(1)
Ge2 2.493(1);4
Ge1 3.5444(5);12
Ge2 3.4472(5);6
Ge3 3.3528(1);2
Rb8Na16Si136
Si1
Si2
Si3
Na
Rb
96g
32e
8a
0.06756(3)
x
x
0.37058(4)
0.0094(3)
0.0092(3)
0.0087(5)
0.0210(6)
0.0314(3)
0.21752(4)
x
1/8
0
1/8
0
1/8
0
Ge3}
Na}
Ge3}
Na}
16c
8b
3/8
3/8
3/8
Rb8Na16Ge136
Na
Cs
5.4732(2)
6.4179(2)
Na
Rb
5.4751(2)
6.4201(3)
Ge1
Ge2
Ge3
Na
96g
32e
8a
0.06770(4)
x
x
0.37071(5)
0.0132(4)
0.0122(4)
0.0104(6)
0.021(2)
0.054(1)
0.21794(4)
x
1/8
0
Cs}
Ge1 4.1356(4);12
Ge1 4.2222(5);12
Ge2 4.2173(7);4
Rb}
Ge1 4.1331(8);12
Ge1 4.2192(7);12
Ge2 4.211(1);4
1/8
0
1/8
0
16c
8b
Rb
3/8
3/8
3/8
Cs
6.7033(3)
Rb
6.7055(3)
? ; is de"ned as one-third of the trace of the orthogonalized ; tensor.
%ꢆ
GH
The thermopower of a hot-pressed pellet of Cs Na Si
ꢁꢈ ꢁꢉꢈ
carefully picked single crystals, which were then ground and was measured by using a steady-state technique over the
ꢆ
ꢁ
pressed under a pressure of 100 ton in a -in. die at room temperature range 70}300 K.
ꢀ
temperature and at 2003C. Only a cold-pressed pellet was
measured at di!erent temperatures in the range of
10}300 K. It revealed progressively diminishing resistivity
with decreasing temperature, which indicates metallic-like
RESULTS AND DISCUSSION
The unit cell parameters of the two Si clathrates,
and
behavior. Nevertheless, due to the grain boundaries, the a"14.7560(4) and 14.7400(4) A for Cs Na Si
ꢁꢈ ꢁꢉꢈ
measurements at room temperature of this pellet were 2 or- Rb Na Si , respectively, are slightly larger than those
ꢁꢈ ꢁꢉꢈ
ꢆ
ꢆ
ders of magnitude higher than those of the hot-pressed reported for the nonstoichiometric Na Si
phase
V ꢁꢉꢈ
pellet and the single crystal. For the latter, on the other (1(x(23), a"14.6428(4) and 14.7030(5) A for the lowest
hand, measurements could be done only at room and highest sodium content, respectively. The latter are
temperature because the resistivity of the samples went out consistent with the suggested increase of the unit cell para-
of the range of the digital multimeter when the temperature meters with increasing alkali metal concentration (23). The-
was lowered. Independent conductivity measurements were oretically optimized values for imaginary empty clathrate-II
also performed on monodisperse (particle size within the structures range between 14.46 and 14.86 A, depending
range of 250}425 lm) selected single crystals of largely on the computational method, and cannot be used
Cs Na Ge
ꢁꢈ ꢁꢉꢈ
free Q-technique.
using a standard, high-frequency, contact- for comparison (34). For the Ge analogs, on the other hand,
ꢆ
only a theoretical value of a"15.13 A for the empty Ge
ꢁꢉꢈ

CLATHRATES OF GROUP 14 WITH ALKALI METALS
99
TABLE 5
Standard and Variable Site Occupation Factors (SOF) and Equivalent Isotropic Displacement Parameters (Ueq)? for Cs8Na16Si136
,
Cs8Na16Ge136, Rb8Na16Si136, and Rb8Na16Ge136
Standard occupancies
Variable occupancies@
Atom
Wycko! site
SOF
;
[Aꢀ]
SOF
;
[Aꢀ]
%ꢆ
%ꢆ
Cs Na Si
ꢁꢈ ꢁꢉꢈ
ꢆ
Si1
Si2
Si3
Na
Cs
96g
32e
8a
16c
8b
0.50000
0.16667
0.04167
0.08333
0.04167
0.00664(5)
0.00666(6)
0.0066(1)
0.0187(2)
0.01990(6)
0.500(1)
0.00662(7)
0.00674(9)
0.0064(2)
0.018(3)
0.1672(5)
0.0413(3)
0.0816(5)
0.04175(8)
0.01994(6)
Cs8Na16Ge136
0.0110(1)
Ge1
Ge2
Ge3
Na
96g
32e
8a
16c
8b
0.50000
0.16667
0.04167
0.08333
0.04167
0.495(3)
0.168(1)
0.0423(4)
0.084(2)
0.04213(8)
0.0108(1)
0.0108(2)
0.0105(3)
0.035(2)
0.01038(1)
0.0099(2)
0.034(1)
Cs
0.0344(3)
0.0349(4)
Rb8Na16Si136
Si1
Si2
Si3
Na
Rb
96g
32e
8a
16c
8b
0.50000
0.16667
0.04167
0.08333
0.04167
0.0094(3)
0.0092(3)
0.0087(5)
0.0210(6)
0.0314(3)
0.502(3)
0.167(1)
0.0429(6)
0.0821(8)
0.0417(2)
0.0095(3)
0.0092(5)
0.0100(9)
0.0200(9)
0.0314(4)
Rb8Na16Ge136
Ge1
Ge2
Ge3
Na
96g
32e
8a
16c
8b
0.50000
0.16667
0.04167
0.08333
0.04167
0.0132(4)
0.0122(4)
0.0104(6)
0.021(2)
0.054(1)
0.484(7)
0.163(3)
0.0399(9)
0.091(3)
0.0422(2)
0.0133(4)
0.0124(5)
0.0096(5)
0.029(3)
0.055(2)
Rb
? ; is de"ned as one-third of the trace of the orthogonalized ; tensor.
