Synthesis, crystal growth and structure of Mg containing β-rhombohedral boron: MgB17.4

Article abstract of DOI:10.1016/j.jssc.2006.03.009

For the first time, single crystals of Mg containing β-rhombohedral boron MgB_17.4 were synthesised from the elements in a Mg/Cu melt at 1600 °C. The crystal structure determined by the refinement of single crystal data (space group R-3m, a = 10.991 (2) A, c = 24.161 (4) A, 890 reflections, 123 variables, R₁ (F) = 0.049, w R₂ (I) = 0.122) improves and modifies the former structure model derived from earlier investigations on powder samples. Mg is located on four different positions with partial occupation. While the occupation of the sites D (53.3%), E (91%) and F (7.2%) is already known from other boron-rich borides related to β-rhombohedral boron, the occupation of the fourth position (18h, 6.7%) is observed for the first time. Two boron positions show partial occupation. The summation reveals the composition MgB_17.4 and Mg_5.85B_101.9, respectively, confirmed by WDX measurements. The single crystals of MgB_17.4 show the highest Mg content ever found. Preliminary measurements indicate no superconductivity.

Full text of DOI:10.1016/j.jssc.2006.03.009

ARTICLE IN PRESS
Journal of Solid State Chemistry 179 (2006) 2900–2907
www.elsevier.com/locate/jssc
Synthesis, crystal growth and structure of Mg containing
b-rhombohedral boron: MgB17.4
Ã
Volker Adascha, Kai-Uwe Hessb, Thilo Ludwigc, Natascha Vojteerc, Harald Hillebrechtc,d,
aDRONCO AG, Wiesenmu¨hle 1, D-95632 Wunsiedel, Germany
bLudwig-Maximilians-Universita¨t Mu¨nchen, Institut fu¨r Mineralogie, Petrologie und Geochemie, Theresienstr. 41/III, D-80333 Mu¨nchen, Germany
cAlbert-Ludwigs-Universita¨t Freiburg, Institut fu¨r Anorganische und Analytische Chemie, Albertstr. 21, D-79104 Freiburg, Germany
dFreiburger Materialforschungszentrum FMF, Stefan-Maier-Str. 25, D-79104 Freiburg, Germany
Received 18 September 2005; received in revised form 13 March 2006; accepted 14 March 2006
Communicated by Barbara Ruth Albert
Available online 18 March 2006
Abstract
For the first time, single crystals of Mg containing b-rhombohedral boron MgB17.4 were synthesised from the elements in a Mg/Cu
˚
melt at 1600 1C. The crystal structure determined by the refinement of single crystal data (space group R-3m, a ¼ 10:991ð2Þ A,
˚
c ¼ 24:161ð4Þ A, 890 reflections, 123 variables, R1ðFÞ ¼ 0:049, wR2ðIÞ ¼ 0:122) improves and modifies the former structure model derived
from earlier investigations on powder samples. Mg is located on four different positions with partial occupation. While the occupation of
the sites D (53.3%), E (91%) and F (7.2%) is already known from other boron-rich borides related to b-rhombohedral boron, the
occupation of the fourth position (18h, 6.7%) is observed for the first time. Two boron positions show partial occupation. The
summation reveals the composition MgB17.4 and Mg5.85B101.9, respectively, confirmed by WDX measurements. The single crystals of
MgB17.4 show the highest Mg content ever found. Preliminary measurements indicate no superconductivity.
r 2006 Elsevier Inc. All rights reserved.
Keywords: Synthesis; Single crystals; Structure analysis; Magnesium boride; Boron-rich boride; b-Rhombohedral boron; WDX measurements
1. Introduction
interstitial voids between the boron icosahedra and the B28-
units. Binary borides related to b-rhombohedral boron are
known for Al, Cr, Cu, Fe, Ge, Li, Mn, Ni, Sc, Si, V, Zn and
Zr [7]. Recently, boron-rich borides of Li [8] and Mg [9,10]
were in the focus because theoretical investigations
predicted superconductivity [5]. The observation of super-
conductivity for MgB2 with Tc ¼ 39 K [11] additionally
increased the interest in Mg borides.
Boron-rich borides exhibit interesting and unique
properties [1] like high hardness, high melting points and
chemical inertness. Owing to their physical properties as
well boron-rich borides are important materials for
thermoelectrics [2], high temperature semiconductors [3]
and possible high-Tc superconductors [4,5]. Most of the
work on boron-rich borides was done with b-rhombohe-
dral boron and related compounds [6].
Several investigations are reported for the binary
system Mg/B [12] and the compounds MgB2, MgB4,
The structure of elemental b-rhombohedral boron is
known to take up different metals. The acceptor levels of
the boron polyhedra are filled up by the electrons of the
metal atoms and the cations occupy a variety of large
MgB7 and MgB
are well established. Very recently,
ꢀ20
synthesis and characterisation of MgB12 was reported [13].
