Planar B4 rhomboids: The rare earth boride halides RE4X5B4

Article abstract of DOI:10.1021/jp971500q

The new compounds RE₄X₅B₄ (RE = La, Ce, Pr, Gd and X = Br, I) and RE₄I₅B₂C (RE = La, Ce) are prepared via the reaction of RE metal, REX₃ and B, or B and C at temperatures 1670 ≥ T ≥ 1270 K in welded tantalum ampoules. Chains of interconnected B₄ rhomboids are the characteristic features of the crystal structures. According to band structure calculations, the compounds are one-dimensional metals which undergo a gradual metal-to-semiconductor transition at low temperature as experimentally indicated by the steep inrease of electrical resistivity.

Full text of DOI:10.1021/jp971500q

J. Phys. Chem. B 1997, 101, 9951-9957
9951
†
Planar B4 Rhomboids: The Rare Earth Boride Halides RE4X5B4
Hj. Mattausch,*,‡ A. Simon, and C. Felser
Max-Planck-Institut fu¨r Festko¨rperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
ReceiVed: May 2, 1997; In Final Form: June 30, 1997X
The new compounds RE4X5B4 (RE ) La, Ce, Pr, Gd and X ) Br, I) and RE4I5B2C (RE ) La, Ce) are
prepared via the reaction of RE metal, REX3 and B, or B and C at temperatures 1670 g T g 1270 K in
welded tantalum ampoules. Chains of interconnected B4 rhomboids are the characteristic features of the
crystal structures. According to band structure calculations, the compounds are one-dimensional metals which
undergo a gradual metal-to-semiconductor transition at low temperature as experimentally indicated by the
steep inrease of electrical resistivity.
Introduction
Rare earth metals exhibit a rich chemistry of borides as
indicated by the general compositions REB2, RE2 B5, REB4,
1,2
REB6, REB12, and REB
.
The structures are characterized
≈66
by extended B-B bonding.
When the REBx frameworks are fragmented as it is done in
boride halides, interconnections between the B atoms are
frequently lost, and one-dimensional, molecular or atomic boron
entities result. The kind of entity is determined by a number
of factors, e.g., size of the voids available and the number of
electrons provided for B-B bonding by the RE-X framework,
as well as by competition between RE-RE, B-B, and RE-B
bonding, respectively. In the case of a sufficient surplus of
metal valence electrons, the boride halides closely mimic the
corresponding carbide halides as indicated by the existence of
the isotypic pairs Gd3Cl3C/Gd3Cl3B,3 Gd4I5C/Gd4I5B,4 or Sc7-
Cl12C/Sc7Cl12B5 which represent examples with three- and one-
dimensionally condensed as well as discrete RE6 octahedra,
respectively, centered by interstitial B and C atoms. At reduced
metal valence electron concentrations (VEC/C2 e 8), the C2
unit is the typical carbon species in rare earth carbide halides.
In the case of mixed carbide boride halides, B-C bonding is
frequently observed,6 e.g., with the quasi molecular BC27- anion,
which is isoelectronic with SO2.7
Figure 1. Projection of the structure of La4I5B4 along [010]. The La
bispenoids around the B4 rhomboids are outlined (I, La, and B atoms
with decreasing size).
Figure 2. Projection of the structure of La4Br5B4 along [010]. The La
bispenoids around the B4 rhomboids are outlined (Br, La, and B atoms
with decreasing size).
Here we report on boride halides and boride carbide halides
with extended B-B bonding. The boride carbide halides
RE4I5B2C exhibit an unusual structural separation of boron and
carbon.
Results and Discussion
Projections of the crystal structures of La4I5B4 and La4Br5B4
are shown in Figures 1 and 2, respectively. The structure of
La4I5B2C is depicted in Figure 3. All iodides RE4I5B4, as well
as Pr4Br5B4, take the La4I5B4 structure. Ce4Br5B4 and Ce4I5B2C
are isotypic with the corresponding La compounds.
The common motif in all three structures is the hitherto
unknown linear chain of interconnected B4 rhomboids embedded
in channels of metal atoms, which are formed from RE
octahedra. The channels are topologically related to those in
the structure of Gd4I5B4. As Figures 4a,b illustrate, the
replacement of a single B atom in the center of the octahedron
Figure 3. Projection of the structure of La4I5B2C along [010]. The La
bispenoids around the B4 rhomboids and the La octahedra around the
C2 pairs are outlined (I, La, B, and C atoms with decreasing size).
by a B4 rhomboid essentially leads to an elongation of the shared
octahedron edges from dGd-Gd ) 381 to 472 pm, which is
reflected in a characteristic change of the unit cell. Whereas
the a and b axes are slightly different for Gd4I5B4 (Gd4I5B), a
) 1850.8 (1872.5) and b ) 426.0 (406.7) pm, the c axes differ
significantly, c ) 975.1 (861.4) pm. The arrangement of the
RE atoms around the B4 rhomboids rather corresponds to
† Dedicated to Prof. Sir John Meurig Thomas on the occasion on his
65th birthday.
‡ Fax: International code + (711) 689-1642. E-mail: hansm@vaxff2.mpi-
stuttgart.mpg.de.
X Abstract published in AdVance ACS Abstracts, November 1, 1997.
S1089-5647(97)01500-9 CCC: $14.00 © 1997 American Chemical Society

9952 J. Phys. Chem. B, Vol. 101, No. 48, 1997
Mattausch et al.
Figure 4. Characteristic building units in the RE boride-
(carbide)-halides: chains of (a) RE6 B octahedra, (b) RE6B4 octahedra
(or rather bispenoids), and (c) RE6C2 octahedra.
Figure 5. Distances and angles in and between the B4 rhomboids in
RE4X5B4 and La4I5B2C.
