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Ion configuration in spinels
Solid State Communications, Vol. 6, pp. 745 -746, 1968. Pergamon Press. Printed in Great Britain
ION CONFIGURATION IN SPINELS* J. Smit Department of Materials Science, University of South California Los Angeles, California 90007, U.S.A. (Received 2 July 1968 by G.W. Rathenau) The polarization of the anions in spinels can stabilize particular ion configurations like Cr3~Ti~~S42. THE Madelung energy of ionic compounds with spinel structure has been calculated by Verwey et al.1 Because of the asymmetrical configuraT{~ofthe metal ions about each anion (three octahedral metal ions along the cube edges on one side and one tetrahedrally coordinated metal ion along the body diagonal on the other) the electrical field E at the center of the anion is not zero. It has been pointed out2 that the corresponding polarization energy a E2 may contribute appreciably to the cohesive energy. The magnitude of this field can be derived from the published curves1 of the Madelung constant M as a function of the oxygen parameter u as
It was already pointed out by Verwe? that this preference is caused by partial covalent sp8 bonding, which can be only effective when it is superimposed on an isotropic charge distribution. Thus if none of the divalent ions from the list is available, the Fe3~ ions will occupy tetrahedral sites and the ferrite is inverse. This rule can explain the ionic distribution of almost all spinels (compare Blasse’).
-~
E=
1 8/3 —
e a2 —
~ du
—
where a is the lattice parameter.
For the values
of the charge of the tetrahedral 2) ion in EqA= are1, 74, 2, 3 and of (e/a In the linear approx39, 49 the and coefficients -43 respectively. imation the energy of the normal structure for 2-3 spinels is lowered with respect 3) e~áper to that formula of the .unit. inverseThe onepolarizability by 2.9 x io~(a/a a of O~ is at least 1.6 A so an energy difference of 7. 7 e2 /a would result, which is about 13 eV. Since the Madelung energy for the normal and inverse structure is about the same, one would then ex~,
-
pect that all 2-3 spinels are normal. The following ions have, however, a preference for tetrahedral sites: 6: Mn2~, Fe3~ 10~ Cu1~ Zn~ Ga~ ~ Cd~ ~ H~ d d _______________
*Work supported by Joint Services Contract No. 23-4510-1713.
This partial covalency effect must therefore be quite appreciable since it has to overcome the anion polarization term, which we will assume is much smaller than the calculated 13 eV because of saturation. Therefore the covalency effect may be of the order of several eV. The anion polarization has been utilized by Blasse4 to explain the cation distribution in LiCrGeO 4 and Li0~5Al2.5S4in which the Li~ occupies A-sites. polarization is largeInbecause the latter of the caselarge the anion a of S2. In Li 0~5,A]~~5 04 lithium is on octahedral sites. The main purpose of this note is to point out that the above mechanism may provide a logical explanation for the structure of several recently found sulio and other spinels containing Cu. There exists considerable evidence6 that in the normal spinels CuCr 2X4 and similar cornpounds, where X = S, Se or Te, the Cu ion is monovalent. These compounds are ferromagnetic and have valent in aCuCr metallic conductivity. The Cu is dietc. is divalent. spinel 2O4,The and Zn, CuCrTiS Cd or Hg in ZnCr2X4 4 is nonmagnetic and insulating. When the Cr/Ti ratio is changed either way, it becomeq coi~uctin~ 5 in that the valences are Cu ~Cr Ti4~S indicating 4
745
746
ION CONFIGURATION IN SPINELS
We shall compare the energy of this configuration with that of Cu24Cr34Ti34S42’. In this cornpound we do not have complications of uncertain energy band terms, The difference between the fourth ionization potential of Ti and the second one of Cu is about 23 eV. The other energy differences are in favor of the Cu’~configuration. The Madelung energy is about 9 eV lower, and the (short range) orcter~ of the Cr84 and Ti44 ions will give another I eV. Taking for the covalency effect of Cu’ together with a similar effect for the Ti4 ion on octahedral sites, an optirnistic 5 eV, then there is still (23-9-1-5) = 8 eV to go before the Cu’4 configuration is stable. This then has to come from the anion polarization, 2 approximation about which thewoulda correspond E -80 eV.is in This to impossibly large polarizations, but it seems reasonable that it may account for the deficient 8 eV necessary to make the Cu’~configuration stable. It is apparently not strong enough in the oxide, (three times smaller ~)and does not stabilize the Zn’~ion either. ~,
+
-
Vol. 6, No.10
anion polarization shoulddetermined give a differenceThe between the u-parameters by means of X-rays and by neutrons, In which the positions of the electrons and of the nucleus are measured respectively. For an induced dipole moment .1 per anion ~u
=
ux
-
U~ =
_____
Zeaf3 with Z the atomic number of the anion. If we assume that the polarization gives an energy difference of about 10 eV, and equate this to 4 x ~ one finds for the selenides ~u 0. 0006 and for the sulfo-spinels t~ua~0. 0014. Both measurements have been performed for CuCr CuCr 6 who found 2Se4 that the and 2 Te4 by the Colominas two u’s were same within experimental error (±0. 0006 for the selenide). It seems possible that for the sulfo-spinel this difference might be detectable.
