Effect of Si addition on Curie temperature and thermal expansion coefficient of (Fe_71.2B₂₄Y_4.8)₉₆Nb₄ Invar bulk metallic glasses

The Invar effect refers to the anomalous low thermal expansion behavior occurring in some weak magnets,¹ below the magnetic transition point known as the Curie temperature, T_c. The room-temperature thermal expansion coefficient, α, of Fe₆₄Ni₃₆, i.e., the Invar alloy, is only 1.2 × 10⁻⁶/°C,^2–5 an order of magnitude lower than that of Fe and Ni. Owing to the low thermal expansion characteristic, the Invar alloy has a wide range of applications in precision measuring instruments, long distance power cable, satellite positioning systems, liquefied natural gas (LNG) carrier, etc.⁶ The Invar alloy however, with the face center cubic (FCC) structure, has a limited strength lower than 1000 MPa.^7,8 In addition, the limited operating temperature range for the Invar effect to be effective is another concern. For example, the ultra-low α of the Invar alloy is only effective below 80 °C; above 80 °C, α begins to increase but still in the order of 10⁻⁶/°C; however, above T_c and in this case 200 °C, the low thermal expansion characteristic completely disappears. The low strength and low T_c of the existing Invar-like alloys, i.e., alloys with ultra-low thermal expansion coefficient, are challenging issues to be tackled. Therefore, it is rewarding to seek other alloys with low thermal expansion, high strength, and high operating temperature (higher T_c).

Interestingly, besides the fcc-structured Fe-Ni alloys, many Fe-based bulk metallic glasses (BMGs) also exhibit the typical Invar effect.⁹ Owing to their disordered structure, these alloys have a strength as high as 4000 MPa.^10–12 Among the Fe-based Invar BMGs, (Fe_71.2B₂₄Y_4.8)₉₆Nb₄ has the strongest Invar effect, i.e., the lowest α of 5.5 × 10⁻⁶/°C, but unfortunately also the lowest T_c of 178 °C.^9,13 On the other hand, (Fe₇₅B₂₀Si₅)₉₆Nb₄ with a much higher T_c of 312 °C also exhibits a clear Invar effect with α of 7.4 × 10⁻⁶/°C.⁹ These two alloys have rather close compositions, with mainly silicon replacing yttrium in the latter. Inspired by that, here we proposed to add silicon into (Fe_71.2B₂₄Y_4.8)₉₆Nb₄ or to add yttrium into (Fe₇₅B₂₀Si₅)₉₆Nb₄ to experiments whether a more balanced α and T_c could be achieved by the alloying effect. The first strategy was employed here in this work, mainly because (Fe_71.2B₂₄Y_4.8)₉₆Nb₄ has a much better glass-forming ability and thus a broader glass-forming compositional range could be expected when adjusting the alloy compositions.¹⁴ In total, 16 new alloys, were developed by adding silicon into the base (Fe_71.2B₂₄Y_4.8)₉₆Nb₄ alloy, to partially substitute boron, yttrium, or niobium, but not iron, because both the Invar effect and the Curie transition originate from the ferromagnetic element,³ iron in this case. Results from this work are expected to facilitate future developments of novel Fe-based Invar BMGs with low thermal expansion and high operating temperatures.

