Simultaneous determination of highly precise Debye–Waller factors and multiple structure factors for chemically ordered tetragonal FePd

Abstract

Accurate Debye-Waller (DW) factors and low-index structure factors up to 222 of chemically ordered FePd have been measured at 120 K. Ordered FePd has a simple tetragonal unit cell (tP2, P4/mmm) with Fe and Pd atoms at 0, 0, 0 and at ½, ½, ½, respectively, requiring the measurement of four different DW factors. It was possible to simultaneously determine all four DW factors and several low-order structure factors using different, special off-zone-axis multi-beam convergent-beam electron diffraction patterns with high precision and accuracy. The different diffraction conditions exhibit different levels of sensitivity to changes in DW and structure factors. Here the sensitivity of different off-zone-axis convergent-beam electron diffraction patterns with respect to changes in DW factors and structure factors is discussed.

Validation of density functionals for transition metals and intermetallics using data from quantitative electron diffraction

“…A detailed description of simultaneous refinement of DWFs and F g can be found in Ref. 24,25. For each material, the lattice constants used in the QCBED refinements and in DFT calculations were equivalent to ensure comparability.…”

“…21 Recently, a multi-beam off-zone axis (MBOZA) QCBED method has been applied successfully for simultaneous measurement of F g and Debye Waller factors (DWFs) with unprecedented high accuracy for binary intermetallics (as high as 0.05% for some low order F g ). [22][23][24] The simultaneous determination of accurate DWFs by CBED is important for the conversion of the F g , which are measured experimentally at finite temperatures, to static F g that can be compared directly to the equivalent set of F g obtained from DFT calculations. Furthermore, simultaneous determination of F g and DWFs from a single sample volume by QCBED avoids possible non-systematic error sources associated with uncertainties introduced by the investigation of two different sample volumes in separate experiments when DWFs are determined by XRD and F g by CBED.…”

“…Hence, we utilize the MBOZA QCBED method for simultaneous high accuracy and precision measurements of DWFs and low-order F g . [22][23][24][25] Low-order F g are introduced as facile experimental metrics for comparison with DFT calculations and validations, which can be more readily determined by experiment than alternative metrics, such as elastic constants for instance.…”

“…The MBOZA method of QCBED uses electron beam-sample orientations where several low-order reflections satisfy their respective Bragg conditions exactly, [22][23][24] rendering strong dynamical interactions between the incident electron beam and several excited diffracted beams. This produces CBED patterns that are very sensitive to the F g of the strongly excited reflections and the DWFs.…”

“…The low-order F g refined from patterns acquired from different thicknesses and orientations are generally very consistent. [22][23][24] The combination of readily available accurate acquisition of QCBED patterns through current generation TEM instrumentation and the significantly improved refinement capabilities resulting from the readily available access to powerful computers enables the systematic measurement of highly precise and accurate F g of elemental transition metals and transition metal based intermetallics in reasonable time frames. The experimentally determined F g can then be used as gauge, directly related to the electron density, to validate different DFT functionals by comparison with the equivalent calculated F g .…”