Nuclear Instruments and Methods in Physics Research B 155 (1999) 143±152
www.elsevier.nl/locate/nimb
In¯uence of alloying eect on Kb=Ka X-ray intensity ratios of V and Ni in VxNi1ÿx alloys S. Raj a, H.C. Padhi a, M. Polasik b
b,*
a Institute of Physics, Bhubaneswar 751005, India Faculty of Chemistry, Nicholas Copernicus University, 87-100 Toru n, Poland
Received 24 November 1998; received in revised form 23 February 1999
Abstract Kb=Ka X-ray intensity ratios of V and Ni in Vx Ni1ÿx alloys for dierent compositions x (x 0.00, 0.10, 0.20, 0.35, 0.50, 0.75, 1.00) have been measured following excitation by 59.54 keV c-rays from a 200 mCi 241 Am point-source. The experimental data indicate deviations of Kb=Ka intensity ratios for V and Ni in certain alloy compositions from the corresponding ratios for pure metals. These deviations of Kb=Ka intensity ratios have been interpreted using the results of multicon®guration Dirac±Fock (MCDF) calculations for various valence electronic con®gurations. Our analysis indicates that the relative changes of the number of 3d electrons (i.e. the changes divided by the number of 3d electrons for pure metals) for V and Ni seem to be very similar if considered as functions of their own concentrations. Comparison (for dierent x) of the change of the number of 3d electrons of V with appropriately rescaled change of the number of 3d electrons of Ni indicates that the transfer of 3d electrons between V and Ni seems to explain the observed change of the valence electronic con®gurations of V and Ni in Vx Ni1ÿx alloys, although other processes, like the rearrangement of electrons between 3d and (4s, 4p) states, cannot be excluded as being responsible for this change. It is very interesting that the presumed transfer of 3d electrons is from atoms of an element (V or Ni) of a higher concentration to atoms of an element of a lower concentration. Ó 1999 Elsevier Science B.V. All rights reserved. PACS: 32.30.Rj; 32.70.Fw; 71.15.-m; 71.20.Be Keywords: 3d-transition metals; Alloying eect; Kb=Ka X-ray intensity ratios; Changes of the valence electronic con®guration
1. Introduction From the early days of X-ray spectroscopy, the Kb=Ka X-ray intensity ratios of dierent elements
* Corresponding author. Tel.: +48 56 6114305; fax: +48 56 6542477; e-mail:
[email protected]
have been extensively studied experimentally, because this quantity can be measured easily with sucient accuracy. Especially with solid state X-ray detectors, such as Si(Li) or intrinsic Ge detectors, numerous experimental data have been reported for the relative K X-ray intensities following photon excitation, radioactive decays, proton irradiation, and charged particle impact. It is usual
0168-583X/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 9 ) 0 0 2 3 5 - 9
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that except for the case of heavy-ion bombardment, the Kb=Ka intensity ratio is considered as a characteristic quantity for each element. The measured values have been compared with the theoretical ones for free atoms. With the exception of the 3dtransition metals, good agreement has been achieved with the relativistic calculations of Sco®eld [1] which take into account the overlap and exchange eects. However it is found that for 3dtransition metals the Kb=Ka intensity ratio depends on the chemical/solid state environment [2± 13]. Several experiments have also been performed to study the in¯uence of alloying eect [2±4] on the Kb=Ka intensity ratios for 3d-transition metals. It has been concluded by Bhuinya and Padhi [2,3] for the case of Tix Ni1ÿx and Crx Ni1ÿx alloys that although the measured signi®cant deviations of the Kb=Ka X-ray intensity ratios for 3d-transition metals can be qualitatively explained by the changes in the 3d-electron population (evidently depending on the alloy composition) using the charge-transfer or rearrangement models, calculations based on dierent initial electronic con®gurations of the atom would be more useful in providing a quantitative interpretation of the data. In the light of these experimental works [2,3] and the theoretical work of Jankowski and Polasik [14] (in which the evident changes of the Kb=Ka X-ray intensity ratios as the result of the changes of the valence electronic con®guration have been shown for Ni) we have had very strong reason to expect that in the case of the alloy consisting of two metals diering dramatically in the number of the 3d electrons (like Ni and V), the Kb=Ka X-ray intensity ratios for both metals in certain alloy composition should dier from those obtained for the pure metals because of the presence of the alien metal. Our expectations can be justi®ed in the following way: (i) the change of the composition of such 3d-transition metal alloys ± as has been shown in earlier studies [2,3] ± should cause the change of the 3d-electron population for every single atom of both the metals in the alloy; (ii) the change of the 3d-electron population for the single atoms in the alloy modi®es 3p orbitals of these atoms more so than 2p orbitals, which must result in a change of the Kb=Ka X-ray intensity ratios for a given atom.