Figure 6. Electrical resistivity as a function of temperature of La4I5B4,
Ce4I5B4, and La4I5B2C (crosses, heating curve, triangles, cooling curve).
channels of edge sharing bisphenoids. La4I5B4 and La4Br5B4
contain only such chains in a parallel arrangement, whereas in
the structure of La4I5B2C these chains alternate layerwise with
chains of C2-centered RE octahedra as shown in Figure 4c. The
one-dimensional RE-B and RE-C substructures are surrounded
by halogen atoms. Assigning the X atoms above edges and
apices of the RE polyhedra as Xi and Xa, respectively, the
planar B4 fragment according to electron spin resonance
measurements.15 The B4 fragment looks very similar in all
investigated compounds, RE4X5B4 and La4I5B2C, respectively.
The edge length is approximately 170 pm, and the distances
across the rhomboid are 200 and 270 pm, respectively. The
B4 units are connected via short distances dB-B ) 160 pm to
form linear chains.
interconnection patterns of the structures can be rationalized
The B-B distances can be analysed in terms of Pauling bond
orders (PBOs), taking d ) d(1) - 60 log n with the single bond
i-a
according to Scha¨fer and Schnering:8 La4I5B4:La4Ii2Ii-i
I
2/2
2/2
Ia-i2/2B4,
La4Br5B4:La4Bri1Bri-i3/2Bri-a3/2Bra-i2/2B4
and
3
distance d(1) ) 159 pm from the Σg ground state of the B2
i-a
a-i
La4I5B2CtLa4I5B4‚La4I5C2:La4Ii2Ii-i
I
I
2/2‚La4-
molecule.16 The distances dB-B ) 160 and 170 pm correspond
to PBOs n ≈ 1 and n ≈ 0.65. The B atoms involved in the
single bond are left with a “valency” of 0.7 for B-RE bonding,
the others with approximately 1.7. It is interesting to note that
the B atoms, which interconnect the B4 rhomboids, have the
same bonding capability to their metal atom environment as do
the atoms in the B6 octahedron in the structure of Gd2B5.17
According to these rather hand waving arguments, two electrons
are involved in the bonding between B4 rhomboids and
approximately five for bonding in the individual B4 units.
The odd number of electrons in the B4 unit, which is closely
linked to adjacent ones, would suggest the phases to be one-
dimensional metals. At low temperatures, electronic localization
due to a Peierls transition is expected.
Figure 6 shows the results of resistivity measurements for
selected samples. One has to be very cautious not to
overinterpret measurements on pressed powder pellets, particu-
larly in the case of one-dimensional metals because grain
boundary effects may overshadow all intrinsic properties.
However, the experimental results seem to corroborate the above
assumption. The examples exhibit good conductivity at room
temperature, and below approximately 50 K a step increase of
the resistivity indicates a gradual transition to insulating
2/2
2/2
Ii2Ii-i
I
2/2
I
.
2/2
i-a
a-i
2/2
The shortest B-X distances range for example from 380 to
400 pm (La4Br5B4) and from 390 to 400 pm (Gd4Br5B4),
respectively.
The compound La4I5B2C is a most unusual intergrowth phase
of La4I5B4 and La4I5C2,9 (which are both known as dicrete
compounds. Instead of B-C bonding as it normally occurs in
boride carbides10,11 and boride carbide halides7 of the rare earth
metals the elements, B and C are structurally separated in
La4I5B2C. The distance dC-C ) 130.5 pm is in the range of
4-
what is found for C2 ions, although with quite a large
uncertainty of the experimental value. The same uncertainty
holds for the B-B distances; however, the boron substructure
occurs rather identical even with respect to geometrical details
in all of the investigated crystal structures. Distances and angles
for the 1 B4 chains in different compounds are compared in
∞
Figure 5.
The B4 rhomboid is hitherto unknown in molecules and solids.
In B4Cl4, distorted tetrahedra (dB-B ) 173 and 170 pm) occur.12
B4H10 has the arachno-type butterfly arrangement (dB-B ) 171
pm).13,14 The topology of the neutral B4(t-Bu)4 is unknown,
-
and it is only the radical ion B4(t-Bu)4 which might have a

Planar B4 Rhomboids
J. Phys. Chem. B, Vol. 101, No. 48, 1997 9953
Figure 7. Reciprocal molar magnetic susceptibility of Ce4I5B4 as a
function of temperature at a magnetic field of 1 T. The inset shows the
low-temperature part of the molar susceptibility with antiferromagnetic
ordering at ≈3.5 K.
Figure 10. The MO diagram (without s-p mixing) of the idealized
square planar B4 unit together with the corresponding integrated LMTO-
3
electron density. (a) The a1g orbital and the electron density (0.2 e/ao )
well localized within the B4 unit. (b) The MO and the electron density
(0.2 e/ao3) between two different B4 units (B(1)-B(1)). (c) The eu orbital
3
and the electron density (0.2 e/ao ) distributed both between neighboring
B4 units as well as in the periphery of one unit. (d) The a2u, b2g, b1g,
and a1g MO’s contributing to the bands above -5.5 eV (compare Figure
9 (right)). (e) The eg MO (HOMO) and an additional MO below EF.
3
The electron density (0.2 e/ao ) has lone-pair character at B(2) and B(3),
also the π interaction between B(1) and B(1) is very weak.
Figure 8. Comparison of the electrical resistivity as a function of
temperature of Gd4I5B and Gd4I5B4.
Figure 9. Left: The calculated total DOS of La4Br5B4. The Fermi
level EF is the zero energy. Right: The band structure of La4Br5B4
from -12 to 2 eV around the Fermi level.
behavior. Such smooth transition is well known from other
compounds, e.g., MMo3X3 (M ) Rb, Cs; X ) Se, Te)18 which
is a one-dimensional metal at room temperature.
La4Br5B4 is essentially nonmagnetic. The measured sample
1
contains a magnetic impurity of less than 0.1% of a spin /2
system. The magnetic properties of Ce4I5B4 (Figure 7) show
the cerium to be in the oxidation state +3 as expected (µeff
)
2.4µB; expected value 2.5µB). The compound orders antifer-
romagnetically at 3 K.
