Unusual Bonding in Ternary Nitrides:
Preparation, Structure and Properties of Ce2MnN3.
Rainer Niewa3, Grigori V. Vajenine3, Francis J. DiSalvo*,a,
Haihua Luob, William B. Yelonb
a Department of Chemistry, Cornell University, Ithaca, NY 14853-1301, USA
b University of Missouri Research Reactor, Columbia, MO 65211, USA
Z. Naturforsch. 53 b, 63-74 (1998); received September 17, 1997
Ternary Nitride, Crystal Structure, Magnetic Susceptibility, Electrical Resistivity, Extended
Hiickel Method
CeiMnNj was prepared by reaction of cerium nitride and manganese with nitrogen gas
at 900 °C. It crystallizes isotypic to AC2 MN 3 (Ac = U, Th; M = Cr, Mn) and Ce^CrN^,
space group Immm (No. 71), a = 3.74994(6) A, b = 3.44450(6) A and c = 12.4601(2) A. The
manganese atoms are coordinated in a nearly square planar fashion by four nitrogen atoms.
These corner-connected MnN* units form infinite J. [MnN2 N 2 / 2 ] chains, which run parallel
to each other along the crystallographic a-axis, forming the motif of hexagonal rod packing.
Cerium atoms connect the chains into a three-dimensional network. The results of measurements
of the magnetic susceptibility, as well as of the electrical resistivity suggest metallic behavior.
Electronic effects leading to shorter bonds between manganese and bridging nitrogen atoms than
between manganese and terminal nitrogen atoms in the J. [MnN2 N 2 / 2 ] chains were investigated
through extended Hiickel and LMTO band structure calculations. Issues pertaining to stability
of this and some other nitridometallate structures are discussed.
Introduction
During the last decade the search for and charac­
terization of ternary and higher nitrides has grown
considerably. This has led to the discovery of many
new compounds, making it easy to imagine that ni­
tride chemistry can provide compounds with struc­
tures and properties as diverse as the chemistry of
oxides or sulfides, as well as some currently unique
features [ 1 -5].
The new nitrides include mainly ternaries of al­
kali and alkaline earth metals with main group or
transition metals. In contrast the number of ternary
nitrides of rare earth elements is still small. The
largest such group is the nitrides of silicon with the
compositions LnS^Ns (Ln = La, Ce, Pr, Nd) [ 6 - 8 ],
L ^SiöN n (Ln = La, Ce, Pr, Nd, Sm) [8 , 9] and
EaYbSi4 N 7 (Ea = Sr, Ba) [10, 11]. In these and other
compounds of main group elements, LiEu4 (BN 2) 3
[ 12] and La2 AIN3 [13], the rare earth metals serve as
electropositive elements, which donate electrons to
nitridometallate anions. In contrast, in Li2 CeN 2 [14,
15] and BaCeN 2 [16] the cerium more likely forms
* Reprint requests to F. J. DiSalvo.
0939-5075/98/0100-0063 $ 06.00
nitridocerate ions, which accept electrons from the
lithium or barium atoms, respectively. Also there
have been reported subnitrides with the perovskite
structure, Ln^AlN (Ln = La, Ce, Pr, Nd, Sm) [17,
18] and Nd3MN (M = Ga, In, Tl, Sn, Pb) [18]. Cal­
cium nitride forms an extensive solid solution with
lanthanum nitride [19].
Currently only a few transition metal nitrides
of lanthanides and actinides are known and wellinvestigated. The older investigations were stimu­
lated by research activities related to the progress
of nuclear energy studies, resulting in UVN 2 [2 0 ]
(UMoC2 -type structure [21]) and AC2 MN 3 (Ac =
U, Th; M = Cr, Mn) [22]. Later ThTaN3 (perovskite
structure) was reported [23]. The interest in mag­
netic properties of intermetallics of iron and rare
earth elements resulted in L ^F enN ß with nitrogen
atoms in interstitial positions of the host compounds
Ln2 Fen [24].
In 1981 Marchand and Lemarchand reported the
formation of “La^C^i N 2 3 ” [25], which recently was
shown to be La3 Crio-xN n by Broil and Jeitschko
[26]. The same authors obtained and investigated
Ln3 Crio_xNn (Ln = La, Ce, Pr) and Ce 2 CrN 3 [26]
(U2 CrN3-type structure). The oxidation states of
the latter compound were discussed in terms of
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64
C e^ [Cr!N 3 ] or C e^tC r 111 N 3 ]. Unfortunately the au­
thors were not able to prepare single-phase samples
of Ce 2 CrN 3 , hence no investigations of magnetic
or electrical properties were attempted. Here we re­
port and discuss preparation, magnetic susceptibil­
ity, electrical resistivity, and electronic structure of
Ce2 MnN 3 , a ternary nitride isotypic with Ce2 CrN 3 .
Experimental and Theoretical
Preparation
All manipulations were carried out in an argon filled
glove box. Cerium metal (Cerac Inc., 99.9 %) was sepa­
rated from the oxide coating by melting it under vacuum
and allowing it to drip through a hole at the bottom of a
tantalum crucible in a water-cooled copper cup. This op­
eration also divides the cerium lumps into smaller pieces.
The latter were placed into an aluminum oxide boat and
heated with flowing ammonia (Matheson Gas Products
Inc.) in a quartz tube lined with tantalum foil at 750 °C.
The product is golden-yellow CeN. To prevent forma­
tion of oxide impurities, the ammonia was dried over
sodium and passed over previously prepared cerium ni­
tride powder at the reaction temperature before it reached
the reactant.
