Corresponding author: Evgenij Artsiukh ( sirfranzferdinand@yandex.ru ) © 2019 Evgenij Artsiukh, Gunnar Suchaneck.
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Citation:
Artsiukh E, Suchaneck G (2019) Evaluation of crystallographic ordering degree of magnetically active ions in Sr_{2}FeMoO_{6δ} by means of the (101) Xray peak intensity. Modern Electronic Materials 5(4): 151157. https://doi.org/10.3897/j.moem.5.4.52810

Strontium ferromolybdate double perovskite is a promising candidate for roomtemperature spintronic applications. Nevertheless, SFMO has not yet found wide application in spintronics. This is attributed to the low reproducibility of its magnetic properties which partially originates from their strong dependence on the ordering degree of Fe and Mo ions in the Bʹ and Bʺ sublattices of double perovskite A_{2}BʹBʺO_{6}.
In this work, we have considered an express method of determining the degree of disorder in strontium ferromolybdate. The sublattice occupation with Fe and Mo ions has been estimated for stoichiometric and nonstoichiometric Sr_{2}FeMoO_{6δ} with a 5% Fe and Mo excess, respectively. We have calculated the intensity ratio between the superstructure (101) XRD peak and the most intense (112 + 200) peak. The calculated curves have been fitted to an analytical expression of a similar case known from literature. The calculation results obtained using the proposed method are within a ± 25 % agreement with Rietveld analysis of experimental data. Thus, this method can be used as an alternative to Rietveld analysis if the exposure time during Xray diffraction experiment was insufficient. We have discussed the dependence of the I (101)/I (112 + 200) peak intensity ratio on various factors including instrumental broadening of diffraction peaks, peak twinning due to grain size reduction, thin film lattice parameter variation due to substrate lattice mismatch and lattice parameter variation due to oxygen vacancies.
The relevance of the method is the evaluation of the degree of superstructure ordering in Sr_{2}FeMoO_{6δ} without large time consumption for Xray diffraction pattern recording and Rietveld data processing which may be essential when dealing with large amounts of experimental data.
strontium ferromolybdate, atomic ordering degree, Xray structural analysis
Strontium ferromolybdate (Sr_{2}FeMoO_{6δ}, SFMO) double perovskite is a promising candidate for roomtemperature spintronic applications since it possesses a halfmetallic character with theoretically 100% spin polarization [
SFMO possesses a tetragonal structure with the I4/m space symmetry group. However, some authors favor a space group I4/mmm with a lowered symmetry [
Perfect SFMO crystal lattice (Sr ions are marked in yellow, Fe ions in blue, Mo ions in orange and O ions in purple). The image was obtained by means of VESTA software [13].
S = 1 – 2ASD. (1)
Antisite disorder (ASD) takes place if a Fe ion from the Fe sublattice occupies a Mo ion site in the Mo sublattice (Fe_{Mo}) and vice versa (Mo_{Fe}). Thus, ASD is distinguished by the formation of Fe_{Mo} and Mo_{Fe} defect pairs. The ASD value may vary from 0 (complete order) to 0.5 (random distribution of Fe and Mo ions in the sublattices). Additionally, single antisite defects may occur if, e.g., excess Fe ions occupy sites in the Mo sublattice to form Fe_{Mo} [
In the perfect SFMO lattice, the (101) crystallographic planes are the ones of either Fe or Mo. Correspondingly, a (101) superstructure peak appears in the Xray diffraction pattern. The intensity of the (101) superstructure peak decreases with the development of ASD. It disappears completely in disordered structures where Fe and Mo ions are distributed randomly between the sublattices. Another superstructure reflection is the (103) peak. However, its intensity is far lower than that of the (101) peak even in a completely ordered material [
On the other hand, the SFMO lattice contains planes whose diffraction peak intensities do not depend on the degree of cation ordering in the Bsite sublattices. Therefore, they can be used for comparison with the (101) superstructure peak intensity in order to determine the degree of antisite disorder. In literature, the double (112) + (200) peak [
For the first time, the I (101)/[I (112) + I (200)] Xray peak intensity ratio was used for ASD evaluation in the Fe and Mo sublattices in [
Antisite disorder was evaluated also by 2D mapping of reciprocal space for the (101) and (404) peaks [
$\mathrm{ASD}=b\sqrt{\frac{I\left(101\right)}{aI\left(404\right)}}$ (2)
where a = 0.5583 ± 0.0005 and b = 0.5225 ± 0.0002 are constants obtained by Xray pattern simulation [
In our case of the I (101)/[I (112) + I (200)] peak intensity ratio, there is no theoretical formula which could be used for evaluating disorder degree avoiding preliminary Xray pattern treatment by means of the Rietveld method. This gap is closed in this work.
