The dynamics of nanocrystalline materials has attracted a lot of scientific interest during the last decade due to the striking differences observed for their atomic vibrations relative to the bulk counterparts. These anomalies are the enhancement of their density of phonon states (DOS) at low and high energies and broadening of the phonon peaks [1]. In addition, the energy dependence of the low-energy part of their phonon DOS has been a source of long-standing debates. The experimental results are contradictory, reporting a linear dependence [2], a power law with n = 1.33 [3], and a quadratic (Debye-like) behaviour ([4, 5], and references therein). On the other hand, the theoretical calculations have also indicated that non-Debye dynamics could originate from the atoms located at the surfaces [6], at the grain boundaries [7], or in the porous areas [8] of the nanocrystalline materials. Therefore the thorough understanding of the atomic dynamics in these materials is of significant importance not only for fundamental physics, but also for tailoring of their beneficial properties like enhanced strength and hardness, and improved plasticity compared to the coarse-grained materials.

In order to investigate the vibrational dynamics of the nanograins and interfaces systematically, we studied a nanocrystalline Fe90Zr7B3 alloy prepared by crystallisation of an amorphous precursor. A ribbon with composition Fe90Zr7B3 enriched to 63% in 57Fe was produced by the melt-spinning technique. Several nanocrystalline samples composed of a-Fe nanograins and homogeneous and porosity-free interfaces were prepared by annealing of the as-quenched ribbon in a vacuum of 1.6 x 10–6 mbar. The samples were characterised by X-ray diffraction (XRD), which did not show the presence of oxides or other crystalline phases. The average grain sizes were determined by Rietveld refinement of the XRD patterns and confirmed by transmission electron microscopy. The high sensitivity of the Mössbauer spectroscopy to the local environment of the resonant nuclei (57Fe) was employed to quantitatively determine the amount of iron located within the nanograins and the interfaces at various crystallisation stages. The partial, Fe-projected DOS was obtained from the nuclear inelastic scattering spectra measured with an energy resolution of 1.0 meV at beamline ID18. A simple model allowed separation of the DOS of the nanograins from that of the interfaces for a wide range of grain sizes and interface thicknesses. Figure 13 shows that the phonon DOS of the nanograins does not depend on their size and remains close to that of the bulk even for 2 nm particles (Figure 13a). Furthermore, Figure 14a and Figure 14b show that the phonon DOS of the interfaces is entirely responsible for the observed anomalies exhibiting a shape typical for matter with a high degree of structural disorder. Reducing the interface thickness to the sub-nanometre range results in a dramatic transformation of the phonon DOS (Figure 14c). The excess of phonon states at low and high energies is suppressed significantly and characteristic peaks for the bulk Fe are observed. This suggests that in such thin interfaces (about 2 atomic layers thick) the atoms follow the vibrations of the neighbouring nanograins.

Fig. 13: The phonon DOS of -Fe nanograins as a function of their size d.

 

Fig. 14: The phonon DOS of -Fe nanograin interfaces as a function of their thickness d.

 

 

In summary, the anomalous dynamics of the bulk nanocrystalline materials originate from the disordered interfaces, while the phonon DOS of the nanograins is close to that of the bulk counterparts and size independent. The low-energy enhancement of the phonon states scales linearly to the atomic fraction of the interfaces and perfectly obeys the Debye law, thus excluding the presence of low dimensional effects. The deviation of the thermo-elastic properties (vibrational entropy, mean-square displacement, average force constants, specific heat) from the corresponding bulk values also follows a similar linear dependence.

 

Principal publication and authors

S. Stankov (a), Y.Z. Yue (b,c), M. Miglierini (d), B. Sepiol (e), I. Sergueev (a), A.I. Chumakov (a), L. Hu (b,c), P. Svec (f), R. Rüffer (a), Phys. Rev. Lett. 100, 235503 (2008).
(a) ESRF
(b) Section of Chemistry, Aalborg University (Denmark)
(c) Shandong University, Jinan (China)
(d) Slovak University of Technology, Bratislava (Slovakia)
(e) University of Vienna (Austria)
(f) Slovak Academy of Sciences, Bratislava (Slovakia)

References

[1] B. Fultz et al., Phys. Rev. Lett. 79, 937, (1997).
[2] U. Stuhr et al., Phys. Rev. Lett. 81, 1449 (1998).
[3] B. Roldan Cuenya et al., Phys. Rev. B 76, 195422 (2007).
[4] T. Slezak et al., Phys. Rev. Lett. 99, 066103 (2007).
[5] S. Stankov et al., Phys. Rev. Lett. 99, 185501 (2007).
[6] A. Kara and T.S. Rahman, Phys. Rev. Lett. 81, 1453 (1998).
[7] P.M. Derlet et al., Phys. Rev. Lett. 87, 205501 (2001).
[8] C. Hudon et al., Phys. Rev. B 76, 045409 (2007).