PHYSICAL REVIEW B, VOLUME 65, 193105

Relative K x-ray intensity studies of the valence electronic structure of 3d transition metals S. Raj and H. C. Padhi Institute of Physics, Bhubaneswar-751005, India

P. Palit and D. K. Basa Department of Physics, Utkal University, Bhubaneswar-751004, India

M. Polasik and F. Pawłowski Faculty of Chemistry, Nicholas Copernicus University, 87-100 Torun´, Poland 共Received 27 September 2001; revised manuscript received 21 December 2001; published 25 April 2002兲 K ␤ -to-K ␣ x-ray intensity ratios have been measured for all the 3d transition metals from titanium to copper, and the valence electronic structures of these metals have been determined by comparing the measured K ␤ -to-K ␣ x-ray intensity ratios with the results of our multiconfiguration Dirac-Fock calculation. Our experimentally determined valence electronic structures for all the metals except V, Cr, and Mn are found to agree reasonably well with the results of augmented plane-wave 共APW兲 band structure calculations. Our results for the valence electronic structure of V and Mn are found to be closer to the free atom values whereas the valence electronic structure of Cr is found to lie in between the valence electronic structure predicted by Compton profile studies and the one given by APW band structure calculations. The electron occupancies of 3d and (4s,4p) states of V, Mn, and Cu are similar to free atom occupancies whereas for the other metals we find rearrangement of electrons between 3d and (4s,4p) states of the metal with the transfer of electrons from 3d to (4s,4p) states for Cr and from (4s,4p) to 3d states in the case of Ti, Fe, Co, and Ni. DOI: 10.1103/PhysRevB.65.193105

PACS number共s兲: 78.70.En, 32.30.Rj, 32.70.Fw

I. INTRODUCTION

The 3d transition metals have played an important role in the development of modern technology, and knowledge of their valence electronic structure is very important for understanding their physical properties. Although some investigations have been made to study their electronic structures individually, no systematic study has been made so far for understanding the valence electronic structure of all the 3d transition metals. The Compton profile studies by Berggren et al.1 suggested a valence electronic structure of 3d 3 4s 1 for Ti which agreed with the one predicted by the augmented plane-wave 共APW兲 band structure calculation of Papaconstantopoulos.2 Subsequent Compton profile studies by Menninen and Paakkari3 and Lasser et al.,4 however, suggested a different valence electronic structure of 3d 2 4s 2 in contrast to the one predicted by the APW theory. The Compton profile study for vanadium by Paakkari et al.5 suggested a valence electronic structure of 3d 3 4s 2 which disagreed with the one given by the APW theory of Papaconstantopoulos.2 Similar disagreement is also reported for the valence electronic structure of Cr. The Compton profile studies on Cr by Paakkari et al.5 and Bauer et al.6 suggested a valence electronic structure of 3d 4 4s 2 which is different from the one given by the APW theory.2 These disagreements between experimental observations and theoretical calculations have motivated us to undertake a detailed and careful study on all the 3d transition metals. A further objective of the present investigation has been to make a systematic study on all the 3d transition metals for checking the results of APW theory2 and also to provide exact valence electronic structures of these metals which will be useful for making a theoretical estimation of the electron momentum 0163-1829/2002/65共19兲/193105共4兲/$20.00

density distributions, required in Compton profile studies,8 using renormalized free atom 共RFA兲 model.9–11 The information on the valence electronic structure of the 3d metals will also be useful for understanding the various physical properties of these metals. The K ␤ -to-K ␣ x-ray intensity ratio has been found to depend strongly on the valence electronic structure of the 3d metals.7 By comparing the measured ratios with the results of multiconfiguration Dirac-Fock 共MCDF兲 calculations one can obtain information on the valence electronic structure of the metal. Accordingly, we have measured the K ␤ -to-K ␣ x-ray intensity ratios of all the 3d metals starting from titanium to copper and compared them with the results of our MCDF calculation for obtaining the information on the valence electronic structures of these metals. This, to the best of our knowledge, is not only the first systematic study for understanding the valence electronic structure of all the 3d transition metals, but also provides a simple method for the determination of valence electronic structure of the all the 3d metals . II. EXPERIMENTAL DETAILS

