- Email: [email protected]
Valence electronic structure of Ni in Ni–Si alloys from relative K X-ray intensity studies
NIM B Beam Interactions with Materials & Atoms
Nuclear Instruments and Methods in Physics Research B 255 (2007) 438–440 www.elsevier.com/locate/nimb
Letter to the Editor
Valence electronic structure of Ni in Ni–Si alloys from relative K X-ray intensity studies Y. Kalayci a, A. Aydinuraz b, B. Tugluoglu c, R.H. Mutlu
c,*
a Saraykoy Nuclear Research and Training Center, 06983 Saray, Ankara, Turkey Ankara University, Faculty of Science, Department of Physics, 06100 Ankara, Turkey Ankara University, Faculty of Engineering, Department of Physics Engineering, 06100 Ankara, Turkey b
c
Received 1 November 2006; received in revised form 13 December 2006 Available online 5 January 2007
Abstract The Kb-to-Ka X-ray intensity ratio of Ni in Ni3Si, Ni2Si and NiSi has been determined by energy dispersive X-ray fluorescence technique. It is found that the intensity ratio of Ni decreases from pure Ni to Ni2Si and then increases from Ni2Si to NiSi, in good agreement with the electronic structure calculations cited in the literature. We have also performed band structure calculations for pure Ni in various atomic configurations by means of linear muffin-tin orbital method and used this data with the normalized theoretical intensity ratios cited in the literature to estimate the 3d-occupation numbers of Ni in Ni–Si alloys. It is emphasized that investigation of alloying effect in terms of X-ray intensity ratios should be carried out for the stoichiometric alloys in order to make reliable and quantitative comparisons between theory and experiment in transition metal alloys. Ó 2007 Elsevier B.V. All rights reserved.
1. Introduction It has been a challenge in X-ray fluorescence analysis to investigate the alloying effect in terms of the Kb-to-Ka Xray intensity ratios which became a useful tool to study the valence electronic structure of 3d metals in various alloys [1–9]. In general for a given 3d metal, intensity ratio decreases with increasing of 3d electron population as has been found by performing the multiconfiguration Dirac– Fock (MCDF) calculations [5,6,10]. For the alloys, although the origin of Kb-to-Ka intensity ratio change should be interpreted due to the change in the electronic structure [7,9], for the reasons that are not very clear to us, conventionally measurements were performed on nonstoichiometric alloys [1–4,6–9] for which the electronic
*
Corresponding author. E-mail address: [email protected] (R.H. Mutlu).
0168-583X/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2006.12.143
structure calculations are not available. For the Ni–Si alloys, to our knowledge, there exists only one study [5] where the comparison between experiment and electronic structure calculations is made. However, the results of [5] disagree quantitatively with theoretical calculations [11,12] and disagree qualitatively both with the electronic structure calculations [11,12] and experiment [13] for NiSi. All these have motivated the present study in which we have measured the Kb-to-Ka X-ray intensity ratio of Ni in Ni3Si, Ni2Si and NiSi. We have also performed electronic structure calculations for pure Ni in different atomic configurations and used this data with the normalized MCDF intensity ratios [5] to estimate the d-occupation numbers of Ni in Ni–Si alloys. Although the results obtained in the present work were all in good agreement with the theoretical calculations [11,12] and K-shell fluorescence yield results [13], we have to emphasize that modern electronic structure calculations should be performed in order to make reliable and quantitative comparisons between theory and experiment in Ni–Si binary alloy system.
