**4.2. Physical models for the evaluation of NFS time-domain patterns**

Fitting of the experimental data was performed by the CONUSS software package [29, 30] which is suitable for the evaluation of individual NFS time-domain patterns. However, the accomplished NFS experiments have provided a huge number of records. Typically, several tens (up to ~140) of time-domain patterns were obtained during one experiment. In order to process and subsequently evaluate such enormous data quantities, we have developed special software called Hubert [31]. The data evaluation is based on the conventional fitting route using CONUSS software. Hubert is designed for NFS time-domain patterns processing, time calibration, transformation from synchrotron output file format to experimental data file readable by CONUSS, a single time-domain pattern evaluation, large data sets analysis, and generation of hyperfine parameters distributions [32].

The investigated MGs are amorphous in the as-quenched state. Depending upon their composition, they are ferromagnetic ((Fe2.85Co<sup>1</sup> )77Mo<sup>8</sup> Cu<sup>1</sup> B14) and paramagnetic (Fe90Zr7 B3 , Fe81Mo<sup>8</sup> Cu<sup>1</sup> B10) at room temperature. Consequently, the originally amorphous matrix is reproduced in the NFS time-domain patterns by distributions of hyperfine magnetic fields and distributions of quadrupole splitting, respectively. With increasing temperature of measurement, magnetic dipole interactions eventually vanish, and only electric quadrupole ones are present. While the latter are fitted by distribution of quadrupole splitting, only this component is used to characterize the amorphous matrix in the particular MG.

plished by a photon beam with the energy of 14.413 keV, flux of ~109

14 X-ray Characterization of Nanostructured Energy Materials by Synchrotron Radiation

B3

furnace. Metallic glasses of Fe90Zr7

investigated MGs.

of MGs were ~1–2 mm wide and ~20 μm thick.

information on the bulk of the samples was obtained.

(intensities) are colour coded in a logarithmic scale.

generation of hyperfine parameters distributions [32].

composition, they are ferromagnetic ((Fe2.85Co<sup>1</sup>

Fe81Mo<sup>8</sup>

Cu<sup>1</sup>

**4.2. Physical models for the evaluation of NFS time-domain patterns**

width of ~3 meV. The spot size of the synchrotron beam was of 0.7×0.3 mm2

, Fe81Mo<sup>8</sup>

heat load at the sample was ~2 μW. Samples of the investigated MGs were placed in a vacuum

Cu<sup>1</sup>

by the method of rapid quenching on a rotating wheel. The chosen compositions of MGs ensure formation of nanocrystalline alloys in which crystalline grains with the size of several nanometres are formed in the early stage of structural transformation. The obtained ribbons

The maximum annealing temperature (up to ~700 °C) was limited by Kapton windows of the furnace. Nevertheless, this temperature was far behind the first crystallization step of the

Two types of studies were performed: (i) dynamical time-dependent temperature increase/ decrease and (ii) isothermal heat treatment. During the first type of experiments, temperature at the sample was continuously increasing with a ramp of 10 K/min. In the second type of experiments, the set temperature was reached with a ramp of 40 K/min and then maintained for up to 3 h. In both cases, NFS time-domain patterns were continuously recorded every minute during the whole duration of the experiment performed in transmission geometry. Thus,

For the sake of more clear presentation of a high quantity of experimentally acquired timedomain patterns within a single experiment, we use contour plots to display the obtained NFS patterns. The latter are stacked with respect to the duration time of the experiment which constitutes the vertical axes of the contour plots. For dynamical experiments, this axis' scale is eventually converted into temperature values assuming a constant ramp of 10 K/min. The elapsed time is then given on the horizontal axes, and the counts of the registered photons

Fitting of the experimental data was performed by the CONUSS software package [29, 30] which is suitable for the evaluation of individual NFS time-domain patterns. However, the accomplished NFS experiments have provided a huge number of records. Typically, several tens (up to ~140) of time-domain patterns were obtained during one experiment. In order to process and subsequently evaluate such enormous data quantities, we have developed special software called Hubert [31]. The data evaluation is based on the conventional fitting route using CONUSS software. Hubert is designed for NFS time-domain patterns processing, time calibration, transformation from synchrotron output file format to experimental data file readable by CONUSS, a single time-domain pattern evaluation, large data sets analysis, and

The investigated MGs are amorphous in the as-quenched state. Depending upon their

reproduced in the NFS time-domain patterns by distributions of hyperfine magnetic fields

)77Mo<sup>8</sup>

B10) at room temperature. Consequently, the originally amorphous matrix is

Cu<sup>1</sup>

B14) and paramagnetic (Fe90Zr7

B3 ,

B10, and (Fe2.85Co<sup>1</sup>

) <sup>77</sup>Mo<sup>8</sup> Cu<sup>1</sup>

photons/s, and band-

. The estimated

B14 were prepared

After the onset of crystallization, that is, when the temperature of measurement reaches the first crystallization step, nanocrystalline grains emerge within the residual amorphous matrix. Because of the samples' composition, they are bcc-Fe or bcc-(Fe,Co) nanocrystals. Both exhibit rather strong magnetic dipole interactions which are represented by quantum beats with relatively high frequency of oscillations (see also **Figure 1f**). The associated fitting component features well-defined hyperfine magnetic field values, and it is ascribed to the inner part of the nanocrystalline grains with well-established crystalline symmetry. Atoms located at the surfaces of the nanograins exhibit broken symmetry, and they are referred to as interface regions [18]. Though still magnetic, their associated fitting component is represented by distributions of hyperfine magnetic fields with average field values lower by ~2–3 T than those of the core of the nanograins. Presence of this component was confirmed by conventional Mössbauer spectrometry [33].

To recapitulate the fitting models applied for the evaluation of the obtained NFS time-domain patterns, it should be noted that we distinguish three structurally different regions in the investigated samples. The first one is amorphous matrix which corresponds to the whole MG in its original as-quenched state as well as during moderate heat treatment up to the onset of crystallization. When the temperature exceeds the crystallization point, this structural component represents the residual amorphous matrix in the newly formed NCA. Both amorphous regions will be denoted in the following as AM—amorphous. Because AM can be either magnetic or paramagnetic (depending upon the sample's composition and/or temperature), this component is refined by distributions of hyperfine magnetic fields and quadrupole splitting, respectively.

Well-defined structural arrangement of the evolving nanocrystalline grains stands for the second structural region which will be labelled as CR—crystalline. In the NFS time-domain

**Figure 3.** Schematic representation of a nanocrystalline structure that includes the residual amorphous matrix (light green)—AM, inner parts (core) of nanocrystalline grains (dark blue)—CR, and interfacial regions (violet)—IF.

patterns, it is refined by a sharp value of magnetic hyperfine field. The third structural component is interpreted as interface region (IF) between the former two structures. It constitutes a shell of the nanograins with undeveloped crystal symmetry. During the evaluation, it is refined by a distribution of hyperfine magnetic fields. Schematic representation of this concept is presented in **Figure 3**.

Hyperfine parameters of all fitting components evolve with temperature/time of the experiment. Eventually, at certain temperatures (e.g., Curie temperature, onset of crystallization), qualitatively different hyperfine interactions appear. Consequently, the physical model should reflect this situation by the use of appropriate type of distributions of hyperfine parameters (magnetic fields vs. quadrupole splitting). Proper type of distribution in certain temperature/ time region is chosen by the help of the Hubert software [32].
