Valence electronic structure of Ti, Cr, Fe and Co in ...

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Nuclear Instruments and Methods in Physics Research B 195 (2002) 367–373 www.elsevier.com/locate/nimb

Valence electronic structure of Ti, Cr, Fe and Co in some alloys from Kb-to-Ka X-ray intensity ratio studies F. Pawłowski a, M. Polasik a

a,*

, S. Raj b, H.C. Padhi b, D.K. Basa

c

Faculty of Chemistry, Nicholas Copernicus University, ul. Gagarina 7, 87-100 Toru n, Poland b Institute of Physics, Bhubaneswar 751005, India c Department of Physics, Utkal University, Bhubaneswar 751004, India Received 19 March 2002; received in revised form 17 April 2002

Abstract Kb-to-Ka X-ray intensity ratios of Ti, Cr, Fe and Co in pure metals and in Cr0:26 Fe0:74 , Cr0:80 Co0:20 and Ti0:80 Cr0:20 alloys have been measured following excitation by 59.54 keV c-rays from a 7400 MBq (200 mCi) 241 Am point-source. The valence electronic structure of Ti, Cr, Fe and Co in the samples have been evaluated by the comparison of the measured Kb-to-Ka intensity ratios with the results of multiconﬁguration Dirac–Fock calculations performed for various electronic conﬁgurations of these metals. The 3d-electron populations obtained for pure metallic Ti, Cr, Fe and Co agree well with the results of band structure calculations of Papaconstantopoulos (Handbook of band structure of elemental solids, Plenum Press, New York, 1986). Our analysis indicates signiﬁcant increase of 3d-electron population of Ti, Cr and Fe in the alloys with respect to the pure metals, except for Cr in Cr0:26 Fe0:74 where the absolute 3d-electron population of Cr is found to be slightly less as compared to that of pure Cr. It has been found that to reliably explain the observed changes in the valence electronic structure of Ti, Cr, Fe and Co in their alloys it is necessary to take into account the rearrangement of electrons between 3d and (4s,4p) states of individual metal atoms, while the transfer of 3d electrons from one element to the other element can be neglected. Ó 2002 Published by Elsevier Science B.V. PACS: 32.30.Rj; 32.70.Fw; 71.15.)m; 71.20.Be Keywords: 3d-transition metals; Alloying eﬀect; Kb=Ka X-ray intensity ratios; Changes of the valence electronic conﬁguration

1. Introduction The variety of physical properties of the 3dtransition metals and the large number of applications of these metals and their compounds and

*

Corresponding author. Tel.: +48-56-6114305; fax: +48-566542477. E-mail address: [email protected] (M. Polasik).

alloys cause the need for understanding the valence electronic structure of 3d-transition metals in various systems. This stimulates the development of experimental and theoretical methods of studying the inﬂuence of chemical/solid state effects on the valence electronic structure of 3dtransition metals. In earlier studies, the Kb-to-Ka X-ray intensity ratios of 3d-transition metals have been found to depend on the chemical environment of these

0168-583X/02/$ - see front matter Ó 2002 Published by Elsevier Science B.V. PII: S 0 1 6 8 - 5 8 3 X ( 0 2 ) 0 1 1 0 6 - 0