In the following, we consider the intensity I of a Xray reflection estimated as the height of the corresponding peak since this parameter can be reliably measured even if the Xray exposure time is short. For example, the exposure time required for a reliable fullprofile analysis of Xray diffraction patterns is one order of magnitude larger than that required for phase analysis [
The calculations were carried out using the VESTA [
Ion positions in the SFMO lattice [8].
Ion  Position  

X  Y  Z  
Sr  0.5  0  0.5 
Fe_{Fe}  0  0  0 
Fe_{Mo}  0  0  0 
Mo_{Mo}  0  0  0 
Mo_{Fe}  0  0  0 
O1  0  0  0.5 
O2  0.25  0.5  0 
The main point defects in SFMO synthesized under oxygen deficiency are Sr vacancies and antisite defects [
The ordering degree in stoichiometric SFMO is given by
$S={\mathrm{Fe}}_{\mathrm{Fe}}{\mathrm{Fe}}_{\mathrm{Mo}}={\mathrm{Mo}}_{\mathrm{Mo}}{\mathrm{Mo}}_{\mathrm{Fe}}$ (3)
In this case, the degree of sublattice occupation with Fe and Mo cations is determined by the following formulae:
${\mathrm{Fe}}_{\mathrm{Fe}}=1\left(\frac{100\mathrm{ASD}}{100\%}\right);{\mathrm{Fe}}_{\mathrm{Mo}}=1{\mathrm{Fe}}_{\mathrm{Fe}}$ (4)
${\mathrm{Mo}}_{\mathrm{Mo}}=1\left(\frac{100\mathrm{ASD}}{100\%}\right);{\mathrm{Mo}}_{\mathrm{Fe}}=1{\mathrm{Mo}}_{\mathrm{Mo}}$ (5)
In nonstoichiometric Sr_{2}Fe_{1}_{x}Mo_{1+}_{x}O_{6δ}, the degrees of sublattice occupation with Fe and Mo cations are determined as follows [
${\mathrm{Fe}}_{\mathrm{Fe}}=(1x)\left(\frac{100\mathrm{ASD}}{100\%}\right);{\mathrm{Fe}}_{\mathrm{Mo}}=(1x){\mathrm{Fe}}_{\mathrm{Fe}}$ (6)
${\mathrm{Mo}}_{\mathrm{Mo}}=x+(1x)\left(\frac{100\mathrm{ASD}}{100\%}\right);{\mathrm{Mo}}_{\mathrm{Fe}}=1+x{\mathrm{Mo}}_{\mathrm{Mo}}$ (7)
and correspondingly in Sr_{2}Fe_{1+}_{x}Mo_{1}_{x}O_{6δ}:
${\mathrm{Fe}}_{\mathrm{Fe}}=x+(1x)\left(\frac{100\mathrm{ASD}}{100\%}\right);{\mathrm{Fe}}_{\mathrm{Mo}}=1+x{\mathrm{Fe}}_{\mathrm{Fe}}$ (8)
${\mathrm{Mo}}_{\mathrm{Mo}}=(1x)\left(\frac{100\mathrm{ASD}}{100\%}\right);{\mathrm{Mo}}_{\mathrm{Fe}}=(1x){\mathrm{Mo}}_{\mathrm{Mo}}$ (9)
In order to determine ASD as a function of the I (101)/[I (112) + I (200)] peak intensity ratio, we have used the sublattice occupation data compiled in Tables
Comparison of the ASD (1–5) calculated as a function of (101) peak intensity ratio with literature data of Rietveld analysis of Xray diffraction patterns [6], [9], [16], [18], [25–32]: (1) calculation excluding the (200) peak, (2) calculation for the sum of (112) and (200) peak intensities, (3) calculation for the sum of (112) and (200) peak intensities for Sr_{2}Fe_{0.95}Mo_{1.05}O_{6δ} (4) calculation for the sum of (112) and (200) peak intensities for Sr_{2}Fe_{1.05}Mo_{0.95}O_{6δ} and (5) calculation using Eq. (11).
