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Influence of electronegativity on the electronic structures and stabilities of microclusters of carbides MCn
(M : transition, rare-earth or normal element, n < 10)
M. Leleyter
To cite this version:
M. Leleyter. Influence of electronegativity on the electronic structures and stabilities of microclusters of carbides MCn (M : transition, rare-earth or normal element, n < 10). Journal de Physique II, EDP Sciences, 1991, 1 (10), pp.1179-1196. �10.1051/jp2:1991127�. �jpa-00247583�
J. Phys. II France 1 (1991) l179-l196 OCTOBRE 1991, PAGE l179
Classificafion Physics Abstracts
31.20N 36.40 79.20N
Influence of electronegafivity on the electronic structures and
stabilities of1nicroclusters of carbides MC~ (M : transition,
rare-earth or normal element, n <10)
M. Leleyter
Groupe de Physique Thkorique, Facultk des Sciences d'Arniens, 33 rue Saint.Leu, 80039 Arniens Cedex, France
also Laboratoire d'lnfornJatique Appfiqube aux Sciences Pbysiques, CUM, 5 rue du Moulin Neuf, 80000 Arniens, France
(Received J2 November J990, accepted in final form 4 July J99J)
Rdsnmk. Les agrkgats MC~ obtenus I partir de carbures par diverses mdthodes expkrirnentales (SIMS, SSMS, vaporisation laser, effusion de Knudsen I haute tempdrature, etc.) prksentent des altemances dans leurs intensitds d'drnission I(MC$) avec maximums pour n impair si M
= H, F, Cl ou Fe, Ni, Rh, Ir, Pt ou au contraire pour n pair si M
= B, Si, Ba, Ge ou Sc, Ti, V, Cr, Y, Zr, La, Ce, W, Th, U ou mdme n'existent que pour n pair ~lod, Dy, Ho, Er). D'autre part,
souls sont connus CO, C~O, CN et C~N piur l'oxygdne et l'azote. Ces phdnomdnes sont
interprdtds tout d'abord I l'aide de la rdgle bien connue de correspondance qui retie de fortes (resp. faibles) intensitds ou frdquences d'drnissions d'ions MCz I de fortes (resp. faibles) stabilitks des amas correspondants. En second lieu, ces rdsultats s'expliquent dans le cadre du moddle de
Pitzer et Clementi ~hybridation sp en thdorie de Hfickel) corrobord par des calculs CNDO : on suppose que les arnas MC$ sont des chaines lindaires C$ portant un atome d'irnpuretd M en bout de chaine. Dans ces conditions, les altemances de stabilitds relatives des MC~ proviennent de ce que l'orbitale moldculaire la plus dlevbe («HOMO») se trouve dans une bande niveaux
w doublement ddgdndrds et qu'i une orbitale w compldte (4 dlectrons) correspond une plus forte stabilitd de l'amas que si l'orbitale est incompldte. Or le nombre d'dlectrons w d'une chaine MC~ est gouvemd par le nombre de niveaux ~ liants et en outre pour les dldments de transition ou
de terres rares, par la position du niveau da et celle du niveau 3 ddgdnkrds dus I la prdsence de
l'atome M. Dans le cas des dlkments norrnaux, si M est plus klectronkgatif que C (EN
= 2,5),
l'orbitale s«~ sera liante (2 dlectrons) alors qu'elle sera antiliante (vide) dans le cas contraire, et entr#nera donc une diffdrence de 2 Electrons
~ ou w, donc un changernent de sens des altemances. Le cas spdcial de H peut aussi s'expliquer dans ce cadre. Los dldments de transition pour leur part, se scindent en 2 groupes suivant que leur dlectrondgativitd EN est supdrieure I 1,7 (dldments ayant beaucoup d'dlectrons d colonne VIIIA ; niveaux 3 et d~ liants) ou non ~peu d'dlectrons d : colonnes IIIA et terres rares I VIIA ; niveaux 3 et d~ vides). Nous donnons deux tableaux rdcapitulant la structure comparde des niveaux des agrkgats MC~ pour les dldments
norrnaux ou de transition. Ce type de structure peut seul expliquer l'origine des altemances des
arnas MC~ et perrnet mdme de pr6voir pour des carbures de transition ou de terres rares non
encore dtudids, si les altemances seront « paires » (EN «1,7) ou « irnpaires » (EN >1,7 ).
