3 FIG. 2: (Color online) Phonon DOS as measured on $^{57}$Fe atoms at 298 K (circles) and as calculated (dotted line) for the α -Fe 52 . 5 Cr 47 . 5 . FIG. 1: (Color online) Phonon DOS as measured on $^{57}$Fe atoms at 298 K for the α - (circles) and the σ -phase (triangles) on the Fe 52 . 5 Cr 47 . 5 samples. spectrum, are observed. Also due to larger dispersion of distances in the σ -phase, its phonon spectrum is much broader than in the α -phase, where the atomic positions are very close to those of the pure bcc-Fe. at 36 meV. The Fe-partial DOS spectrum of the σ -phase demonstrates the additional high-frequency peak at 40 meV, that is not observed neither in α -FeCr nor in pure bcc-Fe. There is also the shift downward of the low- energy peak, which makes the entire spectrum broader than in the α -phase. In Figure 2 the measured and calcu- lated phonon DOS spectra of α -FeCr are compared. The shape of both spectra is similar and two characteristic peaks of measured spectrum are reproduced satisfacto- rily. As in the chosen supercell, there are eight Fe atoms, hence by taking into account five different atomic config- urations, one considers vibrations of forty independent Fe atoms. Their partial DOS turned out to be different, but their shape was not correlated with the particular nearest-neighbor (NN) - next NN shell. Consequently, the final DOS was calculated using the partial contribu- tions with the same weights. The discrepencies between measured and calculated spectrum are likely caused by an incomplete representation of possible atomic configu- ration of FeCr disordered alloy in our model. Likewise, the calculations of σ -FeCr performed for only one configuration yield the phonon DOS exhibiting char- acteristic features of the experimental spectrum (Figure 3). Observed discrepancies, like underestimation of the intensity of low-frequency peak or shift of high-frequency peak, are not significant. Using the theoretical result, it is feasible to separate the individual contributions to the total DOS generated by the Fe atom placed at each par- ticular crystallographic position. The data derived from the experiment and the theoret- ical calculations are displayed in Table I. One can see a very good agreement for some quantities like specific heat and quite good for other ones like force constant and en- tropy. The values of the Debye temperature derived from the specific heat are close to those calculated from the Lamb-M¨ ossbauer factor, and there is a small difference for this quantity found for different phases. These find- ings disagree with experimentally found Θ D -values for the two phases using second-order Doppler shifts from M¨ ossbauer spectroscopy [3]. In those studies, the Θ D - values for the α -phase were larger than the ones for the σ -phase. This apparent discrepancy is explained by the FIG. 3: (Color online) Phonon DOS as measured on $^{57}$Fe atoms at 298 K on the σ - Fe 52 . 5 Cr 47 . 5 sample (triangles) and as calculated (dotted line). DOS-curves for particular crys- tallographic sites are indicated, too. Thus, we see that the Fe atoms on sites A and C are causing the high-energy contributions to the DOS.The NN sites of these Fe atoms are placed at distances shorter than 2.48 ˚ A. In pure bcc-Fe, all 8 NN atoms are situated at the same distance of 2.485 ˚ A. The shorter distances between atoms result in the larger interatomic interation. Therefore, in σ -FeCr, the phonon frequencies higher than 40 meV, which is a high-frequency limit of bcc-Fe DOS