Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses

The XRD pattern in Figure 2 exhibits broad featureless diffraction peaks. The observed reflections demonstrate that the produced ribbon of the (Fe_2.85Co₁)₇₇Mo₈Cu₁B₁₄ MG is XRD amorphous.

Due to its sensitivity, XRD has some limitations in unveiling surface crystallization. The presence of crystallites amounting to less than about 2-3% of the MG is not critical. Thus, the term 'XRD amorphous' is sometimes used.

The initial decrease in the DSC recorded in Figure 3 is caused by the structural relaxation of the as-quenched MG, which takes place during heat treatment at moderate temperatures of up to ~ 400 °C. The following pronounced decrease of the DSC signal corresponds to the first step of crystallization. The temperature of the crystallization onset is about 400 °C with the ramp of 10 K/min. The selected temperatures of annealing are indicated by solid circles.

Well-defined positions of the resonant iron atoms in a crystalline lattice, which exhibit long-range order translation symmetry over several lattice constants, provide narrow spectral lines in the corresponding Mössbauer spectra. They feature discrete values of the spectral parameters which are unique for individual structural arrangements and, in this way, they act as fingerprints for the identification of different crystalline phases.

On the other hand, non-equivalent atomic positions in disordered amorphous materials cause broadening of the spectral lines. Thus, the associated spectral parameters exhibit distributions of their respective values. Distributions of the hyperfine spectral parameters provide information on the short-range order, i.e., the local atomic arrangement of the resonant atoms. Accordingly, Mössbauer spectrometry allows direct identification of the type of structural arrangement, specifically, crystalline (CR) versus amorphous (AM) as shown in Figure 5.

Both narrow and broad spectral lines occur in the Mössbauer spectra of NCA which are obtained from MGs by heat treatment. Moreover, the type of hyperfine interactions including quadrupole splitting (Δ) of a doublet and hyperfine magnetic fields (B) of a sextet can distinguish between non-magnetic and magnetic samples, respectively. In the case of amorphous samples, the corresponding distributions P(Δ) and P(B) are obtained.

In general, amorphous regions in the investigated samples can be of magnetic or paramagnetic origin. They are modeled by distributions of hyperfine magnetic fields P(B) and distributions of quadrupole splitting P(Δ), respectively. In our case, the as-quenched state of (Fe_2.85Co₁)₇₇Mo₈Cu₁B₁₄ MG is magnetic, but paramagnetic regions evolve inside the magnetic matrix after moderate heat treatment (up to the onset of crystallization).

After the onset of crystallization, newly formed nanocrystallites emerge in the residual amorphous matrix. The latter shows the same features as in the as-quenched state, i.e., the presence of magnetic and non-magnetic regions. In addition, atoms that are located at the surfaces of the nanograins exhibit perturbed symmetry. From one side, they experience perfect order of a crystalline lattice; from the other side they are in contact with the disordered amorphous matrix. Consequently, these atoms form a sort of interface between the amorphous rest and the crystallites. Thus, they were modeled by an additional distribution of hyperfine magnetic fields P(B) because this component is highly magnetic²⁹.

The employed fitting software²⁴ constructs the distributions as a convolution of the determining sextet or doublet of Lorentzian lines (with a Mössbauer line width of 0.195 mm/s) with Gaussians. We have used up to three Gaussians to account for the observed asymmetry of the spectra. Isomer shift, hyperfine magnetic field, or quadrupole splitting as well as the area of the determining sextet or doublet were fitted parameters. Line intensities of the 2^nd and the 5^th lines of the sextets were fitted, and the line intensity ratio of the lines (1+6):(3+4) was fixed to 3:1. The widths (standard deviations) of the individual Gauss distributions were fitted.

In all Mössbauer spectra, the presence of only the magnetically split crystalline components was observed. They were fitted with individual sextets of Lorentzian lines. The fitted parameters included isomer shift, hyperfine magnetic field, line width, intensity of the 2^nd and the 5^th lines, and the area of the component. Line intensity ratio of the lines (1+6):(3+4) was fixed to 3:1.