Cerium nitride and manganese powder (Fisher Scien­
tific Comp., 99.94 %) were ground separately to fine pow­
ders before weighing out stoichiometric amounts, which
were then mixed and ground together. This mixture was
cold pressed into a pellet at about 5000 psi and placed in
an aluminum oxide boat. The reaction was carried out in a
quartz tube lined with tantalum foil at 900 °C under a back
pressure of nitrogen of one bar. The nitrogen (Empire Airgas Inc., high purity grade) was purified by passing over
titanium wire at 800 °C before being introduced into the
quartz tube. In addition, it had to pass over fine powder of
CeN at 900 °C before reaching the reaction mixture. The
product of this operation was grayish-green; it still con­
tained CeN and binary manganese nitrides. Consequently
it was ground up to a fine powder again, pressed into a
pellet, and reacted under the above-mentioned conditions.
Full conversion was achieved by repeating this operation
one more time. A higher reaction temperature seems to
lead to a somewhat faster formation of the Ce2 MnN-?, un­
til the manganese sublimes out of the pellet, leaving pure
CeN.
Single-phase Ce2 MnN 3 is a velvet-black powder,
which reacts very slowly with air. This reaction is in­
dicated by a change of color to brown after a two-week
exposure to air. The reaction products are CeC>2 and M n02
as identified by X-ray powder diffraction. Cerium man­
ganese nitrides of other compositions could not be ob­
tained, neither by reacting mixtures with different start­
R. Niewa et al. ■Unusual Bonding in Ternary Nitrides
ing ratios, nor by preparation at different temperatures.
We were also not able to prepare any lanthanum man­
ganese nitrides under the above-mentioned reaction con­
ditions. Reactions of CeN and LaN with manganese give
Ce2 MnN3 with only some two atomic percent of cerium
atoms replaced by lanthanum.
Structure refinement
The X-ray powder diffraction diagram of Ce 2 MnN3
was taken on a Scintag XDS 2000 diffractometer with
CuKa-radiation. Constant wave length neutron diffrac­
tion was performed using the position sensitive detec­
tor diffractometer NPD-PDS at the Research Reactor of
the University of Missouri, Columbia, in the range of 5°
to 102.2° 26. The diagrams can be indexed with an orthorhombic unit cell (a = 3.74994(6), b = 3.44450(6) and
c = 12.4601(2) A). Both independent refinements of the
structure yielded essentially identical results, however a
joint refinement of the structure based on both patterns
was also performed. It was carried out using GSAS [27]
'
1
1
1
1
1
1
1
1
20
30
40
50
60
70
80
90
Diffraction angle 20
10
20
30
40
50
60
70
80
90
100
Diffraction angle 29
Fig. 1. a) X-ray powder diffraction diagram of Ce2 MnN3;
b) neutron powder diffraction diagram of Ce2 MnN3. The
measured data are shown as crosses, the continued line
represents the calculated profile and the lower curve
shows the difference between the calculated and observed
intensities. The marks below the data indicate the posi­
tions of reflections.
R. Niewa et al. • Unusual Bonding in Ternary Nitrides
Table I. Profile refinement parameters for Ce 2 MnN3 (Neu­
tron data / X-ray data).
Space group, Z
a[A ]
b [A]
*[A]
Volume [A ]
Calculated density [g cm-3 ]
Radiation
2(9 Range [deg]
Step size [deg]
Number of
- profile points measured
- parameters refined
- profile parameters
- structural parameters
Reflections
Absorption coefficients
Program used
Reliability values:
wRp[%]
Rp [%]
Total:
wRp [%]
Rv [%]
X
Immm (No. 71), 2
3.74994(6)
3.44450(6)
12.4601(2)
160.943(3)
7.787
1.7636 Ä /C u K a
5 - 1 0 2 .2 /2 0 -9 5
0.05/0.015
1943/5000
33
5 /8
17
4 6 / 122 (K a, + K a 2)
-/0 .0 6 1 7 5 , 0.67575 [28]
GSAS [27]
10.14/6.36
7.15/5.12
65
Magnetic susceptibility
The magnetic susceptibility \ of CezMnN^ at an ap­
proximate field of 11 kG was measured on a Faraday
balance under a pressure of 150 mbars of helium in the
temperature range of 4 to 300 K. The magnetic suscepti­
bility of the sample shows no dependence on the applied
magnetic field at 300 and 4.2 K, indicating absence of
ferromagnetic impurities. The data was fit to \(T ) = \o +
•
This resulted in a positive temperature independent
term \o of 4.05(2) • 10~7 emu/g, C = 9.4 • 10~5 emuK/g,
0 = 7.2 K, giving a /xeff = 0.53 p B- This is too small to
be associated with Ce3+ (f1) moments (pef{ = 2.5 p b ) or
manganese moments (M nl+ (hs), p e{{ = 4.9 pB, M nl+ (Is),
Pen = 0 pb , Mn2+ (hs), p eff = 5.9 p B, Mn2+ (Is), p ef{ =
1.7 pb , Mn3+ (hs), p ef{ = 4.9 p B, Mn3+ (Is), p eff = 0 pb ).
We therefore associate this small “Curie tail” with im­
purities, or with defects which produce moments in their
near neighbor environment.
Electrical resistivity
7.46
5.98
2.93
starting with the positional parameters of Ce2 CrN 3 [26]
in the space group Immm (No. 71) and with manganese
on the site of chromium. For the X-ray diffraction dia­
gram a pseudo-Voigt function, fixed background, and a
cosines row with nine terms were employed in profile fit­
ting. Due to considerable absorption of both cerium and
manganese, an absorption correction (surface roughness
after Suortti [28]) was applied. The profile of the neutron
diffraction diagram was fitted with a Gaussian function,
fixed background and seven parameters in the cosines row.
