The X-ray diffraction patterns (Fig. 1) are typical of amorphous systems for all the alloys investigated in the as-quenched state, except for Gd65Fe15Co5Al10Si5, whose diffractogram showed small reflections marked by stars from an unidentified phase (most probably Gd-rich [25]).
The differential scanning calorimetry curves measured in isochronal mode at a heating rate equal to 20 K/min are shown in Fig. 2. There are two distinct exothermic events above 300 °C for each sample, but other additional shallow and wide peaks are also visible. In general, the Si-containing samples are more structurally stable than the parent alloy Gd65Fe10Co10Al15 (the first exothermic events are marked by arrows in Fig. 2) and crystallize in a more complex way. The enthalpies of the distinct peaks range from 1 to about 6 J/g. A more detailed analysis of the crystallization processes as well as the study of crystallization products is out of the scope of the present paper. It should simply be noted that Gd65Fe10Co10Al15 exhibits the lowest thermal stability (taking into account transition temperatures) from among the studied samples, while for the Si-containing samples the substitution of Fe for Co increases the crystallization temperature (Tp1) even more significantly. The low thermal stability of Gd65Fe15Co5Al10Si5 alloy may be also related to pre-existing nanocrystallites, which may act as crystallization facilitators [26].
The 57Fe Mössbauer spectra recorded at 300 K are shown in Fig. 3. It should be emphasized that the absorption area is quite small (note the relative transmission scale) due to a low content of Fe and a high content of Gd (heavy element and therefore γ-photon absorbing atom). Therefore, the spectrum of Gd65Fe5Co15Al10Si5 (the lowest Fe content) is not shown here. The quadrupolar hyperfine structures result from line broadening, while their asymmetry depends on the chemical composition. The shape of the experimental lines can be successfully fitted by considering (i) a finite number of quadrupolar components describing independently the quadrupolar splitting and isomer shift, or (ii) a continuous distribution of quadrupolar splitting linearly correlated with the isomer shift to reproduce the asymmetry. The parameters obtained from the fit are the mean values of isomer shift and quadrupolar splitting that are independent of the model assumed (see Table 1). The second model is more often applied for the interpretation of the quadrupolar and/or magnetic (Zeeman splitting) 57Fe Mössbauer spectra recorded for the amorphous Fe-containing alloys. The values of q = (< QS2 > / < QS > 2) which lie in the range 1.22–1.27 (see Table 1) are consistent with the results for an amorphous structure [27]. However, the quadrupolar splitting distributions show two peaks, suggesting that there are two main types of local Fe environments. Indeed, the dominant Gd content relative to the Fe and other atomic species contents suggests that Fe is preferentially surrounded by Gd atoms, but the presence of Co, Al and Si modifies the first coordination shell.
Table 1 Refined values of hyperfine parameters for amorphous Gd65Fe15-xCo5+xAl10Si5 (x = 0, 5) and Gd65Fe10Co10Al15 alloys The isothermal magnetization curves of the alloys Gd65Fe15-xCo5+xAl10Si5 (x = 0, 5, 10) and also Gd65Fe10Co10Al15 were measured for the magnetic field increase from 0 to 5 T over a wide temperature range. The first quadrants of these hysteresis loops were taken into account to calculate the changes in magnetic entropy, as a function of temperature and magnetic field, using Maxwell’s relation [28]:
$$\Delta S_{M} = \mu_{0} \mathop \int \limits_{0}^{{H_{\max } }} \left( {\frac{dM}{{dT}}} \right)_{H} dH,$$
where ΔSM, µ0, H, T and M represent the change in magnetic entropy, magnetic permeability of vacuum, magnetic field strength, temperature and magnetization, respectively. The curves of ΔSM(T) are depicted in Fig. 4 with the calculated RC values. The temperature shift of the magnetic entropy peak \({\Delta }S_{M}^{pk}\) with stoichiometry is rather significant and naturally associated with changes in TC. The maximum peaks of the magnetic entropy curves (\({\Delta }S_{M}^{pk}\)) of the samples studied appear in the range 150–200 K and are correlated with the changes in their TC temperatures, which depend on the samples stoichiometry. TC values for Gd65Fe5Co15Al10Si5, Gd65Fe10Co10Al15, Gd65Fe10Co10Al10Si5 and Gd65Fe15Co5Al10Si5 determined on the basis of M(T) curves measured in µ0H = 0.05 T are equal to 154, 160, 175 and 191 K, while those roughly determined on the basis of ΔSM(T) curves are equal to 155, 160, 175 and 195 K, respectively. The maximum values of magnetic entropy changes (Δµ0H = 5 T) are varying from -6.8 to -5.0 J/kg K. Such a distinct change in Curie temperature values has been observed for example in Gd60M30In10 (M = Mn, Fe, Co, Ni, Cu) [16] and Fe80-xB12Cr8Gdx (x = 1, 2, 3, 5, 8, 10, 11) [29], and called the tunable MCE. The refrigerant capacity is calculated as the integral of magnetic entropy changes and is given by the formula [2, 28]:
