Vibrational thermodynamics of ${\text{Fe}}_{90}{\text{Zr}}_7{\text{B}}_3$ nanocrystalline alloy from nuclear inelastic scattering

Recently we determined the iron-partial density of vibrational states (DOS) of nanocrystalline ${\text{Fe}}_{90}{\text{Zr}}_7{\text{B}}_3$ (Nanoperm), synthesized by crystallization of an amorphous precursor, for various stages of nanocrystallization separating the DOS of the nanograins from that of the interfaces [S. Stankov, Y. Z. Yue, M. Miglierini, B. Sepiol, I. Sergueev, A. I. Chumakov, L. Hu, P. Svec, and R. Rüffer, Phys. Rev. Lett. 100, 235503 (2008)]. Here we present quantitative analysis of the evolution of various thermoelastic properties calculated from DOS such as mean-force constant, mean atomic displacement, vibrational entropy, and lattice specific heat as the material transforms from amorphous, through nanocrystalline, to fully crystallized state. The reported results shed new light on the previously observed anomalies in the vibrational thermodynamics of nanocrystalline materials.

Figure 1

(Color online) Differential-scanning calorimetry scan upon an amorphous ${\text{Fe}}_{90}{\text{Zr}}_7{\text{B}}_3$. The first and the second crystallization temperatures are shown (underlined numbers). The annealing temperatures at which the NC samples were obtained are also shown (italic numbers).

Figure 2

(Color online) Conversion electron Mössbauer spectra (open circles) of the studied samples, decomposed to contributions from grains interior (dotted line), grains surface (dashed line), and intercrystalline fraction (filled gray area). The solid red lines mark the fits.

Figure 3

(Color online) Fe-partial vibrational DOS (open circles) of the samples under study. The dashed and dotted lines represent the reference DOS functions of the nanograins and interfaces, respectively, derived as described in Ref. 25 and weighted by their relative atomic fractions. The red solid lines mark the sum of two contributions.

Figure 4

(Color online)The room-temperature values of the (a) vibrational entropy, (b) lattice specific heat, (c) mean atomic displacement, and (d) mean-force constant of ${\text{Fe}}_{90}{\text{Zr}}_7{\text{B}}_3$ derived from the experimental DOS (Fig. 3) as a function of the intercrystalline fraction $X_{IC}$. The open squares at $X_{IC}=1.0$ and the open triangles at $X_{IC}=0.0$ denote the values calculated from the reference vibrational DOS (Ref. 25) of the intercrystalline and the nanograin fractions marked as AM and CR, respectively. The solid triangles mark the corresponding values of $\alpha \text{-Fe}$ foil. The solid red lines are linear fits to the experimental points of samples as-quenched, $A$, $B$, $C$, and $D$ (solid circles). Open asterisks mark the values calculated by Eq. (9). The solid (blue) squares at $X_{IC}=1.0$ denote the mean values of a clean Fe(110) surface (Ref. 44) (see text).

Figure 5

(Color online) A comparison of the interface DOS (solid red triangles) (from Ref. 25), with that of the Fe(110) surface obtained with the wave vector of the photons being parallel to the [001] (solid circles) and to the $\left[1\overline{1}0\right]$ (open blue circles) crystallographic directions (from Ref. 44). The solid black line represents the DOS of the bulk $\alpha \text{-Fe}$.