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Chemical effect on the K X-ray intensity ratios for 4d transition metals
Volume 118, number 1
PHYSICS LETTERS A
22 September 1986
C H E M I C A L E F F E C T O N T H E K X-RAY I N T E N S I T Y R A T I O S F O R 4d T R A N S I T I O N M E T A L S
T. M U K O Y A M A Institute for Chemical Research, l£voto University, Kyoto 606, Japan
H. KAJI and K. Y O S H I H A R A Department of Chemistry, Faculty of Science, Tohoku UniversiO,. Sendai 980, Japan Received 6 January 1986; accepted for publication 31 July 1986
The chemical effect on the K [32/K ~ X-ray intensity ratios for some compounds of Tc and Mo has been estimated using the simple model of Brunner et al. The calculated values are qualitatively in agreement with the experimental results, except for the metallic case.
The K~/Ke~ X-ray intensity ratio has been extensively studied experimentally [1], because this quantity is easy to measure with sufficient accuracy. It is generally assumed that the chemical effect on this ratio is negligibly small and the experimental data have been compared with the theoretical calculations for single free atoms [2,3]. However, there has been reported some experimental evidence that chemical environments do affect on the K[3/K~x ratios for chemical compounds of 3d transition metals [4-8]. According to these results, there are up to 10% differences in the K[3/Kc~ ratios for different chemical compounds. Brunner et al. [8] proposed that the change in the K[3/K~x ratio is caused by the change in screening of the 3p electrons due to delocalization of the 3d electrons and estimated the difference between two chemical compounds in the simple model. Recently Band et al. [9] carried out the scattered-wave-Xe~ molecular orbital calculations for some chromium and manganese compounds and evaluated the relative change in the KI3/K~x intensity ratios. On the other hand, no theoretical studies on the chemical effect on the K X-ray intensity ratios have been reported for 4d transition metals. In these elements, the valence electrons are the 4d, 5s and 5p electrons and the influence of the chemical state on the 3d electrons can be neglected. Since 44
the intensity of Kt32 (4p--* ls) X-rays is about 15% of that of the K[31,3 (3p---, ls) X-rays, the dependence of the K[3/Kcx ratio on the chemical environment is small. However, the chemical effect on the K[~2/K~x is appreciable. This fact can be supported from recent experimental evidence on the energy shift and change in relative intensity of the 4p-electron peaks of the conversion and photoelectron spectra for Tc compounds [10,11]. In the present work, we estimate the chemical effect on the K[~z/Ke~ ratio for Tc and Mo compounds by using the simplified model of Brunner et al. [8] and compare with the experimental results of Yamoto et al. [12]. Following Brunner et al. [8], we assume that the chemical effect on K[~z/Ke~ ratios for 4d transition elements can be ascribed to the change in the screening of 4p electrons caused by the change in the effective occupation number of 4d electrons. Then the relative K[32/Ka emission rate is given by [8] (K~2/Kot)A
(K~2/K~,).
-
1 + Va
~ + G'
(1)
where (KJ32/K~x)~ is the Kf32/K~x intensity ratio for the chemical compound i and V, is the relative deviation defined as [8] Vii = S z G f f , i K d .
