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X-ray K-emission spectra of niobium in niobium metal and some of its compounds
J. Phys. Chcm. Solids. 1972. Vol. 33. pp. 285-292.
Pergamon Press.
Printed in Great Britain
X-RAY K-EMISSION SPECTRA OF NIOBIUM IN NIOBIUM METAL AND SOME OF ITS COMPOUNDS V. G. BHIDE
National Physical Laboratory. New Delhi-12. India and M.
K. BAHL
A.R.S.D. College, University of Delhi, Delhi. India (Received
23 March
I97
I ; in revisedform
I June I97 I)
Abstract-The X-ray K-emission spectra of niobium in niobium metal and in several of its compounds have been investigated using 400-mm bent crystal (mica) spectrograph. The shift AE in the position of the X-ray diagram lines such as Kar,* and KB,2 can be expressed by the equation AE = i[BSf+ (m- l)B,,,] where i and WI are the overall ionicity and valence of niobium in a compound, B, and Bid are the constants which are different for K,,. K,. K,, and K, lines. For K,, B, is positive whereas Bid is negative, while for Kp2 the reverse is true. 1. INTRODUCTION
an atom enters into chemical combination, there is rearrangement of the valence electrons depending upon the nature of the chemical bond, which may be characterised by the degree of ionicity. valence of the participating atoms and the nature of hybridization. It has long been recognised that the rearrangement of the valence electronsGould affect not only the energy and wave function of outer electrons but also of the electrons belonging to the inner shells, thereby causing displacement and asymmetry in the X-ray diagram lines[ 1,2], shift in the position of the absorption edges [3,4] and through Fermicontact interaction the change in the energy of the nucleus[5,6]. Whereas the former, i.e. the changes in the X-ray diagram lines and the position of the absorption edges could be studied through X-ray spectroscopy, the latter could be investigated through Mossbauer spectroscopy. Thus in principle, the X-ray spectroscopic studies of the position of diagram lines and the absorption edges, and the Mossbauer spectroscopic investigations of the emitted y rays by the nucleus would yield information regarding the nature of the WHEN
chemical bond. Both these approaches have been followed with varying degree of success and considerable literature has already been accumulated [ l-63. In the field of X-ray spectroscopy, although extensive studies have been made on lighter elements and elements belonging to the first transition series, very little seems to have been done in respect of the elements belonging to the second transition series which have 4d incomplete shell. Our recent investigations [7,8] on the X-ray K-emission spectra of yttrium and the K-absorption edge of yttrium in several of its compounds have thrown considerable light on the nature of the chemical bond that yttrium has with different ligands, as also on the crystal field symmetry of the yttrium ion in these compounds. Unfortunately since yttrium enters into chemical combination only in one valence state, Y3+, the compounds of yttrium do not constitute a generalized system and is therefore not amenable to generalized approach. Niobium, the third member of the second transition series can exist in various valence states and forms variety of compounds and hence it was thought desirable to investigate the K-emission spectra
286
V.
G.
BHIDE
and
M.
K.
BAHL
of niobium in its several compounds, with a view to at least provide a semiquantitative explanation for the shift of the X-ray diagram lines. 2. EXPERIMENTAL
A 400-mm bent crystal transmission spectrograph using a mica crystal oriented to reflect from ( 100) planes was employed for recording the spectra as described in our earlier communication [7]. Secondary excitation method (tube voltage 35 k.V and current 20 mA) was used to excite the K-emission spectra of niobium in several of its compounds. Niobium K aI.2 lines were photographed in the second order where they could be bracketed between the second order Zr K,,:, and the first order Zn K,, lines. For niobium KP1,? lines. the Zn K,, and Zn Kp, lines were used as reference lines. The experimental set up was such that the experimental niobium compounds pressed between mylar sheets could be replaced by sliding in its position the reference metal. zirconium or zinc as the case may be without disturbing the spectrograph. While eight hours exposure was enough to record the reference lines with good contrast, 60 hr exposure was necessary to obtain niobium lines. particularly KBZ with reasonable intensity. At least three spectra were recorded for each sample and each spectrum was microphotometered at 10 heights. Thus the values reported here are the mean of at least 30 measurements. A typical microphotometer trace of the Kemission spectra of niobium in NbO is shown in Fig. 1. The maxima in the intensity of the corresponding lines marked their positions. The error mentioned along with the values of the K-emission lines denote the spread in values obtained over a large number of microphotometer records. No attempt was made to correct the width of these lines for the instrumental broadening and hence the asymmetry in the lines has not been determined.
Fig. I. niobium appeared
A
typical microphotometer trace obtained for K-emission spectra in NbO (Copper lines due to impurity in aluminium plate holding the sample).
3. RESULTS
3(a) Oxides of rziobiurn Niobium forms three oxides: NbO. NbO, and Nb,O,. Table I gives the wavelength of K,,, lines for various oxides and other compounds of niobium. It is seen that both Kaly2 lines in each of these oxides are shifted from their corresponding position for niobium metal. It is interesting to note that for NbO. both K,, as well as Km2 are shifted towards the higher energy side while in contrast, in Nb,O,. they are displaced on the low energy side. In NbO,, the shift of K,, and K, are on the opposite side: K,, being on the high energy side whereas K, is on the low energy side. It is. however. suggestive that among the oxides themselves. the K,, .L, doublet moves progressively towards lower energy with increase in valence of niobium. Similar displacement in position of the K,, .2 doublet has been reported by Meisel[21 in various oxides of manganese. The shift in the position of K,,:, lines with change in valence seems to reflect the nature of the chemical bond and through it. the magnetic properties of the compounds. Thus while NbO is ferromagnetic. NbO, is paramagnetic and Nb,O, is diamagnetic[9]. It is to be noted from Table 2 that niobium
NIOBIUM
Table
1. Wtrwleqths in niobium
IN
NIOBIUM
Position
I. 2. 3. 4. 56:
Table
2.
