Thermal, magnetic, electronic, and superconducting properties of rareearth metal pentagermanides REGe5 (RE = La, Nd, Sm, Gd) and synthesis of TbGe5

Article abstract of DOI:10.1002/zaac.201000065

A series of isotypic rare-earth metal pentagermanides including the new compound TbGe₅ were prepared by high-pressure synthesis. They crystallize in the orthorhombic space group Immm [No. 71; a = 395.70(9) pm; b = 611.1(2) pm, and c = 983.6(3) pm for TbGe₅]. The crystal structure is isotypic to LaGe₅ and consists of puckered germanium slabs, which sandwich, a second germanium species and the rare-earth metal atoms. At ambient pressure, the thermal, decomposition of the phases REGe₅ (RE = La, Nd, Sm, Gd, and Tb) proceeds via discrete intermediate steps into Ge(cF8) and thermodynamically stable germanium-poorer phases. The investigated com-pounds REGe₅ are paramagnetic metallic conductors, which order antiferromagnetically at low temperatures. Specific heat measurements reveal that the superconducting state of LaGe₅ below T_c = 7.1(1) K is characterized by a critical field of μ₀H_c2 = 0.2 T and weak electronphonon coupling. Density-functional based band-structure calculations yield a very similar electronic structure for all the isotypic REGe₅ compounds. Besides a slight increase in the width of the valence band for smaller RE atoms, only minor differences are found for the two different germanium environments.

Full text of DOI:10.1002/zaac.201000065

ARTICLE
DOI: 10.1002/zaac.201000065
Thermal, Magnetic, Electronic, and Superconducting Properties of Rare-
Earth Metal Pentagermanides REGe5 (RE = La, Nd, Sm, Gd) and Synthesis
of TbGe5
Katrin Meier,[a] Raul Cardoso-Gil,[a] Walter Schnelle,[a] Helge Rosner,[a]
Ulrich Burkhardt,[a] and Ulrich Schwarz*[a]
Dedicated to Professor Rüdiger Kniep on the Occasion of His 65th Birthday
Keywords: Terbium; Germanium; High-pressure synthesis; Rare-earth metal germanides; Physical properties
Abstract. A series of isotypic rare-earth metal pentagermanides in- pounds REGe5 are paramagnetic metallic conductors, which order anti-
cluding the new compound TbGe5 were prepared by high-pressure syn- ferromagnetically at low temperatures. Specific heat measurements
thesis. They crystallize in the orthorhombic space group Immm [No. reveal that the superconducting state of LaGe5 below Tc = 7.1(1) K is
71; a = 395.70(9) pm; b = 611.1(2) pm, and c = 983.6(3) pm for characterized by a critical field of μ0Hc2 = 0.2 T and weak electron-
TbGe5]. The crystal structure is isotypic to LaGe5 and consists of puck- phonon coupling. Density-functional based band-structure calculations
ered germanium slabs, which sandwich a second germanium species yield a very similar electronic structure for all the isotypic REGe5 com-
and the rare-earth metal atoms. At ambient pressure, the thermal de- pounds. Besides a slight increase in the width of the valence band for
composition of the phases REGe5 (RE = La, Nd, Sm, Gd, and Tb) smaller RE atoms, only minor differences are found for the two differ-
proceeds via discrete intermediate steps into Ge(cF8) and thermody- ent germanium environments.
namically stable germanium-poorer phases. The investigated com-
Introduction
Compounds of an electropositive metal and an element of
group 14 often comprise covalent substructures of the post-
transition element, in which electron count and number of co-
valent bonds is strictly interrelated by the 8-N rule. Thus, four-
bonded silicon and germanium atoms are formally uncharged,
i.e., (4b)Si0 and (4b)Ge0. Despite an excess of electrons, some
binary high-pressure phases of silicon like M[(4b)Si0]6·2e–
(M = Ca, Sr, Ba; Eu) [1–5] form four covalent bonds per
framework atom. In germanides, a transfer of electrons typi-
cally induces defects in the germanium partial structure, a for-
mation of lone-pairs [6] and a decrease of the homonuclear
coordination number.