(2)
0375-9601/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume 118, number 1
PHYSICS LETTERS A
Here S z is the sensitivity of the 4p contraction on a 4d charge delocalization, Ccff.i is the valencecharge difference and K d is the 4d share of C~ff. The values of Sz of Tc and Mo are calculated relativistically by using the D i r a c - F o c k - S l a t e r model [13]. The relative increase of the K[32/Ka ratio when one 4d electron is removed is shown in table 1. For the Mo atom, the removal of the 4d3/2 electron gives almost the same increase as the case of the 4d5/2 electron, while in the Tc atom the effect of removal of the 4d3/2 electron is larger than that of the 4d 5/1 electron. The valence-charge difference is evaluated from the Pauling electronegativity concept: Ceff ~-
Vf(1--exp[--(XA--XB)2//4]),
(3)
where Vf is the formal oxidation number and x A and x B are the Pauling electronegativities [14] of the atom A and B, respectively. For the value of K a we adopted the value used by Brunner et al. [8] for the 3d transition elements, 0.52. The calculated results for Tc compounds are listed in table 2 as the form relative to KTcO 4 and compared with experimental values [12]. In the case of 97mTc, the relative K[32/Ka ratios of K2TcC16 and Tc2S v are in good agreement with the measured values. For 99mTc compounds, the calculated values are larger than the measured ones. However, even in this case the present calculations can explain the experimental results qualitatively, i.e. the value for K2TcC16 is smaller than that for KTcO4, but larger than that for Tc2S 7. On the other hand, the calculated KI32/K~x ratios for metallic Tc are the smallest of all the compounds studied, while the experimental values are larger than the values for TczS 7. This discrepancy arises from the fact that for metals the formal oxidation number and the difference in the
Table 1 Relative increase of the KI32/Ka ratio per one removed 4d electron. Shell
Tc
Mo
4d3/2 4d5/2 average
0.02411 0.02364 0.0239
0.02435 0.02424 0.0243
22 September 1986
Table 2 Comparison of the calculated KI82/Kc~ ratios for Tc with the experimental values. Compound
Experimental ~) 99mTc
Theoretical
97mWc
Tcmetal/KTcO 4 0.945_+0.017 0.977_+0.007 0.9605 K2TcC16/KTcO4 0.943_+0.017 0.977_+0.008 0.9730 TC2ST/KTcO 4 0.940__+0.022 0.960_+0.010 0.9677 ~) Ref. [12].
electronegativities are zero. According to the present model, the KI32/Ke~ ratio for metals is the same as that for free atoms. The experimental data indicate that the present model is inadequate for metals. Table 3 presents the chemical effect on the relative KI32/Ke~ ratios for Mo K X-rays. In this case the X-rays are emitted as a result of K capture of the Tc atom and the chemical compounds are indicated by those of the parent atom. Comparison of the calculated values with the measured ones shows the general trend similar to the case of Tc X-rays. However, the agreement between theory and experiment is poorer compared to the case of Tc X-rays. It should be noted that the Mo K X-rays are emitted following K-electron capture decay of radioactive Tc atoms. The electronic configuration of these Mo atoms is different from that produced by other excitation mode, such as internal conversion and photoionization. After electron-capture decay the Mo atom is, in general, neutral, while it is a positive ion after internal conversion. In addition, the electron shakeoff probability is different for electron-capture decay and for internal
Table 3 Comparison of the calculated KI32/Ka ratios for Mo with the experimental values. Compound
Experimental ~ 95mTC c)
Theoretical
95mTc b)
Tcmetal/KTcO 4 0.967_+0.018 0.979_+0.002 0.9599 K2TcCI6/KTcO4 0.971_+0.020 0.960_+0.002 0.9725 Tc2ST/KTcO4 0.933_+0.020 0.954_+0.008 0.9672 a) Ref. [12]. b) 93Nb(a" 2n) 95Tc. c) Mo(d, xn) 95mTc.
45
Volume 118, number 1
PHYSICS L E T r E R S A
conversion, because in the former case the change in nuclear charge partially compensates the change in the central potential due to formation of a K-shell vacancy. This effect also leads to different electronic configurations. The effect of the excitation modes on the K[3/Kcx ratios has already been studied by Arndt et al. for 3d transition elements
[151. The present calculations can qualitatively explain the chemical effect on the KI32/Kcx ratios for 4d transition elements, but the model is found to be invalid for metals. Further studies on this effect employing molecular orbital calculations are in progress. In the case of Mo X-rays, more rigorous treatments of electronic configurations after electron-capture decay are needed.
References [1] S.I. Salem, S.L. Panossian and R.A. Kreuse, At. Data Nucl. Data Tables 14 (1974) 92. [2] J.H. Scofield, Phys. Rev. 179 (1969) 9; At. Data Nucl. Data Tables 14 (1974) 121. [3] J.H. Scofield, Phys. Rev. A 9 (1974) 1041.