These expectations have motivated the present study in which we have measured the Kb=Ka X-ray intensity ratios for V and Ni in Vx Ni1ÿx alloys. Our study indicates appreciable deviations of the Kb=Ka ratios for V and Ni in certain alloy compositions, x, from those obtained for the pure metals. The experimental results are interpreted using the results of MCDF calculations for different valence electronic con®gurations of V and Ni, which provides information about the changes of the valence electronic con®gurations of V and Ni in Vx Ni1ÿx alloys for various compositions. In an earlier theoretical paper Jankowski and Polasik [14] proposed a special average-level (SAL) version of MCDF calculation which gives values of the Kb=Ka intensity ratios for 3d-transition metals in a signi®cantly better agreement with high-accurate experimental data of Perujo et al. [15] than the theoretical predictions of Sco®eld [1] and the results of standard average-level (AL) and extended average-level (EAL) versions of MCDF calculations (see Grant et al. [16]). Therefore in order to provide proper interpretation of the observed Kb=Ka X-ray intensity ratios for V and Ni in Vx Ni1ÿx alloys for dierent alloy compositions the MCDF calculations in the SAL version have been carried out on V and Ni for various valence electronic con®gurations and compared with the observed data. We have successfully applied the results of our systematic MCDF calculations for 3d-transition metals (corresponding to dierent valence electronic con®gurations) to explain reliably the experimentally observed Kb=Ka X-ray intensity ratios for 3d-transition metals in various compounds [17,18]. 2. Experimental details The experiments were carried out using highpure samples in the form of thick pellets procured from Goodfellow Company, UK. The measurements have been made for Vx Ni1ÿx alloys for compositions x 0.00, 0.10, 0.20, 0.35, 0.50, 0.75 and 1.00. Gamma rays of 59.54 keV from a 200 mCi 241 Am point-source were used to ionize the target atoms and the emitted X-rays following the
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ionization were detected by a 30 mm2 3 mm thick Canberra Si(Li) detector having a 12.7 lm thick beryllium window. The resolution of the Si(Li) detector was 165 eV [full width at half maximum (FWHM)] for a 5.9 keV X-ray peak. Details of the experimental arrangement can be found in our earlier paper [2]. Pulses from the Si(Li) detector preampli®er were fed to an ORTEC-572 spectroscopy ampli®er and then recorded in a Canberra PC based Model S-100 multichannel analyzer. The gain of the system was maintained at 15 eV/channel. The counting was continued until the counts under the less intense Kb peak (of V or Ni) were around 5 104 .
3. Data analysis and corrections All the X-ray spectra were carefully analyzed with the help of a multi-Gaussian least-square ®tting programme [19] incorporating a non-linear background subtraction. The Ka and Kb peaks are ®tted independently for V and Ni. No low energy tail was included in the ®tting as its contribution to the ratio was shown to be quite small [20]. The Kb=Ka intensity ratios for V and Ni in Vx Ni1ÿx alloys were determined from the ®tted peak areas after applying necessary corrections to the data. A typical K X-ray spectrum of V for the alloy composition x 0.5 is shown in Fig. 1 in which the ®tted spectrum is also shown. A residue spectrum corresponding to the X-ray spectrum of Fig. 1 is shown in Fig. 2. Corrections to the measured ratios mainly come from the dierence in the Ka and Kb self attenuations in the sample, dierence in the eciency of the Si(Li) detector and air absorption on the path between the sample and the Si(Li) detector window. The eciency of the detector is estimated theoretically as mentioned in our previous paper [2]. Our theoretically estimated eciency was shown to be in good agreement with the measured eciency [21]. It has been found that the discrepancy between the measured and theoretical eciency at the energy region of present interest was less than 1%.