But still there are uncertainties, which arise mainly
from the special properties of boron-rich borides of
magnesium. First the melting points are very different
leading to difficulties for the growth of single crystals.
Additional problems are caused by the high reactivity of
Mg and the tendency of boron-rich borides to incorporate
impurities.
Ã
Corresponding author. Albert-Ludwigs-Universitat Freiburg, Institut
¨
fur Anorganische und Analytische Chemie, Albertstr. 21, D-79104
¨
Freiburg, Germany. Fax: +49 761 203 6102.
E-mail address: harald.hillebrecht@ac.uni-freiburg.de
(H. Hillebrecht).
0022-4596/$ - see front matter r 2006 Elsevier Inc. All rights reserved.
doi:10.1016/j.jssc.2006.03.009

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V. Adasch et al. / Journal of Solid State Chemistry 179 (2006) 2900–2907
2901
These aspects can be taken from the work on Mg
containing b-rhombohedral boron published up to now.
Brutti et al. [9] yielded powder samples by heating the
elements in a Ta-crucible at 1150 1C. MgB7 was formed as a
by-product and ‘‘removed’’ by annealing in vacuum at
1000 1C. The structure refinement was done with Rietveld
methods using conventional X-ray and synchrotron data.
The expected framework of boron polyhedra was con-
firmed and three different partially occupied Mg sites
(Table 7) were found. The Mg positions were localised by
checking the possible metal positions as they were
proposed by Anderson and Lundstrom [14].
Soga et al. [10] doped b-rhombohedral boron with Mg
via the gas phase at 1200 1C. Boron and magnesium were
put into tantalum or boron nitride containers and sealed in
a quartz tube. The highest Mg content and the smallest Si
contamination, which were monitored by EDX measure-
ments, were achieved by twofold heating for 10 h. A
repeated exposure or increased reaction time resulted in
higher Si and/or lower Mg contents. The refinement (X-ray
data, Rietveld method) based on the model given by Brutti
et al. [9] with three partially filled Mg positions. Si was
found to occupy the A1 site and to substitute the B1
position. Because no single crystals were obtained all
structure determinations and measurements of physical
properties were done on powder samples.
detailed analysis especially in consideration of light
elements (4oZo11) was done to exclude their incorpora-
tion (especially carbon), which occur frequently in boron-
rich borides. For the WDX measurement the single crystal
used for the structure determination by X-rays (composi-
tion MgB17.4) was fixed in a matrix with Ag/epoxy resin. It
was polished to get a clear surface and to assure the
measurement of the interior of the crystal [15] and not of
the surface that may be influenced by the contact to the
melt. Boron and magnesium were detected as the only
elements with Z44. The molar ratio B:Mg was found to be
93.3:6.7 leading to the composition MgB14.0 in good
agreement with the composition determined by X-ray
methods. A similar procedure was applied for MgB12 (X-
ray: MgB12.41; WDX: MgB12.35) [13a].
3. Structure refinement
Investigations with
a single crystal diffractometer
equipped with MoKa radiation and an image plate detector
(Fa. Stoe, IPDS II) revealed a rhombohedral unit cell with
˚
˚
a ¼ 10:991ð2Þ A and c ¼ 24:161ð2Þ A in hexagonal setting
˚
(rhombohedral setting: a ¼ 10:139ð2Þ A, a ¼ 65:20ð2Þ1).
The measurement of 18,288 intensities gave a data set of
890 independent reflections (555 with I42s(I)). Because of
the low absorption coefficient (0.21 mmꢁ1) no correction of
absorption effects was done. According to dimension and
symmetry of the unit cell a structure of the b-rhombohedral
boron type was assumed. The refinement was started with
the structure model derived from powder data by Rietveld
methods [9]. The evaluation of thermal displacement
parameters, occupation factors, difference Fourier maps
and of the bond distances found in other boron-rich
borides of Mg (MgB12 [13], MgB7 [15,16]) led to a structure
model with four partially occupied sites for Mg and 15
independent B positions. Two of the boron positions are
partially occupied as well. The thermal displacement
parameter of B1 is unusual high but is also observed in
most of the compounds of the b-rhombohedral B type [7].
For MgB17.4, this high value did not change with a free
occupation factor. The refinement with a shift (disorder) in
the x–y plane is possible with an isotropic thermal
displacement parameter. According to the difference
Fourier syntheses no additional boron atoms between the
boron polyhedra as they were observed in b-rhombohedral
boron [17] and some other related compounds [7] were
found in MgB17.4. We have measured data sets for six
crystals from different batches and refined the crystal
structures. Within the standard deviations Mg-occupations
were the same.