Ion occupation in the SFMO sublattices.
S, %  ASD, %  Fe_{Fe}  Fe_{Mo}  Mo_{Mo}  Mo_{Fe} 

100  0  1  0  1  0 
90  5  0.95  0.05  0.95  0.05 
80  10  0.9  0.1  0.9  0.1 
70  15  0.85  0.15  0.85  0.15 
60  20  0.8  0.2  0.8  0.2 
50  25  0.75  0.25  0.75  0.25 
40  30  0.7  0.3  0.7  0.3 
30  35  0.65  0.35  0.65  0.35 
20  40  0.6  0.4  0.6  0.4 
10  45  0.55  0.45  0.55  0.45 
0  50  0.5  0.5  0.5  0.5 
Ion occupation in the Sr_{2}Fe_{0.95}Mo_{1.05}O_{6δ} sublattices.
S, %  ASD, %  Fe_{Fe}  Fe_{Mo}  Mo_{Mo}  Mo_{Fe} 

100  0  0.95  0  1  0.05 
90  5  0.9025  0.0475  0.9525  0.0975 
80  10  0.855  0.095  0.905  0.145 
70  15  0.8075  0.1425  0.8575  0.1925 
60  20  0.76  0.19  0.81w  0.24 
50  25  0.7125  0.2375  0.7625  0.2875 
40  30  0.665  0.285  0.715  0.335 
30  35  0.6175  0.3325  0.6675  0.3825 
20  40  0.57  0.38  0.62  0.43 
10  45  0.5225  0.4275  0.5725  0.4775 
0  50  0.475  0.475  0.525  0.525 
Ion occupation in the Sr_{2}Fe_{1.05}Mo_{0.95}O_{6δ} sublattices.
S, %  ASD, %  Fe_{Fe}  Fe_{Mo}  Mo_{Mo}  Mo_{Fe} 

100  0  1  0.05  0.95  0 
90  5  0.9525  0.0975  0.9025  0.0475 
80  10  0.905  0.145  0.855  0.095 
70  15  0.8575  0.1925  0.8075  0.1425 
60  20  0.81  0.24  0.76  0.19 
50  25  0.7625  0.2875  0.7125  0.2375 
40  30  0.715  0.335  0.665  0.285 
30  35  0.6675  0.3825  0.6175  0.3325 
20  40  0.62  0.43  0.57  0.38 
10  45  0.5725  0.4775  0.5225  0.4275 
0  50  0.525  0.525  0.475  0.475 
The comparison of the calculated ASD as a function of the I (101)/[I (112) + I (200)] peak intensity ratio with experimental data is shown in Fig.
For the simulated SFMO crystal with the described above parameters (I4/m, a = 0.557 nm and c = 0.790 nm), the (101) peak for CuK_{α} radiation is located at 19.484°, the (112) peak at 32.066° and the (200) peak is shifted to a higher angle beyond the (112) peak by 0.047°. Accounting only the (112) peak, overestimates the ASD in comparison with the literature data. With regard to the very small difference in the (112) and (200) peak positions, the sum of the (112) + (200) peak intensities may be considered as 149.8% of the (112) peak intensity.
The total peak intensity depends on a number of factors:
We will now consider these factors more in detail.