Aiming to substantially expand the coordination environment
of the tetrel atoms and, thus, to modify the physical properties,
high-pressure high-temperature synthesis has emerged as a
Figure 1. Crystal structure of pentagermanides REGe5 (RE = La, Ce,
powerful and versatile tool. Experiments yielded binary com-
Pr, Nd, Sm, and Gd) [5, 7–10]. Ge1 atoms form three short contacts
pounds REGe5 (RE = La, Ce, Pr, Nd, Sm, and Gd) [5, 7–10],
within corrugated layers. Two longer contacts to Ge2 complete the 3+2
in which two different types of germanium atoms are coordi-
nated by five and eight neighbors within the framework, re-
spectively (Figure 1).
coordination. Between the two-dimensional units the species Ge2 is
coordinated by eight Ge1 atoms and the metal atoms center larger
voids of the germanium network.
* PD Dr. U. Schwarz
Fax: +49-351-46464002
E-Mail: schwarz@cpfs.mpg.de
[a] Max-Planck-Institut für Chemische Physik fester Stoffe
Nöthnitzer Str. 40,
Herein we report the high-pressure high-temperature synthe-
sis of TbGe5, a new member of the isotypic series with the
hitherto smallest embedded rare-earth metal.
01187 Dresden, Germany
1466
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Rare-Earth Metal Pentagermanides REGe5 and Synthesis of TbGe5
Thermal stability and decomposition of the new compound
at ambient pressure is discussed in comparison to results for
isotypic atomic patterns. The unusual columnar alignment of
the metal atoms in the phases REGe5 motivated a consequent
theoretical and experimental study of the magnetic, electrical
and superconducting properties.
Results and Discussion
Synthesis
The synthesis experiments reveal that TbGe5 forms only in a
narrow P, T window around 8.3(5) GPa and 820 K. Variation of
pressure by 1 GPa or temperature by 100 K suppresses com-
pletely the formation of the high-pressure phase as evidenced by
subsequent X-ray powder diffraction measurements. Thus, the
parameter window to synthesize the terbium compound is even
narrower than that of recently prepared GdGe5 [9].
A metallographic investigation of a polished sample of the
reaction products after high-pressure high-temperature synthe-
sis evidences the new germanium-rich compound as the main
component (Figure 2). Energy-dispersive X-ray spectroscopy
of this major constituent reveals a ratio Tb:Ge of 1:4.90(5)
in good agreement with a composition TbGe5. Besides, small
amounts of germanium and a phase with a composition close
to TbGe2.1 are present.
Figure 3. Normalized powder X-ray diffraction diagrams of isotypic
pentagermanides REGe5 (RE = La, Nd, Sm, Gd, and Tb). The scatter-
ing experiments were performed with Cu-Kα (La, Nd, Sm, Tb) or Co-
Kα (Gd) radiation, respectively. Arrows indicate diffraction lines of
Ge(cF8). Contributions of the internal standard LaB6 in case of GdGe5
are marked by asterisks. Squares indicate a hitherto unknown phase in
the diagram of TbGe5.
Indexing of the powder diffraction peaks of the new com-
pound on the basis of an orthorhombic body-centered lattice
results in unit cell parameters of a = 395.70(9) pm, b =
611.1(2) pm, and c = 983.6(3) pm. On the basis of the powder
diffraction intensities, the terbium compound is identified as
isotypic to LaGe5. Due to the poor quality of the crystalline
powder and the resulting diffraction data, the parameter refine-
ment using complete diffraction profiles was performed in a
successive manner in order to reduce the number of free pa-
rameters in each least-squares cycle. Applying these limita-
tions, the atomic coordinates converge to Tb (0, 0, 0), Uiso
=
0.0046(6); Ge1 [0.5, 0.2970(3), 0.8314(2)], Uiso = 0.0082(5);
Ge2 (0, 0.5, 0), Uiso = 0.010(1) resulting in interatomic distan-
ces, which are close to those of the other isotypic germanides.