%ꢆ
GH
@ The occupancies of each site were freed while the remaining were kept "xed.
structure is available (35). Practically no other data, except varying site occupation, which can be attributed to either
the brie#y mentioned but not further discussed phase static disorder or vibration of the atom about its equilib-
Na Ge
with a"15.4 A, are known for the germanium rium position. The re"nements with fractional occupancies
V
ꢁꢉꢈ
type II clathrates (22). The calculated lattice parameter or disorder of the alkali metal sites did not improve the
for the empty germanium clathrate is somewhat smaller overall structural parameters, and therefore the "nal least-
(2.3% error) than the experimental values of the completely squares cycles were done with 100% occupancies of all
"lled compounds, a"15.4805(6) and 15.4858(6) A for crystallographic sites. Since the data sets for Cs Na Si
ꢆ
ꢁꢈ ꢁꢉꢈ
Cs Na Ge
ꢁꢈ ꢁꢉꢈ
same time, the energy di!erence between the structure with respectively, while those for Rb Na Si
ꢁꢈ ꢁꢉꢈ
were collected up to 503, the accuracy of the
and Rb Na Ge , respectively. At the and Cs Na Ge
were collected up to 2h"903 and 1003,
ꢆ
ꢆ
ꢁꢈ ꢁꢉꢈ ꢁꢈ ꢁꢉꢈ
ꢆ
and
ꢆ
the experimental coordinates and the one with optimized Rb Na Ge
ꢆ
ꢁꢈ ꢁꢉꢈ
coordinates is only 1.3 meV/atom (35).
Cs compounds is clearly better.
The structure re"nements for all four systems unambigu-
The re"nements con"rm that the completely "lled clath-
ously show that there are no partially occupied positions, rate-II structure is rigid and invariant with respect to the
both at the network and at the alkali metal sites (Table 5). size of the cation. The Si}Si distances range from 2.3584(4)
Varying the occupancies of any Si or Ge site while keeping to 2.3924(5) A for 1 and from 2.362(1) to 2.395(1) A for 3.
the remaining ones "xed does not lead to deviations of more The corresponding ranges for the Si angles are from
than 2.2p. Larger deviations (up to 5p) were observed for the 105.52(1)3 to 119.842(2)3 in 1 and from 105.44(3)3 to
two alkali metal sites for all four clathrates. At the same 119.836(5)3 in 3, the largest angles occurring at the six-
time, their equivalent isotropic displacement parameters member rings of the hexakaidecahedra. For the Ge com-
(; ) tended to increase slightly (within less than 2.5p) with pounds, the Ge}Ge distances range from 2.4859(7) to
%ꢆ

100
BOBEV AND SEVOV
TABLE 6
isolated free alkali metal atoms. This conclusion seems to be
Approximate van der Waals Radii of the Empty Space? in the
Small ([512]-Polyhedra) and Large ([51262]- or [51264]-Poly-
hedra) Cages for Silicon, Germanium, and Tin Clathrate Com-
pounds, Compared with the Ionic Radii@ of the Alkali Metals (A)
applicable only to the nonstoichiometric phase Na Si
V ꢁꢉꢈ
and only at low Na concentrations (x(9), since at higher
Na concentrations insulator-to-metal transition occurs.
Theoretical calculations using the full-potential all electron
linear augmented plane wave method (FLAPW) indicate
that, indeed, the sodium electrons are fairly localized at low
Clathrate-I
Small cage Large cage
1.10 Na 1.35 Na, K
Clathrate-II
alkali metal content (e.g., Na Si ) but are delocalized at
Small cage Large cage
ꢇ ꢁꢉꢈ
higher alkali metal concentrations (e.g., full occupation of
Si
1.10
1.25 Na, K 2.00 Rb, Cs
1.65 Rb, Cs '2.2(est.)
Na
1.85 Rb, Cs
all sites Na Si ), due to signi"cant overlap between the
ꢀꢇ ꢁꢉꢈ
Ge
Sn
1.25 Na, K 1.55 K, Rb
1.65 Rb, Cs 1.85 Rb, Cs
Na and Si orbitals (38). Thus, the extra alkali metal elec-
trons in our case can be considered delocalized and partially
"lling the silicon or germanium conduction bands, which, of
course, are composed of predominantly Si}Si or Ge}Ge
antibonding states. This is also in agreement with the fact
that the observed distances are also longer than those theor-
etically calculated for the empty clathrate-II structures.
