- Email: [email protected]
Calculated valence electronic structure of 3d metals for use in the X-ray intensity ratio studies
ARTICLE IN PRESS Radiation Physics and Chemistry 79 (2010) 938–940
Contents lists available at ScienceDirect
Radiation Physics and Chemistry journal homepage: www.elsevier.com/locate/radphyschem
Technical Note
Calculated valence electronic structure of 3d metals for use in the X-ray intensity ratio studies H. Dagistanli a, Y. Kalayci b, R.H. Mutlu a,n a b
Ankara University, Faculty of Engineering, Department of Physics Engineering, 06100 Ankara, Turkey Saraykoy Nuclear Research and Training Center, 06983 Saray, Ankara, Turkey
a r t i c l e in f o
a b s t r a c t
Article history: Received 29 September 2009 Accepted 14 April 2010
3d occupation numbers of the transition elements corresponding to various types of atomic configurations are calculated by means of the linear muffin-tin orbital (LMTO) method. This data is used with the multiconfiguration Dirac–Fock (MCDF) X-ray intensity ratios to estimate the electron populations of the 3d metals in alloys. & 2010 Elsevier Ltd. All rights reserved.
Keywords: Alloying effect 3d electron population X-ray intensity ratio
1. Introduction Investigation of the alloying effect, especially for the 3d alloys, in terms of the Kb/Ka X-ray intensity ratios has been a challenge in X-ray fluorescence analysis (Bhuinya and Padhi, 1993; Raj et al., 1998, 1999a, 1999b, 2000). In general Kb/Ka X-ray intensity ratios provide a useful tool to study the valence electronic structure of 3d metals in various alloys (Pawlowski et al., 2002; Sogut et al., 2002; Porikli and Kurucu, 2008; Han and Demir, 2009). 3d metal atoms are characterized by the gradual filling of the atomic d-electron shell as the series is traversed. For a given 3d metal, the X-ray intensity ratio decreases with increasing 3d electron population as has been found by means of the multiconfiguration Dirac–Fock (MCDF) calculations (Polasik, 1998). MCDF calculations relate the electron populations of free atoms in different electronic configurations to the theoretical intensity ratios. However, since an alloy or even a pure metal cannot be regarded as a collection of free atoms, the obtained d-occupation numbers are generally unreasonable and disagree quantitatively with the electronic structure calculations (Raj et al., 1998; Sogut et al., 2002; Porikli and Kurucu, 2008; Han and Demir, 2009). The origin of Kb/Ka X-ray intensity ratio change for the alloys should be interpreted due to the change in the electronic structure (Raj et al., 1998, 2000; Pawlowski et al., 2002) and recently we have obtained (Kalayci et al., 2007) quantitative agreement with the electronic structure calculations in estimating the d-occupation numbers of Ni in Ni–Si alloys by performing electronic structure calculations for pure Ni in different atomic configurations and using these data with the normalized MCDF intensity ratios. In this work we have generalized this approach to
n
Corresponding author. Fax: + 90 312 212 73 43. E-mail address: [email protected] (R.H. Mutlu).
