Structure-composition sensitivity in "Metallic" Zintl phases: A study of Eu(Ga1-xTtx)2 (Tt=Si, Ge, 0≤x≤1)

Article abstract of DOI:10.1016/j.jssc.2009.06.032

Two isoelectronic series, Eu(Ga_1-xTt_x)₂ (Tt=Si, Ge, 0≤x≤1), have been synthesized and characterized by powder and single-crystal X-ray diffraction, physical property measurements, and electronic structure calculations. In

Full text of DOI:10.1016/j.jssc.2009.06.032

ARTICLE IN PRESS
Journal of Solid State Chemistry 182 (2009) 2430–2442
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Journal of Solid State Chemistry
journal homepage: www.elsevier.com/locate/jssc
Structure–composition sensitivity in ‘‘Metallic’’ Zintl phases: A study of
Eu(Ga1ꢀxTtx)2 (Tt ¼ Si, Ge, 0rxr1)
Tae-Soo You a, Jing-Tai Zhao b, Rainer Po¨ttgen c, Walter Schnelle d, Ulrich Burkhardt d,
Ã
Yuri Grin d, Gordon J. Miller a,
a Department of Chemistry, Iowa State University, Ames, IA 50011, USA
b Shanghai Institute of Ceramics, Chinese Academy of Sciences, 1295 Dingxi Road, Shanghai 200050, China
c
¨
¨
¨
Institut fu¨r Anorganische und Analytische Chemie, Universitat Munster, Corrensstrasse 30, 48149 Munster, Germany
d Max-Planck-Institut fu¨r Chemische Physik fester Stoffe, No¨thnitzer Straße 40, 01187 Dresden, Germany
a r t i c l e i n f o
a b s t r a c t
Article history:
Two isoelectronic series, Eu(Ga1ꢀxTtx)2 (Tt ¼ Si, Ge, 0rxr1), have been synthesized and characterized
by powder and single-crystal X-ray diffraction, physical property measurements, and electronic
structure calculations. In Eu(Ga1ꢀxSix)2, crystal structures vary from the KHg2-type to the AlB2-type,
and, finally, the ThSi2-type structure as x increases. The hexagonal AlB2-type structure is identified for
compositions 0.18(2)rxo0.70(2) with Ga and Si atoms statistically distributed in the polyanionic 63
nets. As smaller Si atoms replace Ga atoms while the number of valence electrons increases, the lattice
parameters, unit cell volumes, and Ga–Si distances in this phase region decrease significantly. Although
aspects of X-ray diffraction results suggest puckering of the 63 nets for the Si-richest example of the
AlB2-type Eu(Ga1ꢀxSix)2, the complete experimental evidence remains inconclusive. On the other
hand, in Eu(Ga1ꢀxGex)2, six different structural types were observed as x varies. In addition to EuGa2
Received 10 June 2009
Accepted 21 June 2009
Available online 27 June 2009
Keywords:
Polar intermetallics
Electronic structure
Crystallography
¯
(KHg2-type; space group Imma) and EuGe2 (own structure type, space group P3m1), the ternary phases
studied show four different structures: the AlB2-type for Ga-rich compositions; the YPtAs-type
structure for EuGaGe; and two new structures, which are intergrowths of the YPtAs-type EuGaGe and
EuGe2, for Ge-rich compositions. These two Ge-rich phases include: (1) Eu(Ga0.45(2)Ge0.55(2) 2
) containing
two YPtAs-type motifs of EuGaGe plus one EuGe2 motif; and (2) Eu(Ga0.40(2)Ge0.60(2) containing one
)
2
YPtAs-type motif alternating with a split site at x ¼ 23 ; y ¼ and z ¼ 0.4798(2) with ca. 50% site
1
3
occupancy by Ga and Ge along the c-axis. Magnetic susceptibilities of three Eu(Ga1ꢀxGex)2 compounds
display Curie–Weiss behavior above ca. 100 K, and show effective magnetic moments indicative of
divalent Eu with a 4f7 electronic configuration, consistent with. X-ray absorption spectra (XAS). Density
of states (DOS) and crystal orbital Hamilton population (COHP) analyses, based on first principles
electronic structure calculations, rationalize the observed homogeneity ranges of the AlB2-type phases
in both systems and the structural variations as a function of Tt content.
& 2009 Elsevier Inc. All rights reserved.
1. Introduction
pseudogaps in the electronic density of states (DOS) curves and
optimized orbital interactions at the corresponding Fermi levels
[5–7]. On the other hand, the electropositive metals act like
cations, which simply donate valence electrons to the electro-
negative components as in classical valence compounds or Zintl
phases. In polar intermetallic compounds, however, the active
metals do not transfer all valence electrons to the electronegative
component, but are involved in ‘‘lattice covalency’’ through their
valence orbitals [8]. This effect was recently demonstrated
between Eu and its environment in EuRh2Ga8 by means of a
bonding analysis within the electron localization approach [9]. In
addition, the typical presence of a pseudogap at the Fermi level
can lead to potentially interesting physical properties, especially if
rare-earth metals serve as the active metal, because of partially
filled 4f bands [10].
Polar intermetallic compounds represent an exceptional class
of inorganic solids to study relationships among chemical
compositions, crystal structures, physical properties, and chemical
bonding [1]. These compounds involve electropositive metals
(i.e., alkali-, alkaline-earth or rare-earth metals) combined with
electronegative metals close to the Zintl border. The electro-
negative metals form structural fragments that often conform to
simple electron counting rules, such as the Zintl-Klemm formal-
ism [2–4], and give rise to electronic structures characterized by
Ã
Corresponding author.
E-mail address: gmiller@iastate.edu (G.J. Miller).
0022-4596/$ - see front matter & 2009 Elsevier Inc. All rights reserved.
doi:10.1016/j.jssc.2009.06.032