Due to the extra 24 electrons per formula, all four com-
pounds should be metallic conductors. Our preliminary
four-probe conductivity measurements (cold-pressed pel-
Ionic radii for the alkali metals for CN"6:
Na"1.02, K"1.38, Rb"1.49, Cs"1.70
? Calculated based on the shortest A}¹t distances by subtracting the
corresponding van der Waals radii for the Si, Ge, and Sn, respectively.
@ The values are those of Shannon and Prewitt (62), calculated for oxides
(based on the value 1.40 A for six-coordinated Oꢀ\). A certain allowance
should be made due to the di!erent coordination numbers of the alkali
metal cations in the clathrate cages.
lets) for Cs Na Si
ꢁꢈ ꢁꢉꢈ
ambiguous and inconclusive (27). The room temperature
and Cs Na Ge
were somewhat
ꢆ
ꢆ
ꢁꢈ ꢁꢉꢈ
2.5033(9) A and from 2.4911(9) to 2.510(1) A for 2 and 4, resistivities of the two samples were measured at ca. 48 and
respectively, and the Ge angles are in the ranges from 52 m)-cm, respectively, while the corresponding numbers
105.22(2)3 to 119.816(3)3 and from 105.18(4)3 to 119.809(6)3 at 50 K were 30 and 45 m)-cm. Although indicating metal-
for the two compounds, respectively. Both Si}Si and Ge}Ge lic behavior, the temperature dependence in both cases is
distances are somewhat longer than those in the pure ele- very close to linear with slopes of 0.072 and 0.028 m)-
ments, 2.352 A for Si and 2.445 A for Ge. Clearly, the reason cm/3C, respectively. Later, more accurate measurements
for this is not the size of the cations since: (i) there is were performed on single crystals and hot-pressed pellets of
practically no change in the distances moving from Cs to Rb Cs Na Si . The numbers at room temperature were 30
ꢆ
ꢁꢈ ꢁꢉꢈ
and (ii) the voids are larger than the alkali metal cations and 90 l)-cm for a single crystal and a pellet, respectively,
(Table 6). The most likely reasons for the longer distances in and clearly indicated a metallic state, which is in excellent
the clathrates are (i) the 24 extra electrons per 136 network agreement with the suggested electronic structure and
atoms and (ii) the distorted tetrahedral environment since stoichiometry. Four-probe measurements on two single
the deviations from the ideal tetrahedral angle 109.473 are crystals of Rb Na Si
ꢁꢈ ꢁꢉꢈ
average of 80 l)-cm, which is nearly identical to the resis-
at room temperature gave an
ꢆ
not negligible.
The extra electrons could be either delocalized over the tivity of the Cs analog, as expected. It was not possible to
four-bonded network or localized on the alkali metals. The measure over a wide temperature range since at lower
latter are well separated in this structure, 5.2170(1), temperatures the resistivity of the sample dropped out of the
6.1175(2), and 6.3859(2) A for the closest Na}Na, Cs}Na, range of sensitivity of the measuring device. The resistivities
and Cs}Cs contacts, respectively, in 1; 5.4732(2), 6.4179(2), of the two Ge clathrates were measured on a hot-pressed
and 6.7033(3) A for the closest Na}Na, Cs}Na, and Cs}Cs pellet for Rb Na Ge
ꢁꢈ ꢁꢉꢈ
contacts, respectively, in 2; 5.2114(7), 6.1109(2), and for Cs Na Ge . (The Q-method was also intended to
ꢁꢈ ꢁꢉꢈ
and by the contact-free Q-method
ꢆ
ꢆ
6.3826(2) A for the closest Na}Na, Rb}Na, and Rb}Rb serve as a reference for the four-probe measurements.) For
contacts, respectively, in 3; and 5.4751(2), 6.4201(3), and the latter, the resistivity at room temperature was deter-
6.7055(3) A for the closest Na}Na, Rb}Na, and Rb}Rb mined to be the order of 160 l)-cm, comparable with the
contacts, respectively, in 4. Thus, no interaction between resistivities measured for single crystals of the Si clathrates.
them should be expected (the metallic radii for Na, Rb, and The somewhat higher number is perhaps due to the numer-
Cs are 1.90, 2.48, and 2.67 A, respectively) (36). Nevertheless, ous approximations such as assumptions for narrow par-
based on EPR and NMR experiments, some authors specu- ticle size distribution and ideal spherical shape used for the
late that the &&system is better described in terms of encap- calculations. The resistivity of the Rb Na Ge
sulated neutral alkali metal atoms, rather than one, room temperature was 110 l)-cm.
pellet at
ꢆ
ꢁꢈ ꢁꢉꢈ
>
containing Na ions'' (16,23}25,37), i.e., systems with no
electron transfer over the Si or Ge network but rather with consistent with the temperature-independent Pauli
The results of the conductivity measurements are

CLATHRATES OF GROUP 14 WITH ALKALI METALS
101
states of the network becomes more important, as shown
from theoretical calculations (14,35,38).