0969-806X/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.radphyschem.2010.04.006
all the 3d metals for use in estimating the 3d electron populations in various alloys. We have also compared the results of the present approach with the original MCDF calculations for some of the experimental work cited in the literature. 2. Results and discussion For this purpose we have carried out self-consistent electronic structure calculations by means of the linear muffin-tin orbital (LMTO) method (Skriver, 1984) for each of the 3d metals corresponding to various types of atomic configurations. The occupation numbers of 3d metals corresponding to different electronic configurations are calculated as described by Mutlu (1995) and are presented in Table 1. In order to use this data with the theoretical MCDF intensity ratios to estimate the 3d electron population of the 3d metal in any alloy, the MCDF intensity ratios (Polasik, 1998) as normalized with respect to the pure 3d metal are also presented in Table 1. The 3d electron population of a 3d metal in an alloy can be evaluated by solving the linear equation of the form y¼ax+ b, where x is the normalized experimental intensity ratio of a given 3d metal in the alloy and y is the corresponding (unknown) 3d occupation number. The coefficients a and b can be obtained by means of the linear fit of the data presented in Table 1. We should emphasize that use of the normalized intensity ratios is essential in estimating reasonable 3d electron populations, simply because the absolute values of the experimental X-ray intensity ratios differ considerably for the 3d metals (Raj et al., 2000; Pawlowski et al., 2002; Sogut et al., 2002; ¨ Cevik et al., 2007; Ertu˘gral et al., 2007; Gurol, 2008; Porikli and Kurucu, 2008; Han and Demir, 2009). We now turn on some of the experimental work cited in the literature. In Table 2 experimental Kb/Ka X-ray intensity ratios and the calculated 3d electron populations of Cr, Fe and Ni are
ARTICLE IN PRESS H. Dagistanli et al. / Radiation Physics and Chemistry 79 (2010) 938–940
presented. For each of the reference the intensity ratios are given in the first row. (For the MCDF calculations the first number is the theoretical intensity ratio obtained within the Babushkin gauge and the second one refers to the Coulomb gauge.) In Table 2, 3d electron populations are determined by comparing the experimental values of the intensity ratios with the results of MCDF calculations. For each of the reference, 3d occupation Table 1 The theoretical LMTO 3d occupation numbers and normalized MCDF intensity ratios within the Coulomb and Babushkin gauges of 3d metals corresponding to different electronic configurations. Metal
Configuration
LMTO
Coulomb
Babushkin
Sc
3d14s2 3d24s1
1.5561 1.5963
1.0000 0.9605
1.0000 0.9644
Ti
3d24s2 3d34s1
2.5753 2.6103
1.0000 0.9648
1.0000 0.9678
V
3d34s2 3d44s1
3.6050 3.6356
1.0000 0.9682
1.0000 0.9710
Cr
3d54s1 3d44s2
4.5817 4.5584
1.0000 1.0293
1.0000 1.0281
Mn
3d54s2 3d64s1
5.6392 5.6589
1.0000 0.9739
1.0000 0.9743
Fe
3d64s2 3d74s1
6.5680 6.5862
1.0000 0.9763
1.0000 0.9766
Co
3d74s2 3d84s1
7.5647 7.5841
1.0000 0.9779
1.0000 0.9781
Ni
3d84s2 3d94s1
8.5888 8.6050
1.0000 0.9794
1.0000 0.9796
939
numbers determined within the Babushkin gauge are presented in the second row and 3d occupation numbers determined within the Coulomb gauge are presented in the third row. As seen in Table 2, the experimental intensity ratios differ considerably which can be understood in terms of different measurement techniques, sample preparation, purity of the samples and the application of the corrections on the measured intensity ratios. Since the determination of the 3d electron populations depends on the comparison of the experimental data with the free atom computations (Polasik, 1998), this variation leads to significantly different 3d electron populations for the pure metals (Table 2) and 3d alloys. For instance, 3d electron population of Ni in Ni2Si was predicted, within the MCDF, as 10.95 (Kalayci et al., 2007) which is quite unreasonable since the total number of the valence electrons of Ni is 10.00. We should emphasize that calculated 3d electron population of Ni in Ni2Si by the present approach (Table 1) is 8.65 in agreement with the band structure calculations (Kalayci et al., 2007). In Table 3 the changes in the 3d electron population in V and Ni for the V–Ni alloys are presented (Raj et al., 1999b). In general 3d occupation number of a 3d element can be increased by alloying with an element with higher d occupation (Ahuja et al., 1994). Therefore, it is reasonable to expect that 3d electron population at the V site will increase with the V concentration in the V–Ni system. According to Table 3 this is not the case confirming the change in the occupation numbers is due to the change in the electronic structure of the alloy. It is generally accepted that the change of the number of 3d electrons is the only important contribution for the change of Kb/Ka intensity ratios (Raj et al., 1998, 1999a, 1999b, 2000; Pawlowski et al., 2002; Porikli and Kurucu, 2008; Han and Demir, 2009). Therefore, it is
Table 2 Experimental Kb/Ka X-ray intensity ratios and the calculated 3d electron populations of Cr, Fe and Ni. The LMTO refers to the calculated 3d electron populations presented in Table 1. Reference
Cr 3d54s1
Fe 3d64s2
Ni 3d84s2 0.1363 7 0.0005 8.41 8.87
Raj et al. (1999b)
0.1307 70.0007 8.05 7.47
Raj et al. (2000)
Pawlowski et al. (2002)
0.1314 70.0008 5.18 4.53
0.1307 70.0007 8.05 7.47
Sogut et al. (2002)
0.1341 70.0130 4.36 3.71
0.1287 7 0.0110 8.76 8.19
Cevik et al. (2007)
0.13207 0.0050 5.00 4.35
0.1350 70.0070 6.53 5.92
Ertu˘gral et al. (2007)
0.1342 70.0050 4.33 3.68
0.1324 7 0.0050 7.45 6.86
0.1346 7 0.0012 9.09 8.57
0.1466 7 0.0124 4.23 3.62
0.1330 7 0.0030 9.75 9.23 0.1450 7 0.0040 4.88 4.28
Porikli and Kurucu (2008)
Han and Demir (2009)
0.1273 70.0038 6.44 5.78
0.1320 70.0040 7.59 7.00
0.1333 7 0.0040 9.62 9.11
MCDF (Polasik, 1998)
0.1317, 0.1295 5.00 5.00
0.1366, 0.1349 6.00 6.00
0.1374, 0.1361 8.00 8.00
LMTO
4.58
6.57
8.59
ARTICLE IN PRESS 940
H. Dagistanli et al. / Radiation Physics and Chemistry 79 (2010) 938–940
Table 3 The changes in the number of 3d electrons in V and Ni (with respect to pure metals) for the V–Ni alloys within the Babushkin gauge (Raj et al., 1999b). The results of the present approach are also included. Sample
V0.1Ni0.9 V0.2Ni0.8 V0.35Ni0.65 V0.5Ni0.5 V0.75Ni0.25
MCDF
This work
V
Ni
V
Ni
+ 1.25 +0.55 +0.40 0.25 0.55
0.30 0.75 0.65 + 0.50 +2.05
+ 0.03 + 0.02 + 0.01 0.01 0.02
0.01 0.02 0.01 + 0.01 + 0.03
reasonable to expect the number of electrons transferred between V and Ni to be the same. In this context the transfer of 3d electrons from V to Ni or vice versa is unreasonable according to the original MCDF calculations, whereas the present approach gives a more quantitative relation of the electron transfer between V and Ni (Table 3). Finally, we should emphasize that valence electronic structure of a 3d metal can be altered not only by alloying it with another element, but also by applying an external pressure (Ahuja et al., 1994). In this context, it could be a challenge to investigate the effect of pressure on the 3d electron populations in pure metals, which is beyond the scope of the present work.
References ¨ Ahuja, R., Soderlind, P., Wills, J.M., Johansson, B., Eriksson, O., 1994. Electronic structure of platinum at ultrahigh pressure. High Pres. Res. 12, 161.
Bhuinya, C.R., Padhi, H.C., 1993. Alloying effect on the Kb-to-Ka intensity ratios in TixNi1 x and CrxNi1 x alloys studied by g-ray fluorescence and fast proton ionization. Phys. Rev. A 47, 4885. Cevik, U., Kaya, S., Ertugral, B., Baltas, H., Karabıdak, S.M., 2007. K-shell X-ray fluorescence cross-sections and intensity ratios for some pure metals at 59.5 and 123.6 keV. Nucl. Instrum. Methods B 262, 165. Ertu˘gral, B., Apaydın, G., C - evik, U., Ertu˘grul, M., Kobya, A.I., 2007. Kb/Ka X-ray intensity ratios for elements in the range 16 r Zr 92 excited by 5.9, 59.5 and 123.6 keV photons. Radiat. Phys. Chem. 76, 15. ¨ Gurol, A., 2008. Measurements of the K X-ray intensity ratios by using energydispersive X-ray fluorescence spectrometry. Appl. Radiat. Isot. 66, 372. Han, I., Demir, L., 2009. Valence-electron configuration of Fe, Cr, and Ni in binary and ternary alloys from Kb-to-Ka X-ray intensity ratios. Phys. Rev. A 80, 052503. Kalayci, Y., Aydinuraz, A., Tugluoglu, B., Mutlu, R.H., 2007. Valence electronic structure of Ni in Ni–Si alloys from relative K X-ray intensity studies. Nucl. Instrum. Methods B 255, 438. Mutlu, R.H., 1995. Structural phase transitions and specific-heat coefficients of alkaline earth metals. J. Phys.: Condens. Matter 7, 1283. Pawlowski, F., Polasik, M., Raj, S., Padhi, H.C., Basa, D.K., 2002. Valence electronic