Y. Kalayci et al. / Nucl. Instr. and Meth. in Phys. Res. B 255 (2007) 438–440
2. Experimental details and theoretical calculations The Ni–Si alloys are prepared as described in [13]. The pure Ni and the prepared alloys Ni3Si, Ni2Si and NiSi were in the form of powders and all of them are sieved for 400 mesh. Each sample is mixed with powder polyvinyl chloride, sealed in stainless steel annular capsule and pelletized similarly. The experimental set-up [13] consists of an annular 109 Cd radioisotope (providing of 22–25 keV primary beam energy) of 10 mCi activity, a planar Si(Li) detector of 80 mm2 sensitive area and 5 mm thickness. The measurements are performed with a resolution of 190 eV at 5.9 keV, coupled to PC based Accuspec supplied by Genie 2000 software system (Canberra). The Kb-to-Ka intensity ratios were determined from the peak areas of the X-ray spectra after applying necessary corrections to the measured data as described in [4,8]. In the literature, the d-occupation numbers of a transition metal in pure form and in the alloy have been evaluated by means of the MCDF calculations which relate the electron populations of free atoms in different electronic configurations to the theoretical intensity ratios; however since a pure metal or an alloy cannot be regarded as a collection of free atoms, the obtained results generally disagree [5,6,10] quantitatively with the electronic structure calculations. We, therefore, carried out self-consistent electronic structure calculations for Ni corresponding to various types of atomic configurations by means of the linear muffin-tin orbital (LMTO) method using the codes of Skriver [14]. All the calculations are performed within the four different exchange-correlation formalisms cited in the literature. The d-occupation numbers of Ni at the Fermi level are obtained as described in [15]. 3. Results and discussion The experimental Kb-to-Ka X-ray intensity ratios of nickel for pure Ni and Ni–Si alloys are presented in Table 1 including the statistical error bars. Since the absolute values of the experimental intensity ratios differ considerably even for pure Ni [2,4–8], the normalized values are also included in Table 1. The 3d-occupation numbers of Ni, corresponding to various types of electronic configurations, calculated by means of the LMTO method are presented in Table 2. In order to use this data with the theoretical MCDF intensity Table 1 Experimental and normalized (with respect to pure nickel) Kb-to-Ka X-ray intensity ratios of Ni in Ni–Si alloys Alloy
Kb-to-Ka intensity ratios
Normalized Kb-to-Ka intensity ratio
Ni Ni3Si Ni2Si NiSi
0.1378 ± 0.0010 0.1332 ± 0.0012 0.1317 ± 0.0005 0.1343 ± 0.0014
1.0 0.967 ± 0.001 0.956 ± 0.001 0.975 ± 0.001
439
Table 2 The theoretical LMTO 3d-occupation numbers and theoretical MCDF X-ray intensity ratios of Ni corresponding to various types of the electronic configurations Electronic configuration
3d Electron population
Normalized Kb-to-Ka intensity ratio
3d74s24p1 3d84s2 3d94s1
8.545 8.587 8.603
1.0263 1.0000 0.9795
ratios [5,6,10] to estimate the 3d electron population of Ni in any Ni based alloy, the arithmetical averages of the MCDF intensity ratios obtained within the Coulomb and Babushkin gauges [5] are used and presented, as normalized with respect to pure nickel, also in Table 2. The 3d electron population of Ni in Ni–Si alloys have been evaluated by solving the linear equation of the form y = ax + b, where x is the normalized experimental intensity ratio of Ni in the alloy (Table 1) and y is the corresponding (unknown) 3d-occupation number. The coefficients a and b are obtained by means of the linear fit of the data presented in Table 2. We should emphasize that the linear equation between d-occupation number and normalized intensity ratio is used just to obtain an approximately general expression between these quantities that can be used in any Ni based alloy system. The evaluated number of 3d electrons for Ni in Ni–Si alloys, as described above, are presented in Table 3. According to Table 3, the 3d electron population of Ni increases with the decrease of Ni concentration up to Ni2Si, in good agreement both with experimental [5,13] and theoretical results [11,12]. For the NiSi we have found, in contrast to [5], a decrease in the d-occupation number of Ni in good agreement with the electronic structure calculations [11,12]. It should be emphasized that our results agree quantitatively with [11] and qualitatively with [12], even if the uncorrected data is used for the X-ray intensity ratios (Table 3). We have also used the original 3d electron populations (first column of Table 2) and obtained the 3d electronic structure of Ni in Ni–Si alloys. These results (forth column of Table 3) showed only qualitative agreement with the electronic structure calculations [11,12]. Furthermore, the results obtained for the alloying effect on the Kb-to-Ka X-ray intensity ratios of Ni in Ni–Si binary alloy Table 3 The evaluated 3d-occupation numbers of Ni in Ni–Si alloys by use of the 3d electron populations from the LMTO method (second column of Table 2) Sample
Uncorrected
Pure Ni Ni3Si Ni2Si NiSi
8.581 8.622 8.636 8.612
8.581 8.630 8.649 8.619
8.20 10.08 10.95 9.50
[11]
[12]
8.7 8.6
9.1 9.9 9.8
The results obtained for the uncorrected normalized X-ray intensity ratio data are also presented. The forth column refers to the evaluation by use of the original 3d electron populations given in the first column of Table 2. Theoretical values [11,12] are presented for comparison.