Closer inspection of the refinement results evidences a dif-
ference in the displacement parameters of the crystallographi-
cally distinct germanium atoms, which has also been observed
for other members of this rather unusual atomic pattern. Since
refinements of the diffraction data of TbGe5 are hampered by
the high background and the low signal to noise ratio, a more
detailed investigation of this issue was performed with powder
X-ray diffraction diagrams of the isotypic compound SmGe5,
which were measured with synchrotron radiation. In order to
search for local deviations from the average symmetry, a disor-
Figure 2. Electron back-scattering image of the reaction product after
high-pressure high-temperature synthesis. Dark grey indicates unre-
acted germanium, middle gray corresponds to the compound TbGe5,
bright spots show a phase with composition TbGe2.1
.
Crystal Structure
The powder X-ray diffraction diagram of TbGe5 is character- der model with a split position for Ge2 was refined in space
ized by a high background and a low signal to noise ratio group Immm (Table 1). The finding that the Uiso parameters
(Figure 3) indicating a small size of the crystalline domains. of the germanium atoms become the same within estimated
An increase of the annealing time during the synthesis from experimental error is taken as an indication for a thermal dis-
9 h to 45 h at 820 K did not improve the quality of the diffrac- placement rather than a partial occupation of the eightfold co-
tion data. In agreement with the findings from a metallographic ordinated position. A dynamic effect is also consistent with
analysis, additional lines evidence the presence of Ge(cF8) and the specific heat measurements (see below). Consequently, a
a small amount of a phase with a hitherto unknown crystal decrease of symmetry by using the space groups Imm2, I222,
structure.
and I12/m1 does not result in an improvement with respect to
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U. Schwarz et al.
ARTICLE
Table 1. Positional and displacement parameters of two crystallographic models for SmGe5 in the space group Immm.
Atom
Site
x
y
z
Uiso /104 pm2
Ordered model
Sm1
2a
8l
0
0
0
0.0051(1)
0.0070(2)
0.0107(3)
Ge1
Ge2
½
0
0.29406(8)
½
0.83069(5)
0
2d
Disordered model
Sm1
Ge1
Ge2
2a
0
½
0
0
0.0055(1)
0.0069(2)
0.0070(3)
8l
0.29399(8)
½
0.83068(5)
0.0078(4)
8ma)
0.016(1)
a) The site occupancy factor of the position is fixed to 0.25.
the residuals or the magnitude of the displacement parameters.
The finding of intermediate phases is confirmed by in-situ
In the previously known binary terbium-germanium com- powder X-ray diffraction data of the compounds NdGe5 (Fig-
pounds, a wide variety of germanium species covering isolated ure 5) and SmGe5. In agreement with the prolonged holding
atoms, one-bonded germanium atoms in dumbbells, two- time of the experiment, the formation of Ge(cF8) due to the
bonded germanium atoms in chains and rings as well as nets disintegration of NdGe5 is observed already at 513 K. The si-
of three-bonded germanium atoms are observed [11–22]. In milarity of the diffraction diagrams of NdGe5 and the first ger-
Tb3Ge4 (Er3Ge4 type) a square-planar coordinated type of four- manium-poorer phase NdGe5–x (diagram measured at 563 K)
bonded germanium is present. In short, despite a wide variety is consistent with the assumption that the latter is a defect vari-
of structural motifs, the number of homonuclear neighbors has ety of the starting compound. At 598 K, this germanium-
an upper limit of four in the previously characterized com- poorer phase decomposes into NdGe2–δ and Ge(cF8). Further
pounds. Thus, TbGe5 is the first binary compound in the sys- temperature increase induces a significant growth of the crys-
tem Tb-Ge, in which the number of homonulear neighbors of talline domains (see pattern at 823 K). Diffraction data meas-
germanium exceeds four.
ured at 298 K evidence that the formed phases NdGe2–δ and
Ge(cF8) remain stable upon cooling to ambient temperature.
Thermal Stability
A systematic study on thermal properties of compounds
REGe5 (RE = La, Nd, Sm, Gd, and Tb) reveals that all the
synthesized pentagermanides exhibit exothermic decomposi-
tions at ambient pressure (Figure 4). The disintegrations pro-
ceed by intermediate phases into germanium-poorer com-
pounds, which are stable at ambient conditions, i.e., REGe2–δ
(RE = La, Nd, Sm, and Gd) or TbGe3 and Ge(cF8).