Fig. 1. A typical K X-ray spectrum of V for alloy composition x 0.5. The open circles correspond to experimental data, the dashed curves correspond to the ®tted data and the continuous line represents the ®tted background.
Fig. 2. Residues corresponding to the K X-ray spectrum of Fig. 1.
The correction for self absorption in the target was estimated using the method as described in our earlier paper [3]. For this the mass attenuation coecients were obtained using the XCOM programme developed by Berger and Hubbel [22]. Since our results for pure metals agree very well
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S. Raj et al. / Nucl. Instr. and Meth. in Phys. Res. B 155 (1999) 143±152
with the earlier thin target results of Slivinsky and Ebert [20] and Paic and Pecar [23] we are con®dent that our correction for the self absorption is quite satisfactory. The correction for the air path was also estimated in a manner similar to the one described before [3]. 4. Theoretical calculations Detailed MCDF calculations have been carried out for V and Ni atoms to explain reliably the dependence of Kb=Ka X-ray intensity ratios on changes in the electronic con®gurations of the valence electrons of the atoms in the alloy. The MCDF method applied in the present study has been mainly developed by Grant and coworkers and is described in detail in several papers [16,24± 29]. However, for the sake of clarity, some essential details are very brie¯y recapitulated below. The Hamiltonian for the N-electron atom is taken in the form H
N X
hD
i
i1
N X
Cij ;
1
j>i1
where hD
i is the Dirac operator for ith electron and the terms Cij account for electron±electron interactions and come from one-photon exchange process. The latter are a sum of the Coulomb interaction operator and the transverse Breit operator. The atomic state functions with the total
angular momentum J and parity p are represented in the multicon®gurational form X Ws
J p cm
sU
cm J p ;
2 m
where U
cm J p are con®guration state functions (CSF's), cm
s are the con®guration mixing coecients for state s, cm represents all information required to uniquely de®ne a certain CSF. For more details on the MCDF calculations reference may be made to an earlier paper by Jankowski and Polasik [14]. The calculations have been performed for both Coulomb and Babushkin gauges [30,31]. 5. Results and discussion The experimental results for the Kb=Ka X-ray intensity ratios of pure V and Ni metals and V and Ni in various alloy compositions of Vx Ni1ÿx alloys and the normalised Kb=Ka ratios with respect to the pure metals are presented in Table 1. The errors quoted in the table are only statistical. They are calculated by the least-squares ®tting programme [19]. As can be seen from this table, the observed changes of Kb=Ka intensity ratios are a little more signi®cant for Ni than those for V. Additionally they are much more transparent (than those for V) because of smaller values of the statistical errors for Ni. However, for V also the alloying eect is evident and can be experimentally measured and interpreted.
Table 1 Experimental Kb=Ka X-ray intensity ratios and the normalized (with respect to pure metals) experimental Kb=Ka intensity ratios for V and Ni in Vx Ni1ÿx alloys Composition x
0.00 0.10 0.20 0.35 0.50 0.75 1.00
V
Ni
Kb=Ka intensity ratios
Normalized Kb=Ka intensity ratios
Kb=Ka intensity ratios
Normalized Kb=Ka intensity ratios
± 0.1285 0.1306 0.1311 0.1337 0.1352 0.1327
± 0.969 0.984 0.988 1.008 1.019 1.0
0.1363 0.1372 0.1387 0.1383 0.1348 0.1315 ±
1.0 1.008 1.018 1.015 0.989 0.965 ±
0.0008 0.0008 0.0008 0.0008 0.0008 0.0007
0.008 0.008 0.008 0.008 0.008
0.0005 0.0005 0.0005 0.0005 0.0005 0.0005
0.005 0.005 0.005 0.005 0.005
S. Raj et al. / Nucl. Instr. and Meth. in Phys. Res. B 155 (1999) 143±152
The results of Kb=Ka ratio for V in some low x values of the alloy composition are lower than that of the pure metal result. For x 0.10, we ®nd a decrease of about 3% in the Kb=Ka ratio of V with respect to the pure metal value. But for high value of V concentration, x P 0:50, the Kb=Ka ratios are found to be somewhat higher than the pure metal value. In the case of Ni, the Kb=Ka ratios for x 6 0:50 are higher than the pure metal value and for x P 0:50 the Kb=Ka ratio is less than that of pure Ni. The experimental Kb=Ka X-ray intensity ratios for V and Ni as functions of their own concentrations (i.e. x for V and 1 ÿ x for Ni) in Vx Ni1ÿx alloys are shown in Fig. 3. It can be seen in this ®gure that the alloying eect for both V and Ni is evident. Moreover, it may be seen in Fig. 3 that the trends in the changes of Kb=Ka intensity ratios for V and Ni seem to be similar if considered as functions of their own concentrations.