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2431
During our systematic investigations of Eu(M1ꢀxM0x)2 phases
(M, M0 ¼ group 12–14 elements) to study correlations among
atomic, electronic, and possible magnetic structures by varying
atomic sizes and valence electron counts, we observed different
structural trends for two isoelectronic Eu(Ga1ꢀxTtx)2 (Tt ¼ Si, Ge)
series. As x increases in Eu(Ga1ꢀxSix)2, structures vary from the
KHg2-type to the AlB2-type, and, finally, the ThSi2-type structure
type. On the other hand, six different structural types exist in
the germanide system, Eu(Ga1ꢀxGex)2. In addition to the two
binary cases, EuGa2 (KHg2-type) and EuGe2, ternary examples
show four different structures derived from the AlB2-motif. These
ternary AlB2-type compounds are related to the superconducting
AEAlSi (AE ¼ Ca and Sr) phases [11–15], which have attracted
recent attention for their similarity to superconducting MgB2 [16]
with respect to structures and valence electron counts. Moreover,
related ternary phases AEGaTt (AE ¼ Ca, Sr, Ba; Tt ¼ Si, Ge, Sn) are
precursors to form interesting polyanionic hydrides [17]. In our
own previous investigations, we have characterized and analyzed
the influence of the atomic size factor [18] and valence electron
count [19,20] on the structural and chemical bonding features
of the 63 networks, respectively, for EuGaTt (Tt ¼ Si, Ge, Sn) [18]
and Eu(Zn1ꢀxGex)2 (0rxr1) [19,20]. In this work, we examine
the simultaneous influence of size and electronic factors on the
Eu(Ga1ꢀxTtx)2 (Tt ¼ Si, Ge, 0rxr1) series.
15 min. Reactant mixtures were loaded into tantalum ampoules,
which were sealed by arc-melting in an argon-filled glove box
with the concentration of O2 lower than 1 ppm. Each tantalum
ampoule was then sealed in an evacuated silica jacket to prevent
oxidation. After annealing each product at 350 1C for 1 week, there
were no observable changes in the X-ray diffraction patterns,
except for the one sample Eu(Ga0.50(2)Ge0.50(2))2, which showed
significant narrowing of the diffraction peaks by factors of 2–2.5
compared with the as cast sample. EuGa1.1Ge0.9 was prepared in a
sealed tantalum tube. The sample was first heated in a muffle
furnace at 1050 1C for 1 h, then cooled to 700 1C within 1 day
and kept at that temperature for another 7 days followed by
quenching.
All 16 samples of the Eu(Ga1ꢀxTtx)2 series (Tt ¼ Si, Ge, 0rxr1)
appeared to be stable on exposure to both air and moisture over
several weeks. Empirical formulas obtained from single-crystal
X-ray diffraction experiments were verified by energy-dispersive
X-ray spectroscopy (EDXS). EDXS analysis was conducted on a
Hitachi S-2460N variable-pressure scanning electron microscope
(SEM) equipped with an Oxford Instruments Link Isis Model 200
X-ray analyzer, and using samples that were investigated by
single-crystal X-ray diffraction. The pure elements were used as
standards for intensity references.
2.4. Crystal structure determinations
2. Experimental
The Eu(Ga1–xTtx)2 (Tt ¼ Si, Ge, 0rxr1) series were character-
ized at room temperature by both powder and single-crystal
X-ray diffraction. Phase analysis and lattice parameters were
2.1. Synthesis and chemical analysis
determined on a Huber 670 image-plate powder diffraction
˚
Members of the Eu(Ga1ꢀxTtx)2 (Tt ¼ Si, Ge, 0rxr1) series were
synthesized from the pure elements, Eu (Ames Laboratory, rod,
99.99%, or Johnson-Matthey, 499.9%), Ga (Ames Laboratory, ingot,
99.99% or Chempur, 499.99%), Si (Aldrich, piece, 99.999%), and Ge
(Alfa, piece, 99.999% or Wacker, 499.999%) in various molar ratios
targeting sample masses of 1.070.2 g.
camera (Cu Ka1 radiation,
l ¼ 1.54059 A) with a step size of
0.0051, exposure times of 1–2 h, and using Si powder (NIST;
˚
a ¼ 5.43094070.000035 A) as a standard. Data acquisition was
controlled via the in situ program. The lattice parameters were
obtained from Rietveld refinement using program Rietica [24].
For single-crystal X-ray diffraction experiments, several silvery
block- or plate-shaped crystals were selected from the cast of each
product. The quality of each crystal was checked by a rapid scan
2.2. Eu(Ga1ꢀxSix)2
on a Bruker SMART Apex CCD diffractometer with Mo Ka1
Eight different Eu(Ga1ꢀxSix)2 (0rxr1) samples were arc-melted
under a high purity argon atmosphere on a water-cooled copper
hearth. Each pellet was remelted six times after turning to ensure
homogeneity. Weight losses of ca. 0.4–0.7 wt% occurred during arc-
melting, but these losses did not affect the final targeted
compositions, being equally distributed among the three compo-
nents as determined by subsequent chemical analysis and refine-
ments of single-crystal X-ray diffraction experiments [18].
Moreover, samples prepared using either a radio-frequency (RF)
induction furnace (1500 1C for 15min followed by 2h at 650 1C) or a
conventional tube furnace (tantalum ampoules; 850 1C for
4 days, 450 1C for 1 week, naturally cooled to room temperature)
yielded identical products, but crystals extracted from these
samples were less suitable for subsequent diffraction experiments
and the samples often showed other phases. EuGa2 was readily
synthesized by arc-melting without any subsequent low-tempera-
ture annealing procedure, unlike original reports [21,22], but in
agreement with a recent publication [23]. On the basis of powder
X-ray diffraction patterns, all samples obtained simply by arc-
melting showed features suitable to pursue subsequent single-
crystal X-ray diffraction experiments without any further annealing.
˚
radiation (
l
¼ 0.71073 A), and then the best crystals were used
for further data collection. Diffraction data were harvested from
three sets of 606 frames on a full sphere with 0.31 scans in and
o
with an exposure time of 10–20 s per frame. For experiments
conducted on a STOE IPDS diffractometer, data were harvested
from two sets of 180 frames with an exposure time of 1–3 min per
frame. Data collection on the STOE STADI
completed in /2 mode.
4 machine was
y
y
Intensities were extracted and then corrected for Lorentz and
polarization effects using the SAINT program [25]. The program
SADABS [26] was used for empirical absorption correction.
Numerical absorption corrections were applied using the X-RED/
X-SHAPE program [26]. All structures were solved by direct
methods and refined on F2 by full-matrix least-squares methods
using the SHELXTL [27] or WinCSD [28] software packages. The
entire sets of reflections for the ternary Eu(Ga1ꢀxTtx)2 (Tt ¼ Si,
Ge, 0rxr1) series could be matched with hexagonal or
trigonal crystal systems. During refinements of Eu(Ga1ꢀxGex)2
(0.25rxr0.60), the Ga and Ge atoms could not be distinguished
given the X-ray scattering factors for Ga and Ge atoms which
differ by at most 3.1%. Moreover, interatomic distances were also
not a useful guide to distinguish Ga and Ge atoms, due to their
˚
˚
2.3. Eu(Ga1ꢀxGex)2
similar covalent radii: r(Ga) ¼ 1.25 A and r(Ge) ¼ 1.22 A [29].
However, electronic structure calculations performed on several
different models of EuGaGe provided a clear energetic minimum
for one atomic arrangement in EuGaGe [18], which agreed with
Seven of eight Eu(Ga1–xGex)2 (0rxr1) samples were prepared
using RF induction melting at 1300 1C with a holding time of

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structural characterization of EuGaSn. Therefore, we utilized
similar calculations to address these structures and their
compositions.
from the same preparation as the one used for powder diffraction
experiments were used.
2.7. Computational details
2.5. X-ray absorption spectroscopy (XAS)
Tight-binding, linear muffin-tin orbital (TB-LMTO) calculations
of various structural models of Eu(Ga1ꢀxSix)2 and Eu(Ga1ꢀxGex)2
were carried out in the atomic sphere approximation (ASA)
using the Stuttgart program [30]. Exchange and correlation were
treated by the local spin density approximation (LSDA) [31]. All
relativistic effects except spin–orbit coupling were taken into
account by using a scalar relativistic approximation [32]. In the
ASA method, space is filled with overlapping Wigner–Seitz (WS)
atomic spheres. The symmetry of the potential is considered
spherical inside each WS sphere, and a combined correction is
used to take into account the overlapping part [33]. The radii of
WS spheres were obtained by requiring that the overlapping
potential be the best possible approximation to the full potential,
and were determined by an automatic procedure [33]. No empty
spheres (ES) were used [30]. The WS radii for the various elements
XAS measurements on the Eu LIII edge of four Eu(Ga1ꢀxGex)2
(x ¼ 0.45(5), 0.50(2), 0.55(2), 0.60(2)) samples were examined at
the EXAFS beam-line A1 of HASYLAB at DESY (Hamburg,
Germany). Each sample was ground together with dry B4C powder
before the measurement. Wavelength selection was realized by
means of a double-crystal Si(111) monochromator. Resolution
was about 2 eV (fwhm) at the Eu LIII edge of 6977 eV. Eu2O3 was
used as a reference for the 4f6 threshold during the measurement.
2.6. Magnetic susceptibility measurements
Temperature- and magnetic field-dependent magnetic sus-
ceptibilities of Eu(Ga1ꢀxGex)2 (x ¼ 0.50(2), 0.55(2), 0.60(2)) sam-
ples were measured using a Quantum Design, MPMS XL-7 SQUID
magnetometer over the temperature range 1.8–400 K and in
˚
˚
covered the following ranges: Eu, 2.09–2.26 A; Ga, 1.30–1.52 A;
magnetic fields
m0H ¼ 0.01–7 T. Isothermal magnetization curves
˚
˚
Si, 1.33 A; and Ge, 1.46–1.51 A. More computational details are
included in Supporting Information (Table S2). The basis sets
included 6s, 6p, and 5d orbitals for Eu; 4s, 4p, and 4d orbitals for
Ga; 3s, 3p, and 3d orbitals for Si; 4s, 4p, and 4d orbitals for Ge.
The Eu 6p, Ga 4d, Si 3d, and Ge 4d orbitals were treated by the
Lo¨wdin downfolding technique [30–32], and the Eu 4f wave
functions were treated as core functions occupied by 7 electrons.
This assigns all Eu sites as formally Eu(II), which is consistent
with the results of physical property measurements. Crystal
orbital Hamilton population (COHP) curves [6] and integrated
COHP values (ICOHPs) were calculated to determine the relative
influences of various interatomic orbital interactions. k-Space
integrations were performed by the tetrahedron method [34]. The
self-consistent charge densities were obtained using 116–560
irreducible k-points in the Brillouin zones for the corresponding
unit cells.
up to
m0H ¼ 7 T were recorded at 1.8 K. Bulk samples (ca. 100 mg)
Table 1
Crystallographic data as determined by XPD for the Eu(Ga1–xSix)2 and Eu(Ga1–x
Gex)2 (0rxr1) series.
3
x
x
Structure
(c/a)*
˚
˚
˚
˚
a (A)
b (A)
c (A)
V* (A )
(loaded) (EDXS) type
Eu(Ga1ꢀxSix)2 phases
0
0.00
KHg2
4.6449(9) 7.628(2) 7.638(2) 0.8211 67.65(2)
4.6524(5) 7.6461(9) 7.6464(8) 0.8127 68.00(1)
0.18
0.16(2) KHg2
AlB2
4.2640(2)
4.2324(3)
4.2204(2)
4.1699(5)
4.1132(3)
4.0821(1)
4.2989(4)
4.3065(4)
4.6000(2) 1.0788 72.45(5)
4.5885(4) 1.0841 71.17(1)
4.5863(2) 1.0867 70.75(1)
4.5634(6) 1.0946 68.72(2)
4.5412(4) 1.1041 66.53(1)
4.5538(3) 1.1156 65.72(3)
0.26
0.30
0.50
0.67
0.84
0.29(2) AlB2
0.33(2) AlB2
0.50(2) AlB2
0.69(2) AlB2
0.82(2) AlB2
ThSi2
13.864(2)
13.683(1) –
64.06(1)
63.44(1)
Total energy calculations using the Vienna ab initio Simulation
Package (VASP) [35–37] were also conducted for various EuSi2
models to gain insights about the Si-rich end of AlB2-type
Eu(Ga1ꢀxSix)2 cases. In this approach, the Kohn–Sham equations
were solved self-consistently using an iterative matrix diagona-
lization method and an efficient Pulay mixing scheme of the
charge density [37]. For these calculations on EuSi2, the free
parameters of the Si positions and the lattice parameter ratios c/a
for a set of constant volumes were varied simultaneously until
1.00
1.00(2) ThSi2
Eu(Ga1ꢀxGex)2 phases
0
0.00
KHg2
4.6449(9) 7.628(2) 7.638(2) 0.8211 67.65(2)
0.25
0.35
0.45
0.50
0.55
0.60
1.00
0.25(2) AlB2
0.35(2) AlB2
0.45(2) AlB2
0.50(2) YPtAs
4.2905(5)
4.2617(2)
4.241(1)
4.6077(2) 1.0739 73.46(1)
4.5812(2) 1.0749 72.06(1)
4.555(1) 1.079 70.95(5)
18.034(2) 1.0569 71.04(2)
40.889(8) 1.0681 71.18(3)
22.974(1) 1.0857 71.27(2)
4.9996(1) 1.2181 72.94(3)
4.2655(6)
0.55(2) EuGa0.9Ge1.1 4.2537(6)
0.60(2) EuGa0.8Ge1.2 4.2320(1)
1.00(2) EuGe2
4.1044(4)
˚
forces converged to values less than 0.005 eV/A. Ultra-
soft Vanderbilt-type pseudopotentials [38,39] were employed,
and the valence electron configurations of Eu and Si involved,
respectively, 5d16s2 and 3s23p2. Convergency was checked with
V* ¼ volume per formula unit Eu(Ga1–xTtx)2. (c/a)* is c/a for a AlB2-type unit cell,
b/2a for KHg2-type unit cell, c/4a, for YPtAs-type unit cell, c/9a for
EuGa0.9Ge1.1-type unit cell, and c/5a for a EuGa0.8Ge1.2-type unit cell.
a
a
a
EuGa2
(KHg2-type, 8 e )
Eu(Ga1 xSix)2 (0.18(2) x < 0.70(2))
(AlB2-type, 8.36(4) – 9.40(4) e )
EuSi2
(ThSi2-type, 10 e )
Fig. 1. Concentration-induced changes of crystal structure in the Eu(Ga1ꢀxSix)2 (0rxr1) series. The electron numbers show valence electron count per formula unit
Eu(Ga1ꢀxSix)2 (Eu is counted as contributing two valence electrons).

