Dispersion relations for photons and magnons in α-Fe

The room-temperature normal modes of vibration of nuclei in α-Fe have been investigated by means of slow neutron inelastic scattering. The wavelength of the incident neutron beam was 4.181 Å; the energy analysis of the scattered neutrons was performed by the time-of-flight technique. All measurements were made in the (110) plane. In a first step, the scattering curve corresponding to a scattering angle of 100° was determined; from this curve points of the phonon dispersion curves in the symmetry directions were deduced. At that stage it was found that the experimental results agree reasonably well with calculations based on the Krebs force model so long as the values of the three most sensitive parameters are obtained by fitting to the measured elastic constants of pure Fe. In a second step, additional and regularly spaced points of the dispersion relation in the symmetry directions were obtained by a method of successive approximations using the force model to calculate for each point approximate values of the scattering angle and crystal orientation. In the final analysis it appeared that although it is possible to find in the framework of the Krebs model a set of values of the parameters which give a general agreement with the whole results, there remains a slight difference for the [ζ ζ O] T₂ branch which cannot be accounted for by a change of the values for the elastic constants, due to the Si content in the sample (3.5 atom percent). A fraction of the dispersion relation for spin waves has also been measured at 250°C; at small q the results could be fitted by the quadratic approximation, with a value of (270 ± 40) meV Ų for the exchange stiffness parameter.