$$RC = \mathop \int \limits_{{T_{1} }}^{{T_{2} }} \left| { - {\Delta }S_{M} \left( T \right)} \right|dT,$$
where T1 and T2 are the temperatures at half maximum of the ascending and descending parts of the ΔSM peak, respectively. So, the changes in \({\Delta }S_{M}^{pk}\) and the shape of ΔSM(H,T) are of the highest importance when analyzing the refrigerant capacity. The changes in the shape of the magnetic entropy peaks for the melt-spun ribbons studied are typical of glassy systems, i.e., the peaks broaden, which directly affects the RC values. The refrigerant capacity values of Gd65Fe15Co5Al10Si5, Gd65Fe5Co15Al10Si5 and Gd65Fe10Co10Al10Si5 are equal to 668, 680 and 698 J/kg, respectively. The highest RC was found for Gd65Fe10Co10Al15 and equals 700 J/kg. The RC values are comparable with those of the other Gd-based systems, e.g., Gd65Fe20Al15 [30] with RC = 726 J/kg, and Gd55Co20Fe5Al18Si5 [26] with RC = 719 J/kg [31]. This confirms that the presence of nonuniformity of magnetic structure (broad distribution of transition temperature) leads to a reduction in the height of ΔSM(T) peak but also to its broadening, which allows easy control of refrigerant capacity.
The field dependence of the magnetic entropy changes can be used to determine the magnetic properties of the alloys in more details and can be expressed in the following form:
$$n = \frac{{d\ln \left| {{\Delta }S_{M} } \right|}}{d lnH}.$$
In general, the field dependence of the magnetic entropy follows a power law of the field, \({\Delta }S_{M} \propto H^{n}\) [23]. The values of the exponent n versus temperature are plotted in Fig. 5. According to the value of the exponent n, the above-mentioned dependence can be divided into three field independent ranges, below, above and at the Curie temperature. For all samples studied, the value of the exponent n is close to 2/3 at TC, which is in excellent agreement with the mean field theory. Therefore, as expected, it tends to reach 1 at low temperatures and 2 well above TC [32].
V. Franco et al. [23] have proposed a master curve analysis for materials with a second-order phase transition. C.M. Bonilla et al. [33] have constructed a universal curve for the family of Laves phases and mixed manganites. Furthermore, it has been shown that this approach does not work for the systems with a first-order phase transition. The construction of the phenomenological master curve is based on the normalization of magnetic entropy changes ΔSM’ in different external magnetic fields into corresponding values of temperature and is given by the formula [23]:
$$\Theta = \left\{ {\begin{array}{*{20}c} { - \left( {T - T_{C} } \right)/\left( {T_{r1} - T_{C} } \right) T \le T_{C} } \\ { \left( {T - T_{C} } \right)/\left( {T_{r2} - T_{C} } \right) T > T_{C} } \\ \end{array} ,} \right.$$
where Tr1 and Tr2 are the reference points for each curve, determined as \(0.5 \Delta S_{M}^{pk}\) (except Gd65Fe10Co10Al10Si5, for which better scaling was achieved for Tr1 = Tr2 = 0.4). The universal curves for Gd-based amorphous alloys are shown in Fig. 6. All master curves collapse for Θ > 0 (in the paramagnetic region) and no deviations were observed. As we have shown [34], deviations at temperatures below the magnetic phase transition may be related, for example, to dynamic magnetic ordering in crystalline compounds. No clear deviations can be observed in Fig. 6, even below Θ = 0, confirming that the phase transition in all analyzed samples is of the second order, as expected for metallic glasses.
To complement the discussion, we present in Fig. 7 a comparison of two characteristic parameters of magnetocaloric materials. The transition temperature dependences of the refrigerant capacity RC divided by the magnetic field change µ0ΔH (Fig. 7a) and the maximum magnetic entropy changes \({\Delta }S_{M}^{pk}\) divided by the magnetic field change µ0ΔH (Fig. 7b) are shown for the alloys studied (red dots), for various Gd-based metallic glasses described in the literature, for pure Gd and Gd–Mn crystalline alloys for comparison. The µ0ΔH divisor was applied to remove the magnetic field effect, but it should be kept in mind that the magnetic field dependences of the magnetic entropy changes and the refrigerant capacity are not linear in the whole µ0H range. Nevertheless, such a comparison has revealed some additional information about the possible performance of the examined alloys. The most important conclusion that can be drawn from Fig. 7 is the significant impact of transition metal and simple metal substitutions not only on the values of magnetic entropy changes and refrigerant capacity but also on the values of transition temperatures. It was also confirmed that the small variations in chemical composition can allow the Curie temperature to be tuned over a wide range.