It is interesting to note the dramatic differences between the
corresponding physical properties of Gd4I5B, whose structure
is characterized by single B atoms, Gd-Gd bonding, and short
Gd-Gd distance, respectively, and Gd4I5B4 with no Gd-Gd
3
Figure 11. The isosurface of the total electron density (0.6 e/ao )
calculated within the concept of ELF. High localization: white; low
localization, blue.

9954 J. Phys. Chem. B, Vol. 101, No. 48, 1997
Mattausch et al.
TABLE 1: Preparation of the Compounds RE4X5B4
ordering indicates the enhancement of magnetic interaction due
to metal-metal bonding along the short octahedron edge. The
results for Gd4I5B are important to understand the bonding in
the boride carbide halide La4I5B2CtLa4I5B4‚La4I5C2 in terms
of B-B, C-C, and La-La bondings occuring simultaneously.
All relevant interatomic distances in the La4I5B4 part of La4I5B4‚
La4I5C2 are essentially the same as in the compound La4I5B4
itself. Hence, no significant charge transfer is expected to occur
between the boron and the carbon containing substructures. The
C-C distance of 130 pm closely corresponds to that of a double
bond, and the La4I5C2 substructure has to be formulated as
(La3+4I-5C24-‚3e-). Obviously, the excess of the metal valence
electrons populates metal-metal bonding band states as in the
case of Ce4I5B as well as in the compound La4I5C29 where the
La-La bonding states lie well below the Fermi level. In fact,
the bonding is closely related to that in the prototype of all
reacn temp time
compound
educts
(K)
(d)
product
La4I5B4
Ce4I5B4
Pr4I5B4
Nd4I5B4
Gd4I5B4
La4Br5B4 5LaBr3, 7La, 12B
Ce4Br5B4 5CeBr3, 7Ce, 12B
Pr4Br5B4 5PrBr3, 7Pr, 12B
La4I5B2C 1La4I5C2, 1La4I5B4
Ce4I5B2C 5CeI3, 7Ce, 6B, 3C
5LaI3, 7La, 12B
5CeI3, 7Ce, 12B
5PrI3, 7Pr, 12B
5NdI3, 7Nd, 12B
5GdI3, 7Gd, 12B
1370
1340
1420
1320
1420
1450
1420
1270
1670
1460
10 La4I5B4 (100%)
5
6
5
5
7
5
5
1
Ce4I5B4 (100%)
Pr4I5B4 (90%)
Nd4I5B4 (100%)
Gd4I5B4 (80%)
La4Br5B4 (100%)
Ce4Br5B4 (100%)
Pr4Br5B4 (50%)
La4I5B2C (90%)
10 Ce4I5B2C (80%)
TABLE 2: Lattice Constants of the Compounds RE4X5B4
compound
a (pm)
b (pm)
c (pm)
â(deg)
La4I5B4
Ce4I5B4
Pr4I5B4
Nd4I5B4
Gd4I5B4
La4Br5B4
Ce4Br5B4
Pr4Br5B4
La4I5B2C
Ce4I5B2C
1924.2(4)
1903.3(2)
1889.6(4)
1883.1(3)
1850.8(3)
1825.6(1)
1806.2(4)
1790.7(2)
2330.3(9)
2319.4(5)
434.6(1)
432.4(2)
431.4(1)
429.97(4)
426.04(6)
429.4(3)
428.3(1)
427.3(2)
429.9(1)
429.0(1)
1027.6(1)
1013.5(2)
1003.9(2)
997.8(1)
108.21(1)
107.77(1)
107.39(2)
107.18(2)
106.38(2)
118.07(2)
118.48(2)
111.87(1)
126.22(2)
126.50(1)
metal-metal-bonded rare earth compounds, Gd2Cl3
)
Gd3+2Cl-3‚3e-,19-21 which is also a semiconductor.22-24
975.1(2)
The results of band structure calculations on La4Br5B4 are in
agreement with the qualitative arguments on chemical bonding
in this compound and with the measured electrical properties.
Figure 9 shows the total density of states (DOS), together with
the band dispersions. All bands are at least 2-fold degenerate
because of the presence of two formula units in the primitive
cell. Below -5 eV, only s and p states of boron contribute to
the DOS. Between -5 and -2 eV, bands with mainly Br p
and B p, mixed with La d character, occur, and around the Fermi
1925.3(7)
1918.3(5)
960.0(1)
1899.1(4)
1882.2(4)
bonding or long Gd-Gd distance, respectively. The resistivity
of Gd4I5B is much lower than that of Gd4I5B4 (Figure 8), and
the discontinuity at approximately 60K due to antiferromagnetic
TABLE 3: Crystal Data, Data Collection, and Structure Determination
empirical formula La4Br5B4 La4I5B4
formula weight 998.43 [amu] 1233.38 [amu]
Gd4I5B4
1306.74 [amu]
La4I5B2C
1223.77 [amu]
temperature
crystal system
space group
293 K
monoclinic
293 K (143 K)
monoclinic
293 K
monoclinic
293 K
monoclinic
C2/m-C32h (No.12)
a ) 1825.59(12),
b ) 429.42(3),
C2/m-C32h (No.12)
a ) 1924.6(4),
b ) 434.2(1),
C2/m-C32h (No.12)
a ) 1848.8(4),
b ) 425.7(1),
C2/m-C32h (No.12)
a ) 2330.3(9),