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2433
respect to the plane-wave cutoff of 300 eV and the number
EuGa2
(KHg2-type)
of k-points used in the summation over the Brillouin zone,
k-points which were obtained by the Gamma-Pack method and
sampled on a dense 32 ꢁ 32 ꢁ 32 grid.
3. Results and discussion
3.1. Crystal structures and compositions
Table 1 summarizes the phase analyses of Eu(Ga1ꢀxTtx)2
(Tt ¼ Si, Ge) in this study based on EDXS and X-ray powder
diffraction (XPD). Nearly all Eu(Ga1ꢀxSix)2 and Eu(Ga1ꢀxGex)2
phases adopt structures based on eclipsed stackings of planar or
puckered 63 [Ga1ꢀxTtx] nets; the only exceptions are silicides
at and near the composition EuSi2, which show three-dimensional
3-connected tetragonal nets of locally trigonally planar Si atoms
[40]. The other binary phases, EuGa2 and EuGe2, contain eclipsed
stackings of puckered 63 nets: in EuGa2 [41], Ga atoms form a
three-dimensional 4-connected net with each Ga atom sur-
rounded by a distorted tetrahedral environment [23]; whereas,
in EuGe2 [42,43], Ge atoms create a two-dimensional 3-connected
net with each Ge atom in trigonal pyramidal surroundings. As
the results in Table 1 indicate, Eu(Ga1ꢀxTtx)2 phases for low Si
or Ge content, x, adopt the hexagonal AlB2-type structure with
apparently statistical distributions of Ga and Tt atoms throughout
the planar 63 nets. Furthermore, the unit cell volumes per formula
unit for these AlB2-type phases are larger than that for EuGa2, and
show decreasing volumes with increasing Tt content x. When x
reaches and slightly exceeds 0.50 in Eu(Ga1ꢀxTtx)2, puckering of
the 63 [Ga1ꢀxTtx] nets becomes clearly evident in the germanides,
but not for the silicides. In the silicides, the volume per formula
unit monotonically decreases through EuSi2; in the germanides,
loaded: Eu(Ga0.83Si0.17
)
2
mixture of KHg2- & AlB2-type
Eu(Ga0.50(2)Si0.50(2)
(AlB2-type)
)
Eu(Ga0.32(2)Si0.68(2)
(AlB2-type)
)
the volume passes through
a
minimum near x ¼ 0.55 for
Eu(Ga1ꢀxGex)2. These peculiarities in the Eu(Ga1ꢀxTtx)2 series
were further examined by both single-crystal diffraction and
theoretical calculations.
3.2. Eu(Ga1ꢀxSix)2
loaded: Eu(Ga0.16Si0.84
)
2
Three different structure types (Fig. 1) were identified along
the entire Eu(Ga1ꢀxSix)2 series, as seen in XPD patterns (Fig. 2).
Among ternary cases, single-phase products appear for the four
loaded compositions ranging from x ¼ 0.26 to 0.67 and could be
indexed by the hexagonal AlB2-type structure, space group
P6/mmm. In all cases, no commensurately or incommensurately
modulated structures were observed in the XPD patterns nor were
they apparent from single-crystal diffraction. Thus, Ga and Si
atoms refined to occupy the 2d sites statistically, with results that
are consistent with both loaded compositions and EDXS analyses.
Table 2 summarizes crystallographic results from single-crystal
diffraction experiments recorded on samples extracted from the
single-phase AlB2-type products.
mixture of AlB2- & ThSi2-type
EuSi2
(ThSi2-type)
Two-phase regions surround this single-phase region based on
XPD patterns of the loaded compositions x ¼ 0.18 and 0.84. Both
of these XPD patterns (Fig. 2b and e) contain reflections consistent
with an AlB2-type phase, although analysis of the Si-rich sample
(x ¼ 0.84) suggests some puckering of the 63 net (see subsequent
discussion). The remaining reflections in each of these samples
could be matched with the structure type of the corresponding
binary phase, i.e., either orthorhombic KHg2-type EuGa2 [41] for
x ¼ 0.18 or tetragonal ThSi2-type EuSi2 [40] for x ¼ 0.84, but with
lattice parameters sufficiently different from each binary phase,
respectively, to suggest a small degree of mutual replacements of
Ga and Si atoms in each binary phase. KHg2-type Eu(Ga1ꢀxSix)2 in
20
25 30 35
40
45 50
55 60
(°)
65
70 75 80 85
90
2
Fig. 2. XPD patterns of selected samples of the Eu(Ga1ꢀxSix)2 (0rxr1) series. For
the two-phase samples (b) and (e), reflection positions for the AlB2-type phase are
noted below the diffraction pattern.