structure of Ti, Cr, Fe and Co in some alloys from Kb-to-Ka X-ray intensity ratio studies. Nucl. Instrum. Methods B 195, 367. Polasik, M., 1998. Influence of changes in the valence electronic configuration on the Kb-to-Ka X-ray intensity ratios of the 3d transition metals. Phys. Rev. A 58, 1840. Porikli, S., Kurucu, Y., 2008. Effects of the external magnetic field and chemical combination on Kb/Ka X-ray intensity ratios of some nickel and cobalt compounds. Appl. Radiat. Isot. 66, 1381. Raj, S., Dhal, B.B., Padhi, H.C., Polasik, M., 1998. Influence of solid-state effects on the Kb-to-Ka X-ray intensity ratios of Ni and Cu in various silicide compounds. Phys. Rev. B 58, 9025. Raj, S., Padhi, H.C., Basa, D.K., Polasik, M., Pawlowski, F., 1999a. Kb-to-Ka X-ray intensity ratio studies on the changes of valence electronic structures of Ti, V, Cr, and Co in their disilicide compounds. Nucl. Instrum. Methods B 152, 417. Raj, S., Padhi, H.C., Polasik, M., 1999b. Influence of alloying effect on Kb/Ka X-ray intensity ratios of V and Ni in VxNi1 x alloys. Nucl. Instrum. Methods B 155, 143. Raj, S., Padhi, H.C., Polasik, M., Pawlowski, F., Basa, D.K., 2000. Valence electronic structure of Fe and Ni in FexNi1 x alloys from relative K X-ray intensity studies. Solid State Commun. 116, 563. Skriver, H.L., 1984. The LMTO Method. Springer, New York. ¨ ukkasap, ¨ Sogut, O., Buy E., Erdo˘gan, H., 2002. Chemical-effect variation of Kb/Ka X-ray intensity ratios in 3d elements. Radiat. Phys. Chem. 64, 348.
Contents lists available at ScienceDirect
Radiation Physics and Chemistry journal homepage: www.elsevier.com/locate/radphyschem
Technical Note
Calculated valence electronic structure of 3d metals for use in the X-ray intensity ratio studies H. Dagistanli a, Y. Kalayci b, R.H. Mutlu a,n a b
Ankara University, Faculty of Engineering, Department of Physics Engineering, 06100 Ankara, Turkey Saraykoy Nuclear Research and Training Center, 06983 Saray, Ankara, Turkey
a r t i c l e in f o
a b s t r a c t
Article history: Received 29 September 2009 Accepted 14 April 2010
3d occupation numbers of the transition elements corresponding to various types of atomic configurations are calculated by means of the linear muffin-tin orbital (LMTO) method. This data is used with the multiconfiguration Dirac–Fock (MCDF) X-ray intensity ratios to estimate the electron populations of the 3d metals in alloys. & 2010 Elsevier Ltd. All rights reserved.
Keywords: Alloying effect 3d electron population X-ray intensity ratio
1. Introduction Investigation of the alloying effect, especially for the 3d alloys, in terms of the Kb/Ka X-ray intensity ratios has been a challenge in X-ray fluorescence analysis (Bhuinya and Padhi, 1993; Raj et al., 1998, 1999a, 1999b, 2000). In general Kb/Ka X-ray intensity ratios provide a useful tool to study the valence electronic structure of 3d metals in various alloys (Pawlowski et al., 2002; Sogut et al., 2002; Porikli and Kurucu, 2008; Han and Demir, 2009). 3d metal atoms are characterized by the gradual filling of the atomic d-electron shell as the series is traversed. For a given 3d metal, the X-ray intensity ratio decreases with increasing 3d electron population as has been found by means of the multiconfiguration Dirac–Fock (MCDF) calculations (Polasik, 1998). MCDF calculations relate the electron populations of free atoms in different electronic configurations to the theoretical intensity ratios. However, since an alloy or even a pure metal cannot be regarded as a collection of free atoms, the obtained d-occupation numbers are generally unreasonable and disagree quantitatively with the electronic structure calculations (Raj et al., 1998; Sogut et al., 2002; Porikli and Kurucu, 2008; Han and Demir, 2009). The origin of Kb/Ka X-ray intensity ratio change for the alloys should be interpreted due to the change in the electronic structure (Raj et al., 1998, 2000; Pawlowski et al., 2002) and recently we have obtained (Kalayci et al., 2007) quantitative agreement with the electronic structure calculations in estimating the d-occupation numbers of Ni in Ni–Si alloys by performing electronic structure calculations for pure Ni in different atomic configurations and using these data with the normalized MCDF intensity ratios. In this work we have generalized this approach to
n
Corresponding author. Fax: + 90 312 212 73 43. E-mail address: [email protected] (R.H. Mutlu).
