Vibrational Properties ofα- andσ-Phase Fe-Cr Alloy

Abstract

Experimental investigation as well as theoretical calculations, of the Fe-partial phonon density-ofstates (DOS) for nominally Fe52.5Cr47.5 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-Mössbauer 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, CV , and vibrational entropy, S were calculated using the Fe-partial DOS. Using the values of f and CV , we determined values for Debye temperatures, ΘD. An excellent agreement for some quantities derived from experiment and first-principles theory, like CV and quite good one for others like D and S was obtained.For many years Fe-Cr alloy system has been of exceptional scientific and technological interest. The former stems on one hand from its interesting physical properties 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 different theoretical models and theories. The latter follows from the fact that Fe-Cr alloys constitute the basic ingredient 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 tetragonal structure (type D 14 4h P4 2 /mnm) with 30 atoms distributed 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 hardness of the σ-phase is by a factor of ∼ 3 larger than that of the α-phase. To clarify this situation a more detailed 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 FrankKasper phases and is one of the closest low-order crystalline approximants for dodecagonal quasicrystals which have similar local structural properties with the icosahedral glass (ICG) [4]. The...

Lattice instabilities in metallic elements

“…When a phase is dynamically stable, ab initio results for the enthalpy and vibrational entropy can be used as input data without any problem Š ob et al, 2009;Dubiel et al, 2010;Pavlů, Vřeštál, and Š ob, 2010). From a practical point of view, one can often assume that the Gibbs free energy is a well-defined quantity even in the region of a dynamically unstable phase, as long as G is not given a physical interpretation in terms of extracted quantities H and S that are thought to represent truly metastable states.…”

Study of phase stability in the σ-FeCr system

“…On the other hand, the total S ph was also determined experimentally on the basis of a phonon DOS spectrum measured on the s-and a-phase samples for three different concentrations. In that case the difference S ph s À S ph a z0:08k B , being a bit less than the value of 0.095k B for one concentration only [17]. Mentioned values are also comparable to the ones calculated for imaginative s-phases formed by pure elements, Fe and Cr, equal 0.084k B for botch of them [18].…”

“…The phonon contribution to the entropy of the s-phase, S ph, was already calculated but only for one configuration of atoms in an ordered unit cell, namely the one corresponding to s-21373 [17]. The difference between S ph of s and a phases, S ph s À S ph a z0:058k B ; where S ph a is the average value of results calculated for several atomic configurations of a-phase.…”

Influence of atomic ordering on sigma phase precipitation of the Fe50Cr50 alloy

“…Sigma phase has tetrahedral structure with 30 atoms in its unitary cell, which are distributed among five crystallographically non-equivalent sites named A, B, C, D and E with occupancy numbers 2, 4, 8, 8 and 8, respectively. A and D sites are preferably occupied by iron atoms, while sites B, C and E are preferentially occupied by chromium atoms [6][7][8][9].…”