46
22 September 1986
[4] Y. Tamaki, T. Omori and T. Shiokawa, Radiochem. Radioanal. Lett. 20 (1975) 255; 27 (1979) 39; Japan J. Appl, Phys. 17 (1978) $245. [5] E. Lazzarini, A.L. Lazzarini-Fantola and M. MandelliBettoni, Radiochim. Acta 25 (1978) 8l. [6] B. Paci-Mazzilli and D.S. Urch, in: Inner shell and X-ray physics of atoms and solids, eds. D.J. Fabian, H. Kleinpoppen and L.M. Watson (Plenum, New York, 1981) p. 741. [7] K.E. Collins, C.H. Collins and C. Heitz, Radiochim. Acta 28 (1981) 7. [8] G. Brunner, M. Nagel, E. Hartmann and E. Arndt, J. Phys. B 15 (1982) 4517. [9] I.M. Band, A.P. Kovtun, M.A. Listengarten and M.B. Trzhaskovskaya, J. Elec. Spec. Rel. Phenom. 36 (1985) 59. [10] V.N. Gerasimov, A.G. Zelenkov, V.M. Kulakov, V.A. Pchelin, M.V. Sokolovskaya, A.A. Soldatov and L.V. Chistyakov, Soviet Phys. JETP 55 (1982) 205; 59 (1984) 683. [11] O. Dragoun, M. Figer, V. Brabec, A. Kovalik, A. Kuklik and P. Mikuglk, Phys. Lett. A 99 (1983) 187. [12] I. Yamoto, J. Kaji and K. Yoshihara, J. Chem. Phys., to be published. [13] T. Mukoyama and H. Adachi, J. Phys. Soc. Japan 53 (1984) 984. [14] L. Pauling, The nature of chemical bond (Cornell Univ. Press, Ithaka, 1960). [15] E. Arndt, G. Brunner and E. Hartmann, J. Phys. B 15 (1982) L887.
PHYSICS LETTERS A
22 September 1986
C H E M I C A L E F F E C T O N T H E K X-RAY I N T E N S I T Y R A T I O S F O R 4d T R A N S I T I O N M E T A L S
T. M U K O Y A M A Institute for Chemical Research, l£voto University, Kyoto 606, Japan
H. KAJI and K. Y O S H I H A R A Department of Chemistry, Faculty of Science, Tohoku UniversiO,. Sendai 980, Japan Received 6 January 1986; accepted for publication 31 July 1986
The chemical effect on the K [32/K ~ X-ray intensity ratios for some compounds of Tc and Mo has been estimated using the simple model of Brunner et al. The calculated values are qualitatively in agreement with the experimental results, except for the metallic case.
The K~/Ke~ X-ray intensity ratio has been extensively studied experimentally [1], because this quantity is easy to measure with sufficient accuracy. It is generally assumed that the chemical effect on this ratio is negligibly small and the experimental data have been compared with the theoretical calculations for single free atoms [2,3]. However, there has been reported some experimental evidence that chemical environments do affect on the K[3/K~x ratios for chemical compounds of 3d transition metals [4-8]. According to these results, there are up to 10% differences in the K[3/Kc~ ratios for different chemical compounds. Brunner et al. [8] proposed that the change in the K[3/K~x ratio is caused by the change in screening of the 3p electrons due to delocalization of the 3d electrons and estimated the difference between two chemical compounds in the simple model. Recently Band et al. [9] carried out the scattered-wave-Xe~ molecular orbital calculations for some chromium and manganese compounds and evaluated the relative change in the KI3/K~x intensity ratios. On the other hand, no theoretical studies on the chemical effect on the K X-ray intensity ratios have been reported for 4d transition metals. In these elements, the valence electrons are the 4d, 5s and 5p electrons and the influence of the chemical state on the 3d electrons can be neglected. Since 44
the intensity of Kt32 (4p--* ls) X-rays is about 15% of that of the K[31,3 (3p---, ls) X-rays, the dependence of the K[3/Kcx ratio on the chemical environment is small. However, the chemical effect on the K[~2/K~x is appreciable. This fact can be supported from recent experimental evidence on the energy shift and change in relative intensity of the 4p-electron peaks of the conversion and photoelectron spectra for Tc compounds [10,11]. In the present work, we estimate the chemical effect on the K[~z/Ke~ ratio for Tc and Mo compounds by using the simplified model of Brunner et al. [8] and compare with the experimental results of Yamoto et al. [12]. Following Brunner et al. [8], we assume that the chemical effect on K[~z/Ke~ ratios for 4d transition elements can be ascribed to the change in the screening of 4p electrons caused by the change in the effective occupation number of 4d electrons. Then the relative K[32/Ka emission rate is given by [8] (K~2/Kot)A
(K~2/K~,).