Fig. 3. The experimental Kb=Ka X-ray intensity ratios for V and Ni as functions of their own concentrations in Vx Ni1ÿx alloys.
147
The experimental data for dierent alloy compositions have been analyzed using the results of MCDF calculations which provides information about the electronic con®gurations of V and Ni in particular Vx Ni1ÿx alloys. The results of MCDF calculations on V and Ni for various valence electronic con®gurations of the 3dmÿrÿt 4sr 4pt (for r 2; 1; 0 and t 1; 0) type (i.e. keeping the total number of electrons, m, unchanged) and the results of additional MCDF calculations on V and Ni for various electronic con®gurations of the 3dn type (i.e. testing the eect of removing all 4s and 4p electrons) are presented in Table 2. In each case the Coulomb and Babushkin gauge formulae for the electric dipole transitions have been used. It can be found from Table 2 that for V and Ni the greatest values of the Kb=Ka intensity ratios are for con®gurations 3d2 and 3d7 (or 3d2 4s2 4p1 and 3d7 4s2 4p1 if keeping the total number of electrons unchanged), respectively. The smallest values are for con®gurations 3d5 in case of V and 3d10 in case of Ni. We can easily deduce from Table 2 that it is the number of 3d electrons which determines Kb=Ka X-ray intensity ratios, and the eect of removing 4s and 4p electrons can practically be neglected. Electronic con®gurations of V and Ni in Vx Ni1ÿx alloys have been obtained by comparison of the experimental Kb=Ka X-ray intensity ratios with the results of MCDF calculations for dierent valence electronic con®gurations. (see Figs. 4 and 5). As is seen from Figs. 2 and 3 the calculations based on the Babushkin gauge give higher 3delectron population than those based on the Coulomb gauge. The dependence of changes of the number of 3d electrons in V and Ni (with respect to pure metals) versus the composition of Vx Ni1ÿx alloys is presented in Table 3. The predicted electronic con®guration for V in the alloy shows a little lower 3d-electron population than that of pure V for x P 0:35. But for 0:35 P x P 0:10 the 3d-electron population increases over the pure metal value. It is also seen that the 3d-electron population of Ni for concentration x 6 0:5 is lower than that of the pure Ni whereas for x P 0:50 the 3d-electron population of Ni is higher than that in the pure metal. As functions of x, the results for Ni show opposite behaviour to the results for V at all alloy compositions.