b ) 429.9(1),
unit-cell dimension
c ) 1925.3(7)pm,
â ) 118.07(2)°
c ) 1028.3(2)pm,
â ) 108.28(3)°
(a ) 1919.6(4),
b ) 434.2(1),
c ) 974.0(2)pm,
â ) 106.40(3)°
c ) 1899.1(4)pm,
â ) 126.22(2)°
c ) 1026.5(2) pm,
â ) 108.17(3)°)
0.8159(3) nm3
volume
1.3317(5) nm3
0.7354(3) nm3
1.5349(8) nm3
(0.8129(3) nm3)
2
Z
4
2
4
density (calculated)
absorption coefficient
color, habit
4.980 mg m-3
14.636 mm-1 (Ag KR)
bluish-green, needles
1692
5.020 mg m-3 (5.039 mg m-3
19.677 mm-1 (Mo KR)
bluish-green, needles
1026
)
5.901 mg m-3
15.053 mm-1 (Ag KR)
bluish-green, needles
1082
5.296 mg m-3
11.057 mm-1 (Ag KR)
black, needles
2036
F(000)
crystal dimension
data collection
0.02 × 0.2 × 0.02 mm
0.03 × 0.2 × 0.02 mm
0.05 × 0.1 × 0.05 mm
0.05 × 0.2 × 0.05 mm
CAD4 (Nonius)
IPDS (Stoe)
CAD4 (Nonius)
CAD4 (Nonius)
Plane graphite monochromator Plane graphite monochromator Plane graphite monochromator Plane graphite monochromator
λ(Ag KR) ) 56.086 pm
ω scan, ∆ω ) 0.9°
4.00° e 2ϑ e 52.00°
0 e h e 28, 0 e k e 6,
-30 e l e 26
λ(Mo KR) ) 71.073 pm
λ(Ag KR) ) 56.086 pm
λ(Ag KR) ) 56.086 pm
ω/ϑ scan, ∆ω ) 0.9°
4.00° e 2ϑ e 48.00°
-33 e h e 0, 0 e k e 6,
-22 e l e 27
Detector distance 50,120 mm ω/ϑ scan, ∆ω ) 1.0°
7.00° e 2ϑ e 56°
-26 e h e 26, -5 e k e 5,
-14 e l e 10
4.00° e 2ϑ e 48.00°
0 e h e 24, -6 e k e 6,
-14 e l e 13
reflections collected
3012
2726 (2754)
2341
2569
independent reflections
2941 (Rint ) 0.052)
993 (Rint ) 0.028)
(992 (Rint ) 0.034))
FMLS on F2 [30]
none
1315 (Rint ) 0.030)
2503 (Rint ) 0.019)
structure refinement
absorption correction
FMLS on F2 [30]
FMLS on F2 [30]
FMLS on F2 [30]
empirical, ψ scans
empirical, ψ scans
(9 reflections, µr ) 0.10,
0.69 e transmission e 0.87)
1315 / 0 / 43
empirical, ψ scans
(8 reflections, µr ) 0.32,
0.70 e transmission e 0.90)
2503 / 0 / 73
(15 reflections, µr ) 0.05,
0.86 e transmission e 0.98)
data/restraints/parameters 2854/0/79
goodness of fit on F2
1.260
final R indices [I g 2σ(I)] R1 ) 0.0411, wR2 ) 0.0642
991/0/43 (985/0/43)
1.038 (1.055)
1.159
1.103
R1 ) 0.0232, wR2 ) 0.0417
(R1 ) 0.0248, wR2 ) 0.0477)
R1 ) 0.0382, wR2 ) 0.0450
(R1 ) 0.0360, wR2 ) 0.0514)
1031/-929 e nm-3
R1 ) 0.0187, wR2 ) 0.0403
R1 ) 0.0579, wR2 ) 0.1051
R indices [all data]
R1 ) 0.0643, wR2 ) 0.0787
2141/-1982 e nm-3
R1 ) 0.0241, wR2 ) 0.0428
2153 and -1028 e nm-3
R1 ) 0.0642, wR2 ) 0.1082
8340 and -11772 e nm-3
largest max/min
(1031 / -1151 e nm-3
)

Planar B4 Rhomboids
J. Phys. Chem. B, Vol. 101, No. 48, 1997 9955
TABLE 4: Atomic Coordinates, Equivalent Ueq and Anisotropic Displacement Coefficients Uij (pm2 )a
atom
x
y
z
Ueq
U11
U22
U33
U23
U13
U12
(a) La4I5B4 at 293 (and 143 K), for All Atoms U23 ) U12 ) 0
La(1)
(La(1)
La(2)
(La(2)
I(1)
(I(1)
I(2)
(I(2)
I(3)
(I(3)
B(1)
(B(1)
B(2)
(B(2)
0.1370(1)
0.1375(1)
0.5101(1)
0.5114(1)
0.3287(1)
0.3294(1)
0.6879(1)
0.6895(1)
0.5143(2)
0
0
0
0
0
0
0
0.0686(1)
0.0682(1)
0.2538(1)
0.2547(1)
0.1498(1)
0.1503(1)
0.3218(1)
0.3217(1)
0.5098(6)
0.5066(16)
0
139(1)
75(1))
117(1)
66(1))
190(2)
96(1))
206(2)
101(2))
352(9)
202(13))
100(20)
90(20))
140(20)
90(20))
127(2)
77(2)
169(2)
94(2)
162(2)
90(2)
198(3)
99(3)
810(3)
460(4)
150(30)
110(40)
180(40)
200(50)
131(2)
69(2)
92(2)
54(2)
186(3)
98(3)
187(3)
95(3)
136(5)
79(5)
20(40)
100(50)
70(40)
20(40)
166(3)
87(3)
107(3)
57(3)
249(4)
114(3)
203(3)
99(3)
190(2)
120(2)
130(40)
70(40)
160(50)
60(50)
58(2)
37(2))
65(2)
35(2))
101(2)
52(2))
19(2)
16(2))
260(2)
170(4))
40(30)
30(30))
30(40)
20(40))
0
1
/
/
2
2
1
0.5097(5)
1
/
0.1803(18)
0.1862(22)
0
0
2
1
/
0
2
0.9964(4)
0.9960(5)
0.9021(10)
0.9014(11)
(b) La4Br5B4 at 293 K
1
La(1)
La(2)
La(3)
La(4)
Br(1)
Br(2)
Br(3)
Br(4)
Br(5)
Br(6)
B(1)
0.1622(1)
0.3755(1)
0.3858(1)
0.1588(1)
0.2242(1)
0.0426(1)
0.3340(1)
0.0069(1)
/
0.2749(1)
0.3749(1)
0.1975(1)
0.0829(1)
0.4052(1)
0.1674(1)
0.0661(1)
119(1)
110(2)
105(2)
108(2)
119(2)
251(5)
122(4)
204(4)
130(4)
372(9)
171(6)
120(20)
40(30)
110(40)
108(2)
83(2)
157(2)
93(2)
0
0
0
0
0
0
0
0
76(2)