Due to little differences in the resulting unit cell parame­
ters from both experiments it was necessary to refine the
neutron wave length resulting in A = 1.7636 A. All atoms
were refined with anisotropic thermal displacement fac­
tors. Fig. 1 shows both powder diffraction diagrams, the
calculated profiles, and the differences between the cal­
culated and observed intensities. For further information
see Tables I and II.
In order to perform a four-point electrical resistivity
measurement on CeoMnN.s, 0.677 g of a single-phase
sample were pressed to a pellet, wrapped in tantalum foil
and sintered in a sealed quartz tube at 750 °C for four days
Temperature (K)
Fig. 2. Electrical resistivity (in 10~3 Qcm) of CdM nNs
as a function of temperature (in K).
Table II. Strucural refinement parameters for Ce2 MnN 3 .
Atom
Site
X
y
z
100-Uiso
100-Un
100-U22
IOOU33
Ce
Mn
N (l)
N(2)
4i
2a
2b
4i
0
0
0
0
0
0
'/ 2
0
0.35332(9)
0
'/2
0.1638(2)
2.4
2.7
2.1
1.9
1.91(6)
2.2(2)
2.3(2)
1.3(1)
2.56(6)
2.7(2)
2.8(3)
1.6(2)
2.69(6)
3.4(2)
1.3(3)
2.8(2)
For all sites: U12 = U13 = U23 = 0.
R. Niewa et al. ■Unusual Bonding in Ternary Nitrides
66
Table III. Slater-type orbital energies and exponents.
Atom
Orbital
H ü, eV
c.
N
2s
2p
3d
4s
4p
3d
4s
4p
5d
6s
6p
-26.0
-13.4
-11.22
-8.66
-5.24
-11.67
-9.75
-5.89
-6.43
-4.91
-4.97
1.950
1.950
4.95
1.7
1.7
5.15
1.8
1.8
2.399
1.398
1.398
Cr
Mn
Ce
(diameter: 8.9 mm, thickness: 2.9 mm). Copper contacts
were attached with silver epoxy (Epo-tek HZOE, Epoxy
Technology Inc.). The sample was electrically isolated
by a plate of sapphire and mounted on a copper plate to
provide an isothermal surface. The apparatus was filled
with approximately 50 mbars of helium gas. The tem­
perature change (< 1 K/min) was achieved by slowly
lowering the apparatus into liquid helium. The resistivity
decreases from about 1.0 • 10~? Qcm at 270 K to about
1.8 • 10~4 Qcm at 4 K (Fig. 2).
Electronic structure calculations
All extended Hiickel [29 - 33] calculations were car­
ried out using the YAeHMOP program [34], Slater-type
atomic orbitals with energies and exponents given in Ta­
ble III (double-zeta expansion with coefficients ci and c2
was used for the Cr 3d, Mn 3d and Ce 5d orbitals) com­
prised the basis set. The parameters for nitrogen [30],
chromium [35], and manganese [35] were taken from
previous work. The cerium parameters were estimated
according to the procedure of Ortiz and Hoffmann [36].
The modified Wolfsberg-Helmholz expression [37] was
employed to calculate the off-diagonal Hamiltonian ma­
trix elements. Average properties of the one-dimensional
^ [MN 2 N 2 / 2 ] chains (M = Cr, Mn) were computed with
a 100 k-point set. The k-point sets for the calculations on
arrays of the ^ [MN2N2/ 2 ] chains and on bulk Ce2 MN3
structures were constructed according to Ramirez and
Böhm [38, 39].
The Linear Muffin-Tin Orbital (LMTO) method
[40, 41] in the Tight-Binding implementation with
Atomic Sphere Approximation (TB-LMTO-ASA) [42]
was used to compute the electronic structures of CeiCrNj
and Ce 2 MnN 3 with a 294 k-point set. Calculations on
NaCl-like CeN were carried out with the Ce-N bond
length of 2.51 A [43] and with a 145 k-point set.
C2
C|
Cl
1.80
0.5058
0.6747
1.90
0.5311
0.6479
1.168
0.7477
0.3891
Results and Discussion
Structure and properties
As mentioned in the experimental part, Ce2 MnN 3
can be obtained from the reaction of cerium nitride
with manganese and nitrogen gas at 900 °C within
several hours. In contrast, a mixture of cerium
nitride and chromium under the same conditions
forms binary chromium nitride, with cerium ni­
tride left unreacted. A solid-state reaction of these
two binary nitrides takes several weeks to form a
small amount of Ce 2 CrN 3 with most CeN and CrN
left unreacted. When the temperature is increased
considerably, CesCrio-xNn is formed in a much
faster reaction. This difference in behavior between
chromium and manganese is probably due to the
refractory nature of binary chromium nitrides, re­
sulting in small diffusion coefficients of chromium
and nitrogen in these compounds. In contrast, atoms
seem to have much higher mobility in the metallic
nitrides M ^ N and Mo^N.
Ce2 MnN 3 crystallizes isotypic to Ce 2 CrN 3 [26]
and the earlier reported AC2 MN 3 (Ac = Th, U; M =
Cr, Mn) [22] (see Fig. 3). The manganese atoms
are coordinated in a nearly square planar fashion
by nitrogen atoms. These MnN 4 units are comer
connected into infinite ^[M nN 2 N 2 / 2 ] chains with
an angle Z(Mn-N(l)-Mn) of 180° at the bridging
nitrogen atom. The chains are stacked together in
the motif of hexagonal rod packing. Fig. 3 shows
a view of the structure along the 0 -axis. The nitro­
gen atoms have only slightly distorted octahedral
surroundings of four cerium and two manganese
or five cerium and one manganese atoms. In most
ternary nitrides the coordination number of nitro-
R. Niewa et al. • Unusual Bonding in Ternary Nitrides
Table IV. Interatomic distances [A] and angles [°] for
Ce2MnN3.
