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ESR investigation of Fe3+ diffusion in rutile
J. Phys. Chem. Solids Vol.
57. No.
I, pp. 137-138.
1996
CopyrightQ 1995 Eketier SciettceLtd PrintedittGreat Britain. All ricks reserved 0022-3697/96
Si5.00
+ 0.00
Technical Note ESR INVESTIGATION
OF Fe3+ DIFFUSION
R. S. DE BIASIt
IN RUTILE
and M. L. N. GRILL01
tSe$Ho de Engenharia MecHnica e de Materiais, Instituto Militar de Engenharia, 22290-270 Rio de Janeiro, RJ, Brazil
SInstituto de Fisica, Universidade do Estado do Rio de Janeiro, 20550-013 Rio de Janeiro, RJ, Brazil (Received 12 April 1995; accepted 28 April 1995)
Abstract-The electron spin resonance (ESR) technique was used to investigate the diffusion of Fe3+ in rutile (TiOr). ESR absorption intensity was measured for several annealing times and three different temperatures of isothermal annealing: 1273,1323 and 1373K. The activation energy for diffusion, calculated from the experimental data using a theoretical model based on the Fick equation, was found to be EA = 215 kJmol_‘. This result is consistent with experimental data using the radioactive-tracer sectioning technique and represents an independent measurement of the activation energy for diffusion of trivalent iron in r-utile, which is difficult to achieve by other means in this mixed-valence system. A. ceramics, D. diffusion.
Keywords:
1. INTRODUCTION
intensity of an ESR spectrum may be expressed as:
Rutile (Ti02) is a ceramic material with many industrial applications, the properties of which can be changed significantly by the presence of transition elements such as iron, chromium and manganese [l-3]. Electron spin resonance (ESR) spectroscopy is a convenient method for studying these transitionmetal impurities within the Ti02 structure. In this paper we investigate the diffusion of Fe3+ in rutile. Analysis of the ESR spectrum in a single crystal of iron-doped rutile [4,5] shows that trivalent iron atoms substitutionally replace titanium ions in the lattice. The spectrum can be fitted to the spin Hamiltonian: X’ =gj3H.S + @S_? - (1/3)S(S + l)] + E(Sx’ - S;) + (a/6)@ - (1/5)S(s+
+ S,” + S: 1)(3S2 +3S-
l)]
+ (F/180)[35&? - 3OS(S + 1,s; + 25s; - 6S(S + 1) + 3S2(S + 1)2]
(1)
with g = 2.00, D/h = 10.12 GHz, E/h = 2.19GHz, a/h = 1.08 GHz and F/h = 0.51 GHz [S]. The spectrum of Fe-doped t-utile powder has been investigated [3, 61; the peaks in the powder spectrum corresponding to the Fe3+ ion are easily identified as the turning points of the Hamiltonian given by eqn (1). The theory of ionic diffusion in powders as applied to ESR measurements was developed by Davidson and Che [7]. Using the Fick equation, they showed that the PCS W:‘-.I
1 = 1, - kr-if2
(2)
where I, is the saturation intensity and k = CD-‘/~, where c is a constant and D is the diffusion constant. The thermal behaviour of the D factor can be described by an Arrhenius law: for each annealing temperature T, the value of k is obtained by fittingeqn (2) to the data points. A plot of In k versus 1/T leads to the activation energy EA.
2. RESULTS AND DISCUSSION
The samples used in this study were prepared from pure oxides by grinding them together and then annealing the mixture in air. The starting composition corresponded to a 0.2% Fe/Ti atomic ratio. Magnetic resonance measurements were performed at room temperature and at 9.5 GHz. The spectrum of a typical sample is shown in Fig. 1, where the lines are labelled according to the convention used in Ref. [5]. In principle, intensity data can be extracted from any of the lines in the powder spectrum; the most convenient for this purpose, however, is the l/2 -+ -1/2(x) line observed at magnetic fields near 0.2T. The dependence of the intensity of the l/2 + -1/2(x) line on annealing time is shown in Fig. 2 for three different annealing temperatures; the best fits to eqn (2) are also shown. A plot of Ink versus l/T (Fig. 3) yields an activation energy EA = 2 15 kJ mol-’ . 137
138
R. S. DE BIAS1 and M. L. N. GRILL0
I
1
I
00
0.2
a1
I
I
I
0.3
0.4
0.5
MAGNETIC
Fig. 1. ESR spectrum
FIELD
by Sasaki et al. [6], using
From the results obtained
(EAll + 2EA1)/3
sectioning
activation
technique,
one can
energy for 5gFe in rutile
= 132 kJmol_‘,
much
smaller
than
the present results. It should be kept in mind, however, that the radioactive sensitive; Fe/TiOz
in
tracer
technique
mixed-valence
solid solution,
is not valence-
systems
such
as
the
where part of the iron ions
are present as Fe3+ and part as Fe’+, this technique expected constants Evidence through
to yield a value for the divalent suggests
[6] that
is
between the diffusion and trivalent states. trivalent
ions
the rutile lattice by an interstitial
diffuse
mechanism
and avoid the open channels parallel to the c-axis,
while divalent ions diffuse rapidly along the channels. The difference between the activation energies for the two mechanisms may be estimated by considering divalent impurities such as Co. In this case, the
ao1
*
3.0’
of a rutile sample doped with 0.2% Fe.
the radioactive-tracer derive an average
(T)
7.2
.
