Extraordinarily short Pb-Pb bonds in the new binary intermetallic Ti6Pb4.8

Article abstract of DOI:10.1006/jssc.2001.9141

Ti₆Pb_4.8 is accessible via reactions in a Pb flux starting from the elements in evacuated silica tubes at 680°C. Larger single crystals can be obtained by adding traces of iodine to promote crystal growth. At higher temperatures, Ti₆Pb_4.8 decomposes into Ti₄Pb and Pb. Ti₆Pb_4.8 crystallizes in the hexagonal α-Ti₆Sn₅ type, space group P6₃/mmc, with the lattice dimensions a=939.23(8) and c= 579.01(5) pm for Ti₆Pb_4.824(7) (Z=2). While the structure is dominated by the heteronuclear Ti-Pb bonds, linear Ti and Pb chains run parallel to the c axis with interatomic distances being equidistant by symmetry c/2=289.5 pm). This results in a Pb-Pb distance being much shorter than a Pb-Pb single bond (typically 310 pm). Longer homonuclear distances of about 315 pm (Ti-Ti) and between 357 and 374 pm (Pb-Pb) occur perpendicular to the chain direction. All these interactions have bonding character, as the LMTO calculations of Ti₆Pb_4.8 reveal.

Full text of DOI:10.1006/jssc.2001.9141

Journal of Solid State Chemistry 159, 134}138 (2001)
doi:10.1006/jssc.2001.9141, available online at http://www.idealibrary.com on
Extraordinarily Short Pb+Pb Bonds in the
New Binary Intermetallic Ti Pb
6
4.8
Holger Kleinke
Department of Chemistry, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Received December 16, 2000; in revised form February 14, 2001; accepted March 5, 2001; published online April 27, 2001
Jeitschko. However, adding tin in syntheses aiming at early
Ti
6
Pb4.8 is accessible via reactions in a Pb 6ux starting from transition metal antimonides would cause inherent prob-
the elements in evacuated silica tubes at 6803C. Larger single
crystals can be obtained by adding traces of iodine to promote
lems due to possible tin/antimony mixing, which would be
di$cult to examine with X-ray investigations because of the
comparable scattering factors of the Sn and Sb atoms.
Focusing on lead instead of tin, it is exciting to realize
that lead is most unwilling to form compounds with anti-
mony or early transition metal atoms*especially when
being interested in early transition metal antimonides (8).
The only known group 4 plumbides are Ti Pb (9), Zr Pb
crystal growth. At higher temperatures, Ti
Ti Pb and Pb. Ti Pb4.8 crystallizes in the hexagonal a-Ti
type, space group P6 /mmc, with the lattice dimensions
a ؍ 939.23(8) and c ؍ 579.01(5) pm for Ti
6
Pb4.8 decomposes into
4
6
6
Sn
5
3
6
Pb4.824(7) (Z ؍ 2).
While the structure is dominated by the heteronuclear Ti+Pb
bonds, linear Ti and Pb chains run parallel to the c axis with
interatomic distances being equidistant by symmetry
ꢂ
ꢃ
c/2 ؍ 289.5 pm). This results in a Pb+Pb distance being much and Zr Pb
(10), and Zr Pb (11). In order to further
ꢃ
ꢂ\V
ꢃ
ꢄ
shorter than a Pb+Pb single bond (typically 310 pm). Longer explore especially the Pb-rich part of these systems, various
homonuclear distances of about 315 pm (Ti+Ti) and between 357 experiments were performed, the results of which proved the
and 374 pm (Pb+Pb) occur perpendicular to the chain direction.
All these interactions have bonding character, as the LMTO
calculations of Ti Pb4.8 reveal. ( 2001 Academic Press
existence of at least one more titanium plumbide, namely
Ti Pb , which is the most Pb-rich compound in the Ti/Pb
system under the reactions conditions applied. This article
will tackle the synthesis and crystal and electronic structure
ꢅ
ꢂꢆꢇ
6
Key Words: intermetallics; titanium plumbide; structure and
bonding; electronic structure; hypervalent bonding.
of Ti Pb
.