As already discussed, the clathrates are considered prom-
ising thermoelectric materials because of the belief that &&the
rattling of the doping atoms within the voids of the struc-
ture'' would improve their thermoelectric performance (31).
In the context of this idea, the larger equivalent isotropic
displacement parameter for the alkali metals residing in the
clathrate-II cages indicates larger mean-square displace-
ment amplitude of the corresponding atom, averaged over
all directions. This is in agreement with the fact that the
sodium thermal parameters in the Ge clathrates are larger
than those in the Si clathrates. Sodium has an ionic radius of
1.02 A, which "ts the smaller cage for the silicon clathrates
FIG. 3. Molar magnetic susceptibility (emu/mol) of Cs Na Si
ꢁꢈ ꢁꢉꢈ
as a function of the temperature (K) at a "eld of 3 T.
and
ꢆ
(r
ꢇ!ꢁ$%ꢈ5!!ꢉꢊ
clathrates (r
ꢇ!ꢁ$%ꢈ5!!ꢉꢊ
+1.10 A) better than that of the germanium
Cs Na Ge
ꢁꢈ ꢁꢉꢈ
ꢆ
+1.25 A). Also, the rubidium thermal
parameters are larger than those of cesium in both the
silicon and germanium structures. This, of course, should be
paramagnetism for all four phases. The plots of the molar expected since the lattice parameters for the Cs and Rb
>
magnetic susceptibilities versus the temperature are shown clathrates are nearly identical. Cs with a radius of 1.70 A
>
in Figs. 3 and 4. The raw data for all measurements were "ts better in the larger cage than Rb with a radius 1.49 A
corrected for the holder and for the ion-core diamagnetism for both silicon and germanium clathrates with vander
>
>
>
ꢇ>
ꢇ>
of Na , Cs , Rb , Si , and Ge . No superconductivity at Waals radii the large cage of 1.85 and 2.00 A, respectively
low "elds (0.1}0.3 T) and low temperatures down to 2 K (Table 6). This also accounts for the larger thermal para-
were found. These results are in agreement with pre- meter for Cs in 2 than in 1. These oversized cages, with
vious measurements on Na Si and Na Si
Pauli-like temperature-independent paramagnetism and good thermoelectric e$ciency as demonstrated for some
(22,24). The respect to the cations, are believed to be responsible for the
ꢆ ꢇꢈ
V ꢁꢉꢈ
metallic conductivity of Cs Na Si , Cs Na Ge
,
clathrate-I phases (e.g., Sr Ga Ge ) (39) and some "lled
ꢁꢈ ꢉꢂ
combined with the dia- skutterudites (mineral structures with voids, e.g.,
ꢆ
ꢁꢈ ꢁꢉꢈ ꢁꢈ ꢁꢉꢈ
ꢁꢈ ꢁꢉꢈ
ꢆ
ꢁꢈ ꢁꢉꢈ
ꢆ
Rb Na Si , and Rb Na Ge
ꢆ
ꢆ
magnetic semiconducting behavior of the nonstoichiometric LaFe Sb ) (40). For maximum performance (Z¹'1), high
ꢇ
ꢁꢀ
phase Na Si
prove that the alkali metal does not form an thermopower and high electrical and low thermal conduct-
V ꢁꢉꢈ
impurity band near the bottom of the framework conduc- ivity would be required. However, good conductors of elec-
tion band. Rather, it supports the idea that there are strong tricity are usually good conductors of heat as well, whereas
charge-transfer interactions between the Si(Ge) and the al- the thermopower reaches its maximum for small band-gap
kali metal atoms, although the resulting structure can not be semiconductors. Therefore, the results from the four-probe
considered entirely ionic. Apparently, the involvement of conductivity measurements discussed above imply that
the unoccupied p orbitals of the alkali metals in the empty clathrate-II will not have high thermopower at room tem-
perature, similar to that of Na Si
(about!100 lV/K)
V ꢁꢉꢈ
(22) or that of clathrate-I Sr Ga Ge (!320 lV/K) (39),
ꢆ
ꢁꢈ ꢉꢂ
for instance. Figure 5 shows the thermopower of a cold-
pressed pellet of Cs Na Si
deed, the value at room temperature, !29 lV/K, is clearly
not favorable for high thermoelectric e$ciency. The slope,
versus the temperature. In-
ꢆ
ꢁꢈ ꢁꢉꢈ
ꢀ
as expected, is negative, !0.07 lV/K , and indicates n-type
conductivity. Simple calculations show that to have Z¹51
at room temperature, our sample should have thermal con-
ductivity of j40.8 W/m)K.