0969-806X/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.radphyschem.2010.04.006
all the 3d metals for use in estimating the 3d electron populations in various alloys. We have also compared the results of the present approach with the original MCDF calculations for some of the experimental work cited in the literature. 2. Results and discussion For this purpose we have carried out self-consistent electronic structure calculations by means of the linear muffin-tin orbital (LMTO) method (Skriver, 1984) for each of the 3d metals corresponding to various types of atomic configurations. The occupation numbers of 3d metals corresponding to different electronic configurations are calculated as described by Mutlu (1995) and are presented in Table 1. In order to use this data with the theoretical MCDF intensity ratios to estimate the 3d electron population of the 3d metal in any alloy, the MCDF intensity ratios (Polasik, 1998) as normalized with respect to the pure 3d metal are also presented in Table 1. The 3d electron population of a 3d metal in an alloy can be evaluated by solving the linear equation of the form y¼ax+ b, where x is the normalized experimental intensity ratio of a given 3d metal in the alloy and y is the corresponding (unknown) 3d occupation number. The coefficients a and b can be obtained by means of the linear fit of the data presented in Table 1. We should emphasize that use of the normalized intensity ratios is essential in estimating reasonable 3d electron populations, simply because the absolute values of the experimental X-ray intensity ratios differ considerably for the 3d metals (Raj et al., 2000; Pawlowski et al., 2002; Sogut et al., 2002; ¨ Cevik et al., 2007; Ertu˘gral et al., 2007; Gurol, 2008; Porikli and Kurucu, 2008; Han and Demir, 2009). We now turn on some of the experimental work cited in the literature. In Table 2 experimental Kb/Ka X-ray intensity ratios and the calculated 3d electron populations of Cr, Fe and Ni are
ARTICLE IN PRESS H. Dagistanli et al. / Radiation Physics and Chemistry 79 (2010) 938–940
presented. For each of the reference the intensity ratios are given in the first row. (For the MCDF calculations the first number is the theoretical intensity ratio obtained within the Babushkin gauge and the second one refers to the Coulomb gauge.) In Table 2, 3d electron populations are determined by comparing the experimental values of the intensity ratios with the results of MCDF calculations. For each of the reference, 3d occupation Table 1 The theoretical LMTO 3d occupation numbers and normalized MCDF intensity ratios within the Coulomb and Babushkin gauges of 3d metals corresponding to different electronic configurations. Metal
Configuration
LMTO
Coulomb
Babushkin
Sc
3d14s2 3d24s1
1.5561 1.5963
1.0000 0.9605
1.0000 0.9644
Ti
3d24s2 3d34s1
2.5753 2.6103
1.0000 0.9648
1.0000 0.9678
V
3d34s2 3d44s1
3.6050 3.6356
1.0000 0.9682
1.0000 0.9710
Cr
3d54s1 3d44s2
4.5817 4.5584
1.0000 1.0293
1.0000 1.0281
Mn
3d54s2 3d64s1
5.6392 5.6589
1.0000 0.9739
1.0000 0.9743
Fe
3d64s2 3d74s1
6.5680 6.5862
1.0000 0.9763
1.0000 0.9766
Co
3d74s2 3d84s1
7.5647 7.5841
1.0000 0.9779
1.0000 0.9781
Ni
3d84s2 3d94s1
8.5888 8.6050
1.0000 0.9794
1.0000 0.9796
939
