3.2.1. Constant Frequency Measurements

Dynamic mechanical analysis is very sensitive to the atomic and molecular mobility of amorphous materials. The (La0.5Ce0.5)65Al10(Co0.4Cu0.6)25 metallic glass dynamic mechanical response was measured from room temperature to 550 K with a heating rate of 3 K/min and a driving frequency of 1 Hz. Figure 2 exhibits the normalized storage modulus *E* and loss modulus *E*" as a function of temperature, where *Eu* represents the unrelaxed modulus at room temperature. The temperature dependence of *E* and *E*" is very similar to most other BMGs [9,26,27]. It is worth noticing that when the temperature is below the *<sup>T</sup>*g, loss modulus curve showed no apparent β relaxation [9,28,29]. The storage modulus and loss modulus of the LaCe-based metallic glass vary with temperature, and the process can be segmented into three different regions:

Region (I): In the low temperature region, i.e., beneath 350 K, the normalized storage modulus is large and close to unity. Contrarily, the loss modulus *E*" is negligible. Therefore, the glassy material mainly exhibits elastic deformation in this temperature range, and the viscoelastic component can be neglected.

Region (II): The medium temperature region comprises the temperature range of 390 K to 460 K. A large increase of the loss modulus *E*" is observed reaching a peak at the temperature *T*<sup>α</sup>, denoting the α relaxation characteristic of amorphous materials. This process is the dynamic glass transition. The storage modulus *E* starts to diminish while the loss modulus *E*" boosts. This temperature range falls within the super-cooled liquid region of metallic glasses.

Region (III): The high temperature region starts at 460 K. The storage modulus *E* increases again reaching a value similar to that at room temperature, due to crystallization. The loss modulus *E*" falls to a relatively low value.

As shown in Figure 2, the β relaxation is not observed below *Tg* [22,23]. β relaxation in this glass should be found in the temperature range from 300 to 400 K.

**Figure 2.** Thermal dependence of the normalized storage *E* /*Eu* and loss modulus *E*"/*Eu* of (La0.5Ce0.5)65Al10(Co0.4Cu0.6)25 metallic glass. Measurement was carried out at a fixed frequency of 1 Hz and a heating rate of 3 K/min. *Eu* is the unrelaxed modulus, which equals the value of *E* at room temperature.

Figure 3 exhibits the normalized dynamic loss modulus *E"* as a function of temperature at a constant frequency (1 Hz) in (La0.5Ce0.5)65Al10(CoxCu1−x)25 at% (x = 0, 0.2, 0.4, 0.6, and 0.8) glass alloys. The data are normalized to the values of temperature and loss modulus at the peak of the α relaxation, namely *T*α and *E"max*. Interestingly, the secondary relaxation process depends significantly on the chemical composition of the glass. The intensity of β relaxation of (La0.5Ce0.5)65Al10(CoxCu1−x)25 at% (x = 0, 0.2, 0.4, 0.6, and 0.8) decreases with the increase of the Cu content. The behavior of the loss module reveals a noticeable change in the features of the β relaxation around 0.8 *T*g for the different compositions. For (La0.5Ce0.5)65Al10Cu25 metallic glass, the β relaxation merely declares as a weak shoulder. It is significant that in several metallic glasses that exhibit an evident β relaxation, this has been correlated to plasticity [30]. It has also been proven that the mechanical relaxation process, especially the β relaxation, is sensitive to the micro-alloying in metallic glasses.

Previous works indicate that the β relaxation reflects the inherent structural heterogeneities in metallic glasses, described for instance as soft domains, liquid-like regions, local topological structure of loose packing regions, and flow units [1]. In the current study, minor addition of Cobalt in the (La0.5Ce0.5)65Al10(CoxCu1−x)25 at% (x = 0, 0.2, 0.4, 0.6, and 0.8) bulk metallic glasses is very important and reshapes the relaxation mode (i.e., β relaxation).

In order to associate the different behavior of β relaxation and the deformability of metallic glass with its structure, transmission electron microscopy (TEM) was carried out to reveal the microstructural characteristics of metallic glass [31]. The most notable structural feature is that the metallic glass is composed of two types of regions: Light regions with typical sizes ranging from 50 to 200 nm are enveloped by dark boundary regions, which are about 5–20 nm in width. It was further confirmed that both of the two regions are of a glassy nature. It is proposed that the local atomic motions of soft regions are responsible for β relaxations, and the heterogeneous structure improves the plasticity of metallic glasses though the formation of multiple shear bands [32].

