Determination of order parameter of L 1 ₀ -FePd nanoparticles by electron diffraction

Long-range order (LRO) parameters of two-dimensional dispersed single-crystalline 10-nm -sized FePd nanoparticles with the L 10 structure have been determined accurately by electron diffraction in transmission electron microscopes (TEMs) under accelerating voltages of 300 kV and 1 kV. Diffraction patterns by exciting hh0 systematic reflections effectively reduced the numbers of diffracted beams and simplified the thickness dependence of intensity ratio I110 I220 for 110 and 220 reflections. Mean thickness of the nanoparticles was estimated to be 7.8 nm by electron holography. The relation between the intensity ratio and the order parameter was calculated on the basis of multiple-scattering intensity calculation. By comparing the relation and experimentally obtained intensity ratios, the order parameters of 0.65 and 0.79 were obtained using 300-kV TEM for FePd nanoparticles after annealing at 873 K for 3.6 and 36 ks, respectively. Also, the order parameter of 0.82 was obtained using 1-MV TEM for the same specimen annealed at 873 K for 36 ks. These order parameters were determined using the Debye-Waller factors for bulk Fe and Pd. The order parameter decreased about 7.3% when a very large Debye-Waller factor as large as 0.01 nm2 was assumed. A combination of electron diffraction under the conditions of hh0 systematic reflections and the diffraction experiment at the high accelerating voltage makes the LRO parameter analysis easy and correct.