ꢅ
ꢂꢆꢇ
EXPERIMENTAL
INTRODUCTION
Synthesis
Ti Pb readily forms at elevated temperatures (6803C)
For several decades, di!erent research and industrial
ꢅ
ꢂꢆꢇ
groups have been using high-temperature #ux methods that from the elements in a 1:1 ratio in an evacuated fused silica
use di!erent melts of elements (or, e.g., oxides and salts like tube. The small excess of elemental lead remains unreacted.
LiCl/KCl) to get large, high-quality crystals (1). Some suit- Starting from Pb-de"cient Ti:Pb ratios, e.g., 3:2, gave the
able elements are found among the main groups, e.g., alumi- same main product, i.e., Ti Pb . Ti Pb
num (2), tin (3), antimony (4), and bismuth (5), while the upon annealing at 13003C under inert atmosphere into
decomposes
ꢅ
ꢂꢆꢇ
ꢅ
ꢂꢆꢇ
transition metals are less propagated because of their higher Ti Pb and Pb. This is assumed to be the main reason for
ꢂ
melting points. Rare exceptions include the use of chro- this compound to stay concealed until today (in analogy to
mium and iron for the crystal growth of Zr S (6) and H P
the recently uncovered most Sn-rich Ti stannide Ti Sn (12),
ꢀ
ꢁ ꢂ
ꢀ
ꢄ
(7), respectively.
but in contrast to Ti Sn (13) which melts congruently at
ꢅ
ꢃ
Ideally, good #ux materials occur in the molten state over 14903C (14)). Better crystals of Ti Pb can be obtained by
ꢅ
ꢂꢆꢇ
a wide temperature range. They should be highly unreactive annealing a mixture of the elements in a 1:1 ratio at 6003C
toward the crystals to be prepared, unless their constituent under addition of traces of iodine as a mineralizator. EDX
elements are also part of the desired products. It is further- investigation carried out on selected crystals revealed the
more advantageous when the #ux can easily be removed, existence of solely Ti and Pb, in the ratio of 52(3):48. For
such as tin with weak acids. Therefore, tin has been used as comparison: the re"ned composition Ti Pb corresponds
ꢅ
ꢂꢆꢇ
the #ux for the crystallization of a multitude of di!erent to 55.6:44.4, thus the EDX investigations suggest a slightly
phosphides at di!erent temperatures in the group of smaller Ti content.
1
34
0
022-4596/01 $35.00
Copyright ( 2001 by Academic Press
All rights of reproduction in any form reserved.

Pb}Pb BONDS IN Ti Pb
ꢂꢆꢇ
135
ꢅ
Structure Determination
A single crystal data collection was performed using a dif-
TABLE 1
Crystallographic Data for Ti Pb
6
4.8
fractometer with an area detector. The data were corrected Chemical formula: Ti Pb
for Lorentz and polarization e!ects. The space group of the Formula weight: 1287.1 g/mol
Space group: P6 /mmc (No. 194)
Crystal size [mm]: 0.10;0.08;0.06
¹"223C
j"71.069 pm
2h range: 5.0}60.73
ꢅ
ꢂꢆꢇꢀꢂ(ꢁ)
ꢄ
a"939.23(8) pm
a-Ti Sn type, P6 /mmc, is consistent with the systematic
extinctions observed experimentally (l"2n#1 for all hhl
re#ections). The structure re"nement in the centrosymmet-
ꢅ
ꢃ
ꢄ
c"579.01(5) pm
<
Z"2
"442.34(7) 10ꢅpmꢄ
o
#!ꢀ#$"9.66 g/cmꢄ
ric space group was successful (program SHELXL (15)). The Collected re#ections: 4342
high displacement parameter ; of Pb1 pointed toward
Independent
re#ections:
286
(R*ꢁꢂ"0.086)
%
ꢇ
Observed
55/19
re#ections/parameter:
a not completely "lled position. Re"nement of the occu-
pancy factor f (Pb1) yielded f"0.824(7) by lowering the
2
Extinction coe$cient: 0.0128(6)
Absorption correction: numerical
k"964.5 cm\ꢈ
¹
"0.0068, ¹ "0.0537
ꢃ*ꢁ ꢃ!ꢄ
residual factor R(F ) from 0.0327 to 0.0217; it still gave
R(F )?"0.022; R (Fꢀ)@ "0.047
ꢅ
ꢅ
ꢆ
ꢅ
a high ; of Pb1 due to enlarged vibrations along the c axis,
%
ꢇ
as re#ected in ; , which corresponds to almost 10 times
?R(F )"+#F "!"F #/+"F ".