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metals in their compounds [1–9] and alloys [10– 12]. This dependence can be explained as the result of the changes of the 3d-electron population of the transition metal because of chemical/solid state eﬀects, which modify 3p orbitals more than 2p orbitals resulting in a change in the Kb-to-Ka X-ray intensity ratio of the metal. Thus the Kb-toKa ratio becomes a sensitive tool to study the valence electronic structure of the 3d-transition metals in various systems. Earlier, in a series of papers we have worked out and tested the new method of studying the valence electronic structure of the 3d-transition metals in their compounds [13–19] and alloys [20,21]. This method is based on the comparison of the experimental Kb-to-Ka X-ray intensity ratio values of 3d-transition metals in various systems with the theoretical values of this ratio, obtained from the multiconﬁguration Dirac–Fock (MCDF) calculations performed for various valence electronic conﬁgurations of 3d-transition metals [22]. Among others, we successfully applied this method to investigate the dependence of the changes of the 3d-electron population for V and Ni (with respect to pure metals) versus the composition of Vx Ni1x alloys [20]. Very recently we evaluated the average 3d-electron population and the average number of (4s,4p) electrons per atom for Fex Ni1x alloys (x ¼ 0:2, 0.5 and 0.58) [21]. We found that in the case of Fe0:20 Ni0:80 alloy (which has special magnetic properties) the valence electronic structure was drastically diﬀerent from the other two alloys, i.e. it had the largest average number of 3d electrons and the (4s,4p) band of this alloy was almost empty. Therefore, in the present paper we ﬁx our attention on some other binary alloys, in which the ratio of the molar fractions of both 3d-transition metals is the same or similar as in the case of Fe0:20 Ni0:80 alloy. Our study on the valence electronic structure of 3d-transition metals alloys is a two-sided problem. The ﬁrst aspect, being the main goal of this study is concerned with the evaluation (by the comparison of the experimental Kb-to-Ka ratio values with the theoretical ones) of the numbers of 3d electrons and (4s,4p) electrons for both metals constituting a given alloy. Obtained in this way, the valence electronic structure of a given metal in

an alloy is found to be diﬀerent – due to the presence of alien metal atoms – from that of the pure metal. We try to ﬁnd the mechanisms responsible for these changes, considering the charge transfer and electron rearrangement processes. The second aspect of our study is to obtain information on the valence electronic structure of both metals in a given alloy, and to estimate the average number of 3d electrons and average number of (4s,4p) electrons per atom in this alloy. Then we are answering the question to what extent the valence electronic structure of a given alloy diﬀers from a superposition of the structure of pure metals constituting this alloy, and how it is connected with the mechanisms of changes of valence electronic structure of individual metals in alloys.

2. Experimental details The measurements were carried out using high purity alloys (in powder form) procured from Alpha, a Johnson Matthey Company, UK. The powder material is pelletized into the size of 10 mm diameter 3 mm thickness for ﬁnal use in the experiments. The experiments were performed using 59.54 keV gamma rays from a 7400 MBq (200 mCi) 241 Am point-source that ionize the target atoms. The emitted X-rays 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 about 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 an earlier paper by Bhuinya and Padhi [23]. Pulses from the Si(Li) detector preampliﬁer were fed to an ORTEC-572 spectroscopy ampliﬁer and then recorded in a Canberra PC based Model S-100 multichannel analyzer. The gain of the system was about 16 eV/channel. For each sample three separate measurements have been made just to see the consistency of the results obtained from diﬀerent measurements. It was found that the results from diﬀerent measurements agreed with a deviation of <1%. Finally, the data from diﬀerent

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runs have been averaged to determine the ﬁnal Kbto-Ka ratio.

3. Data analysis and corrections

Table 1 The experimental Kb-to-Ka X-ray intensity ratio values of Ti, Cr, Fe and Co in the pure metals and in various alloys Sample

Constitution element

Kb-to-Ka intensity ratios

22

Ti Cr Fe Co Cr Fe Cr Co Ti Cr

0.1265 0.0006 0.1314 0.0008 0.1307 0.0007 0.1335 0.0008 0.1320 0.0010 0.1295 0.0010 0.1273 0.0010 0.1333 0.0010 0.1230 0.0010 0.1269 0.0010