Name S.No.
and shift X.U. AA,
hhol
Nb metal NbO NbOz Nb,O, NbN NbC
Wurelettgtlts
287
of K,,, emission lines tnetctl utld its cornpowtds
Name of the compound
S.No.
METAL
746.14 745.94 746.02 746.28 746.08 746.26
-0.20 -0.12 +0.14 -0.06 +0.12
of K,, 2 emission ~0~04X.U. (II
750.35 750.22 750.38 750.48 750.38 750.31
ttiobiuttt of the
Position
Nb metal
t-o.04 hAlll -
NbO
665.70 665.67
NbOZ Nb,O, NbN NbC
665.68 665.56 665.62
lines AA,
AK a*
K,,, :! etnission littes tnetal trnd irs comporrnds
compound
of
of niobiutn
K,j, line is almost at the same position in all the three oxides. while the shift in K,, line is considerably large. From Table 2. it can be seen that for NbO. K,,, line shifts towards negative energy side while for NbO, and Nb,O,. it moves towards higher energy side as compared to niobium metal. However, it is to be noticed that among the oxides, K,, shifts towards higher energy side with increase in valency. It is interesting to note that the effect of valency on the shift of KBI line is just opposite to what has been observed in K,, .’ lines.
3(b) Niobium oxide, nitride rrtld carbide (NbO, NbN and NbC) It is to be noted that there is a systematic shift of the K,,::! lines (Table 1) towards low energy side. as one moves from NbO-NbN(Table 2) shift towards NbC. while K,,, higher energy side. Similar displacement in the position of the K,,,2 emission lines has
uz
-0.13' +0.03 +0.13 +0.03 -0.04
of
niobitrtn
and shift of Kt, ,, emission lines AA,, I’- Aho2 to.05 0, -0.03 -0.02 -0.02 -0.14 -0.08
in
654.20 654.34 654.00 653.89 654.08 654.16
in
in X.U. IAK
or
fO.14 -0.20 -0.31 -0.12 -0.04
been reported by Vainshtein et crl.[ IO] in the series TiO-TiN-Tic. From Table 1 and 2. it is interesting to note that in the series NbO-NbN-NbC. the dependence of the shift of K,,,., and that of K,, lines on the valency (equal to 2, 3,4 respectively) as well as ionicity of the chemical bond (Table 3) is similar to that observed in various oxides of niobium. 4. DlSCUSSION
The understanding of the nature of the chemical bond, an atom of a given element has with surrounding ligands in a chemical compound has been the subject of intense investigation in recent years. Various experimental techniques have been brought to bear on this problem. The chemical bond can in general be characterised by the three parameters, viz. (1) ionicity of the bond, (2) valence of the participating ions and (3) the nature of hybridization. These three factors essentially determine the rearrangement of
288
V.
G.
AEh.
S.No.
Compound
I.
NbO NbO, Nb,O, NbC NbN
2. 3. 4. 5.
eV”’ +4.46 +2.67 -3.12 -2.67 +1.33
BHIDE
and
AE,
eV ‘ti +'.86 -0.66 -2.86 -0.66 +0.89
the outer valence electrons in an atom, as it enters into chemical combination. Although inner electrons do not themselves participate in chemical combination, their energies and wavefunctions are altered by the rearrangement of outer electrons through screening, exchange interactions, etc. The changes in the wavefunction and energy of the inner electrons are reflected in the shift and asymmetry of various X-ray diagram lines[ 1,2], as also in the shift of different absorption edges [3.4]. Although experimental-determination of the shift in the X-ray diagram lines, the position of X-ray absorption edges is not difficult, their correlation with the exact rearrangement of outer electrons and hence with the nature of chemical bond offer considerable difficulties. We will discuss some of these difficulties and as a first step to the solution of the problem, analyse the data for niobium compounds, through semi-quantitative and semi-emperical formalism. Let us first consider an isolated atom of a given element. Each of the electrons has certain wavefunction and an energy, which can be determined by self-consistent calculations. The energy E of any subshell for a neutral atom can be expressed as E
=
RhC(Z-u)2
n2
(1)
where u the screening constant has different values for different subshells. This expression presupposes the nucleus as a point charge. If one takes into consideration the finite
M.
I(.
BAHL
LEA 112
eV
Coordination no.
-4.06 +5.80 +8.99 +3.48 +I.16
4 6 6 6 6
lonicity 0.80 0.73 0.66 0.46 0.69
charge density of the nucleus, then the S electron energies are altered. This factor is given by 2/5rZe”R,,‘I$(O)I’ where I$(O)I’ is the S electron density at the nucleus and is different for different S subshells and R, is the radius of the nucleus in the ground state. This factor will not appear for other subshells such as p. d, etc., except when we have relativistic pi electron. When an atom goes into chemical combination, because of the rearrangement of outer electrons, the screening constant changes and for the s electrons I$(O)I’ term also changes. We may write the energy of various shells as
where 6 is finite for s electrons and zero for other electrons. Thus consequent on the atom entering into chemical combination cr and 6 change to (T’ and 6’ respectively, and hence the energy of the subshell changes by an amount AE given by AE=y
[(z-u’)‘-(Z-a)‘]+(6’-c3).