Distances:
Mn - N (l)
N(2)
Ce
Ce - N (l)
N(2)
2x
2x
8x
2x
4x
4x
Mn
Ce
N (l) - Mn
Ce
N(2) - Mn
Ce
2x
4x
4x
Angles:
N (l) - Mn - N (l)
N(2)
N(2) - Mn - N(2)
Mn - N (l) - Mn
O
O
o O
1.87497(3) (bridge)
2.041(3) (terminal)
3.1340(6)
2.5112(8)
2.362(3)
2.5548(2)
3.1340(6)
> 3.44450(6)
1.87497(3)
2.5112(8)
2.041(3)
2.362(3)
2.5548(2)
180
2x 90
180
180
O O o (^ g -Q -< C o o O
cQ o
o
O
Fig. 3. View into the structure of CeaMnNi along the
a-axis. Distances are given in A.
gen is also six [1 - 5]. Further data on distances and
angles are given in Table IV.
An interesting structural feature of the cerium
compounds in this structure type is the difference in
the bond lengths between the two inequivalent tran­
sition metal to nitrogen bonds. Contrary to usual
expectations for terminal and bridging ligands, the
bonds to the terminal nitrogen atoms are about
0.2 A longer than the bonds to the bridging nitro­
gen atoms. The Mn-Nteminai bond length of 2.04 A is
similar to Mn-N single bond lengths of about 2.01 A
known from organometallic manganese compounds
with N-donor ligands. Triple bonds between man­
ganese and nitrogen are known to be around 1.51 A
[44,45]. Hence the Mn-Nbridge bond length of 1. 8 8 A
is somewhat longer than that expected for a double
bond. Manganese to nitrogen distances in isolated
67
trigonal planar [MnNß] 6 ions, found in several al­
kaline earth compounds, range from 1.74 to 1.80 A
[46 - 48],
The a and c unit cell parameters of Ce2 MnN 3 de­
crease by about 1 % compared to that of Ce 2 CrN 3
due to the slightly shorter Mn-N bond lengths
within the chains. To conserve the distances be­
tween cerium and nitrogen atoms, the b-axis conse­
quently increases by about 1 %.
The cerium surroundings in Ce 2 MnN 3 and
Ce 2 CrN 3 show one shorter distance to a terminal
nitrogen atom of about 2.36 A, compared to the
remaining Ce-N distances of 2.53 A, which are
quite similar to that in CeN (2.51 A) [43], CeSiC^N
(2.55 Ä) [49] and Li2 CeN 2 (2.53 A) [15]. BaCeN 2
is an intermediate case with d(Ce-N) = 2.42 A [16].
The sum of the covalent radii of cerium and nitro­
gen is 2.40 A [50], hence the distance of 2.36 A
indicates a bonding interaction between cerium and
nitrogen in the single bond range.
It is remarkable that Ce2 CrN 3 and Ce 2 MnN 3 do
not form rocksalt type (super-) structures, while the
binaries CeN and CrN do, as well as MnöNs and
Mn3 N2 (defect rocksalt type structures, no MnN
known). The ionic radii of Ce4+ and M+ are not
that different: r(Ce3+) = 1.14 Ä (CN = 8 ), r(Ce4+) =
0.87 A, r(Cr3+) = 0.62 A, rtCr2*) = 0.73 A, r(Mn3+) =
0.58 A, r(Mn2+) = 0.67 A (all CN = 6 ) [51]. Hence it
is interesting to point out that parts of the structure of
the title compound resemble motifs of the rocksalt
structure: the cerium atoms are surrounded by five
terminal (with respect to the nitridometallate chains)
nitrogen atoms forming angles Z(N-Ce-N) close to
90° and 180°. The nitridometallate chains can also
be viewed as one-dimensional infinite fragments of
the rocksalt structure.
The magnetic susceptibility and electrical resis­
tivity measurements clearly indicate that Ce2 MnN 3
is a metal with no intrinsic local moments. The
order of magnitude of the electrical resistivity at
different temperatures is in the range of that of
manganese metal and rare earth intermetallic com­
pounds [51]. We expect similar metallic behavior
for black Ce2 CrN 3 .
Electronic structure calculations
Extended Hückel and L M T O calculations were
employed to understand why the M-Nbridge bonds
are about 0 . 2 A shorter than the M - N terminai bonds
68
in Ce 2 MN 3 (M = Cr, Mn). In this analysis the corre­
sponding uranium and thorium compounds are not
considered, because we believe that further struc­
tural analysis is necessary in order to accurately de­
termine the M-Nterminai bond lengths (the M-Nbridge
bond lengths in these compounds are known more
reliably because they are directly related to the a
cell parameter).
There are three plausible assignments of oxida­
tion states for the metals based on the fact that
cerium is typically trivalent or tetravalent and pro­
vided that the nitrogen centers are formally N3 -:
Ce^vMIN3, Ce^IIMIIIN3, or CemCeIVMnN 3 . The
questions of oxidation state assignment and of the
nature of the only valence electron in Ce3+ are not
new in cerium chemistry. Metallic CeN has kept
both physicists and chemists arguing for many years
about its electronic structure. CeN is quite different
from the other cerium pnictides and most other rare
earth compounds with f-electrons because its only
valence electron cannot be described as fully lo­
calized in an f orbital. Instead, unit cell parameter
measurements [52, 53], magnetic [54] and XPS [55,
56] data suggest that Ce in CeN is closer to tetrava­
lent, with its electron having substantial d-character
in addition to f-character and strongly delocalized.
