Lattice dynamics and related diffusion properties of intermetallics: I. Fe₃Si

Abstract

Abslrad. The phonon dispersion of iron-rich FBSi alloys of DO3 struclwe (space gmup F m -3m) has been studied by inelastic neulron scaltering. The mea~wements were carried out on two crystals of different composition: Fe7,Siz at 20 and 930°C. and FesoSilo at 20. 930 and IIOO'C. The respective degree of order was determined by powder diffraction measurements. A general decrease of phonon frequencies with increasing temperature is found. the temperature dependence being strongest for lransvene phonons with IB50] propagation. With decreasing order, phonon gaps close and lhe highest optical band degeuerates into a broad distribution of inelastic intensity due to disorder scattering, The dependence of the dispersion on lhe alloy composition is nM very pronounced. The migration enthalpies as well as several other thermodynamic quantities have been calculated from the densities of states. Although the low frequencies of the uansverae phonons indicate particularly Imv migsation barriers. they o ~o t explain the pronounced change of the diffusivity with composition. This composition dependence is tentatively explained by high vacancy concenmtions.

First-principles calculations of phonon and thermodynamic properties of Fe-Si compounds

“…The three different methods give almost the same phonon dispersion curves, with the exception of the PAW GGA-PBE method that results in a slightly smaller acoustic frequency at the X point. For Fe 3 Si, good agreement is obtained for the acoustic frequencies among all of the calculation methods and the experimental values [76]. However, at the higher frequency regions, the PAW methods predict larger frequencies in comparison with experimental data.…”

Vibrational thermodynamics of materials

“…From quantum mechanical perturbation theory we expect the first-order lineshape broadening to originate with the cubic term in the potential, and this is calculated to be linear in T . Such behavior is sometimes reported, but at higher temperatures the broadening often increases faster than T 1 (e.g., [333]). Perhaps this can be understood as follows.…”

“…The curve for Grossularite shows a particularly striking increase above the harmonic curve (and the classical limit), but it may indicate a change in defect density or another structural change in the material. Studies of phonons in Fe 3 Si alloys at temperatures of 20, 930, and 1100 • C showed large phonon broadenings, approximately proportional to phonon wavevector [333]. These broadenings were interpreted as effects of chemical disordering in this material, which undergoes an order-disorder transformation at elevated temperatures.…”

Inelastic neutron scattering and migration energies in FePd

“…This model was first applied successfully to pure fcc and bcc metals and recently to intermetallic compounds Fe 3 Si [14] and Fe 1−x Al x [15] with the D0 3 and B2 structures. In this model, the migration energy is derived from the following relation:…”

“…In pure fcc metals, excellent agreement between calculated and measured values of E M was found, whereas in bcc metals, where the experimental values are less well known, predictions were obtained that show a pronounced chemical group systematics. More recently the same method has been used by Randl et al [14] in Fe 1−x Si x and Kentzinger et al [15] in Fe 1−x Al x alloys to estimate the migration energies. Strictly speaking, this method to determine E M is valid only for monoelemental structures.…”