References 1.
VERWEY E.J.W.,
DEBOER F. and VAN SANTEN J.H.,
J. chem. Phys.
18, 1032 (1950).
2. 3.
SMIT J., LOTGERING F.K. and VAN STAPELE R.P., J. phys. Soc. Japan 17, B-I, 268 (1962). VERWEY E.J.W. and HEILMANN E. L., J. chem. Phys. 15, 174 (1947).
4.
BLASSE G.,
5.
LOTGERING F.K. and VAN STAPELE R.P., J. appl. Phys. 39, 47 (1968).
6.
COLOMINAS C., Phys. Rev.
—
Philips Res. Rep. Suppl. No. 3 (1964).
153, 558 (1967).
Die Polarization der Anionen in Spinell Gitter kann spezielle lonen Verteilungen stabilisieren, zurn Beispel Cu14Cr3~Ti44S 2 4 -.
ION CONFIGURATION IN SPINELS* J. Smit Department of Materials Science, University of South California Los Angeles, California 90007, U.S.A. (Received 2 July 1968 by G.W. Rathenau) The polarization of the anions in spinels can stabilize particular ion configurations like Cr3~Ti~~S42. THE Madelung energy of ionic compounds with spinel structure has been calculated by Verwey et al.1 Because of the asymmetrical configuraT{~ofthe metal ions about each anion (three octahedral metal ions along the cube edges on one side and one tetrahedrally coordinated metal ion along the body diagonal on the other) the electrical field E at the center of the anion is not zero. It has been pointed out2 that the corresponding polarization energy a E2 may contribute appreciably to the cohesive energy. The magnitude of this field can be derived from the published curves1 of the Madelung constant M as a function of the oxygen parameter u as
It was already pointed out by Verwe? that this preference is caused by partial covalent sp8 bonding, which can be only effective when it is superimposed on an isotropic charge distribution. Thus if none of the divalent ions from the list is available, the Fe3~ ions will occupy tetrahedral sites and the ferrite is inverse. This rule can explain the ionic distribution of almost all spinels (compare Blasse’).
-~
E=
1 8/3 —
e a2 —
~ du
—
where a is the lattice parameter.
For the values
of the charge of the tetrahedral 2) ion in EqA= are1, 74, 2, 3 and of (e/a In the linear approx39, 49 the and coefficients -43 respectively. imation the energy of the normal structure for 2-3 spinels is lowered with respect 3) e~áper to that formula of the .unit. inverseThe onepolarizability by 2.9 x io~(a/a a of O~ is at least 1.6 A so an energy difference of 7. 7 e2 /a would result, which is about 13 eV. Since the Madelung energy for the normal and inverse structure is about the same, one would then ex~,
-
pect that all 2-3 spinels are normal. The following ions have, however, a preference for tetrahedral sites: 6: Mn2~, Fe3~ 10~ Cu1~ Zn~ Ga~ ~ Cd~ ~ H~ d d _______________
*Work supported by Joint Services Contract No. 23-4510-1713.