l180 JOURNAL DE PHYSIQUE II M 10
Abstract, MC~ clusters (n < lo) produced from carbides by various experimental techniques (SIMS, SSMS, LAMMA, Knudsen effusion, etc.) show strong altemations in their emission
intensities I( MC ) according to the parity of the carbon atom nuraber n. Maxima take place for odd n (« odd » altemations) if M
= H, F, Cl or Fe, Ni, Rh, Ir, Pt or for even n («even»
altemations) if M
= B, Si, Ba, Ge or Sc, Ti, V, Cr, Y, Zr, La, Ce, W, Th, U or even the ions exist only for even n ~Nd, Dy, Ho, Er). Moreover, only CO, C~O, CN and C~N are known for O and N. Such phenomena are due to the stability properties of the clusters themselves (« correspon-
dence rule ») and can be interpreted with the Pitzer and Clementi model (sp hybridization in Hfickel approximation): the clusters are assumed to be linear chains of «curnulene»- type :C=C=..C=C=M and the altemations in the relative stabilities of these chains are mainly due to the fact that the HOMO ~highest occupied molecular orbital) of the clusters lies in a double
degenerate w level band. Now HOMO may be either full or half-filled, and an aggregate with a
complete (or ahnost complete) HOMO is more stable than an aggregate with a half-filled HOMO. Consequently, the number of w electrons is governing the parity effect in the stability
altemations. However, this number is depending on the number of ~ electrons of the chain and besides, for the transition or rare-earth metals, on the positions of the da and degenerate d3 levels due to the M atom, which are govemed by Pauling's electronegativity (EN ) of atom M.
For transition or lanthanide metals, the altemations are «even» if ENS1.7 (deficient d electron-elements : columns IIIA to VIIA ; empty da and 3 levels) or « odd » in the reverse case
(rich d electron elements : column VIIIA ; bonding da and 3 levels). For normal elements, the limit of EN seems to be the EN of C (2.5) and the altemations are « even » TEN « 2.5 or « odd » in the other case.
Thus it is possible to infer a likely electronic configuration of the MC~ clusters and 2 tables give
the compared electronic structures of these clusters for normal or transition elements. Such a kind of structure is only able to explain the parity effect origin of the MCn clusters and even enable to foreknow for transition or rare-earth metal carbides which are not studied yet if the altemations will be « even » (EN « 1.7 ) or « odd ».
1. Introduction.
It is now well known that carbon aggregates C~(n
< 10) produced by various experimental techniques such as secondary ion mass spectrometry (SIMS), spark source mass spectrometry (SSMS), laser vaporization... etc., or observed in interstellar clouds, show a very markedly parity effect with alternations in the emission intensities of C( ions (maxima for odd
n) or Cp ions (maxima for even n) [I].
In these experiments, especially SIMS, carbides of transition metals or normal elements M
give MC~ clusters (n <10) which also present altemations with the parity of n in the variations of their emission intensities I(MC~ [I]. Many other experimental results exist in
high temperature mass spectrometry (HTMS) about rare-earth carbides and show the same behaviour too [2-10].
The purpose of this paper is to show that the knowledge of the intensity altemation parity is enough to get relatively precise information on the electronic structures of the corresponding M~ clusters and that this phenomenon is strongly related to the Pauling electronegativity of M.
In section 2, we recall the experimental results which will be interpreted in section 3 from
our model within Hfickel framework, which enables us to show the influence of the M
electronegativity (EN) on the electronic structures, and, then we shall give tables
summarizing the various structures of the M~ clusters.