Ti Cr 26 Fe 27 Co Cr0:26 Fe0:74 24

All the X-ray spectra were carefully analyzed with the help of a multiGaussian least-square ﬁtting programme [24] using a non-linear background subtraction. No low energy tail was included in the ﬁtting as its contribution to the ratio was shown to be negligible [25]. The Kbto-Ka intensity ratios were determined from the ﬁtted peak areas after applying necessary corrections to the measured data. Corrections to the measured ratios mainly come from the diﬀerences in the Ka and Kb self attenuations in the sample, in the eﬃciency of the Si(Li) detector and in air absorption on the path between the sample and the Si(Li) detector window. The eﬃciency of the detector is estimated theoretically according to Bhuinya and Padhi [10]. Our theoretically estimated eﬃciency was shown to be in good agreement with the measured eﬃciency [26] and at the energy region of present interest the diﬀerence was found to be negligible. The self attenuation correction in the sample and the absorption correction for the air path are determined as described before [25]. For the estimation of these corrections we have used the mass attenuation coeﬃcients compiled in a computer programme XCOM by Berger and Hubbell [27]. The mass attenuation coeﬃcients for the compounds are calculated by the BraggÕs-rule formula [28], l X wi li ¼ ; ð1Þ q qi i where wi is the proportion by weight of the ith constituent and li =qi is the mass attenuation coeﬃcient for the ith constituent in the compound.

4. Results and discussion The experimental Kb-to-Ka X-ray intensity ratio values of Ti, Cr, Fe and Co in pure metals and in Cr0:26 Fe0:74 , Cr0:80 Co0:20 and Ti0:80 Cr0:20 alloys

369

Cr0:80 Co0:20 Ti0:80 Cr0:20

are presented in Table 1. The errors quoted in the table are statistical only. It can be seen from Table 1 that the Kb-to-Ka intensity ratio values for 3dtransition metals in some of examined alloys are signiﬁcantly diﬀerent from the appropriate values for pure metals. However, for Cr in Cr0:26 Fe0:74 and Co in Cr0:80 Co0:20 the Kb-to-Ka ratios are almost unchanged with respect to the pure metals. The Kb-to-Ka intensity ratio values for Ti, Cr, Fe and Co in all the alloys are smaller than the pure metals values, except for Cr in Cr0:26 Fe0:74 , where the Kb-to-Ka ratio is slightly higher than the corresponding value for pure Cr. The measured Kb-to-Ka X-ray intensity ratios of Ti, Cr, Fe and Co in pure metals and in various alloys have been interpreted with the use of the results of the MCDF calculations (including the transverse Breit interaction and quantum electrodynamics corrections) [29–31] performed for various valence electronic conﬁgurations of the 3dmr 4sr type (where m is the total number of valence electrons for isolated atom and r ¼ 2, 1, 0) for Ti, Cr, Fe and Co. Additionally, in the case of Cr and Fe we have calculated the Kb-to-Ka intensity ratio values for the 3dmþ1 conﬁguration type. In the performed MCDF calculations of the Kb-to-Ka intensity ratios the Coulomb gauge was applied [31]. The results of these calculations are presented in Table 2. It can be found from the table that for every atom the Kb-to-Ka ratio changes signiﬁcantly with the change of the valence electronic conﬁguration and decreases with increasing number of 3d electrons. For each type

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Table 2 The theoretical Kb-to-Ka X-ray intensity ratio values of Ti, Cr, Fe and Co, obtained from the MCDF calculations performed for various valence electronic conﬁgurations with the Coulomb gauge applied Element

Atomic number

Electronic conﬁguration

Kb-to-Ka intensity ratios

Ti

22

3d2 4s2 3d3 4s1 3d4

0.1308 0.1262 0.1230

Cr

24

3d4 4s2 3d5 4s1 3d6 3d7

0.1333 0.1295 0.1268 0.1250

Fe

26

3d6 4s2 3d7 4s1 3d8 3d9

0.1349 0.1317 0.1294 0.1280

Co

27

3d7 4s2 3d8 4s1 3d9

0.1356 0.1326 0.1304

of electronic conﬁguration the Kb-to-Ka intensity ratios increase evidently with increasing atomic number. Moreover, it has been earlier shown [20] that the Kb-to-Ka X-ray intensity ratios of the 3dtransition metal atoms depend only slightly on the number of 4s and 4p valence electrons. As there is no physical reason to expect any point of inﬂection for the theoretical dependence of the Kb-to-Ka intensity ratio on the 3d-electron number, it seems natural to approximate this dependence with the decreasing branch of the second order polynomial. The coeﬃcients of such polynomials for Ti, Cr, Fe and Co, have been estimated (basing on the results from Table 2) with the least-squares ﬁtting method. The 3d-electron populations of Ti, Cr, Fe and Co in pure metals and in the alloys have been evaluated by solving the quadratic equation of the form aX 2 þ bX þ ðc Y Þ ¼ 0;