In this contribution, we report on the first crystal growth
of Mg containing b-rhombohedral boron by use of a Cu/
Mg melt. On the basis of single crystal data the crystal
structure was refined and some features were specified. The
sum of the occupation factors of 15 boron atoms and four
magnesium atoms revealed the composition MgB17.4
.
2. Synthesis
Single crystals of Mg containing b-rhombohedral boron
were synthesised from the elements in a Cu/Mg melt. Cu,
Mg and B (crystalline, ꢀ325 mesh, 99.7%, Alfa Aesar)
were mixed in a molar ratio of 12:4:3 and pressed to a pellet
(ca. 2 g). The pellet was put into an h-BN crucible and the
crucible into a tantalum ampoule, which was sealed by
welding with an electric arc. The ampoule was heated
under argon atmosphere up to 1600 1C held for 40 h,
cooled with 10 K/h to 800 1C and with 100 K/h to room
temperature. The ampoule was opened and the excess melt
was dissolved in conc. nitric acid. Single crystals of MgB17.4
were of dark brown colour and irregular shape with a size
of up to 0.5 mm. As by-products single crystal of MgB12
[13] and Mg3B50C8 [15] were found. The latter can be
explained by the carbon content of ‘‘elemental’’ boron.
Qualitative and quantitative analyses on selected single
crystals were done by EDX and WDX measurement.
Several single crystals were checked by EDX (Jeol, JSM
6400 with Ge detector, sample fixed with conducting glue
on a graphite platelet mounted on an aluminium sample
holder). It was confirmed that magnesium is the only heavy
element (Z410). By WDX (Jeol, JXA 8200) a more
Finally, R-values of R1ðFÞ ¼ 0:049 and wR2ðIÞ ¼ 0:122
were yielded for 890 reflections and 123 free variables. All
atoms were refined with anisotropic thermal displacement
parameters.
Details for the best refinement of a single crystal are
listed in Table 1. Coordinates and thermal displacement
parameters are given in Tables 2 and 3. Selected distances

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V. Adasch et al. / Journal of Solid State Chemistry 179 (2006) 2900–2907
2902
Table 1
Details of the crystal structure determination of MgB17.4
Table 2
2
˚
Coordinates, thermal displacement parameters (in [A ]) and site occupa-
tion factors
Crystal shape and colour
Crystal dimensions
Crystal system
Irregular polyhedron, dark brown
0.6 ꢂ 0.4 ꢂ 0.5 mm
Atom Site
x
y
z
Ueq
Occupation
Rhombohedral
R-3m
B1a
B2
3b 0a
6c
0
0
0.5
0.044(3)a
0.3849(2) 0.0238(11)
1
1
1
1
1
1
1
1
1
1
Space group
Lattice constants
0
˚
˚
a ¼ 10:992ð2Þ A, c ¼ 24:161ð4Þ A
B3
B4
18h 0.0541(2) 0.9459(2) 0.9434(1) 0.0234(6)
18h 0.0850(2) 0.9150(2) 0.0130(1) 0.0228(6)
18h 0.1080(2) 0.8920(2) 0.8887(1) 0.0241(7)
18h 0.1683(2) 0.8317(2) 0.0276(1) 0.0248(7)
18h 0.1301(2) 0.8699(2) 0.7674(1) 0.0242(7)
18h 0.1017(2) 0.8983(2) 0.6986(1) 0.0243(7)
18h 0.0580(2) 0.9420(2) 0.3279(1) 0.0257(7)
18h 0.0898(2) 0.9102(2) 0.3971(1) 0.0244(7)
˚
[rhomb. setting: a ¼ 10:139ð2Þ A,
a ¼ 65:29ð2Þ1]
B5
B6
3
˚
2527.5 A
Cell volume
No. of formula units
Composition in unit cell
Density calculated
Radiation
3
Mg17.55B305.6
2.557 g/cm3
B7
B8
B9
MoKa (IPDS II), graphite
monochromator
ꢁ15php15, ꢁ15pkp15, ꢁ32plp32
5–591
B10
B11
B12
B13
B14
B15
18h 0.0556(3) 0.9444(3) 0.5569(2) 0.0281(17) 0.639(18)
Range (hkl)
Range (2Y)
Temperature of measurement
Scan modus/measurement
Reflections measured
Unique reflections
Internal R-value
36i 0.1742(2) 0.1726(3) 0.1741(1) 0.0246(5)
36i 0.3183(2) 0.2929(2) 0.1281(1) 0.0242(5)
36i 0.2625(2) 0.2180(3) 0.4182(1) 0.0259(5)
1
1
1
21 1C
90 frames, 14 min with 21j increment
18,288
36i 0.2387(4) 0.2531(6) 0.3468(1) 0.0239(12) 0.92(2)
0.2342(1) 0.0230(7) 0.910(11)
Mg2 18h 0.1990(1) 0.8010(1) 0.1777(1) 0.0336(8) 0.533(7)
Mg1 6c
0
0
890 (555 with I42s)
0.1444 (s ¼ 0:0605)
0.21 mmꢁ1
Mg3 18f 0.2876(15) 0.3333 0.034(9)
Mg4 18h 0.2080(12) 0.7920(12) 0.4121(9) 0.049(8)
0.3333
0.072(12)
0.067(7)
Absorption coefficient
Absorption correction
Structure solution
Refinement
None
Direct methods/SHELXTL [18]
SHELXꢁTL [18]
aRefinement with disorder model: site 18g; x ¼ 0:0243ð12Þ;
Uiso ¼ 0:0150ð34Þ.
