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Comparison of covalency parameters for Fe3+ in oxides and fluorides
T E C H N I C A L NOTES 0,81
t
0.7
i
r
T
[]
i T = IO00*C Euu : 1,0 k.cal,/mote
0.6 O
0.5
8~ i"iJ
0.4 First neighbors only Including second neighbors with t1=01 [] Including second ond third neighbors with t I = O.l ~nd
IZE~ 0.3 0.2
t2 = 0 . 0 5 .
0.1
Number of Terms in Expansion
Fig. I. Contributions to the partial enthalpy of solute atoms due to successive cumulants. The temperature is 1000~ and E,, = 1.0 k.cal/mole. 1.4
[]
i
f
i Y = IO00*C
l 0
~ IO
•UU = 2 . 0 k.cal,/mole if]
8=
1147
expected from a high temperature expansion. This is in accord with recent findings that departures from strictly regular behavior in many dilute solid solutions arises from a composition-dependent partial enthalpy whereas the configurational entropy is virtually ideal [5]. A c k n o w l e d g e m e n t - T h e authors are grateful for the support provided by the Robert A. Welch Foundation. K. A L E X R. B. M c L E L L A N Department o f Mechanical and Aerospace Engineering and Materials Science William Marsh Rice University Houston, Texas 77001, U.S.A. REFERENCES 1. A L E X K. and M c L E L L A N R. B., A c t a Met. 19, 439 (1971). 2. ALEX K. and M c L E L L A N R. B., Acta Met. 20, 11 (1972). 3. A L E X K. and M c L E L L A N R. B., Acta Met. to be published. 4. A L E X K. and M c L E L L A N R. B., Scripta Met. 4, 967 (1970). 5. M c L E L L A N R. B., Mater. Sci. Engng 9, 121 (1972).
II
i I~
05 irst neighbors only | Including second neighbors with tl = O.I E]lncluding second ond third neighbors with h=O.I and tz,: 0 . 0 5
Number of Terms in Expansion
=
Fig. 2. Contributions to the partial enthalpy o f solute atoms due to successive cumulants. The temperature is 1000~ and E.. is 2.0 k.cal/mole.
calculate fifth or higher cumulants (a difficult procedure). It can be concluded that provided the appropriate ranges of temperature and composition, (a and 0,), are chosen the cumulant expansion technique yields results which converge rapidly. For any reasonable behavior of the mutual pairwise interaction strengths, q, it suffices to consider up to third nearest neighbor interactions. Finally, it should be pointed out that the partial configurational entropy obtained by these techniques converges toward the ideal value very quickly as would, of course, be
J. Phys. Chem. Solids, 1973, V o l . 34, pp. 1 1 4 7 - 1 1 4 8 .
Comparison of covalency parameters for in oxides and fluorides*
F e 3+
(Received 11 May 1972)
COVALENCY parameters of transition ions have been determined from several experimental methods, among them EPR and neutron diffraction. In particular, Tofield and Fender[I] measured by neutron diffraction the sum of parameters f ~ + 2f=+f~ for Fe 3+ in LaFeO3 and YFeO3. In order to obtain each of these parameters, they compared this sum with the difference f ~ - - f , obtained by Hall et al. [2] by EPR measurements in KMgFa. For this purpose, they assumed similar covalency *Work performed in the frame of a research supported by the Swiss National Foundation for Scientific Research.
1148
T E C H N I C A L NOTES
parameters for oxides and fluorides. This assumption might be questionable, electronegativity being different for oxygen and fluorine. This is why we undertook a theoretical calculation of these parameters in the Wolfsberg-Helmholz[3] approximation with charge consistency. The chosen parameters of our calculation were:
From these values we deduced the combinations of parameters to be compared with experiments:
LaFeOa YFe03 KMgF3
f~ + 2f,, +fs
fo+2f~+fs f~ -f,~
Theory
Experiment
10.3 11"5 3-3
10• 11----.1 3-3 -+ 0.6
(1) (I) (2)
k~ = 2.10, k~ = 1.70, k~ = 1.50 and k = 1.0 for the Hamiltonian matrix elements between ligand orbitals. As for the electronegativities, we took the values: 9eV for Fe(3d), 13 eV for O (2,o), 28 eV for O (2s), 14.6 eV for F (2p) and 36 eV for F(2s). Furthermore, we chose 1.95 ,~ for the F e - - F distance instead of the lattice value 2.0 ,~, taking into account the ionic radius difference between Fe 3+ and Mg 2+. We obtained the following covalency parameters as percentages:
LaFeO3 YFeO~ KMgF3
fr
f~
f~
6,59 7,11 3,95
1.49 1-72 0.67
0.77 0-94 0.36
Although the method we used was somewhat crude, it shows without doubt that the covalency parameters are very different for oxides and fluorides. This is what we wished to point out. Department of Physical Chemistry, University of Geneva, Switzerland
J. WEBER
R. L A C R O I X
REFERENCES
1. T O F I E L D B. C. and F E N D E R B. E. F., J. Phys. Chem. Solids 31, 2741 (1970). 2. H A L L T. P. P., HAYES W., S T E V E N S O N R. W. H. and W l L K E N S J.,J, chem. Phys. 38, 1977 (1963). 3. W O L F S B E R G M. and H E L M H O L Z L., J. chem, Phys. 20, 837 (1952).
t
0.7
i
r
T
[]
i T = IO00*C Euu : 1,0 k.cal,/mote
0.6 O
0.5
8~ i"iJ
0.4 First neighbors only Including second neighbors with t1=01 [] Including second ond third neighbors with t I = O.l ~nd
IZE~ 0.3 0.2
t2 = 0 . 0 5 .
