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The fine structure in the K-absorption spectrum of niobium
J. Phys. Chem. Solids, 1972,Vol.33. pp. 1669-1674. PergamonPress. Printedin Great Britain
THE
FINE
STRUCTURE SPECTRUM
IN THE K-ABSORPTION OF NIOBIUM
V. G. BHIDE
National Physical Laboratory, New Delhi, India and
M. K. BAHL A.R.S.D. College, University of Delhi, Delhi, India ( R e c e i v e d 4 J u n e 1971 )
A b s t r a c t - T h e fine structure of X-ray K-absorption edge of niobium in niobium metal and in four its compounds has been investigated. An attempt has been made to account for the fine structure niobium K-absorption edge in niobium metal in the light of Hayasi's theory. The bond lengths niobium metal and four of its compounds have been computed using Lytle's analysis and are found be in good agreement with the values reported by the X-ray diffraction data. 1. INTRODUCTION
IT IS well known that X-ray absorption discontinuity in solids is usually accompanied by the fine structure on the higher energy side which extends up to several hundred electron volts. This fine structure arises out of several simultaneous and]or competitive processes. Two recent review articles[I,2] have summarized the experimental results and the various theories which have been proposed so far with their relative merits. Unfortunately none of the theories is capable of explaining the fine structure over the complete energy range (near the absorption edge as well as on the higher energy region) in a satisfactory manner. Kronig's[3] theory based on the presence of allowed and forbidden energy regions is suitable in the higher energy range, whereas Hayasi's theory[4] based on the formation of quasi-stationary states through 90 ° Bragg reflection of the ejected electron is satisfactory in the low energy range. The short range theories such as due to Kozlenkov [5] and of Shiraiwa, lshimura and Sawada [6] ascribe the observed maxima and minima in the absorption spectrum to the variation in
of of in to
the transition probability because of the scattering of the ejected electrons by the neighbouring atoms. Lytle[7] has recently calculated the extended absorption fine structure by treating the ejected photoelectron as a spherical wave which expands in the lattice and is partially scattered by the neighbours of the absorbing atom. The neighbouring atoms are treated as point scatterers and the total scattered wave is summed from the wave scattered by each atom. The fine structure is determined from the dipole transition matrix between the initial K-state and the final photoelectron state. We report here the fine structure of the X-ray K-absorption edge of niobium in niobium metal and its explanation in the light of Hayasi's theory. The structure on the high energy side can be satisfactorily explained on Hayasi's as well as Lytle's models. From the fine structure of the K-absorption edge of niobium in the metal and in some of its compounds, it has been possible to calculate the radius of the first coordination sphere. The computed values agree reasonably well with the X-ray diffraction data.
1669
I670
V . G . B H I D E and M. K. B A H L 2. EXPERIMENTAL
The K-absorption edge of niobium in niobium metal and its compounds was photographed using the 400-mm bent crystal (mica, (100) planes) transmission type spectrograph as described in our earlier communications [8, 9]. The curve shown in Fig. 1 is the one obtained by taking the average of at least 20 curves and smoothing out the effects caused by the finite grain size in the photographic plate. The position of the absorption edge was taken at half the maximum of the absorption curve as described in our earlier communications [8, 9].
T~ te
Jo
3. RESULTS AND DISCUSSION
Figure 1 shows the X-ray K-absorption edge of niobium in niobium metal. The wavelength of the absorption discontinuity is 651-69__+0-02, in excellent agreement with that reported by Ross[10] (651-71+__0.02). A possible explanation of the fine structure of the absorption edge was first proposed by Kronig. Though Kronig's theory is in partial agreement with the experimental observations in the energy region far removed from the absorption edge, it does not give satisfactory results in the vicinity of the principal absorption edge. 3(a) Hayasi theory Hayasi suggested that the fluctuations in the absorption edge may be considered as a series of absorption maxima superposed over the absorption curve as the background. He argued that the ejected electron is reflected and localized by certain crystallographic planes which prevent it from moving very far from the absorbing atom. Using Bragg's law, he concluded that such reflections will occur for electrons having energies (in electron volts) given by Enkt =
h s + ks + Is 4a s × 150
(1)
where (h, k, l) are the Miller indices of the
,
iC,
40
I
q
I
,
I
,
I
80
120 160 200
E,
eV
Fig. I. The fine structure of the X-ray K-absorption edge of metallic niobium.
