Vibrational properties of alpha- and sigma-phase Fe-Cr alloy arXiv:1001.1211v1 [cond-mat.mtrl-sci] 8 Jan 2010 S. M. Dubiel ∗ and J. Cieslak Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakow, Poland W. Sturhahn Advanced Photon Source, Argonne National Laboratory, 9700 South Cass Ave, Argonne Illinois 60439, USA M. Sternik, P. Piekarz, and K. Parlinski Institute of Nuclear Physics, Polish Academy of Sciences, PL-31-342 Krakow, Poland S. Stankov European Synchrotron Radiation Facility, BP 220, F-38043 Grenoble, France. Present address: Karlsruher Institute of Technology, DE-76344 Eggenstein-Leopoldshafen, Germany (Dated: August 27, 2018) Experimental investigation as well as theoretical calculations, of the Fe-partial phonon density-of- states (DOS) for nominally Fe 52 . 5 Cr 47 . 5 alloy having (a) α - and (b) σ -phase structure were carried out. The former at sector 3-ID of the Advanced Photon Source, using the method of nuclear resonant inelastic X-ray scattering, and the latter with the direct method [K. Parlinski et al., Phys. Rev. Lett. 78 , 4063 (1997)]. The characteristic features of phonon DOS, which differentiate one phase from the other, were revealed and successfully reproduced by the theory. Various data pertinent to the dynamics such as Lamb-M¨ ossbauer factor, f , kinetic energy per atom, E k , and the mean force constant, D , were directly derived from the experiment and the theoretical calculations, while vibrational specific heat at constant volume, C V , and vibrational entropy, S were calculated using the Fe-partial DOS. Using the values of f and C V , we determined values for Debye temperatures, Θ D . An excellent agreement for some quantities derived from experiment and first-principles theory, like C V and quite good one for others like D and S was obtained. The master alloy ( α -phase) was prepared by melting, in appropriate proportion, $^{57}$Fe- enriched ( ∼ 95%) iron with chromium. The ingot was then cold-rolled down to a thickness of about 30 µm from which two 5 × 5 mm 2 plates were cut out. They were next solution- treated at 1273 K for 72 h. One of the samples was afterwards transformed into the σ -phase by the isothermal anneal- ing at 973 K for 7 days. The verification of the transfor- mation into the σ -phase caused by such thermal proce- dure was done by recording a $^{57}$Fe M¨ ossbauer spectrum at 295 K. Experiments were conducted at sector 3-ID of that of the α -phase. To clarify this situation a more de- tailed knowledge of vibrational properties of the σ - and α -phases is essential. In addition, the σ -phase belongs to an important family of tetrahedrally close-packed Frank- Kasper phases and is one of the closest low-order crys- talline approximants for dodecagonal quasicrystals which have similar local structural properties with the icosahe- dral glass (ICG) [4]. The latter implies that the study of the vibrational properties of the σ -phase should shed some light on similar properties in ICGs. Challenged by this possibility and motivated by a lack of available knowledge on dynamical properties of the real σ -phase we have carried out both, an experimental investigation as well as theoretical calculations, of the Fe-partial phonon density-of-states (DOS) for nominally Fe 52 . 5 Cr 47 . 5 alloy having (a) α - and (b) σ -phase structure. For many years Fe-Cr alloy system has been of excep- tional scientific and technological interest. The former stems on one hand from its interesting physical proper- ties such as magnetic ones, and on the other hand from the fact that it forms a solid solution within the whole concentration range preserving, at least metastably, the same crystallographic structure (bcc). This, in turn, gives a unique chance for investigating the influence of the composition on various physical properties within the same structure as well as adequatly testing differ- ent theoretical models and theories. The latter follows from the fact that Fe-Cr alloys constitute the basic in- gredient of stainless steels (SS) that for a century have been one of the most important structural materials [1], and, consequently, some properties of SS are inherited from the parent alloy. To the latter belongs a σ -phase that can precipitate if a quasi-equiatomic Fe-Cr alloy undergoes an isothermal annealing in the temperature range ∼ 800K ≤ T ≤∼ 1100 K. The σ -phase has a tetrag- onal structure (type D 14 4 h P4 2 /mnm) with 30 atoms dis- tributed over five different sites (Table 1). Its physical properties are, in general, quite different than those of the α -phase of similar composition. Some properties, like the magnetic ones, are even dramatically different [2], other properties, like the Debye temperature, seem to be very similar [3]. The latter is rather unexpected as the hard- ness of the σ -phase is by a factor of ∼ 3 larger than