This delocalization was also confirmed for CeN in
a recent theoretical study of cerium pnictides [57].
Our LMTO calculations on CeN also suggest strong
d-character for the delocalized Ce electron.
We expect to face similar problems when assign­
ing the Ce oxidation state in Ce2 MN 3 . As will be
shown later in the discussion, chromium and man­
ganese are much more likely to have the + 1 oxi­
dation state, corresponding to d5 and d6 configura­
tions, respectively. Also, presence of Ce f-electrons
is likely to be accompanied by a magnetic moment
on Ce, which was not observed experimentally. Our
LMTO calculations suggest the higher formal ox­
idation state for Ce: the empty Ce d-bands were
found about 6 eV above the Fermi level, while the
mostly empty Ce f-bands lie in the 2 eV energy
window immediately above the Fermi level. One
band, mostly f in character, per two Ce centers is
partially occupied by approximately 0 . 2 electrons
in the Mn case, suggesting the Ce^ 9+Mn' 2+N 3 for­
malism. Therefore, the C e^M 1^ assignment was
chosen for the following discussion.
This conclusion contradicts the knowledge on rel­
ative stability of cerium and manganese cations in an
R. Niewa et al. • Unusual Bonding in Ternary Nitrides
aqueous solution. The E° values for the Ce:}q/Ce3q
and M n]q/M n^ couples are +1.61 V and +0.902
V, respectively. Thus M n ^ cannot oxidize Ce3q to
C e£; in other words C e ^ will readily oxidize M n^
to Mn3q. Assuming that Mn* is approximately as
good a reducing agent as M n^, Mn+q and Ce:jq can­
not co-exist in an aqueous solution. They appear
to co-exist, however, in Ce 2 MnN3 , suggesting that
coordination of cerium and manganese in this com­
pound, very different from coordination of Mn+q and
Ce**, reverses the relative stability of the cations ob­
served in solution chemistry.
Analysis of the full three-dimensional Ce 2 MN 3
structure would be somewhat complicated, as well
as not very informative. For the sake of simplifica­
tion, in the following the bonding between cerium
and nitrogen atoms is viewed as ionic, and between
the transition metal and nitrogen atoms as polar co­
valent. This assumption, together with the interest in
M-N bond length differences, leads to considering
bonding in the isolated ^ [M'N 2 N 2 / 2 8~] chains. The
Ce-N interactions and direct interactions between
the chains were found not to affect the following dis­
cussion within the extended Hückel approximation.
We chose M = Mn for our analysis, although the
chromium case yields essentially identical results.
The bonding in an idealized (D4 h symmetry),
isolated square planar MnN 4 unit has to be ex­
amined first. For now we will not specify the fill­
ing of molecular orbitals; rather the attention will
be focused on the orbitals themselves. The coordi­
nate system is chosen differently from Fig. 3. The
molecule now lies in the xy plane - the standard
orientation for square planar geometry. We separate
the Mn-N interactions into a and ir with respect
to the Mn-N bonds. Fig. 4 schematically depicts
the Mn-N cr-interactions. Four Mn-N cr-bonding or­
bitals are localized mainly on the nitrogen atoms.
The five cr-antibonding orbitals have heavy man­
ganese contributions (d-2 , dx2_y2, s, and pt>>,)- The
mainly Mn d ,2 orbital is only weakly cr-antibonding.
Similarly, there are four Mn-N 7r-bonding orbitals,
mainly N 2p in character, and four 7r-antibonding
orbitals, which are mostly Mn dvv, dxz, dvz, and pz.
These are drawn out in Fig. 5. The overall interac­
tion diagram for an MnN 4 unit with all Mn-N bond
lengths set to 1.96 A (the average of the experi­
mentally observed Mn-N distances in Ce2 MnN 3 ) is
shown in Fig. 6 . Here are more orbitals than in Figs.
4 and 5 combined; these “extra” orbitals are nitro-
R. Niewa et al. • Unusual Bonding in Ternary Nitrides
Fig. 4. Schematic interaction diagram for a hypotheti­
cal isolated square planar MnN4 unit with D4 h symmetry
(only Mn-N cr-interactions are shown). The nitrogen hy­
brids pointing toward the central manganese are used to
construct this diagram. Placement of the orbitals on the
energy scale is approximate.
gen lone pairs not participating in Mn-N bonding.
The “four below one” splitting of the Mn d-block is
observed, as expected for square planar coordina­
tion. The oxidation states of - 3 and +1 for nitrogen
and manganese, respectively, correspond to filling
up all of the mainly N 2s and 2p states with 32 elec­
trons (and with that, all a - and 7r-bonding orbitals
are filled) and partial filling of the lower four Mn
d-orbitals (some of which are 7r-antibonding) with
six electrons.
Understanding of the filling of the lower four
d-orbitals is crucial in explaining the observed MnN distances. Hence we concentrate on bands de­
rived from these orbitals when considering bonding
in a one-dimensional ^ [MnN2 N 2 / 2 ] chain. Again
both Mn-Nterminai and Mn-Nbridge distances are set
to 1.96 A. Bands which are mostly dxy, dxz, and
dxz in character are shown in Fig. 7. The dc2 band
acquires some dispersion when the interchain inter­
actions are taken into account. Due to the essentially
Mn-N nonbonding nature of this orbital, however,
69
Fig. 5. Schematic interaction diagram for a hypotheti­
cal isolated square planar MnN4 unit with D4h symmetry
(only Mn-N ^-interactions are shown). Placement of the
orbitals on the energy scale is approximate.