-
1 + Va
~ + G'
(1)
where (KJ32/K~x)~ is the Kf32/K~x intensity ratio for the chemical compound i and V, is the relative deviation defined as [8] Vii = S z G f f , i K d .
(2)
0375-9601/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume 118, number 1
PHYSICS LETTERS A
Here S z is the sensitivity of the 4p contraction on a 4d charge delocalization, Ccff.i is the valencecharge difference and K d is the 4d share of C~ff. The values of Sz of Tc and Mo are calculated relativistically by using the D i r a c - F o c k - S l a t e r model [13]. The relative increase of the K[32/Ka ratio when one 4d electron is removed is shown in table 1. For the Mo atom, the removal of the 4d3/2 electron gives almost the same increase as the case of the 4d5/2 electron, while in the Tc atom the effect of removal of the 4d3/2 electron is larger than that of the 4d 5/1 electron. The valence-charge difference is evaluated from the Pauling electronegativity concept: Ceff ~-
Vf(1--exp[--(XA--XB)2//4]),
(3)
where Vf is the formal oxidation number and x A and x B are the Pauling electronegativities [14] of the atom A and B, respectively. For the value of K a we adopted the value used by Brunner et al. [8] for the 3d transition elements, 0.52. The calculated results for Tc compounds are listed in table 2 as the form relative to KTcO 4 and compared with experimental values [12]. In the case of 97mTc, the relative K[32/Ka ratios of K2TcC16 and Tc2S v are in good agreement with the measured values. For 99mTc compounds, the calculated values are larger than the measured ones. However, even in this case the present calculations can explain the experimental results qualitatively, i.e. the value for K2TcC16 is smaller than that for KTcO4, but larger than that for Tc2S 7. On the other hand, the calculated KI32/K~x ratios for metallic Tc are the smallest of all the compounds studied, while the experimental values are larger than the values for TczS 7. This discrepancy arises from the fact that for metals the formal oxidation number and the difference in the
Table 1 Relative increase of the KI32/Ka ratio per one removed 4d electron. Shell
Tc
Mo
4d3/2 4d5/2 average
0.02411 0.02364 0.0239
0.02435 0.02424 0.0243
22 September 1986
Table 2 Comparison of the calculated KI82/Kc~ ratios for Tc with the experimental values. Compound
Experimental ~) 99mTc
Theoretical
97mWc
Tcmetal/KTcO 4 0.945_+0.017 0.977_+0.007 0.9605 K2TcC16/KTcO4 0.943_+0.017 0.977_+0.008 0.9730 TC2ST/KTcO 4 0.940__+0.022 0.960_+0.010 0.9677 ~) Ref. [12].