reflecting planes and a is the length of the unit cell for a cubic crystal. That such a theory accounts satisfactorily for the fine structure up to 100eV from the principle edge has been amply demonstrated by several workers [11-13]. Since we are interested in a region close of the edge, it was thought worthwhile to make a comparison of the observed data with that predicted on Hayasi's theory. Niobium metal crystallizes in body centered cubic lattice with a = 3.2941A°[14]. We need consider only those atomic planes which allow the existence of quasi-stationary states. For a body centered cubic lattice, planes having sum of the Miller indices equal to even numbers allow the existence of quasistationary states. Using the expression[l], the values for the quasi-stationary states having p character are calculated and compared with the experimentally observed values (Table 1). It is to be noted (Table 1) that the agreement between the experi-
K-ABSORPTION SPECTRUM OF NIOBIUM
Table 1. Comparison o f the observed and the calculated values for the absorption maxima in the K-absorption spectrum for niobium metal (in electron volts )
Maxima
Energy observed
Energy calculated (based on Hayasrs theory)
A B C D E F G
16.21 34.42 55" 15 96.33 138.50 166.15 196.27
13.7 34-5 55-3 89.8 138"2 173.8 193.2
Crystal planes (200) (310) (400) (510) (620) (550) (642)
mentally observed values and that calculated on the basis of Hayasi's theory is very good. 3(b) Lytle theory Recently Lytle[15] has proposed an explanation for the fine structure of the absorption edge by taking into account only the nearest neighbours. He considers the ejected photoelectrons as a particle in a Wigner Seitz cell constructed around the absorbing atom. The various maxima observed on the higher energy side of the absorption edge is ascribed to the transition of the photoelectron into various allowed energy states in the cell. Making use of certain approximations, he solved the Shrondinger equation which gives the energy values of these bound states as h2
Ref. [15] for states having p character) for niobium metal is shown in Fig. 2 (Graph 1). Contrary to the expectation, we do not observe a linear relationship. This discrepancy may be due to the fact that in addition to the electric dipole transition (s--p), electric quadrupole transition ( s - - d ) may be responsible for some of the peaks observed in the fine structure of the K-absorption edge. In this connection it is worthwhile to mentio:~ that lines corresponding to quadrupole transition have been observed by several investigators [16-17] in emission spectra of various elements. These lines are always of low intensity as compared to lines corresponding to the dipole transition. A comparison of the intensity of various maxima of fine structure of niobium metal shows that the intensity of the absorption maxima F is small as compared to other maxima. Since probability of quadrupole transition (s--d) is small as compared to dipole transition (s--p), it is natural to infer that the absorption maxima F may be
2
200
/.0~//
180 160 > 140 o 120 L~
(2)
ioo 80
where Q is the zeroth rooth of a half order Bessel function and rs is the radius of the first coordination sphere. For fine structure of the K-absorption edge we must consider only those Q's which have p-character. It is to be seen that equation (2) predicts a linear relation between E and Q such that the slope of the E - - Q plot helps to evaluate the radius rs of the first coordination sphere. A plot of E vs. Q (Q values taken from
6o
E = 8mrsz Q
1671
Ft//6 E~///" /
C
I
I
I
I
I
I
I
I
I0 20 30 40 50 60 FO 80 Q Fig. 2. Plot of E vs. Q for niobium metal. (l) Q values for all maxima correspond to p states. (2) Q values for all maxima except F correspond to p state while for F, it corresponds to d states.
