- Email: [email protected]
Shape anisotropy of ultrafine magnesium ferrite precipitates
Journal of Magnetism and Magnetic Materials 35 (1983) 121-122 North-Holland Publishing Company
121
SHAPE ANISOTROPY OF ULTRAFINE MAGNESIUM
FERRITE PRECIPITATES
R.S. de B I A S I a n d T.C. D E V E Z A S Sefao de Engenharia e Ci~ncia dos Materiais, Instituto Militar de Engenharia, Rio de Janeiro, Brasil
The temperature dependence of the resonance anisotropy field for a coherent assembly of ultrafine magnesium ferrite precipitates was investigated in the range 100-400 K. The results are interpreted in terms of the shape anisotropy of the precipitates.
1. I n t r o d u c t i o n
Magnesium ferrite (MgFe204) exsolves very rapidly at 973 K in Fe3+-doped MgO [1,2]. The precipitates form as coherent octahedra bounded by (111) planes that project as squares on the (1(30) planes. Particle size may be characterized by the edge length, a, lying parallel to the (110> directions and related to particle volume through the equation a = (6V) I/3. In a previous study [3] the precipitation kinetics of Fe 3+ :MgO was investigated using superparamagnetic analysis of ferrimagnetic resonance data. However, since the shape anisotropy of the precipitates was neglected, it was not possible to extend the analysis to very small particle sizes. In the present investigation, the ferrimagnetic resonance technique, with the inclusion of shape anisotropy effects, was used to obtain information about the early stages in the precipitation of magnesium ferrite from iron-doped MgO. 2. Theory The anisotropy field of a coherent assembly of small magnetic particles is given by [4]:
H A = < H c > +
power of x, while the shape anisotropy varies linearly with x. Therefore, for x sufficiently small, crystal anisotropy becomes negligible as compared with shape anisotropy and the value of the anisotropy form factor can be obtained from magnetic resonance measurements. 3. Experimental procedure Small MgFe204 particles were produced by precipitation from solid solution of Fe 3+ in single-crystal MgO, using the technique described by Kruse and Fine [5]. The total iron content of the samples, as determined by chemical analysis, was 1.42 cations%. The samples were aged at 973 K in air. The anisotropy field was measured at 9.25 GHz for several aging times. Experimental results a n d d i s c u s s i o n
4.
For large aging times, and hence large particle sizes, the anisotropy field was found to be negative, and a good fit to eq. (2) was obtained, as reported previously [3,6]. A different behavior was observed for small aging times. The anisotropy field was positive and increased
(I)
where H c and H s are the contributions of crystal and shape anisotropy, respectively, and the averages are taken over a distribution in thermal equilibrium. If both crystal and shape anisotropy are cubic, it can be shown [4] that: K ( H c ) = --~s[l - lOx-' coth x + 45x -2
T(K)
105x- 3 coth x + 105x-4]/[coth x - x - '],
300 I
20(~) I
lO0 I
7
E
20,4
g
Q.
-
500 I
0.6
0.2
o
I--,
(2)
o Z
< Hs) = N/%Is(coth x - x - ' ) ,
(3)
where K is the anisotropy constant, I, is the intrinsic magnetization of the particles, N is the anisotropy form factor and x = l y H / k T , where V is the average particle volume and H is the applied magnetic field. For small x, the crystal anisotropy varies as the third 0304-8853/83/0000-0000/$03.00
0.002
0
0.004
0.006
0.008
0.010
1/T (K "x)
Fig. 1. Temperature dependence of the anisotropy field of MgFe204 precipitates in MgO, for a sample aged for 1 h at 973 K. The solid line is a fit to eZl. (3) with N = 3 . 5 x I 0 -2, V
© 1983 N o r t h - H o l l a n d
=
3.8
X
10 - 2 6 m 3.
R.S. de Biasi and T.C. Devezas / Shape anisotropy of ultrafine precipitates
122 0.50
,
i
i
,
I00
o .d
bJ ~.
0.25
•
°
*
•
~
t
•
.
