Static and Dynamic Thermal Properties of a Pd₄₀Ni₄₀Si₂₀ Glassy Alloy

Abstract

The thermal properties of a Pd₄₀Ni₄₀Si₂₀ glassy alloy with the largest supercooled liquid region among the glassy alloys containing Si as a metalloid element are studied using static and dynamic measurement methods. The relatively wide supercooled liquid region of 45 K, defined by the temperature interval between the glass transition temperature (T_g) and the onset temperature of crystallization (T_x), and the viscosity of the supercooled liquid, varying from 2.7 × 10¹⁰ to 3.2 × 10¹¹ Pa·s, make this glass suitable for the introduction of controlled pores by a viscous flow in the temperature range T_g~T_x. The obtained activation energy for crystallization, 272 ± 19 kJ/mol, is slightly higher than that of T_g (228 ± 11 kJ/mol), indicating the dominant contribution of the atomic transport barrier in the overall energy barrier for crystallization.

1. Introduction

Amorphous metals are significantly different from conventional metals because of their atomic structure, mechanical properties, and specific behavior in a solid state [1,2]. Reflecting their non-periodic disordered atomic arrangement, amorphous alloys have outstanding mechanical properties, such as high yield strength, a large elastic strain of about 2%, and a wide range of tensile strength (1.5–5.5 GPa) [3,4,5]. These unique properties make them extremely interesting materials, and many studies have been carried out over the last four decades. At present, these materials can be made up to a few centimeters (bulk metallic glassy alloys) [1,2,3,4,5]. The largest thickness value of the bulk glassy alloys reaches about 30 mm for the Zr-Al-Ni-Cu system [6], 50 mm for the Zr-Be-Ti-Cu-Ni system [7], and 80 mm for the Pd-Cu-Ni-P system [8]. This is expected to enable the production of bulk glassy metal foams that have high strength combined with a very low specific weight and high mechanical energy absorption capability [9]. The evolution of porosity in bulk glassy alloys is supposed to be controlled through changes in the viscosity with the strain rate and temperature in the supercooled liquid region [10,11]. The subsequent annealing in the temperature range with high viscous flowability also gives an opportunity to control the structure and morphology of the metal foam. Considering the Pd- and Ni-rich compositions, which are favourable and have high potential for the preparation of amorphous foam, in the present study, it was important to clarify the feature of the static and dynamic thermal properties of the Pd₄₀Ni₄₀Si₂₀ glassy alloy. The other attractive characteristic of this glassy alloy is its low glass transition and melting temperatures and ease of preparation [12].

2. Materials and Methods

A glassy Pd₄₀Ni₄₀Si₂₀ alloy ribbon with a thickness of about 40 μm and a width of 2 mm was prepared by the melt-spinning technique. The circumferential velocity of the copper wheel was 25 m/s. X-ray diffraction (Co Kα radiation) and DSC were used to prove the glassy structure of the as-spun alloy ribbon. Thermal properties were examined by differential scanning calorimetry (DSC) (Perkin Elmer DSC7) at heating rates of 10–80 K/min and the thermo-mechanical analysis (Perkin Elmer quartz thermomechanical TMS2) at a heating rate of 20 K/min [13,14]. The thermo-mechanical analysis was undertaken based on the Free Volume Model (FVM) [15].

3. Results and Discussion

The X-ray diffraction and DSC analysis revealed the glassy structure of the as-spun Pd₄₀Ni₄₀Si₂₀ alloy (Figure 1).