440
Y. Kalayci et al. / Nucl. Instr. and Meth. in Phys. Res. B 255 (2007) 438–440
system are all in excellent agreement with the K-shell fluorescence yield results [13] including Ni5Si2 and Ni3Si2. However, since the theoretical results considerably controversial (Table 3), modern electronic structure calculations (full-potential, fully relativistic, etc.) have to be performed in order to make reliable quantitative comparisons between theory and experiment in Ni–Si alloys. In this context, it should be emphasized that investigation of alloying effect in terms of the X-ray intensity ratios should be carried out for the stoichiometric alloys for which the modern electronic structure calculations are available. References [1] Y. Tamaki, T. Omori, T. Shiokawa, Radiochem. Radioanal. Lett. 37 (1979) 39. [2] C.R. Bhuinya, H.C. Padhi, Phys. Rev. 47 (1993) 4885. [3] C. Chang, C. Chen, C. Yen, Y. Wu, C. Su, S.K. Chiou, J. Phys. B 27 (1994) 5251.
¨ . So¨g˘u¨t, E. Bu¨yu¨kkasap, A. Ku¨c¸u¨ko¨nder, M. Ertug˘rul, O ¨. S [4] O ß imsßek, Appl. Spectrosc. Rev. 30 (1995) 175. [5] S. Raj, B.B. Dhal, H.C. Padhi, M. Polasik, Phys. Rev. B 58 (1998) 9025. [6] S. Raj, H.C. Padhi, M. Polasik, Nucl. Instr. and Meth. B 155 (1999) 143. [7] S. Raj, H.C. Padhi, M. Polasik, F. Pawlowski, D.K. Basa, Solid State Commun. 116 (2000) 563. [8] O. Sogut, E. Bu¨yu¨kkasap, H. Erdog˘an, Radiat. Phys. Chem. 64 (2002) 343. [9] F. Pawlowski, M. Polasik, S. Raj, H.C. Padhi, D.K. Basa, Nucl. Instr. and Meth. B 195 (2002) 367. [10] M. Polasik, Phys. Rev. A 58 (1998) 1840. [11] O. Bisi, C. Calandra, J. Phys. C 14 (1981) 5479. [12] K.L. Peterson, J.S. Hsiao, D.R. Chopra, T.R. Dillingham, Phys. Rev. B 83 (1988) 9511. [13] Y. Kalayci, Y. Agus, S. Ozgur, N. Efe, A. Zararsiz, P. Arikan, R.H. Mutlu, Spectrochim. Acta B 60 (2005) 277. [14] H.L. Skriver, The LMTO Method, Springer, New York, 1984. [15] R.H. Mutlu, J. Phys. Condens. Matter 7 (1995) 1283.
Nuclear Instruments and Methods in Physics Research B 255 (2007) 438–440 www.elsevier.com/locate/nimb
Letter to the Editor
Valence electronic structure of Ni in Ni–Si alloys from relative K X-ray intensity studies Y. Kalayci a, A. Aydinuraz b, B. Tugluoglu c, R.H. Mutlu
c,*
a Saraykoy Nuclear Research and Training Center, 06983 Saray, Ankara, Turkey Ankara University, Faculty of Science, Department of Physics, 06100 Ankara, Turkey Ankara University, Faculty of Engineering, Department of Physics Engineering, 06100 Ankara, Turkey b
c
Received 1 November 2006; received in revised form 13 December 2006 Available online 5 January 2007
Abstract The Kb-to-Ka X-ray intensity ratio of Ni in Ni3Si, Ni2Si and NiSi has been determined by energy dispersive X-ray fluorescence technique. It is found that the intensity ratio of Ni decreases from pure Ni to Ni2Si and then increases from Ni2Si to NiSi, in good agreement with the electronic structure calculations cited in the literature. We have also performed band structure calculations for pure Ni in various atomic configurations by means of linear muffin-tin orbital method and used this data with the normalized theoretical intensity ratios cited in the literature to estimate the 3d-occupation numbers of Ni in Ni–Si alloys. It is emphasized that investigation of alloying effect in terms of X-ray intensity ratios should be carried out for the stoichiometric alloys in order to make reliable and quantitative comparisons between theory and experiment in transition metal alloys. Ó 2007 Elsevier B.V. All rights reserved.
1. Introduction It has been a challenge in X-ray fluorescence analysis to investigate the alloying effect in terms of the Kb-to-Ka Xray intensity ratios which became a useful tool to study the valence electronic structure of 3d metals in various alloys [1–9]. In general for a given 3d metal, intensity ratio decreases with increasing of 3d electron population as has been found by performing the multiconfiguration Dirac– Fock (MCDF) calculations [5,6,10]. For the alloys, although the origin of Kb-to-Ka intensity ratio change should be interpreted due to the change in the electronic structure [7,9], for the reasons that are not very clear to us, conventionally measurements were performed on nonstoichiometric alloys [1–4,6–9] for which the electronic
*
Corresponding author. E-mail address: [email protected] (R.H. Mutlu).