1672
v . G . BHIDE and M. K. BAHL
due to quadrupole transition. Therefore a graph for E vs. Q was redrawn for those points which correspond to dipole transition (for all maxima except F) and it was found to be a straight line as shown in graph 2 of Fig. 2, which is in accordance with the theory of Lytle. It is interesting to point out that the value of energy corresponding to F lies above straight line between E and Q, only when the Q va.lues corresponding to the d-type of symmetry is taken, which further shows that F corresponds to electric quadrupole transition. It is worthwhile to point out that even the observed energy values of the point F (Table 1) does not agree very satisfactorily with that predicted on Hayasi's theory. A plot of E vs. Q for niobium metal and four of its compounds, whose fine structure was reported in our earlier communication is shown in Fig. 3. It is to be noted that the values of rs calculated from the slope of these curves (column 3, Table 2) are in good agreement with the values reported by diffraction data. This further confirms the applicability of Lytle's theory to the interpretation of the
/I III4 . //I
~1
///
160 140 >
1/1 Z/i
120 loo
','S
80 60 4.0 20
O
,2 I 5
I I0
I 15
I 20
I 25
I 30
I 35
Co S.No. 1 2 3 4 5
Absorption (Lytle's method, Diffraction unit sphere (interatomic Compound r a d i u s ) distances) Niobiummetal Nb3Te4 NbSe2 NbO2 Nb2Os
2.88 2.84 2.43 2.99 2.10
2"85 2.83 2.53 2.05 2.0
X-ray spectra. [Equation (2) suggests that the straight line E vs. Q should pass through the origin. But for the above compounds this situation does not arise, though the straight line passes very near to the origin. This slight discrepancy is to be expected in view of the various assumptions made in the derivation of equation (2). In particular, in compounds, the atomic like character may not be truly maintained. It should be pointed out that LyriCs own curves also do not pass through the origin.] 3(c) Comparison of fine structure of niobium and Yttrium metal with characteristic energy losses
200 180
Table 2. Comparison of bond lengths from X-ray K-absorption edge fine structure with those reported from X-ray diffraction (in angstrom units )
I 40
I 45
O
Fig. 3. Plot of E vs. Q for 1. Niobium metal. 2. Nb3Te4 3. NbS~. 4. NbO2.5. NB205.
It is well known that electrons on transmission through the metal foil lose rather small but well defined amounts of energy. The distribution in the energy of the electrons after the interaction measured either in transmission through thin films or in reflection from the solid gives sharp peaks corresponding to characteristic energy losses. The range of energies of the observed losses [18, 19] is approximately between 5-75 eV. Cauchois[20] and others[21] compared the characteristic energy losses in various metals with the fine structure of the X-ray K-absorption edges. The approaches of Watanabe [21], Rudberg [ 18] and Cauchois are all essentially the same, since they all postulate excitation o ~" a free
K-ABSORPTION SPECTRUM OF NIOBIUM
electron to higher energy levels. Since the fine structure of K and L-absorption edge also corresponds to higher empty levels of solids, it is worthwhile to compare the characteristic energy loss spectra with the fine structure of the K-absorption edge of Yttrium (taken from our previous work, Ref. [22]) and niobium metal respectively. Tables 3 and 4 compare the characteristic losses for Yttrium and niobium metals respectively with the maxima of the fine structure as measured from the K-absorption edge of the respective metals. The characteristic energy losses are taken from the work of Zashkvara et al. [23] and are measured in eV from zero loss (elastic peak). It is worthwhile to note a striking correlation between the characteristic energy loss of electrons in solids and the fine structure found on the short wavelength side of the X-ray absorption edge. The absence of 10.2, 41-5 eV maxima in the fine structure of niobium and 40.6 eV in the
Table 3. Comparison of the observed absorption maxima in the K-absorption spectrum of Yttrium metal* with characteristic losses Fine structure (Maxima of absorption eV)
Characteristic energy losses eV
11.1 22.0 31.6 40.6 46.4
10-7 24.8 34-6 44.9
*Taken from Ref. [22].