Taking the case of K, radiation, the change in the energy of K, radiation will be given by AEK, = RhC
(Z-a’)2-(Z-u)2 n’
_ (Z-CT’)‘-(Z-a)2 n? i
I 21,
-~)sclec IIIS+(6’
NIOBIUM
IN NIOBIUM
The term (6’ - 6) is very small (- 1OmseV) as compared to the first term (- eV) and hence (6’ -6) is generally omitted in the expression for the shift of emission lines. AEK, is what one measures experimentally. Through its experimental determination. if we want to get an idea about the nature of the chemical bond, it is necessary to get the value of (T and CJ’ for Is and 2p subshells for various possible combination of the rearrangement of outer electrons and then obtain the best fit. The determination of u and u’ for any subshell involves Hartree-Fock self consistent Using Hartree-Fockfield calculations. Slater method. Lindgren [ 1 l] calculated for a series of atoms (13 G Z < 36) the shift in K, (2p- 1s) and Kp, (3p- 1s) transition energy of an isolated atom due to removal of an electron from various subshells. Indeed since 1960’s numerous authors [ 121 have developed computational techniques to obtain atomic wavefunctions in the nonrelativistic approximation. Some work[ 131 has been done more recently to take account of the relativistic effects. However. all these efforts suffer from the same drawback and that is these computations do not take into consideration the band formation consequent on the fact that we are considering a solid and not an isolated atom or a molecule. It is, therefore, necessary to undertake anti-emperical and semi-quantitative analysis of the results. Recently it has been shown by electron spectroscopic techniques [ 14, 151 that the binding energies of electrons in various subshells of an atom change on chemical combination. The change in the energy of a given subshell is determined by three factors: viz. (1) degree of ionicity, (2) valence of the atom in a compound and (3) the nature of hybridization. We may, therefore, express the energy of any subshell consequent on the atom getting into a chemical combination as follows:
289
METAL
where i is the overall ionicity, mj is the contribution of various electrons to the chemical bond, j= s, p, d ------, with T mj = m = valence of the element concerned. Cj is the change in energy of the subshell because of the jlh electron participating in chemical combination. The above equation recognizes the fact that the change in energy of the subshell will be determined by the nature of the bonding electron, and at the same time assumes that the changes in the energy of a given subshell brought about by various bonding electrons are additive. Taking the particular case of K, radiation. we have
E,,, = ~(z-~Jz] [
+ C imjCj 2,) j
+z
j
imjCj-x
C mjCj-C mjCf j j
j
imjCj
imjCi
1
AEx, = i Cmj(Cj-Cl) j AEKu= i 2 mjBj.
(2)
j
We may examine the applicability of the above equation with reference to the compounds of Niobium. Niobium atom has the following electronic configuration, 4d45s1. Since all niobium compounds have valency greater than two, we assume that 5s electron takes part in chemical combination in all these compounds. Thus equation (2) takes the form
AEK,, = i[@; +(m - I)@:;]. E=y(Z--a)“+C
j
Since in Kp, 2 and K,, different
(3)
levels are
190
V.
G.
involved in the transitibn. we similar equations for these lines ilEhmL = i[/3;;+(m-
may
BHIDE
and
write
I)@;,?,]
M.
K.
BAHL
line. AExU,/i decreases as 177 increases. From the plot of AEli against 171. we now calculate B ,,, and B,,v for K,, and KB1 and find that
(4) B,, = +6.4
and so on. In Fig. 3 we plot the graph between AEli and m for K,,, KBz lines. The ionicity i has been calculated using Pauling formulation
[IfA. i = 1 -y[exp
(-0.251~~1
where tn is the valency. N is the coordination number and LLY is the difference in the electronegativities of the partners in the compound. It is interesting to see that AEA,12/i and .lEhli21i when plotted against valency I?I (Fig. 2) falls on a straight line with negative slope for K,, and positive slope for K,,,. Although LIE,-,,/I’ and 1)~ curve is not strictly a straight
I
KB2
*Nb20,
Fig.
2. A plot of .l15/i as a function and K,,? lines of niobium in some
of valence ~1 for of its compounds.
A’,,!
eV
and B ,,, = -2.6
Br,,< = -1 I .26 eV and B,,, = t-6.2
eV for K,, eV for Kljc.
It is interesting to see that the effect of the removal of 4d electron is opposite to the effect of the removal of 5s electron. It is equally significant to note that whereas removal of 5s electron increases the energy of ti,, line. its removal decreases the energy of K,,, line. It is interesting to note that even in the first transition series. K,,, line shifts towards higher energy side for the loss of 4s electron and towards lower energy for the loss of 3~1 electrons1 I I]. Although no self consistent field calculations have yet been made for Niobium and its ions. Roothan ct trl. [ 171 have recently computed using self consistent methods the energy levels of various subshells for MO (4tl” 5,s’) and MO+ (4d”). His calculations clearly show that on removal of 5s electron. the k’,,, line should shift towards higher energy. whereas KliL line should shift towards lower energy. essentially confirming the validity of the above approach. Similar approach has been followed by Shumbaev[I8] for oxides of various elements. It may now be of interest to examine the relative magnitudes of Bgr and B.,,, for K,,, and K,, lines and to see whether they have any physical significance. It is to be noted that the magnitude of B,,$ for K,, as well as for K,, is greater than the B,,,. This means that the energy of the inner levels of the atom are more affected by the removal of 5s electron than that by the removal of St/ electron. This indeed is to be expected because S electrons have a greater probability of being near the nucleus. It is equally significant to note that the magnitude of both B,, and B.,,, for K,j, are greater than for K,,,. Since K,, corresponds to transition 7p- Is and K,,, involves a transition 4p - 1s. the higher values of both B,,q and
NIOBIUM
IN
NIOBlUM
B -1,, imply that valence electrons penetrate 4p shell more than the 2p shell. which is rather obvious. As pointed out earlier, the nature of the chemical bond could also be explored through the corresponding changes in the energy of the nucleus which can be studied through Mossbauer spectroscopy. The energy of the nucleus for a neutral atom can be expressed as E = E,,+ h-r~,e~~$(O)~‘R,;~
where II/J,CO)I’is the s electron density at the nucleus and R,, is the radius of the nucleus in the ground state. and E,, is the energy of the nucleus taken as a point. The energy of the nucleus in the excited state may be given by E’ = E,; ++~,r’)1,5(0)(‘R;,
where R,, is the radius of the nucleus in the excited state. The emitted y-ray has an energy
x (Rf,-R.‘)
which may be expressed as
Thus the shift in the y-ray energy because of electrostatic interaction hhv = ~i~,7~~~(R;,- R,,‘)(JI(O)(‘.