Figure 5. In-situ powder X-ray diffraction experiment of the thermal
decomposition of metastable NdGe5. Arrows indicate diffraction lines
of Ge(cF8), stars those of NdGe5, squares the defect phase NdGe5–x
and triangles NdGe2–δ
.
Despite the formation of different final products, the thermal
decomposition of the pentagermanides REGe5 exhibits a sys-
tematic decrease of the onset temperature with increasing
atomic number of the metal atom (Figure 4). Since the stability
of a certain crystal structure motif is, among other factors, in-
Figure 4. DSC measurements of pentagermanides REGe5 for increas-
ing temperatures between 298 K and 1473 K.
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Rare-Earth Metal Pentagermanides REGe5 and Synthesis of TbGe5
fluenced by the geometric features of the constituents, the de-
composition temperature was investigated as a function of the
radius of the metal atom (Figure 6). The descent can be de-
scribed by a linear fit in good approximation, which clearly
indicates that the stability of the structural pattern decreases
monotonously with the size of the metal ions in the investi-
gated series.
Figure 7. Upper panel: Total electronic density of states for LaGe5
(shaded) and TbGe5. The Fermi level is at zero energy. The narrow
peaks at about –10 eV originate from the localized Tb 4f states. Lower
panel: Partial density of states (per atom) for TbGe5. Despite the differ-
ent coordination environment, the two germanium sites exhibit a simi-
lar electronic structure.
Figure 6. Onset temperature of the thermal decomposition of pentager-
manides REGe5 as a function of the metal ion RE3+ radius.
Electronic Structure
investigated metals RE. An explicit population analysis exhi-
bits a difference of 0.09 additional electrons at the Ge(2) site
for TbGe5 (only 0.01 for LaGe5). Thus, a simple model for the
charge transfer between the metal atoms RE and the different
germanium sites as suggested earlier [7] is not confirmed by
our calculations. We rather obtain a picture of a Ge5 “polyan-
ion” with considerable covalent interactions with the included
RE constituents, typical for intermetallic systems. According
to the electronic structure calculations, the intermetallic char-
acter of the compound is also in line with the absence of any
indication of a lone pair at the germanium (!) site, which would
be presumably directed towards the channels filled with RE
atoms.
To study the electronic structure of compounds REGe5 on a
microscopic level, especially the changes regarding the ex-
change of the RE atoms and the role of the two different ger-
manium environments for the crystal chemistry, band structure
calculations within the density-functional theory were carried
out. As a representative result, the electronic densities of states
(DOS) for LaGe5 and TbGe5 are shown in the upper panel of
Figure 7. For LaGe5, our results are in good agreement with
earlier calculations [7]. In general, apart from a change of the
position of the narrow 4f band complex, the DOS for isotypic
compounds REGe5 is very similar.
The main difference is a systematic, slight broadening of the
valence band by about 0.6 eV going from LaGe5 to TbGe5.
This is caused by an increasing Ge–Ge overlap related to the
smaller cell volume due to the lanthanide contraction [23]. The
states at the Fermi level EF originate mainly from germanium
4p electrons. Although we obtain a stable magnetic solution
Transport Properties
The electrical resistivity ρ(T) of the compounds REGe5 (Fig-
for all compounds except for LaGe5, the germanium states are ure 8) is typically metallic with room temperature values
essentially unpolarized. This results in a very similar DOS(EF) ρ(300 K) of 43–72 μΩ·cm. Inflections in ρ(T) are visible for
between 2.4 and 2.6 states per eV and unit cell for all REGe5 SmGe5, GdGe5, and TbGe5, which are due to the reduced scat-
systems, corresponding to a bare electronic γbs between 5.65 tering of the charge carriers in the magnetically ordered phases
and 6.13 mJ·mol–1·K–2 (see specific heat measurements be- (see below). The residual resistivity of the LaGe5 sample is
low).
2.8 μΩ·cm (residual resistance ratio ≈ 15), which indicates a
The lower panel of Figure 7 shows the partial DOS for the good crystalline sample quality for a high-pressure synthesis.
two different germanium sites in TbGe5. They are very similar Zero resistance is observed at 7.1 K, in agreement with the
despite the rather different crystallographic environments [five magnetic shielding data (see below). The residual resistivity
and eight homonuclear contacts for Ge(1) and Ge(2), respec- (16 μΩ·cm) of the TbGe5 sample is significantly higher than
tively]. This similarity holds for all pentagermanides of the that of the other samples.
