Electronic structure, charge distribution and x-ray emission spectra of V3Si

Solid State Communications, Vol. 29, pp. 185—190. Pergamon Press Ltd. 1979. Printed in Great Britain. ELECTRONIC STRUCTURE, CHARGE DISTRIBUTION AND X-RAY EMISSION SPECTRA OF V3Si V.1. Anisimov, V.A. Gubanov, AL. Ivanovskii Institute of Chemistry, Ural Science Center, Academy of Sciences of the USSR, Sverdlovsk GSP-145, USSR E.Z. Kurmaev Institute of Metal Physics, Ural Science Center, Academy of Sciences of the USSR, Sverdlovsk GSP.170, USSR J. Weber and R. Lacroix Department of Physical Chemistry, University of Geneva, 1211 Geneva 4, Switzerland (Received 7 August 1978; in revised form 17 October 1978 by A.R. Miedema)

Cluster calculations of the electronic structure and charge distribution in V3Si have been performed using two different molecular orbital methods: a semiempirical LCAO and the MS Xa model. The results are compared with X-ray emission spectra and band structure calculations. An analysis of the calculated electronic distribution reveals a charge transfer from Si-atoms to V-atoms, the additional charge on a V-atom being 0.6e (LCAO) and 0.4e (MS Xc~method). The results are in good agreement with experiment, which indicates that the cluster approach is adequate for the description of charge distributions and spectra characteristics of the A-l5 compounds. THE CONCEPT of charge transfer has been the subject of a growing interest for the description of various physical properties of transition metal alloys and compounds. Indeed, Miedema has shown [1] that it is possible to describe quantitatively the dependence of electronic heat capacity, ‘y, and transition temperature, T~,on concentration for binary and ternary disordered alloys of transition metals. The model used by Miedema rests on simple concepts, such as the electronegativity of chemical elements and the additivity of component contributions to the electronic structure and charge transfer in alloys, Recently, a further development of this approach has been made by Bongi [2] who used it successfully in the analysis of superconducting properties of A-l 5 compounds. According to this work, two groups among the A3B compounds with A-iS structure can be distinguished. The first one (“typical”, according to the terminology of [31) is characterized by a redistribution of electrons from the B-component (nontransition element: Al, Ga, Sn, Sb, .) to the A-transition metal. In the second group (“atypical” [3]), the redistribution of electrons occurs in the opposite diiection: from the A-transition metal to the B-component (in this case, B is also a transition metal: Os, lr, Pt, . Direct experimental measurements of the electron density distribution (by X-ray diffraction) in V3Si and Cr3Si [4, 5] also reveal an electron transfer from Si to V-atoms and strong covalent bonding

between V-atoms along linear chains of the A-15 structure. We found, thus, it worthwhile to undertake molecular orbital (MO) calculations for a V3Si4 cluster in order to see whether the cluster approach is able to describe adequately the electron transfer in V3Si. In addition, it was interesting to use the same model in an attempt to interpret the X-ray emission spectra measured for V3 Si. Recently, we have used with success the cluster approach for a study of the X-ray emission spectra in the carbides, nitrides and oxides of Ti, V and Nb [6, 71. In the present work, such calculations are reported for the first time for intermetallic compounds.

,

. .

. .).

185

1. METHOD OF CALCULATION AND PARAMETERS In the A-lS structure (space group O,~)of V3Si, each V-atom has two other V-atoms as the nearest neighbors located in pairs on the cube faces (at a/2 distance), forming sets of linear chains, and four Siatoms as second neighbors at distance \/5/4a, occupying the body-centered positions [Fig. 1(a)]. The V3Si4 cluster [Fig. 1(b)] was chosen for the calculation, its geometry being determined from the lattice parameter [8] . The calculations have been performed using two MO methods: (i) the semiempirical LCAO model of Mulliken—Wolfsberg—Helmholz with self-consistency of central atom charge [9] and (ii) the multiple scattering(MS)Xc~method of Johnson [10].