Table 4. Comparison of the observed absorption maxima in the K-absorption spectrum of niobium metal with characteristic losses Fine structure (maxima of absorption eV) - -
16"21 34.42 - -
55.15
Characteristic energy losses eV 10-2 18"5 34.6 41.5
54.8
1673
energy loss spectrum for Yttrium metal may be noted. It may be mentioned that Bohm and Pines [24] have attempted to explain the characteristic losses on the basis of excitation of plasmons. Recently a number of workers have attributed the first two or three maxima in the fine structure of the X-ray absorption edge of the metal due to this process. According to Bohm and Pines, the plasma energy is given by
where n is the valence electron density, m is the mass and e is the electronic charge. Since the number of electrons per atom taking part in metallic bonding for niobium as well as for Yttrium metal is not known, it is not possible to compare the values of the characteristic energy loss or maxima of the fine structure with the theoretical calculated value of plasma energy. But Boster and Edwards [25] studied the fine structure of the K-absorption edge of niobium at various temperatures from 300 down to 4-2°K. They observed that the position of the fine structure (first three or four maxima) does no~ change with temperature. Although data on crystal structure and thermal expansion of niobium metal is not yet available at low temperatures, yet Edwards et a1.[28] have studied the crystal structure and lattice parameter of niobium metal at 291°K and from 1100 to 2500°K. Their results show that niobium metal undergoes expansion over the temperature range investigated without undergoing any structural change. If we extrapolate their high temperature thermal data for low temperature (from 300 down to 4°K), then one expects change in plasmon frequency at low temperature due to small changes in the electron concentration resulting from density variation of the metal as a function of temperature. In fact, such an effect has been reported in aluminium metal by Leder and Marton[29]. Thus the absence of change in the position of the fine structure
1674
V . G . B H I D E and M. K. B A H L
of niobium in K-absorption edge of niobium metal with change of temperature precludes the possibility of plasmon excitation being responsible for the fine structure. In this connection, it may be pointed out that recent theoretical studies of Ferrel[26] indicate that the X-ray induced plasmon excitation probabilities are much lower than those previously suggested by Sobelman and Feinberg [27].
REFERENCES 1. P A R R A T T L. G., Rev. Mod. Phys. 31, 616 (1959). 2. A Z A R O F F L. V.,Rev. Mod. Phys. 35, 1012 (1963). 3. KRON1G R. de L.,Z. Phys. 70, 317 (1931); 75, 191 (1932). 4. H A Y A S I T., Sci. Rept. Tohoku Univ. 33, 123, 183 (1949). 5. K O Z L E N K O V A. I., lzvest. Akad. Nauk SSSR Ser. Fiz. 25, 957 (1961). 6. S H I R A I W A T., I S H I M U R A T. and S A W A D A M., J. phys. Soc. Japan 13,847 (1958). 7. SAYERS D. E., L Y T L E F. W. and S T E R N E. A., Boeing Scientific Research Laboratories, U.S.A. Document No. D 1-82-0880, July 1969. 8. B H I D E V. G. and B A H L M. K.,J. chem. Phys. 52, 4093 (1970). 9. B H I D E V. G. and B A H L M. K., J. Phys. Chem. Solids 32, 1001 ( 1971 ). 10. ROSS P. A., Phys. Rev. 44,977 ( 1933). I!. J O H N S T O N R. W. and T O M B O U L I A N D. H., Phys. Rev. 94, 1585 (1954).