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T.-S. You et al. / Journal of Solid State Chemistry 182 (2009) 2430–2442
Table 2
Crystallographic data for Eu(Ga1–xSix)2 (structure type AlB2, space group P6/mmm).
Loaded composition
EDXS composition
Eu(Ga0.74Si0.26
)
Eu(Ga0.70Si0.30
)
Eu(Ga0.50Si0.50
)
Eu(Ga0.33Si0.67)
2
2
2
2
Eu(Ga0.71Si0.29(1)
Eu(Ga0.72Si0.28(2)
267.18
)
Eu(Ga0.67Si0.33(1)
Eu(Ga0.67Si0.33(2)
263.91
)
Eu(Ga0.50Si0.50(1)
Eu(Ga0.50Si0.50(2)
249.77
)
)
Eu(Ga0.31Si0.69(1))
2
2
2
2
2
2
Refined composition
Formula weight (g molꢀ1
)
)
Eu(Ga0.32Si0.68(2)
)
2
2
)
233.95
c/a
1.0841
1.0867
1.0946
1.1041
3
71.17(1)
70.75(1)
68.72(2)
66.53(1)
˚
Volume (A )
Density calc. (g cmꢀ3
)
5.80
5.85
6.04
5.90
Diffractometer
STOE IPDS
8.90–68.4
ꢀ6rhr6,
ꢀ6rkr6,
ꢀ6rlr7
1263
SMART Apex
8.9–70.04
ꢀ6rhr6,
ꢀ6rkr6,
ꢀ7rlr7
1020
STOE IPDS
8.94–69.72
ꢀ6rhr6,
ꢀ6rkr6,
ꢀ7rlr7
1030
STOE IPDS
8.98–69.44
ꢀ6rhr5,
ꢀ6rkr6,
ꢀ7rlr6
1312
2y range (deg)
Index ranges
Reflections collected
Independent reflections
Data/refined parameters
GOF on F2
86 [Rinit ¼ 0.049]
86/7
89 [Rinit ¼ 0.021]
89/7
87 [Rinit ¼ 0.017]
87/7
84 [Rinit ¼ 0.066]
84/7
1.192
1.146
1.190
1.173
R indices (all data)
R1 ¼ 0.021,
wR2 ¼ 0.059
1.57/–1.81
R1 ¼ 0.010,
wR2 ¼ 0.024
0.48/–0.63
R1 ¼ 0.009,
wR2 ¼ 0.022
0.67/–0.41
R1 ¼ 0.013,
wR2 ¼ 0.032
0.44/–0.78
Largest diff. peak and hole (eꢀ/A )
3
˚
2
Eu (1a)
0.017(1)
0.021(1)
0.7
0.011(1)
0.013(1)
0.8
0.010(1)
0.016(1)
0.9
0.015(1)
0.027(1)
0.8
˚
Ueq (A )
Ga/Si (2d)
Eu (1a)
U33/U11
Ga/Si (2d)
1.5
2.7
3.8
3.7
2.4436(2)
2.4366(1)
2.4075(3)
2.3748(2)
˚
d (Ga/Si–Ga/Si) (A)
3.3518(2)
3.3460(1)
3.3170(4)
3.2856(2)
˚
d (Eu–Ga/Si) (A)
the x ¼ 0.18 sample shows a volume expansion of ca. 0.5%
compared to that of EuGa2; ThSi2-type Eu(Ga1ꢀxSix)2 in the
x ¼ 0.84 sample shows a volume expansion of ca. 1.0% compared
to that of EuSi2.
For the single-phase AlB2-type Eu(Ga1ꢀxSix)2 products, the
lattice parameters and unit cell volumes decrease linearly with x
74
72
70
68
x = 0.18(3)
˚
as smaller Si atoms replace Ga atoms (covalent radii: r(Si) ¼ 1.17 A,
˚
r(Ga) ¼ 1.25 A) [29]. Fig. 3 illustrates the trend in unit cell volumes
EuGa2
vs. refined Si content x with the dashed line indicating the linear
fit for the four single-phase samples (black dots). The Ga/Si–Ga/Si
(2d–2d) distances, which are proportional to the a parameters,
decrease with increasing Si content in excellent agreement with
statistical occupation of the 2d sites: e.g., for Eu(Ga0.72Si0.28(2))2,
x = 0.75(3)
66
64
62
"Puckered "
EuSi2
˚
the experimental distance of 2.440(2) A compares favorably
˚
with the value 2.455 A as predicted from the covalent radii; for
0.0
0.2
0.4
0.6
0.8
1.0
˚
Eu(Ga0.32Si0.68(2))2, the distance is 2.375(1) A, as compared to the
x in Eu(Ga1−xSix)2
˚
expected value of 2.390 A. Furthermore, the Ga/Si–Ga/Si (2d–2d)
˚
distance of 2.375(1) A in Eu(Ga0.32Si0.68(2))2 is slightly smaller than
Fig. 3. Variation in unit cell volume with composition for the Eu(Ga1ꢀxSix)2
samples identified as single-phase products (see Table 1). The dashed line is the
linear fit to the four phases shown as black dots. Open circles indicate the volumes
of the AlB2-type phases observed in the two-phase samples; corresponding x
values are determined by extrapolating the linear fit (see text for further
discussion).
˚
˚
the average Si–Si distance in EuSi2 (2.383 A; based on 2.306 A
˚
a parameters
(1 ꢁ ) and 2.421 A (2 ꢁ ) [40]). Moreover, the
drop faster than the c parameters with increasing x, so that
the c/a ratios increase with increasing Si content. These two
structural features suggest that the 63 [Ga1ꢀxSix] nets in
AlB2-type Eu(Ga1ꢀxSix)2 phases could become puckered at
higher Si levels.
two-phase diagram (Fig. 2e), which was obtained by loading
x ¼ 0.84 for Eu(Ga1ꢀxSix)2 could be better attributed to a puckered
63 net. On the other hand, the XPD diagrams for all other AlB2-type
samples are better modeled by planar 63 nets. Linear extrapola-
tion of the curve in Fig. 3 to lower x values gives x ¼ 0.18(3) for
the AlB2-type phase in the two-phase Ga-rich sample. A compar-
able extrapolation at the Si-rich end estimates x ¼ 0.75(3) for the
corresponding phase in the two-phase Si-rich sample. However,
since the XPD patterns suggest different structures for Eu(Ga0.32-
Puckering of the 63 [Ga1ꢀxSix] nets in Eu(Ga1ꢀxSix)2 was not
apparent in the results from single-crystal diffraction experiments
on crystals extracted from the single-phase AlB2-type products
(see Table 2), although the U33/U11 ratio of the 2d (Ga/Si)
site steadily increases from 1.5 in Eu(Ga0.72Si0.28(2) 2
Eu(Ga0.32Si0.68(2))2. Structural refinements of these phases in the
) to 3.7 in
¯
space group P3m1, which allows the z-coordinate of the 2d site to
be varied, keep this coordinate at 1/2. Nevertheless, the XPD
patterns of all AlB2-type phases, including those observed in the
two-phase patterns (Fig. 2b and e), reveal the reflection intensity
ratios I(0 01)/I(0 0 2) and I(110)/I(0 0 2) increase as the Si content
increases. Simulated XPD patterns based on planar (AlB2-type,
space group P6/mmm) and puckered (EuGe2-type, space group
Si0.68(2))2 and Eu(Ga0.25Si0.75(3))2, we estimate the observed range
for AlB2-type Eu(Ga1ꢀxSix)2 phases to be 0.18(2)rxo0.70(2).
Subsequent theoretical calculations corroborate this conclusion.
Moreover, related work on EuTxSi2ꢀx (T ¼ Fe, Co, Ni, Cu, Ag, Au)
achieved similar results, but with limited ranges for single-phase
products [44].
2
1
¯
P3m1) ½Ga1ꢀxSixꢂ nets suggest that the pattern observed in the