186

X-RAY EMISSION SPECTRA OF V3Si

Table 1. Charge distribution in the [V3Si4] ~° Q0~t:outer sphere charge) Symmetry type, energy (in eV) and population of orbitals a1 e b2 b1 e b2 a1 a1 e a1 b2 a2 a1 e e b2 b2 b~ b1 a1 a2 e

—9.21 —8.73 —8.61 —4.08 —4.02 —4.00 —3.78 —3.71 —3.47 —3.19 —3.17 —2.84 —2.46 —2.43 —2.37 —2.36 —1.90 —1.81 —1.77 —1.28 —1.28 —1.21

2 4 2 2 4 2 2 2 4 2 2 2 2 4 4 1 0 0 0 0 0 0

Q~1

-

Q~1

cluster (per cent) as calculated by MS XCI (Q1~t:intersphere charge,

Q~1

1

Q~2

1 1 1

Q~2

1 2

1

1 2 1

1 1 2

Q~r2

1 2

12

0

Vol. 29, No. 3

18 5 10 17 8 26 34

2

3 4 4 2 23 44

2

2

4

1

Q~

65 73 74

Q0~

Q~j

3

Q~

3 3 4

26 21 18

7

30

8

44

10 7 12 14 15 35 8 32 31 11 42 55 78 60 13 38 51 52

23 28 34 28 34 16 32 28 4 37 12 6

7 11 9 8 12 5 10 7 26 13 16 8 6

40 49 32 33 29 18 15 33 39 34 25 26 14 16 21 20 18 15

16

1 6 42 25 15

16 36 6 13

0.7235 3. Three MS Xa calculations were performed, and [V charges on the corresponding to different 6additional

=

/

I ~

\\

/

I —

(a)

~1 I

•

I

-.

cluster: [V3Si4]’°, [V3Si4I

,~

ative charge on the cluster was compensated by use

~-‘

I-

/ //

Ib)

3Si4]g. The neg-

of a Watson sphere of the same radius as the out sphere and bearing a6charge of + 10 for [V3Si4]10 andof+6for[V3Si4] The cluster charge in the LCAO calculation was determined from the formal valency of atoms, according to which it is necessary to have 12 additional electrons in the V

Fig. 1. The A-is crystal structure (a) and the V3Si4 cluster (b) (•: V; 0: Si). In the latter case, the choice of calculation parameters deserves some comments. The radii of muffin-tin spheres were taken for the

V-atoms as 1/2 of V—V distance (a/4) and for Si-atoms according to the “touching spheres” requirement (Rv = 2.2308 a.u.;R51 = 2.7575 a.u.;Routerspheye = 7.7458 a.u.). The atomic exchange parameters a were taken from reference [11]: = 0.71556; ~ = 0.72751. In intersphere (a1~~)and outer sphere (a0~~) regions, weighted averages (as functions of the number of atoms) were chosen: a~n~ = 0.72239; a0~

3 Si4 cluster, i.e. [V3Si4

]12_.

2. RESULT AND DISCUSSION The electronic structures of [V3 Si4 ]b0_, [V3 Si4]’ and [V3Si4I° as predicted by MS Xcx are presented in Table I and Fig. 2. Let us consider first the energy diagrams of the different.MO’s. The lowest levels (a1, e and b2) are predominantly of Si 3s character. At higher energies (4.5 eV), one fmds the MO’s of Si 3p type with substantial contributions of V 3d orbitals. These V 3d contributions increase in proportion of the increasing energies of the MO’s and, thus, the highest occupied levels have a predominantly V 3d character.

When decreasing the cluster charge, the valence levels

Vol. 29, No. 3

X-RAY EMISSION SPECTRA OF V3Si

(V. S~)°X-~ MS (V

MS

5X-~

Fey (~SL4)~°X-~MS(V3 ~Y

3 SL~YaLCAD

-5

o 5 -,

6

—e

e

-

I-

4

—~

___

a, a,

-.

e

:N:=_e

~

6 ~=t:t:~~~- a,

~

e

a,

Ii~_~

e

a, /7 e ~-

a, a,

s~:-:

6,

-~

1.