12. F U J I M O T O H., Sci. Rept. Tohoku Univ. 39, 189 (1956). 13. K A W A H A R A D A H., Sci. Rept. Tohoku Univ. 45, 1 (1961). 14. W Y C H O F F R. W. G., Crystal Structures, Vol. 1, Chap. 11, p. 9. Interscience, New York ( 1951 ). 15. L Y T L E F. W.,Adv. X-rayAnal. 9, 398 (1966). 16. N I G A M A. N., G A R G K. B. and K A P O O R Q. S., J. Phys. B (Proc. Phys. Soc.) 1,492 (1968). 17. G O K H A L E B. G. and N I G A M A. N., Proc. Phys. Soc. gg, 475 (1966). 18. R U D B E R G E., Proc. Roy Soc. Lond. A127, 1 II (1930); Phys. Rev. 50, 138 (1936). 19. M A R T O N L., L E D E R L. B. and M E N D L O W I T Z H., Advances in Electronics and Electron Physics, Vol. 7, p. 183, Academic Press, New York (1955). 20. C A U C H O I S Y.,Acta crystallogr. 5, 35 ! (1952). 21. W A T A N A B E H., J. phys. Soc. Japan 9, 920 (1954); 11, 112 (1956). 22. B H I D E V. G. and B H A T N. V., J. chem. Phys. 50, 42 (1969). 23. Z A S H K V A R A V. V., K O R S U N S K I I M. 1., R E D K I N V. S. and M A S Y A G I N V. E., Soviet Phys. solidState 11, 3083 (1970). 24. P I N E S D. and B O H M D., Phys. Rev. 85, 338 (1952). 25. BOSTER T. A. and E D W A R D S J. E., Phys. Rev. 170, 12 (1968). 26. F A R E L L R. A., Bull. Am. Phys. Soc. 10, 1218 (1965). 27. S O B L M A N 1. 1. and F E I N B E R G E. O., Soviet Phys-JETP7, 339 (1958). 28. E D W A R D S J. W., S P E I S E R R. and J O H N S T O N H. L., J. appl. Phys. 22,424 ( 1951 ). 29. LEDER, L. B. and M A R T O N L., Phys. Rev. 112, 341 (1958).
THE
FINE
STRUCTURE SPECTRUM
IN THE K-ABSORPTION OF NIOBIUM
V. G. BHIDE
National Physical Laboratory, New Delhi, India and
M. K. BAHL A.R.S.D. College, University of Delhi, Delhi, India ( R e c e i v e d 4 J u n e 1971 )
A b s t r a c t - T h e fine structure of X-ray K-absorption edge of niobium in niobium metal and in four its compounds has been investigated. An attempt has been made to account for the fine structure niobium K-absorption edge in niobium metal in the light of Hayasi's theory. The bond lengths niobium metal and four of its compounds have been computed using Lytle's analysis and are found be in good agreement with the values reported by the X-ray diffraction data. 1. INTRODUCTION
IT IS well known that X-ray absorption discontinuity in solids is usually accompanied by the fine structure on the higher energy side which extends up to several hundred electron volts. This fine structure arises out of several simultaneous and]or competitive processes. Two recent review articles[I,2] have summarized the experimental results and the various theories which have been proposed so far with their relative merits. Unfortunately none of the theories is capable of explaining the fine structure over the complete energy range (near the absorption edge as well as on the higher energy region) in a satisfactory manner. Kronig's[3] theory based on the presence of allowed and forbidden energy regions is suitable in the higher energy range, whereas Hayasi's theory[4] based on the formation of quasi-stationary states through 90 ° Bragg reflection of the ejected electron is satisfactory in the low energy range. The short range theories such as due to Kozlenkov [5] and of Shiraiwa, lshimura and Sawada [6] ascribe the observed maxima and minima in the absorption spectrum to the variation in
of of in to
the transition probability because of the scattering of the ejected electrons by the neighbouring atoms. Lytle[7] has recently calculated the extended absorption fine structure by treating the ejected photoelectron as a spherical wave which expands in the lattice and is partially scattered by the neighbours of the absorbing atom. The neighbouring atoms are treated as point scatterers and the total scattered wave is summed from the wave scattered by each atom. The fine structure is determined from the dipole transition matrix between the initial K-state and the final photoelectron state. We report here the fine structure of the X-ray K-absorption edge of niobium in niobium metal and its explanation in the light of Hayasi's theory. The structure on the high energy side can be satisfactorily explained on Hayasi's as well as Lytle's models. From the fine structure of the K-absorption edge of niobium in the metal and in some of its compounds, it has been possible to calculate the radius of the first coordination sphere. The computed values agree reasonably well with the X-ray diffraction data.