Now as the atom goes into chemical combination. because of rearrangement of the outer valence electrons. the s electron density of the nucleus changes. which is reflected in the shift of the Mossbauer spectrum. Thus Mossbauer studies give an idea about the total change in the s electron density consequent on the atom entering into chemical combination. Here again to get the precise understanding of the nature of the chemical
METAL
291
bond characterised by valency. ionicity, hybridization. one has to relate changes in I$(O)(’ to these three parameters. Similar to the approach we have followed above for the analysis of the shifts in the X-ray diagram lines. Hafemeister [ 191 and others have shown that the isomer shift for 1”” changes linearly as the number of I-’ holes increase consequent on iodine enter into chemical combination. Perlow[20] has used the same method of analysis for Xelns. Although these approaches are not rigorous. this is the only approach that is possible at the moment. It may be mentioned that while X-ray spectroscopy gives the changes in the energy differences of two subshells. the Mossbauer spectroscopy gives an integrated effect and that also caused by S electrons. This advantage is offset to an extent by higher accuracy with which y-ray energies can be measured in Mossbauer spectroscopy. We shall attempt to bring out the detailed comparison of the Mossbauer techniques and X-ray spectroscopic techniques for the study of chemical bond in a separate communication. A~,~,lo~~,/rd,~~,nre,lts - We wish to express our grateful thanks to Prof. E. Sam of Giessen University. Germany for supplying us samples of pure NbN. 0neofusfM.K.B.) wishes- to express his sincere thanks to the Council of Scientific and Industrial Research for the award of a research fellowship held during the course of this study.
REFERENCES A. and DORING E.. Z. Plr~s. Chrnr. 220. I. MEISEL 397 (1962). 2. MENSHIKOV A. 2.. NEMNONOV S. A. and MICHCHENKO L. B.. Phys. Mercrll. Metdloced. 14. No. 3.54 (1962). W. W.. FORSS J. and HUMPHRY 3. BEEMAN J. N..Pltx~. Rec.67.217 (1945). V. G. and BAHL M. K..J. c/rent. Phys. 52, 4. BHIDE 4093 ( 1970); J. P/I.w. Chm. Solids (in press). 5 SHIRLEY D. A.. Rec. mod. Ph.vs. 36. 339 (1964). 6: BOYLE A. J.. BUNBURY D. S. P.and EDWARDS C.. Proc. Phys. Sot. Lad. 79. 4 I6 ( 1962). 7. BHIDE V. G. and BHAT N. V., J. rrppl. Phys. 41, 3159(1970). V. G. and BHAT N. V.. J. chrm. Ph.w. 48. 8. BHIDE 3 103 (1968). 9. BRAUER G.. Z. A,rorg. A//~c’nr. Clrern. 256. 10 (1948).
292
V.
G.
BHIDE
10. CHIRKOV V. I., BLOKHIN S. M. and VAINSHTEIN E. E.. F‘i: rcerd. Teln 9. 11 16 ( 1967). 1 1. LINDGREN 1.. In Rorugen Spekwe,~ rrnd Cl~rmisrhr Bindung (Edited A. Meisel). pp. 182. VEB Reprocalor. Leipzig ( 1966). 12. HERMAN F. and SKILLMAN S..AromicSrruc~ture Calculafions. Prentice Hall, New York (1963). 13. LIBERMAN B.. WABER J. T. and CROMER D. T., Phys. Rec. 137, A27 (1965). 14. NORDBERG R., HAMRIN K., FAHLMAN A.. NORDLING C. and SIEGBAHN K.. Z. Pl7.vsik 192.462 ( 1966). 15. FAHLMAN A.. HAMRIN K.. HEDMAN J..
and
M.
16. 17. 18. 19. 20.
K.
BAHL
NORDBERG R.. NORDLING C. and SIEGHBAHN K.. Notrrre. Land. 210, 4 (1966). PAULING L.. The Norrrre of IIW Clwmiccrl Bond. pp. 77. Russian Translation Godkhimizdat (1947). ROOTHAN CLEMENS C. J. and SYNEK MIROSLAV. P/qs. Rec. 133A. 1263 (1964). SUMBAEV 0. I.. Sorier Phys. JEPT 30. 927 (1970). HAFEMEISTER D. W.. DePASQUALl G. and DEWAARD H.. Phys. Rec. 135. B 1089 (1964). PERLOW G. J., In Chemical Applications of Miissbauer Spectroscopy (Edited by Goldanskii V. 1. and Herber R. H.). pp. 377. Academic Press, New York (I 968).