ꢆ ꢅ ꢅ # ꢅ
ꢄꢄ
ꢅ
ꢅ
#
ꢅ
@
R (Fꢀ)"[+[w(Fꢀ!Fꢀ)ꢀ]/+[w(Fꢀ)ꢀ]]ꢈꢉꢀ.
;ꢈꢈ (; "; by symmetry).
ꢈꢈ
ꢀꢀ
In this structure model, Pb1 occupies the site 2a, i.e.,
(
0, 0, 0) and (0, 0, ꢈ), forming a linear chain with equidistant
ꢀ
LMTO-ASA: tight binding linear mu$n tin orbitals atomic
spheres approximation) (16, 17), the density functional the-
ory (18) is used with the local density approximation (LDA).
The ASA radii were determined to be 1.624 (Ti1), 1.623 (Ti2),
Pb1}Pb1 distances of c/2"289.5 pm. Re"nements of split
positions or in lower symmetry space groups failed: at-
tempts were made in P6 mc, a direct subgroup of P6 /mmc,
ꢄ
ꢄ
wherein the Pb1 atom would be on the still symmetry
1
.672 (Pb1), 1.693 (Pb2), and 1.694 pm (Pb3). The integra-
equivalent positions (0, 0, z) and (0, 0, z#ꢈ), and in P3m1,
ꢀ
a direct subgroup of P6 mc, wherein Pb1 would be located
ꢄ
tion in k space was performed by an improved tetrahedron
method (19) on a grid of 549 irreducible k points in the
irreducible section of the "rst Brillouin zone.
on two nonequivalent positions (0, 0, z) and (0, 0, zꢀ). The
latter would enable a distortion in the linear Pb1 chain
running parallel to [001]. However, no di!erences between
the two Pb1 positions in P3m1 were found; within the
RESULTS AND DISCUSSION
standard deviations, they were re"ned to be on (0, 0, 0) and Crystal Structure
0, 0, ꢈ). Allowing Pb1 to move away from x"0 and y"0
(
ꢀ
Ti Pb
ꢂꢆꢇ
While the hexagonal a-Ti Sn was originally reported to be
crystallizes in the hexagonal a-Ti Sn type.
neither improved nor changed the structure model. Also, no
superstructure re#ections were found using longer exposure
times with the area detector (three minutes per frame).
However, mixed Ti/Pb occupancies cannot be ruled out, but
they are rather unlikely because of the character and size
di!erences between Ti and Pb atoms. Also, that could not
explain the high anisotropy of the thermal parameter. Such
ꢅ
ꢅ ꢃ
ꢅ
ꢃ
the high-temperature modi"cation (13), the existence of the
low-temperature orthorhombic variant could not be con-
"rmed in a recent reinvestigation of the Ti/Sn phase dia-
gram (14). During our studies on Ti Pb we found no
evidence for a low-temperature modi"cation in the Ti/Pb
system, either.
In addition to Ti Pb and a-Ti Sn , only a few gallides
are known to form this type, namely Ti Mn
ꢅ
ꢂꢆꢇ
a
re"nement led to
a
re"ned stoichiometry of
&
&Ti
Pb ,'' a Ti:Pb ratio of 56.6:43.4, contradicting
ꢅ
ꢂꢆꢇ
ꢅ
ꢃ
ꢅꢆꢀꢄ ꢂꢆꢁꢁ(ꢈ)
Ga
the EDX results.