3
ꢁ
3
˚
˚
Residual electron density
+0.47 e /A , ꢁ0.36 e /A
ꢁ
3
˚
(s ¼ 0:07 e =A )
2
1=½s2ðF20Þ þ ð0:0850PÞ þ 0:00Pꢃ with
Weighting function
P ¼ ðF20 þ 2F2c Þ=3
123
composition is given as MgB19.6. Although synchrotron
data were used, no anisotropic refinement could be done,
the values of the thermal parameters differ by a factor of
2.6, and the standard deviations of the atom positions are
not completely consistent. The occupation factors were not
refined as free parameters, but determined according to a
trial and error strategy for assumed positions [14].
The samples investigated by Soga and coworkers [10]
contained varying amounts of silicon because of the
method of preparation. While the a lattice constant is
Number of parameters
R-values
R1ðFÞ ¼ 0:049, wR2ðIÞ ¼ 0:122
are shown in Tables 4–6. Further details on the structure
refinement (complete list of distances and angles, Fo/Fc-list)
may be obtained from: Fachinformationszentrum Karls-
ruhe, D-76344 Eggenstein-Leopoldshafen (Germany) (fax:
+49 724 808 666: e-mail: crysdata@fiz-karlsruhe.de) on
quoting the registry number CSD-416332.
˚
nearly the same (a ¼ 10:9880ð8Þ A), the c lattice constant
˚
with a value of 24.084(2) A is distinctly smaller and
Compared to other single crystals of boron-rich borides
and boridecarbides obtained from molten metals the
quality of MgB17.4 single crystals is remarkably lower.
Therefore we assume the single crystals were formed by
diffusion of Mg into the b-rhombohedral boron crystals.
Furthermore, the ‘‘interstitial’’ boron atoms (B16, site 18h,
x ¼ 0:0546, z ¼ 0:1176, occupation 27% [17]) of b-rhom-
bohedral boron, which are needed for electronic reasons in
the structure of elemental boron cannot be detected in the
crystal structure of MgB17.4, so the exchange of these
boron atoms has to be assumed as well.
according to the work of Soga et al. [10] correlated to the
lower Mg content (MgSi0.06B23.7). The lower Mg content
results from a smaller occupation factor on the E-site and
the empty position of Mg4. The occupation factors of all
atoms were refined, but no positional parameters and
thermal displacement parameters are given. In a very
recent contribution, the same group presented results on
powder samples without silicon and a higher Mg content
after an improvement of the synthesis [20].
4. Results and discussion
Similar observations were made for Li containing b-
rhombohedral boron, LiB10. On single crystal growth and
structure refinement of LiB10 we will report elsewhere [19].
Our results obtained from single crystal investigations
confirm and improve the data published by Brutti et al. [9]
and by Soga et al. [10] but reveal also some new
observations. The lattice constants in [9] are slightly
The crystal structure of MgB17.4 is closely related to b-
rhombohedral B. It contains B12-icosahedra and B28-units
in a ratio of 2:1. The B28-unit can be constructed by
connecting three icosahedra via common triangle planes.