In some spectra, as many as six individual sextets were used. Here, two sextets were assigned to magnetic oxides. We have used up to four sextets to represent the newly formed nanograins in the annealed samples. The corresponding crystalline phase is that of bcc-Fe,Co in which Co replaces Fe at some lattice sites. Taking into consideration the binomial distribution of the most probable number of Co nearest neighbors, up to four sextets were used to model this situation depending also on the total crystalline contents in the individual annealed samples.

CEMS spectra taken from the near surface regions (to the depth of about 200 nm) reflect the structural arrangement that was induced by a 30-min annealing at the chosen temperature. CEMS spectra taken from the air and wheel sides of the ribbons at room temperature are shown in Figure 6.

CXMS spectra that illustrate structural arrangement of the investigated MG in deeper subsurface regions (down to about 5-10 µm) are shown in Figure 7.

Relative areas of spectral components corresponding to crystalline phases are plotted as a function of annealing temperature in Figure 8 as derived from both methods.

Well distinguished narrow Mössbauer lines in Figure 6 and Figure 7 indicate the formation of bcc-Fe,Co crystalline grains that appear after annealing at 410 °C. With the rising temperature of annealing, their amount progressively increases as shown in Figure 8. They are identified in close to surface layers by CEMS as well as in deeper regions by CXMS.

Traces of narrow Mössbauer lines are revealed also after low temperature of annealing and even in the as-quenched state, namely at the wheel side (see Figure 6b and Figure 7b). They belong to Fe oxides of corrosion products. During the production process, some humid air is trapped between the melt and the quenching wheel. The humidity immediately evaporates and forms air pockets inside which corrosion might be initiated. The Mössbauer signal from this component is very weak and after annealing at higher temperatures it is overlapped with that of the emerging bcc-Fe,Co nanocrystals. It is noteworthy that the identification of the corrosion products was enabled mainly due to high content of ⁵⁷Fe in these samples. Should a natural iron be used for their production, this spectral component would not have been detected. In this respect, Mössbauer spectrometry is more sensitive for the identification of iron-containing crystalline phases than for example, XRD.

It should be noted that narrow Mössbauer lines, which indicate a presence of nanocrystallites, are well distinguished after annealing at 410 °C. Nevertheless, traces of these lines are revealed also after annealing at 370 °C, which is a lower temperature than T_x1 suggested by DSC. They are more pronounced on the air side where the quenching conditions are not so effective as on the wheel side. Thus, the crystallization has started on this surface of the ribbons.

Mössbauer spectra of the bcc-Fe,Co crystalline phase were evaluated using four narrow sextets marked as Co0, Co1, Co2, and Co3. They represent Fe positions with zero, one, two, and three Co nearest neighbors, correspondingly. The obtained hyperfine magnetic fields are shown in Figure 9. With increasing number of Co atoms, the hyperfine magnetic fields at Fe sites increase. They were averaged over all annealing temperatures for individual methods, that is, CEMS and CXMS applied to both sides of the ribbons. Finally, the average of the four partial values was obtained. The resulting hyperfine magnetic fields are plotted in Figure 9a.

The evolution of the hyperfine magnetic fields, which correspond to a different number of Co nearest neighbors, is plotted in Figure 9b against the annealing temperature. They are scattered around the average values taken from Figure 9a. Notable deviations are observed for Co0 and Co2 at low annealing temperatures. It is noteworthy that the Co2 component has appeared even after annealing at 370 °C. This indicates that bcc-Fe,Co nanocrystals start to grow already at this temperature. The associated hyperfine magnetic fields diverge from the average mainly due to the size effects of the newly formed grains. This spectral component was identified as the only one because of its highest probability in a binomial distribution.

After annealing at 410 °C, the crystallization at the surface of the ribbon is well documented (see also Figure 8). The corresponding spectral components exhibit stable hyperfine magnetic fields except one – Co0. Fe positions with zero Co nearest neighbors only begin to appear because their probability is relatively low (probability of Co0 is 0.09 while that of Co2 is 0.31). Consequently, their hyperfine magnetic field values are also affected.

Ex situ Mössbauer spectrometry is a suitable method for identifying the type of crystalline phase(s) produced by heat treatment of an as-quenched MG. Moreover, because it probes the hyperfine interactions it can distinguish among lattice sites with a different number of substitution atoms.

