Application of statistical beam‐rocking
TEM
‐
EDX
analysis to quantitative occupation site determination of
Z
n substituted for multiple
F
e sites in
W
‐type hexagonal ferrite
Authors: Ohtsuka Masahiro , Muto Shunsuke , Anan Yoshihiro , Kobayashi Yoshinori 
Published: December 2016

W‐type strontium hexagonal ferrite, SrMe
2+
2
Fe
3+
16
O
27
(Me
2+
: divalent cation), is a hard magnetic material that exhibits strong magneto‐crystalline anisotropy (MCA), showing saturation magnetization,
M
s
, approximately 10% higher than that of M‐type ferrite, one of the current mainstream materials. It is known that partial substitution of a divalent magnetic, nonmagnetic cations or a combination of both for Me
2+
occupying appropriate Fe sites improves MCA and
M
s
, and it is thus important to investigate which Fe site and how much fraction in each site the dopant atoms are actually substituted for in order to find a guiding principle for further improvements of MCA and
M
s
.

In this study, we have quantitatively determined the occupation sites of Zn
2+
in Zn‐doped W‐type ferrite, SrZn
2
Fe
16
O
27
, using a suite of beam‐rocking transmission electron microscopy (TEM), energy‐dispersive X‐ray spectroscopy (EDX), theoretical dynamical elastic/inelastic electron scattering simulation and statistical analysis, an extended version of high‐angular resolution electron channeling X‐ray spectroscopy (HARECXS) [1]. The sintered specimen includes small amounts of hetero‐phases which hamper the application of more macroscopic methods, such as neutron diffraction and synchrotron radiation. In this statistical beam‐rocking TEM‐EDX analysis, the intensity variations of characteristic X‐ray peaks (incoherent channeling patterns (ICPs)) as functions of the incident beam direction with respect to a crystalline specimen reflect the occupation sites of the elements of interest, applicable to a small crystal grain, and the multivariate linear regression between the ICPs from the trace dopants and host elements allows us to quantitatively evaluate the dopant concentrations and their occupancies on different crystallographic sites [2]. The present material, however, has seven crystallographically inequivalent sites (the 2c as the hexagonal site, the 4e and 4f
IV
as the tetrahedral sites, and the 4f, 4f
VI
, 6g and 12k as the octahedral sites in the Wyckoff notation) for Fe, and accordingly the site‐specific ICPs of the seven sites cannot be obtained separately. We have developed a scheme combining theoretical prediction of the site‐specific ICPs, based on dynamical electron diffraction theory and the statistical atom‐location by channeling‐enhanced microanalysis (ALCHEMI) method [2] to overcome this difficulty, which was successfully applied to Co‐doped M‐type ferrite [3]. We have thus applied the scheme to present analysis.

Figure 1 shows X‐ray ICPs of the Sr‐L, Fe‐K, O‐K and Zn‐K lines obtained around the [1‐20] zone axis, in which seven Fe sites are definitely separated in the projected atomic structure. The Zn‐K ICP looks apparently different from some of the Fe‐K ICPs, which qualitatively implies that Zn preferentially occupies some of the specific Fe sites, rather than all of them uniformly. Figure 2(a) shows the theoretical Fe‐K ICP of the non‐doped SrFe
18
O
27
, corresponding to Fig. 1(b), showing sufficiently good agreement with each other. The experimental site‐specific Fe‐K ICPs for the 12k, 6g, 4f
VI
, 4f
IV
, 4f, 4e and 2c sites can be thus obtained by the proportional distribution scheme of the experimental Fe‐K ICP, as shown in Figs. 2(b‐h), then followed by applying the statistical ALCHEMI method to Zn‐K ICP (Fig. 1(d)) and site‐specific Fe‐K ICPs. Table 1 shows the derived parameters. This quantified result suggests that Zn mainly occupies 4e and 4f
IV
sites. The estimated Zn concentration of 3.1 atom% is slightly lower than the stoichiometric concentration, which is attributable to a grain‐to‐grain variation of impurity concentration.
M
s
arises due to a spontaneous molecular magnetic moment
M
0
, the vector sum of the magnetic moments of Fe
3+
, Fe
2+
and Zn
2+
cations of 5μ
B
, 4μ
B
and 0μ
B
, respectively, with the spin orientation considered.
M
0
was estimated to be 36.0μ
B
and 37.6μ
B
for the cases assuming the estimated Zn concentration and the stoichiometric Zn concentration, respectively. These values are close to the magnetization saturations of 35.0μ
B
[4] and 38.2μ
B
[5] previously reported for a similar W‐type ferrite BaZn
2
Fe
16
O
27.