1669
I670
V . G . B H I D E and M. K. B A H L 2. EXPERIMENTAL
The K-absorption edge of niobium in niobium metal and its compounds was photographed using the 400-mm bent crystal (mica, (100) planes) transmission type spectrograph as described in our earlier communications [8, 9]. The curve shown in Fig. 1 is the one obtained by taking the average of at least 20 curves and smoothing out the effects caused by the finite grain size in the photographic plate. The position of the absorption edge was taken at half the maximum of the absorption curve as described in our earlier communications [8, 9].
T~ te
Jo
3. RESULTS AND DISCUSSION
Figure 1 shows the X-ray K-absorption edge of niobium in niobium metal. The wavelength of the absorption discontinuity is 651-69__+0-02, in excellent agreement with that reported by Ross[10] (651-71+__0.02). A possible explanation of the fine structure of the absorption edge was first proposed by Kronig. Though Kronig's theory is in partial agreement with the experimental observations in the energy region far removed from the absorption edge, it does not give satisfactory results in the vicinity of the principal absorption edge. 3(a) Hayasi theory Hayasi suggested that the fluctuations in the absorption edge may be considered as a series of absorption maxima superposed over the absorption curve as the background. He argued that the ejected electron is reflected and localized by certain crystallographic planes which prevent it from moving very far from the absorbing atom. Using Bragg's law, he concluded that such reflections will occur for electrons having energies (in electron volts) given by Enkt =
h s + ks + Is 4a s × 150
(1)
where (h, k, l) are the Miller indices of the
,
iC,
40
I
q
I
,
I
,
I
80
120 160 200
E,
eV
Fig. I. The fine structure of the X-ray K-absorption edge of metallic niobium.
reflecting planes and a is the length of the unit cell for a cubic crystal. That such a theory accounts satisfactorily for the fine structure up to 100eV from the principle edge has been amply demonstrated by several workers [11-13]. Since we are interested in a region close of the edge, it was thought worthwhile to make a comparison of the observed data with that predicted on Hayasi's theory. Niobium metal crystallizes in body centered cubic lattice with a = 3.2941A°[14]. We need consider only those atomic planes which allow the existence of quasi-stationary states. For a body centered cubic lattice, planes having sum of the Miller indices equal to even numbers allow the existence of quasistationary states. Using the expression[l], the values for the quasi-stationary states having p character are calculated and compared with the experimentally observed values (Table 1). It is to be noted (Table 1) that the agreement between the experi-
K-ABSORPTION SPECTRUM OF NIOBIUM
Table 1. Comparison o f the observed and the calculated values for the absorption maxima in the K-absorption spectrum for niobium metal (in electron volts )
Maxima
Energy observed
Energy calculated (based on Hayasrs theory)
A B C D E F G
16.21 34.42 55" 15 96.33 138.50 166.15 196.27
13.7 34-5 55-3 89.8 138"2 173.8 193.2
Crystal planes (200) (310) (400) (510) (620) (550) (642)
mentally observed values and that calculated on the basis of Hayasi's theory is very good. 3(b) Lytle theory Recently Lytle[15] has proposed an explanation for the fine structure of the absorption edge by taking into account only the nearest neighbours. He considers the ejected photoelectrons as a particle in a Wigner Seitz cell constructed around the absorbing atom. The various maxima observed on the higher energy side of the absorption edge is ascribed to the transition of the photoelectron into various allowed energy states in the cell. Making use of certain approximations, he solved the Shrondinger equation which gives the energy values of these bound states as h2