A part of this paper has been presented at the Congrds de la Socidtd Frangaise de Physique in Lyon- Villeurbanne (September 1989).
N 10 INFLUENCE OF ELECTRONEGATIVITY ON ELECTRONIC STRUCTURES l181
2. Experimental results.
2,1 TRANSITION oR RARE-EARTH METALS.- Figure I shows the variations of emission
intensities I(MC~ ) versus n, the carbon atom number, in SSMS (curves (a) for Fe [II], Y and Zr [12]) or SIMS (M=Ti, Cr, Ni and curve (b) for Zr [I]) experiments. Nict ions have been
given by a Ni-4 wtfb-C carbide and observed in the same way as TiC(, CrC( or ZrC( (b) ions in the Castaing-Slodzian microanalyser. Experimental conditions have already
been described elsewhere [I].
The two curves about ZrC( ions show almost the same alternating behaviour except for
ZrC( (b) which is at the sensibility limit of our apparatus. We have already presented SIMS results on FeC( ions [13] and found altemations quite analogous to those of SSMS
experiments [11] shown in figure I.
Figure 2 summarizes the high temperature mass spectrometry results obtained by Gingerich
et al, in many experiments on transition and rare-earth metal carbides [2-10].
All these curves of emission intensities exhibit a very strong even-odd effect as a function of
n whatever the kind of experiments : so it can be seen that both curves for YC( ions (in SSMS
lo
zr+ Yj
~' Yc(ia)
~
~ ~
i ~~
ji
zrc~ ~
~~~ al
e'°~ ~
, ~Zrc((dl
~
g ix0.f)
) .
FeC* 'b ~
g'° ~,, lb)
~
jfeci
~
~ Fecn '°J
' ~
/ ix10)
, . ,
Ticii ',,
. ./ ~ Ii
iO~ 'jl(/"--.,
r i j,, crcn~
Nicj ",,(xf00)
, ~; "
~~ ~ / '~
,.
fl NiC(
' I
0 2 3 4 6 8 9
Carbon atom number n
Fig. 1. Rilative intensities ofMC~ ions versus n, the carbon atom number. a) SSMS experiments [11, 12]. The other curves are obtained in SIMS experiments ~primary ions : 6.5 kev Ar+ ions) [ii. In the
case of Ti, Cr, Y and Zr, the maxima occur for even n, and for odd n in the case of Fe or Ni.
1182 JOURNAL DE PHYSIQUE II bt 10
ThC~
$ 1~
, l
j j j I ',
, '
j 'j/ [
/ ThC~
©
~ ., Q
; / ;~ll~
i~ iu,~~i)ceci
~[&i', %~uc[
% /
U / YC6+
~ o .-.--,
~
lrc((xlo~ ~~)$,il
LCCj ',
.-""'
c
~ (xi0T3l
PtC(
sac°xc* (xio~3) SCC[
~ (x10-31 o--]
0 2 3 4 5 6 7
Carbon atom number n
Fig. 2. Relative intensities versus the carbon atom number n, of MC~ ions obtained in Knudsen effusion high temperature mass spectrometry ~IITMS) [2.10] for Y, Th, U, lanthanum and platinum
metals. All the maxima occur for even n except for IrC(, RhC~ and PtC~, the maxima of which take place for odd n.
in Fig. I an/~n HTMS in Fig. 2)
are quite s1nlilar. Finally, in the cases of Nd, Dy, Er and Ho,
the only carbides known are MC~ and MU [6~.
