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Mössbauer charge density in 129I−
Volume 70A, number 5,6
PHYSICS LETTERS
MOSSBAUER CHARGE DENSITY IN
2 April 1979
1291-
K.N. SHRIVASTAVA Schoolof Physics, University of Hyderabad, Hyderabad-500001, India Received 11 December 1978
The electronic charge density at 1291— is calculated from the Hartree—Fock wave functions in the lithium iodide lattice and from that it is found that the charge density varies approximately as the inverse seventh power of the interatomic distance.
In this work, the charge density at the site of the 1 nucleus in lithium iodide is calculated from the Hartree—Fock wave functions taking into account the overlap of core s-functions of the 1 with U+ in an octahedral arrangement of atoms. The normal core contribution is independent of the neighbouring atoms. However, we find that the overlap integrals depend on the interatomic distance leading to an isomer shift in the Mössbauer effect that varies approximately as R7. An interesting power law is thus predicted. Including the overlap effect [1] p(O)=
~
k~(O)I2
~(O)I2
(~ +
(1)
where el iP(O)I2 is the charge density at the site of the nucleus, q~sare the core electron functions and Snsk <~SI Xk> are the overlap integrals of Ø,~with Xk taking into account the k orbits on Li~which is just the is
in the present case (see tables 1 and 2). Making use of the Hartree—Fock wave functions of 1 and U~given by Clementi [21 we have calculated all the non-zero functions. For the octahedral arrangement of U+ atoms, the overlap contributions are given as a = 121 ‘O~12 I I >12 i ,“~s’~ 1 “is Xi~ These values are given in table 3 as a function of the Li~—Fdistance. After taking into account the spin degeneracy, we find that ~‘•
5
2~ I~ns(O)I2= lO5O27.68a~~, (3) to which the overlap contribution given in table 3 is to be added. From a logarithmic calculation it is found that d ~ ‘d 1 R Pi n —7.3 (4) .
Table 1 The overlap integrals between the core functions 4ns of!— and the Xis function of Li+. R
(4~j 5lXis)
(~25IXis)
(~35IXis)
(~‘4SIX15~
(ø5SIXis~
—0.00011925 —0.00004576 —0.000 017 10 —0.00000401 —0.00000152 —0.00000161 —0.000 001 33
0.00051624 0.000 192 19 0.00006707 0.00001293 0.00000698 0.00000911 0.000007 85
0.00410489 0.00171216 0.000 701 83 0.000 18893 0.00005397 0.00004587 0.00003668
0.10396457 0.07358962 0.051 377 37 0.029 391 73 0.011 30770 0.00441760 0.001 85456
(A) 1.8 2.0 2.2 2.5 3.0 3.5 4.0
0.0002099 0.000 01048 0.00000555 0.000 001 90 —0.00000056 —0.00000113 —0.00000099
483
Volume 70A, number 5,6
2 April 1979
PHYSICS LETTERS
Table 2 Core s-electron Hartree--Fock charge densities for F (Is).
4ns(O) I~~~(O) 2
ls
2s
3s
4s
Ss
215.47 46426.28
69.97 4896.15
31.19 972.69
—14.04 197.23
4.64 21.49
Table 3 Overlap contribution to the electronic probability density in atomic units as a function of interatomic distance. R(A)
a
1.8 2.0 2.2 2.5 3.0 3.5 4.0
0.0002 0.000 061 0.0000175 0.000 002 0.000 000 17 0.00000071 0.00000054
1
a2
a3
a4
a5
~jaj
0.0008 0.000 123 0.000 017 2 0.0000009 0.000 000 13 0.000 000 15 0.000 000 10
0.1967 0.0004 0.000 052 0.000 002 0.00000057 0.00000097 0.00000072
0.0399 0.0069 0.001 166 0.000 084 3 0.00000689 0.00000498 0.000 003 18
2.787 3 1.3965 0.6807 0.2229 0.03297360 0.00503250 0.00088695
3.0249 1.4040 0.681 95 0.2230 0.032 981 0.005 039 0.000 891
This power law 67Zn is very close to the one found in ref. [I] in oxide lattices. It is because forthis 61 Ni and of strong dependence on the lattice constant that the values calculated [3] for a fixed distance should be carefully exaniined. This new law, p ~ of the probability density on interatomic distance may be useful to predict the effect of thermal expansion on the Mössbauer charge density as well as the change in the charge density in going from one lattice to another. The effect of the crystal field H. can be incorporated by replacing the overlap integral (q~ 5Ix~~) by + (~jSlH~jxjk). Although we expect the con-
484
tribution of that the crystal field alone to be perhaps small, one should be cautious the overlap overestimates the dependence of the charge density on the interatornic distance.
References Ill K.N. Shrivastava, Phys. Rev. B13 (1976) 2782. [21 E. Clementi and C. Roetti, At. Data NucI. Data Tables 14 (1974) 177. [3] W.H. Flygare and D.W. 1-latemeister, J. Chem. Phys. 43 (1965) 789.