The unit cell with a rhombohedral setting is shown in
Fig. 1. Four B12 icosahedra in a ratio of 1:3 occupy the
corners (icosahedron 1; B3, B4) and the middle of the
˚
˚
smaller (a ¼ 10:9830ð4Þ A, c ¼ 24:1561ð15Þ A) and the

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V. Adasch et al. / Journal of Solid State Chemistry 179 (2006) 2900–2907
2903
Table 3
Anisotropic thermal displacement parameters (A )
2
˚
Atom
U11
U22
U33
U23
U13
U12
B1
B2
0.060(4)
0.060(4)
0.013(4)
0.023(3)
0
0
0.030(2)
0.0240(15)
0.0232(10)
0.0239(10)
0.0237(10)
0.0252(11)
0.0243(10)
0.0252(11)
0.0252(11)
0.0255(11)
0.033(2)
0.0240(15)
0.0232(10)
0.0239(10)
0.0237(10)
0.0252(11)
0.0243(10)
0.0252(11)
0.0252(11)
0.0255(11)
0.033(2)
0
0
0.0120(8)
0.0105(12)
0.0125(12)
0.0113(12)
0.0116(12)
0.0111(12)
0.0133(12)
0.0131(13)
0.0143(12)
0.019(2)
B3
B4
0.0223(15)
0.0214(14)
0.0240(16)
0.0227(14)
0.0224(14)
0.0235(16)
0.0272(17)
0.0242(15)
0.022(3)
0.0004(6)
ꢁ0.0006(6)
0.0016(6)
ꢁ0.0002(6)
0.0000(6)
0.0010(6)
ꢁ0.0003(6)
ꢁ0.0003(6)
ꢁ0.0016(10)
ꢁ0.0001(8)
ꢁ0.0010(8)
0.0002(8)
ꢁ0.0001(13)
0
ꢁ0.0004(6)
0.0006(6)
ꢁ0.0016(6)
0.0002(6)
ꢁ0.0000(6)
ꢁ0.0010(6)
0.0003(6)
0.0003(6)
0.0016(10)
0.0009(8)
ꢁ0.0002(8)
ꢁ0.0004(9)
0.0003(11)
0
B5
B6
B7
B8
B9
B10
B11
B12
B13
B14
B15
Mg1
Mg2
Mg3
Mg4
0.0243(10)
0.0240(11)
0.0262(11)
0.0259(16)
0.0240(8)
0.0341(10)
0.031(9)
0.0256(10)
0.0230(10)
0.0249(10)
0.023(2)
0.0232(11)
0.0245(11)
0.0276(11)
0.0239(15)
0.0212(11)
0.0306(12)
0.044(11)
0.044(13)
0.0119(8)
0.0108(8)
0.0136(9)
0.0131(17)
0.0120(4)
0.0156(10)
0.012(11)
0.024(11)
0.0240(8)
0.0341(10)
0.024(20)
0.050(11)
0.0046(5)
0.013(11)
0.002(5)
ꢁ0.0046(5)
0.007(5)
ꢁ0.002(5)
0.050(11)
Table 4
B–B distances (A), exohedral distances in italics, icosahedron 1: B3, B4;
Table 5
Mg–B distances (A) in MgB17.4
˚
˚
icosahedron 2: B5, B7, B12, B13; B28-unit: B2, B6, B8, B9, B10, B11, B14,
B15
Mg1–B12 (6x) 2.396(3)
Mg1–B7 (3x) 2.477(3)
Mg1–B9 (3x) 2.518(4)
Mg3–B15 (2x) 0.835(6) Mg4–B9 2.19(2)
Mg3–B6 (2x) 2.224(10) Mg4–B10 2.28(2)
B1–B11 (6x)
B2–B10 (3x)
B2–B11 (3x)
B2–B9 (3x)
B3–B5
1.736(6)a B8–B7
1.749(5) B13–B14 1.757(3)
Mg3–B14 (2x) 2.352(4)
Mg3–B8 (2x) 2.361(3)
Mg3–B9 (2x) 2.462(9)
Mg3–B10 (2x) 2.506(9)
Mg4–B12 2.29(2)
(2x)
1.735(3)
1.759(7)
1.767(6)
B8–B9 (2x)
B8–B15 (2x)
B8–B6
1.800(3)
1.864(4)
1.875(5)
1.767(6)
1.779(5)
1.800(3)
1.851(5)
1.914(6)
1.735(3)
1.779(5)
B13–B5
B13–B7
1.810(3)
1.817(3)
Mg1–B8 (2x) 2.527(4)
Mg4–B8 2.471(17)
(2x)
B13–B12 1.844(3)
B13–B13 1.886(5)
B13–B12 1.896(3)
B14–B13 1.757(3)
1.673(5) B9–B2
Mg2–B11
Mg2–B12 (2x) 2.355(3)
Mg2–B10 2.377(4)
2.221(6)
Mg4–B7 2.490(11)
(2x)
B3–B4 (2x)
B3–B4
1.767(4)
1.781(5)
1.783(6)
1.624(5
1.735(4)
1.767(3)
1.781(5)
1.673(5)
1.810(3)
1.829(4)
1.831(5)
B9–B10
B9–B8 (2x)
B9–B15 (2x)
B9–B9 (2x)
B10–B2
Mg4–B13 2.506(12)
(2x)
B3–B3 (2x)
B4–B6
B14–B6
1.800(4)
B14–B10 1.800(3)
B14–B15 1.815(5)
B14–B11 1.829(6)
B14–B14 1.907(5)
B15–B15 1.659(12)
Mg3–B15 (2x) 2.693(16) Mg4–B14 2.534(18)
(2x)
B4–B4 (2x)
B4–B3 (2x)
B4–B3
B10–B9
Mg2–B13 (4x) 2.397(3)
Mg3–B4 (2x) 2.897(16) Mg4–B15 2.546(19)
(4x)