0168-583X/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2006.12.143
structure calculations are not available. For the Ni–Si alloys, to our knowledge, there exists only one study [5] where the comparison between experiment and electronic structure calculations is made. However, the results of [5] disagree quantitatively with theoretical calculations [11,12] and disagree qualitatively both with the electronic structure calculations [11,12] and experiment [13] for NiSi. All these have motivated the present study in which we have measured the Kb-to-Ka X-ray intensity ratio of Ni in Ni3Si, Ni2Si and NiSi. We have also performed electronic structure calculations for pure Ni in different atomic configurations and used this data with the normalized MCDF intensity ratios [5] to estimate the d-occupation numbers of Ni in Ni–Si alloys. Although the results obtained in the present work were all in good agreement with the theoretical calculations [11,12] and K-shell fluorescence yield results [13], we have to emphasize that modern electronic structure calculations should be performed in order to make reliable and quantitative comparisons between theory and experiment in Ni–Si binary alloy system.
Y. Kalayci et al. / Nucl. Instr. and Meth. in Phys. Res. B 255 (2007) 438–440
2. Experimental details and theoretical calculations The Ni–Si alloys are prepared as described in [13]. The pure Ni and the prepared alloys Ni3Si, Ni2Si and NiSi were in the form of powders and all of them are sieved for 400 mesh. Each sample is mixed with powder polyvinyl chloride, sealed in stainless steel annular capsule and pelletized similarly. The experimental set-up [13] consists of an annular 109 Cd radioisotope (providing of 22–25 keV primary beam energy) of 10 mCi activity, a planar Si(Li) detector of 80 mm2 sensitive area and 5 mm thickness. The measurements are performed with a resolution of 190 eV at 5.9 keV, coupled to PC based Accuspec supplied by Genie 2000 software system (Canberra). The Kb-to-Ka intensity ratios were determined from the peak areas of the X-ray spectra after applying necessary corrections to the measured data as described in [4,8]. In the literature, the d-occupation numbers of a transition metal in pure form and in the alloy have been evaluated by means of the MCDF calculations which relate the electron populations of free atoms in different electronic configurations to the theoretical intensity ratios; however since a pure metal or an alloy cannot be regarded as a collection of free atoms, the obtained results generally disagree [5,6,10] quantitatively with the electronic structure calculations. We, therefore, carried out self-consistent electronic structure calculations for Ni corresponding to various types of atomic configurations by means of the linear muffin-tin orbital (LMTO) method using the codes of Skriver [14]. All the calculations are performed within the four different exchange-correlation formalisms cited in the literature. The d-occupation numbers of Ni at the Fermi level are obtained as described in [15]. 3. Results and discussion The experimental Kb-to-Ka X-ray intensity ratios of nickel for pure Ni and Ni–Si alloys are presented in Table 1 including the statistical error bars. Since the absolute values of the experimental intensity ratios differ considerably even for pure Ni [2,4–8], the normalized values are also included in Table 1. The 3d-occupation numbers of Ni, corresponding to various types of electronic configurations, calculated by means of the LMTO method are presented in Table 2. In order to use this data with the theoretical MCDF intensity Table 1 Experimental and normalized (with respect to pure nickel) Kb-to-Ka X-ray intensity ratios of Ni in Ni–Si alloys Alloy
Kb-to-Ka intensity ratios
Normalized Kb-to-Ka intensity ratio
Ni Ni3Si Ni2Si NiSi
0.1378 ± 0.0010 0.1332 ± 0.0012 0.1317 ± 0.0005 0.1343 ± 0.0014
1.0 0.967 ± 0.001 0.956 ± 0.001 0.975 ± 0.001
439
Table 2 The theoretical LMTO 3d-occupation numbers and theoretical MCDF X-ray intensity ratios of Ni corresponding to various types of the electronic configurations Electronic configuration
3d Electron population
Normalized Kb-to-Ka intensity ratio
3d74s24p1 3d84s2 3d94s1
8.545 8.587 8.603
1.0263 1.0000 0.9795