Since Ti Pb
lead, it represents the upper limit of Pb occupancy of this
position. No shifts in the lattice parameters were observed
by going to Ti-rich starting compositions (e.g., Ti:Pb"3:2).
It is concluded that Ti Pb exhibits no signi"cant phase
range. Crystallographic details may be found in Table 1.
Atomic positions, equivalent displacement parameters, and
occupancy factors are given in Table 2.
ꢀꢆꢃ ꢀꢆꢊꢃ ꢂꢆꢃꢃ
(
20), Mn Cu Ga (21), (V Nb ) Ga (04x40.55)
formed in equilibrium with unreacted
ꢃꢆꢂ ꢋꢆꢅ ꢃ ꢈ\V V ꢅ ꢃ
ꢅ
ꢂꢆꢇꢀꢂ(ꢁ)
(22), and Ta Ga (high-pressure phase) (23). Only powder
X-ray data were reported in all of these cases.
ꢅ
ꢃ
TABLE 2
ꢅ
ꢂꢆꢇ
Atomic Positions, Equivalent Displacement Parameters,
and Occupancy Factors of Ti Pb
6
4.8
Atom
site
x
y
z
; /pmꢀ
f
%
ꢇ
Ti1
Ti2
Pb1
Pb2
Pb3
6g
6h
2a
2d
6h
ꢈ
ꢀ
0
0
ꢄ
ꢂ
0
ꢄ
ꢂ
ꢈ
ꢂ
43(4)
66(5)
138(4)
37(2)
50(2)
1
1
Electronic Structure Calculations
0.1568(2) 0.3137
0
0
0.824(7)
Calculations were carried out using the LMTO approach
on Ti Pb , assuming full occupancies of all positions.
ꢈ
ꢀ
1
1
ꢄ
ꢄ
ꢅ
ꢃ
0.20068(3) 0.79932
Within the self-consistent TB-LMTO-ASA program (TB-

1
36
HOLGER KLEINKE
also part of the next pentagons. Four Ti1 neighbors in
distances of 315 pm complete the Ti2 surrounding to a poly-
hedron with 11 corners. Therein, the Ti2 atom is situated
between a Pb ring and a Pb-capped Ti Pb ring. Including
ꢂ
ꢂ
ꢀ
the surrounding Ti2 atoms within 315 pm, the Ti1 atom is
located in the center of a (distorted) Ti Pb icosahedron,
ꢅ
ꢅ
which can be viewed as two interwoven Ti and Pb oc-
tahedra. The coordination spheres of all "ve symmetry
inequivalent atom sites are highlighted in Fig. 2.
ꢅ
ꢅ
Including all neighboring atoms up to a distance of
3
15 pm, the coordination numbers for the Pb atoms are
eight for Pb1 (located in a Pb bi-capped Ti octahedron),
ꢅ
nine for Pb2 (a tri-capped trigonal prism comprising solely
Ti atoms), and eight for Pb3 (a bi-capped trigonal prism,
again consisting of Ti atoms only).
The heteronuclear interactions outweigh the homonuc-
FIG. 1. Structure of Ti Pb in a projection along [001]. (Small, white lear interactions by number and shortness. The Ti}Pb dis-
ꢂꢆꢇ
circles) Ti; (large, gray circles) Pb. Only Ti}Ti and Pb}Pb bonds are shown.
ꢅ
tances vary from 287 to 307 pm, which is slightly larger than
the sum of the atomic radii of 282 pm (taken from Pauling's
single bond radii: r "132 pm; r "150 pm (24)). The
2
*
."
The projection of Ti Pb along the hexagonal c axis is Ti}Ti contacts of 289.5 and 315 pm are inconspicuous as
shown in Fig. 1, emphasizing the homonuclear interactions. well. Elemental titanium crystallizes in the hexagonal closed
ꢅ
ꢂꢆꢇ
The structure of Ti Pb can be described based on the packing (Mg type) with interatomic distances of 289 and
ꢅ
ꢂꢆꢇ
homonuclear interactions as follows. The Pb1 atoms, form- 295 pm, and linear Ti}Ti chains with di!erent interatomic
ing linear chains along the c axis, are surrounded by six separations were found in (Zr, Ti)Sb (d"284 pm (25)),
chains of trigonal Pb2-centered Pb3 prisms. All of these Ti Sn (d"298 pm (12)), and TiSb (d"315 pm).