B10–B14 (2x) 1.800(3)
B10–B11 (2x) 1.863(4)
B10–B15 (2x) 1.867(5)
B5–B3
Mg2–B14 (4x) 2.438(2)
Mg2–B11 (2x) 2.486(3)
B5–B13 (2x)
B5–B12 (2x)
B5–B7
B15–B6
1.742(4)
B11–B1
1.736(6) B15–B14 1.815(5)
1.759(7)
Mg2–B1
2.571(2)
B11–B2
B15–B9
B15–B8
B15–B10 1.867(5)
1.851(5)
1.864(4)
B6–B4
1.624(5) B11–B14 (2x) 1.829(5)
B6–B15 (2x)
B6–B14 (2x)
B6–B8
1.743(4)
1.800(4)
1.875(5)
B11–B11 (2x) 1.835(9)
B11–B10 (2x) 1.863(4)
B12–B5
1.829(4)
1.844(3)
1.878(5)
1.883(4)
1.896(3)
1.933(5)
B7–B8
1.749(5) B12–B13
B7–B13 (2x)
B7–B5
B7–B12 (2x)
1.817(3)
1.831(5)
1.883(4)
B12–B12
B12–B7
Table 6
Mg–Mg distances (A) and occupation factors in MgB17.4
B12–B13
B12–B12
˚
aRefinement with disorder (see above): B1–B11: 1.610(8) (2x), 1.756(6)
(2x), 1.900(10) (2x), B1?B1: 0.534(27).
Distance
Occupation
Mg1–Mg4 (3x)
Mg2–Mg2 (2x)
Mg2–Mg4
2.44(2)
2.611(3)
2.33(2)
2.66(3)
2.45(2)
2.44(2)
2.33(2)
2.45(2)
0.910(11)/0.067(7)
0.533(7)/0.533(7)
0.533(7)/0.067(7)
0.072(12)/0.072(12)
0.072(12)/0.067(7)
0.067(7)/0.910(11)
0.067(7)/0.533(7)
0.067(7)/0.072(12)
Mg3–Mg3
Mg2–Mg4 (2x)
Mg4–Mg1
Mg2–Mg2
vertices of the unit cell (icosahedron 2; B5, B7, B12, B13).
Two B28-units are placed on the main body diagonal and
connected by a single boron atom (B1). The Mg atoms are
in voids between the boron polyhedra.
Mg2–Mg3 (2x)

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for boron-rich borides. Furthermore, the coordination of
B1 changes to a situation as it is found for other boron-rich
borides with additional exohedral boron atoms like MgB12
[13] and a-AlB12 [22]. Although this model is quite
plausible the refinement with anisotropic thermal para-
meters led to large standard deviations for the site
parameter x and the Uij-values. Therefore, a clear decision
for MgB17.4 is not possible on the basis of our data.
˚
The boron–boron distances up to 2.0 A are listed in
Table 4. It is well known for boron-rich borides that B–B
distances within the polyhedra are in general longer than in
between but there are significant differences for the
different polyhedra. The endohedral B–B distances in
˚
˚
icosahedron 1 are between 1.735 and 1.783 A (+: 1.764 A).
In icosahedron 2 they are significantly longer with values
˚
˚
between 1.810 and 1.896 A (+: 1.857 A). The same
tendency is found for the exohedral bonds. For icosahe-
˚
dron 1 they range from 1.624 A (to the B28-unit) up to
˚
1.673 A (to icosahedron 2). The values for icosahedron 2
˚
cover a larger range from 1.673 A (to icosahedron 1) and
˚
1.749/1.757 A (to the B28-unit) to 1.933 A (to icosahedron
˚
˚
2) (+: 1.800 A). The endohedral B–B distances of the B28-
˚
˚
unit are between 1.735 and 1.914 A (+: 1.824 A), the
˚
exohedral distances between 1.624 and 1.757 A (+:
˚
1.706 A). According to these values the polyhedra show a
different ‘‘volume’’ in the order icosahedron 1oB28-
unitoicosahedron 2. This may be explained by different
effective charges for the polyhedra. The ‘‘isolated’’ boron
atom (B1) connects two B28-units via bonds to B11
Fig. 1. Unit cell of MgB17.4 (rhombohedral setting).