The high-purity samples in the form of thick foils of 25 mm diam⫻2 mm thick were procured from Goodfellow Company, UK. Gamma rays of 59.54 keV from a 200 mCi 241 Am radioactive source were used for ionizing the target atoms and the x rays emitted were detected by a 30 mm2 ⫻3 mm thick Canberra Si共Li兲 detector having a 12.7-␮ m-thick beryllium window. The resolution of the Si共Li兲 detector was ⬃165 eV 关full width at half maximum 共FWHM兲兴 for a 5.9-keV x-ray peak. Details regarding the experimental arrangement have been reported elsewhere.12

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©2002 The American Physical Society

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PHYSICAL REVIEW B 65 193105 TABLE I. Experimental K ␤ -to-K ␣ ratio of the transition metals which have been compared with the previously published results 共Refs. 17 and 18兲.

Element 22

Ti V 24 Cr 25 Mn 26 Fe 27 Co 28 Ni 29 Cu 23

a

Experimental K ␤ -to-K ␣ intensity ratio

K ␤ -to-K ␣ ratio from previous study

0.1265⫾0.0006 0.1312⫾0.0008 0.1314⫾0.0008 0.1344⫾0.0009 0.1307⫾0.0007 0.1335⫾0.0008 0.1346⫾0.0012 0.1343⫾0.0012

0.1243⫾0.0028a 0.1305⫾0.0040a 0.1332⫾0.0016a 0.1365b 0.1353b – – 0.1349b

Reference 17. Reference 18.

b

FIG. 1. A typical K x-ray spectrum of Mn. The open circles correspond to experimental data, the dashed curve corresponds to the fitted data, and the solid line represents the fitted background.

Pulses from the Si共Li兲 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 maintained at ⬃16 eV/channel. The counting was continued until the count under the less intense K ␤ peak was around 5⫻104 . Two sets of measurements were carried out for each sample, and an average of the two measurements was found for the K ␤ -to-K ␣ x-ray intensity ratio which is reported. III. DATA ANALYSIS

All the x-ray spectra were carefully analyzed with a multi-Gaussian least-squares fitting program using a nonlinear background subtraction. No low-energy tail was included in the fitting as its contribution to the ratio was shown to be quite small.13 The K ␤ -to-K ␣ x-ray intensity ratios were determined from the fitted peak areas after applying necessary corrections to the data. A typical K x-ray spectrum of Mn along with the fit is shown in Fig. 1. The figure suggests a good fit of the data. Corrections to the measured ratios mainly come from the difference in the K ␣ and K ␤ self-attenuations in the sample, the difference in the efficiency of the Si共Li兲 detector and air absorption on the path between the sample and the Si共Li兲 detector window. The efficiency of the detector is estimated theoretically as mentioned in an earlier paper by Bhuinya and Padhi.14 Our theoretically estimated efficiency was shown to be in good agreement with the measured efficiency,15 and at the energy region of present interest the

discrepancy between them was found to be quite small. The self-attenuation correction in the sample and the absorption correction for the air path are determined as per the procedure described before.14 For an estimation of these corrections we have used the mass attenuation coefficients compiled in a computer program XCOM by Berger and Hubbell.16 IV. RESULTS AND DISCUSSION