ð2Þ

where Y is an experimental value of Kb-to-Ka X-ray intensity ratio for a 3d-transition metal in a given system, X is the corresponding (unknown) number of 3d electrons and a, b and c are the

coeﬃcients of appropriate second order polynomial. Obviously, only the solutions for decreasing branch have been taken into account. The 3delectron populations of Ti, Cr, Fe and Co in pure metals and in the alloys are presented in the third column of Table 3. The obtained 3d-electron populations for pure metals are in close agreement with the numbers of the 3d-electrons per atom predicted by the band structure calculations of Papaconstantopoulos [32] (see the last column of Table 3), what conﬁrms the validity of our approach. Moreover, our present results for pure metals are in good agreement with the X-ray measurements of the atomic scattering factors of Batterman [33] (who concluded that, to an accuracy of about one electron, the number of 3d electrons in metallic Fe is not diﬀerent from that in the free atom) and Weiss and DeMarco [34] (who found 8:4 0:3 3d-electron population for Co in the pure metal). In the ﬁfth and sixth column of Table 3 one can ﬁnd respectively the changes and the rescaled (i.e. multiplied by the molar fraction of a given metal in an alloy) changes of the 3d-electron populations of Ti, Cr, Fe and Co in Cr0:26 Fe0:74 , Cr0:80 Co0:20 and Ti0:80 Cr0:20 alloys with respect to the pure metals. It can be seen that the 3d-electron populations of Cr and Fe in Cr0:26 Fe0:74 and Co in Cr0:80 Co0:20 are unchanged within the experimental error limits. For the other cases the 3d-electron populations of the metals in the examined alloys are signiﬁcantly larger than the pure metal values. To ﬁnd out the physical mechanism of these changes we considered two possibilities: (i) the transfer of 3d electrons from atoms of one element to atoms of the other element and (ii) the rearrangement of electrons between 3d and (4s,4p) states of individual metal atoms. One can easily deduce from the sixth column of Table 3 that the charge transfer mechanism cannot explain the 3d-electron population changes in the case of Cr0:80 Co0:20 and Ti0:80 Cr0:20 alloys, where both constituents of a given alloy have the same direction of these changes. Only for Cr0:26 Fe0:74 alloy the change of the 3d-electron population for Fe has the opposite direction to that of Cr. Also in this case the charge transfer mechanism cannot explain the observed changes of 3d-electron

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Table 3 The evaluated numbers of 3d and (4s,4p) electrons for Ti, Cr, Fe and Co in the pure metals and in various alloys, the changes and the rescaled (i.e. multiplied by the fraction of a given metal in an alloy) changes of 3d-electron numbers of Ti, Cr, Fe and Co in various alloys with respect to pure metalsa Sample

Pure Pure Pure Pure

Constitution element

Ti Cr Fe Co

Cr0:26 Fe0:74 Cr0:80 Co0:20 Ti0:80 Cr0:20

Cr Fe Cr Co Ti Cr

Evaluated number of 3d-electron

Evaluated number of (4s,4p) electrons

Change of 3delectron number w.r.t pure metal

Rescaled change of 3d-electron number w.r.t pure metal

3d-electrons number from band structure calculations [32]

2.92 0.15 4.46 0.21 7.39 0.29 7.67 0.28

1.08 0.15 1.54 0.21 0.61 0.29 1.33 0.28

– – – –

– – – –

2.91 4.96 6.93 7.87

4.31 0.25 7.95 0.53 5.78 0.60 7.74 0.36 4.00 0.40 5.94 0.48

1.69 0.25 0.05 0.53 0.22 0.60 1.26 0.36 0.00 0.40 0.06 0.48

0.15 0.33 0.56 0.60 1.32 0.64 0.07 0.46 1.08 0.43 1.48 0.52

0.04 0.09 0.41 0.44 1.06 0.51 0.01 0.09 0.86 0.34 0.30 0.10

a In the last column the 3d-electron numbers evaluated from the band structure calculations [32] for metallic Ti, Cr, Fe and Co are cited for comparison.