Pergamon Press.
Printed in Great Britain
X-RAY K-EMISSION SPECTRA OF NIOBIUM IN NIOBIUM METAL AND SOME OF ITS COMPOUNDS V. G. BHIDE
National Physical Laboratory. New Delhi-12. India and M.
K. BAHL
A.R.S.D. College, University of Delhi, Delhi. India (Received
23 March
I97
I ; in revisedform
I June I97 I)
Abstract-The X-ray K-emission spectra of niobium in niobium metal and in several of its compounds have been investigated using 400-mm bent crystal (mica) spectrograph. The shift AE in the position of the X-ray diagram lines such as Kar,* and KB,2 can be expressed by the equation AE = i[BSf+ (m- l)B,,,] where i and WI are the overall ionicity and valence of niobium in a compound, B, and Bid are the constants which are different for K,,. K,. K,, and K, lines. For K,, B, is positive whereas Bid is negative, while for Kp2 the reverse is true. 1. INTRODUCTION
an atom enters into chemical combination, there is rearrangement of the valence electrons depending upon the nature of the chemical bond, which may be characterised by the degree of ionicity. valence of the participating atoms and the nature of hybridization. It has long been recognised that the rearrangement of the valence electronsGould affect not only the energy and wave function of outer electrons but also of the electrons belonging to the inner shells, thereby causing displacement and asymmetry in the X-ray diagram lines[ 1,2], shift in the position of the absorption edges [3,4] and through Fermicontact interaction the change in the energy of the nucleus[5,6]. Whereas the former, i.e. the changes in the X-ray diagram lines and the position of the absorption edges could be studied through X-ray spectroscopy, the latter could be investigated through Mossbauer spectroscopy. Thus in principle, the X-ray spectroscopic studies of the position of diagram lines and the absorption edges, and the Mossbauer spectroscopic investigations of the emitted y rays by the nucleus would yield information regarding the nature of the WHEN
chemical bond. Both these approaches have been followed with varying degree of success and considerable literature has already been accumulated [ l-63. In the field of X-ray spectroscopy, although extensive studies have been made on lighter elements and elements belonging to the first transition series, very little seems to have been done in respect of the elements belonging to the second transition series which have 4d incomplete shell. Our recent investigations [7,8] on the X-ray K-emission spectra of yttrium and the K-absorption edge of yttrium in several of its compounds have thrown considerable light on the nature of the chemical bond that yttrium has with different ligands, as also on the crystal field symmetry of the yttrium ion in these compounds. Unfortunately since yttrium enters into chemical combination only in one valence state, Y3+, the compounds of yttrium do not constitute a generalized system and is therefore not amenable to generalized approach. Niobium, the third member of the second transition series can exist in various valence states and forms variety of compounds and hence it was thought desirable to investigate the K-emission spectra
286
V.
G.
BHIDE
and
M.
K.
BAHL
of niobium in its several compounds, with a view to at least provide a semiquantitative explanation for the shift of the X-ray diagram lines. 2. EXPERIMENTAL
A 400-mm bent crystal transmission spectrograph using a mica crystal oriented to reflect from ( 100) planes was employed for recording the spectra as described in our earlier communication [7]. Secondary excitation method (tube voltage 35 k.V and current 20 mA) was used to excite the K-emission spectra of niobium in several of its compounds. Niobium K aI.2 lines were photographed in the second order where they could be bracketed between the second order Zr K,,:, and the first order Zn K,, lines. For niobium KP1,? lines. the Zn K,, and Zn Kp, lines were used as reference lines. The experimental set up was such that the experimental niobium compounds pressed between mylar sheets could be replaced by sliding in its position the reference metal. zirconium or zinc as the case may be without disturbing the spectrograph. While eight hours exposure was enough to record the reference lines with good contrast, 60 hr exposure was necessary to obtain niobium lines. particularly KBZ with reasonable intensity. At least three spectra were recorded for each sample and each spectrum was microphotometered at 10 heights. Thus the values reported here are the mean of at least 30 measurements. A typical microphotometer trace of the Kemission spectra of niobium in NbO is shown in Fig. 1. The maxima in the intensity of the corresponding lines marked their positions. The error mentioned along with the values of the K-emission lines denote the spread in values obtained over a large number of microphotometer records. No attempt was made to correct the width of these lines for the instrumental broadening and hence the asymmetry in the lines has not been determined.
Fig. I. niobium appeared
A
typical microphotometer trace obtained for K-emission spectra in NbO (Copper lines due to impurity in aluminium plate holding the sample).
3. RESULTS
3(a) Oxides of rziobiurn Niobium forms three oxides: NbO. NbO, and Nb,O,. Table I gives the wavelength of K,,, lines for various oxides and other compounds of niobium. It is seen that both Kaly2 lines in each of these oxides are shifted from their corresponding position for niobium metal. It is interesting to note that for NbO. both K,, as well as Km2 are shifted towards the higher energy side while in contrast, in Nb,O,. they are displaced on the low energy side. In NbO,, the shift of K,, and K, are on the opposite side: K,, being on the high energy side whereas K, is on the low energy side. It is. however. suggestive that among the oxides themselves. the K,, .L, doublet moves progressively towards lower energy with increase in valence of niobium. Similar displacement in position of the K,, .2 doublet has been reported by Meisel[21 in various oxides of manganese. The shift in the position of K,,:, lines with change in valence seems to reflect the nature of the chemical bond and through it. the magnetic properties of the compounds. Thus while NbO is ferromagnetic. NbO, is paramagnetic and Nb,O, is diamagnetic[9]. It is to be noted from Table 2 that niobium
NIOBIUM
Table
1. Wtrwleqths in niobium
IN
NIOBIUM
Position
I. 2. 3. 4. 56:
Table
2.