electronegativities are zero. According to the present model, the KI32/Ke~ ratio for metals is the same as that for free atoms. The experimental data indicate that the present model is inadequate for metals. Table 3 presents the chemical effect on the relative KI32/Ke~ ratios for Mo K X-rays. In this case the X-rays are emitted as a result of K capture of the Tc atom and the chemical compounds are indicated by those of the parent atom. Comparison of the calculated values with the measured ones shows the general trend similar to the case of Tc X-rays. However, the agreement between theory and experiment is poorer compared to the case of Tc X-rays. It should be noted that the Mo K X-rays are emitted following K-electron capture decay of radioactive Tc atoms. The electronic configuration of these Mo atoms is different from that produced by other excitation mode, such as internal conversion and photoionization. After electron-capture decay the Mo atom is, in general, neutral, while it is a positive ion after internal conversion. In addition, the electron shakeoff probability is different for electron-capture decay and for internal
Table 3 Comparison of the calculated KI32/Ka ratios for Mo with the experimental values. Compound
Experimental ~ 95mTC c)
Theoretical
95mTc b)
Tcmetal/KTcO 4 0.967_+0.018 0.979_+0.002 0.9599 K2TcCI6/KTcO4 0.971_+0.020 0.960_+0.002 0.9725 Tc2ST/KTcO4 0.933_+0.020 0.954_+0.008 0.9672 a) Ref. [12]. b) 93Nb(a" 2n) 95Tc. c) Mo(d, xn) 95mTc.
45
Volume 118, number 1
PHYSICS L E T r E R S A
conversion, because in the former case the change in nuclear charge partially compensates the change in the central potential due to formation of a K-shell vacancy. This effect also leads to different electronic configurations. The effect of the excitation modes on the K[3/Kcx ratios has already been studied by Arndt et al. for 3d transition elements
[151. The present calculations can qualitatively explain the chemical effect on the KI32/Kcx ratios for 4d transition elements, but the model is found to be invalid for metals. Further studies on this effect employing molecular orbital calculations are in progress. In the case of Mo X-rays, more rigorous treatments of electronic configurations after electron-capture decay are needed.
References [1] S.I. Salem, S.L. Panossian and R.A. Kreuse, At. Data Nucl. Data Tables 14 (1974) 92. [2] J.H. Scofield, Phys. Rev. 179 (1969) 9; At. Data Nucl. Data Tables 14 (1974) 121. [3] J.H. Scofield, Phys. Rev. A 9 (1974) 1041.
46
22 September 1986
[4] Y. Tamaki, T. Omori and T. Shiokawa, Radiochem. Radioanal. Lett. 20 (1975) 255; 27 (1979) 39; Japan J. Appl, Phys. 17 (1978) $245. [5] E. Lazzarini, A.L. Lazzarini-Fantola and M. MandelliBettoni, Radiochim. Acta 25 (1978) 8l. [6] B. Paci-Mazzilli and D.S. Urch, in: Inner shell and X-ray physics of atoms and solids, eds. D.J. Fabian, H. Kleinpoppen and L.M. Watson (Plenum, New York, 1981) p. 741. [7] K.E. Collins, C.H. Collins and C. Heitz, Radiochim. Acta 28 (1981) 7. [8] G. Brunner, M. Nagel, E. Hartmann and E. Arndt, J. Phys. B 15 (1982) 4517. [9] I.M. Band, A.P. Kovtun, M.A. Listengarten and M.B. Trzhaskovskaya, J. Elec. Spec. Rel. Phenom. 36 (1985) 59. [10] V.N. Gerasimov, A.G. Zelenkov, V.M. Kulakov, V.A. Pchelin, M.V. Sokolovskaya, A.A. Soldatov and L.V. Chistyakov, Soviet Phys. JETP 55 (1982) 205; 59 (1984) 683. [11] O. Dragoun, M. Figer, V. Brabec, A. Kovalik, A. Kuklik and P. Mikuglk, Phys. Lett. A 99 (1983) 187. [12] I. Yamoto, J. Kaji and K. Yoshihara, J. Chem. Phys., to be published. [13] T. Mukoyama and H. Adachi, J. Phys. Soc. Japan 53 (1984) 984. [14] L. Pauling, The nature of chemical bond (Cornell Univ. Press, Ithaka, 1960). [15] E. Arndt, G. Brunner and E. Hartmann, J. Phys. B 15 (1982) L887.