**Figure 3.** Temperature dependence of the loss modulus *E"*/*E"max* in the (La0.5Ce0.5)65Al10(CoxCu1−x)25 at% (x = 0, 0.2, 0.4, 0.6, 0.8) metallic glass (Heating rate: 3 K/min; frequency: 1 Hz).

The relationship between enthalpy of mixing and β relaxation can be used to qualitatively anticipate the intensity β relaxation of some metallic glasses [33]. An empirical rule on β relaxation has been established [34]: Pronounced β relaxation is associated with alloys where all the atomic pairs have larger and similar negative values of the mixing enthalpy. On the other hand, positive or large fluctuations in the values of mixing enthalpy reduce and even suppress β relaxation [33].

Regarding the β relaxation in (La0.5Ce0.5)65Al10(CoxCu1−x)25 at% metallic glasses, the features of the mixing enthalpy between the constituent atoms correspond to the apparent β relaxation. Figure 4 shows the mixing enthalpy of the constituents of the (La0.5Ce0.5)65Al10(CoxCu1−x)25 at% (x = 0, 0.2, 0.4, 0.6, and 0.8) metallic glasses (The data of mixing enthalpy are derived from the reference [35]). The mixing enthalpy Hm of the "solvent" atoms, La/Ce, with the "solute" atoms are almost identical: Hm (La/Ce-Al) = −38 kJ/mol, Hm (La/Ce-Cu) = −21 kJ/mol, Hm (La-Co) = −17 kJ/mol and Hm (La-Cu) = −18 kJ/mol, reflecting the chemical similar chemistry of the rare-earth elements. As for the "solute" atoms, the mixing enthalpy of Cu-Co is positive, 6 kJ/mol, and the main difference appears when comparing the mixing enthalpies of Al-Cu, −1 kJ/mol, to that of Al-Co, −18 kJ/mol. Based on the empirical rules to determine ΔHmix, the mixing enthalpy of (La0.5Ce0.5)65Al10(CoxCu1−x)25 at% (x = 0, 0.2, 0.4, 0.6, 0.8) metallic glasses is given in Figure 4. We observed an actual decrease of the enthalpy of mixing as the concentration of Co increases. However, due to substitution of Cu by Co, the fluctuation on mixing enthalpies decreases, as the Al-Co mixing enthalpy is substantially more negative than that of Al-Cu and similar to those of La/Ce-Cu. According to the literature, this reduction on the mixing enthalpy fluctuation enhances the β relaxation [27].

Previous works proved that relaxation is connected to dynamic heterogeneity in glasses and related to the local movement of "weak spots" [36]. In particular, the microstructure inhomogeneity of metallic glass has been proven by means of microscopy and simulation [37].

**Figure 4.** Mixing enthalpy of the (La0.5Ce0.5)65Al10(CoxCu1−x)25 at% (x = 0, 0.2, 0.4, 0.6, and 0.8) metallic glasses. The inset displays the mixing enthalpy of constituent atoms (the data are taken from the reference [35]).

3.2.2. Physical Aging on the Secondary Relaxation of LaCe-Based Metallic Glass

From the thermodynamics point of view, annealing below the *Tg* drives the glassy state towards a more stable state of lower energy. Figure 5 presents the storage and loss factor of (La0.5Ce0.5)65Al10(Co0.8Cu0.2)25 metallic glass after annealing at 363 K for 24 h, which certainly illustrates that the intensity of the β relaxation reduces by physical aging below *<sup>T</sup>*g.

As proposed in previous works, the β relaxation of metallic glasses is ascribed to the structural heterogeneity or local motion of the "defects" [1,33]. These defects are denominated as flow units [33,38], quasi-point defects (QPDs) [39], liquid-like sites [40], weakly bonded zones or loose packing regions [41]. According to Figure 5, annealing below the glass transition temperature can lead to disappearance of "defects" in metallic glasses. Physical aging causes rearrangemen<sup>t</sup> of atoms, resulting in an increase of density and elastic modulus. In the metallic glass, the mobility of atoms is closely related to "defects" concentration. Annealing causes the metallic glass to evolve towards a higher density state with a consequent reduction of the local "free volume" available for atomic rearrangement. Subsequent cooling after the annealing does not alter the glassy state, since the cooling rate is much lower than in the initial production of the glass.