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2435
3.3. Eu(Ga1ꢀxGex)2
Eu(Ga0.55(5)Ge0.45(5))2 with Ga in the 2d position yielded a
relatively good residual (RF ¼ 0.0491), but revealed extreme
anisotropy of the displacement parameters (U33/U11 ¼ 12). This
clearly suggested a disorder around the 2d site, which was
confirmed by calculating the difference electron density in the
vicinity of this position (Fig. 6a). Location of a Ga or Ge atom at
The germanide series differs from the analogous silicides by
exhibiting puckered hexagonal variants of the AlB2 structure type,
which are also commensurately modulated along the c-axis. This
difference may be due, in part, to the ground state structure of
1
¯
z ¼ takes into account only part of the experimental density;
EuGe2 (space group P3m1), which is the simplest puckered
2
some unaccounted density is observed along [0 01] below and
above this region (Fig. 6b). If the Ga or Ge atom is located at
z ¼ 0.56 (4h site) with one-half occupation, the experimental data
are better described than the previous case (cf. absolute values in
Fig. 6b and c). Nevertheless, a small residual density remains at
derivative of the AlB2 structure [42], as compared to the tetragonal
structure of EuSi2. Loaded compositions for Eu(Ga1ꢀxGex)2 ranged
from x ¼ 0.25 to 0.60; no multi-phase products were detected by
XPD (see Fig. 4).
Three Ga-rich samples, Eu(Ga0.75Ge0.25(2))2, Eu(Ga0.65
Ge0.35(2))2, and Eu(Ga0.55Ge0.45(2))2, crystallize in the AlB2-type
structure (Fig. 5) with decreasing lattice parameters as the Ge
1
2
z ¼ (Fig. 6c). The difference density map without noticeable
maxima was observed only by locating Ga or Ge atoms in both
positions with different occupations (Fig. 6d). This also reduced
the residuals remarkably (RF ¼ 0.0239) as compared to the
primary anisotropic refinement above. Table 3 includes the
crystallographic results for these three specimens.
content increases; the XPD pattern of Eu(Ga0.75(2)Ge0.25(2) 2 is
)
shown in Fig. 4a. As in the analogous Eu(Ga1ꢀxSix)2 phases, we
assume that the Ga and Ge atoms are statistically distributed at
the 2d site, as there is no evidence to suggest any in-plane or out-
of-plane ordering of Ga and Ge atoms throughout the structure.
Furthermore, we did observe deviation of atoms in the 2d
sites away from the ab-mirror plane (i.e., za12) as the Ge
content increases. Refinement of the crystal structure of
At the equiatomic ratio, EuGaGe adopts the YPtAs-type
structure, which is a puckered, ordered, ternary derivative of
the AlB2-type yielding a quadrupled c parameter because of the
stacking sequence of the 63 nets (see also Fig. 5) [18]. The
diffraction peaks in Fig. 4b that differentiate the YPtAs-type from
the related AlB2-type are clearly detected at 2
y ¼ 28.621, 34.331,
and 62.031. As we discussed previously [18], the Ga and Ge atoms
alternate in each 63 net, and adjacent nets are puckered to locate
Ga atoms closer to each other. Nevertheless, in EuGaGe, this
Eu(Ga0.75(2)Ge0.25(2)
(AlB2-type, Z=1)
)
2
a
b
c
d
˚
Ga?Ga distance remains quite long, ca. 3.726 A. The distribution
of Ga and Ge atoms could not be conclusively determined from
experiment, but was assigned from comparison with the EuGaSn
analogue as well as computational results.
For x exceeding 0.50 in Eu(Ga1ꢀxGex)2, two new phases,
Eu(Ga0.45Ge0.55(2))2 and Eu(Ga0.40Ge0.60(2))2, have been discovered
and adopt distinct, yet related complex structures, which can also
be described as puckered derivatives of the AlB2-type structure.
Eu(Ga0.45Ge0.55(2))2
contains nine puckered 63 nets stacked along
the c-axis (see Fig. 5). Among these nine layers, eight show
stacking environments similar to those in EuGaGe (YPtAs-type)
and one resembles the stacking of 63 nets in EuGe2. Thus, during
refinement, we assigned alternating Ga and Ge atoms to the
EuGaGe-type nets and Ge atoms only to the remaining puckered
net. This assignment agrees with the results of EDXS measure-
ments and the loaded composition. Therefore, the structure
Eu(Ga0.50(2)Ge0.50(2)
)
2
(YPtAs-type, Z=4)
of Eu(Ga0.45Ge0.55(2) 2 is a 2:1 intergrowth of two YPtAs-type
)
Eu(Ga0.45(2)Ge0.55(2)
)
2
EuGaGe unit cells (each unit cell of this type contains 4 EuGaGe
formulas) with one EuGe2 unit cell, which can be formulated
as [(EuGaGe)4]2[EuGe2] ¼ ‘‘Eu9Ga8Ge10’’ ¼ Eu(Ga0.44Ge0.56)2. The
corresponding Ga?Ga distances between adjacent 63 [GaGe]
nets in the EuGaGe portions are also much longer than expected
for significant covalently bonded interactions, i.e., 3.676(1) and
(EuGa0.9Ge1.1-type, Z=9)
˚
3.995(1) A.
On the other hand, the unit cell of Eu(Ga0.40Ge0.60(2))2, contains
five puckered 63 nets stacked along the c-axis in the unit cell.
Eu(Ga0.40(2)Ge0.60(2)
)
2
¯
During refinement in the space group P6m2, an anomalously large
(EuGa0.8Ge1.2-type, Z=5)
U33 parameter occurred for one 1f site at (2/3, 1/3, 1/2), so we
refined this site as split into two symmetrically identical 2i sites
with ca. 50% Ga or Ge site occupancies at (2/3, 1/3, 0.4798(2)). This
solution creates two differently puckered 63 nets, which are
disordered in a 50:50 ratio along the c-axis; the remaining four
layers are well behaved. Alternative refinement strategies in the
¯
space group P3m1, with and without twinning, led to higher
residual factors, significantly higher differential electron densities,
and tremendous variation in isotropic displacement parameters,
so these alternatives were rejected. Therefore, in keeping with
the atomic distributions in EuGaGe and Eu(Ga0.45Ge0.55(2))2, the
five 63 nets per unit cell were assigned as follows: (i) two nets are
15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
(°)
2
Fig. 4. XPD patterns of Eu(Ga1ꢀxGex)2 (x ¼ 0.25(2), 0.50(2), 0.55(2), 0.60(2)).
Z indicates the number of formula units Eu(Ga1ꢀxGex)2 in one unit cell (see also
Fig. 5).

ARTICLE IN PRESS
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T.-S. You et al. / Journal of Solid State Chemistry 182 (2009) 2430–2442
c
a
AlB2
YPtAs
EuGa0.9Ge1.1
EuGa0.8Ge1.2
EuGe2
KHg2
Eu(Ga0.75(2)Ge0.25(2)
)
)
Eu(Ga0.50(2)Ge0.50(2)
)
Eu(Ga0.45(2)Ge0.55(2)
)
Eu(Ga0.40(2)Ge0.60(2))
2
EuGe2
EuGa2
2
2
2
2
Eu(Ga0.65(2)Ge0.35(2)
Fig. 5. Crystal structures along the Eu(Ga1ꢀxGex)2 (0rxr1) series. The structure types are given in italics. The shaded region emphasizes the YPtAs-type building blocks
contained in the three phases EuGaGe, EuGa0.9Ge1.1, and EuGa0.8Ge1.2
.
alternating [GaGe] layers; (ii) the net containing the split 2i site
is an alternating [GaGe] layer with Ga atoms assigned to the
2i site; and (iii) the remaining two nets are each disordered
interactions based on the extended periodicities along the c-axis.
A small bump in 1/ of Eu(Ga0.50(2)Ge0.50(2))2 (and an even smaller
one in 1/ of Eu(Ga0.45(2)Ge0.55(2))2) near 70 K is due to the
ferromagnetic ordering of a trace of EuO impurity phase. All
three compounds show Curie–Weiss behavior for temperatures
w
w
50:50 mixtures of [GaGe] and [Ge2] nets. Eu(Ga0.40Ge0.60(2) 2
)
thus
represents a 1:1 intergrowth between one YPtAs-type EuGaGe
unit cell and one EuGe2 cell, and can be formulated as
[(EuGaGe)4][EuGe2] ¼ ‘‘Eu5Ga4Ge6’’ ¼ Eu(Ga0.40Ge0.60)2. Further-
more, as in EuGaGe and Eu(Ga0.45Ge0.55(2))2, the Ga?Ga distances
above ca. 150 K. Fitting a linear equation to these 1/
in the following paramagnetic effective moments (
Weiss temperatures
W): Eu(Ga0.50Ge0.50)2, meff ¼ 8.02(4) mB
yW ¼ +9.3 K; Eu(Ga0.45Ge0.55)2, meff ¼ 8.08(4) mB yW ¼ ꢀ2.1 K;
and Eu(Ga0.40Ge0.650)2, meff ¼ 8.08(4) mB yW ¼ +4.9 K. The values
of eff are close to the value of 7.94
B for the 8S7/2 state of the 4f7
w
data results
m
eff) and
(
y
,
between adjacent 63 [GaGe] nets are 3.678(1) and 3.873(1) A. The
˚
,
crystallographic results for these two phases are summarized in
the Supporting Information. Since our survey of the Eu(Ga1ꢀxGex)2
series is not exhaustive and the XPD patterns for each product do
not show multiple phases, it is possible that other phases may
exist in this ternary system.
A comparison of the structural features for the four Ge-rich
phases Eu(Ga1ꢀxGex)2, summarized in Table 4, reveals some
interesting trends that impact their electronic structures. As
the Ge content increases from EuGaGe to EuGe2, a decreases,
,
m
m
configuration of Eu, thus indicating clearly that Eu is divalent
in these compounds, a feature that is also characteristic of Eu
in EuTxSi2ꢀx based on Mo¨ssbauer spectroscopy [44]. The Weiss
temperatures are small and decrease and change sign with
increasing x. This suggests weak ferromagnetic (x ¼ 0.50) or
antiferromagnetic (x ¼ 0.55 and 0.60) leading interactions
7
2
between Eu S ¼ moments or eventually competing interactions.
c
increases, and both c/a and volume per formula unit
Below ca. 100 K, the susceptibilities become dependent on
the external magnetic field, which is partially due to the EuO
impurity. At even lower temperatures, the susceptibility curves
Eu(Ga1ꢀxGex)2 increase. The variations in unit cell parameters
can be attributed primarily to the pyramidalization at the main
group elements rather than changes in interatomic distances.
Pyramidalization at each Ga/Ge site can be quantified by the
angular deficiency of the sum of the three bond angles from 3601;
the greater this deficiency, the more pyramidal is the local
structure. The results in Table 4 indicate that pyramidaliza-
tion increases as the Ge content increases in these Ge-rich
Eu(Ga1ꢀxGex)2.
w
(T) of all three samples rise sharply and attain maxima at ca. 25 K
(x ¼ 0.50), ca. 22 K (x ¼ 0.55), and ca. 14 K (x ¼ 0.60) (tempera-
tures are taken from (T) curves measured during cooling in a
field of
w
m
0H ¼ 0.01 T). Below these corresponding temperatures,
the susceptibilities decrease slightly. These features are very
broad, but, nevertheless, indicate a magnetic ordering of the Eu
moments.
Isothermal magnetization curves recorded at 1.8 K are given in
Fig. 7b. The magnetizations after cooling in zero field rise quickly
3.4. Magnetic susceptibilities of Eu(Ga1ꢀxGex)2
at first and then slower; the Eu(Ga0.50Ge0.50)2 sample shows the
fastest and strongest rise, which agrees with its positive Weiss
temperature. All three M(H) curves do not saturate at 7 T. For a full
alignment of the Eu moments, 7.0 mB are expected. The magnetic
hysteresis behavior for fields below ca. 1 T indicates that the
magnetic structures of all three samples are basically anti-
ferromagnetic but have significant ferromagnetic components.
The temperature-dependent magnetic susceptibilities (
and inverse susceptibilities (1/ ) of three Eu(Ga1ꢀxGex)2 com-
pounds (x ¼ 0.50(2), 0.55(2), 0.60(2)) are plotted in Fig. 7a for a
field
0H ¼ 0.1 T. We specifically targeted these samples for
magnetic measurements to explore possible magnetic exchange
w ¼ M/H)
w
m