population, because the change for Cr and Fe are negligible within the experimental error limits. Thus, to reliably explain the changes (with respect to the pure metals) of the 3d-electron population of Cr in Cr0:80 Co0:20 and Ti and Cr in Ti0:80 Cr0:20 alloys, the rearrangement of electrons between 3d and (4s,4p) states of individual metal atoms has to be assumed. This conclusion is the same as in the case of our recent studies [21], in which the rearrangement mechanism has been found to be responsible for the changes (with respect to the pure metals) of the 3d-electron populations of Fe and Ni in the Fex Ni1x alloys of diﬀerent composition x. In our earlier studies on Vx Ni1x alloys (for x ¼ 0:10, 0.35, 0.50 and 0.75) neither the rearrangement nor charge transfer mechanism could be excluded when explaining the observed changes in the valence electronic conﬁgurations of V and Ni [20]. However, for x ¼ 0:20 the charge transfer mechanism did not explain these changes, and this is consistent with our present results. The numbers of (4s,4p) electrons (playing an active role in the described electron rearrangement processes) for Ti, Cr, Fe and Co in the pure metals (see the fourth column of Table 3) have been evaluated by subtracting from the total number of valence electrons of neutral atom the number of 3d

electrons of this atom in a pure metal (which has been taken from the third column of Table 3). The same has been done in the case of Cr0:26 Fe0:74 , Cr0:80 Co0:20 and Ti0:80 Cr0:20 alloys, for each metal separately. The results concerning the second aspect of our study (i.e. the electronic structure of the Cr0:26 Fe0:74 , Cr0:80 Co0:20 and Ti0:80 Cr0:20 alloys) are presented in Table 4. In the last three rows of this table the corresponding results for various Fex Ni1x alloys (obtained in our earlier studies [21]) are presented for comparison. To obtain information about the valence electronic structure of the Cr0:26 Fe0:74 , Cr0:80 Co0:20 and Ti0:80 Cr0:20 alloys we calculated the weighted average numbers of 3delectrons per one atom in these alloys (the second column of Table 4), taking in this average the numbers of 3d electrons evaluated separately for each metal in a given alloy (the third column of Table 3) with the weights equal to the molar fractions of metals in this alloy. Similarly, we evaluated the weighted average number of the (4s,4p) valence band electrons per metal atom for the examined alloys (the fourth column of Table 4). It can be seen from Table 4 that the average number of 3d electrons is large for the Cr0:26 Fe0:74 , Cr0:80 Co0:20 and Ti0:80 Cr0:20 alloys while the (4s,4p)

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Table 4 The weighted average numbers of 3d electrons and the weighted average numbers of (4s,4p) electrons for Cr0:26 Fe0:74 , Cr0:80 Co0:20 and Ti0:80 Cr0:20 alloys; the superpositions of 3d electrons and the superpositions of (4s,4p) electrons obtained from the pure metal valuesa Sample

Weighted average number of 3d electrons

Superposition of 3d electrons from pure metal values

Weighted average number of (4s,4p) electrons

Superposition of (4s,4p) electrons from pure metal values

Cr0:26 Fe0:74 Cr0:80 Co0:20 Ti0:80 Cr0:20

7.00 0.40 6.17 0.48 4.39 0.33

6.63 0.22 5.10 0.18 3.23 0.13

0.48 0.40 0.43 0.48 0.01 0.33

0.85 0.22 1.50 0.18 1.17 0.13

Fe0:20 Ni0:80 Fe0:50 Ni0:50 Fe0:58 Ni0:42

9.28 0.42 7.34 0.16 7.36 0.16

8.31 0.32 7.97 0.24 7.87 0.24

0.32 0.42 1.66 0.16 1.48 0.16

1.29 0.32 1.03 0.24 0.97 0.24

a For comparison the corresponding results for various Fex Ni1x alloys (obtained in our earlier studies [21]) are presented in the last three rows.