24(2)
67(2)
26(2)
139(4)
72(3)
0
0
0
0
0
0
0
0
2
0
103(1)
116(1)
118(1)
189(2)
155(2)
179(2)
169(2)
349(4)
199(3)
108(110)
90(20)
140(20)
1
/
114(2)
102(2)
175(5)
165(4)
168(5)
180(5)
143(7)
214(7)
70(20)
80(40)
60(40)
137(2)
101(2)
185(4)
180(4)
156(4)
216(4)
220(7)
175(6)
110(20)
140(40)
170(40)
2
0
0
0
0
78(3)
96(3)
1
/
0.3147(1)
2
1
0
0
0
/
0
0
-119(6)
0
0
2
1
/
0
52(5)
2
0.2693(4)
0.2268(5)
0.3119(6)
0.1843(16)
0.2285(4)
0.1725(6)
0.2866(6)
10(20)
0
0
40(20)
30(30)
0(30)
10(20)
0
0
1
B(2)
B(3)
/
/
2
1
2
(c) Gd4I5B4 at 293 K, for All Atoms U23 ) U12 ) 0
Gd(1)
Gd(2)
I(1)
I(2)
I(3)
B(1)
B(2)
0.1329(1)
0.5059(1)
0.3266(1)
0.6821(1)
0
0
0
0.0673(1)
0.2498(1)
0.1463(1)
0.3186(1)
0.5068(7)
0
117(1)
96(1)
160(1)
168(1)
278(7)
127(100)
89(90)
124(1)
151(1)
145(2)
168(2)
630(2)
190(20)
180(20)
102(1)
74(1)
148(2)
151(2)
118(3)
80(20)
30(20)
132(1)
72(1)
204(2)
161(2)
128(10)
110(20)
80(20)
45(1)
45(1)
80(1)
9(1)
170(2)
40(20)
80(20)
0
1
0.5113(2)
/
2
1
/
0.1871(15)
0
2
0.9988(3)
0.8966(10)
(d) La4I5B2 C at 293 K, for All Atoms U23 ) U12 ) 0
La(1)
La(2)
La(3)
La(4)
I(1)
I(2)
I(3)
I(4)
I(5)
C(1)
B(1)
B(2)
0.4874(1)
0.4955(1)
0.1325(1)
0.1512(1)
0.3215(1)
0.3368(1)
0.3164(1)
0.0174(1)
0.3355(1)
0
0
0
0
0
0
0
0
0
0
0.1250(1)
0.4052(1)
0.1050(1)
0.6004(1)
0.2529(1)
0.7419(1)
0.9782(1)
0.7419(1)
0. 5153(1)
0.5231(19)
0
140(2)
358(3)
158(2)
441(4)
219(2)
240(2)
214(2)
410(4)
250(3)
560(70)
150(30)
120(30)
195(4)
130(4)
163(4)
932(12)
182(5)
253(6)
200(5)
802(12)
236(5)
870(190)
280(80)
120(70)
114(4)
744(10)
138(4)
187(5)
219(5)
229(6)
203(5)
254(7)
227(6)
510(160)
100(70)
30(60)
144(4)
169(5)
167(4)
329(6)
178(5)
180(5)
282(5)
421(8)
346(6)
610(170)
100(60)
160(70)
118(3)
71(4)
95(3)
440(8)
63(4)
96(4)
165(5)
498(9)
206(5)
610(170)
130(60)
60(60)
0.0343(16)
1
/
0.1860(42)
2
1
0.4968(8)
/
0. 0491(11)
2
a The Uij are defined as exp[-2π2(U11h2a*2 + ... + 2U23klb*c*)].
level both B p and La d states contribute to the bands. The
highly dispersive partly filled bands at EF give evidence for the
metallic nature of La4Br5B4; a pseudogap is found 0.6 eV below
the Fermi level. The one-dimensional character of La4Br5B4
is obvious from the flat bands between Γ and A, which is the
direction orthogonal to the B4 chains. The Γ-A relates to the
c axis. The Γ-Z and A-M run parallel to the chain direction.25
In order to reach a more quantitative interpretation of the
electronic band structure, we refer to the MO diagram of the
idealized square planar B4 unit and in addition to the interaction
between neighboring units as shown in Figure 10. Some of
the orbital character is well preserved in discrete bands. The
flat band having its bottom near -12 eV corresponds to the
lowest a1g orbital formed from the B s electrons. Integrating
over all states through a suitably chosen energy window leads
to the electron density which is plotted at a level of 0.2 e/ao3 in
Figure 10a. It is obvious that the electron density is well
localized within the B4 unit, and there is no significant
interaction between adjacent units. The (degenerate) band with
its bottom near -10 eV does not contain a contribution from a
B4-MO, but the band is due to the interaction between
neighboring B4 units. Because this band is also energetically
well separated from all other bands, the electron density can
easily be evaluated. It is depicted in Figure 10b, again at a
3
level of 0.2 e/ao . The electron density is localized in the short
bond between the B(1)-type atoms belonging to different B4
units. The next sets of bands with their bottoms near -7 and
-6.5 eV are derived from the eu-type MO, which is degenerate
in the case of a planar discrete B4 unit. In the chain of
interconnected rhomboids, two sets of doubly degenerate bands
result. The one has s character at the B(1)-type atoms and
exhibits large dispersion; the other is flat and corresponds to

9956 J. Phys. Chem. B, Vol. 101, No. 48, 1997
Mattausch et al.
