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LIII absorption discontinuity of lutetium
TECHNICAL NOTE L,,, ABSORPTIONDISCONTINUITY OF LUTETIUM N. R. LOKHANDE. P. R. SARODE and A. R. CHETAL Department of Physics. Nagpur University, Nagpurd40010, India (Received 28 he
1977: accepted
in revised
jonn
2 lkcember
W’YI)
I. IHTRtHRJCTlON
Recently Carter[l. 21 has proposed the bidirectional orbital ap preach (BOA) for deriving the density of states picture in systems having closed packed structures. The density of states picture consists of bonding and antibonding orbitals. However. the theory does not give quantitatively the energy separation between them. In the present paper we are reporting this energy separation for Lu metal from X-ray spectroscopic studies.
A Cauchois type bent crystal X-ray spectrograph of diameter 40 cm was used for photographing the spectra. The spectrograph was equipped with a well-tested mica crystal whose (201) reflccting planes were employed to record the spectra. A Mschktt X-ray tube with tungsten target was used as a source of white radiation. In course of this work the X-ray tube was operated at l4kV. the tube current was maintained at IOmA. The wavelength measurement of the absorption discontinuity was made at the inllection point on microphotometer records of magnification x 100. A large number of measurements of the discontinuity were made in order to obtain reliable results. The standard deviation in the measurements was found to be of the order of +0.5eV. The standard deviation in the energy of discontinuity being 0.5eV. the maximum possible error in the energy separation AE between the inflection point X and white line A is 0.5 x d(2) = 0.7 eV. A Jutetium ingot (purity 99.996) was obtained from KochLight Laboratories Ltd., Buckinghamshire, England. In order to study the X-ray absorption spectrum of the metal. a uniform absorbing screen of the metal was prepared by spreading the line powder on cellophane adhesive tape which was fixed on an aluminium frame. This frame was mounted on the shield on an X-ray tube in front of the X-ray window. Other experimental details are described elsewhere(3.41.
The shape of the Lnl absorption discontinuity of lutetium in pure metal is shown in Fii. I. The curve represents the transmitted intensity as a function of energy, and consequently the maxima and minima on this curve correspond to minima and maxima respectively in the values of the absorption coefficients. In Fig. I the point X denotes the inflection point and A thepeak position of the white line. The results of our measurements are given in Table I. The electronic structure of Lu metal is [Xe]4j”5d’6sz. where [Xe] refers to the full shell xenon core. This metal crystallises with a closed packed hexagonal A3 type structure[S]. Following Carter[l. 2] we obtain the density of states picture for Lu metal as consisting of four bands, namely F, C, L and S shown in Fig. 2. The first sharp F band is associated with highly localized 4j electrons. The medium broad covalent bonding band C is formed from the interaction of the 5d (d,. d,,, d,,) and 6p &, p,, p,) atomic orbitals. The narrow localized band L is of 5d (d,l_,q d,,) atomic orbitals with a little contribution from 6p orbitals. The broad free electron-like band S has a 6s and a littk Jd,l character. We see in Fii. 2 that only the C band is half-filled, as the number of electrons taking part in the covalent bond formation is 3 for Lu metal according to Pauling[6]. 807
L ”
-
I”
Energy ( ev )
Fig. 1. Lm absorption discontinuity of lutetium metal.
Tabk
I. Data on the Lm absorption discontinuity of LU
Lu metal
Wavekngth (X.U.)
f-Ill discontinuity 1337.49 1336.50 White line
Energy E (eV) 2 0.5 eV
Energy separation between inflection point and white line AE(eV) f 0.7 eV
9250.48 9257.33
6.85
Fig. 2. Density of statespicture of lutehun metal.