numbers determined within the Babushkin gauge are presented in the second row and 3d occupation numbers determined within the Coulomb gauge are presented in the third row. As seen in Table 2, the experimental intensity ratios differ considerably which can be understood in terms of different measurement techniques, sample preparation, purity of the samples and the application of the corrections on the measured intensity ratios. Since the determination of the 3d electron populations depends on the comparison of the experimental data with the free atom computations (Polasik, 1998), this variation leads to significantly different 3d electron populations for the pure metals (Table 2) and 3d alloys. For instance, 3d electron population of Ni in Ni2Si was predicted, within the MCDF, as 10.95 (Kalayci et al., 2007) which is quite unreasonable since the total number of the valence electrons of Ni is 10.00. We should emphasize that calculated 3d electron population of Ni in Ni2Si by the present approach (Table 1) is 8.65 in agreement with the band structure calculations (Kalayci et al., 2007). In Table 3 the changes in the 3d electron population in V and Ni for the V–Ni alloys are presented (Raj et al., 1999b). In general 3d occupation number of a 3d element can be increased by alloying with an element with higher d occupation (Ahuja et al., 1994). Therefore, it is reasonable to expect that 3d electron population at the V site will increase with the V concentration in the V–Ni system. According to Table 3 this is not the case confirming the change in the occupation numbers is due to the change in the electronic structure of the alloy. It is generally accepted that the change of the number of 3d electrons is the only important contribution for the change of Kb/Ka intensity ratios (Raj et al., 1998, 1999a, 1999b, 2000; Pawlowski et al., 2002; Porikli and Kurucu, 2008; Han and Demir, 2009). Therefore, it is
Table 2 Experimental Kb/Ka X-ray intensity ratios and the calculated 3d electron populations of Cr, Fe and Ni. The LMTO refers to the calculated 3d electron populations presented in Table 1. Reference
Cr 3d54s1
Fe 3d64s2
Ni 3d84s2 0.1363 7 0.0005 8.41 8.87
Raj et al. (1999b)
0.1307 70.0007 8.05 7.47
Raj et al. (2000)
Pawlowski et al. (2002)
0.1314 70.0008 5.18 4.53
0.1307 70.0007 8.05 7.47
Sogut et al. (2002)
0.1341 70.0130 4.36 3.71
0.1287 7 0.0110 8.76 8.19
Cevik et al. (2007)
0.13207 0.0050 5.00 4.35
0.1350 70.0070 6.53 5.92
Ertu˘gral et al. (2007)
0.1342 70.0050 4.33 3.68
0.1324 7 0.0050 7.45 6.86
0.1346 7 0.0012 9.09 8.57
0.1466 7 0.0124 4.23 3.62
0.1330 7 0.0030 9.75 9.23 0.1450 7 0.0040 4.88 4.28
Porikli and Kurucu (2008)
Han and Demir (2009)
0.1273 70.0038 6.44 5.78
0.1320 70.0040 7.59 7.00
0.1333 7 0.0040 9.62 9.11
MCDF (Polasik, 1998)
0.1317, 0.1295 5.00 5.00
0.1366, 0.1349 6.00 6.00
0.1374, 0.1361 8.00 8.00
LMTO
4.58
6.57
8.59
ARTICLE IN PRESS 940
H. Dagistanli et al. / Radiation Physics and Chemistry 79 (2010) 938–940
Table 3 The changes in the number of 3d electrons in V and Ni (with respect to pure metals) for the V–Ni alloys within the Babushkin gauge (Raj et al., 1999b). The results of the present approach are also included. Sample
V0.1Ni0.9 V0.2Ni0.8 V0.35Ni0.65 V0.5Ni0.5 V0.75Ni0.25
MCDF
This work
V
Ni
V
Ni
+ 1.25 +0.55 +0.40 0.25 0.55
0.30 0.75 0.65 + 0.50 +2.05
+ 0.03 + 0.02 + 0.01 0.01 0.02
0.01 0.02 0.01 + 0.01 + 0.03
reasonable to expect the number of electrons transferred between V and Ni to be the same. In this context the transfer of 3d electrons from V to Ni or vice versa is unreasonable according to the original MCDF calculations, whereas the present approach gives a more quantitative relation of the electron transfer between V and Ni (Table 3). Finally, we should emphasize that valence electronic structure of a 3d metal can be altered not only by alloying it with another element, but also by applying an external pressure (Ahuja et al., 1994). In this context, it could be a challenge to investigate the effect of pressure on the 3d electron populations in pure metals, which is beyond the scope of the present work.