˚
(1.736 A). Because the position of B11 is only partially
The coordination of the boron atoms reflects the
bonding mode of the boron polyhedra. All boron atoms
which form the icosahedra have one short exohedral bond
and five longer endohedral bonds. The same pattern (one
short exohedral and five long endohedral bonds) is found
for those B atoms of the B28-unit (B6, B8, B14, B15) which
form the 12 half-icosahedra of the B84-units (see below).
The remaining boron atoms of the B28-unit (B2, B9, B10,
B11) have no exohedral bonds to other boron polyhedra.
B2 belongs to all of the three icosahedra and has nine
neighbours (or eight, respectively, if the 2/3 occupation of
B11 is considered). B9 and B10 with eight boron
neighbours are part of the common triangles and belong
to two icosahedra. The shorter distances of B10 may result
from the lower coordination number because of the B11
deficit. B11 has eight (or seven) endohedral bonds, five
within the icosahedron, two (or one) to a B11 atom of the
icosahedron condensed at it and one to the connecting B1
atom. The bonds of B1 are a special case. With a full
occupation of B11 the coordination would be an elongated
trigonal antiprism, but the 2/3 occupation results in a
fourfold coordination which might be described as a more
or less distorted tetrahedron and is obviously correlated
with the ‘‘suspicious’’ thermal displacement parameter of
B1. The refinement with a disorder model in x-direction
occupied (about 2/3), the effective coordination of B1 is
reduced from 6 to 4. If the partial occupation of B15 is
taken into consideration, too, the real composition of the
B28-unit is about B26.5
.
The surroundings of Mg are shown in Fig. 2. Coordina-
tion numbers between 12 and 16 are found. Mg–B
˚
distances range from 2.19 to 2.90 A (Table 5) as it is
known for other boron-rich borides [MgB7, MgB12] and
boridecarbides (MgB12C2, Mg2B24C, [15]). The only
˚
exception is the short distance Mg3–B15 (0.84 A), but the
site of B15 is only partially occupied and the deficit
corresponds to the occupation factor of Mg3. This
observation was also reported in earlier investigations
[9,10] and is confirmed by our results. The shortest Mg–Mg
˚
distances are between 2.33 and 2.66 A but they are
combined with the occupation factors in a way that a
sum of 1 is not significantly exceeded (Table 6).
There are several ways for the description of the 3D
structure of b-rhombohedral boron. Callmer [21] used a
cubic closest packing of B84-units and B10-units in trigonal
voids. The B84-units are formed by a central B12
icosahedron (icosahedron 1) and 12 half-icosahedra
(six from icosahedron 2, six from the B28-units):
B84 ¼ B12(B6)12. The B10-fragment is the ‘‘rest’’ of the
B28-units. The deviation of the rhombohedral angle of a ¼
65:21 from 601 represents the distortion of the cubic closest
packing (Table 7). A second way of description shows the
˚
(site 18g) results in a shift of 0.267(13) A. The initially large
value for Ueq is reduced to a value of Uiso as it is common

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2905
similarity to MgB12 [13a], a-AlB12 and g-AlB12 [22].
According to this a 3.6.3.6.-net (Kagome-net) is formed
MgB17.4 shows the highest metal content ever found,
except the Li compound LiB10 [19]/LiB [8]. This high
´
ꢀ13
by icosahedra 2 (Fig. 3). The nets are stacked in a sequence
ABC in direction (001) of the unit cell (hexagonal setting).
The orientation of the nets is in a way that in c-direction
metal content originates mainly from the high occupation
factor for the D site (53%) with a multiplicity of 18, but
also the nearly full occupation of the E site (91%) makes a
considerable contribution. The closest similarity is found to
ScB28 [23]. This is easy to understand because Mg and Sc
have nearly the same atomic radii and are both very
electropositive metals. The main difference is the charge of
the cation leading to the corresponding compositions. In
ScB28 scandium occupies three sites (site D: 31.4(3)%; site
E: 72.7(5)%; site F: 5.7(3)%), the position of Mg4 remains
empty. Furthermore the same partial occupation of boron
sites was observed (61.3(4)% and 92.5(10)%). Also, the
structure of ZnB25 is related [24]. In ZnB25 nearly the same
positions are occupied as in ScB28 (site D: 28(1)%; site E:
34(1)%; site G 13(1)%, very close to site F), additionally
the A1-site (6c; 0,0,0.136) is occupied with 49(1)%.
two triangles of the Kagome-net (rotated by 1801) and a
´
hexagon are alternating. Icosahedron 1 is placed between
the two triangles and connects the nets. The B28-units are
located in the voids above and below the hexagons and are
connected by the B1 atom. Icosahedron 1 and the B28-unit
´
form layers (Fig. 4) that are placed between the Kagome-
nets. Fig. 5 shows the rhombohedral unit cell as a fragment
of the layers with the hexagon in the middle, above and
below the B28-units and two other triangles of the Kagome
´
-
net, connected by the icosahedra 1.