In addition, physical aging below the glass transition temperature *Tg* leads to enthalpy relaxation of glassy materials. Figure 6 shows the DSC trace of the (La0.5Ce0.5)65Al10(Co0.8Cu0.2)25 metallic glass annealed at 363 K for 24 h. Comparison to the as-produced sample allows the identification of a notable enthalpy recovery, a consequence of the glass relaxation during annealing.

**Figure 5.** Temperature dependence of the normalized storage modulus (**a**) and loss factor (**b**) of (La0.5Ce0.5)65Al10(Co0.8Cu0.2)25 metallic glass (heating rate: 3 K/min and frequency: 0.3 Hz) (1) As-cast (2) annealed one (annealing temperature: 363 K and annealing time: 24 h).

**Figure 6.** Enthalpy relaxation in (La0.5Ce0.5)65Al10(Co0.8Cu0.2)25 metallic glass bulk metallic glasses after aging at 363 K.

The structural relaxation observed in the DMA test can be analyzed by the growth of the loss factor (tan δ = *E"*/*E )* [42,43]. Figure 7 shows the loss factor (tan δ) evolution versus annealing time in the (La0.5Ce0.5)65Al10(Co0.8Cu0.2)25 bulk metallic glass at 363 K. Previous works have characterized the

structural relaxation below *Tg* in amorphous materials, particularly in bulk metallic glasses, by using the Kohlrausch–Williams–Watts (KWW) equation [9,44].

$$\tan \delta(t\_a) - \tan \delta(t\_a = 0) = A \langle 1 - e^{\left[-\left(\frac{4\mu}{\pi}\right)^{\beta\_{\text{sign}}}\right]} \rangle \tag{1}$$

where *A* = tan δ(*ta* → ∞) − tan δ(*ta* = 0) is the maximum value of the dynamic relaxation. τ is the relaxation time, and β*aging* is the Kohlrausch exponent with values between 0 and 1. The best fit of Equation (1) to the data on the loss factor of the (La0.5Ce0.5)65Al10(Co0.8Cu0.2)25 metallic glass was obtained with τ = 10,594 s and βaging = 0.4.

**Figure 7.** Evolution of the storage modulus *E* and loss factor tanδ for (La0.5Ce0.5)65Al10(Co0.8Cu0.2)25 metallic glass with the annealing time. The aging temperature is *T*α = 363 K, and the driving frequency is 1 Hz. The red curve is the best fit from Equation (1) obtained for the parameters τ = 10,594 s and β*aging* = 0.4.

The Kohlrausch exponent βKWW reveals the presence of a broad distribution of relaxation times in the glass, with βKWW aging = 1 corresponding to a single Debye relaxation time.

Experimental values of the parameter β*KWW* in amorphous alloys are in the range of 0.24–1 [45]. For amorphous polymers, values extend from 0.24 (polyvinyl chloride) to 0.55 (polyisobutylene), for alcohols from 0.45 to 0.75, while for orientational glasses and networks values are up to 1. In bulk metallic glasses, it appears that β*KWW* is related to the fragility of the amorphous materials [42]. Values of β*KWW* close to 1 indicate that the system is a strong glass former while values less than 0.5 sugges<sup>t</sup> that the glass is a fragile glass [46,47]. According to the available literature, no defined trend characterizes the stretching parameters β*KWW* in bulk metallic glasses, as it is either temperature dependent or temperature independent [48–50]. For example, Pd42.5Ni7.5Cu30P20 bulk metallic glass has very similar fragility parameters, 59 < m < 67, and similar stretched exponents, 0.59 < β*KWW* < 0.6 [44]. However, experimental data indicate that the Kohlrausch exponent β*aging* is around 0.4 for temperatures close to *T*g [44], as found in the present case.

As proposed by Wang et al. [51], the kinetic parameter β*KWW* is associated with the dynamic heterogeneity. The β*KWW* parameter takes low values when the temperature is below the β relaxation peak and increases dramatically when the temperature surpasses the glass transition temperature. The β relaxation in metallic glasses is related to the reversible displacement of the "defects". When the stress relaxation is performed around the β relaxation temperature, only a small fraction of atoms are allowed to move. Thus, it can be concluded that lower β*KWW* values around the β relaxation are ascribed to reversible "defects".