Name S.No.
and shift X.U. AA,
hhol
Nb metal NbO NbOz Nb,O, NbN NbC
Wurelettgtlts
287
of K,,, emission lines tnetctl utld its cornpowtds
Name of the compound
S.No.
METAL
746.14 745.94 746.02 746.28 746.08 746.26
-0.20 -0.12 +0.14 -0.06 +0.12
of K,, 2 emission ~0~04X.U. (II
750.35 750.22 750.38 750.48 750.38 750.31
ttiobiuttt of the
Position
Nb metal
t-o.04 hAlll -
NbO
665.70 665.67
NbOZ Nb,O, NbN NbC
665.68 665.56 665.62
lines AA,
AK a*
K,,, :! etnission littes tnetal trnd irs comporrnds
compound
of
of niobiutn
K,j, line is almost at the same position in all the three oxides. while the shift in K,, line is considerably large. From Table 2. it can be seen that for NbO. K,,, line shifts towards negative energy side while for NbO, and Nb,O,. it moves towards higher energy side as compared to niobium metal. However, it is to be noticed that among the oxides, K,, shifts towards higher energy side with increase in valency. It is interesting to note that the effect of valency on the shift of KBI line is just opposite to what has been observed in K,, .’ lines.
3(b) Niobium oxide, nitride rrtld carbide (NbO, NbN and NbC) It is to be noted that there is a systematic shift of the K,,::! lines (Table 1) towards low energy side. as one moves from NbO-NbN(Table 2) shift towards NbC. while K,,, higher energy side. Similar displacement in the position of the K,,,2 emission lines has
uz
-0.13' +0.03 +0.13 +0.03 -0.04
of
niobitrtn
and shift of Kt, ,, emission lines AA,, I’- Aho2 to.05 0, -0.03 -0.02 -0.02 -0.14 -0.08
in
654.20 654.34 654.00 653.89 654.08 654.16
in
in X.U. IAK
or
fO.14 -0.20 -0.31 -0.12 -0.04
been reported by Vainshtein et crl.[ IO] in the series TiO-TiN-Tic. From Table 1 and 2. it is interesting to note that in the series NbO-NbN-NbC. the dependence of the shift of K,,,., and that of K,, lines on the valency (equal to 2, 3,4 respectively) as well as ionicity of the chemical bond (Table 3) is similar to that observed in various oxides of niobium. 4. DlSCUSSION
The understanding of the nature of the chemical bond, an atom of a given element has with surrounding ligands in a chemical compound has been the subject of intense investigation in recent years. Various experimental techniques have been brought to bear on this problem. The chemical bond can in general be characterised by the three parameters, viz. (1) ionicity of the bond, (2) valence of the participating ions and (3) the nature of hybridization. These three factors essentially determine the rearrangement of
288
V.
G.
AEh.
S.No.
Compound
I.
NbO NbO, Nb,O, NbC NbN
2. 3. 4. 5.
eV”’ +4.46 +2.67 -3.12 -2.67 +1.33
BHIDE
and
AE,
eV ‘ti +'.86 -0.66 -2.86 -0.66 +0.89
the outer valence electrons in an atom, as it enters into chemical combination. Although inner electrons do not themselves participate in chemical combination, their energies and wavefunctions are altered by the rearrangement of outer electrons through screening, exchange interactions, etc. The changes in the wavefunction and energy of the inner electrons are reflected in the shift and asymmetry of various X-ray diagram lines[ 1,2], as also in the shift of different absorption edges [3.4]. Although experimental-determination of the shift in the X-ray diagram lines, the position of X-ray absorption edges is not difficult, their correlation with the exact rearrangement of outer electrons and hence with the nature of chemical bond offer considerable difficulties. We will discuss some of these difficulties and as a first step to the solution of the problem, analyse the data for niobium compounds, through semi-quantitative and semi-emperical formalism. Let us first consider an isolated atom of a given element. Each of the electrons has certain wavefunction and an energy, which can be determined by self-consistent calculations. The energy E of any subshell for a neutral atom can be expressed as E
=
RhC(Z-u)2
n2
(1)
where u the screening constant has different values for different subshells. This expression presupposes the nucleus as a point charge. If one takes into consideration the finite
M.
I(.
BAHL
LEA 112
eV
Coordination no.
-4.06 +5.80 +8.99 +3.48 +I.16
4 6 6 6 6
lonicity 0.80 0.73 0.66 0.46 0.69
charge density of the nucleus, then the S electron energies are altered. This factor is given by 2/5rZe”R,,‘I$(O)I’ where I$(O)I’ is the S electron density at the nucleus and is different for different S subshells and R, is the radius of the nucleus in the ground state. This factor will not appear for other subshells such as p. d, etc., except when we have relativistic pi electron. When an atom goes into chemical combination, because of the rearrangement of outer electrons, the screening constant changes and for the s electrons I$(O)I’ term also changes. We may write the energy of various shells as
where 6 is finite for s electrons and zero for other electrons. Thus consequent on the atom entering into chemical combination cr and 6 change to (T’ and 6’ respectively, and hence the energy of the subshell changes by an amount AE given by AE=y
[(z-u’)‘-(Z-a)‘]+(6’-c3).