5><D o-55
-
10 -
-
15-
-
20 -
Fig. 6. Full interaction diagram for a hypothetical isolated
square planar MnN4 in D4h symmetry (both a- and ninteractions are included). All Mn-N bond lengths are set
to 1.96 A.
this does not affect the following discussion. The
d .2 band is not plotted in Fig. 7. The correspond­
ing crystal orbitals (infinite analogues of molecular
70
Fig. 7. Band structure for an isolated one-dimensional
^ [MnN2 N 2 / 2 ] chain along the direction in the reciprocal
space parallel to the direction of the chain. The crystal
orbitals corresponding to the dxy, d*z, and dvz bands at
the r and X special points are shown. The filled d .2
band is not plotted. The horizontal dashed line indicates
the position of the Fermi level for six d-electrons (Mn(I)
in ' [MnN2 N 2 / 2 8 -])- All Mn-N bond lengths are set to
1.96 A.
orbitals) for the dxy, dxz, and dvz bands are drawn
at two special points in the Brillouin zone: F (a
crystal orbital has the same phase in neighboring
unit cells) and X (a crystal orbital changes phase
between neighboring unit cells). At the r point
all three bands are Mn-Nbridge 7r-nonbonding, while
both dxy and dyz are M n -N terminai 7r-antibonding. In
contrast, at X the dxy and dxz bands contribute to M nNbridge 7r-antibonding, while the same two bands as
at r (dxv and d>z) are M n-N terminai 7r-antibonding.
In short, the Mn-Nbridge antibonding states are con­
centrated at the top of this four-band block, whereas
the Mn-Nterminai antibonding states are spread more
uniformly between -11.6 and -10.2 eV.
If the manganese centers are viewed as isolated
Mn(I) d 6 ions, one would probably expect a highspin state to be found. After all, the lower four d
bands are contained in a less than 2 eV energy win­
dow. However, the experimentally observed Pauli
paramagnetism suggests that these bands are filled
in a metallic fashion, resulting in no magnetic mo­
ment on manganese.
The Mn-N a - and 7r-bonding states, which are
centered m ostly on the nitrogen atom s with small
contribution from Mn 3d, 4s, and 4p, rem ain filled
R. Niewa et al. • Unusual Bonding in Ternary Nitrides
in ^ [M n N 2 N 2 / 2 8~ ] chains, as in the isolated M n N 4
unit. They are still found in the N 2s and 2p blocks,
below the M n 3d states. Therefore, filling of the d ,2
band will result in small weakening of the M n -N a bonding, while filling of the dxy, d v-, and dyz bands
will cancel the effect of the filled M n -N 7r-bonding
states. The two extreme cases are instructive. If there
were no d-electrons on the M n atoms, both a - and 7rbonding would be at their maximum, corresponding
to double Mn-Nterminai and double Mn-Nbridge bonds.
If all four bands were filled with eight electrons, the
cr-bonding would be slightly reduced and the 7rbonding would be absent, corresponding to single
Mn-Nterminai and single Mn-Nbridge bonds. But when
the number of d-electrons is between zero and eight,
the effects of 7r-antibonding on the Mn-Nbridge and
Mn-Nterminai bonds are different. As it was men­
tioned earlier, the M n -N bridge 7r-antibonding states
are filled last. This suggests that for some electron
counts the Mn-Nbridge 7r-antibonding is weaker than
the Mn-Nterminai 7r-antibonding, resulting in stronger
Mn-Nbridge bonds.
To quantify the M n -N bond strengths, the corre­
sponding crystal orbital overlap population (COOP)
[31, 32] values were calculated. The value of COOP
for a given X -Y bond is made up of positive contri­
butions from filled X -Y bonding orbitals and neg­
ative contributions from filled X -Y antibonding or­
bitals. When the COOP values for two X -Y bonds
are compared, it is important that the bond lengths
are made identical: in the extended Hiickel method
shorter bonds are artificially stronger than the longer
ones. Therefore we chose to model the M n -N bond­
ing in C e 2 M n N 3 by systems with equal M n -N bond
lengths. Fig. 8 shows the COOP values for the M n Nbridge and M n -N terminai as a function of the d elec­
tron count. In agreement with previous discussion,
the M n -N bonds are strongest for the d° and weak­
est for the d 8 configurations. The strengths of the
different M n -N bonds are very similar in both con­
figurations. But the d 3 (equivalent to Cr(I)) and d6
(M n (I)) cases correspond to the largest difference
in the COOP values between the two bond types.
When there are five or six d-electrons on the metal
center, the M n -N terminai 7r-antibonding states are
largely filled, while the Mn-Nbridge 7r-antibonding
states remain essentially unoccupied. In a simpli­
fied bonding picture the M n -N terminai interactions are
best described as single bonds, and the Mn-Nbridge
as double bonds.
R. Niewa et al. ■Unusual Bonding in Ternary Nitrides
71
on a nitrogen atom, which are already involved in
Mn-N 7r-bonding, with four cerium atoms. Thus in
this model there are two electrons responsible for
the shorter Ce-N contact, while there is on aver­
age only one electron corresponding to each of the
longer Ce-N contacts, accounting for the observed
Ce-N bond length difference.