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U. Schwarz et al.
ARTICLE
Figure 8. Electrical resistivity of polycrystalline samples of REGe5
(RE = La, Nd, Sm, Gd, and Tb) against temperature. The anomalies at
29 K for LaGe5 and TbGe5 are experimental artefacts.
Figure 9. Inverse magnetic susceptibilities 1/χ(T) vs. temperature for
polycrystalline samples of REGe5 (RE = Nd, Sm, Gd, and Tb). The
curve for SmGe5 has been multiplied by 0.25.
The thermal conductivity of the three tested REGe5 samples
(RE = Nd, Sm, and Gd) is estimated to be of the order 8–
13 W·K–1·m–1 at 300 K. Below 100 K it decreases rapidly. The
Seebeck coefficient at room temperature has a range of –1.5
to –2.5 µV·K–1, which is surprisingly small for a compound
with such a high germanium content. The small values as well
as the relatively low resistivities indicate typical intermetallic
behavior of the compounds.
Magnetic Properties
The magnetic susceptibilities χ(T) = M/H of NdGe5, GdGe5,
and TbGe5 follow a Curie–Weiss law at high temperatures
(Figure 9). From fits to the data above 100 K the following
effective paramagnetic moments and paramagnetic Weiss tem-
peratures are obtained: NdGe5, μeff = 3.69 μB, θP = –36.9 K
(the effective moment is in agreement with earlier data [8]);
GdGe5, μeff = 8.28 μB, θP = –43.4 K; TbGe5, μeff = 9.79 μB,
θP = –25.9 K. SmGe5 displays van-Vleck-type paramagnetism,
as reported previously [8]. From the slope of the experimental
susceptibility data above 300 K the typical minimum of χ(T)
for Sm3+ compounds is expected to occur just above 400 K
(the maximum temperature of our measurement). The observed
paramagnetic behaviors are in good agreement with the pres-
Figure 10. Magnetic susceptibilities χ(T) of REGe5 (RE = Nd, Sm, Gd,
and Tb) samples for low temperatures and μ0H = 0.1 T.
ence of rare-earth ions in the oxidation state +3 with respective the Fermi level. The strong decrease of the susceptibility with
4
Hund’s rule ground multiplets: NdGe58, I9/2, μfree = 3.62 μB; increasing temperature is consistent with the steep decrease of
6
SmGe5, H5/2, (see above); GdGe5, S7/2, μfree = 7.94 μB; the calculated DOS right above the Fermi level (Figure 7).
7
TbGe5, F6, μfree = 9.72 μB. At low temperatures kinks in χ(T) Taking into account the Curie-paramagnetic “tail” we extrapo-
due to antiferromagnetic ordering of the rare-earth moments late a value of χ(T → 0) of +135(30) × 10–6 emu·mol–1. With
are observed (Figure 10): NdGe5: TN = 5.7 K (not detected the sum of the diamagnetic core contributions
earlier [8]); SmGe5: TN ≈ 10 K (cf. 10.4 K [8]); GdGe5: –55 × 10–6 emu·mol–1 a Pauli paramagnetism χP(T → 0) of
TN ≈ 29 K; TbGe5: TN ≈ 41 K.
+190(30) × 10–6 emu·mol–1 is derived. This value corresponds
LaGe5 is a Pauli paramagnet with pronounced temperature to a γ of 13.9 mJ·mol–1·K–2 in agreement with the value for
dependence. Only at the lowest temperatures a second para- γexp extracted from the specific heat data.