Taking the case of K, radiation, the change in the energy of K, radiation will be given by AEK, = RhC
(Z-a’)2-(Z-u)2 n’
_ (Z-CT’)‘-(Z-a)2 n? i
I 21,
-~)sclec IIIS+(6’
NIOBIUM
IN NIOBIUM
The term (6’ - 6) is very small (- 1OmseV) as compared to the first term (- eV) and hence (6’ -6) is generally omitted in the expression for the shift of emission lines. AEK, is what one measures experimentally. Through its experimental determination. if we want to get an idea about the nature of the chemical bond, it is necessary to get the value of (T and CJ’ for Is and 2p subshells for various possible combination of the rearrangement of outer electrons and then obtain the best fit. The determination of u and u’ for any subshell involves Hartree-Fock self consistent Using Hartree-Fockfield calculations. Slater method. Lindgren [ 1 l] calculated for a series of atoms (13 G Z < 36) the shift in K, (2p- 1s) and Kp, (3p- 1s) transition energy of an isolated atom due to removal of an electron from various subshells. Indeed since 1960’s numerous authors [ 121 have developed computational techniques to obtain atomic wavefunctions in the nonrelativistic approximation. Some work[ 131 has been done more recently to take account of the relativistic effects. However. all these efforts suffer from the same drawback and that is these computations do not take into consideration the band formation consequent on the fact that we are considering a solid and not an isolated atom or a molecule. It is, therefore, necessary to undertake anti-emperical and semi-quantitative analysis of the results. Recently it has been shown by electron spectroscopic techniques [ 14, 151 that the binding energies of electrons in various subshells of an atom change on chemical combination. The change in the energy of a given subshell is determined by three factors: viz. (1) degree of ionicity, (2) valence of the atom in a compound and (3) the nature of hybridization. We may, therefore, express the energy of any subshell consequent on the atom getting into a chemical combination as follows:
289
METAL
where i is the overall ionicity, mj is the contribution of various electrons to the chemical bond, j= s, p, d ------, with T mj = m = valence of the element concerned. Cj is the change in energy of the subshell because of the jlh electron participating in chemical combination. The above equation recognizes the fact that the change in energy of the subshell will be determined by the nature of the bonding electron, and at the same time assumes that the changes in the energy of a given subshell brought about by various bonding electrons are additive. Taking the particular case of K, radiation. we have
E,,, = ~(z-~Jz] [
+ C imjCj 2,) j
+z
j
imjCj-x
C mjCj-C mjCf j j
j
imjCj
imjCi
1
AEx, = i Cmj(Cj-Cl) j AEKu= i 2 mjBj.
(2)
j
We may examine the applicability of the above equation with reference to the compounds of Niobium. Niobium atom has the following electronic configuration, 4d45s1. Since all niobium compounds have valency greater than two, we assume that 5s electron takes part in chemical combination in all these compounds. Thus equation (2) takes the form
AEK,, = i[@; +(m - I)@:;]. E=y(Z--a)“+C
j
Since in Kp, 2 and K,, different
(3)
levels are
190
V.
G.
involved in the transitibn. we similar equations for these lines ilEhmL = i[/3;;+(m-
may
BHIDE
and
write
I)@;,?,]
M.
K.
BAHL
line. AExU,/i decreases as 177 increases. From the plot of AEli against 171. we now calculate B ,,, and B,,v for K,, and KB1 and find that
(4) B,, = +6.4
and so on. In Fig. 3 we plot the graph between AEli and m for K,,, KBz lines. The ionicity i has been calculated using Pauling formulation
[IfA. i = 1 -y[exp
(-0.251~~1
where tn is the valency. N is the coordination number and LLY is the difference in the electronegativities of the partners in the compound. It is interesting to see that AEA,12/i and .lEhli21i when plotted against valency I?I (Fig. 2) falls on a straight line with negative slope for K,, and positive slope for K,,,. Although LIE,-,,/I’ and 1)~ curve is not strictly a straight
I
KB2
*Nb20,
Fig.
2. A plot of .l15/i as a function and K,,? lines of niobium in some
of valence ~1 for of its compounds.
A’,,!
eV
and B ,,, = -2.6
Br,,< = -1 I .26 eV and B,,, = t-6.2
eV for K,, eV for Kljc.
It is interesting to see that the effect of the removal of 4d electron is opposite to the effect of the removal of 5s electron. It is equally significant to note that whereas removal of 5s electron increases the energy of ti,, line. its removal decreases the energy of K,,, line. It is interesting to note that even in the first transition series. K,,, line shifts towards higher energy side for the loss of 4s electron and towards lower energy for the loss of 3~1 electrons1 I I]. Although no self consistent field calculations have yet been made for Niobium and its ions. Roothan ct trl. [ 171 have recently computed using self consistent methods the energy levels of various subshells for MO (4tl” 5,s’) and MO+ (4d”). His calculations clearly show that on removal of 5s electron. the k’,,, line should shift towards higher energy. whereas KliL line should shift towards lower energy. essentially confirming the validity of the above approach. Similar approach has been followed by Shumbaev[I8] for oxides of various elements. It may now be of interest to examine the relative magnitudes of Bgr and B.,,, for K,,, and K,, lines and to see whether they have any physical significance. It is to be noted that the magnitude of B,,$ for K,, as well as for K,, is greater than the B,,,. This means that the energy of the inner levels of the atom are more affected by the removal of 5s electron than that by the removal of St/ electron. This indeed is to be expected because S electrons have a greater probability of being near the nucleus. It is equally significant to note that the magnitude of both B,, and B.,,, for K,j, are greater than for K,,,. Since K,, corresponds to transition 7p- Is and K,,, involves a transition 4p - 1s. the higher values of both B,,q and
NIOBIUM
IN
NIOBlUM
B -1,, imply that valence electrons penetrate 4p shell more than the 2p shell. which is rather obvious. As pointed out earlier, the nature of the chemical bond could also be explored through the corresponding changes in the energy of the nucleus which can be studied through Mossbauer spectroscopy. The energy of the nucleus for a neutral atom can be expressed as E = E,,+ h-r~,e~~$(O)~‘R,;~
where II/J,CO)I’is the s electron density at the nucleus and R,, is the radius of the nucleus in the ground state. and E,, is the energy of the nucleus taken as a point. The energy of the nucleus in the excited state may be given by E’ = E,; ++~,r’)1,5(0)(‘R;,
where R,, is the radius of the nucleus in the excited state. The emitted y-ray has an energy
x (Rf,-R.‘)
which may be expressed as
Thus the shift in the y-ray energy because of electrostatic interaction hhv = ~i~,7~~~(R;,- R,,‘)(JI(O)(‘.
