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YbGaGe Zero Thermal Expansion as a Result of an Electronic Valence Transition.

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Expansion-Free Materials
YbGaGe: Zero Thermal Expansion as a Result of an
Electronic Valence Transition?
Klaus Stwe*
solid-state chemistry · functional materials · intermetallic phases · thermal expansion
Usually materials expand upon heating: They have a positive coefficient of
thermal expansion (PTE or positive
CTE). Some compounds, however, show
near-zero (NZTE), zero (ZTE) or even
negative thermal expansion (NTE). The
best-known NZTE material may be the
ceran glass ceramics of the company
Schott, from which main mirror supports for astronomical reflector telescopes and stove taps are produced.
The oldest known NZTE material is
invar, which was described by Guillaume[1] as early as 1897 and can be
formulated chemically as Fe64Ni36. Its
expansion coefficient is about a tenth of
that of steel. The CTE of invar is at its
lowest when the alloy has been
quenched from high temperatures or if
it has been treated in a cold state. For
superinvar—cobalt-doped invar of the
composition Fe63Ni33Co4—even a negative thermal expansion coefficient
(NTE) can be achieved this way. Recently it was also shown that invar can
be inserted into carbon nanotubes at
800 8C by pyrolysis of aerosols from
Cp2Fe/Cp2Ni mixtures in benzene. In
this way flakes of filled and paralleloriented nanotubes of % 200 mm in
length and % 80 nm in diameter are
created.[2] The magnetic and mechanic
properties of this material promise very
interesting applications in the production of magnetic storage media and
[*] Priv.-Doz. Dr. K. Stwe
Technische Chemie
Universit$t des Saarlandes
Postfach 151150
66041 Saarbr+cken (Germany)
Fax: (+ 49) 681-302-2343
nanoscale thermostates. Materials without thermal expansion that are also
extremely light, thin, and very stable
would be ideal raw materials for the
thermal protection of reusable space
shuttles. ZTE materials are much in
demand as precision substrates for electronic components, as positioning devices that are ultraprecise on a nanometer
scale for semiconductors, and as other
highly precise machine components and
circuits. Therefore, there have been
numerous attempts to invent such materials or to develop them from systems
with well-known thermal properties.
Only a few compounds show intrinsic NZTE, ZTE, or NTE behavior.
These compounds include the minerals
akaganeite (the b form of iron oxide
hydroxide), b-cristobalite, and b-eukryptite. Through temperature-resolved
X-ray powder-diffraction data the structural
2O) and
0:4 6.35
its transformation into hematite in the
temperature range of 26 to 800 8C were
investigated.[3] Between room temperature and about 225 8C, the unit cell of
akaganeite shows NZTE behavior,
above 225 8C the cell volume slowly
decreases, and at about 290 8C the transformation into hematite starts. The
structural mechanisms of the NZTE
behavior of tetragonal b-eukryptite
(LiAlSiO4) were elucidated in detail
through a Rietveld refinement of combined synchrotron and neutron diffraction data.[4] The unusual thermal behavior of b-eukryptite can be explained as a
result of several processes, including
tetrahedral tilting, tetrahedral deformation, and shortening of the Si/AlO
bond. Furthermore, the thermal expan-
sion in ordered eukryptite differs from
that in disordered eukryptite. In this
context it is interesting that some silicates show an auxetic effect. Auxetic
compounds have a negative Poisson
ratio (defined as the quotient of lateral
to longitudinal expansion) and differ
from other compounds in that, unlike a
rubber band, their diameter is not
decreased but increased upon elongation. Besides “molecular” auxetic materials, such as a-cristobalite, lanthanum
niobate, and some fcc (face-centered
cubic) metals, there are also composites,
polymers, and foams with a negative
Poisson ratio known. Subtle structural
differences can be decisive for the
properties of a compound: a-Quartz is
not auxetic, a-cristobalite is auxetic, and
b-eukryptite is an NZTE material. All
these phenomena depend on the existence of polyhedra with acute corners in
the crystal structures of the compounds.
As an alternative to the development of materials with intrinsic ZTE
behavior, one approach is to combine
PTE and NTE substances to create ZTE
composites. For example, the pore-free
functional ceramic nexcera of the company Nippon Steel is a material with
practically zero thermal expansion at
room temperature.[5] The company Matsushita Electric Industrial has applied
for a European patent for another
material.[6] This ZTE material contains
double oxides of the formula RQ2O8
(R = Zr, Hf und Q = Mo, W) as an
NTE component and MQX4 (M = Mg,
Ca, Sr, Ba and X = O, S) as a PTE
component. When the two components
are mixed in a 1:1 ratio, the material that
forms has a thermal expansion of nearly
zero over a wide temperature range. The
DOI: 10.1002/anie.200401757
Angew. Chem. Int. Ed. 2004, 43, 4982 –4984
2004 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
NTE component ZrW2O8 has already
been used in mixtures with cement and
sand to decrease the thermal expansion
and to avoid cracks in paving stones.[7]
Salvador et al. recently discovered a
novel intrinsic ZTE material,[8] the compound YbGaGe, which crystallizes like
YbGaSn, CaGaGe, and SrGaSn in the
YPtAs structure type with the space
group P63/mmc. The YPtAs type can be
derived as described by Hoffmann and
PFttgen[9] from the AlB2 structure type.