6

9

~

e

-7

e 0,

1

6,

_____

-e

~ ___

e

l0

a, 6,

-8

8, 8,

5,

~

6, 6, ~i_________ -‘ a 6,

1

a

______

-

—6

~

~-~.~----

7~77/\~

I ~

~‘ ‘

I

::::::

~

187

-13 -/4

6,

-a,

e

-15

-10

e

6,

~ -16

-11

a,

-77

-12 -/8 -79 -20

6, Fig. 2. Calculated MO energy levels of the [V3Si4] 10- [V3Si4] Theoretical

a,

[V

2 clusters. 3Si4]° and [V3Si4f’ Ex~erimer,tal

C~, 0(S~3s3p

f.0

C~(V~)

p111

C~(V~p)

1 11’

,

-15

-/0

-5

E,.,~(eV)

Fig. 3. Theoretical (MS Xa) and experimental X-ray emission spectra of V3Si.

-

E

188

X-RAY EMISSION SPECTRA OF V

3Si

Vol. 29, No. 3

Table 2. Total charges in the V spheres, obtained in the

prediction of a (negative) additional charge on the

MS Xa calculation of [V3Si4 ]‘° cluster Central Neighboring Si-atom Intersphere Out atom atoms ~, region molecular V1 region

central V-atom in the Vi3 Si4 cluster. In the MS Xa

21.63

21.48

13.50

12.59

3.80

Distribution of charge on the central V.atom Core electrons

Valence s-electrons

Valence p-electrons

calculation performed for [V3Si4]’° ~,the total electronic charge - in the sphere of central V-atom is 23.43e when distributing the interatomic charge equally among all atoms in the cluster (Table 2), which represents an excess charge of 0.43e on this atom. In the LCAO calculation performed for [V3Si4 112 -, the additional charge on the central V-atom is 0.6le. X-ray diffraction measurements [4] conclude to an additional

Valence d-electrons

18.0 0.04 0.20 3.39 __________________________________________________ are lowered and the highest occupied level is shifted to the low edge of the compact group of V 3d levels. Let us compare the present results with band structure calculations performed for V3Si [12, 13] According to these calculations, the low energy band of N(E) has also a Si 3s character and it is separated by an energy gap from the higher energy Si 3p and V 3d bands. The Fermi level is located at the upper edge of the region of high density of states with predominantly V 3d character. Thus, the MO schemes of the V, Si4 clusters are in agreement with the band structure calculations performed for V3Si. However, some quantitative discrepancies remain between the energy separations of Si 3p and V 3d subbands of the spectrum and corresponding groups of MO’s. In cluster calculations, this energy separation is underestimated as compared with the band structure results, i.e. the overlapping of Si Ip and V 3d subbands is predicted to be much more important. The results of the semiempirical LCAO calculation of the [V3S14~ - cluster are presented in Fig. 2, where it is seen that they are qualitatively in agreement with the MS Xa results. However, some differences between the two sets of results may be observed: in the LCAO scheme, the energy gap between Si 3s and 3p-type MO’s is 5 eV (as compared with 4.5 eV in MS Xa) and the width of the subband arising from occupied Si 3~ and V 3d MO’s is 3.8 eV (MS Xa: 1.7 eV). In addition, the LCAO model predicts a larger energy separation between the levels of predominantly Si 3p and V 3d characters, and this is in better agreement with the results of band structure calculations, Concerning the charge distribution in the V3 Si4 cluster, it is interesting to remark that the central V-atom has two V-atoms as first neighbors and, thus, the charge on central atom in the cluster calculation may be a good approximation to the charge of this atom in the crystal. Both LCAO and MS Xa methods lead to the

charge on this atom ranging from 0.6e for R~/R~1 = 1.45 to 0.8e for Rv/Rs1 = 1.7, where ~ and ~ are the V and Si radii, respectively. As the MS Xa result (0.43e) has been obtained with the ratio R~/Rs1= 0.81, the agreement with experiment is satisfactory. As a conclusion, it is worth mentioning that the two independent calculations, performed with different methods, conclude to an additional negative charge on the central V-atom in V3 Si4 . Together with the experimental results of reference [4], this conclusion substantiates the validity of the charge transfer model for A-iS compounds [2]. We are going now to discuss the possibility to describe the X-ray emission spectra of V3Si using the present calculations. Usually, such a description rests on band structure calculations, since MO models have the well-known drawback to consider isolated groups of atoms as representative of the entire crystal. However, taking into account that the X-ray emission is localized in the first coordination sphere of the emitting atom, our opinion is that the cluster approximation may be used to describe X-ray emission spectra. Such an approach has the advantage of considerably simplifying the calculations, which allows us to consider many more compounds than in the band theory, including low symmetry and strongly distorted structures. Nefedov has shown [14] how to use the results of MO LCAO calculations for the interpretation of X-ray emission spectra. In first approximation, each level i in the valence region gives a contribution I~to the spectrum intensities determined by the coefficients of the atomic components of this MO: 11(K)—c/(np); f~(L)— c7(ns) + c/(nd). We use in this way the results of the LCAO calculation to present in Fig. 4 the predicted K and L emission bands of V and Si. The same figure displays the corresponding experimental spectra obtained by one of us [15] . Examination of Fig. 4 shows that the cluster calculation reproduces well the main features of the spectra. The vanadium K and L spectra are specially well described by the calculation, the agreement with experiment being good for both the energy separations of subbands and the distribution of intensities. The low energy subbands of