Why are there so many compounds with the clathrate-I
structure and so few of clathrate-II structure? What is the
reason for the preferred formation of one over the other?
After all, as already pointed out, their stoichiometries are
very similar, A¹t
vs A¹t
. For the gas and liquid
hydrates, it is well known that the size of the guest and the
available volume of the host determine which clathrate will
ꢃꢄꢅꢃ
ꢃꢄꢈꢅ
FIG. 4. Molar magnetic susceptibility (emu/mol) of Rb Na Si
ꢁꢈ ꢁꢉꢈ
as a function of the temperature (K) at a "eld of 3 T.
and
ꢆ
Rb Na Ge
ꢁꢈ ꢁꢉꢈ
ꢆ

102
BOBEV AND SEVOV
>
cation like Cs . Therefore, the most reoccurring com-
pounds in the binary and pseudo-binary systems A}Sn are
clathrate-I and the clathrate-like phase A
ing chains of Sn dodecahedra only.
Prior to this work, the synthesis of phases with the clath-
Sn , contain-
ꢆ$V ꢀꢃ
rate-II structure such as Na Si
was done by the thermal
V ꢁꢉꢈ
decomposition of the Zintl compounds NaSi at high tem-
peratures (300}4003C) and dynamic vacuum. The resulting
products are usually inhomogeneous powders with unde-
"ned stoichiometry and contain both clathrate structures
and unreacted NaSi, and even the elements, and further
puri"cation is necessary to separate the phases. Further-
more, small changes in the experimental conditions result in
quite di!erent overall compositions of the mixtures, and
therefore poor reproducibility. Powder di!raction in this
case is not a very useful tool for stoichiometry con"rma-
tion since the composition could vary substantially
FIG. 5. Thermopower (lV/K) of Cs Na Si
ꢁꢈ ꢁꢉꢈ
as a function of the
ꢆ
temperature (K).
form. The same, i.e., the relative sizes of the guest cation and from particle to particle without noticeable changes in
the host cavity, play an essential role in the formation of the lattice parameters due to the rigidity and covalency
intermetallic clathrates as well. Apparently, the electronic of the framework. Following the approach described
e!ects are not important since the A}¹t interactions are above about the guest}host interactions, one can design
more or less purely electrostatic and similar for all alkali compositions that are promising for the synthesis of
metals (except Li). Furthermore, since the ¹t}¹t distances clathrate-II: Cs Na Si , Cs Na Ge , Rb Na Si
ꢁꢈ ꢁꢉꢈ ꢁꢈ ꢁꢉꢈ ꢁꢈ ꢁꢉꢈ
are similar for both clathrate types and are independent of Rb Na Ge , Cs K Ge , and Rb K Ge . Never-
,
ꢆ
ꢆ
ꢆ
ꢆ
ꢁꢈ ꢁꢉꢈ
ꢆ ꢁꢈ ꢁꢉꢈ
ꢆ ꢁꢈ ꢁꢉꢈ
ꢁꢀ
the size of the cation, the volume of the [5 ] polyhedra will theless, only the "rst four compounds were success-
be almost the same in both structures. Also, since there are fully synthesized. All reactions, intended to produce
two types of cages in each clathrate, two alkali metals will be Cs K Ge
and Rb K Ge , failed, and the products
ꢆ ꢁꢈ ꢁꢉꢈ
ꢆ ꢁꢈ ꢁꢉꢈ
preferred for their formation and stabilization. Therefore, were unreacted Ge and the known Zintl compounds
the choice of cations with appropriate sizes and in appropri- K Ge and Cs Ge (or Rb Ge ). Apparently, the
ꢁꢀ ꢁꢅ
ꢁꢀ ꢁꢅ
ꢁꢀ ꢁꢅ
ate ratios will be the product-directing factors. Thus, cations existence of these stable phases obscures the eventual forma-
of only one size as in binary A}¹t systems stabilize the tion of clathrates of any type for both K}Rb}Ge and
structure with cavities of similar sizes, i.e., that of clathrate-I, K}Cs}Ge.
even when the reactions are designed to produce clathrate-
Following the same size relations, we also designed
II. Also, di!erent cations but with similar sizes will stabilize some stoichiometric mixtures favorable for the formation
clathrate-I as well. The smaller sodium and potassium form of clathrate-I (Table 6). These proposed compositions
clathrate-I with the smaller silicon and germanium, while are Na Si , K Si , Na K Si , Na Rb Si , Na K Ge ,
ꢆ ꢇꢈ ꢆ ꢇꢈ
Na Cs Ge ,
ꢇꢈ
two types of cavities in clathrate-II are quite di!erent in size, K Cs Ge , K Rb Sn , K Cs Sn , Rb Cs Sn , K Sn ,
ꢇꢈ ꢇꢈ ꢇꢈ ꢇꢈ ꢇꢈ
on the other hand, its formation will be facilitated by a com- Rb Sn , and Cs Sn . All of them, excluding those that
ꢀ ꢈ ꢇꢈ
ꢈ
ꢀ
ꢆ
ꢈ ꢇꢈ
K Ge ,
ꢇꢈ
ꢀ ꢈ ꢇꢈ
K Rb Ge ,
ꢇꢈ
the larger rubidium and cesium match with tin. Since the Na Rb Ge ,
ꢀ
ꢈ
ꢇꢈ
ꢀ
ꢀ
ꢈ
ꢀ
ꢈ
ꢀ
ꢈ
ꢀ
ꢈ
ꢀ
ꢈ
ꢆ
ꢆ
ꢇꢈ
ꢆ
ꢇꢈ
bination of cations with very di!erent sizes. The radius of were already reported (Table 1), were tried and the
the smaller cavity in Si and Ge phases is comparable only results con"rmed the importance of the choice of cations.