ꢅ
ꢀ
ꢄ
interactions are presumably weak with distances between
All of the Ti}Ti distances named above were calculated to
3
57 and 374 pm (dashed lines in Fig. 1), except for the short be of bonding nature (12, 25). The character of the longer
Pb1}Pb1 bond within the linear chain of 289.5 pm. Inter- Pb}Pb interactions in Ti Pb of 357}374 pm is question-
ꢅ
ꢂꢆꢇ
woven with the Pb network is a Ti network with interatomic able. These distances may be compared to the bonds in
distances of 289.5 pm in the linear Ti1 chain, running paral- elemental lead (350 pm in the cubic face-centered packing),
lel to [001], and of 315 pm for the Ti1}Ti2 interactions being much longer than typical Pb}Pb single bonds. Note
(solid lines in Fig. 1). (see Table 3.)
that lead is more electronegative than titanium on any
Alternatively, the structure can be regarded as an inter- electronegativity scale; e.g., the Allred}Rochow elec-
growth of Ti1Pb octahedra, which are face-condensed to tronegativities are 1.32 for Ti and 1.55 for Pb (Pauling, 1.54
ꢅ
linear chains parallel to [001], and bi-capped Ti2Pb penta- vs 2.33). The Ti atoms therefore will reduce the Pb atoms to
ꢃ
gons, which are edge-condensed to form chains parallel to some extent, so that one should consider Pb}Pb single
[
001]. The two Pb caps of every single Ti2Pb pentagon are bonds of negatively charged Pb atoms. Examples may be
ꢃ
found among the Zintl phases, including 310 pm in Pbꢂ\
ꢂ
tetrahedra in KPb (26) and 313 pm in in"nite zigzag Pbꢀ\
chains in BaPb (27). These distances are considerably longer
TABLE 3
Selected Interatomic Distances of Ti Pb
6
4.8
(by more than 7%) than the shortest Pb}Pb bond observed
here (289.5 pm), which may be compared to the bond in the
Ti1}Pb3
287.27(3)
289.51(3)
307.40(2)
314.7(2)
4;
2;
2;
4;
Ti2}Pb2
}Pb1
287.1(2)
293.4(2)
297.3(2)
298.16(6)
314.7(2)
385.9(2)
1;
2;
2;
2;
4;
4;
slightly de"cient linear Pb chain in Zr Pb
(10). Therein,
}
}
}
Ti1
Pb2
Ti2
ꢃ
ꢂ\V
}Pb3
}Pb3
the Pb}Pb distance increases with increasing Pb content,
i.e., from 299.6 pm with a 87% Pb occupancy to 300.5 pm
with a 94% Pb occupancy.
}
Ti1
Pb1}Pb1
289.51(3)
293.4(2)
357.12(4)
2;
6;
6;
}Ti2
Band structure calculations of linear chains comprising
late main group elements (like Sn, Pb, and Sb) have in-
dicated the ideal electron count being seven electrons per
}
}
Ti2
Pb3
Pb3}Ti1
287.27(3)
297.3(2)
298.16(7)
357.12(4)
361.05(3)
373.78(5)
4;
2;
2;
2;
2;
2;
}
Ti2
Pb2}Ti2
287.1(3)
307.40(2)
361.05(3)
3;
6;
6;
}Ti2
}Pb1
}Pb2
atom, i.e., a bond order of ꢈ (8, 25, 28, 29). It is concluded
ꢀ
}
}
Ti1
Pb3
that the extraordinary shortness of the interatomic distan-
ces in the Pb chain in Ti Pb (i.e., matrix e!ects) is respon-
}
Pb3
ꢅ
ꢂꢆꢇ
sible for the defects, re#ected in the 82.4(7)% occupancy of

Pb}Pb BONDS IN Ti Pb
ꢂꢆꢇ
137
ꢅ
FIG. 3. (left) DOS curves of Ti Pb ; (right) cumulated Ti}Pb COHP
ꢅ
ꢃ
curves.
the Fermi level, i.e., increasing the number of valence elec-
trons, would further strengthen the Ti}Pb bonds by "lling
more bonding states. Note that bonding interactions exhibit
negative COHP values by de"nition (30), in contrast to the
crystal orbital overlap populations (COOPs (31)).