The experimental results for the K ␤ -to-K ␣ x-ray intensity ratios of the 3d metals after all the corrections are presented in Table I. We also present in column 3 of Table II the results for the K ␤ -to-K ␣ x-ray intensity ratios reported by Lepy et al.17 and some recommended by International Atomic Energy Agency 共IAEA兲.18 Our experimental results for the K ␤ -to-K ␣ ratios of Ti, V, and Cr agree reasonably well with the recent results of Lepy et al.17 Our results for Mn and Cu are in good agreement with the values recommended by the IAEA,18 whereas the Fe result is somewhat lower as compared to the IAEA-recommended value. In order to have a further check on the correctness of our experimental results for the K ␤ -to-K ␣ x-ray intensity ratios of these metals we have determined the 3d electron occupancies of these metals by comparing the experimental K ␤ -to-K ␣ x-ray intensity ratios with the results of our theoretical MCDF calculation7 assuming various valence electronic configurations for the metals with an integral number of electrons occupying the 3d and (4s,4p) states. The theoretical K ␤ -to-K ␣ ratios for various valence electronic configurations are interpolated through a nonlinear fit to finally get a valence electronic configuration with fractional electron occupancy for which the K ␤ -to-K ␣ ratio is in agreement with the measured K ␤ -to-K ␣ x-ray intensity ratio. The interpolation is done by fitting the theoretical K ␤ -to-K ␣ ratios for different valence electronic configurations 关for example, for titanium the configurations are 3d 4 4(sp) 0 , 3d 3 4(sp) 1 , 3d 2 4(sp) 2 , and 3d 1 4(sp) 3 兴 with integral electron numbers using the equation

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ax 2 ⫹bx⫹c⫽y,

共1兲

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PHYSICAL REVIEW B 65 193105

TABLE II. The experimentally determined valence electronic structures of 3d transition metals are compared with the valence electronic structures of free atoms and those obtained from APW band structure calculations.

3d metal

No. of valence electrons

No. of 3d electrons (n d ) 共Expt.兲

No. of 3d electrons (n d ) 共Theory兲

No. of (4s,4p) electrons 共Expt.兲

No. of (4s,4p) electrons 共Theory兲

Valence electronic configuration of atoms

Ti V Cr Mn Fe Co Ni Cu

4 5 6 7 8 9 10 11

2.92⫾0.18 3.21⫾0.18 4.46⫾0.21 4.84⫾0.18 7.39⫾0.29 7.67⫾0.28 8.54⫾0.39 9.87⫿0.51

2.91 3.98 4.96 5.99 6.93 7.87 8.97 9.91

1.08⫿0.18 1.79⫿0.18 1.54⫿0.21 2.16⫿0.18 0.61⫿0.29 1.33⫿0.28 1.46⫿0.39 1.13⫿0.51

1.09 1.02 1.04 1.01 1.07 1.13 1.03 1.09

3d 2 4s 2 3d 3 4s 2 3d 5 4s 1 3d 5 4s 2 3d 6 4s 2 3d 7 4s 2 3d 8 4s 2 3d 104s 1

where x stands for 3d electron occupancy and y stands for the theoretical K ␤ -to-K ␣ ratio. The fit resulted in the values of the coefficients a, b, and c which have been used in Eq. 共1兲 along with the experimental K ␤ -to-K ␣ ratios for y to get the value of x. From the two values of x thus found, one is rejected on physical grounds and the other one is quoted. The results for the 3d electron occupation thus obtained have been compared with the results of the band structure calculation2 共see columns 3 and 4 of Table II兲. The experimental 3d electron populations of V and Mn are found to be closer to the free atom populations whereas the experimental results for Ti, Fe, Co, Ni, and Cu are found to be in good agreement with the results of APW band structure calculation.2 In the case of Cr, the valence elecronic structure is found to be in between the results of Compton profile studies5,6 and band structure calculations2 of 3d 4 (4s,4p) 2 and 3d 4.96(4s,4p) 1.04, respectively. Our valence electronic structure of titanium is found to be 3d 2.91(4s,4p) 1.09 which is in agreement with the APW calculation of Papaconstantopoulos2 and RFA calculation of Berggren et al.14 However, Compton profile studies by Mannien and Paakkari3 and Lasser et al.4 suggested a 3d 2 4s 2 configuration for titanium which is in disagreement with our present finding. Our valence electronic structure for vanadium is found to be in good agreement with the result obtained by Bauer et al.6 and Paakkari et al.5 from their Compton profile studies but it does not agree with the band structure calculation.2 The valence electronic structure of chromium is found to be in between the experimental Compton profile study result of Paakkari et al.5 who predicted a 3d 4 4s 2 configuration for