Nuclear resonant scattering can be effectively accomplished with synchrotron radiation featuring extremely high brilliance and tunable energy³⁰. The choice of the appropriate energy that matches with separation of nuclear levels in ⁵⁷Fe enables the involvement of NFS for many experimental studies in materials research³¹. In fact, this technique can be considered analogous to Mössbauer spectrometry³².

Pulses of synchrotron radiation with a typical duration of ~ 50 ps provide photons with a bandwidth of several meV. Because hyperfine interactions are on the order of several neV, such a pulse excites simultaneously all possible transitions among the nuclear levels. Consequent deexcitation photons are coherent and interfere with one another. In contrast, in conventional Mössbauer spectrometry both excitation and deexcitation are activated sequentially when the unique energy of photons released from a radioactive source is modulated via the Doppler effect to the requested energy. The interference of photons is schematically drawn in Figure 10.

NFS time-domain patterns represent plots of the number of photons emitted by the sample as a function of a delayed time. The latter is a time that has elapsed from the excitation of nuclear levels with a synchrotron-radiation pulse until the detection of these 'delayed' photons.

Depending upon the temperature of measurement, three separate temperature regions can be distinguished. Consequently, we have employed three fitting models which take into consideration the temperature evolution of hyperfine interactions and accompanying structural transformations within the individual temperature regions.

In the first region which comprises low temperatures up to the Curie point, the investigated MG is amorphous and exhibits magnetic interactions. The corresponding physical model consisted of two distributions of hyperfine magnetic fields. They were assigned to two types of short-range order (SRO) arrangements representing amorphous regions with rather high (~ 22 T) and low (~ 8 T) average hyperfine magnetic fields (at room temperature). Values of the average hyperfine magnetic fields corresponding to both distributions were fitted. Relative contributions of both components were fitted only in the NFS time-domain pattern, which was recorded at room temperature. For increasing temperature of the in situ experiments, their relative ratio was kept fixed.

In the second, i.e., intermediate temperature region between the Curie point and the onset of the first crystallization, the investigated MG is still amorphous but already paramagnetic. The resulting structure is modeled by a single distribution of quadrupole splitting. Thus, only its average value was fitted.

After the onset of the first crystallization, i.e., in the high temperature region, the formation of bcc-Fe,Co nanograins begins. They are embedded in a residual amorphous matrix that is paramagnetic due to the considerably high temperature of the experiment. Consequently, the third fitting model consisted of a distribution of quadrupole splitting which was the same as in the previous case. The presence of nanograins was accounted for by the additional four magnetic components with unique values of hyperfine magnetic fields (i.e., not distributed). Their relative fractions were derived from a binomial distribution of the Co nearest neighbors similar as in the case of conventional Mössbauer spectrometry. The contribution of other crystallites was not identified in the bulk of the sample and that is why no additional magnetic components were needed. The fitted parameters included relative contribution of the nanocrystalline phase and the amorphous residual matrix, the average quadrupole splitting of the latter phase, and four values of hyperfine magnetic fields assigned to the individual crystallographic sites. The obtained temperature evolutions of the fitted parameters are presented in separate figures below for all three regions.

Before evaluating the experimental data, five adjacent points were summed to increase the counted intensity and thus, improve the signal-to-noise ratio. Considering that the time resolution of the used avalanche photo diode detector is greater than 0.1 ns, such data treatment caused diminution of the detector's resolution to about 0.5 ns, which is still satisfactory for the determination of hyperfine parameters. In addition, the used detector exhibits negligible background count rate in comparison to the NFS signal. Consequently, the background parameter was kept at zero during the evaluation procedure.

The NFS experiments were performed during the continuous increase of temperature which was rising at a rate of 10 K/min. The acquisition of the data was also continuous, and the NFS time-domain patterns were stored at the end of every minute. During one experiment, several tens of individual NFS time-domain records were collected. In this way, a progress of structural transformations that are taking place in the whole bulk of the investigated MG can be followed in situ with respect to the time and/or temperature.

Examples of individual NFS time-domain patterns are shown in Figure 11 where the experimental data (full dots with errors) and theoretically calculated curves (solid lines) are given. The latter were evaluated using different fitting models for different temperature intervals as described above. Note that the y-axes are given in logarithmic scale. Thus, even small deviations between the experimental points and the theoretically calculated curves are visually enhanced. Nevertheless, because of the rather low counts especially in longer delayed time regions, where also some differences occur, their effect upon the resulting hyperfine interactions is negligible.