>
>
>
with the radii of Na and Na or K , respectively. Both The loading stoichiometry proved to be less important
>
>
Rb and Cs are too large to be incorporated into these than the type of the available cations. Thus, reactions
ꢁꢀ ꢇ
cages but they can "t well into the larger [5 6 ]-hexa- loaded with stoichiometries Na Rb Si , Na Rb Ge , and
kaidecahedra. No single size cation can "t e$ciently enough Na Cs Ge and intended to produce clathrate-I yielded
in both cavities of clathrate-II. Bearing this idea in mind and instead clathrate-II. These results are somewhat under-
ꢀ
ꢈ ꢇꢈ
ꢀ
ꢈ
ꢇꢈ
ꢀ
ꢈ
ꢇꢈ
moving one period down in group 14, one comes across Sn, standable, keeping in mind that the calculated relative ther-
>
where both cavities are large enough to be "lled with Rb
modynamic stability of the two clathrate structures are
>
>
and Cs but too large for Na and therefore no Na}Rb}Sn nearly equal, with slight preference toward type-II. Chang-
and Na}Cs}Sn clathrates of both types shall be expected. ing the temperature pro"le or slightly modifying the ratio
We can speculate that tin will most likely form only clath- for these three systems led to the formation of stable
rate-I, mainly with Rb and/or Cs. This structure would be A Ge phases, similar to the results in Na K Ge ,
ꢁꢀ ꢁꢅ
ꢀ ꢈ ꢇꢈ
more stable than clathrate-II since the size of the larger void K Rb Ge , and K Cs Ge . Only a Na}K}Si reaction
ꢇꢈ ꢇꢈ
'2.2 A), even for a large a!orded the formation of clathrate-I, but in low yield and as
ꢇ!ꢁ$%ꢈ5!!ꢉꢊ
ꢀ
ꢈ
ꢀ
ꢈ
in the latter is too big (r

CLATHRATES OF GROUP 14 WITH ALKALI METALS
103
a "ne powder. In the case of the A}Sn systems, two major slight di!erences in re"nement on the partially occupied Sn
phases comprised the results from nearly all reactions. site, or might be attributed to experimental errors. Never-
These are the clathrate-like A Sn
and clathrate-I theless, the measured temperature-independent diamag-
ꢆ!V ꢀꢃ
A Sn compounds (21). For instance, the products of netism of the Cs Sn
at a "eld of 3-T down to
ꢆ
ꢇꢇ
K Rb Sn
ꢇꢈ
ꢆ
ꢇꢇ
were the two clearly distinguished phases a temperature of 10 K con"rms the structure re"nement and
ꢀ
ꢈ
K
Sn and K Rb Sn (or Rb Sn ), which were the suggested stoichiometry Cs Sn ᮀ , which had been
ꢆ!V ꢀꢃ
V
ꢆ\V ꢇꢇ
ꢆ
ꢇꢇ
ꢆ
ꢇꢇ ꢀ
identi"ed from both powder XRD and single crystals. There previously reported as Cs Sn (43).
ꢆ
ꢇꢈ
is considerable sensitivity to the cation size. Apparently, due
The clathrate-I phases with vacancies are typical for the
to the quite similar sizes of the K and Rb cations, a wide binary and pseudo-binary A}Sn systems, while as already
degree of mixing occurs, which was con"rmed from the discussed, clathrate-I compounds of Si and the alkali metals
slightly shifted lines in the XRD powder patterns and in are believed to be &&defect-free'' (16). Germanium clathrates
agreement with the results for the K}Cs}Sn systems (21). are somewhat on the border line and the structure}proper-
The observation that the K cations are preferably located ties relations for the A}Ge systems are still questionable.