808
Technical Notes
Unfortunately the rekvant wave-functionsnecessaryfor calculations of the exact transition probabilities are not availabk. Therefore we have consideredonly the dipole sekction ruk to justify our assignmentof the transition. In lutetium metal the first unoccupiedlevel lies in the C band which has admixed p and d character. The inlkction point X on the Liii absorptiondiscontinuityof lutetium in the metal can be attributed to the transition of photoelectronsejected from the 2p,,, sub-shell kvel of the absorbii atom (lutetium) to the half-tilled C band. According to Cauchoisand Mott[7]. the white line, i.e. the pronounced absorption maximum associatedwith the discontinuitycorrespondsto the inner electron transition to the allowed and unoccupiedstates of high density of states. In the present case the next band after C is the L band. It has a high, narrow density of states which has Sd and a little 6p character.Therefore the white line on the high energy side of the discontinuity results from the favoured transition of the inner Zp,,, electrons to the narrow local&d band L. In the above transitions the dipole selection ruk Al = 2 I is obeyed. The energy separation, AE given in Table I between the inflection point X on the Lul absorptiondiscontinuityof lutetium metal and the peak positionof the white line A then correspondsto the distance between the covaknt bonding band C and the nonbonding localized band L., in Carter’s bonding picture for Lu metal.
Aclmowfedgentcnts-We are grateful to Professor C. Mande for his interest in the present study. Two of us (NRL and PRS) are indebted to the University Grants Commission,New Delhi and Council of Scientificand Industrial Research,New Delhi respectively for the award of researchfellowships.
I. Carter F. L.. Proc. 5th Ran Eortik Research Conf. p. 103. Iowa State University, Ames, Iowa II (1965). 2. Carter F. L.. Ekctron At&y of Stoles. (Edited by L. H. Bennett), p. uI5. NBS Special PublicationNo. 323 (1971). 3. Mande C. and Chetal A. R. Froc. Int. Conf. on X-my spectra and chemical bindkg. p. 1%. Karl Marx University, Leiixig (1%6). 4. Kondawar V. K. and Mande Chintamani,1. Phys. Chem. Solid &ate Phys. 9. 1351 (1976). 5. Pearson W. B.. A Hondbood of LoNice Spacing ad Sirwturn of Mets/s and Alloys, p. II. Pergatnon Press. Oxford (1958). 6. Pauling L.. The Nature of Chemical Bond, 3rd Edn. p. 403. Oxford and IBH. Calcutta (1960). 7. CauchoisY. and Mott N. F. Phil. Mag. 0.1260 (1949).
1977: accepted
in revised
jonn
2 lkcember
W’YI)
I. IHTRtHRJCTlON
Recently Carter[l. 21 has proposed the bidirectional orbital ap preach (BOA) for deriving the density of states picture in systems having closed packed structures. The density of states picture consists of bonding and antibonding orbitals. However. the theory does not give quantitatively the energy separation between them. In the present paper we are reporting this energy separation for Lu metal from X-ray spectroscopic studies.
A Cauchois type bent crystal X-ray spectrograph of diameter 40 cm was used for photographing the spectra. The spectrograph was equipped with a well-tested mica crystal whose (201) reflccting planes were employed to record the spectra. A Mschktt X-ray tube with tungsten target was used as a source of white radiation. In course of this work the X-ray tube was operated at l4kV. the tube current was maintained at IOmA. The wavelength measurement of the absorption discontinuity was made at the inllection point on microphotometer records of magnification x 100. A large number of measurements of the discontinuity were made in order to obtain reliable results. The standard deviation in the measurements was found to be of the order of +0.5eV. The standard deviation in the energy of discontinuity being 0.5eV. the maximum possible error in the energy separation AE between the inflection point X and white line A is 0.5 x d(2) = 0.7 eV. A Jutetium ingot (purity 99.996) was obtained from KochLight Laboratories Ltd., Buckinghamshire, England. In order to study the X-ray absorption spectrum of the metal. a uniform absorbing screen of the metal was prepared by spreading the line powder on cellophane adhesive tape which was fixed on an aluminium frame. This frame was mounted on the shield on an X-ray tube in front of the X-ray window. Other experimental details are described elsewhere(3.41.