Vol. 29, No. 3

X-RAY EMISSION SPECTRA OF V3Si

189

V

Qd 1.0

0,8

-

0.6

-

(2p-3d4~)

Q2 0,4 S.

S~.

Qs,Qp

~<

1,0 0.8 -

0.6

0,4 0,2

(/5

___________________________________ -15

-10

-5

ip)

S~L,,,,(_2p-is)

0

Fig. 4. Theoretical (LCAO) and experimental X-ray emission spectra of V35i. these spectra were interpreted in reference [15]as arising from Si 3s states and this is confirmed in the present calculation. On the other hand, the predictions for the silicium K and L bands are not in very good agreement with the experiment. There is no doubt that this is due to the choice of the cluster: it would be more adequate for the description of Si emission bands to use another

cluster centered at an Si-atom. A second reason for this discrepancy may be found in the absence of Si 3d atomic orbitals in the one-electron basis set used, Indeed, the results of band structure calculations [13] performed for V3Si have shown the Si 3d states to contribute significantly to the intensities of the Si L0 ~ emission spectrum. As the MS Xcx method is not of LCAO type, the relative intensities of emission bands can not be calculated in the same way. Nevertheless, the relative contributions of each MO can be estimated from an angular momentum analysis of its normalized fractions of charge in the different atomic spheres. As the MS Xa calculations performed for the three different cluster charges lead to very similar distributions of charge, we report here only the results obtained for the [V3Si4] 10Figure 3 presents a comparison between the spectra calculated by MS Xcs and the experimental ones [151.

experimental spectrum meets with difficulties. This is possibly connected with the choice of a V3Si4 cluster and further investigations are in progress in order to see whether the use of a larger cluster leads to a better description in this respect. Nevertheless, when taken as a whole, the present results demonstrate that the cluster model is a reasonable approximation for the description of X-ray emission spectra of the A-l5 compounds. This confirms that the characteristics of the X-ray emission spectra of solids are primarily determined by the nearest environment of the emitting atom.

Acknowledgement The calculations have been partly performed at the Computer Center of the University of Geneva, which is gratefully acknowledged for a grant —

of computer time.

REFERENCES 1. 2.

3. 4.

As in the LCAO case (Fig. 3), examination of Fig. 3 reveals that the main features of the experimental

5.

spectra are well reproduced by the calculations. However, the description of the fine structure of the

6.

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X-RAY EMISSION SPECTRA OF V3Si V.A. Gubanov & E.Z. Kurmaev, mt. J. Quant. C’hem. 9, 297 (1975). G.S. Zhdanov & S.M. Kuznetsova, Kristallographia 16, 1230 (1971). C.J. Ballhausen & H.B. Gray,Molecular Orbital Theory, Benjamin, New York (1964); H. Basch, A Viste & H.B. Gray,J. Chem. Phys. 44, 10 (1966). K.H. Johnson, Adv. Quant. Chem. 7 (1973). K. Schwarz,Phys. Rev. B5, 2466 (1972). L.F. Mattheiss, Phys. Rev. Bl2, 2161 (1975).

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Vol. 29, No. 3

T. Jarlborg & G. Arbman, J. Phys. F7, 1635 (1977). V.1. Nefedov, Valentnye Elektronnye Urovni Chimitcheskih Soedinenii, VINITI, Moskwa (1975). E.Z. Kurmaev, V.P. Belash, S.A. Nemnonov & A.S. Shulakov,Phys. Status Solidi(b) 61, 365

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