All NFS patterns are presented in Figure 12 by contour plot. Delayed time of resonantly scattered photons constitutes the abscissa, and the heating temperature during acquisition of NFS data experiment is given on the y-axis. The intensities of the records are color-coded in logarithmic scale.

Obvious deviations in the shapes of NFS records in Figure 11 and Figure 12 clearly indicate changes in hyperfine interactions observed at certain temperatures. The Curie temperature T_C corresponds to the transition from ferromagnetic to paramagnetic arrangement of the studied MG. It is a phase transition of the second order. From a structural point of view, however, the system is still amorphous.

A dramatic change in the shapes of NFS time-domain records at T_x1 relates to the onset of crystallization when nanocrystallites emerge from the amorphous matrix. This structural transformation is accompanied by the re-appearance of magnetic hyperfine interactions. They are established among the newly formed bcc-Fe,Co nanograins. Even with the rising temperature of the experiment, the ferromagnetic order survives.

The evolution of hyperfine magnetic fields at the nanocrystals and their relative amount with temperature are shown in Figure 13a and Figure 13b, respectively. Note that due to high sensitivity of NFS, the presence of a different number of Co atoms that are incorporated into the bcc lattice as the nearest neighbors of Fe atoms can be distinguished via differences in their hyperfine magnetic fields. They are denoted as Co0 to Co3 in Figure 13 and correspond to zero, one, two, and three Co nearest neighbors.

Rather small values of hyperfine magnetic fields that are observed in Figure 13a at the beginning of crystallization are due to the size effect of evolving crystalline grains. Their lattice gradually acquires its final order which also determines the corresponding hyperfine magnetic fields. After reaching the temperature of approximately 500 °C, the latter are stabilized and their values are governed exclusively by the variations of temperature. The almost unnoticeable slow decrease of hyperfine magnetic fields with rising temperature of the experiment suggests a rather high value of the Curie temperature of the newly formed crystalline phase.

The number of nanocrystals progressively increases for T > T_x1 as demonstrated in Figure 13b. The temperature evolution of the individual fitting components is also displayed. In this case, the size of symbols is higher than the corresponding error range. It is noteworthy that the components denoted as Co0 and Co3 exhibit very similar values. This is caused by the low probabilities of zero and three Co nearest neighbors as derived from the associated binomial distribution.

The temperature development of hyperfine magnetic and quadrupole electric interactions inside the amorphous matrix is demonstrated in Figure 14. In the low temperature region where T < T_C, an expected temperature driven decrease in hyperfine fields of both evaluation components is observed in Figure 14a. Here, the fitting model consists of two distributions of hyperfine magnetic fields.

The whole MG is amorphous, though non-magnetic, until the onset of crystallization at T_x1. After that, the nanocrystalline grains emerge but the residual amorphous matrix is still non-magnetic. Consequently, the amorphous part of the alloy is reproduced by one distribution of quadrupole splitting and the obtained average values are plotted in Figure 14b against temperature. An abrupt change in this parameter is seen near T_x1. The latter was determined as an inflection point of the curve.

The evolution of the total number of counts (areas) of the individual NFS time-domain patterns with respect to temperature of the in situ NFS experiment is shown in Figure 15. It can be used for the characterization of the investigated system even without any need for precise evaluation of the individual parameters. Three well-distinguished regions can be identified. They are separated by characteristic temperatures T_C and T_x1. Note that at T_C, the NFS signal has almost vanished.

The initial decrease of the total counts toward T_C reflects the temperature reduction of hyperfine magnetic fields in the amorphous phase. Consequently, the originally well resolved sextet, that is observed in the energy domain, eventually collapses at T_C to poorly resolved broad single-line signal, i.e., when the dipolar magnetic interactions completely vanish. In the time domain, the absorbed and re-emitted photons interfere after the excitation pulse. Because the energy and the time domains are coupled via the Fourier transformation, some consequences should be considered. For example, broad lines in the energy domain are represented by rapidly decaying signal in the time domain and vice versa. Thus, at T_C the time signal is squeezed into a very narrow time interval just after the excitation pulse as demonstrated by the upper pattern in Figure 11b. Here, the relevant experimental data are seen only during the first 40 ns. The possible evolution of the time signal for longer times is documented only by the theoretically calculated curve.