I
a
7.4
’
0.0
7.0
7.6 104iT(K-‘)
Fig. 3. Arrhenius plot for the diffusion of Fe3+ in rutile. The solid line is a least-squares fit to the data points. activation the
energy parallel
diffusion
activation
energy
along
to the c-axis, E,.,ll, reflects the
perpendicular
channels,
while
the
to the c-axis, EAT,
is related to the interstitial mechanism. According to Sasaki et al. [6], ,!?A11 (Co) = 133 kJmol_’ and EAI (Co) = 213 kJ mol-' This last value is only slightly smaller than the activation energy measured for Fe3+ in the present work. Thus, if we assume that the concentration of divalent iron ions is significant in Sasaki’s samples, the present results are consistent with the results reported in Ref. [6]. They represent, in fact, an independent measurement of the activation energy for the diffusion of trivalent iron in rutile, something difficult to achieve by other means in this mixed-valence system. The results reported in the present work suggest that ESR can be a useful technique for investigating the diffusion process in mixed-valence systems.
REFERENCES
2
4
6
a
10
Annealing time (h)
Fig. 2. Intensity of the ESR spectrum as a function of annealing time, for annealing times of 1273 K (m), 1323 K (0) and 1373 K (A). The solid lines are fits to eqn (2).
1. Grant F. A., Rev. Mod. Phys. 31,646 (1959). 2. Frederikse H. P. R., J. Appl. Phys. 32,221l (1961). 3. Amorelli A., Evans J. C., Rowlands C. C. and Eagerton T. A., J. Chem. Sot. Faraday Trans. 183,354l (1987). 4. Carter D. L. and Okaya A., Phys. Rev. 118,1485 (1960). 5. Kim S. S., Jun S. S. and Park M. J., J. Korean Phys. Sot. 23,73 (1990). 6. Eggleston H. S. and Thorp J. S., J. Mater. Sci. Lert. 16, 537 (1981). 7. Davidson A. and Che M., J. Phys. Chem. 96,9909 (1992). 8. Sasaki J., Peterson N. L. and Hoshino K., J. Phys. Chem. Solids46, 1267 (1985).
57. No.
I, pp. 137-138.
1996
CopyrightQ 1995 Eketier SciettceLtd PrintedittGreat Britain. All ricks reserved 0022-3697/96
Si5.00
+ 0.00
Technical Note ESR INVESTIGATION
OF Fe3+ DIFFUSION
R. S. DE BIASIt
IN RUTILE
and M. L. N. GRILL01
tSe$Ho de Engenharia MecHnica e de Materiais, Instituto Militar de Engenharia, 22290-270 Rio de Janeiro, RJ, Brazil
SInstituto de Fisica, Universidade do Estado do Rio de Janeiro, 20550-013 Rio de Janeiro, RJ, Brazil (Received 12 April 1995; accepted 28 April 1995)
Abstract-The electron spin resonance (ESR) technique was used to investigate the diffusion of Fe3+ in rutile (TiOr). ESR absorption intensity was measured for several annealing times and three different temperatures of isothermal annealing: 1273,1323 and 1373K. The activation energy for diffusion, calculated from the experimental data using a theoretical model based on the Fick equation, was found to be EA = 215 kJmol_‘. This result is consistent with experimental data using the radioactive-tracer sectioning technique and represents an independent measurement of the activation energy for diffusion of trivalent iron in r-utile, which is difficult to achieve by other means in this mixed-valence system. A. ceramics, D. diffusion.
Keywords:
1. INTRODUCTION
intensity of an ESR spectrum may be expressed as:
Rutile (Ti02) is a ceramic material with many industrial applications, the properties of which can be changed significantly by the presence of transition elements such as iron, chromium and manganese [l-3]. Electron spin resonance (ESR) spectroscopy is a convenient method for studying these transitionmetal impurities within the Ti02 structure. In this paper we investigate the diffusion of Fe3+ in rutile. Analysis of the ESR spectrum in a single crystal of iron-doped rutile [4,5] shows that trivalent iron atoms substitutionally replace titanium ions in the lattice. The spectrum can be fitted to the spin Hamiltonian: X’ =gj3H.S + @S_? - (1/3)S(S + l)] + E(Sx’ - S;) + (a/6)@ - (1/5)S(s+
+ S,” + S: 1)(3S2 +3S-
l)]
+ (F/180)[35&? - 3OS(S + 1,s; + 25s; - 6S(S + 1) + 3S2(S + 1)2]
(1)
with g = 2.00, D/h = 10.12 GHz, E/h = 2.19GHz, a/h = 1.08 GHz and F/h = 0.51 GHz [S]. The spectrum of Fe-doped t-utile powder has been investigated [3, 61; the peaks in the powder spectrum corresponding to the Fe3+ ion are easily identified as the turning points of the Hamiltonian given by eqn (1). The theory of ionic diffusion in powders as applied to ESR measurements was developed by Davidson and Che [7]. Using the Fick equation, they showed that the PCS W:‘-.I
1 = 1, - kr-if2
(2)
where I, is the saturation intensity and k = CD-‘/~, where c is a constant and D is the diffusion constant. The thermal behaviour of the D factor can be described by an Arrhenius law: for each annealing temperature T, the value of k is obtained by fittingeqn (2) to the data points. A plot of In k versus 1/T leads to the activation energy EA.