N
75 ~
z
0
I 5
I
/
10
AGING TIME,
15
l
50
20
t (HOURS ]
Fig. 2. Anisotropy field at 300 K (e) and particle size ( +, Zi, n) as functions of aging time. $, +, this work; n, ref. [2]; A, ref.[5].
with aging time. When the anisotropy field was plotted against inverse absolute temperature, the data could be fitted fairly accurately to eq. (3). This is shown in fig. 1 for an aging time of 1 h. The fitting was made by assuming a dependence of I s on T of the form I s = I0[1 - ( T / T o ) E ] I/2, with I 0 = 3.1 x 105 A m - I and Tc = 520 K [2]. The parameters N and V were then chosen to give the best fit to eq. (3). This procedure yielded N = 3.5 × 10 -2 and V = 3.8 × 10 -26 m 3. The fact that N is small and positive is consistent with the morphology of the precipitates [2].
For intermediate aging times, between 5 and 20 h, the room-temperature anisotropy field decreased with aging time (fig. 2). This is the range where ( H c ) and ~ H s ) are of the same order and the full eq. (1) must be used. Once the value of N is known, eq. (1) can be used to determine the particle size as a function of aging time. The crosses in fig. 2 show the values of a = (6V) 1/3 computed from eq. (1) with T = 300 K, N = 3.5 × 10 -2, H = 0.33 T, I s = 2.55 × 105 A m - l [2] and K / I s = - 11.7 m T [3]. The computed particle sizes for aging times of 2 and l0 h are fairly close to the sizes measured directly by electron microscopy [2,5] and indicated by a square and a triangle in fig. 2.
References [1] G.W. Groves and M.E. Fine, J. Appl. Phys. 35 (1964) 3587. [2] G.P. Wirtz and M.E. Fine, J. Appl. Phys. 38 (1967) 3729. [3] R.S. de Biasi and T.C. Devezas, J. Am. Ceram. Soc. 59 (1976) 55. [4] R.S. de Biasi and T.C. Devezas, J. Appl. Phys. 49 (1978) 2466. [5] E.W. Kruse Ill and M.E. Fine, J. Am. Ceram. Soc. 55 (1972) 32. [6] R.S. de Biasi and T.C. Devezas, Physica 86-88B (1977) 1425.
121
SHAPE ANISOTROPY OF ULTRAFINE MAGNESIUM
FERRITE PRECIPITATES
R.S. de B I A S I a n d T.C. D E V E Z A S Sefao de Engenharia e Ci~ncia dos Materiais, Instituto Militar de Engenharia, Rio de Janeiro, Brasil
The temperature dependence of the resonance anisotropy field for a coherent assembly of ultrafine magnesium ferrite precipitates was investigated in the range 100-400 K. The results are interpreted in terms of the shape anisotropy of the precipitates.
1. I n t r o d u c t i o n
Magnesium ferrite (MgFe204) exsolves very rapidly at 973 K in Fe3+-doped MgO [1,2]. The precipitates form as coherent octahedra bounded by (111) planes that project as squares on the (1(30) planes. Particle size may be characterized by the edge length, a, lying parallel to the (110> directions and related to particle volume through the equation a = (6V) I/3. In a previous study [3] the precipitation kinetics of Fe 3+ :MgO was investigated using superparamagnetic analysis of ferrimagnetic resonance data. However, since the shape anisotropy of the precipitates was neglected, it was not possible to extend the analysis to very small particle sizes. In the present investigation, the ferrimagnetic resonance technique, with the inclusion of shape anisotropy effects, was used to obtain information about the early stages in the precipitation of magnesium ferrite from iron-doped MgO. 2. Theory The anisotropy field of a coherent assembly of small magnetic particles is given by [4]:
H A = < H c > +
power of x, while the shape anisotropy varies linearly with x. Therefore, for x sufficiently small, crystal anisotropy becomes negligible as compared with shape anisotropy and the value of the anisotropy form factor can be obtained from magnetic resonance measurements. 3. Experimental procedure Small MgFe204 particles were produced by precipitation from solid solution of Fe 3+ in single-crystal MgO, using the technique described by Kruse and Fine [5]. The total iron content of the samples, as determined by chemical analysis, was 1.42 cations%. The samples were aged at 973 K in air. The anisotropy field was measured at 9.25 GHz for several aging times. Experimental results a n d d i s c u s s i o n
4.