TABLE 5: Selected Bond Lengths (pm) with Standard Deviation at 293 K
(a) La4I5B4
La(1)
La(2)
I(1)
I(2)
I(3)
La(1): 434.2(1). La(2), 415.0(2), 422.3(2). I(1): 333.5(2), 351.8(3). I(2): 329.4(1). B(1): 286.5(4). B(2): 267.7(9) pm.
La(2): 434.2(1). I(1): 331.5(2). I(2): 327.1(3). I(3): 339.4(5), 340.0(5). B(1): 267.3(3). B(2): 267.8(6) pm.
I(1): 418.6(3), 434.2(1). I(2): 426.5(2). I(3): 441.1(4). B(1): 412.8(3). B(2): 417.8(8) pm.
I(2): 428.5(2), 434.2(1). B(1): 413.9(3). B(2): 418.0(6) pm.
I(3): 434.2(1). B(2): 415.5(12), 417.6(12) pm.
B(1)
B(2)
B(1): 156.6(16), 277.6(16). B(2): 170.3(9) pm.
B(2): 197.4(21) pm.
(b) La4Br5B4
La(1)
La(1): 429.42(3). La(2): 405.31(9). La(4): 425.0(1). Br(1): 308.4(1). Br(2): 306.68(8). Br(4): 326.6(1). B(1): 284.7(8). B(2):
273.3(14).B(3): 263.5(12) pm.
La(2)
La(3)
La(2): 429.42(3). La(3): 411.3(1). Br(1): 307.9(1). Br(4): 311.6(1). Br(5): 322.90(8). B(1): 268.0(6). B(3): 264.4(5) pm.
La(3): 429.42(3). La(4): 424.8(1). Br(2): 317.7(1). Br(3): 310.6(1). Br(4): 314.58(9). B(1): 281.3(8). B(2): 271.0(10). B(3):
263.5(14) pm.
La(4)
Br(1)
Br(2)
Br(3)
Br(4)
Br(5)
Br(6)
B(1)
La(4): 429.42(3). Br(2): 322.3(2). Br(3): 336.3(1). Br(6): 334.73(6). B(1): 269.0(6). B(2): 266.7(5) pm.
Br(1): 394.9(2), 429.42(3). Br(2): 420.3(2). Br(4): 411.0(1). B(1): 393.8(9). B(3): 397.8(12) pm.
Br(2): 429.42(3). Br(3): 399.1(1). Br(4): 385.0(2). Br(6): 363.9(1). B(1): 381.5(7). B(2): 395.1(9) pm.
Br(3): 362.7(2), 429.42(3). Br(4): 431.8(2). Br(6): 379.9(1). B(1): 390.8(9). B(2): 405.1(11) pm.
Br(4): 429.42(3). Br(5): 421.6(2). B(1): 392.6(7). B(3): 397.0(10) pm.
Br(5): 429.42(3). B(3): 392.4(9) pm.
Br(6): 429.42(3). B(2): 390.3(8) pm.
B(1): 158.3(13), 271.2(13). B(2): 167.8(8). B(3): 169.5(8) pm.
B(2): 200.6(13) pm.
B(2)
(c) Gd4I5B4
Gd(1)
Gd(2)
I(1)
I(2)
I(3)
Gd(1): 425.7(1). Gd(2): 394.5(1), 402.3(1). I(1): 320.9(1), 344.3(1). I(2): 317.7(1). B(1): 270.8(3). B(2): 255.7(5), 256.7(6) pm.
Gd(2): 425.7(1). I(1): 318.1(1). I(2): 313.4(1). I(3): 326.6(5), 326.8(5). B(1): 253.3(2). B(2): 255.0(3) pm.
I(1): 383.2(1), 425.7(1). I(2): 424.2(1). I(3): 449.7(5). B(1): 382.9(2). B(2): 392.6(5) pm.
I(2): 425.7(1), 428.0(2). I(3): 459.6(5). B(1): 396.2(2). B(2): 401.8(4) pm.
I(3): 425.7(1). B(2): 386.8(9), 388.1(9) pm.
B(1)
B(2)
B(1): 159.3(13), 266.4(13). B(2): 166.6(6) pm.
B(2): 200.2(12) pm.
(d) La4I5B2C
La(1)
La(2)
La(3)
La(4)
I(1)
I(2)
I(3)
La(1): 429.9(1). La(3): 413.3(2), 420.9(2). I(2): 330.7(2). I(3): 324.5(2). I(4): 337.1(2). B(1): 268.0(6). B(2): 266.9(15) pm.
La(2): 348.1(3), 429.9(1). La(4): 395.3(2), 398.6(3). I(1): 330.9(2). I(4): 339.4(2). I(5): 328.0(3). C(1): 284.1(23), 284.3(31) pm.
La(3): 429.9(1). I(1): 355.8(2). I(2): 333.6(2). I(3): 327.9(2). B(1): 283.8(9). B(2): 268.6(13) pm.
La(4): 429.9(1). I(1): 327.1(2). I(2): 349.2(3). I(5): 321.5(2). C(1): 219.5(33)pm.
I(1): 429.9(1). I(2): 431.9(2). I(4): 418.8(2). I(4): 427.6(3). C(1): 413.3(22) pm.
I(2): 429.9(1). I(5): 428.8(3). B(1): 413.5(4). B(2): 415.1(11) pm.
I(3): 429.9(1). I(5): 428.8(3). B(1): 412.7(4). B(2): 417.3(18) pm.
I(4): 429.9(1). I(5): 442.1(2). C(1): 440.0(45) pm.
I(4)
I(5)
I(5): 429.9(1). C(1): 411.4(40) pm.