In MgB12 there are also 3.6.3.6.-nets of icosahedra which
are connected by the second kind of icosahedra, but the
stacking sequence is ABAB and the B28-units are replaced
by B21-units. In g-AlB12 there is the same arrangement of
boron polyhedra as in MgB12, but instead of B21-units
there are two different types of B20-units leading to a
symmetry reduction and a different electron demand.
A comparison to other binary boron-rich borides
derived from b-rhombohedral boron [7] reveals that
´
Fig. 3. 3.6.3.6.-nets (Kagome-nets) of icosahedra 2: (a) sequence ABCA,
view in a–b plane, (b) sequence ABC as projection along (001).
Fig. 2. Coordinations of Mg atoms in MgB17.4
.
Table 7
Comparison of structure models and occupation factors (%) for MgB17.4
B15
B11
Mg1
Mg2
Mg3
Mg4
Si (A1)
Composition
Brutti et al.
Soga et al.
This work
92
92(1)
92(2)
59
67(1)
64(2)
88
68(1)
91(1)
49
44.2(4)
53.3(2)
8
—
—
—
11.9(5)
—
Mg5.18B101.6
Mg4.3Si0.24B102.1
Mg5.85B101.9
MgB19.6
MgSi0.06B23.7
MgB17.4
4.8(7)
7.2(12)
6.7(7)
Atom numbers referred in Table 2.

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2906
˚
in this range are known (for example 2.117 A in Mg2B24C
[15]), it seems to be more favourable to occupy another
position, i.e. the site of Mg4, if a higher metal content is
realised. To increase the occupation of Mg2 or Mg3 may be
impossible because of the necessity of additional defects in
the boron polyhedra (B11/Mg3) or short Mg–Mg contacts
(Mg2). The latter may be important because it was
predicted, that the occurrence of superconductivity is
correlated to the occupation of the D site [10]. A second
interesting point is the extent of Mg-doping in MgB17.4. It
is generally acknowledged, that the intrinsic acceptor level
of b-rhombohedral boron can take up 8 electrons [10] and
the incorporation of metal atoms takes place to fill up these
levels. Up to now all compounds of the b-rhombohedral
boron type are semiconductors. The Mg-content of 5.85
atoms corresponds to 11.7 electrons, the highest value ever
found for a compound of the b-rhombohedral boron type.
Because band structure calculations are still in progress, a
rough estimation can be made by the Wade rules [25],
which can also be applied to solid state compounds [26]. It
is well known that a nido-cluster needs two electrons more
than a closo-cluster with the same number of atoms.
Therefore a missing boron atom in an icosahedron
increases the uptake of electrons. This may explain the
deficit for B11 and especially B15, which was only observed
for MgB17.4, ScB28 and LiB10. Also in the case of ScB28 the
metal atoms can transfer 11 electrons to the boron
polyhedra, significantly more than the expected 8 electrons.
Similar observations were made for LiB10 [19].
Fig. 4. Layers of icosahedra 1 and B10-fragments of the B28-units.
5. Conclusions
The use of a mixture of Mg and Cu as a solvent enables
the formation of single crystals of Mg containing b-
rhombohedral boron. The crystal structure determination
is based on single crystal data and reveals the composition
MgB17.4, as determined from the sum of the occupation
factors and confirmed by WDX measurements. The
evaluation of the difference Fourier map reveals that Mg
atoms partially occupy four different positions. One of
them was observed for the first time for a compound
related to b-rhombohedral boron and not detected in the
earlier investigations on powder samples. Two of the boron
positions have partial occupation factors as well.
According to preliminary results the single crystalline
samples are also non superconducting as it was already
observed for the powder samples.
Fig. 5. Rhombohedral unit cell of MgB17.4 as a part of the layers, Mg
atoms omitted (see text).
On the first sight the structure of MgB17.4 just seems to
extend the series of binary borides related to b-rhombohe-
dral boron, but a closer view shows several details, which
improve the understanding of this class of compounds.
Together with ScB28 it is the only compound without
occupation of the A1 site. Obviously Mg2+ is too big for
this site. A virtual occupation would lead to Mg–B
Acknowledgments
Thanks are due to the Bayerisches Geo-Institut (BGI,
Universitat Bayreuth) for the access to WDX measure-
¨
ments and to Detlev KrauXe for his support.
This work was supported by the programme ‘‘Neue
Werkstoffe in Bayern’’, project B21092.
˚
distances of about 2.12–2.14 A. Although Mg–B distances

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2907
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