References ¨ Ahuja, R., Soderlind, P., Wills, J.M., Johansson, B., Eriksson, O., 1994. Electronic structure of platinum at ultrahigh pressure. High Pres. Res. 12, 161.
Bhuinya, C.R., Padhi, H.C., 1993. Alloying effect on the Kb-to-Ka intensity ratios in TixNi1 x and CrxNi1 x alloys studied by g-ray fluorescence and fast proton ionization. Phys. Rev. A 47, 4885. Cevik, U., Kaya, S., Ertugral, B., Baltas, H., Karabıdak, S.M., 2007. K-shell X-ray fluorescence cross-sections and intensity ratios for some pure metals at 59.5 and 123.6 keV. Nucl. Instrum. Methods B 262, 165. Ertu˘gral, B., Apaydın, G., C - evik, U., Ertu˘grul, M., Kobya, A.I., 2007. Kb/Ka X-ray intensity ratios for elements in the range 16 r Zr 92 excited by 5.9, 59.5 and 123.6 keV photons. Radiat. Phys. Chem. 76, 15. ¨ Gurol, A., 2008. Measurements of the K X-ray intensity ratios by using energydispersive X-ray fluorescence spectrometry. Appl. Radiat. Isot. 66, 372. Han, I., Demir, L., 2009. Valence-electron configuration of Fe, Cr, and Ni in binary and ternary alloys from Kb-to-Ka X-ray intensity ratios. Phys. Rev. A 80, 052503. Kalayci, Y., Aydinuraz, A., Tugluoglu, B., Mutlu, R.H., 2007. Valence electronic structure of Ni in Ni–Si alloys from relative K X-ray intensity studies. Nucl. Instrum. Methods B 255, 438. Mutlu, R.H., 1995. Structural phase transitions and specific-heat coefficients of alkaline earth metals. J. Phys.: Condens. Matter 7, 1283. Pawlowski, F., Polasik, M., Raj, S., Padhi, H.C., Basa, D.K., 2002. Valence electronic structure of Ti, Cr, Fe and Co in some alloys from Kb-to-Ka X-ray intensity ratio studies. Nucl. Instrum. Methods B 195, 367. Polasik, M., 1998. Influence of changes in the valence electronic configuration on the Kb-to-Ka X-ray intensity ratios of the 3d transition metals. Phys. Rev. A 58, 1840. Porikli, S., Kurucu, Y., 2008. Effects of the external magnetic field and chemical combination on Kb/Ka X-ray intensity ratios of some nickel and cobalt compounds. Appl. Radiat. Isot. 66, 1381. Raj, S., Dhal, B.B., Padhi, H.C., Polasik, M., 1998. Influence of solid-state effects on the Kb-to-Ka X-ray intensity ratios of Ni and Cu in various silicide compounds. Phys. Rev. B 58, 9025. Raj, S., Padhi, H.C., Basa, D.K., Polasik, M., Pawlowski, F., 1999a. Kb-to-Ka X-ray intensity ratio studies on the changes of valence electronic structures of Ti, V, Cr, and Co in their disilicide compounds. Nucl. Instrum. Methods B 152, 417. Raj, S., Padhi, H.C., Polasik, M., 1999b. Influence of alloying effect on Kb/Ka X-ray intensity ratios of V and Ni in VxNi1 x alloys. Nucl. Instrum. Methods B 155, 143. Raj, S., Padhi, H.C., Polasik, M., Pawlowski, F., Basa, D.K., 2000. Valence electronic structure of Fe and Ni in FexNi1 x alloys from relative K X-ray intensity studies. Solid State Commun. 116, 563. Skriver, H.L., 1984. The LMTO Method. Springer, New York. ¨ ukkasap, ¨ Sogut, O., Buy E., Erdo˘gan, H., 2002. Chemical-effect variation of Kb/Ka X-ray intensity ratios in 3d elements. Radiat. Phys. Chem. 64, 348.