Now as the atom goes into chemical combination. because of rearrangement of the outer valence electrons. the s electron density of the nucleus changes. which is reflected in the shift of the Mossbauer spectrum. Thus Mossbauer studies give an idea about the total change in the s electron density consequent on the atom entering into chemical combination. Here again to get the precise understanding of the nature of the chemical
METAL
291
bond characterised by valency. ionicity, hybridization. one has to relate changes in I$(O)(’ to these three parameters. Similar to the approach we have followed above for the analysis of the shifts in the X-ray diagram lines. Hafemeister [ 191 and others have shown that the isomer shift for 1”” changes linearly as the number of I-’ holes increase consequent on iodine enter into chemical combination. Perlow[20] has used the same method of analysis for Xelns. Although these approaches are not rigorous. this is the only approach that is possible at the moment. It may be mentioned that while X-ray spectroscopy gives the changes in the energy differences of two subshells. the Mossbauer spectroscopy gives an integrated effect and that also caused by S electrons. This advantage is offset to an extent by higher accuracy with which y-ray energies can be measured in Mossbauer spectroscopy. We shall attempt to bring out the detailed comparison of the Mossbauer techniques and X-ray spectroscopic techniques for the study of chemical bond in a separate communication. A~,~,lo~~,/rd,~~,nre,lts - We wish to express our grateful thanks to Prof. E. Sam of Giessen University. Germany for supplying us samples of pure NbN. 0neofusfM.K.B.) wishes- to express his sincere thanks to the Council of Scientific and Industrial Research for the award of a research fellowship held during the course of this study.
REFERENCES A. and DORING E.. Z. Plr~s. Chrnr. 220. I. MEISEL 397 (1962). 2. MENSHIKOV A. 2.. NEMNONOV S. A. and MICHCHENKO L. B.. Phys. Mercrll. Metdloced. 14. No. 3.54 (1962). W. W.. FORSS J. and HUMPHRY 3. BEEMAN J. N..Pltx~. Rec.67.217 (1945). V. G. and BAHL M. K..J. c/rent. Phys. 52, 4. BHIDE 4093 ( 1970); J. P/I.w. Chm. Solids (in press). 5 SHIRLEY D. A.. Rec. mod. Ph.vs. 36. 339 (1964). 6: BOYLE A. J.. BUNBURY D. S. P.and EDWARDS C.. Proc. Phys. Sot. Lad. 79. 4 I6 ( 1962). 7. BHIDE V. G. and BHAT N. V., J. rrppl. Phys. 41, 3159(1970). V. G. and BHAT N. V.. J. chrm. Ph.w. 48. 8. BHIDE 3 103 (1968). 9. BRAUER G.. Z. A,rorg. A//~c’nr. Clrern. 256. 10 (1948).
292
V.
G.
BHIDE
10. CHIRKOV V. I., BLOKHIN S. M. and VAINSHTEIN E. E.. F‘i: rcerd. Teln 9. 11 16 ( 1967). 1 1. LINDGREN 1.. In Rorugen Spekwe,~ rrnd Cl~rmisrhr Bindung (Edited A. Meisel). pp. 182. VEB Reprocalor. Leipzig ( 1966). 12. HERMAN F. and SKILLMAN S..AromicSrruc~ture Calculafions. Prentice Hall, New York (1963). 13. LIBERMAN B.. WABER J. T. and CROMER D. T., Phys. Rec. 137, A27 (1965). 14. NORDBERG R., HAMRIN K., FAHLMAN A.. NORDLING C. and SIEGBAHN K.. Z. Pl7.vsik 192.462 ( 1966). 15. FAHLMAN A.. HAMRIN K.. HEDMAN J..
and
M.
16. 17. 18. 19. 20.
K.
BAHL
NORDBERG R.. NORDLING C. and SIEGHBAHN K.. Notrrre. Land. 210, 4 (1966). PAULING L.. The Norrrre of IIW Clwmiccrl Bond. pp. 77. Russian Translation Godkhimizdat (1947). ROOTHAN CLEMENS C. J. and SYNEK MIROSLAV. P/qs. Rec. 133A. 1263 (1964). SUMBAEV 0. I.. Sorier Phys. JEPT 30. 927 (1970). HAFEMEISTER D. W.. DePASQUALl G. and DEWAARD H.. Phys. Rec. 135. B 1089 (1964). PERLOW G. J., In Chemical Applications of Miissbauer Spectroscopy (Edited by Goldanskii V. 1. and Herber R. H.). pp. 377. Academic Press, New York (I 968).