FIG. 2. Coordination spheres of the "ve crystallographically di!erent
atom sites. Central atoms, from top left to bottom right are: Ti1, Ti2, Pb1,
Pb2, and Pb3.
The COHPs of the cumulated homonuclear interactions
that Pb site (Pb1 in Table 2). Accordingly, the high displace- are shown in Fig. 4. As for the Ti}Pb interactions, no
ment parameter along the chain direction ; (Pb1) indi- antibonding Ti}Ti states occur below the Fermi level. The
ꢄꢄ
cates the tendency of the Pb1 atoms shifting away from one short Ti}Ti bond (289.5 pm) is almost twice as strong as the
another toward the voids, which does not lower the sym- longer bond (315 pm), which is re#ected in the integrated
metry in the averaged structure as determined by the X-ray COHP values of !1.52 vs !0.87 eV per bond. Calcu-
investigation. No anomalies are to be expected among the lations of a structure model with equally short Ti}Ti distan-
other representatives of the a-Ti Sn type, for therein, the ces reveal this being solely due to the di!erent lengths, which
ꢅ
ꢃ
interatomic distances in the linear chains are not unusual come from optimized Ti}Pb bond lengths. However, as the
because of the smaller sizes of the main group atoms Ga and
Sn, respectively.
Electronic Structure
The calculated densities of states (DOS) and Ti}Pb crys-
tal orbital Hamiltonian populations (COHP (30)), cumulat-
ed over all Ti}Pb bonds per unit cell, of the structure model
Ti Pb are shown in Fig. 3. The DOS curve is typical for
ꢅ
ꢃ
metallic intermetallic compounds. A signi"cant number of
states are "lled at the Fermi level E , which consist mainly
$
of Ti-based orbitals. The contributions of the more elec-
tronegative main group element Pb to the conduction band
are concentrated at lower energies, but still present at and
above the Fermi level. The Ti contributions at these ener-
gies, i.e., below !3 eV, indicate covalent mixing. These
general features are comparable to those of the densities of
states of the stannides and antimonides (see, e.g., (8, 12, 25)).
Averaged over the "rst Brillouin zone, only bonding
Ti}Pb interactions are "lled up to the Fermi level. Raising
FIG. 4. (left) Cumulated Ti}Ti and (right) Pb}Pb COHP curves.

1
38
HOLGER KLEINKE
3. P. Kaiser and W. Jeitschko, J. Solid State Chem. 124, 346 (1996).
longer Ti}Ti bond occurs twice as often per unit cell, the two
di!erent Ti}Ti COHP curves are most similar after cumu-
lating over the whole unit cell.
On the other hand, antibonding Pb}Pb states are "lled
starting at !2 eV. In the case of the short bond of
2
antibonding states, whereas the ratio of "lled bonding states
to "lled antibonding states is almost equal in the longer
interactions (357}374 pm). Their integrated COHPs range
from !0.10 to !0.06 eV, indicating weak bonding charac-
ter, which is about 10% of the short bond (!1.04 eV).
4
. K. D. Myers, S. L. Bud'ko, I. R. Fisher, Z. Islam, H. Kleinke,
A. H. Lacerda, and P. C. Can"eld, J. Magn. Magn. Mater. 205, 27
(
1999).
. R. A. Logan and C. D. Thurmond, J. Electrochem. Soc. 119, 1727
1972).
5
(
89.5 pm, the "lled bonding states outweigh by far the
6. X. Yao and H. F. Franzen, J. ¸ess-Common Met. 142, L27 (1988).
7
. H. Kleinke and H. F. Franzen, Angew. Chem. Int. Ed. Engl. 35, 1934
1996).