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S. Raj et al. / Nucl. Instr. and Meth. in Phys. Res. B 155 (1999) 143±152
Table 2 The results of MCDF calculations on Kb=Ka X-ray intensity ratios for various valence electronic con®gurations of dierent ions of V and Ni Z
Ions in the moment of X-ray emission
Valence electronic con®guration
Kb=Ka intensity ratios Coulomb gauge
Babushkin gauge
23
V4 V V3 V V2 V V
3d2 3d2 4s2 4p1 3d3 3d3 4s2 3d4 3d4 4s1 3d5
0.1391 0.1377 0.1330 0.1322 0.1281 0.1280 0.1251
0.1417 0.1400 0.1355 0.1345 0.1307 0.1306 0.1276
28
Ni4 Ni Ni3 Ni Ni2 Ni Ni
3d7 3d7 4s2 4p1 3d8 3d8 4s2 3d9 3d9 4s1 3d10
0.1403 0.1397 0.1364 0.1361 0.1333 0.1333 0.1313
0.1415 0.1410 0.1376 0.1374 0.1345 0.1345 0.1325
The changes of the number of 3d electrons for V and Ni as functions of their own concentrations in Vx Ni1ÿx alloys are shown in Fig. 6(a). In Fig. 6(b) the relative changes of the number of 3d electrons (i.e. the changes of the number of 3d electrons divided by the number of 3d electrons for pure metals) for V and Ni are presented. It can be found from Fig. 6(a) that the trends in the changes of the number of 3d electrons for V and Ni seem to be similar if these changes are considered as functions of their own concentrations (for Ni these changes are much more transparent than those for V). We have found it extremely interesting that the relative changes of the number of 3d electrons for V and Ni seem to be not just similar, but almost identical (again, if considered as functions of their own concentrations) [see Fig. 6(b)]. We also notice that, although the electronic con®gurations obtained using the Coulomb and Babushkin gauges are quite dierent (see Figs. 4 and 5), the relative changes of the number of 3d electrons extracted from them are almost the same [see Fig. 6(b)]. Our analysis shows that the changes of the Kb=Ka X-ray intensity ratios for V and Ni in Vx Ni1ÿx alloys (from those obtained for the pure metals) can be explained as a result of changes in
the valence electronic con®gurations of V and Ni in certain alloy compositions due to the presence of an alien metal. The most essential modi®cation of the valence electronic con®gurations for V and Ni which in¯uences the Kb=Ka intensity ratios is the change in the number of 3d electrons. As has been mentioned above, the results of Table 2 provide the proof that the change of the number of 3d electrons is the only important contribution for the change of the Kb=Ka intensity ratios. On the other hand, it would be very interesting to ®nd out what is the physical mechanism of the changes of the valence electronic con®gurations themselves. That is, what kind of processes are responsible for the transition from electronic con®gurations of V and Ni in pure bulk metals to those in Vx Ni1ÿx alloy of given composition x. Among other processes, we can cite: (i) the transfer of 3d electrons from atoms of one element (V or Ni) to atoms of the other element, or (ii) rearrangement of electrons between 3d and (4s, 4p) states of individual atoms. Trying to interpret the results as an eect of the transfer of 3d electrons from V to Ni or vice versa, we have to take into account the fact that the ratio of the number of atoms of one element to that of
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Fig. 4. Comparison of the experimental Kb=Ka X-ray intensity ratios for V in Vx Ni1ÿx alloys with the results of MCDF calculations for dierent valence electronic con®guration of V. C denotes Coulomb gauge results; B denotes Babushkin gauge results.
Fig. 5. Comparison of the experimental Kb=Ka X-ray intensity ratios for Ni in Vx Ni1ÿx alloys with the results of MCDF calculations for dierent valence electronic con®guration of Ni. C denotes Coulomb gauge results; B denotes Babushkin gauge results.
the other changes dramatically with x. Comparison (for dierent compositions x) of the change of the number of 3d electrons of V with appropriately rescaled [i.e. multiplied by
1 ÿ x/x] change of the number of 3d electrons of Ni is presented in Table
4. For better comparison the change of the number of 3d electrons of V and appropriately rescaled change (with reverse sign) of the number of 3d electrons of Ni as a function of the alloy composition (x) are shown in Fig. 7. It can be easily
Table 3 The dependence of changes of the number of 3d electrons in V and Ni (with respect to pure metals) versus the composition of Vx Ni1ÿx alloys. In each case the Coulomb and Babushkin gauge have been used Composition x
0.10 0.20 0.35 0.50 0.75
Coulomb gauge
Babushkin gauge
V
Ni
V
Ni
1.00 0.22 0.50 0.19 0.35 0.19 ÿ0.20 0.14 ÿ0.45 0.14
ÿ0.25 0.14 ÿ0.65 0.14 ÿ0.55 0.14 0.50 0.18 1.95 0.25
1.25 0.27 0.55 0.24 0.40 0.23 ÿ0.25 0.20 ÿ0.55 0.15
ÿ0.30 0.17 ÿ0.75 0.14 ÿ0.65 0.14 0.50 0.19 2.05 0.25
150
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Fig. 6. (a) The changes of the number of 3d electrons for V and Ni (with respect to pure metals) as functions of their own concentrations in Vx Ni1ÿx alloys. (b) The relative changes of the number of 3d electrons (i.e. the changes of the number of 3d electrons divided by the number of 3d electrons for pure metals) for V and Ni as functions of their own concentrations in Vx Ni1ÿx alloys.