valence band is almost empty in these alloys (within the experimental errors limits). It is opposite to the properties of Fe0:50 Ni0:50 and Fe0:58 Ni0:42 alloys, for which we found [21] the number of (4s,4p) valence band electrons to be signiﬁcant (see the last two rows of Table 4). However, for Fe0:20 Ni0:80 alloy, i.e. the alloy in which the ratio of molar fractions of both 3d-transition metals is the same as in the case of Cr0:80 Co0:20 and Ti0:80 Cr0:20 alloys and close to that of Fe0:74 Cr0:26 alloy, the average number of 3d electrons was the largest and the (4s,4p) valence band was also almost empty (Table 4). We found it very interesting to answer the question to what extent the estimated valence electronic structure of a given alloy diﬀers from a superposition of the electronic structure of pure metals (constituting this alloy), and how it is connected with the mechanisms of changes of valence electronic structure of individual metals in the alloys. In the third column of Table 4 we, therefore, present for the examined alloys of the type Ax B1x a superposition of the number of 3d electrons, calculated as xnA þ ð1 xÞnB , where nA and nB are the numbers of 3d electrons taken from the third column of Table 3 for pure metals (i.e. without the alloying eﬀect). In a similar way we have calculated the superposition of the number of (4s,4p) electrons (the ﬁfth column of Table 4). It can be seen from the table that for all studied alloys these superposition numbers are totally different from the discussed above weighted average

numbers of 3d electrons and the weighted average numbers of (4s,4p) electrons, respectively.

5. Conclusions In the ﬁrst step of the presented work we have evaluated the 3d-electron populations of Ti, Cr, Fe and Co in the pure metals and in Cr0:26 Fe0:74 , Cr0:80 Co0:20 and Ti0:80 Cr0:20 alloys, by comparing the measured Kb-to-Ka X-ray intensity ratios with the theoretical values of this ratio obtained from the MCDF calculations (performed for various valence electronic conﬁgurations of Ti, Cr, Fe and Co). The 3d-electron populations evaluated for the pure metals agree well with the results of band structure calculations of Papaconstantopoulos [32], which conﬁrms the validity of our approach. We have found that the alloying eﬀect is generally signiﬁcant in the case of the studied alloys and is reﬂected in the changes (with respect to the pure metals) of the 3d-electron populations of the transition-metals in these alloys (what causes the observed changes of the Kb-to-Ka X-ray intensity ratios). The rearrangement of electrons between 3d and (4s,4p) states of individual metal atoms has been found to be responsible for these changes, while the charge transfer mechanism can practically be neglected. In the second step of our studies we used the obtained information about the valence electronic structure of both the metals in a given alloy to

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estimate the weighted average number of 3d electrons and weighted average number of (4s,4p) electrons per atom in this alloy. According to our expectations, we have found that in the case of studied Cr0:26 Fe0:74 , Cr0:80 Co0:20 and Ti0:80 Cr0:20 alloys, i.e. the alloys in which the ratio of the molar fractions of both constituents is equal to or close to 1=4, the average number of 3d electrons is large while the (4s,4p) valence band is almost empty (similarly to our recently studied Fe0:20 Ni0:80 alloy [21]). We have found that for all studied alloys the superposition of the numbers of 3d electrons (obtained from the pure metals values) and the superposition of the numbers of (4s,4p) electrons are totally diﬀerent from the corresponding weighted averages. It should be so, because the rearrangement mechanism has been found to be the dominant channel of the 3d-electron population changes of both constituents in the studied alloys (it is important to note that if the charge transfer was the only mechanism of the 3d-electron population changes, the considered superpositions should be exactly equal to the appropriate weighted averages).

Acknowledgements The authors H.C. Padhi and S. Raj acknowledge the ﬁnancial support of Council of Scientiﬁc and Industrial Research, India. This work was also partly supported by the Polish Committee for Scientiﬁc Research (KBN), Grant no. 2 P03B 019 16.

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