Instrumental broadening of diffraction peaks can be evaluated experimentally using the NISTSistandard 640d [
$\mathrm{FWHM}=\frac{K\lambda}{d\mathrm{cos}\theta}$ (10)
where d is the average grain size, k a dimensionless coefficient of approximately 0.5 (for spherical particles), λ is the Xray wavelength and θ is the diffraction angle. The calculated broadening of (112) and (200) peaks for 100 nm diameter spherical particles is 0.083°. This broadening further increases the total peak intensity (112) + (200) to 147.9% of the (112) peak intensity. The small lattice mismatch between SFMO and substrate only slightly changes the SFMO superstructure peak intensities. This was proved by additionally considering the lattice parameter combinations a = 0.557 nm with c = 0.804 nm, a = 0.562 nm with c = 0.792 nm and a = 0.795 nm with c = 0.560 nm simulating SrTiO_{3}, MgO and LaAlO_{3} substrates, respectively [
The calculated curves follow Eq. (2), but with the X axis data being compressed since the (404) peak intensity is lower than the (112) peak intensity. Therefore, we fitted our calculated curve with regard to Eq. (2) as follows:
$\mathrm{ASD}=AB\sqrt{\frac{I\left(101\right)}{\left[I\right(112)+I(200\left)\right]}}$ (11)
The parameter A is defined by the boundary condition: in disordered SFMO , i.e., for I (101)/[I (112) + I (200)] → 0, A takes the value of 0.5. The parameter B equals to 2.318. The curve calculated using Eq. (11) is shown in Fig.
Since the decrease in the (101) peak intensity is a measure of the concentration of Fe_{Mo} and Mo_{Fe} antisite pairs, the equilibrium condition
${\mathrm{Fe}}_{\mathrm{Fe}}+{\mathrm{Mo}}_{\mathrm{Mo}}\rightleftarrows {\mathrm{Fe}}_{\mathrm{Mo}}+{\mathrm{Mo}}_{\mathrm{Fe}}$ (12)
with the constant
$k=\left[{\mathrm{Fe}}_{\mathrm{Mo}}\right]\left[{\mathrm{Mo}}_{\mathrm{Fe}}\right]={\left[{\mathrm{Fe}}_{\mathrm{Mo}}\right]}^{2}$ (13)
yields a concentration of Fe_{Mo} and Mo_{Fe} antisite pairs in the form k^{1/2} and hence, the decrease in the (101) peak intensity is the square root of the antisite pair concentration. Equation (11) allows express ASD evaluation from the (101) peak intensity and the sum of the (112) + (200) peak intensities.
For nonstoichiometric Sr_{2}Fe_{1+}_{x}Mo_{1}_{x}O_{6δ}, the ASD is calculated by [
$\mathrm{ASD}=\frac{{S}_{\mathrm{max}}S}{2}$ (14)
where S is the order parameter determined by Eq. (3) and S_{max} the maximum degree of superstructure order which, e.g. for SFMO with excess Mo, is determined by the formula:
S _{max} = Fe_{Fe} – Fe_{Mo} = 2 – (Mo_{Mo} + Mo_{Fe}) < 1. (15)
The intensities of the (112) and (200) peaks depend on instrumental error, grain size and degree of crystallinity. They are also affected by incorrect specimen preparation (specimen crushing, specimen holder preparation etc.). Nevertheless, the method of the degree of superstructure ordering from the ratio of the I (101)/[I (112) + I (200)] peak intensities can be considered as a fairly simple evaluation method for SFMO compositions with the Fe/Mo ratio close to 1 since a peak intensity ratio is compared and the impact of the abovementioned factors was taken into account to a large extent.
In this work, an express method of ASD evaluation from the I (101)/[I (112) + I (200)] peak intensity ratio by means of Eq. (11) was proposed. The method allows saving exposure time of the Xray experiment and provides reliable results for nearstoichiometric SFMO specimens with Fe ≈ Mo.
The work was financially supported by the European Union within the Horizon 2020, H2020MSCARISE2017 Program (Grant No. 778308 SPINMULTIFILM).