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T.-S. You et al. / Journal of Solid State Chemistry 182 (2009) 2430–2442
2437
tions. Similar magnetic data have been observed for several EuTX
phases [45] and the EuTMg ferromagnets [46].
3.5. Eu LIII XAS measurements
Sharp absorption maxima in XAS spectra (see Fig. 8) are
observed at ca. 6977 eV for four Eu(Ga1ꢀxGex)2 (x ¼ 0.45(5),
0.50(2), 0.55(2), 0.60(2)) samples, which further confirms a 4f7
electronic configuration at the Eu atoms. Small shoulders are
observed in these spectra at ca. 10 eV higher than the main
absorption peak, which are assigned to small traces of Eu2O3
(electronic configuration 4f6, Eu3+) in all three samples.
3.6. Electronic structure calculations
To examine the electronic structure and chemical bonding
features that contribute to the structural trends and atomic
distributions in Eu(Ga1ꢀxTtx)2 (Tt ¼ Si, Ge, 0rxr1), TB-LMTO-ASA
electronic structure calculations were carried out on selected
models of the crystal structures. In particular, DOS and COHP
curves were carefully analyzed to understand the observed
homogeneity ranges of the AlB2-type Eu(Ga1ꢀxTtx)2 phases. For
all systems, the DOS curves for the majority and minority spin
states differed only slightly, so subsequent DOS curves illustrate
their superposition; the Fermi level (EF) is the energy reference in
all curves. For valence electron counting purposes, the Eu atoms
are considered divalent, which is supported by the magnetic
susceptibility and XAS measurements discussed above. Since Ga is
trivalent and the Tt atoms are tetravalent, the valence electron
count per formula unit for Eu(Ga1ꢀxTtx)2 is (8+2x) electrons, and
thus varies from 8 to 10 electrons.
3.7. Eu(Ga1ꢀxSix)2 (AlB2-type)
Our experimental results concluded the stability range to be
0.18(2)rxo0.70(2) with statistical mixing of Ga and Si atoms on
the 2d sites. These values correspond to 8.36(4)–9.40(4) valence
electrons per Eu(Ga1ꢀxSix)2 formula unit. To model this system for
TB-LMTO calculations, we considered EuGaSi with planar, alter-
nant 63 [GaSi] layers in three different stacking modes along the
c-axis: (i) eclipsed stacking giving only Ga?Ga and Si?Si
contacts; (ii) alternate stacking giving only Ga ꢃ ꢃ ꢃ Si contacts;
and (iii) a 1:1 mixture of eclipsed and alternate stacking [18]. The
calculated total electronic energy is lowest for model (ii) with just
Ga–Si and Ga?Si first- and second-nearest-neighbor interactions
(Fig. 9, top), by 0.14 and 0.75 eV/formula unit, respectively, with
respect to models (iii) and (i). Thus, we utilized model (ii) for
subsequent DOS and COHP analysis.
Fig. 9 (bottom) displays the DOS and COHP curves within 4 eV
of the Fermi level (EF) for 9-electron EuGaSi in model (ii).
Throughout the entire DOS curve, significant mixing between
valence orbitals of Eu, Ga, Si atoms is observed with no clear
energy gaps. There is a pseudogap ca. 1 eV below EF, the states
below which have mostly Si and some Ga character, whereas the
region just above this pseudogap is dominated by Eu valence 5d
and 6s orbitals. The position of this pseudogap in the DOS curve
corresponds to a band filling of 8 valence electrons per formula
unit, which also nearly matches the top of Ga–Si bonding states
Fig. 6. Difference electron density for Eu(Ga0.55Ge0.45
) (AlB2-type) in the (010)
2
plane at y ¼ 2/3 in vicinity of the position 1/3 2/3 1/2: (a) without atoms in this
¼ 5eꢀ
A
ꢀ1); (b) Ga at z ¼ 1/2 (
D
r
¼ 5eꢀ
ꢀ1); (c) Ga at z ¼ 0.56
˚
˚
A
position (
D
r
A
˚
A
˚
(
(
D
D
r
r
¼ 0.5eꢀ
ꢀ1); (d) Ga at z ¼ 1/2 and z ¼ 0.5871, occupations cf. Table S3
¼ 0.1eꢀ
ꢀ1). Zero line is dashed, positive difference density is shown by full
shown in the adjacent COHP curve. The Ga–Si COHP curves for
s
˚
lines, negative one-by dotted-dashed lines. The axes step is 0.2 A.
and overlaps are optimized at 8.4 valence electrons, and remain
p
essentially nonbonding until ca. 9.2 valence electrons. Above this
electron count, the Ga–Si orbital interactions develop significant
Competing interactions may play a role in generating such
complex behavior. The disorder of the Ga and Ge atoms possibly
leads to the strong broadening of the magnetic ordering transi-
s* character. The COHP curve for Ga?Si second nearest-neighbor
contacts along the c-axis show weak, essentially nonbonding
orbital interactions (the curve is magnified by 10), but has