magnetic contribution with Brillouin behavior due to minor
In a low field (μ0H = 1 mT) a sharp transition to the super-
paramagnetic impurities becomes evident. Thus, at elevated conducting state is observed between 6.95 K and 7.15 K
temperatures mostly Pauli paramagnetism is observed, which (shielding signal 10 %/90 %) in accordance to earlier data
is temperature-dependent due to a strongly structured DOS at (Tc = 7.0 K [7]). However, besides low-field susceptibility and
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Rare-Earth Metal Pentagermanides REGe5 and Synthesis of TbGe5
zero-field resistivity no superconducting data have been re- the expected entropy R ln8 well above TN. As typical for Gd3+
ported. For our sample, the volume susceptibility χvol,zfc meas- compounds we observe a hump-like anomaly well below TN,
ured after zero-field cooling indicates that the shielding is com- which is due to the highly degenerate ground state of this ion.
plete (χvol is 137 % of –1/4 π due to the neglected For TbGe5 an entropy of 1.48 R is observed at ΤN,cal = 41 K,
demagnetization correction). The field-cooling Meissner effect which may indicate that the ordering TbGe5 involves 6 out of
is very small (only 5 % of –1/4 π) as often observed experi- a total of 13 singlet levels [25].
mentally for type-II superconductors due to strong flux line
pinning.
The specific heat of LaGe5 for various magnetic fields is
displayed in Figure 12. The superconducting transition step
centered at Tc(H = 0) = 6.80(2) K is already broad for zero
magnetic field, which is probably due to chemical inhomoge-
neity of the sample. With increasing field the transition broad-
ens further. For fields μ0H ≥ 200 mT the specific heats below
Tc(0) become indistinguishable, thus for these fields the mate-
rial is in the normal state.
Specific Heat and Superconductivity of LaGe5
The specific heat capacity of the investigated REGe5 com-
pounds is plotted in cp/T representation in Figure 11. Clear
anomalies indicating antiferromagnetic long-range ordering are
visible at the Néel temperatures. For NdGe5 the anomaly at TN
has a typical λ shape. At a temperature TN2 a sharp kink in
cp(T) probably indicates a spin-reordering transition. For
SmGe5, GdGe5, and TbGe5 the anomalies at TN are more simi-
lar to a mean-field transition, i.e., step-like. Moreover, in
GdGe5 a double transition of unknown origin is visible. The
specific heat of the compounds REGe5 consists of the terms
cp(T) = cph + cel + cmag. In LaGe5 the only contributions are
the phonon cph(T) and conduction electron cel = γT terms (for
their determination see below), thus cp(T) of LaGe5 in the nor-
mal state may serve as a reference for the respective contribu-
tions in the “magnetic” REGe5 compounds assuming that
cel(REGe5) = cel(LaGe5). The phonon terms cph(REGe5) are cal-
culated from cph(LaGe5) (see below) by a scaling to the equiva-
lent Debye temperature θD(T) with the square root of the molar
mass ratio of the compounds (see reference [24]).
Figure 12. Specific heat cp/T plotted as a function of T2 for LaGe5 in
various magnetic fields up to μ0H = 200 mT.
A fit to these data in the range 2.3 K to 8.2 K requires be-
sides the electronic Sommerfeld term γT a phonon contribution
beyond the simplest Debye T 3 models. We have tried both the
3
5
harmonic lattice approximation cph = βT + δT +… and a
3
combination of a Debye and an Einstein term cph = βT
+
εE(T/θE), in which E is the Einstein function und θE represents
the characteristic phonon frequency ħωΕ/kB [24]. Regarding
the least-squares deviation the latter model is far superior to
the first. The resulting parameters are γexp
=
11.39(3) mJ·mol–1·K–2, β = 4.76(2) × 10–4 J·mol–1·K–4 corre-
sponding to an initial Debye temperature θD(0) = 290 K for 6
atoms, and
a
relatively small contribution
ε
=
6.9(4) J·mol–1·K–1, and θE = 74.8(7) K. The “spectral weight”
ε of the Einstein term has to be compared to the gas constant
R = NAkB expected for one vibrational degree of freedom.
ε/R ≈ 1 signifies that the Einstein term is due to the weak
Figure 11. Specific heat capacity cp(T) for REGe5 (RE = La, Nd, Sm,
Gd, and Tb) samples.