C(1): 130.5(66) pm.
B(1): 160.5(37), 269.4(37). B(2): 166.4(21) pm.
B(2): 195.3(41) pm.
C(1)
B(1)
B(2)
the configuration with px character at the B(1) type atoms. The
electron density for the two sets of bands averaged over the
entire Brillouin zone is shown at a level of 0.2 e/ao in Figure
of localization as it is calculated within the electron localization
function (ELF) concept is shown by appropriate color of the
isosurface. The region between the B(1)-type atoms, as well
as positions at the other B atoms easily associated with lone
pairs, are characterized by colors red to white indicating a large
degree of localization.
3
10c. The electron density is distributed both between the B
atoms of neighboring B4 units as well as in the periphery of
one unit itself. Last but not least the a2u, b2g, b1g, and a1g MOs
contribute to the bands above -5.5 eV. These bands are
strongly mixed with La d character; indeed, the latter dominates
the band character. The eg-type MOs split into highest occupied
molecular orbital (HOMO) and lowest unoccupied molecular
orbital (LUMO). Again covalent mixing with La d states adds
to the dispersion of these bands. The HOMO is characterized
by the node at the B(1) type atoms and pz configuration at the
other B atoms. The HOMO is half-occupied. It corresponds
to the nearly degenerate band which crosses the Fermi level.
The configuration depicted in the upper right of the Figure 10
leads to the flat bands around -1 eV. These bands contribute
Experimental Section
3.1. Preparation. Metals La, Ce, Pr, Nd, and Gd (sublimed,
99.99, Alfa/J. Matthey) were crushed directly with the exception
of Gd which was hydrogenated, crushed, and dehydrogenated
in vacuo at 1070 K (Mo container, 24 h). REX3 was prepared
from the oxides (99.9%, Alfa/J. Matthey), was with HX and
NH4 X (p.a. Merck)26,27 and distilled under vacuum in tantalum
containers. Boron (99.4%, Ventron) and graphites (99.4%,
Aldrich) were heated in vacuo at 1400 K for 12 h and 2 days,
respectively, prior to use. Reactions were performed with
stoichiometric mixtures of RE, REX3, B, and C sealed in Ta
capsules under Ar. Conditions are specified in Table 1. All
boride halides exhibit a bluish-green metallic luster, and the
boride carbide halides are black. The air and moisture sensitive
products need to be handled in Ar.
3
to the electron density which is depicted at a level of 0.1 e/ao
in Figure 10e, indicating nonbonding interaction between all B
atoms in these bands. The localization of nonbonding electron
pairs at the B atoms is nicely demonstrated in Figure 11, which
shows the isosurface of the total electron density at a level of
3
0.6 e/ao . For the sake of clarity, the bromine atoms and the
3.2. X-ray Structure Investigation. The compounds are
charactized by X-ray powder diffraction (modified Guinier
electron density related to these atoms is omitted. The degree

Planar B4 Rhomboids
J. Phys. Chem. B, Vol. 101, No. 48, 1997 9957
technique;28 λ(Cu KR1) ) 154.056 pm, internal standard Si, a
) 543.035 pm, coincidence measurement). The lattice constants
of all investigated compounds determined from powder data
are summarized in Table 2. Single-crystal investigations were
performed on selected compounds sealed in glass capillaries
under Ar. Details on data collection and structure refinement
are summarized in Table 3. The positions of the heavy atoms
were derived by direct methods,29 the light atoms were localized
in ∆F maps. Full-matrix least-squares refinement30 on F2 led
to the parameters shown in Table 4a for La4I5B4 together with
interatomic distances in Table 5a (Tables 4b and 5b for La4-
Br5B4, Tables 4c and 5c for Gd4I5B4 and Tables 4d and 5d for
La4I5B2C).37
ments, and Dr. R. K. Kremer and E. Bru¨cher for the electrical
and magnetic measurements.
References and Notes
(1) Gmelin Handbook RE Main; Springer Verlag: Berlin, 1990; Vol.
C 11a.
(2) Etourneau, J. J. Less-Common Met. 1985, 110, 267.
(3) Warkentin, E.; Simon, A. ReV. Chim. Miner. 1983, 20, 488.
(4) Simon, A.; Mattausch, Hj.; Miller, G. J.; Bauhofer, W.; Kremer,
R. K. Handbook on the Physics and Chemistry of Rare Earth, Gschneidner,
K. A., Jr, Eyring, L., Eds.; Elsevier Science Publishers: New York, 1991;
Vol. 15, p 191.
(5) Dudis, D. S.; Corbett, J. D.; Hwu, S.-J. Inorg. Chem. 1986, 25,
3434.
(6) Mattausch, Hj.; Simon, A. Angew. Chem. 1995, 107, 1764; Angew.
Chem., Int. Ed. Engl. 1995 34, 1633.
The atoms I(3) (La4I5B4 (293 and 143 K) and Gd4I5B4 (293
K)) are temperature independently characterized by pronounced
anisotropy of the displacement coefficients (U11/U22, U33 ≈ 15).
Occupation of a split position x1/2z (x ≈ 0.510, z ≈ 0.510)
(7) Mattausch, Hj.; Simon, A.; Felser, C.; Dronskowski, R. Angew.
Chem. 1996, 108, 1805; Angew. Chem., Int. Ed. Engl. 1996, 35, 1685.
(8) Scha¨fer, H.; Schnering, H. G. Angew. Chem. 1964, 76, 833; Angew.
Chem., Int. Ed. Engl. 1964, 3, 3117.
(9) Mattausch, Hj. Unpublished results, 1993.
(10) Wiitkar, F.; Kahlal, S.; Halet, J.-F.; Saillard, J.-Y.; Bauer, J.; Rogl,
P. J. Am. Chem. Soc. 1994, 116, 251.
(11) Ansel, D.; Bauer, J.; Bonhomme, F.; Boucekinne, G.; Frapper,
G.;Halet, J.-F.; Gougeon, P. Angew. Chem. 1996, 108, 2245; Angew. Chem.,
Int. Ed. Engl. 1996, 35, 2098.