PHYSICS LETTERS
MOSSBAUER CHARGE DENSITY IN
2 April 1979
1291-
K.N. SHRIVASTAVA Schoolof Physics, University of Hyderabad, Hyderabad-500001, India Received 11 December 1978
The electronic charge density at 1291— is calculated from the Hartree—Fock wave functions in the lithium iodide lattice and from that it is found that the charge density varies approximately as the inverse seventh power of the interatomic distance.
In this work, the charge density at the site of the 1 nucleus in lithium iodide is calculated from the Hartree—Fock wave functions taking into account the overlap of core s-functions of the 1 with U+ in an octahedral arrangement of atoms. The normal core contribution is independent of the neighbouring atoms. However, we find that the overlap integrals depend on the interatomic distance leading to an isomer shift in the Mössbauer effect that varies approximately as R7. An interesting power law is thus predicted. Including the overlap effect [1] p(O)=
~
k~(O)I2
~(O)I2
(~ +
(1)
where el iP(O)I2 is the charge density at the site of the nucleus, q~sare the core electron functions and Snsk <~SI Xk> are the overlap integrals of Ø,~with Xk taking into account the k orbits on Li~which is just the is
in the present case (see tables 1 and 2). Making use of the Hartree—Fock wave functions of 1 and U~given by Clementi [21 we have calculated all the non-zero functions. For the octahedral arrangement of U+ atoms, the overlap contributions are given as a = 121 ‘O~12 I I >12 i ,“~s’~ 1 “is Xi~ These values are given in table 3 as a function of the Li~—Fdistance. After taking into account the spin degeneracy, we find that ~‘•
5
2~ I~ns(O)I2= lO5O27.68a~~, (3) to which the overlap contribution given in table 3 is to be added. From a logarithmic calculation it is found that d ~ ‘d 1 R Pi n —7.3 (4) .
Table 1 The overlap integrals between the core functions 4ns of!— and the Xis function of Li+. R
(4~j 5lXis)
(~25IXis)
(~35IXis)
(~‘4SIX15~
(ø5SIXis~
—0.00011925 —0.00004576 —0.000 017 10 —0.00000401 —0.00000152 —0.00000161 —0.000 001 33
0.00051624 0.000 192 19 0.00006707 0.00001293 0.00000698 0.00000911 0.000007 85
0.00410489 0.00171216 0.000 701 83 0.000 18893 0.00005397 0.00004587 0.00003668
0.10396457 0.07358962 0.051 377 37 0.029 391 73 0.011 30770 0.00441760 0.001 85456
(A) 1.8 2.0 2.2 2.5 3.0 3.5 4.0
0.0002099 0.000 01048 0.00000555 0.000 001 90 —0.00000056 —0.00000113 —0.00000099
483
Volume 70A, number 5,6
2 April 1979
PHYSICS LETTERS
Table 2 Core s-electron Hartree--Fock charge densities for F (Is).
4ns(O) I~~~(O) 2
ls
2s
3s
4s
Ss
215.47 46426.28
69.97 4896.15
31.19 972.69
—14.04 197.23
4.64 21.49
Table 3 Overlap contribution to the electronic probability density in atomic units as a function of interatomic distance. R(A)
a
1.8 2.0 2.2 2.5 3.0 3.5 4.0
0.0002 0.000 061 0.0000175 0.000 002 0.000 000 17 0.00000071 0.00000054
1
a2
a3
a4
a5
~jaj
0.0008 0.000 123 0.000 017 2 0.0000009 0.000 000 13 0.000 000 15 0.000 000 10
0.1967 0.0004 0.000 052 0.000 002 0.00000057 0.00000097 0.00000072
0.0399 0.0069 0.001 166 0.000 084 3 0.00000689 0.00000498 0.000 003 18
2.787 3 1.3965 0.6807 0.2229 0.03297360 0.00503250 0.00088695
3.0249 1.4040 0.681 95 0.2230 0.032 981 0.005 039 0.000 891
This power law 67Zn is very close to the one found in ref. [I] in oxide lattices. It is because forthis 61 Ni and of strong dependence on the lattice constant that the values calculated [3] for a fixed distance should be carefully exaniined. This new law, p ~ of the probability density on interatomic distance may be useful to predict the effect of thermal expansion on the Mössbauer charge density as well as the change in the charge density in going from one lattice to another. The effect of the crystal field H. can be incorporated by replacing the overlap integral (q~ 5Ix~~) by + (~jSlH~jxjk). Although we expect the con-
484
tribution of that the crystal field alone to be perhaps small, one should be cautious the overlap overestimates the dependence of the charge density on the interatornic distance.
References Ill K.N. Shrivastava, Phys. Rev. B13 (1976) 2782. [21 E. Clementi and C. Roetti, At. Data NucI. Data Tables 14 (1974) 177. [3] W.H. Flygare and D.W. 1-latemeister, J. Chem. Phys. 43 (1965) 789.