(about 2/3 of occupancy) within the small cavity in To clarify the electronic structures and the properties of the
K
Cs
ꢁꢄꢈ(ꢁ) ꢈꢄꢇ(ꢁ) ꢇꢇ
rakaidecahedra may also serve as proof of the above-dis- of the A}Si and A}Sn clathrates, we tried to synthesize the
Sn while the Cs cations occupy the tet- binary A}Ge clathrates-I and to compare them with those
cussed cation-size relations.
binary K Ge from pure elements. Unfortunately, all at-
ꢆ
ꢇꢈ
The composition Rb Cs Sn was also examined and tempts were unsuccessful. However, a reaction carried out
ꢇꢈ
yielded clathrate-I, as predicted, in nearly 100% yield. The in Ga #ux readily produced K Ga Ge with a clathrate-I
ꢀ
ꢈ
ꢆ
ꢆ
ꢉꢆ
crystals looked rather shiny and had a metallic luster rather structure in high yield and good crystal quality. Data were
than the &&dark gray appearance'' of the tin clathrates pre- collected and the structure was re"ned routinely without
viously described. To our surprise they turned out to be also fractionally occupied network sites. Since Ge and Ga can-
stable at ambient conditions, oxygen, moisture, etc., con- not be distinguished, the stoichiometry K Ga Ge was
ꢆ
ꢆ
ꢉꢆ
trary to the initially suggested sensitivity. Selected crystals deduced from the fact that the unit cell parameter
were soaked in water for more than 12 h and they retained (a"10.7706(5) A) (44) was invariant with respect to the
their quality. Moreover, careful measurements of the posi- amount of Ga loaded. Furthermore, the unit cell is slightly
tions of the lines in the powder pattern revealed a lattice larger than the unit cell of K Ge (a"10.71 A) (11) but
ꢆ
ꢇꢈ
parameter somewhat larger (a"12.200(1) A) than those of compares well with the cell parameters of K Al Ge (45)
ꢉꢆ
and K In Ge (46), a"10.785(1) and 11.033(2) A, respec-
ꢉꢆ
ꢆ
ꢆ
the previously reported Cs Sn , K
Cs
Sn
,
ꢆ
ꢇꢈ ꢁꢄꢈ(ꢁ) ꢈꢄꢇ(ꢁ) ꢇꢇꢄꢂ(ꢁ)
ꢆ ꢆ
and Rb Sn
with a"12.096(1), 12.084(1), and tively. Also, four-probe resistivity measurements on a cold-
ꢆ
ꢇꢇꢄꢈ(ꢁ)
12.054(1) A, respectively. Single-crystal X-ray di!raction pressed pellet gave o +0.37 )-cm and its temperature
data were collected, and the structure was re"ned as a defect dependence clearly indicated a semiconducting state.
ꢀꢊꢉ
Cs}Sn clathrate-I structure with exactly two tin vacancies
per formula, i.e., Cs Sn ᮀ (ᮀ"vacancy). The re"ne-
CONCLUSIONS
ꢆ
ꢇꢇ ꢀ
ments were entirely routine and revealed fractional occu-
pancy for the Sn 6c site only (41). The Sn}Sn distances in
For the "rst time, large single crystals of Cs Na Si
,
ꢆ
ꢇꢇ ꢀ ꢇꢇ ꢀ ꢁꢈ ꢁꢉꢈ ꢁꢈ ꢁꢉꢈ ꢁꢈ ꢁꢉꢈ
ꢁꢈ ꢁꢉꢈ
Cs Sn ᮀ are longer than those in Rb Sn ᮀ . The re"ne- Cs Na Ge , Rb Na Si , and Rb Na Ge
clath-
ꢆ
ꢆ
ꢆ
ꢆ
ꢆ
ment carried out with variable site occupancy of the 6c site rate-II compounds have been synthesized from pure ele-
resulted in 61(1) % site occupation for Cs Sn com- ments. The rational synthesis is reproducible and
ᮀ
ꢆ
ꢇꢇ ꢀ
pared to 77(2) % for Rb Sn ᮀ (21). Therefore, the corre- quantitative. The structures of these four compounds were
ꢇꢇ ꢀ
sponding formulas are Cs Sn
ꢇꢉꢄꢈ(ꢁ)
was measured on a cold-pressed di!raction data and the re"nements unambiguously con-
ꢆ
vs Rb Sn
. The elucidated with high accuracy from single-crystal X-ray
ꢇꢇꢄꢈ(ꢁ)
ꢆ
ꢆ
resistivity of Cs Sn
ꢇꢉꢄꢈ(ꢁ)
ꢆ
pellet made from selected crystals. The room temperature "rmed the "rst &&defect-free and fully stu!ed'' clathrate-II
value, 320 l)-cm, is consistent with the reported resistivity structures. The measured transport and magnetic properties
of K
ꢁꢄꢈ(ꢁ) ꢈꢄꢇ(ꢁ) ꢇꢇꢄꢂ(ꢁ)
cantly from the resistivity of Cs Zn Sn , 52 m)-cm (42), stoichiometry and indicate that these compounds do not
Cs
Sn
, 288 l)-cm (21). It di!ers signi"- are consistent with the suggested ideal clathrate-II
ꢆ
ꢇ
ꢇꢀ
although both compounds are expected to exhibit similar have a future as thermoelectric materials. Our report on the
properties typical for electronically balanced Zintl com- clathrate exploration also adds some more information on
pounds. Apparently, substitution of the ¹t atoms with elec- the structural chemistry of silicon and germanium and tin at
tron-poorer elements balances the charges more e$ciently negative oxidation states. Thus, until now, in the systems
than that in phases with vacancies. The estimated alkali metal(s)}silicon, alkali metal(s)}germanium, and al-
semiquantitative band gaps for K Cs Sn
and for kali metal(s)}tin, proven to exist by single-crystal X-ray
ꢁꢄꢈ ꢈꢄꢇ ꢇꢇ
ꢇ\
ꢇ\
deltahedra (mono-
Cs Sn , E +0.25 and E +0.07 eV, respectively, either di!raction, are ¹t
tetrahedra, ¹t
ꢆ
ꢇꢇ
'
'
ꢇ
ꢊ
indicate di!erent carrier concentrations, implied from the capped square antiprisms or tricapped trigonal prisms) (47),

104
ꢆ\
BOBEV AND SEVOV
¹t clathrate alike chiral chains, and clathrate-I (21) and 17. N. F. Mott, J. Solid State Chem. 6, 348 (1973).