Ref. [15] for states having p character) for niobium metal is shown in Fig. 2 (Graph 1). Contrary to the expectation, we do not observe a linear relationship. This discrepancy may be due to the fact that in addition to the electric dipole transition (s--p), electric quadrupole transition ( s - - d ) may be responsible for some of the peaks observed in the fine structure of the K-absorption edge. In this connection it is worthwhile to mentio:~ that lines corresponding to quadrupole transition have been observed by several investigators [16-17] in emission spectra of various elements. These lines are always of low intensity as compared to lines corresponding to the dipole transition. A comparison of the intensity of various maxima of fine structure of niobium metal shows that the intensity of the absorption maxima F is small as compared to other maxima. Since probability of quadrupole transition (s--d) is small as compared to dipole transition (s--p), it is natural to infer that the absorption maxima F may be
2
200
/.0~//
180 160 > 140 o 120 L~
(2)
ioo 80
where Q is the zeroth rooth of a half order Bessel function and rs is the radius of the first coordination sphere. For fine structure of the K-absorption edge we must consider only those Q's which have p-character. It is to be seen that equation (2) predicts a linear relation between E and Q such that the slope of the E - - Q plot helps to evaluate the radius rs of the first coordination sphere. A plot of E vs. Q (Q values taken from
6o
E = 8mrsz Q
1671
Ft//6 E~///" /
C
I
I
I
I
I
I
I
I
I0 20 30 40 50 60 FO 80 Q Fig. 2. Plot of E vs. Q for niobium metal. (l) Q values for all maxima correspond to p states. (2) Q values for all maxima except F correspond to p state while for F, it corresponds to d states.
1672
v . G . BHIDE and M. K. BAHL
due to quadrupole transition. Therefore a graph for E vs. Q was redrawn for those points which correspond to dipole transition (for all maxima except F) and it was found to be a straight line as shown in graph 2 of Fig. 2, which is in accordance with the theory of Lytle. It is interesting to point out that the value of energy corresponding to F lies above straight line between E and Q, only when the Q va.lues corresponding to the d-type of symmetry is taken, which further shows that F corresponds to electric quadrupole transition. It is worthwhile to point out that even the observed energy values of the point F (Table 1) does not agree very satisfactorily with that predicted on Hayasi's theory. A plot of E vs. Q for niobium metal and four of its compounds, whose fine structure was reported in our earlier communication is shown in Fig. 3. It is to be noted that the values of rs calculated from the slope of these curves (column 3, Table 2) are in good agreement with the values reported by diffraction data. This further confirms the applicability of Lytle's theory to the interpretation of the
/I III4 . //I
~1
///
160 140 >
1/1 Z/i
120 loo
','S
80 60 4.0 20
O
,2 I 5
I I0
I 15
I 20
I 25
I 30
I 35
Co S.No. 1 2 3 4 5
Absorption (Lytle's method, Diffraction unit sphere (interatomic Compound r a d i u s ) distances) Niobiummetal Nb3Te4 NbSe2 NbO2 Nb2Os
2.88 2.84 2.43 2.99 2.10
2"85 2.83 2.53 2.05 2.0
X-ray spectra. [Equation (2) suggests that the straight line E vs. Q should pass through the origin. But for the above compounds this situation does not arise, though the straight line passes very near to the origin. This slight discrepancy is to be expected in view of the various assumptions made in the derivation of equation (2). In particular, in compounds, the atomic like character may not be truly maintained. It should be pointed out that LyriCs own curves also do not pass through the origin.] 3(c) Comparison of fine structure of niobium and Yttrium metal with characteristic energy losses
200 180
Table 2. Comparison of bond lengths from X-ray K-absorption edge fine structure with those reported from X-ray diffraction (in angstrom units )
I 40
I 45
O
Fig. 3. Plot of E vs. Q for 1. Niobium metal. 2. Nb3Te4 3. NbS~. 4. NbO2.5. NB205.