1

K.F. Berggren, S. Manninen, and T. Paakkari, Phys. Rev. B 8, 2516 共1973兲. 2 D. A. Papaconstantopoulos, Handbook of Band Structure of Elemental Solids 共Plenum, New York, 1986兲. 3 S. Manninnen and T. Paakkari, J. Phys. C 9, 95 共1976兲.

Cr and the band structure result2 of 3d 4.96, (4s,4p) 1.04. As mentioned before, our K ␤ -to-K ␣ ratio for Mn agrees reasonably well with the result recommended by the IAEA,18 but our valence electronic structure of Mn does not agree with the band structure calculation.2 Our results for the valence electronic structure of Fe, Co, and Ni agree with the results of Compton profile studies by Paakkari et al.5 Our Ni result also agrees very well with the RFA calculation result of Kanhere and Singru.19 The present results for Fe, Co, and Ni also agree with the theoretical prediction of Papaconstantopoulos.2 Our result for the valence electronic structure of Cu agrees reasonably well with the result of the RFA model calculation of Kanhere and Singru19 for explaining the Compton profile of Cu and also with the prediction of band structure calculations.2 V. CONCLUSION

In conclusion, we have demonstrated that the K ␤ -to-K ␣ x-ray intensity ratio is a useful and sensitive physical quantity for probing the valence electronic structure of 3d transition metals. Our present results suggest no change in the valence electronic structure of V, Mn, and Cu from the free atom structure whereas the 3d metals of Ti, Fe, Co, and Ni indicate rearrangement of electrons between 3d and (4s,4p) states with transfer of electrons from (4s,4p) states to 3d states of the metal. Our Cr result suggests an intermediate configuration between one predicted by Compton profile results5,6 and the other predicted by the APW band structure calculation2 with transfer of electrons from 3d to (4s,4p) states.

4

R. Lasser, B. Lengler, and G. Arnold, Phys. Rev. B 22, 663 共1980兲. 5 T. Paakkari, S. Manninen, and K.F. Berggren, Phys. Fenn. 10, 207 共1975兲. 6 G.E.W. Bauer, J.R. Schneider, and J.M. Welter, Phys. Lett. 100A,

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207 共1984兲. M. Polasik, Phys. Rev. A 58, 1840 共1998兲. 8 Compton Scattering, edited by B. Williams 共McGraw-Hill, London, 1977兲. 9 M. Chodorow, Phys. Rev. 55, 675 共1939兲. 10 B. Segall, Phys. Rev. 125, 109 共1962兲. 11 K.F. Berggren, Phys. Rev. B 6, 2156 共1972兲. 12 C.R. Bhuinya and H.C. Padhi, J. Phys. B 22, 5283 共1992兲. 13 G. Paic and V. Pecar, Phys. Rev. A 14, 2190 共1976兲. 14 C.R. Bhuinya and H.C. Padhi, Phys. Rev. A 47, 4885 共1993兲. 7

15

B.B. Dhal, T. Nandi, and H.C. Padhi, Nucl. Instrum. Methods Phys. Res. B 101, 327 共1995兲. 16 M. J. Berger and J. H. Hubbell, Computer code XCOM Centre for Radiation Research, National Bureau of Standards, Gaithersburg, MD 20899 共unpublished兲. 17 M.C. Lepy, J. Plasnard, and J. Morel, Nucl. Instrum. Methods Phys. Res. A 339, 241 共1994兲. 18 IAEA, x-ray and gamma-ray standards for detector calibration, IAEA Teedoc-619 共September 1991兲. 19 D.G. Kanhere and R.M. Singru, J. Phys. F: Met. Phys. 5, 1146 共1975兲.

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