ꢀꢃ
18. H.-G. von Schnering, Nova Acta ¸eopold. 59, 168 (1985). H.-G. von
Schnering, Bol. Soc. Chil. Quim. 33, 41 (1988).
ꢆ\
ꢉ\
in type
clathrate-II frameworks, formally ¹t
I and type II, respectively.
and ¹t
ꢇꢈ
ꢉꢇ
19. R. Nesper and H.-G. von Schnering, Tschermaks Mineral. Petrogr. Mitt.
32, 195 (1983).
20. Some direct but unpublished veri"cations of A ¹t compositions
ACKNOWLEDGMENTS
ꢆ
ꢇꢇ
were brought to our knowledge with the courtesy of H.-G. von Schner-
ing: J. Llanos, Doctoral Dissertation, University of Stuttgart, 1983.
R. Kroner, Doctoral Dissertation, University of Stuttgart, 1989.
M. Baitinger, Y. Grin, and H.-G. von Schnering, &&Abstracts from the
VI-th European Conference of Solid State Chemistry'', Zurich, 1997, p.
116. ETH Zurich, Switzerland, 1997.
We thank John Greedan and his co-workers (McMaster University,
Hamilton, Ontario) for the thermopower measurements, Paul Maggard
(Iowa State University, Ames) for the Q-measurements, the donors of The
Petroleum Research Fund administered by the ACS for support of this
research, and the NSF for an equipment grant (DMR-9703732) for the
SQUID magnetometer.
21. J. T. Zhao and J. D. Corbett, Inorg. Chem. 33, 5721 (1994).
22. C. Cros, M. Pouchard, and P. Hagenmuller, J. Solid State Chem. 2, 570
(1970).
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CLATHRATES OF GROUP 14 WITH ALKALI METALS
105
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ꢆ
ꢇꢈ
(0.10;0.10;0.08 mm, 2h "503) were collected on a CAD-4 at
ꢄ!ꢅ
room temperature with monochromated MoKa radiation. The struc-
ture was re"ned as Cs Sn
. No evidence for Rb content was
ꢆ
ꢇꢉꢄꢈ(ꢁ)
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d
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Z. Kristallogr. NCS 213, 677 (1998).
#!ꢉ#
ꢁ
ꢀ
4.22/7.22% for 300 observed (I52r ) and 347 total number of re#ec- 50. H.-G. von Schnering, W. Carrillo-Cabrera, R. Kroner, K. Peters, E.-M.
'
tions, respectively, and 16 variables, including the extinction coe$c-
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ient.
Important
Sn}Sn
distances:
Sn1}Sn1"2.876(2); 51. R. Kroner, K. Peters, H.-G. von Schnering, and R. Nesper, Z. Kristal-
Sn1}2Sn1"2.8494(7); Sn1}Sn3"2.7981(9); Sn2}3Sn1"2.8494(7);
Sn2}Sn2"2.826(2); Sn3}4Sn1"2.7981(9) A.
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ꢆ
ꢆ
ꢉꢆ
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ꢄ!ꢅ
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ꢉꢆ
Z"1, a"10.7706(5) A, l"273.43 cm\ꢁ,
ꢆ
ꢆ
d
"4.823 g cm\ꢉꢌ
(1986); Angew. Chem. Int. Ed. Engl. 25, 350 (1986).
#!ꢉ#
R /wR "2.09/4.02% and 4.49/4.14% for 156 observed (I52p ) and 57. R. F. W. Herrmann, K. Tanigaki, S. Kuroshima, and H. Suematsu,
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ꢁ
ꢀ
'
Chem. Phys. ¸ett. 283, 29 (1998).
Ge1}Ge1"2.537(1);
Ge1}2Ge1"2.4936(4);
Ge1}Ge3"
logr. NCS 213, 669 (1998).
59. R. Kroner, K. Peters, H.-G. von Schnering, and R. Nesper, Z. Kristal-
logr. NCS 213, 671 (1998).
2.5105(5);
Ge2}3Ge1"2.4936(4); Ge2}Ge2"2.467(1);
Ge3}4Ge1"2.5105(5) A.
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