It should be noted that all time-domain patterns start only 20 ns after the excitation pulse. This is because of the extremely high number of prompt and delayed photons that might seriously damage the used detectors. That is why the detectors are electronically gated and do not register the incoming photons during the initial 20 ns. Nevertheless, after the transition into the paramagnetic state, the qualitatively new hyperfine interactions emerge that provide rather narrow lines in the energy domain and, thus, the corresponding time-domain signal decays more slowly. As a result, well-established quantum beat patterns appear as shown by the lower pattern in Figure 11b and the total number of counts in Figure 15 has dramatically increased.

The subsequent fall of counts (namely after T_x1) can be ascribed mainly to the formation of nanocrystallites that are strongly ferromagnetic featuring dipolar magnetic interactions. The corresponding time-domain patterns are represented by many high-frequency beats which, however, encompass a lower area than those of a still partially amorphous phase (see Figure 11c).

After reaching the destination temperature of 700 °C, the NFS experiment continued with time dwell for 10 min at this temperature and subsequent cooling. The recorded time-domain patterns are shown in Figure 16 with respect to the time of experiment. Within the isothermal region, the shape of the NFS time-domain patterns does not change substantially. Only a moderate increase in intensity of some peaks is observed. This is attributed to the evolution of crystalline grains which grow with time. Consequently, their corresponding hyperfine interactions rise in intensity, which is clearly seen in the isothermal region in Figure 16.

During the cooling, the NFS peaks move towards their final positions that are expected at room temperature. At the same time, their intensities also rise due to increase in the probability of the resonance effect with decreasing temperature. These changes can be seen after the 10^th min of the experiment in the upper half of Figure 16 (i.e., the cooling region).

Figure 1: Apparatus for planar flow casting. (a) Schematic diagram and (b) photo of a real device. Please click here to view a larger version of this figure.

Figure 2: XRD of the as-quenched (Fe_2.85Co₁)₇₇Mo₈Cu₁B₁₄ metallic glass. Broad featureless reflections indicate that the ribbon is XRD amorphous. Please click here to view a larger version of this figure.

Figure 3: DSC record of the as-quenched (Fe_2.85Co₁)₇₇Mo₈Cu₁B₁₄ metallic glass. Solid circles indicate the intended temperatures of annealing; the temperature of the onset of crystallization T_x1 is marked with the arrow. Please click here to view a larger version of this figure.

Figure 4: Apparatus for ex situ heat treatment of the as-quenched metallic glass ribbons. Please click here to view a larger version of this figure.

Figure 5: Model Mössbauer spectra. Crystalline (CR) materials exhibit narrow Mössbauer lines (left) which provide discrete values of hyperfine interactions (right). Amorphous (AM) materials are characterized by broad lines (middle) and distributions of non-magnetic P(Δ) and magnetic P(B) hyperfine interactions. This figure has been modified from [23]. Please click here to view a larger version of this figure.

Figure 6: CEMS spectra of the (Fe_2.85Co₁)₇₇Mo₈Cu₁B₁₄ metallic glass. Spectra were taken from (a) the air side and (b) the wheel side of the ribbons annealed at the indicated temperatures (a.q. = as-quenched). Mössbauer spectral lines corresponding to crystalline phases are plotted in blue (bcc-Fe,Co) and green (Fe oxides). This figure has been modified from [23]. Please click here to view a larger version of this figure.

Figure 7: CXMS spectra of the (Fe_2.85Co₁)₇₇Mo₈Cu₁B₁₄ metallic glass. Spectra were taken from (a) the air side and (b) the wheel side of the ribbons annealed at the indicated temperatures (a.q. = as-quenched). Mössbauer spectral lines corresponding to crystalline phases are plotted in blue (bcc-Fe,Co) and green (Fe oxides). This figure has been modified from [23]. Please click here to view a larger version of this figure.

