A 3D network of four-bonded germanium: A link between open and dense

Article abstract of DOI:10.1002/anie.200800914

(Figure Presented) Under pressure: The new modification Ge(hR8) is obtained upon pressurization of clathrate-type Ge(cF136) or controlled decompression of a Ge(tI4)-type high-pressure phase. The atomic arrangement comprises four-bonded germanium atoms with a topological organization bearing remarkable similarity to high-pressure host-guest assemblies of other main-group elements.

Full text of DOI:10.1002/anie.200800914

Communications
DOI: 10.1002/anie.200800914
Germanium Modifications
A 3D Network of Four-Bonded Germanium: A Link between Open
and Dense**
Ulrich Schwarz,* Aron Wosylus, Bodo Böhme, Michael Baitinger, Michael Hanfland, and
Yuri Grin
Solids comprising three-dimensional networks of mainly
p elements, such as intermetallic clathrates or substituted
skutterudites, are currently the subject of intense investiga-
tion. New materials are sought that display novel combina-
tions of physical characteristics.[1,2]
Elemental germanium adopts a large number of open-
framework structures. At ambient pressure, covalent inter-
actions provide sufficiently high energy barriers to impede
transformations so that phase formation becomes controlled
kinetically, for example in allo-germanium Ge(oP128), Ge-
(hP8),[3] and Ge(cF136). This clathrate-II-type &24Ge136 host
assembly[4] persists at temperatures up to 693 K (Figure 1).
Two more germanium modifications, Ge(tP12) and Ge(cI16),
can be generated by decompression.[5,6] In all these allotropes,
the four-bonded atoms adopt next-neighbor distances that are
similar to those of diamond-type Ge(cF8).
Upon pressure increases to about 10.6 GPa, Ge(cF8)
transforms into b-Sn-type Ge(tI4) with (4+2) coordination
(Figure 1).[7] Above 75 GPa, the so-called Imma phase Ge-
(oI4)[8] with (4+2+2) coordination is formed. Around
80 GPa, hexagonal primitive Ge(hP1)[9] with coordination
number eight is stable. Upon further compression, Ge(oC16)
adopts a crystal structure in which two types of atoms are
coordinated by 10 and 11 neighbors, respectively.[10] This
atomic pattern transforms at higher pressures into the
hexagonal-close-packed (hcp) arrangement Ge(hP2) with
Figure 1. Germanium frameworks in elemental crystal structures. Most
modifications formed at moderate pressures are related to b-Sn-like
Ge(tI4) or to the new allotrope Ge(hR8) rather than to diamond-like
Ge(cF8). The name of the new phase is shaded gray.
coordination number 12.[10]
The pressure-induced structural changes of the modifica-
tion Ge(cF136) are, to date, unexplored. The material for our
study, &24Ge136 , is synthesized by mild oxidation of Na12Ge17
with HCl.[11] With increasing pressure, in situ X-ray powder
diffraction indicates a continuous compression of the clath-
rate between ambient pressure and 12.7(5) GPa (Figure 2). In
these experiments, additional diffraction lines indicate a
second, new phase above 7.6(5) GPa before a third, Ge(tI4)-
type phase starts to form at 8.3(5) GPa. Above 12.7(5) GPa,
the transformation into the Ge(tI4) pattern is completed.
With decreasing pressure, a mixture of the Ge(tI4)-type phase
and the new phase (formed at 9.8 GPa after several days)
yields nearly pristine new diffraction patterns below approx-
imately 6 GPa (Figure 2). Pressure decrease to 1.4 GPa
induces a further transition into mainly Ge(cI16). In these
experiments, the phases may contain small amounts of
hydrogen, oxygen, and sodium from the starting material.
To confirm the new phase unambiguously as a germanium
allotrope, a second set of measurements was performed
starting with pure Ge(tP12). After formation of Ge(tI4), a
stepwise pressure release down from 15.4 GPa induces the
formation of the new allotrope Ge(hR8) mixed with Ge(cF8)
and Ge(tP12) below 7 GPa (Figure 2). The volume fraction of
the phases as estimated from diffraction intensities is
approximately 1:2:2 at 2.4 GPa.