As a result, madma of I(M~Q ) occur for even n if
M
= Ti, Zr ; V ; Cr, W (SIMS)
= Zr, Y (SSMS)
= Sc, Y La, Ce, Nd, Dy, Er, Ho; Th, U (HTMS) that is if M belongs to columns IIIA through VIIA of the periodic table, and
for odd n if M
= Fe, Ni (SIMS)
= Fe (SSMS)
= Rh, Ir, Pt (HTMS)
that is if M belongs to column .VIIIA (triad or plati~ium metals).,
2.2 NORMAL ELEMENTS.- Figure 3 presents experimental results on C~H+ (SIMS on
bt 10 INFLUENCE OF ELECTRONEGATIVITY ON ELECTRONIC STRUCTURES l183
grapl~ite, (curve (a) [14]) or polythenes (curve (b) [15]), FC~ and CIC( ill, with maxima of emission intensifies for odd n and on BC( [16] and SiC( [17] with maxima for even
n. Moreover, recent results on GeC( II8] et BaC( [19] also show altemations with maxima for even n.
Besides, carbon oxides, CnO and nitrides, CnN are only known for odd n (n
= 1.3_) [20, 21].
3. Interpretation model,
3. I GENERALITIES AND MAIN HYPOTHESES. Since the altemations of MCt intensifies are
almost the same whatever the kind of experiment (see for instance the curves of
I(ZrC( in Fig. I or those of I(YC( SSMS in Fig. I and HTMS in Fig. 2), it means that tl~is
parity effect is very likely to come from the clusters themselves and not from some emission mechanism which could only lead to a monotonic effect on the emission probability of a
polyatomic ion (the bigger the ion, the weaker its emission probability). The saw-toothed behaviour of the intensity curves is then reflecting a parity efsect in the stabilities of the
corresponding clusters, hence in their binding energies. T%s is summarized in our
correspondence rule » which states that strong (resp. weak) emission intensities of some kinds of ions are corresponding to strong (resp. weak) stabilities of these clusters [1, 22].
Our interpretation model ill is built on three main ideas. The first one is the above
correspondence rule. The second point is that the oscillations in the cluster stabilities can be well understood from the Pitzer and Clementi model [23] within the HUckel framework : the
MC~ clusters are assumed to be linear chains C~ ~llence in sp hybridization) with an impurity
C~H°
~ ~.
~ 10 'b- ~( C~H~
( ~, ~j C~H~lal
1 ~
Ctfj ~sf
~'
_
~@j?
~
C~H~IN
~ 10 .-. ' Clcn
.
= ;~ .~ C~H
flc F§° SIC( ~ ,_(
i (
C~
SiC( ~~ ~
i "~~
~ ~~. '
i FCi ~i~ £~ FC~
t F° ?, ~~I',
°',j
~
BC ~
~
/~~
/
Fc;,cic~ BC( .
7~
0 2 3 4 5 6 7 8 9
Carbon atom number n
Fig. 3.- Relative intensities versus n, of MCQ ions obtained form normal element carbides.
SiC( [171, C~H+ : SIMS on graphite (a) [14], on polythenes (b) [15]; BC( : laser mass spectrometry [16]. Maxbna occur for even n for B, Si and for odd n in the other cases.
184 JOURNAL DE PHYSIQUE II bt 10
atom M at one end of C~ chain. The assumption of a linear chain is quite pertinent since, for instance, interstellar molecules such as HCJQ with x
= 1, 3, 5,..., ll (cyanopolyynes) are
known to be linear [21] in the same way, recent ab-initio studies on C6[24] and on C~S and C~S [25] have pointed out that a linear structure containing «cumulene type » bonding
as :C=C=...=C=C: is one of its most stable shapes (C6), or the most stable shape
(C~S). ~we have already discussed this point with more detail [26].) So MC~ nlicrodusters are assumed to have the structure M=C=C...=C=C :.
On the other hand, it has already been shown that, in the Hfickel approximation, the alternations for C~ chains arise from the fact that the l~ighest occupied molecular orbital (HOMO or « Fermi level ») of the linear chain falls in a double degenerate w molecular
orbital band, and HOMO may be either filled up (very stable chain) or half-filled ~less stable chain). Therefore the stability of a cluster strongly depends on whether HOMO is full or not.
