Fractal characteristic of the microstructure in Alnico8

Abstract

Alnico alloys are of technological importance owing to their excellent magnetic stability and good comprehensive properties. Considerable interest has arisen concerning the chemical compositions of the Fe-Co and Ni-Al rich phases which evolve from the spinodal decomposition of a bcc single phase solution at high temperatures [1–5]. However, emphasis has been seldom placed on kinetics of microstructural evolution at high temperatures. Recently, we have observed the splitting of Fe-Co rich particles in Alnico8 thermomagnetically treated [6]. On the other hand, some investigations [7– 9] have shown that microstructures in some materials have been found to be of fractal characteristics. However, different structures often exhibit different fractal natures, which implies that they are formed usually by different kinetic mechanisms. To this end, in this paper, our attention is focused on development of fractal characteristics in the microstructure formed during thermomagnetic treatment, which is expected to enhance understanding of the mechanisms of the microstructural evolution in Alnico8. The chemical composition of the Alnico8 studied is as follows (at mass percentage): 33.2Co, 16.3Ni, 5.3Al, 3.6Ti, 3.0Cu, 1.5Si, 1.0Nb, bal. Fe. The bulk Alnico8 was solution treated for 50 min at 1250 ◦C and then vacuum quenched. Thin laminar samples were cut from the quenched Alnico8 and subsequently subjected to a magnetic heat treatment with a field of 270 kA m−1 perpendicular to the section plane at 800 ◦C for various times such as 1.5, 5 and 10 min, and finally vacuum quenched. Transmission electron microscope (TEM) observations were made using a JEOL 200CX microscope with an accelerating voltage of 200 kV. Small angle X-ray scattering (SAXS) performed in transmission geometry with Cu Kα radiation on a Rigaku diffractometer was employed to evaluate the spatial fractal characteristics in size and morphology of Fe-Co rich particles. Fig. 1 shows TEM micrographs of the samples thermomagnetically treated at 800 ◦C for various times. TEM images were taken with electron beams along the [001] direction. The dark and isolated areas in all TEM images corresponded to rod-like Fe-Co rich particles, the long axis of which was parallel to the [001] direction [6]. The splitting of large Fe-Co rich particles was observed in the specimens with thermomagnetic treatment for 1.5 and 5 min, respectively, as the arrows in Fig. 1a and b indicate. In Fig. 1a small particles originated from the splitting of larger ones [6]. To compare Fig. 1a with b, it is easily found that the split particles coarsened. As a result of splitting, the resultant microstructure was fine and homogenous as shown in Fig. 1c. For a fractal object, N (R) is proportional to Rdf , where N (R) represents the number of particles within a radius R around a given particle, and df is the fractal dimension [10]. Based on this, direct measurements from TEM images have been taken on Fe-Co rich particles for all samples in two-dimensional Euclidian space, which covered wide ranges of R. Logarithmic plots of N (R) versus R for all samples measured are shown in Fig. 2. Each set of data are well described by a power-law behavior, as expected for a fractal. The linear least-squares fits to the data sets give estimates of fractal dimensions for 1.5, 5 and 10 min, which are 1.941, 1.945 and 1.784, respectively. In addition, SAXS experiments were also performed on all samples with different treatments to obtain directly three-dimensional information about the fractal behavior of Fe-Co rich particles. It has been however pointed out that since a fractal object has the spatial self-similarity, the scattering intensity obeys a power-law decay: I ∼ q−p [11]. If p 3, then p= df− 2d, where d is the Euclidian space dimension 3, which is the case of a compact object with smooth or rough surface depending on the value of p. Fig. 3 shows the curves of lgI versus lgq for the samples thermomagnetically treated for various times. On the curves, there exist obvious linear regions between lgI and lgq for all samples, which also indicates clearly that Fe-Co rich particles with different sizes are self-similar and of fractal characteristic in statistical sense. The exponents p for 1.5, 5 and 10 min are 2.566, 2.687 and 1.917, respectively, which are all less than 3 and thus equivalent exactly to the fractal dimensions. The fractal dimensions 2.566 and 2.687 obtained from the SAXS data for 1.5 and 5 min are in good agreement with the theoretical dimension 2.5, which has been figured out by Meakin on the basis of the diffusion-limited aggregation (DLA) model in threedimensional space [12]. In addition, for 10 min, a fractal dimension 1.917 derived from the SAXS data is also basically in accord with the fractal dimension 1.8 calculated from the cluster-cluster aggregation (CCA) growth model reported in Reference [13]. This gives a hint that the evolution of Fe-Co rich particles for