[*] Dr. U. Schwarz, A. Wosylus, B. Böhme, Dr. M. Baitinger, Prof. Y. Grin
Max-Planck-Institut für Chemische Physik fester Stoffe
Nöthnitzer Strasse 40, 01187 Dresden (Germany)
Fax: (+49)351–4646–4002
E-mail: schwarz@cpfs.mpg.de
Dr. M. Hanfland
European Synchrotron Radiation Facility
6 rue Jules Horowitz, 38043 Grenoble Cedex (France)
[**] We thank Dr. Horst Borrmann, Dr. Yurii Prots, Dr. Raul Cardoso-Gil,
and Steffen Hückmann for in-house X-ray diffraction experiments,
Dr. Gudrun Auffermann, Ulrike Schmidt, and Anja Völzke for
chemical analyses as well as Katrin Meier and Miriam Schmitt for
support with the synchrotron measurements.
Supporting information for this article is available on the WWW
under http://dx.doi.org/10.1002/anie.200800914.
6790
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Figure 3. Atomic volumes of germanium as a function pressure:
Ge(cI16) (diamond,[5]), Ge(cF136) (open squares), b-Sn-type Ge(tI4)
(triangles), Ge(hR8) (stars), diamond-type Ge(cF8) (dashed gray
line,[10]). The structural phase transitions are shown in clearly discon-
tinuous volume changes.
À
À
Whereas the distances Ge1 Ge2 and Ge2 Ge2 change
only little upon compression, a more distinct decrease is
À
observed for the Ge1 Ge1 separations (Figure 4). The
Figure 2. X-ray powder diffraction patterns at elevated pressures. Upon
pressure increase (›), the starting material Ge(cF136) persists up to
12.7(5) GPa (a); a phase isotypic to Ge(hR8) coexists with clathrate
and a b-Sn-type structure between 8.3(5) GPa and 12.7(5) GPa (b). An
arrangement isotypic to Ge(tI4) is stable at pressures exceeding
12.7(5) GPa (c). In direction of decreasing pressures (fl), the new
phase is observed down to approximately 2 GPa (d). Starting from
Ge(tP12), the new phase coexists with Ge(cF8) and Ge(tP12) upon
decompression (e). Reflection positions are indicated by tick marks.
Figure 4. Pressure dependence of interatomic distances in Ge(hR8)
The calculated values for diamond-type Ge(cF8) are shown as a gray
dashed line. Estimated standard deviations are shown as bars.
Despite the pronounced differences in atomic volumes
(Figure 3), the compressibility as revealed by the bulk moduli
of the clathrate Ge(cF136) [B0 = 76(6) GPa, B0’ = 6(2)]and
the new modification Ge(hR8) [B0 = 73(3) GPa, B0’ = 4]are
strikingly similar to the value of 75 GPa[12] for Ge(cF8).
The crystal structure of Ge(hR8) comprises a germanium
network with two types of atoms. Often such an occupation of
inequivalent sites is correlated with a differentiation of the
atomic coordination, for example in metals such as Mn-
(cI58),[13] Ti(hP3),[14] or Ge(oC16)[10] and isotypic phases[15,16]
as well as in more complex high-pressure modifications.[17,18]
In Ge(hR8), both types of germanium atoms bond to four
neighbors, Ge1(Ge1)1(Ge2)3 and Ge2(Ge1)1(Ge2)3. Further-
more, one type of germanium atom features a fifth contact
pronounced anisotropy of the compressibility suggests an
alternative description of the atomic arrangement. The atoms
Ge2 form spirals around a 31 screw axis, a substructure which
is similar to elemental a-Te or a-Se, Te(hP3) and Se(hP3).
À
These one-dimensional building blocks are linked by Ge2
Ge2 contacts into a 3D host network enclosing channels along
the c axis. The other germanium guest atoms (Ge1) form
chains with alternating long and short separations in the
resulting tubular voids (Figure 5). A similar structural organ-
ization is observed in the tetragonal high-pressure modifica-
tions of K-III (Rb-IV) and Sb-II (Figure 5), which exhibit
incommensurate identity periods of the partial structures
along the chain direction.[17]
The special partitioning of the Ge(hR8) crystal structure
implicates dissimilar guest–guest, host–host, and host–guest
interactions; therefore, the chemical bonding was analyzed by
means of the electron localizability indicator (ELI[21]).
À
with d(Ge1 Ge1) = 3.24 Š at 2.4 GPa. This expansion of the
coordination sphere and the significantly reduced density of
Ge(hR8) with respect to Ge(cF8) is reflected by an elongation
of the next-neighbor distances. The spatial organization of the
new allotrope may be derived from cubic Ge(cI16)[6] by
symmetry reduction (t4, “translationsgleicher Übergang” of
the order four[19]) and is isotypic to the high-pressure phase
Si(hR8).[20]
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Communications
In summary, the structural organization of the new
germanium allotrope bears some similarity to that of several
recently described incommensurate high-pressure host–guest
assemblies of elemental metals. However, both germanium
atoms adopt the same bonding topology, which results in
equivalent interactions within and between the partial
structures of Ge(hR8). The covalent character of the bonds
interconnecting network “host” and channel “guest” atoms
stabilizes the commensurate order of this arrangement.