Stability o f nitridom etallates
Fig. 8. C O O P values for the M n - N terminai and M n-Nbridge
bonds as a function of the electron count as computed for
interacting one-dimensional j. [MnN2N 2 / 2 ] chains with
all M n - N bond lengths set to i .96 A.
It is interesting to note that the distribution of
the M n -N 7r-antibonding states in energy is closely
related to the symmetry of the problem. The M n Nterminal interactions are independent of the trans­
lational symmetry imposed on crystal orbitals. In
other words, the dxy and dvz bands are destabi­
lized due to the M n -N terminai 7r-antibonding to the
same extent throughout the Brillouin zone. O n the
other hand, translational symmetry does not allow
for Mn-Nbridge 7r-antibonding interactions to take
place in the dixy and d xz bands at the r point and
in its vicinity - there is simply no nitrogen orbital
that can overlap with these mostly M n d crystal
orbitals. Such interactions occur near the X point,
pushing the bands higher in energy. Therefore the
latter two bands are dispersed in energy, with the
Mn-Nbridge 7r-antibonding states concentrated at the
top. This symmetry analysis thus supports both the
band structure and the distribution of 7r-antibonding
states obtained from our calculations. The overall
shape of the M n d-bands was also confirmed by our
L M T O calculations.
It was mentioned previously that one Ce-N con­
tact (2.36 A) is shorter than the others (2.51 A and
2.55 A). The Ce-N interactions can be viewed simplistically as electrostatic between Ce4+ and filled
nitrogen orbitals left after the Mn-N bond forma­
tion. The shorter Ce-N contact corresponds to an
interaction of the nitrogen lone pair orbital, oppo­
site to the Mn-Nterminai bond, with Ce, one lone pair
orbital per contact. The other two contacts can be
described as interactions of only two filled p-orbitals
For the formation of a given structure or coor­
dination of a transition metal atom in ternary ni­
trides there are two characteristics of the transi­
tion metal that are important: oxidation state and
the number of d-electrons. We begin by surveying
low-dimensional substructures adopted by known
nitrides of electropositive metals and first row tran­
sition metals with partially filled d-block. Some ex­
amples are given below (most of them are shown in
Fig. 9):
1. Six compounds of (RE)2 MN 3 stoichiometry
(RE = U, Th, Ce; M = Cr, Mn) [22, 26, this work]
contain ^ [Cr1^ ^ ^ 8 -] and ^ [Mn1^ ^ ^ 8 -]
chains (here we assume that the uranium and tho­
rium compounds can be described by the same ox­
idation states as the cerium ones - perhaps, an ar­
guable assumption).
2. Isolated linear [Co1^ ] 5- units in LiSr2 CoN 2
[58] and [Co 1 2 5 +N2]4-75- in Sr39 Co 12 N 3 i [59],
Analogous [Ni1^ ] 5- moieties are present in
Ca(Lii_xNix)N [60], Sr(Li,_xN iJN [61], and
Li4 Sr2 (Lii_xN y N 3 [62].
3. One-dimensional ^ [NiIN 2 / 2 2_] chains,
straight in CaNiN [63, 64], bent at some nitro­
gen atoms in SrNiN [65], BaNiN [6 6 ], BagNiöN?
[67], and Li3 Sr3 Ni4 N4. (The last compound con­
tains ^ [NiN2 / 2 2'25~] chains with Ni in the oxida­
tion state 0.75 [6 8 ]). Similar ^ [CoIN 2 / 2 2_] chains
are found in BaCoN [69].
4. In Li2 (Lij_xCox)N (xmax = 0.51) and
Li2 (Lii_ANix)N (jtmax = 0.63) the transition metal
occupies statistically the metal site of the a-Li^N
structure type two-fold coordinated by nitrogen
atoms. This leads to isolated [M,N2]5_ units (M
= Co, Ni) which might be partially connected to
[MIN 2 / 2 2_] chains due to partial occupation of this
metal site [61, 70].
5. The structure of Ba2 (N ii_rLir)Ni2 N2 also fea­
tures ^ [NiN2 / 2 2,5~] chains, now connected at ni­
trogen atoms by two-coordinated (Nii_xLiv) sites
[71]. The latter nickel atoms are assumed to be Ni1,
while the nickel atoms in the chains are assigned the
+0.5 oxidation state. This compound is not included
in Fig. 9.
6 . Distorted trigonal planar FenN 3 units form
either [NFenN 2 FenN]8~ dimers (Ca2 FeN2 and
Sr2 FeN 2 ) or one-dimensional ^ [Ni/ 2 FenN 2 Fen
N i/ 2 5~] chains (Sr2 LiFe2 N 3 and Ba2 LiFe2 N 3 ) [72],
7. Isolated linear [Fe11^ ] 4- anions are present in
Li4 FeN 2 and along with trigonal planar coordinated
iron ([NFe1,N 2 FeIIN]8~ dimers) in Sr2 FeN2 [72].
8 . Isolated linear [NinN 2 ]4~ units constitute
Sr2 NiN 2 [59].
9. Isolated trigonal planar [MmN 3 ]6~ units (in
D3h geometry or distorted to C 2V) are found in
Ea 3 MN 3 with several combinations of M = V, Cr,
Mn, Fe, Co and Ea = Ca, Sr, Ba [46,47,72 - 76], The
[MmN3]6“ groups are also present in (Ca3 N)2 MnN 3
[48] and in (Ca3 N)2 FeN 3 [72]. The electronic struc­
ture of these compounds has been addressed else­
where [77].
10. ^ [FeinN 4 / 2 3“ ]: one-dimensional chains of
edge-sharing Fe N4 tetrahedra in Li3 FeN2 [72].