Figure 8: Relative areas of the Mössbauer spectral components plotted against temperature of annealing. Components correspond to Fe-oxide (circles) and bcc-Fe,Co (squares). They were derived from (a) CEMS and (b) CXMS spectra of the (Fe_2.85Co₁)₇₇Mo₈Cu₁B₁₄ metallic glass taken from the air (full symbols) and wheel (open symbols) sides of the ribbons (a.q. = as-quenched). This figure has been modified from [23]. Please click here to view a larger version of this figure.

Figure 9: Hyperfine magnetic fields of the crystalline component. Hyperfine magnetic fields obtained from CEMS (red symbols) and CXMS (blue symbols) spectra of the (Fe_2.85Co₁)₇₇Mo₈Cu₁B₁₄ metallic glass plotted against (a) number of Co nearest neighbors in a bcc lattice and (b) temperature of annealing. Spectra were taken from the air side (full symbols) and wheel side (open symbols). Average values of hyperfine fields are plotted by green symbols and dashed lines. Please click here to view a larger version of this figure.

Figure 10: Comparison of Mössbauer spectra and NFS time-domain patterns. Sequential recording of nuclear transitions among split nuclear levels (middle) gives rise to Mössbauer spectra (left) in the energy domain. During simultaneous excitation by a single pulse of incident synchrotron radiation, the subsequent de-excitation photons of different energies interfere and provide a NFS time-domain pattern (right). The effect of the non-magnetic and magnetic hyperfine interactions is also compared. This figure has been modified from [23]. Please click here to view a larger version of this figure.

Figure 11: Examples of selected NFS time-domain patterns of the (Fe_2.85Co₁)₇₇Mo₈Cu₁B₁₄ metallic glass. Experimental data plotted by full symbols (including error range) are refined by theoretically calculated curves (solid lines). NFS data were taken at the indicated temperatures and comprise different temperature ranges: (a) below the Curie point, (b) between the Curie point and the onset of crystallization, and (c) beyond the onset of crystallization. This figure has been modified from [23]. Please click here to view a larger version of this figure.

Figure 12: Contour plot of NFS time-domain patterns of the (Fe_2.85Co₁)₇₇Mo₈Cu₁B₁₄ metallic glass taken during in situ temperature experiment. Transition temperatures including the Curie point (T_C) and the onset of crystallization (T_x1) divide the whole temperature range into three distinguished intervals. This figure has been modified from [23]. Please click here to view a larger version of this figure.

Figure 13: NFS in situ experiment on the (Fe_2.85Co₁)₇₇Mo₈Cu₁B₁₄ metallic glass. Parameters of the time-domain patterns that correspond to the crystalline phase plotted against the temperature of measurement: (a) hyperfine magnetic fields and (b) relative areas of specific atomic sites in bcc-Fe,Co lattice featuring 0, 1, 2, and 3 Co nearest neighbors of Fe atoms. This figure has been modified from [21] with permission from the PCCP Owner Societies. Please click here to view a larger version of this figure.

Figure 14: NFS in situ experiment on the (Fe_2.85Co₁)₇₇Mo₈Cu₁B₁₄ metallic glass. Hyperfine parameters of the residual amorphous matrix plotted against temperature of measurement: (a) average hyperfine magnetic fields and (b) average quadrupole splitting. The parameters were refined by specific fitting models applied for different temperature regions. Temperature of the onset of crystallization (T_x1) is marked with an arrow. This figure has been modified from [23]. Please click here to view a larger version of this figure.

Figure 15: NFS in situ experiment on the (Fe_2.85Co₁)₇₇Mo₈Cu₁B₁₄ metallic glass. Total area of NFS time-domain patterns plotted against temperature of measurement. Distinguished temperature transitions are labeled with T_C (Curie point) and T_x1 (onset of crystallization) and marked with arrows. ©2017 Marcel B. Miglierini and Vít Procházka Adapted from ref. [22]; originally published under CC BY-NC 4.0 license. Available from: DOI: 10.5772/66869. Please click here to view a larger version of this figure.

Figure 16: Contour plot of NFS time-domain patterns of the (Fe_2.85Co₁)₇₇Mo₈Cu₁B₁₄ metallic glass taken after temperature heating. NFS time-domain patterns were recorded during a 10-min dwell after reaching the destination temperature of 700 °C and consequent cooling. Note the y-coordinate which is the time of experiment. Please click here to view a larger version of this figure.