ISSN 1062-8738, Bulletin of the Russian Academy of Sciences: Physics, 2009, Vol. 73, No. 3, pp. 425–427. © Allerton Press, Inc., 2009. Original Russian Text © A.A. Lavrent’ev, B.V. Gabrel’yan, I.Ya. Nikiforov, 2009, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2009, Vol. 73, No. 3, pp. 442–443
Influence of the Nearest Environment Symmetry on the Character of the p–d Interaction in Binary Copper Sulfides A. A. Lavrent’ev, B. V. Gabrel’yan, and I. Ya. Nikiforov Don State Technical University, Rostov-on-Don, 344010 Russia e-mail:
[email protected] Abstract—The energy structure of copper sulfides CuS and CuS2 has been theoretically investigated by the modified method of associated plane waves (WIEN2k program). CuS is considered in two different cubic modifications of the sphalerite and NaCl (hypothetical) types, in which Cu atoms are in different coordinations. The density distribution of the electronic p states of sulfur and d states of copper are calculated taking into account the separation into the eg and t2g states. The specific features of these distributions are interpreted. DOI: 10.3103/S1062873809030447
According to the theory of ligands [1], the degeneracy of atomic d states is partially removed in cubic, octahedral, and tetrahedral lattices: t2g and eg metal states are formed. The splittings of the d states into the t2g and eg states are different in different lattice types. To reveal the effect of the symmetry of the nearest environment of copper atoms in sulfides on the energy distribution of their d electrons, we considered copper monosulfide in the sphalerite structure (tetrahedral coordination) and hypothetical CuS in the NaCl structure (octahedral coordination), as well as CuS2 in the fluorite structure (cubic coordination). The lattice parameters used in the consideration are listed in the table. For the hypothetical CuS in the NaCl structure, the lattice parameter was determined as the sum of the covalent copper and sulfur radii, according to Poling [2].
The band calculations of the electronic structure were performed by the modified method of associated plane waves using the WIEN 2k program [3]. The self-consistent approach made it possible to find the density distribution for the electronic p states of sulfur and d states of copper, taking into account the separation of the latter into the eg and t2g states. The general character of the interaction of the p states of S with the d states of Cu is on the whole similar for different crystalline modifications (Figs. 1–3). Mixing (hybridization) of these states occurs when the S–Cu chemical bond is formed. We can select three regions: the central one contains the peak of Cu d states and the peaks of density of the S p states are located on the left and right from the main peak of the d states of Cu. At the transition from the tetrahedral coordination of a Cu atom by S
Space groups, lattice parameters, and atomic coordinates for the investigated copper sulfides Compound
CuS
CuS
CuS2
Space group
F – 4 3 m (sphalerite)
F m 3 m (NaCl type)
F m 3 m (CaF2 type)
Atomic coordinates a, Å
element
x
z
y
ëu
0
0
0
S
0.25
0.25
0.25
Cu
0
0
0
S
0
0
0.5
Cu
0
0
0
S
0.25
0.25
0.25
5.387
4.78
5.789
425
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LAVRENT’EV et al.
Cu d states and S p states gradually changes. Both the S p and Cu d bands broaden. The internal band gap, characteristic of the sphalerite structure, disappears. Some of the d and p bands, lying in the ranges from –5 to –3 eV for the sphalerite structure (Fig. 1), from –7.5 to –3.2 eV for the NaCl structure (Fig. 2), and from –7.5 to –4 eV for the fluorite structure (Fig. 3), diffuse, and two pronounced peaks merge into one. The centroid of the Cu d states shifts from –2 to –2.5 eV and then from –3 eV to the Fermi level. The shape of the main peak (doublet) of the d band changes: the ratio of the doublet component intensities changes in favor of the peak with a lower binding energy (Figs. 1–3).
CuS (sphalerite) Cu dt2g
5
G F
E D B A C
0 Cu deg
10 5 0 15 10
Cu d
5
Sp
0 –10
–5 0 Energy, eV
5
Fig. 1. Densities of the sulfur p states and projections of the copper d states for the CuS compound (sphalerite). Zero energy corresponds to the calculated Fermi level.
atoms to the octahedral coordination and then to the cubic coordination (coordination numbers 4, 6, and 8, respectively), the distribution of the density of the
F
Cu dt2g
According to the crystal field theory, the transition from the cubic to tetrahedral coordination is accompanied by a decrease in the energy gap between bonding (eg) and antibonding (t2g) states. The transition to the octahedral symmetry leads to an exchange in the roles of these states, i.e., the t2g state becomes bonding and the eg state becomes antibonding. In our calculations, we did not observe any splitting between the eg and t2g states. However, in the octahedral coordination, the forms of the Cu eg and t2g states repeat the forms of, respectively, the t2g and eg states for the cubic and tetrahedral coordinations of a Cu atom by S atoms. In the CaF2 (Fig. 3) and sphalerite (Fig. 1) structures, the S p states interact mainly with the Cu t2g states, whereas in the hypothetical NaCl structure, vice versa, they interact with
CuS (NaCl)
ED BA C
Cu dt2g
F
I HG D B A EC
5
CuS2 (CaF2)
5 0 10 0 5
Cu deg 0 10
Cu deg
0 10 Cu d Cu d
5
5
Sp 0 –10
Sp –5 0 Energy, eV
5
Fig. 2. Densities of the sulfur p states and projections of the copper d states for the CuS compound (hypothetical NaCl structure). Zero energy corresponds to the calculated Fermi level.
0 –10
–5 0 Energy, eV
5
Fig. 3. Densities of the sulfur p states and projections of the copper d states for the CuS2 compound (CaF2 structure type). Zero energy corresponds to the calculated Fermi level.
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the Cu eg states; this situation corresponds to the ligand-field theory.
2. Krebs, G., Osnovy kristallokhimii neorganicheskikh soedinenii (Fundamentals of Crystal Chemistry of Inorganic Compounds), Moscow: Mir, 1971.
REFERENCES
3. Blaha, P., Schwarz, K., Madsen, G.K.H., et al., WIEN2k, an Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties, Wien: Karlheinz Schwarz, Techn. Universität, 2001.
1. Bersuker, I.B., Elektronnoe stroenie i svoistva koordinatsionykh soedinenii (Electronic Structure and Properties of Coordination Compounds), Leningrad: Khimiya, 1976.
BULLETIN OF THE RUSSIAN ACADEMY OF SCIENCES: PHYSICS
Vol. 73
No. 3
2009