Figure 2a shows the typical elongation vs. temperature curves of the glassy Pd₄₀Ni₄₀Si₂₀ alloy ribbon under four different loads. The overall strain of the glassy ribbon attained at temperature T under an applied tensile stress σ, under a continuous heating condition, is given by

$$\mathsf{\epsilon }(T)=[l_{(T)}-l_0]/l_0={\mathsf{\epsilon }}_{\mathsf{\sigma }}^{\mathrm{el}}(T)+{\mathsf{\epsilon }}_{\mathsf{\sigma }}^{\mathrm{an}}(T)+{\mathsf{\epsilon }}_{\mathsf{\sigma }}^{\mathrm{rel}}(T)+{\mathsf{\epsilon }}_{\mathsf{\sigma }}^{\mathrm{te}}(T)+{\mathsf{\epsilon }}_{\mathsf{\sigma }}^{\mathrm{vf}}(T)$$

(1)

where l₀ and l_(T) are the initial length and the current length of the specimen at temperature T, respectively, and ${\mathsf{\epsilon }}_{\mathsf{\sigma }}^{\mathrm{el}}(T)=\mathsf{\sigma }/E(T)$ is the elastic strain of the ribbon at the Young’s modulus of the material, E(T). It is worth adding that ${\mathsf{\sigma }}_{\mathsf{\sigma }}^{\mathrm{an}}(T)$ represents the possible anelastic contribution to the overall strain, and ${\mathsf{\sigma }}_{\mathsf{\sigma }}^{\mathrm{rel}}(T)$ takes into account the contribution of any relaxation effects to the overall strain, ${\mathsf{\epsilon }}_{\mathsf{\sigma }}^{\mathrm{te}}(T)$ represents the contribution of the thermal expansion to the overall strain, while ${\mathsf{\epsilon }}_{\mathsf{\sigma }}^{\mathrm{vf}}(T)$ takes into account the viscous flow contribution to the overall strain. It is shown that the subtraction of the strains obtained at different loads gives [5]

$${\mathsf{\Delta }\mathsf{\epsilon }}_{1,2}(T)={\mathsf{\epsilon }}_{{\mathsf{\sigma }}_1}(T)-{\mathsf{\epsilon }}_{{\mathsf{\sigma }}_2}(T)\cong {\mathsf{\epsilon }}_{{\mathsf{\sigma }}_1}^{\mathrm{vf}}(T)-{\mathsf{\epsilon }}_{{\mathsf{\sigma }}_2}^{\mathrm{vf}}(T)$$

(2)

where ${\mathsf{\Delta }\mathsf{\epsilon }}_{1,2}(T)$ is caused by the effective stress Δσ_1,2 = σ1 – σ2. Applying the Newtonian relation for viscous flow $\mathsf{\eta }=\mathsf{\tau }/\dot{\mathsf{\epsilon }}$ and taking into account the shear stress τ = σ/3, one obtains

$$\mathsf{\Delta }{\dot{\mathsf{\epsilon }}}_{1,2}\left(T\right)=\frac{\mathsf{\Delta }{\mathsf{\tau }}_{1,2}}{\mathsf{\eta }\left(T\right)}.$$

(3)

where $\mathsf{\Delta }{\dot{\mathsf{\epsilon }}}_{1,2}\left(T\right)={\dot{\mathsf{\epsilon }}}_1\left(T\right)-{\dot{\mathsf{\epsilon }}}_2\left(T\right)$ is the difference of the strain rates ${\dot{\mathsf{\epsilon }}}_1$ and ${\dot{\mathsf{\epsilon }}}_2$, caused by the applied shear stresses τ₁ and τ₂, while Δτ_1,2 = τ₁ – τ₂.

Thus, the experimental elongation vs. temperature results (Figure 2a) was used to determine the temperature dependence of the viscosity around the glass transition temperature T_g. The typical temperature dependences of the strain rates $\mathsf{\Delta }\dot{\mathsf{\epsilon }}(T)$, caused by shear stress differences ${\mathsf{\Delta }\mathsf{\tau }}_{1-2}=\frac{1}{3}({\mathsf{\sigma }}_1-{\mathsf{\sigma }}_2)$ for Pd₄₀Ni₄₀Si₂₀, are shown in Figure 2b. The curves are obtained by numerical differentiation of the temperature dependence of the degree of deformation (l_(T) − l₀). The strain rate increases smoothly up to approximately 660 K and then rapidly near T_g. Well-outlined maxima are observed in the range of the onset temperature of crystallization.