(12) Atoji, M.; Lipscomb, W. N. Acta Crystallogr. 1953, 6, 547.
(13) Nordman, C. E.; Lipscomb, W. N. J. Chem. Phys. 1953, 21, 1856.
(14) Moore, E. M.; Nordman, C. E.; Lipscomb, W. N. J. Chem. Phys.
1957, 27, 209.
(15) Klusik, H.; Berndt, A. J. Organometal. Chem. 1982, C17, 234.
(16) Douglas, A. E.; Herzberg, G. Phys. ReV. 1940, 57, 752.
(17) Schwarz, C.; Simon, A. Z. Naturforsch. 1987, 42b, 935.
(18) Tarascon, J. M.; DiSalvo, F. J.; Waszczak, J. V. Solid State Comm.
1984, 52, 227.
(19) Mee, J. E.; Corbett, J. D. Inorg. Chem. 1965, 4, 88.
(20) Lokken, D. A.; Corbett, J. D. Inorg. Chem. 1973, 12, 556.
(21) Simon, A.; Holzer, N.; Mattausch, Hj. Z. Anorg. Allg. Chem. 1979,
456, 207.
(22) Bauhofer, W.; Simon, A. Z. Naturforsch. 1982, 37a, 568.
(23) Bullett, D. W. Inorg. Chem. 1980, 19, 1780.
(24) Bullett, D. W. Inorg. Chem. 1985, 24, 3319.
(25) Bradley, C. J.; Cracknell, A. P. Theory of Symmetry in Solids;
Clarendon Press: Oxford, 1979.
(26) Brukl, A. Angew. Chem. 1939, 52, 152.
(27) Meyer, G.; Ax, P. Mater. Res. Bull. 1982, 17, 1447.
(28) Simon, A. J. Appl. Crystallogr. 1970, 3, 11.
(29) Sheldrick, G. M. SHELXTL-PLUS, An Integrated System for
SolVing, Refining and Displaying Crystal Structures from Diffraction Data;
Go¨ttingen: Germany, 1994.
(30) Sheldrick, G. M. SHELXL-93; Go¨ttingen, Germany, 1993.
(31) van der Pauw, L. J. Philips Res. Rep. 1958, 13, 1.
(32) Krier, G.; Jepsen, O.; Burkhardt, A.; Andersen, O. K. Program
TB-LMTOASA 4.7 (tight binding-linear muffin tin orbital-atomic sphere
approximation).
1
1
instead of 1/2 /1 /2 by this I(3) atom results in a “more isotropic”
ratio U11/U22, U33 ≈ 5 (Table 4a,c). Equivalent atoms in La4-
Br5B4 (Br(5): U11/U22, U33 ≈ 2) and in La4Br5B2C (I(4): U11/
U22, U33 ≈ 3) show similar anisotropy.
3.3. Electrical Conductivity. Measurements of the electrical
conductivity were taken on pressed pellets (8 mm diameter)
according to van der Pauw31 at temperatures 4 g T g 300 K in
He atmosphere. All compounds RE4X5B4 as well as RE4X5B2C
exhibit metal-like resistivity at room temperature, and the
resistivity increases strongly at low temperature. In the range
100 g T g 300 K, the compounds seem to be small band gap
semiconductors with gaps varying between the extremes Eg )
60 meV for Gd4I5B4 and Eg ) 10 meV for La4Br5B4. Such
assignment, however, is erroneous as both crystal and electronic
band structures give evidence for one-dimensional metallic
systems that gradually undergo localization.
3.4. Magnetic Susceptibility. Magnetic measurements in
the range 2 g T g 300 K were performed in a VTS-SQUID
magnetometer (SHE) at a field of 1.0 T on samples (≈150 mg)
enclosed in gelatine capsules.
3.5. Band Structure Calculations. Electronic band struc-
tures were calculated ab initio in the local density approximation
within the TB-LMTO-ASA formalism.32,33 Chemical bonding
in La4Br5B4 is visualized in real space as charge density and
via the electron localization function ELF.34 Calculations
involve the La 6s, 5d, 4f, Br 4s, 4p and B 2s, 2p orbitals as
basis sets. The La 6p, Br 4d and B 3d orbitals were treated in
the socalled downfolding procedure. The exchange correlation
potential is calculated according to,35 and the band structure is
based on 164 k points (tetrahedron method). The rather open
structure needed the introduction of 98 empty spheres/primitive
cell to meet the requirement of the atomic sphere approximation.
(33) Andersen, O. K. Phys. ReV. B. 1975, 12, 3060. Andersen, O. K.;
Jepsen, O. Phys. ReV. Lett. 1984, 53, 2571.
(34) Savin, A.; Becke, A. D.; Flad, J.; Nesper, R.; Preuss, H.; von
Schnering, H. G. Angew. Chem. 1991, 103, 421; Angew. Chem., Int. Ed.
Engl. 1991, 30, 789.
(35) Barth, U.; Hedin, L. J. Phys. C 1972, 5, 1629.
(36) Pauling, L. Die Natur der chemischen Bindung; Verlag Chemie:
GmbH., Weinheim/Bergstrasse, 1973.
(37) Further details on the crystal structures may be obtained from the
Fachinformationszentrum Karlsruhe, Gesellschaft fu¨r wissenschaftlich-
technische Information mbH, D-76344 Eggenstein-Leopoldshafen upon
quoting the numbers CSD-405290 (La
CSD-406548 (Gd4I5B4), CSD-405294 (La4I5B2C), and names of the authors
4I5B4 ), CSD-405291 (La4Br5B4),
Acknowledgment. We thank R. Eger for experimental help,
Dr. R. Po¨ttgen and H. Ga¨rttling for the diffractometer measure-
and the journal citation.