The shape of the Lnl absorption discontinuity of lutetium in pure metal is shown in Fii. I. The curve represents the transmitted intensity as a function of energy, and consequently the maxima and minima on this curve correspond to minima and maxima respectively in the values of the absorption coefficients. In Fig. I the point X denotes the inflection point and A thepeak position of the white line. The results of our measurements are given in Table I. The electronic structure of Lu metal is [Xe]4j”5d’6sz. where [Xe] refers to the full shell xenon core. This metal crystallises with a closed packed hexagonal A3 type structure[S]. Following Carter[l. 2] we obtain the density of states picture for Lu metal as consisting of four bands, namely F, C, L and S shown in Fig. 2. The first sharp F band is associated with highly localized 4j electrons. The medium broad covalent bonding band C is formed from the interaction of the 5d (d,. d,,, d,,) and 6p &, p,, p,) atomic orbitals. The narrow localized band L is of 5d (d,l_,q d,,) atomic orbitals with a little contribution from 6p orbitals. The broad free electron-like band S has a 6s and a littk Jd,l character. We see in Fii. 2 that only the C band is half-filled, as the number of electrons taking part in the covalent bond formation is 3 for Lu metal according to Pauling[6]. 807
L ”
-
I”
Energy ( ev )
Fig. 1. Lm absorption discontinuity of lutetium metal.
Tabk
I. Data on the Lm absorption discontinuity of LU
Lu metal
Wavekngth (X.U.)
f-Ill discontinuity 1337.49 1336.50 White line
Energy E (eV) 2 0.5 eV
Energy separation between inflection point and white line AE(eV) f 0.7 eV
9250.48 9257.33
6.85
Fig. 2. Density of statespicture of lutehun metal.
808
Technical Notes
Unfortunately the rekvant wave-functionsnecessaryfor calculations of the exact transition probabilities are not availabk. Therefore we have consideredonly the dipole sekction ruk to justify our assignmentof the transition. In lutetium metal the first unoccupiedlevel lies in the C band which has admixed p and d character. The inlkction point X on the Liii absorptiondiscontinuityof lutetium in the metal can be attributed to the transition of photoelectronsejected from the 2p,,, sub-shell kvel of the absorbii atom (lutetium) to the half-tilled C band. According to Cauchoisand Mott[7]. the white line, i.e. the pronounced absorption maximum associatedwith the discontinuitycorrespondsto the inner electron transition to the allowed and unoccupiedstates of high density of states. In the present case the next band after C is the L band. It has a high, narrow density of states which has Sd and a little 6p character.Therefore the white line on the high energy side of the discontinuity results from the favoured transition of the inner Zp,,, electrons to the narrow local&d band L. In the above transitions the dipole selection ruk Al = 2 I is obeyed. The energy separation, AE given in Table I between the inflection point X on the Lul absorptiondiscontinuityof lutetium metal and the peak positionof the white line A then correspondsto the distance between the covaknt bonding band C and the nonbonding localized band L., in Carter’s bonding picture for Lu metal.
Aclmowfedgentcnts-We are grateful to Professor C. Mande for his interest in the present study. Two of us (NRL and PRS) are indebted to the University Grants Commission,New Delhi and Council of Scientificand Industrial Research,New Delhi respectively for the award of researchfellowships.
I. Carter F. L.. Proc. 5th Ran Eortik Research Conf. p. 103. Iowa State University, Ames, Iowa II (1965). 2. Carter F. L.. Ekctron At&y of Stoles. (Edited by L. H. Bennett), p. uI5. NBS Special PublicationNo. 323 (1971). 3. Mande C. and Chetal A. R. Froc. Int. Conf. on X-my spectra and chemical bindkg. p. 1%. Karl Marx University, Leiixig (1%6). 4. Kondawar V. K. and Mande Chintamani,1. Phys. Chem. Solid &ate Phys. 9. 1351 (1976). 5. Pearson W. B.. A Hondbood of LoNice Spacing ad Sirwturn of Mets/s and Alloys, p. II. Pergatnon Press. Oxford (1958). 6. Pauling L.. The Nature of Chemical Bond, 3rd Edn. p. 403. Oxford and IBH. Calcutta (1960). 7. CauchoisY. and Mott N. F. Phil. Mag. 0.1260 (1949).