ARTICLE IN PRESS
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T.-S. You et al. / Journal of Solid State Chemistry 182 (2009) 2430–2442
Table 3
Crystallographic data for Eu(Ga1–xGex)2.
Composition:
Eu(Ga0.75Ge0.25
293.20
)
Eu(Ga0.65Ge0.35
)
Eu(Ga0.55Ge0.45
293.60
)
Eu(Ga0.45Ge0.55
)
Eu(Ga0.40Ge0.60
294.85
)
2
2
2
2
2
Formula weight (g molꢀ1
Space group
)
293.40
294.56
¯
¯
P6/mmm (no. 191)
1.0739
P6/mmm (no. 191)
1.0749
P6/mmm (no. 191)
1.079
P3m1 (no. 164)
1.0681
P6m2 (no. 187)
1.0857
(c/a)*
3
73.46(1)
72.06(1)
70.95(5)
639.02(3)
356.34(2)
˚
Vol (A )
Z
1
1
1
9
5
Density calc. (g cmꢀ3
Diffractometer
)
6.62
6.76
6.88
6.864
6.87
STOE IPDS
11.00–70.60
ꢀ6rhr6,
ꢀ6rkr6,
ꢀ5rlr7
1377
SMART Apex
8.9–69.88
ꢀ6rhr6,
ꢀ6rkr6,
ꢀ7rlr7
712
STOE STADI 4
8.95-64.78
ꢀ6rhr5,
0rkr6,
ꢀ6rlr6
573
SMART Apex
2.00–56.8
ꢀ5rhr5,
ꢀ3rkr5,
ꢀ51rlr53
3913
SMART Apex
1.76–55.84
ꢀ5rhr5,
ꢀ5rkr5,
ꢀ30rlr29
3075
2y range (deg)
Index ranges
Reflections collected
Independent reflections
Data/parameters
GOF on F2
92 [Rinit ¼ 0.122]
92/7
82 [Rinit ¼ 0.094]
86/7
75 [Rinit ¼ 0.084]
71/11
742 [Rinit ¼ 0.089]
742/42
419 [Rinit ¼ 0.025]
419/27
1.192
1.073
0.850
0.089
1.125
Residuals [I4 2
s
(I)]
R1 ¼ 0.031,
wR2 ¼ 0.063
R1 ¼ 0.035,
wR2 ¼ 0.064
2.38/ꢀ1.55
R1 ¼ 0.034
wR2 ¼ 0.073
R1 ¼ 0.035
wR2 ¼ 0.073
2.23/ꢀ2.75
R1 ¼ 0.024,
wR2 ¼ 0.036
R1 ¼ 0.028,
wR2 ¼ 0.037
0.24/ꢀ0.45
R1 ¼ 0.048,
wR2 ¼ 0.108
R1 ¼ 0.131,
wR2 ¼ 0.142
2.188/ꢀ2.686
R1 ¼ 0.028,
wR2 ¼ 0.052
R1 ¼ 0.038,
wR2 ¼ 0.056
0.94/ꢀ1.14
Residuals (all data)
Largest differential density (eꢀ/A )
3
˚
Table 4
Selected interatomic distances and angular deficiencies at anionic sites in Ge-rich Eu(Ga1–xGex)2 phases.
Composition:
Eu(Ga0.50(2)Ge0.50(2)
2.531(1)
)
2
Eu(Ga0.45(2)Ge0.55(2)
)
Eu(Ga0.40(2)Ge0.60(2))
2
EuGe2 [33]
2.551
2
1st layera
2nd layer
3rd layer
4th layer
5th layerb
2.533(1)
2.530(1)
2.528(1)
2.473(1)
2.535(1)
2.511(1)
2.556(1)
2.487(1)
˚
d(Ga-Ge) (A)
Angular deficiency (1)c
15.9
1st layer
2nd layer
3rd layer
4th layer
5th layer
18.5
16.4
16.5
4.3
15.5
24.8
10.2
39.0
17.8
a
The order of layers starts from the origin of a unit cell.
b
c
Due to the inversion center located in the 5th layer of a unit cell, five out of nine layers were sufficient to describe structural details.
Angular deficiency from 3601 at each site indicates the tendency of pyramidalization at a given site.
repulsive character just below the pseudogap at
8
valence
lattice constants are as follows: for the EuGe2-type, aVASP ¼ 3.956
3
˚
˚
˚
electrons. Furthermore, the Eu–Ga and Eu–Si COHP curves
are slightly bonding in the Ga–Si nonbonding region. Therefore,
within a rigid-band approximation applied to the DOS and based
on these various COHP curves, Eu(Ga1ꢀxSix)2 can tolerate a range
of valence electron counts from ca. 8.4 to 9.2 electrons without
significantly disrupting the nearest-neighbor Ga–Si interactions
and the planarity of the 63 [Ga1ꢀxSix] nets. This range of electron
counts agrees reasonably well with the experimental range; poor
agreement with the observed upper bound (Si-rich end) may be
due to the limitations of the rigid-band approximation applied in
this analysis as well as an increased tendency toward puckering of
the 63 nets for larger x values.
Therefore, to assess the theoretical preference of planar vs.
puckered 63 nets in Si-rich Eu(Ga1ꢀxSix)2 phases, optimized
structures of EuSi2 were determined using the VASP code for
three different structure types: the tetragonal ThSi2-type; the
hexagonal AlB2-type; and the trigonal EuGe2-type. Accordingly,
the ThSi2-type is preferred, in agreement with experiment, by
61 meV/EuSi2 over the EuGe2-type, and by 164 meV/EuSi2 over the
AlB2-type. Furthermore, the theoretical lattice constants of the
ThSi2-type structure are in excellent agreement with experimen-
A, cVASP ¼ 4.849 A, c/a ¼ 1.226, V ¼ 65.715 A ; for the AlB2-type,
3
˚
˚
˚
aVASP ¼ 4.080 A, cVASP ¼ 4.439 A, c/a ¼ 1.088, V ¼ 63.989 A . These
theoretical results are especially interesting, in light of the results
presented in Table 1, and strongly suggest that the Eu(Ga0.25-
Si0.75)2 phase observed in the two-phase product (Fig. 1e) contains
puckered 63 nets. To establish the homogeneity range for this
puckered variant, COHP analysis of the Si–Si contacts in the 63
nets based on TB-LMTO calculations of the optimized EuGe2-type
EuSi2 (see Supporting Information) revealed maximum bonding
character at ca. 8.30 valence electrons with Si–Si nonbonding
character ranging up to ca. 9.70 valence electrons. Thus, as the
tendency toward puckering of the 63 [Ga1ꢀxSix] net increases,
the number of valence electrons also increases and extends the
observed range above based on EuGaSi. The VASP calculations
also shed light on the unusual lattice parameters refined for the
AlB2-type phase in the sample loaded with x ¼ 0.84 (see Table 1):
the calculated c/a ratio for the EuGe2-type EuSi2 is significantly
larger than that of the AlB2-type EuSi2. Therefore, in addition
to the arguments based on experimental evidence and these
computational results, we propose
a Si-rich region in the
Eu(Ga1ꢀxSix)2 system that adopts the trigonal EuGe2-type struc-
ture with puckered [Ga1ꢀxSix] nets. Further results of VASP
calculations are available in the Supporting Information.
˚
˚
˚
tal values: aVASP ¼ 4.318 A, cVASP ¼ 13.708 A; aEXP ¼ 4.3065(4) A,
˚
aEXP ¼ 13.683(1) A [40]. For the other alternatives, the optimized

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2439
Fig. 8. XAS spectra of Eu(Ga1ꢀxGex)2 (x ¼ 0.45(5), 0.50(2), 0.55(2), 0.60(2)).
observed compounds adopting the AlB2-type structures have,
respectively, 8.5 and 8.7 valence electrons. Furthermore, the
crystallographic results for Eu(Ga0.55Ge0.45(2) 2
)
suggested
puckered 63 nets, as in the EuGe2-type.
3.9. Ge-rich Eu(Ga1ꢀxGex)2
Fig. 7. (a) Temperature-dependent magnetic susceptibilities
w(T) (left and upper
axes) and inverse magnetic susceptibilities 1/ (T) (right and lower axes) for
w
From the structures of the four known examples, x ¼ 0.50,
0.55, 0.60, and 1.00, these phases may be formulated as
[EuGaGe]2ꢀ2x[EuGe2]2xꢀ1 to emphasize the intergrowth structures
detected in the x ¼ 0.55 and 0.60 phases. The theoretical
electronic structure of EuGaGe was previously discussed, and its
DOS and COHP curves show features resembling those found for
the AlB2-type ‘‘EuGaGe’’ in Fig. 10 (see Fig. 7 of Ref. [18]). However,
there is one distinct difference in the DOS curves between the
AlB2-type and YPtAs-type structures: the pseudogap close to 8
valence electrons observed in the AlB2-type DOS is less
pronounced in the YPtAs-type DOS, which is caused by the
overlapping Eu 5d bands (see Supporting Information). Also, the
Ga–Ge COHP curves in the two structure types are different.
The Ga–Ge COHP curve [18] for the YPtAs-type structure is
optimized at 8.50 valence electrons per formula unit (ca. 0.6 eV
below EF) and remains essentially nonbonding up to ca. 9.25
valence electrons (ca. 0.3 eV above EF); in AlB2-type ‘‘EuGaGe,’’ the
optimal range is ca. 8.3–9.0 valence electrons. The difference
between these two nearest-neighbor Ga–Ge COHP curves can be
attributed to the different s–p hybridization occurring at the Ga
and Ge atoms in the puckered vs. planar 63 nets as well as the
different involvement of Eu 5d states. Previous computational
studies invoking analysis by electron localization functions
indicated that the Eu 5d orbitals are involved in multi-center
orbital interactions with Ga 4s and 4p orbitals, interactions, which
contribute to the puckering of the 63 nets and their relative
orientations [18].
Eu(Ga1ꢀxGex)2 with x ¼ 0.50(2), 0.55(2), and 0.60(2). (b) Isothermal magnetization
curves M(H) up to 7.0 T at T ¼ 1.8 K for the same samples.
3.8. Eu(Ga1ꢀxGex)2 (AlB2-type)
Experimental results indicate the stability range is limited to
xo0.50. Although we did not attempt to determine the precise
upper or lower boundaries of this phase region, there is certainly a
homogeneity width between at least x ¼ 0.25 and ca. 0.40. As
in the silicides, we considered ‘‘EuGaGe’’ with only Ga–Ge
and Ga ꢃ ꢃ ꢃ Ge first- and second-nearest-neighbor interactions for
TB-LMTO calculations.
DOS and COHP curves are illustrated in Fig. 10. While most
features of these curves are similar to those of AlB2-type EuGaSi, a
noticeable difference is seen in the nearest-neighbor Ga–Ge COHP
curve. Whereas the Ga–Si COHP curve of EuGaSi shows essentially
nonbonding states between ca. 8.4 and 9.2 valence electrons per
EuGaSi, the corresponding Ga–Ge COHP curve of ‘‘EuGaGe’’ is
optimized at ca. 8.25 valence electrons and clearly shows
antibonding states above 8.5 valence electrons. Decomposing
the Ga–Ge interactions into
this feature to arise from
s
s
and
p overlap components shows
* overlap. Therefore, on the basis
of COHP analyses, the upper limit of the homogeneity range for
Eu(Ga1ꢀxGex)2 should not exceed that of Eu(Ga0.50Ge0.50)2 with 9.0
valence electrons, but can extend to a lower bound of ca. 8.3
valence electrons, i.e., Eu(Ga0.85Ge0.15)2. The two experimentally