It differs from the latter type in that the
planar 63 boron nets in YPtAs are
composed alternately of Pt and As
atoms, and the nets are wavy. Because
of the different atom types in the wavy
63 nets there are several possibilities for
stacking along the c axis; in the YPtAs
type the unit cell is quadrupled relative
to the AlB2 unit cell. LiGaGe with a
doubled unit cell is also known. It
contains three dimensionally linked
units 13[GaGe] analogous to hexagonal
diamond. If two more electrons per
[GaGe] unit are formally added to this
partial structure, puckered hexagonal
layers 12[GaGe]3 analogous to black
phosphorus are formed according to the
(8N) rule. Thus, the two additional
electrons effectively neutralize one of
the four GaGe bonds per atom by
occupying antibonding states, and a free
electron pair forms on each Ga and Ge
atom. The compounds MGaT (M = Ca,
Sr, Yb and T = Ge, Sn) therefore bridge
the two extremes mentioned above.
Their 12[GaT]2 units are interconnected
by GaGa bonds to form double layers.
The GaGa distance in these compounds varies considerably: In CaGaGe
it is the longest at 358 pm, followed by
Figure 1. Crystal structure of YbGaGe.[8]
330 pm in SrGaSn and 325 pm in YbGaGe (Figure 1). This distance is shortest in YbGaSn at 299 pm. These differences in the GaGa bond lengths are
the most apparent in the electron localization function (ELF) shown in Figure 2 for the compounds CaGaGe, YbGaGe, and YbGaSn in a section through
the six-membered rings exactly in line
with the Ga atoms. In Figure 2, the bond
order decreases from right to left, and
two free-electron pairs develop from the
GaGa bond. Furthermore, with a
lengthening of the GaGa bond, a
shortening of the GaT bond within
the six-membered rings of 2–3 pm results. The atoms M bridge the voids
between the 63 rings, strung together
lengthwise [001] like pearls on a necklace. Two different crystallographic positions are occupied in the space group
P63/mmc. M(1) is surrounded by six Ga
atoms in a trigonal prism; M(2) is
surrounded octahedrally by six T atoms
(see Figure 1). As a result of the different coordination surroundings two different valencies are possible for M,
which is exactly what the authors suggest for the compounds YbGaGe and
YbGaSn. The fact that the GaGa bond
is longer in YbGaGe than in YbGaSn
means that more antibonding states
must be occupied in the former compound; that is, the charge of the [GaGe]
unit must formally be a little higher than
that of the [GaSn] unit. In YbGaGe, this
higher formal charge is balanced by the
presence of two cations with different
valencies, and the valencies of these
cations also change with temperature, as
shown by magnetic-susceptibility measurements on YbGaGe. As the valency of
Yb changes with decreasing temperature from about + 2.6 towards + 2, the
contraction of the whole lattice as a
result of the decreasing temperature is
compensated. Thus, two lattice parameters, a1 and a2, increase with decreasing
temperature, whereas the third parameter, c, decreases to the extent that the
total volume remains constant. The
CTE of the a axis in YbGaGe varies a
little depending on the composition, as
the phase exhibits a certain phase width.
According to the authors, the CTE lies
between 1.3·105 and 1.8·105 K1.
For comparison, the corresponding value for YbGaSn is + 1.0·104 K1.
This result shows that the ZTE effect
in YbGaGe is based on a completely
new mechanism. In contrast to classic
ZTE materials, such as ZrW2O8 and
related oxides, the ZTE behavior in
YbGaGe is not of a geometric origin,
nor caused by a cooperative rotation of
Figure 2. Total electron localization function (ELF) for CaGaGe, YbGaGe, and YbGaSn, calculated with LMTO-ASA. Section through the M atoms
with the GaGa bond, as indicated in the structural representation on the right.
Angew. Chem. Int. Ed. 2004, 43, 4982 –4984
2004 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
oxide tetrahedra. No rotations of the
polyhedra occur in YbGaGe, as the lowtemperature X-ray diffraction investigations showed. Instead, an internal electron transfer between the Yb atoms and
the anionic partial structure [GaGe]n
occurs. YbGaGe has the additional
advantage over the oxides of being a
metallic conductor. YbGaGe thus unites
two interesting characteristics, which
makes it a promising material for new
2004, 131, 431–433), has just appeared in
which another two recent publications
on this topic were cited. All three papers
report that YbGaGe has a distinctly
more positive thermal expansion coefficient than that reported by Salvador et
al.[8] The differences may be due to a
deviation in the composition, that is, a
variation in x in YbGa(1+x)Ge(1x). These
newest results prompted the author of
this Highlight to add a question mark to
the title.
Published Online: August 20, 2004
Note added after online publication on
August 20, 2004: An article entitled
"Thermal expansion in YbGaGe" (S.
Bobev, D. J. Williams, J. D. Thompson,
J. L. Sarrao, Solid State Communications
[1] C. E. Guillaume, C. R. Acad. Sci. 1897,
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[2] N. Grobert, M. Mayne, M. Terrones, J.
Sloan, R. E. Dunin-Borkowski, R. Kamalakaran, T. Seeger, H. Terrones, M.
2004 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
RNhle, D. R. M. Walton, H. W. Kroto,
J. L. Hutchison, Chem. Commun. 2001,
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Angew. Chem. Int. Ed. 2004, 43, 4982 –4984
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thermal, valence, electronica, zero, results, transitional, ybgage, expansion
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