2. RESULTS AND DISCUSSION
The samples used in this study were prepared from pure oxides by grinding them together and then annealing the mixture in air. The starting composition corresponded to a 0.2% Fe/Ti atomic ratio. Magnetic resonance measurements were performed at room temperature and at 9.5 GHz. The spectrum of a typical sample is shown in Fig. 1, where the lines are labelled according to the convention used in Ref. [5]. In principle, intensity data can be extracted from any of the lines in the powder spectrum; the most convenient for this purpose, however, is the l/2 -+ -1/2(x) line observed at magnetic fields near 0.2T. The dependence of the intensity of the l/2 + -1/2(x) line on annealing time is shown in Fig. 2 for three different annealing temperatures; the best fits to eqn (2) are also shown. A plot of Ink versus l/T (Fig. 3) yields an activation energy EA = 2 15 kJ mol-’ . 137
138
R. S. DE BIAS1 and M. L. N. GRILL0
I
1
I
00
0.2
a1
I
I
I
0.3
0.4
0.5
MAGNETIC
Fig. 1. ESR spectrum
FIELD
by Sasaki et al. [6], using
From the results obtained
(EAll + 2EA1)/3
sectioning
activation
technique,
one can
energy for 5gFe in rutile
= 132 kJmol_‘,
much
smaller
than
the present results. It should be kept in mind, however, that the radioactive sensitive; Fe/TiOz
in
tracer
technique
mixed-valence
solid solution,
is not valence-
systems
such
as
the
where part of the iron ions
are present as Fe3+ and part as Fe’+, this technique expected constants Evidence through
to yield a value for the divalent suggests
[6] that
is
between the diffusion and trivalent states. trivalent
ions
the rutile lattice by an interstitial
diffuse
mechanism
and avoid the open channels parallel to the c-axis,
while divalent ions diffuse rapidly along the channels. The difference between the activation energies for the two mechanisms may be estimated by considering divalent impurities such as Co. In this case, the
ao1
*
3.0’
of a rutile sample doped with 0.2% Fe.
the radioactive-tracer derive an average
(T)
7.2
.
I
a
7.4
’
0.0
7.0
7.6 104iT(K-‘)
Fig. 3. Arrhenius plot for the diffusion of Fe3+ in rutile. The solid line is a least-squares fit to the data points. activation the
energy parallel
diffusion
activation
energy
along
to the c-axis, E,.,ll, reflects the
perpendicular
channels,
while
the
to the c-axis, EAT,
is related to the interstitial mechanism. According to Sasaki et al. [6], ,!?A11 (Co) = 133 kJmol_’ and EAI (Co) = 213 kJ mol-' This last value is only slightly smaller than the activation energy measured for Fe3+ in the present work. Thus, if we assume that the concentration of divalent iron ions is significant in Sasaki’s samples, the present results are consistent with the results reported in Ref. [6]. They represent, in fact, an independent measurement of the activation energy for the diffusion of trivalent iron in rutile, something difficult to achieve by other means in this mixed-valence system. The results reported in the present work suggest that ESR can be a useful technique for investigating the diffusion process in mixed-valence systems.
REFERENCES
2
4
6
a
10
Annealing time (h)
Fig. 2. Intensity of the ESR spectrum as a function of annealing time, for annealing times of 1273 K (m), 1323 K (0) and 1373 K (A). The solid lines are fits to eqn (2).
1. Grant F. A., Rev. Mod. Phys. 31,646 (1959). 2. Frederikse H. P. R., J. Appl. Phys. 32,221l (1961). 3. Amorelli A., Evans J. C., Rowlands C. C. and Eagerton T. A., J. Chem. Sot. Faraday Trans. 183,354l (1987). 4. Carter D. L. and Okaya A., Phys. Rev. 118,1485 (1960). 5. Kim S. S., Jun S. S. and Park M. J., J. Korean Phys. Sot. 23,73 (1990). 6. Eggleston H. S. and Thorp J. S., J. Mater. Sci. Lert. 16, 537 (1981). 7. Davidson A. and Che M., J. Phys. Chem. 96,9909 (1992). 8. Sasaki J., Peterson N. L. and Hoshino K., J. Phys. Chem. Solids46, 1267 (1985).