recognized from Table 4 and Fig. 7 that a decrease of the number of 3d electrons (with respect to the pure metal) in atoms of one species (V or Ni) always corresponds to an increase of the number of 3d electrons in atoms of the second species. Thus the authors have found it reasonable to consider the transfer of 3d electrons between V and Ni as a possible channel for the change in the valence electronic con®gurations of V and Ni in Vx Ni1ÿx alloys. It is very interesting that the transfer of 3d electrons is always (see Table 4 and Fig. 7) from atoms of an element (V or Ni) of a higher concentration to atoms of an element of a lower concentration. For x < 0:50 the transfer of 3d electrons is from Ni to V whereas for x P 0:50 it is from V to Ni. However, there is no simple quantitative relation between the number of 3d electrons given away by atoms of one element (V or Ni) and taken by atoms of second element. We can see from Table 4 and Fig. 7 that the change of the number of 3d electrons in V does not always correspond to the change (with reverse sign) of the number of 3d electrons in Ni. This is manifest for x 0:20 and probably holds also for x 0:35. Therefore, there must exist other channels leading to the change of the valence electronic con®guration of V and Ni in Vx Ni1ÿx alloys, like the rearrangement of electron between 3d and (4s, 4p) states of individual atoms. 6. Conclusions We have shown in this paper that the Kb=Ka X-ray intensity ratios can be used as a sensitive
Table 4 Comparison of the change of the number of 3d electrons of V with appropriately rescaled [i.e. multiplied by
1 ÿ x=x] change of the number of 3d electrons of Ni Composition x
0.10 0.20 0.35 0.50 0.75
Coulomb gauge
Babushkin gauge
V
Ni
V
Ni
1.00 0.22 0.50 0.19 0.35 0.19 ÿ0.20 0.14 ÿ0.45 0.14
ÿ2.25 1.26 ÿ2.60 0.56 ÿ1.02 0.26 0.50 0.18 0.65 0.08
1.25 0.27 0.55 0.24 0.40 0.23 ÿ0.25 0.20 ÿ0.55 0.15
ÿ2.70 1.53 ÿ3.00 0.56 ÿ1.21 0.26 0.50 0.19 0.68 0.08
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electronic structure of V and Ni in Vx Ni1ÿx alloys for dierent alloy compositions. Moreover, the results of this work can stimulate both experimental and theoretical research for other 3d-metal alloys. Acknowledgements One of us (M.P.) would like to thank Dr. M. Janowicz and F. Pawµowski for helpful discussions. This work was partially supported by the Polish Committee for Scienti®c Research (KBN), Grant No. 2 P03B 019 16, and by the Council of Scienti®c and Industrial Research, India. H.C. Padhi gratefully acknowledges the partial ®nancial support from Department of Science and Technology, Government of India for carrying out this work. References [1] [2] [3] [4] Fig. 7. The change of the number of 3d electrons of V and appropriately rescaled [i.e. multiplied by
1 ÿ x=x] change of the number of 3d electrons of Ni (with reverse sign) as functions of compositions x.
[5] [6] [7]
tool to study the changes of the valence electronic con®gurations of 3d-transition metals in alloys. Furthermore, the transfer of 3d electrons between V and Ni (from the atoms of element of higher concentration to the atoms of element of lower concentration) seems to explain the observed change of the valence electronic con®gurations of V and Ni in Vx Ni1ÿx alloys, although other processes, like the rearrangement of electrons between 3d and (4s, 4p) states of individual atoms, cannot be excluded as being responsible for this change. The authors believe that the results of this study will be helpful in better understanding of the dependence of Kb=Ka intensity ratios on changes in the valence electronic con®gurations of 3d-transition metals and throw some light on the valence
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