There are four ways to change M (theoretically,
of course) in IJI 2 MN 3 from Cr or Mn to another
transition metal. The first two involve changing the
oxidation state of M from +1 to 0 or +2. Nitridometallates based solely on the M°-N interactions (such
as with d 5 V(0) or d6 Cr(0), I) are unlikely. Inci­
dentally, the Ln2 M°N 3 stoichiometry requirement
will place an average formal charge of +4.5 on
the Ln cations, a condition that may be difficult
to satisfy. The opposite direction leads to consider­
ing divalent metal centers, such as d5 Mn(II) or d6
Fe(II) (II). The known structures suggest the reason
for instability of such hypothetical Ln2 MnN 3 com­
pounds. The iron nitrides from categories 6 and 7
have two or three fold coordinated Fe(II) centers.
The nitrides with trivalent metals have M(III) ions
in either trigonal planar (category 9) or tetrahedral
(category 10) coordination. On going from nearly
square planar M‘N4 units to MnN4 or MmN4 , the NN repulsion, increasing due to substantial shorten­
ing of the M-N bonds, is likely to either distort these
units to tetrahedral geometry or reduce the coordina­
tion number of the metal. The other possible direc­
tions involve keeping the oxidation state at + 1 , but
changing the electron count on the transition metal.
For instance, one could imagine ^ [M1^ ^ ^ 8 -]
R. Niewa et al. ■Unusual Bonding in Ternary Nitrides
0
+1
+2
+3
d2
VN3
d3
CrN®'
d4
M nN 36'
FeN36'
J [C rN 2N®2]
d5
J L -
J [F e N 43/2]
- A
11)
d6
' J [M n N 2N®2] ‘
f
FeNg
N FeN2 F eN 8’
C oN 36‘
J lN ^ F e N . F e N ^ ]
d7
CL
co
72
C oN 25"
NiN2
J [ C o N * 2]
d9
N iN 25’
J [ N 'N * 2]
Fig. 9. Some known low-dimensional transition metal
nitride units found in ternary and quaternary nitrides with
electropositive metals. The formal charge on the transition
metal and the number of d-electrons are used to classify
these structures. Directions I - IV indicate possible ways
of extending the group of compounds containing linear
chains of vertex-sharing square planar MN4 units.
chains with four or fewer d-electrons on the tran­
sition metal (d3 Ti(I) or d4 V(I), III) or with seven
or eight d-electrons (d7 Fe(I) or d 8 Co(I), IV). We
do not consider the d 9 and d 10 cases because they
are clearly not compatible with square planar co­
ordination. Low electron counts, such as d? or d4,
would lead to tetrahedral coordination again, though
mainly for electronic reasons: the “two below three”
d-orbital splitting provides for lower energy of such
systems compared to the “four below one” square
planar splitting. Our calculations indicate that the
distortion from square planar to tetrahedral geom­
etry is indeed favored for d° to d4 configurations
in an J. [MnN 2 N 2 / 2 ] chain (see Fig. 10a). The same
distortion raises the total energy in the d 5 to d 8 cases.
The fourth direction, substituting Mn(I) or Cr(I)
for Fe(I) or Co(I), is a bit more interesting. The d 7
and d 8 electron counts would be optimal for square
planar FeN 4 and C 0 N4 units. The only significant
consequence of having the d 7 or d 8 metal config­
urations in the l, [MN2 N 2 / 2 ] chains is weakening
of the M-Nbridge bonds due to loss of 7r-bonding.
Therefore, distortions removing co-planarity of the
R. Niewa et al. • Unusual Bonding in Ternary Nitrides
a)
b) - V s
d)
,-ot
= > -+4 + 0-
Fig. 10. Possible distortions in a J. [MN 2 N 2/ 2 ] linear
chain: (a) forming a linear chain of vertex-sharing MN 4
tetrahedra; (b) bending at the bridging nitrogen and keep­
ing the planarity of the MN4 groups; (c) twisting of the
square-planar MN4 units relative to each other, and (d)
breaking the chain into isolated MN2 and MN4 moieties.
Metal atoms are represented by filled circles and nitrogen
atoms by empty circles.
neighboring MN4 units may stabilize the chains.
However, our calculations for two such distortions
depicted in Fig. 10b,c show that the total energy
actually increases. Weaker M -N ^ge bonds should
be substantially longer than 1.875 A in the Mn case,
perhaps as long as 2.0-2.1 A. The strain thus im­
posed on the Ce2 MN3 structure (the a cell param­
eter should increase simultaneously by 0.2 - 0.4 A)
may be enough to destabilize it. The last possibil­
ity is suggested by the existence of nitridometallates with two-coordinate Co(I) (categories 2 - 4). A
^ [MiN 2 N 2 / 2 8~] (M = Fe, Co) chain may undergo a
distortion, in which isolated M1^ 5- and M1^ 11units are formed (see Fig. lOd). For cobalt we ac­
tually calculate such distortion to be slightly stabi­
lizing. However, the extended Htickel method does
not deal properly with bond-breaking: the calculated
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Conclusions
A new ternary nitride, Ce2 MnN3 has been pre­
pared and characterized with respect to its crystal
structure, electrical, and magnetic behavior. The dif­
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Acknowledgments
R. N. and F. J. D. are grateful to the National Science
Foundation for support through Research Grant DMR9508522. R. N. thanks the Deutsche Forschungsgemein­
schaft for providing a Forschungsstipendium. G. V. V.
would like to thank the National Science Foundation for
support through Research Grant No. CHE 94-08455 and
the Olin Foundation for support through a graduate fel­
lowship. We thank Roald Hoffmann for comments on the
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