After subtraction of the phonon and electronic terms the bonding of one atom (per formula unit) in only one space di-
magnetic specific heats cmag(T) are obtained. The magnetic en- rection, viz. the Ge(2) atom within the rigid channels along the
tropies Smag(T) are calculated by integration of cmag/T. It is a axis formed by the Ge(1) atoms. This correlates well with
found that TN,cal (the critical temperature of the peak) and the powder X-ray diffraction refinements (see above) and espe-
S
mag(TN,cal) is 5.5 K and 0.57 R for NdGe5 and 9.5 K and cially the large anisotropic displacement parameter U11 of the
0.54 R for SmGe5, which indicate that the crystal field ground Ge(2) atom as reported earlier [7].
state of these ions are Kramers doublets (expected entropy
< ≈ R ln2 [25]). For GdGe5 we find 1.94 R, which indicates perconducting electronic term cel(T) can be compared with the
After subtraction of the phonon specific heat cph(T) the su-
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1471

U. Schwarz et al.
ARTICLE
predictions of the BCS theory (weak electron-phonon coupling coupling and a Tc of 7.1 K. The analysis of the phonon specific
limit) and the phenomenological two-fluid model (suitable for heat contribution evidences a low-frequency Einstein mode,
strong e-ph coupling) [26]. In the least-squares deviation the which is attributed to an anomalous one-dimensional vibration
fit with the BCS model (including a Gaussian smearing of the of the eightfold coordinated atom Ge2 in the structural pattern.
transition) is superior by a factor of two to the two-fluid model, This finding is in agreement with a pronounced dynamic dis-
indicating weak e-ph coupling. A midpoint Tc.mid = 6.80(2) K placement as indicated by refinements of X-ray diffraction
and
a
reduced specific heat jump Δcp/Tc
=
data.
17.0(2) mJ·mol–1·K–2 are obtained. The ratio Δcp/γTc = 1.493
is slightly larger than for the weak-coupling BCS limit (1.426).
The experimental value agrees also with that derived from Δcp/
γTc = 1.426 (1 + 53 ln(x/3) / x2) with x = θD/Tc [27] giving
1.536.
Experimental Section
Preparation and sample handling was performed in glove boxes [argon
atmosphere, p(H2O) ≤ 0.1 ppm; p(O2) ≤ 0.1 ppm]. The precursor sam-
ples with a nominal composition Tb:Ge = 1:5 (TbGe3 + Ge) were
prepared by arc melting of elemental terbium (Lamprecht, 99.99 %
By using the McMillan formula ln(1.45 Tc/θD) = –1.04
(1 + λ) / [l – μ*(1 + 0.62 λ)] we can estimate an electron-pho-
non coupling parameter λ of 0.76 when assuming a typical metals basis) and germanium (Chempur 99.999 %). High-pressure and
high-temperature conditions were realized by means of an octahedral
multianvil press described earlier [29]. Pressure and temperature cali-
bration is performed prior to the experiments by in-situ monitoring of
the resistance changes of bismuth [30] and by runs using a thermocou-
ple, respectively. As crucible material hexagonal boron nitride was
used. For determining the stability field of TbGe5, experiments were
performed in a parameter field around the formation conditions, i.e.,
at pressures of 8 GPa, 8.3 GPa, and 9 GPa and temperatures of 720 K,
820 K, and 920 K for 540 min. The high-temperature high-pressure
treatment was followed by quenching to ambient temperature before
value for the Coulomb pseudopotential μ* of 0.15. This value
of λ correlates well with the calculated interval derived from
the Sommerfeld coefficient γbs in the band structure calculation
(see above): γexp = γbs × (1 + λ) resulting in 0.85 < λ < 0.95.
In agreement with the magnetic susceptibility results (see
above), the normal state γN corresponds to a Pauli susceptibil-
ity χP of approximately 156 × 10–6 emu·mol–1.
From the observed pinning and the behavior of the specific
heat step in magnetic fields LaGe5 is a type-II superconductor.