For large aging times, and hence large particle sizes, the anisotropy field was found to be negative, and a good fit to eq. (2) was obtained, as reported previously [3,6]. A different behavior was observed for small aging times. The anisotropy field was positive and increased
(I)
where H c and H s are the contributions of crystal and shape anisotropy, respectively, and the averages are taken over a distribution in thermal equilibrium. If both crystal and shape anisotropy are cubic, it can be shown [4] that: K ( H c ) = --~s[l - lOx-' coth x + 45x -2
T(K)
105x- 3 coth x + 105x-4]/[coth x - x - '],
300 I
20(~) I
lO0 I
7
E
20,4
g
Q.
-
500 I
0.6
0.2
o
I--,
(2)
o Z
< Hs) = N/%Is(coth x - x - ' ) ,
(3)
where K is the anisotropy constant, I, is the intrinsic magnetization of the particles, N is the anisotropy form factor and x = l y H / k T , where V is the average particle volume and H is the applied magnetic field. For small x, the crystal anisotropy varies as the third 0304-8853/83/0000-0000/$03.00
0.002
0
0.004
0.006
0.008
0.010
1/T (K "x)
Fig. 1. Temperature dependence of the anisotropy field of MgFe204 precipitates in MgO, for a sample aged for 1 h at 973 K. The solid line is a fit to eZl. (3) with N = 3 . 5 x I 0 -2, V
© 1983 N o r t h - H o l l a n d
=
3.8
X
10 - 2 6 m 3.
R.S. de Biasi and T.C. Devezas / Shape anisotropy of ultrafine precipitates
122 0.50
,
i
i
,
I00
o .d
bJ ~.
0.25
•
°
*
•
~
t
•
.
N
75 ~
z
0
I 5
I
/
10
AGING TIME,
15
l
50
20
t (HOURS ]
Fig. 2. Anisotropy field at 300 K (e) and particle size ( +, Zi, n) as functions of aging time. $, +, this work; n, ref. [2]; A, ref.[5].
with aging time. When the anisotropy field was plotted against inverse absolute temperature, the data could be fitted fairly accurately to eq. (3). This is shown in fig. 1 for an aging time of 1 h. The fitting was made by assuming a dependence of I s on T of the form I s = I0[1 - ( T / T o ) E ] I/2, with I 0 = 3.1 x 105 A m - I and Tc = 520 K [2]. The parameters N and V were then chosen to give the best fit to eq. (3). This procedure yielded N = 3.5 × 10 -2 and V = 3.8 × 10 -26 m 3. The fact that N is small and positive is consistent with the morphology of the precipitates [2].
For intermediate aging times, between 5 and 20 h, the room-temperature anisotropy field decreased with aging time (fig. 2). This is the range where ( H c ) and ~ H s ) are of the same order and the full eq. (1) must be used. Once the value of N is known, eq. (1) can be used to determine the particle size as a function of aging time. The crosses in fig. 2 show the values of a = (6V) 1/3 computed from eq. (1) with T = 300 K, N = 3.5 × 10 -2, H = 0.33 T, I s = 2.55 × 105 A m - l [2] and K / I s = - 11.7 m T [3]. The computed particle sizes for aging times of 2 and l0 h are fairly close to the sizes measured directly by electron microscopy [2,5] and indicated by a square and a triangle in fig. 2.
References [1] G.W. Groves and M.E. Fine, J. Appl. Phys. 35 (1964) 3587. [2] G.P. Wirtz and M.E. Fine, J. Appl. Phys. 38 (1967) 3729. [3] R.S. de Biasi and T.C. Devezas, J. Am. Ceram. Soc. 59 (1976) 55. [4] R.S. de Biasi and T.C. Devezas, J. Appl. Phys. 49 (1978) 2466. [5] E.W. Kruse Ill and M.E. Fine, J. Am. Ceram. Soc. 55 (1972) 32. [6] R.S. de Biasi and T.C. Devezas, Physica 86-88B (1977) 1425.