Here, our tl~ird assumption can play a role : the Pauling electronegativity (EIQ~ of the
« impurity » element M, that is, the ability of M atom in a molecule to attract electrons to
itself, migl~t indeed explain the inversions in the alternation parities.
Tiffs fact has already been pointed out for transition elements [27~, but figure 2 shows that it
is also relevant for lanthanide, platinum or actinide metals. We see indeed that
MC ion emissions split up into 2 groups according to the altemation parity (Sect. 2): on the
one hand, elements of colun1nsIIIA tl~rough VIIA with few d electrons (maxima of intensities for even n) and on the other hand, rich d electron elements of the « triad », or
platinum metals, that is column VIIIA (maxima for odd n).
Rh . . Pt
lr
.~
Ni c~
Co ._.
~ Fe
/
r .
£ /
$ W /
m . /
I ~. /
~ T;/ ~~~/
# . .
~ Mn
U
~
.Sc
Ce
~La
lllA TVA VA VIA VITA -VlllA- lB
Fig. 4. Pauling's electronegativities of the different transition elements studied in the text versus the columns of Mendeleev table (data from Ref. [28]).
bt lo INFLUENCE OF ELECTRONEGATIVITY ON ELECTRONIC STRUCTURES l185
H0ckei:sp hybridization
chain Cn chain CnTi chain CnNi
Err#«
Ep~2fln _,
Ep --
~(~"
'bur~~c~'
nn ,2el.
E~
E
2n pt. pt.
2net.
Fig. 5. Comparison of the energy levels of the chains C~, C~Ti and C~Ni according to the Pitzer and Clement model. E~,E~, p,, fl~ and A~ are quantifies used in Hiickel approxbnation with hybridization [14]. E~
= (E~+E~)/2. The main difference between C~Ti and C~Ni lies in the position of the 8 level which is antibonding for Ti and bonding for Ni. The electron number in the various levels is also
given.
Figure 4 presents Pauling electronegativities [28] of the various elements quoted above,
versus the co1unlns of the periodic table and we also find a split into 2 groups according to
their EN values (the limit being 1.7). We shall see below how EN is acting on the structures.
In figure 5 we recall the well-known Pitzer and Clementi electronic structures of C~ chain [14, 23]; levels are ordered with increasing energies and the various parameters are
those of the Hfickel theory [14] spa (resp. spAB) is the bonding (resp. antibonding) band of
~r levels, and ~r~, the « surface levels », winch come from the dangling bonds on the 2 terminal C atoms, and are mainly localised on the ends of the chain there are 2 n 2 electrons in the
w band. It is therefore obvious that HOMO is a closed shell when n is odd. This is quite
consistent with the fact that the emission intensities of C~~~, ions are stronger than those of C~~ ions in the data on graphite.
3.2 TRANSITION AND RARE-EARTH ELEMENTS. The case of MC~ chains is a little more
complicated because the transition (or rare-earth) atom M makes a degenerate 8 level
appeared which is either antibonding (or non-bonding) and therefore empty if M elec-
tronegativity is weak enough (EN « 1.7 ) as in the case of column IIIA to VIIA elements, or bonding and hence half-filled (with 2 electrons for Fe or Ir) or full up (4 electrons for Ni or Pt)
if M is more electronegative (EN ~ l.7 ).
Figure 5 gives the examples of C~Ti for the first case and C~Ni for the second one. The electronic structure of linear MC~ chain is siInilar enough to that of C~. Because of the M-C
bonding, atom M forms hybrids orbitals from its N d~r, (N + I) s~r and (N + I) p~r atoInic orbitals (N
= 3 for Ti and Ni, 4 for Y or Zr, 5 for La, Ir or Pt, etc.). The hybrid orbital which derives from (N + I p~r, combines with one of the ~r~ levels of Cn chain in order to give rise