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c
b
a
b
a
DOS
−COHP
Ga-Si
Ga-Si
(along a-axis)
(along c-axis, 10 ×)
4
3
−
+
σ-bond
π-bond
Eu−Si
Eu−Ga
2
1
9.2 e−
9.0 e−
0
EF
8.4 e−
8.0 e−
-1
-2
-3
-4
−
+
−
+
0
0
0
0
Fig. 9. (Top) Structural model of AlB2-type Eu(Ga0.50Si0.50)2. Eu: gray; Ga: red; Si: green. (Bottom) DOS and COHP curves for AlB2-type Eu(Ga0.50Si0.50)2. (Left) Total DOS
(solid line), Eu PDOS (white region) and Si PDOS (gray region), and Ga PDOS (black region). (Right) Ga–Si (along the a-axis, c-axis), Eu–Si, and Eu–Ga COHP curves. The Fermi
level is indicated by the solid line. Other Fermi levels for various valence electron counts are indicated. (For interpretation of the references to color in this figure legend, the
reader is referred to the web version of this article).
Eu(Ga0.45Ge0.55(2) 2
)
contains 8 [GaGe] and 1 [Ge2] puckered 63
nearly optimized at EF with 10 valence electrons. The difference
between these COHP curves can be understood from different
local environments surrounding this Ge layer. The 63 [Ge2] layer in
Eu(Ga0.45Ge0.55(2))2 does not pucker as much (angular deficiency is
17.51; see Table 4) as it does in EuGe2 (angular deficiency is 39.01)
because of the spatial restriction in Eu(Ga0.45Ge0.55)2 as measured
by the (c/a)* ratios (see Table 1). The wider separation between 63
nets, and given this description, its DOS curve, shown in Fig. 11, is
similar to the DOS curve of EuGaGe [18].The strongest peak occurs
at ca. 1.7 eV below EF, while there are no apparent pseudogaps.
There is more Ge 4p orbital contribution to the total DOS than Eu
5d orbitals or Ga 4p orbitals below EF because of the Ge-rich
composition and relative electronegativities, while Eu 5d orbital
contributions become greater near and above EF. The intergrowth
character of this structure is validated by evaluating the number
of valence electrons assigned to each 63 net as determined by the
integrated total DOS curve: the net assigned as [Ge2] gives 9.98
electrons (as in EuGe2), while the others assigned as [GaGe]
integrate to 8.98–9.01 electrons (as in EuGaGe). These results are
listed in detail in the Supporting Information.
nets in EuGe2 than in Eu(Ga0.45Ge0.55 2 causes this structural
)
effect. Furthermore, and as a result, a shorter Ge–Ge bond
˚
distance is observed in Eu(Ga0.45Ge0.55)2, i.e., 2.527 A for
˚
Eu(Ga0.45Ge0.55)2 and 2.552 A for EuGe2 [42], and can explain
the antibonding character of this Ge–Ge COHP curve at EF.
3.10. Eu(Ga1ꢀxTtx)2: Si vs. Ge
The Ga–Ge COHP curve for Eu(Ga0.45Ge0.55(2))2 is optimized at
ca. 8.6 valence electrons per [GaGe] 63 net (ca. 0.5 eV below EF),
and shows nonbonding character up to ca. 9.6 valence electrons
(ca. 0.7 eV above EF), which is similar to that of EuGaGe. The
Ge–Ge COHP curve for the puckered hexagonal layer consisting of
entirely Ge atoms is optimized at ca. 1.4 eV below EF, and shows
antibonding states at EF [42]. This Ge-only layer can be compared
with Ge layers in EuGe2, for which the Ge–Ge COHP curve is
The differences between the structural and phase behavior
of Eu(Ga1ꢀxSix)2 and Eu(Ga1ꢀxGex)2 are subtle yet distinct. In
particular, the occurrence of AlB2-type phases shows different
compositional ranges in the two cases: in the silicides, the range is
wide (0.18(2)rxo0.70(2)), which corresponds to 8.36(4)–
9.40(4) electrons; in the germanides, the range is narrower,

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2441
DOS
− COHP
Ga-Ge
Ga-Ge
(along a-axis)
(along c-axis, 10 ×)
4
3
−
+
σ-bond
π-bond
Eu−Ge
Eu−Ga
2
1
9.0 e−
EF
0
8.7 e−
8.5 e−
-1
-2
-3
-4
8.25 e−
−
+
−
+
0
0
0
0
Fig. 10. DOS and COHP curves for AlB2-type Eu(Ga0.50Ge0.50
)
2 to model Eu(Ga1ꢀxGex)2 (0.25rxr0.35). (Left) Total DOS (solid line), Eu PDOS (white region), Ge PDOS (gray
region), and Ga PDOS (black region). (Right) Ga–Ge (along the a-axis, c-axis), Eu–Ge, and Eu–Ga COHP curves. The Fermi level for Eu(Ga0.50Ge0.50)2 is indicated by the solid
line. Other Fermi levels for various valence electron counts are indicated.
Table 5
DOS
− COHP
4
3
Interaction energies (
and
bonds for sp2 and sp3 hybridized Ga, Si, and Ge, and estimated energies for 8-
electron and 9-electron configurations for 63 nets.
DE), estimated by Hu¨ckel calculations, for Ga–Si and Ga–Ge s
p
+
−
Ge−Ge
sp2/
D
E (sp3)
p s
p
(eV)
sp3
(eV)
E (sp2)
D
E
Ga−Ge
D
s
2
2
8
Ga–Si 8.63
1.83 7.49
8eꢀ
9eꢀ
(
s
)6(
p
)
ꢀ55.45 8eꢀ
ꢀ53.63 9eꢀ
(
s
)
ꢀ59.94
ꢀ52.45
1
0
(
s
)6(
p
)2(
)6(
p
*)1
(
s
)8(
s
*)1
2
8
8eꢀ
9eꢀ
(
s
p
)
ꢀ50.56 8eꢀ
ꢀ49.00 9eꢀ
(
s)
ꢀ56.88
ꢀ49.77
EF
Ga–Ge 7.91
1.56 7.11
9.11 e−
(
s
)6(
p
)2(
p
*)1
(
s
)8(
s
*)1
-1
-2
-3
-4
Boldfaced values indicate lower energy for each electron count and bond type.
0
0
Fig. 11. DOS and COHP curves for Eu(Ga0.45Ge0.55)2. (Left) Total DOS (solid line), Eu
PDOS (white region), Ge PDOS (gray region), and Ga PDOS (black region). (Right)
Ga–Ge, Eu–Ga, and Eu–Ge COHP curves. The Fermi level is indicated by the solid
line.
1
2
We can demonstrate this difference between Si and Ge semi-
(ꢄ0.25rxrꢄ0.45), or ꢄ8.5–8.9 electrons. For more electron-rich
cases, the germanides exhibit puckered 63 nets [41]. Also, the
binary tetrelides, EuSi2 and EuGe2, are distinctly different and
quantitatively in Eu(Ga1ꢀxTtx)2 by estimating the relative ener-
getics of GaꢀTt
s- and p
-interactions based on either sp2 (1) or
sp3 (2) hybridized Ga and Tt atoms for 8- and 9-electron systems
within simple Hu¨ckel theory [48]. For these calculations, model
structures [H2GaꢀTtH2] (1) and [H3GaꢀTtH3] (2) were employed
using covalent radii to set interatomic distances. All atoms were
modeled by Slater-type orbitals and their atomic orbital energies
were given by configuration energies [49], which indicate that
show two different modes of disrupting the
p-antibonding
interactions [3,47]. In EuSi2, all Si atoms are locally trigonally
planar by three Si atoms, but the planes of adjacent Si atoms are
perpendicular to each other. On the other hand, all Ge atoms in
EuGe2 are trigonally pyramidally coordinated by three Ge atoms
to create puckered 63 nets. Both of these observations suggest that
under slightly reduced environments, Si prefers sp2 hybridization
while Ge prefers sp3 hybridization.
Ge is more electronegative than Si. The specific GaꢀTt
-interactions were then determined by averaging the differences
between bonding/antibonding orbitals in [HnGaꢀTtHn] (n ¼ 2, 3)
s- and
p

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and the orbitals of the isolated fragments, [GaHn] and [TtHn]
(n ¼ 2, 3). These results are summarized in Table 5. As expected,
GaꢀSi interactions are stronger than GaꢀGe. The estimated
relative energies associated with 8-electron and 9-electron
planar (sp2) or puckered (sp3) 63 [GaTt] nets are evaluated using
these interaction energies applied to the appropriate electronic
configuration, which is also listed in Table 5. This semi-
quantitative analysis indicates that at 9eꢀ, local sp2 hybridization
is favored for the silicides whereas local sp3 hybridization is
preferred for the germanides. For 8eꢀ, local sp3 hybridization is
preferred for both silicides and germanide systems.
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This work was supported by NSF DMR 02-41092 and 06-05949.
The authors are grateful to Dr. Warren Straszheim for the EDXS
measurements and Stefan Hu¨ckmann for powder diffraction
measurements. G.J.M., T.-S.Y. and J.T.Z. also thank the Max-Planck
Society for the research fellowships.
Supporting Information Available: X-ray crystallographic
files in CIF format, atomic coordinates and equivalent displace-
ment parameters for Eu(Ga1ꢀxGex)2 (x ¼ 0.25(2), 0.35(2), 0.45(5),
0.50(2), 0.55(2), 0.60(2)), Wigner-Seitz (WS) atomic sphere radii
of elements used for LMTO calculations, computational details
and energy comparison for two ‘‘EuSi2’’ models, calculated IDOS
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patterns of Eu(Ga1ꢀxSix)2, the Si-Si COHP curve of the relaxed
EuGe2-type ‘‘EuSi2’’, and band structure of Eu(Ga0.5Ge0.5)2 with
fatband contributions of Eu 5d orbitals. This material is available
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free of charge via the Internet at http://pubs.acs.org.
Appendix 1. Supporting Information
Supplementary data associated with this article can be found
in the online version at doi:10.1016/j.jssc.2009.06.032.