Figure 3a shows the temperature dependence of the viscosity (points) calculated from the experimental data for the deformation velocity. The line is a smoothed curve (fits in least squares) across all experimental data. Two linear sections of the curve are observed. The steeper part of the viscosity temperature dependence represents a quasi-equilibrium structural state of the supercooled liquid of the alloy. The one in the lower temperature region is the non-equilibrium viscosity of the vitrified alloy. Figure 3b reveals the measured (points) and calculated (curvilinear) temperature dependencies of the viscosity for the glassy alloy according to the Free Volume Model at a heating rate of 20 K/min. A detailed description of the theory and experimental method used are presented in our previous studies [13,14]. Thus, the glass transition temperature T_g determined by the thermo-mechanical analysis is 611 K, and theviscosities are in the range of 2.7 × 10¹⁰ to 3.2 × 10¹¹ Pa·s are obtained in the temperature range of the supercooled liquid. Similar viscosity values of the supercooled liquid were reported for a glassy alloy with a composition of Pd₄₀Ni₄₀P₂₀ [16] and for the Zr₆₅Cu₁₈Ni₇Al₁₀ bulk metallic glass [17].

To confirm the glassy character of the as-spun alloy, in addition to XRD (Figure 1), DSC measurements with different heating rates were also carried out. Figure 4a presents the DSC curves for the as-spun Pd₄₀Ni₄₀Si₂₀ ribbon, measured with heating rates in the range of 10–80 K/min. Both, T_g and T_x can clearly be detected over the whole heating rate range. It is necessary to note that the T_g obtained by DSC is slightly higher than that determined from the viscosity measurement (611 K) due to the dynamic character in the thermomechanical measurement. The T_g value obtained from the thermomechanical experiments corresponds to the beginning of the transition from glass to supercooled liquid measured by DSC at a lower heating rate of 10 K/min.

The change of T_g with the heating rate was used to determine the activation energy of the glass transition, applying the Kissinger equation [18] (Figure 4b). The value of the activation energy 228 ± 11 kJ/mol is close to that obtained for the glassy Pd₄₀Ni₄₀P₁₆Si₄ alloy [19]. The activation energy of the glass transition can be considered as an energy barrier for mass transport, which is usually evaluated by the temperature dependence of the viscosity. Indeed, both activation energies (of the viscous flow and glass transition) reflect the transition from a frozen glassy state to a supercooled liquid, i.e., cooperative atomic mobility unlocking [19]. The obtained activation energy for the crystallization of the Pd₄₀Ni₄₀Si₂₀ glassy alloy, 272 ± 19 kJ/mol (Figure 4c) is slightly higher than that of T_g, indicating the dominant contribution of the atomic transport barrier compared to the nucleation barrier in the overall energy barrier for crystallization. The last conclusion is expected for a solid state crystallization process like the one studied. This relatively large temperature interval of the supercooled liquid (T_x − T_g > 40 K) is proof of the alloy’s high glass forming ability and suggests an opportunity for the development of porous glassy by appropriate thermomechanical treatment in the supercooled liquid.

4. Conclusions

A glassy Pd₄₀Ni₄₀Si₂₀ alloy was obtained by melt spinning. The thermal behaviour of the as-spun glassy alloy ribbon was studied by DSC and thermomechanical analysis, and the glass transition temperature T_g and the onset temperature of crystallization T_x were determined under static and dynamic heating conditions. The activation energies for glass transition and crystallization obtained by DSC are 228 ± 11 kJ/mol and 272 ± 19 kJ/mol, respectively, suggesting that these transitions occur through a mass transport mechanism rather than a nucleation-controlled process. It was established that the supercooled liquid region between T_g and T_x for the present glassy alloy is large enough (> 40 K) and the viscosity is in a low enough range (2.7 × 10¹⁰–3.2 × 10¹¹ Pa·s) to allow the development of a porous glass by appropriate thermomechanical treatment of the supercooled liquid.