0.1
Number of Terms in Expansion
Fig. I. Contributions to the partial enthalpy of solute atoms due to successive cumulants. The temperature is 1000~ and E,, = 1.0 k.cal/mole. 1.4
[]
i
f
i Y = IO00*C
l 0
~ IO
•UU = 2 . 0 k.cal,/mole if]
8=
1147
expected from a high temperature expansion. This is in accord with recent findings that departures from strictly regular behavior in many dilute solid solutions arises from a composition-dependent partial enthalpy whereas the configurational entropy is virtually ideal [5]. A c k n o w l e d g e m e n t - T h e authors are grateful for the support provided by the Robert A. Welch Foundation. K. A L E X R. B. M c L E L L A N Department o f Mechanical and Aerospace Engineering and Materials Science William Marsh Rice University Houston, Texas 77001, U.S.A. REFERENCES 1. A L E X K. and M c L E L L A N R. B., A c t a Met. 19, 439 (1971). 2. ALEX K. and M c L E L L A N R. B., Acta Met. 20, 11 (1972). 3. A L E X K. and M c L E L L A N R. B., Acta Met. to be published. 4. A L E X K. and M c L E L L A N R. B., Scripta Met. 4, 967 (1970). 5. M c L E L L A N R. B., Mater. Sci. Engng 9, 121 (1972).
II
i I~
05 irst neighbors only | Including second neighbors with tl = O.I E]lncluding second ond third neighbors with h=O.I and tz,: 0 . 0 5
Number of Terms in Expansion
=
Fig. 2. Contributions to the partial enthalpy o f solute atoms due to successive cumulants. The temperature is 1000~ and E.. is 2.0 k.cal/mole.
calculate fifth or higher cumulants (a difficult procedure). It can be concluded that provided the appropriate ranges of temperature and composition, (a and 0,), are chosen the cumulant expansion technique yields results which converge rapidly. For any reasonable behavior of the mutual pairwise interaction strengths, q, it suffices to consider up to third nearest neighbor interactions. Finally, it should be pointed out that the partial configurational entropy obtained by these techniques converges toward the ideal value very quickly as would, of course, be
J. Phys. Chem. Solids, 1973, V o l . 34, pp. 1 1 4 7 - 1 1 4 8 .
Comparison of covalency parameters for in oxides and fluorides*
F e 3+
(Received 11 May 1972)
COVALENCY parameters of transition ions have been determined from several experimental methods, among them EPR and neutron diffraction. In particular, Tofield and Fender[I] measured by neutron diffraction the sum of parameters f ~ + 2f=+f~ for Fe 3+ in LaFeO3 and YFeO3. In order to obtain each of these parameters, they compared this sum with the difference f ~ - - f , obtained by Hall et al. [2] by EPR measurements in KMgFa. For this purpose, they assumed similar covalency *Work performed in the frame of a research supported by the Swiss National Foundation for Scientific Research.
1148
T E C H N I C A L NOTES
parameters for oxides and fluorides. This assumption might be questionable, electronegativity being different for oxygen and fluorine. This is why we undertook a theoretical calculation of these parameters in the Wolfsberg-Helmholz[3] approximation with charge consistency. The chosen parameters of our calculation were:
From these values we deduced the combinations of parameters to be compared with experiments:
LaFeOa YFe03 KMgF3
f~ + 2f,, +fs
fo+2f~+fs f~ -f,~
Theory
Experiment
10.3 11"5 3-3
10• 11----.1 3-3 -+ 0.6
(1) (I) (2)
k~ = 2.10, k~ = 1.70, k~ = 1.50 and k = 1.0 for the Hamiltonian matrix elements between ligand orbitals. As for the electronegativities, we took the values: 9eV for Fe(3d), 13 eV for O (2,o), 28 eV for O (2s), 14.6 eV for F (2p) and 36 eV for F(2s). Furthermore, we chose 1.95 ,~ for the F e - - F distance instead of the lattice value 2.0 ,~, taking into account the ionic radius difference between Fe 3+ and Mg 2+. We obtained the following covalency parameters as percentages:
LaFeO3 YFeO~ KMgF3
fr
f~
f~
6,59 7,11 3,95
1.49 1-72 0.67
0.77 0-94 0.36
Although the method we used was somewhat crude, it shows without doubt that the covalency parameters are very different for oxides and fluorides. This is what we wished to point out. Department of Physical Chemistry, University of Geneva, Switzerland
J. WEBER
R. L A C R O I X
REFERENCES
1. T O F I E L D B. C. and F E N D E R B. E. F., J. Phys. Chem. Solids 31, 2741 (1970). 2. H A L L T. P. P., HAYES W., S T E V E N S O N R. W. H. and W l L K E N S J.,J, chem. Phys. 38, 1977 (1963). 3. W O L F S B E R G M. and H E L M H O L Z L., J. chem, Phys. 20, 837 (1952).