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Register a new userEffect of magnetism on the lattice dynamics in the sigma-phase Fe-Cr alloys
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Anomalies in the temperature dependences of the recoil-free factor, f, and the average center shift, <CS>, measured by 57-Fe Mossbauer Spectroscopy, were observed for the first time in the archetype of the sigma-phase alloys system, Fe-Cr. In both cases the anomaly started at the temperature close to the magnetic ordering temperature, and in both cases it was indicative of lattice vibrations hardening. As no magnetostrictive effects were found, the anomalies seem to be entirely due to a spin-phonon coupling. The observed changes in f and in <CS> were expressed in terms of the underlying changes in the potential, Delta E_p, and the kinetic energy, Delta E_k, respectively. The former, with the maximum value larger by a factor of six than the latter, decreases, while the latter increases with T. The total mechanical energy change, Delta E, was, in general, not constant, as expected for the Debye-like vibrations, but it resembled that of Delta E_p. Only in the range of 4-15 K, Delta E was hardly dependent on T.
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Neutron diffraction technique was used to study distribution of Co and Cr atoms over different lattice sites as well as lattice paramaters in sigma-phase Co100-xCrx compounds with x = 57.0, 62.7 and 65.8. From the diffractograms recorded in the temperature range of 4.2 - 300 K it was found that all five sites A, B, C, D and E are populated by both kinds of atoms. Sites A and D are predominantly occupied by Co atoms while sites B, C and E by Cr atoms. The unit cell parameters a and c, hence the unit cell volume, increase with x, the increase being characteristic of the lattice paramater and temperature. Both a and c show a non-linear increase with temperature.
A series of sigma-phase Fe_{100-x}V_x samples with 34.4 < x < 59.0 were investigated by neutron and X-ray diffraction and Mossbauer spectroscopy (MS) techniques. The first two methods were used for verification of the transformation from alpha to sigma phase and they also permitted to determine lattice parameters of the unit cell. With MS the Debye temperature, T_D, was evaluated from the temperature dependence of the centre shift, <CS>, assuming its entire temperature dependence originates from the second-order Doppler shift. To our best knowledge, it is the first ever-reported study on T_D in sigma-FeV alloys. Both attice parameters i.e. a and c were revealed to linearly increase with x. T_D shows, however, a non-monotonic behaviour as a function of composition with its extreme values between 425K for x=40 and 600K for x=59. A local maximum of 525K was found to exist at x=43.
Formation energy of the sigma-phase in the Fe-V alloy system, Delta E, was computed in the full compositional range of its occurrence (34 < x < 60) using the electronic band structure calculations by means of the KKR method. Delta E-values were found to strongly depend on the Fe concentration, also its variation with different site occupancies was characteristic of a given lattice site. Calculated magnetic and configuration entropy contributions were used to determine sublattice occupancies for various compositions and temperatures. The results agree well with those obtained from neutron diffraction measurements.
Experimental investigation as well as theoretical calculations, of the Fe-partial phonon density-of-states (DOS) for nominally Fe_52.5Cr_47.5 alloy having (a) alpha- and (b) sigma-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-Mossbauer 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, T_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.
A low-temperature magnetism was revealed in a series of sigma-Fe(100-x)Mo(x) alloys (x=45-53). Its characterization has been done using vibrating sample magnetometry, Mossbauer spectroscopy, and ac magnetic susceptibility. The magnetic ordering temperature was determined to lie in the range of 46 K for x=45 and 22K for x=53, and the ground magnetic state was found to be typical of a spin-glass.
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