(
8
9
. H. Kleinke, Chem. Soc. Rev. 29, 411 (2000).
. H. Nowotny and J. Pesl, Monatsh. Chem. 82, 344 (1951).
1
0. Y.-U. Kwon and J. D. Corbett, J. Alloys Compd. 190, 219 (1993).
11. H. Nowotny and H. Schachner, Monatsh. Chem. 84, 169 (1953).
1
1
1
1
2. H. Kleinke, M. Waldeck, and P. Gu
K tlich, Chem. Mater. 12, 2219
(2000).
SUMMARY
3. J. H. N. van Vlucht, H. A. C. M. Bruning, H. C. Donkersloot, and
A. H. Gomes de Mesquita, Philips Res. Rep. 19, 407 (1964).
4. C. Kuper, W. Peng, A. Pisch, F. Goesmann, and R. Schmid-Fetzer,
Z. Metallk. 89, 855 (1998).
The new metallic compound Ti Pb
has been un-
ꢅ
ꢂꢆꢇ
covered and structurally characterized. Its structure (a-
Ti Sn type) comprises*in addition to the dominating het-
eronuclear Ti}Pb bonds*bonding homonuclear interac-
tions of both kind, namely Ti}Ti as well as Pb}Pb bonds.
The most striking feature of the crystal structure is the
5. G. M. Sheldrick, &&SHELXL-97.'' Universita
997.
6. O. K. Andersen, Phys. Rev. B 12, 3060 (1975).
K t G oK ttingen, Germany,
ꢅ
ꢃ
1
1
1
7. H. L. Skriver, &&The LMTO Method.'' Springer-Verlag, Berlin/New
York, 1984.
presence of the parallel running equidistant linear Ti and Pb 18. U. van Barth and L. Hedin, J. Phys. C 4, 2064 (1971).
1
9. P. E. Blo
K chl, O. Jepsen, and O. K. Andersen, Phys. Rev. B 49, 16,223
chains. The latter exhibits Pb}Pb bonds being shorter than
a single bond, causing de"ciencies and enlarged thermal
parameters within the linear Pb chain.
(1994).
20. V. Y. Markiv and A. I. Skripta, Russ. Metall. 196 (1986).
21. V. Y. Markiv and N. N. Belyavina, Russ. Metall. 204 (1986).
22. F. S. Kreidenko, V. Y. Markiv, and E. M. Sokolovskaya, Mosc. ;niv.
Chem. Bull. 29, 83 (1974).
ACKNOWLEDGMENT
2
2
3. S. V. Popova and V. G. Putro, Inorg. Mater. 15, 947 (1979).
4. L. Pauling, &&The Nature of the Chemical Bond,'' 3rd ed. Cornell Univ.
Press, Ithaca, NY, 1948.
Financial support from the Natural Sciences and Engineering Research
Council of Canada is appreciated.
2
2
2
5. H. Kleinke, J. Am. Chem. Soc. 122, 853 (2000).
6. C. Ro
7. D. E. Sands, D. H. Woods, and W. J. Ramsey, Acta Crystallogr. 17, 986
1964).
K hr, Z. Naturforsch. 50b, 802 (1995).
REFERENCES
(
2
2
8. H. Kleinke, Chem. Commun. (Cambridge) 2219 (1998).
9. G. A. Papoian and R. Ho!mann, Angew. Chem. Int. Ed. 39, 2408
(
1
. D. Elwell, High-temperature Solution Growth, in &&Crystal Growth''
B. R. Pamplin, Ed.), 2nd ed. Pergamon Press, Oxford, 1980, and
references cited therein.
. X. Z. Chen, S. Sportouch, B. Sieve, P. Brazis, C. R. Kannewurf,
J. A. Cowen, R. Patschke, and M. G. Kanatzidis, Chem. Mater. 10, 3202
(
2000).
0. R. Dronskowski and P. Blo
1. T. Hughbanks and R. Ho!mann, J. Am. Chem. Soc. 105, 3528
1983).
3
3
K chl, J. Phys. Chem. 97, 8617 (1993).
2
(
(1998).