Due to the broad transition steps in fields the determination of decompression.
the midpoint of the transitions, Tc,mid(μ0, H), is only possible
for fields ≤ 50 mT. The slope dμ0Hc2/dT thus determined is
–25 mT·K–1, which yields an upper critical field μ0Hc2(0) of
only 120 mT using the (dirty-limit) WHH extrapolation
μ0Hc2(0) = –0.693 Tcμ0 dHc2/dT [28]. Taking the onset temper-
atures Tc,on(μ0, H) of the transitions for the same fields we
obtain dμ0Hc2/dT = –52 mT·K–1 and a μ0Hc2(0) = 260 mT. This
would be however the value for a hypothetical homogeneous
LaGe5–x sample with the optimum Tc of 7.3 K. Actually, we
observe that cp(T) is independent from field above μ0H ≥
200 mT and T > 1.8 K, thus the average μ0Hc2(1.8 K) is about
200 mT for our sample.
Differential Scanning Calorimetry (DSC) was performed with a
Netzsch DSC 449 apparatus in Al2O3 crucibles in the temperature
range from 295 K to 1473 K with a heating rate of 10 K min–1.
X-ray powder diffraction data were collected in transmission alignment
with a Huber Image Plate Guinier Camera G670 employing Cu-Kα1
(λ
= 154.056 pm) radiation. An internal LaB6 standard [a =
415.962 pm] was added before placing the mixture between two Mylar
foils. For lattice parameters refinement a set of 25 reflections was used.
Crystallographic calculations were performed with the program pack-
age WinCSD [31]. High-temperature measurements are realized with
a STOE-STADIP-MP, Ge-Monochromator, Debye–Scherrer geometry
and a linear position sensitive detector using heating rates of
10 K·min–1 and a holding time for diffraction measurements of
170 min.
Summary
The quality of the prepared samples is independently examined by
optical metallography followed by a verification of the chemical com-
position using a Philips XL30 scanning electron microscope (LaB6-
cathode, accelerating voltage: 25.0 kV, Magnification: 1000 ×) with an
integrated EDXS system
The new compound TbGe5 can be prepared by high-pressure
high-temperature synthesis at 8.3(5) GPa and 820(50) K. At
ambient pressure, the decomposition temperature of the meta-
stable high-pressure phases REGe5 (RE = La, Nd, Sm, Gd, and
Tb) decreases linearly with increasing atomic number of the
metal atoms indicating that the stability of the structural pattern
Polycrystalline sample pieces were used for the physical characteriza-
decreases with the size of the metal ions. Band structure calcu- tion measurements. Magnetization at various external fields μ0H be-
tween 1 mT and 7 T (temperature range 1.8–400 K) was measured in a
SQUID magnetometer (MPMS XL-7, Quantum Design). The electrical
resistivity ρ(T) of the LaGe5 and TbGe5 samples was determined by
an ac four-point method (1.8–320 K), that of the other samples by a
dc method (4–320 K). For the NdGe5, SmGe5 and GdGe5 samples
the thermal conductivity λ(T) and the Seebeck coefficient S(T) of the
thermopower was measured between 1.8 K and 320 K (PPMS, Quan-
tum Design). Due to the insufficient length of the bar-shaped samples
the inaccuracies are very large. Moreover, the determination of the
lations reveal a very similar electronic structure of the studied
compounds apart from the 4f configuration and slight changes
of the valence band-width due to different radii of the metal
atoms. The different germanium environments cause only mi-
nor differences of the occupied germanium valence states.
The temperature dependences of the magnetic susceptibility
indicate the oxidation state +3 for the rare-earth metals in
REGe5 (RE = La, Nd, Sm, Gd, and Tb) and magnetic ordering
of the moments between 5.7 K (NdGe5) and 41 K (TbGe5).
high-temperature values of λ(T) is hampered by thermal radiation
3
LaGe5 is a type-II superconductor with weak electron-phonon losses resulting in an erroneous contribution proportional to T . We
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© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Z. Anorg. Allg. Chem. 2010, 1466–1473

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Acknowledgement
The authors thank Susann Leipe for supporting high pressure synthesis.
We are grateful to Dr. Stefan Hoffmann, Susann Scharsach, and Philipp
Marasas for the DSC and TG measurements. Helpful discussion with
Carola J. Müller, Alexander Kerkau, Marcus Schmidt and Juri Grin
are acknowledged.
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Received: February 1, 2010
Published Online: June 11, 2010
Z. Anorg. Allg. Chem. 2010, 1466–1473
© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
www.zaac.wiley-vch.de
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