ratios [5,6,10] to estimate the 3d electron population of Ni in any Ni based alloy, the arithmetical averages of the MCDF intensity ratios obtained within the Coulomb and Babushkin gauges [5] are used and presented, as normalized with respect to pure nickel, also in Table 2. The 3d electron population of Ni in Ni–Si alloys have been evaluated by solving the linear equation of the form y = ax + b, where x is the normalized experimental intensity ratio of Ni in the alloy (Table 1) and y is the corresponding (unknown) 3d-occupation number. The coefficients a and b are obtained by means of the linear fit of the data presented in Table 2. We should emphasize that the linear equation between d-occupation number and normalized intensity ratio is used just to obtain an approximately general expression between these quantities that can be used in any Ni based alloy system. The evaluated number of 3d electrons for Ni in Ni–Si alloys, as described above, are presented in Table 3. According to Table 3, the 3d electron population of Ni increases with the decrease of Ni concentration up to Ni2Si, in good agreement both with experimental [5,13] and theoretical results [11,12]. For the NiSi we have found, in contrast to [5], a decrease in the d-occupation number of Ni in good agreement with the electronic structure calculations [11,12]. It should be emphasized that our results agree quantitatively with [11] and qualitatively with [12], even if the uncorrected data is used for the X-ray intensity ratios (Table 3). We have also used the original 3d electron populations (first column of Table 2) and obtained the 3d electronic structure of Ni in Ni–Si alloys. These results (forth column of Table 3) showed only qualitative agreement with the electronic structure calculations [11,12]. Furthermore, the results obtained for the alloying effect on the Kb-to-Ka X-ray intensity ratios of Ni in Ni–Si binary alloy Table 3 The evaluated 3d-occupation numbers of Ni in Ni–Si alloys by use of the 3d electron populations from the LMTO method (second column of Table 2) Sample
Uncorrected
Pure Ni Ni3Si Ni2Si NiSi
8.581 8.622 8.636 8.612
8.581 8.630 8.649 8.619
8.20 10.08 10.95 9.50
[11]
[12]
8.7 8.6
9.1 9.9 9.8
The results obtained for the uncorrected normalized X-ray intensity ratio data are also presented. The forth column refers to the evaluation by use of the original 3d electron populations given in the first column of Table 2. Theoretical values [11,12] are presented for comparison.
440
Y. Kalayci et al. / Nucl. Instr. and Meth. in Phys. Res. B 255 (2007) 438–440
system are all in excellent agreement with the K-shell fluorescence yield results [13] including Ni5Si2 and Ni3Si2. However, since the theoretical results considerably controversial (Table 3), modern electronic structure calculations (full-potential, fully relativistic, etc.) have to be performed in order to make reliable quantitative comparisons between theory and experiment in Ni–Si alloys. In this context, it should be emphasized that investigation of alloying effect in terms of the X-ray intensity ratios should be carried out for the stoichiometric alloys for which the modern electronic structure calculations are available. References [1] Y. Tamaki, T. Omori, T. Shiokawa, Radiochem. Radioanal. Lett. 37 (1979) 39. [2] C.R. Bhuinya, H.C. Padhi, Phys. Rev. 47 (1993) 4885. [3] C. Chang, C. Chen, C. Yen, Y. Wu, C. Su, S.K. Chiou, J. Phys. B 27 (1994) 5251.
¨ . So¨g˘u¨t, E. Bu¨yu¨kkasap, A. Ku¨c¸u¨ko¨nder, M. Ertug˘rul, O ¨. S [4] O ß imsßek, Appl. Spectrosc. Rev. 30 (1995) 175. [5] S. Raj, B.B. Dhal, H.C. Padhi, M. Polasik, Phys. Rev. B 58 (1998) 9025. [6] S. Raj, H.C. Padhi, M. Polasik, Nucl. Instr. and Meth. B 155 (1999) 143. [7] S. Raj, H.C. Padhi, M. Polasik, F. Pawlowski, D.K. Basa, Solid State Commun. 116 (2000) 563. [8] O. Sogut, E. Bu¨yu¨kkasap, H. Erdog˘an, Radiat. Phys. Chem. 64 (2002) 343. [9] F. Pawlowski, M. Polasik, S. Raj, H.C. Padhi, D.K. Basa, Nucl. Instr. and Meth. B 195 (2002) 367. [10] M. Polasik, Phys. Rev. A 58 (1998) 1840. [11] O. Bisi, C. Calandra, J. Phys. C 14 (1981) 5479. [12] K.L. Peterson, J.S. Hsiao, D.R. Chopra, T.R. Dillingham, Phys. Rev. B 83 (1988) 9511. [13] Y. Kalayci, Y. Agus, S. Ozgur, N. Efe, A. Zararsiz, P. Arikan, R.H. Mutlu, Spectrochim. Acta B 60 (2005) 277. [14] H.L. Skriver, The LMTO Method, Springer, New York, 1984. [15] R.H. Mutlu, J. Phys. Condens. Matter 7 (1995) 1283.