Experimental Section
The prepared germanium with clathrate as a main phase contained
traces of sodium (0.34 wt%), oxygen (1.1 wt%), and hydrogen
(0.27 wt%). A detailed discussion of contaminations can be found
in references [4,22]. The modification Ge(tP12) was synthesized from
99.9999% semiconductor-grade germanium in a multianvil device at
10(1) GPa and 1000(100) K. For the in situ high-pressure experi-
ments, powdered samples were placed in steel gaskets using
methanol/ethanol 4:1 as a pressure-transmitting medium. The dia-
mond anvil cells for generating high pressures had culet sizes of
typically 0.4 mm. Pressures were determined by the ruby lumines-
cence method.[23]
X-ray powder diffraction measurements at high pressure were
performed at the undulator beamline ID 09 A of the European
Synchrotron Radiation Facility (ESRF, Grenoble). A bent Si(111)
monochromator was used to select radiation of l = 0.413 Š from the
white (pink) beam. During exposure, samples were oscillated by Æ 38
to enhance powder statistics. Intensities were recorded with imaging
plates. For calibration of detector distance and wavelength we used a
standard silicon sample, Si(cF8). Integration of the two-dimensional
diffraction patterns was performed with the Fit2d software.[24] The
crystal structure was refined using the data of isotypic Si(hR8) as
starting values in the full-profile method. In the least-squares
procedures performed with the program Fullprof,[25] we fixed the
isotropic displacement factor to Biso = 1 Š2. In case of weak intensity
contributions of phases, refinements were restricted to optimization
of lattice parameters. Supplementary diffraction experiments were
carried out in Debye–Scherrer geometry with MoKa radiation. The
ambient-pressure volume of Ge(cF136) was determined with CuKa1
radiation using a focusing setup (Huber Image Plate Guinier Camera
G670) and LaB6 as an internal standard. Diffraction data up to 2q =
1008 were evaluated with the software WinCSD.[26] Equations of state
were obtained by least-squares fits of Murnaghan-type functions to
the experimental data.[27]
Figure 5. Atomic arrangements in the crystal structures of Ge(hR8)
(Ge1: smaller spheres, Ge2: larger spheres), Sb-II and Rb-IV (K-III;[17]
guest atoms smaller spheres, host atoms larger spheres). Crystallo-
graphic unit cells are indicated by gray lines. Projections are oriented
along the c axes.
Despite the different interatomic distances within the
À
germanium framework, each of the short Ge Ge contacts in
the crystal structure has its own attractor in ELI (Figure 6).
This finding clearly confirms the directional character of the
bonding. The positioning of the four maxima around the Ge2
atoms reflects a topological situation similar to that of
Ge(cF8). Although the configuration of ELI around Ge1 is
À
different, an additional maximum on the longer Ge1 Ge1
contact is not observed. In other words, the Ge1 atom exhibits
(3+1+1) next-neighbor contacts while forming only four
covalent bonds.
Electronic structure calculation and bonding analysis was carried
out using the TB-LMTO-ASA program package.[28] The Barth–Hedin
exchange potential[29] was employed for the LDA calculations. The
radial scalar-relativistic Dirac equation was solved to get the partial
waves. The calculation within the atomic sphere approximation
(ASA) included corrections for the neglect of interstitial regions and
partial waves of higher order; an addition of empty spheres was
necessary. The following radii of the atomic and empty spheres were
applied: r(Ge1) = 1.398 Š, r(Ge2) = 1.398 Š, r(E1) = 1.065 Š,
r(E2) = 1.024 Š.
A basis set containing Ge(4s,4p) orbitals was
employed for a self-consistent calculations, with Ge(4d) functions
being downfolded. The electron localizability indicator (ELI, Y) was
evaluated according to reference [30]with an ELI module imple-
mented within the TB-LMTO-ASA package. The topology of ELI
was analyzed using the program Basin.[31]
Figure 6. Isosurfaces of the electron localizability indicator Y for Ge-
(hR8). Top: view along [001]; bottom: view along [010]. Maxima of ELI
clearly reveal the four-bonded character of both types of germanium
atoms.
Received: February 25, 2008
Revised: May 8, 2008
Published online: July 31, 2008
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