It is well known that electrons on transmission through the metal foil lose rather small but well defined amounts of energy. The distribution in the energy of the electrons after the interaction measured either in transmission through thin films or in reflection from the solid gives sharp peaks corresponding to characteristic energy losses. The range of energies of the observed losses [18, 19] is approximately between 5-75 eV. Cauchois[20] and others[21] compared the characteristic energy losses in various metals with the fine structure of the X-ray K-absorption edges. The approaches of Watanabe [21], Rudberg [ 18] and Cauchois are all essentially the same, since they all postulate excitation o ~" a free
K-ABSORPTION SPECTRUM OF NIOBIUM
electron to higher energy levels. Since the fine structure of K and L-absorption edge also corresponds to higher empty levels of solids, it is worthwhile to compare the characteristic energy loss spectra with the fine structure of the K-absorption edge of Yttrium (taken from our previous work, Ref. [22]) and niobium metal respectively. Tables 3 and 4 compare the characteristic losses for Yttrium and niobium metals respectively with the maxima of the fine structure as measured from the K-absorption edge of the respective metals. The characteristic energy losses are taken from the work of Zashkvara et al. [23] and are measured in eV from zero loss (elastic peak). It is worthwhile to note a striking correlation between the characteristic energy loss of electrons in solids and the fine structure found on the short wavelength side of the X-ray absorption edge. The absence of 10.2, 41-5 eV maxima in the fine structure of niobium and 40.6 eV in the
Table 3. Comparison of the observed absorption maxima in the K-absorption spectrum of Yttrium metal* with characteristic losses Fine structure (Maxima of absorption eV)
Characteristic energy losses eV
11.1 22.0 31.6 40.6 46.4
10-7 24.8 34-6 44.9
*Taken from Ref. [22].
Table 4. Comparison of the observed absorption maxima in the K-absorption spectrum of niobium metal with characteristic losses Fine structure (maxima of absorption eV) - -
16"21 34.42 - -
55.15
Characteristic energy losses eV 10-2 18"5 34.6 41.5
54.8
1673
energy loss spectrum for Yttrium metal may be noted. It may be mentioned that Bohm and Pines [24] have attempted to explain the characteristic losses on the basis of excitation of plasmons. Recently a number of workers have attributed the first two or three maxima in the fine structure of the X-ray absorption edge of the metal due to this process. According to Bohm and Pines, the plasma energy is given by
where n is the valence electron density, m is the mass and e is the electronic charge. Since the number of electrons per atom taking part in metallic bonding for niobium as well as for Yttrium metal is not known, it is not possible to compare the values of the characteristic energy loss or maxima of the fine structure with the theoretical calculated value of plasma energy. But Boster and Edwards [25] studied the fine structure of the K-absorption edge of niobium at various temperatures from 300 down to 4-2°K. They observed that the position of the fine structure (first three or four maxima) does no~ change with temperature. Although data on crystal structure and thermal expansion of niobium metal is not yet available at low temperatures, yet Edwards et a1.[28] have studied the crystal structure and lattice parameter of niobium metal at 291°K and from 1100 to 2500°K. Their results show that niobium metal undergoes expansion over the temperature range investigated without undergoing any structural change. If we extrapolate their high temperature thermal data for low temperature (from 300 down to 4°K), then one expects change in plasmon frequency at low temperature due to small changes in the electron concentration resulting from density variation of the metal as a function of temperature. In fact, such an effect has been reported in aluminium metal by Leder and Marton[29]. Thus the absence of change in the position of the fine structure
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V . G . B H I D E and M. K. B A H L
of niobium in K-absorption edge of niobium metal with change of temperature precludes the possibility of plasmon excitation being responsible for the fine structure. In this connection, it may be pointed out that recent theoretical studies of Ferrel[26] indicate that the X-ray induced plasmon excitation probabilities are much lower than those previously suggested by Sobelman and Feinberg [27].
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