This partial covalency effect must therefore be quite appreciable since it has to overcome the anion polarization term, which we will assume is much smaller than the calculated 13 eV because of saturation. Therefore the covalency effect may be of the order of several eV. The anion polarization has been utilized by Blasse4 to explain the cation distribution in LiCrGeO 4 and Li0~5Al2.5S4in which the Li~ occupies A-sites. polarization is largeInbecause the latter of the caselarge the anion a of S2. In Li 0~5,A]~~5 04 lithium is on octahedral sites. The main purpose of this note is to point out that the above mechanism may provide a logical explanation for the structure of several recently found sulio and other spinels containing Cu. There exists considerable evidence6 that in the normal spinels CuCr 2X4 and similar cornpounds, where X = S, Se or Te, the Cu ion is monovalent. These compounds are ferromagnetic and have valent in aCuCr metallic conductivity. The Cu is dietc. is divalent. spinel 2O4,The and Zn, CuCrTiS Cd or Hg in ZnCr2X4 4 is nonmagnetic and insulating. When the Cr/Ti ratio is changed either way, it becomeq coi~uctin~ 5 in that the valences are Cu ~Cr Ti4~S indicating 4
745
746
ION CONFIGURATION IN SPINELS
We shall compare the energy of this configuration with that of Cu24Cr34Ti34S42’. In this cornpound we do not have complications of uncertain energy band terms, The difference between the fourth ionization potential of Ti and the second one of Cu is about 23 eV. The other energy differences are in favor of the Cu’~configuration. The Madelung energy is about 9 eV lower, and the (short range) orcter~ of the Cr84 and Ti44 ions will give another I eV. Taking for the covalency effect of Cu’ together with a similar effect for the Ti4 ion on octahedral sites, an optirnistic 5 eV, then there is still (23-9-1-5) = 8 eV to go before the Cu’4 configuration is stable. This then has to come from the anion polarization, 2 approximation about which thewoulda correspond E -80 eV.is in This to impossibly large polarizations, but it seems reasonable that it may account for the deficient 8 eV necessary to make the Cu’~configuration stable. It is apparently not strong enough in the oxide, (three times smaller ~)and does not stabilize the Zn’~ion either. ~,
+
-
Vol. 6, No.10
anion polarization shoulddetermined give a differenceThe between the u-parameters by means of X-rays and by neutrons, In which the positions of the electrons and of the nucleus are measured respectively. For an induced dipole moment .1 per anion ~u
=
ux
-
U~ =
_____
Zeaf3 with Z the atomic number of the anion. If we assume that the polarization gives an energy difference of about 10 eV, and equate this to 4 x ~ one finds for the selenides ~u 0. 0006 and for the sulfo-spinels t~ua~0. 0014. Both measurements have been performed for CuCr CuCr 6 who found 2Se4 that the and 2 Te4 by the Colominas two u’s were same within experimental error (±0. 0006 for the selenide). It seems possible that for the sulfo-spinel this difference might be detectable.
References 1.
VERWEY E.J.W.,
DEBOER F. and VAN SANTEN J.H.,
J. chem. Phys.
18, 1032 (1950).
2. 3.
SMIT J., LOTGERING F.K. and VAN STAPELE R.P., J. phys. Soc. Japan 17, B-I, 268 (1962). VERWEY E.J.W. and HEILMANN E. L., J. chem. Phys. 15, 174 (1947).
4.
BLASSE G.,
5.
LOTGERING F.K. and VAN STAPELE R.P., J. appl. Phys. 39, 47 (1968).
6.
COLOMINAS C., Phys. Rev.
—
Philips Res. Rep. Suppl. No. 3 (1964).
153, 558 (1967).
Die Polarization der Anionen in Spinell Gitter kann spezielle lonen Verteilungen stabilisieren, zurn Beispel Cu14Cr3~Ti44S 2 4 -.