Journal of Nuclear and Radiochemical Sciences, Vol. 6, No. 3, pp. 215-216, 2005

Quantum Chemical Model of Technetium Carbide
Yu. V. Plekhanov* and K. E. German
119991, A.N.Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences, 31,
Leninskii pr., Moscow, Russia
Received: July 31, 2005; In Final Form: September 30, 2005
The discrete-variational (DV-Xα) method and Mulliken bond overlap population analyses were performed to study
the electronic structure of technetium carbide and clarify the chemical formula Tc6C proposed for this compound.

Technetium carbide is an interesting alternative material ofmetallic technetium with respect to target fabrication for transmutation of radioactive 99 Tc. Its properties, although briefly
investigated,1 suppose that the targets are somewhat easier tofabricate, they should be quite stable under the neutron fluxand could help to increase the transmutation rate by supplementary neutron thermalization inside the targets due to carbon
atoms present. Also, according to the instability of ruthenium
carbide, the partially transmuted targets should be less noble
compared to Tc-Ru alloy and should be easily dissolved 2 forthe further Tc/Ru separation. This compound presents allproperties of a metal phase and because of its C-deficient structure it could be considered as a quasi-equilibrium metallic
phase stabilized with C-impurity, in contrast to the well-known
hexagonal structure of Tc metal.
To clarify a proposed chemical formula1 forTc6C, quantum
chemical calculations based on the hypothetical structure isrequired. As reported in Reference 3 for a metallic Tc, the calculations were made by non-empirical electron density functional in DV-X α approximation by the DVSCAT code.4 We
used the full electronic basis of numerical 1s-5p atomic orbitals
for Tc and 1s-2p functions for C. The electron exchange wasaccounted for by the Slater procedure5 with the parameter α =0.7 for all atoms. The individual contributions of the atomic
orbitals were estimated by the Mulliken population analysis.6
The number of integrating points for numerical estimation ofmatrix elements were 500 Na, where Na is the number of atoms
in model clusters.
As a starting model of metallic face-centred cubic (a = 3.98Å) lattice,3 we used the fragment Tc 42 , containing two metallayers. In this fragment the number of octahedral holes withdiameter 3.98 Å is 13 or 25% of Tc. Moreover, 24 unoccupied
tetrahedral sites have a smaller diameter. Regular carbon allocation in accordance with the stoichiometry was realised as
Tc42C7 (Figure 1). The model size was completely satisfied forthis task, as the relative limiting number of placing carbon
atoms exceeded the expecting value of 1:6.
At present, unfortunately, straight energy calculations forsuch a size of Tc compounds are not reliable due to computing
difficulties and theory errors. For diatomic molecules, however, the stability may be estimated by the Mulliken bond overlap population index7 P. For more complex compounds, thesum of these indexes Σ P by overall bonds may be used. To get
comparable results for different sizes and contents, it should bebetter to use a value related to one atom Pa = Σ P/Na. For themodel carbide, the stability may be found as a difference in ∆P
between carbide Pa (MC) and pure metal Pa (M) indexes:*Corresponding author. E-mail: plekhanov@ipc.rssi.ru. FAX:
+7-095-335-17-38.

Figure 1. A model for technetium carbide cluster.

Figure 2. A model for α-molybdenum carbide cluster.

∆P = [(Σ P(TcTc) + Σ P(TcC))/(NTc + NC)] – [(Σ P(TcTc))/NTc].
To verify the ∆P –criterion, we carried out calculations similar to the case of Mo carbide as the nearest Tc neighbour. The
most stable carbide α-Mo2 C (Figure 2) crystallizes in theorthorhombic lattice.8 Octahedral hole (4.195 Å) sites in thislattice are half occupied by carbon regularly. In the model
crystal with several tens of atoms but without surface C-atoms,
the stoichiometry must be greater than 2:1. The Mo44Cx fragment contains 4 metal layers. There are 17 octahedral holes inthis model crystal. The real carbide composition corresponds
to x = 11 (25%). The ∆P values (Figure 3) are not quite regularrow because the small size of model crystal and the small number of trial carbon positions. The minimum area at C/Mo =16% (or 33% for crystal) should be defined more exactly using
expanded model crystals. Nevertheless, these data show thatthe ∆P tendency is fairly good. The stable composition corresponds to ∆ P > 0. The maximum C:Mo value is slightly© 2005 The Japan Society of Nuclear and Radiochemical Sciences
Published on Web 12/28/2005

216 J. Nucl. Radiochem. Sci., Vol. 6, No. 3, 2005

0,020

0%

5%

10%

15%

20%

25%

30%

35%

∆P

0,005

0,000-0,025

y = -0,4349x 2 + 0,1261x-0,030C/Tc %
0,00

5%

10%

15%

20%

25%

-0,04-0,06-0,08-0,1230%

35%

C/Tc , at.%

-0,005-0,020

y = -0,0513x + 0,0139

0,02-0,10

25%-0,015
Delta P
Linear trend
Quadratic trend

Figure 3. Bond overlap population index for a model molybdenum
carbide.

0%

20%-0,010-0,020

-0,02

15%

0,010
0,000

-0,015

10%

0,015

0,005

-0,010

5%

0,020

0,010

-0,005

∆P

0%

40%

C /Mo, at.%

0,015

∆P

PlekhanovOh holesT d holes-0,14

Figure 4. Bond overlap population index for octahedral and tetrahedral holes in a model technetium carbide.

greater than 25%. On the contrary, the metal body-centred lattice hole filling is accompanied by ∆P decreasing, and in fact
this carbide does not exist.
The good estimation for accepted criterion of a Mo2C composition allows us to apply it for the model Tc-carbide Tc42CX.
Analysis of different coordination hole filling by this criterion
shows that octahedral carbon position is much preferable(Figure 4). This is why we can use only octahedral carbon
coordination models (Figure 1). Indeed, the tendency of ∆Pchanging (Figure 5) gives a stable area close to the experiment.
The C/Tc ratio does not exceed 15%, and the Tc6C composition
would be reasonable within the error limits of calculations (~asfor Mo2C).

Delta P
Linear trend
Quadratic trend

y = -0,0723x + 0,0067
y = -0,3691x 2 + 0,048x

Figure 5. Bond overlap population index for a model technetium
carbide.

On the other hand, the ∆P curve in the stable area contains
sine-like parts. This region corresponds to local carbon concentration for more (maximum) and less (minimum) compound
stability. It can be supposed that the alternate carbide phaseformation is unregularly and unordered. It can included statistically averaged set of dissimilar fragments based on more stable local concentrations.
We can conclude that the ∆P criterion model is adequate forthe stability estimation of rather complex compounds. The
experimental Tc-carbide composition can be described by two
possible models (regular and unregular) using the ∆P dependence.
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