The master alloys were prepared by arc melting in a Ti-gettered high-purity argon atmosphere. First, pure Fe (99.99%), Nb (99.99%) and Si (99.9999%) were mixed and melted three times in the copper crucible. Pure Y (99.99%) and high-purity Fe₇₈B₂₂ (99.99%) binary alloys were then added and the mixture was melted four times. BMG rods with a diameter of 1 mm and a length of 50 mm were prepared by copper mold casting. The amorphous state was verified by x-ray diffraction (XRD Bruker D8 Advance, 40 KV × 200 mA). The thermal expansion behavior was evaluated by the dilatometer (NETZSCH DIL 402C) using samples with a diameter of 1 mm and a length of 20 mm. The applied push load was 0.3 N and the heating rate was 5 °C/min. The glass transition temperature T_g and crystallization temperature T_x were measured by the differential scanning calorimeter (NETZSCH DSC 404F3) with a heating rate of 5 °C/min. The thermomagnetic behavior was measured by the vibrating sample magnetometer (VSM-HH15) under 1.5 T of external magnetic field, with a heating rate of 5 °C/min. The quasistatic-compression tests were carried out on the BMG rod with a dimension of ϕ1 mm × 2 mm using a universal testing machine (MTS, CMT5205) with an initial strain rate of 1 × 10⁻⁴/s. The commercial Invar alloy (Fe₆₄Ni₃₆, wt. %) rod and cold-drawn SUS 304 rod were also compression tested with the same initial strain rate for comparison. Rod samples with a larger dimension of ϕ5 mm × 2 mm were employed for an accurate determination of the yield strength, since these two FCC alloys have a much poorer strength than the Fe-based BMG. The compression tests for the BMG ended when the sample fractured, with the data presenting as the engineering stress and strain, while the tests for the Invar alloy and SUS 304 ended when the load reached 50 KN, with the data presenting as the true stress and strain.

Silicon was added into the base (Fe_71.2B₂₄Y_4.8)₉₆Nb₄ alloy, i.e., Fe_68.352B_23.04Y_4.608Nb₄. In total, 16 new alloys were designed, including Fe_68.352B_23.04−xY_4.608Nb₄Si_x (x = 0.25, 0.5, 0.75, 1, 2, 3, 4.3, 4.8, 8, 9), Fe_68.352B_23.04Y_4.608−yNb₄Si_y (y = 1, 2, 3) and Fe_68.352B_23.04Y_4.608Nb_4−zSi_z (z = 1, 2, 3). As shown in the XRD patterns given in Fig. 1, all alloys with a diameter of 1 mm had a fully amorphous structure. Indeed, BMGs with a diameter of at least 2 mm could be formed in most of these alloys. However, when the silicon content was higher than 4%, fully amorphous samples could only be made with a diameter of 1 mm. Therefore, all samples with a diameter of 1 mm were used for consistency.

Figure 2 shows that all alloys exhibited the typical Invar effect, manifested as a low thermal expansion in the low temperature region and a higher thermal expansion in the high temperature region. The transition temperature is the Curie temperature, T_c-DIL, determined by the dilatometer (DIL) test.^9,13,15 The ferromagnetic transformation is abrupt in the DIL trace, and the alloys are ferromagnetic below T_c-DIL and paramagnetic above T_c-DIL. In the thermomagnetic (TM) test done under an applied magnetic field, as shown in Fig. 3, the ferromagnetic transformation is a prolonged process. The magnetization intensity decreased continuously with the increase of temperature. The ending temperature of the prolonged ferromagnetic transition is also the Curie temperature, T_c-TM. T_c-TM was very close to T_c-DIL, and as an example this could be clearly seen for the base (Fe_71.2B₂₄Y_4.8)₉₆Nb₄ alloy, as shown in Fig. 4. Figure 5 further shows that the Curie temperatures determined by these two methods were rather close. T_c-DIL is, therefore, simplified to T_c in the following discussion.

T_c of the base Fe_68.352B_23.04Y_4.608Nb₄ alloy is 178 °C, which is significantly lower than T_c of 374 ∼ 487 °C of the binary Fe_100−xB_x (x = 20–28) amorphous alloys.^24–26 Apparently, the unusually low T_c in the base Fe_68.352B_23.04Y_4.608Nb₄ alloy is attributed to the doping of niobium and yttrium. As shown in Figs. 2(c) and 3(c), when adding 1% of silicon to substitute niobium and yttrium, T_c increased by 39 and 28 °C, respectively; when adding 3% of silicon to substitute niobium and yttrium, T_c increased by 118 and 87 °C, respectively. Apparently, niobium has a more significant effect to elevate T_c than yttrium. Similar phenomena were also reported in the Fe–B–Nb and Fe–B–Y amorphous alloys,²⁷ as shown in Fig. 7. T_c increased by ∼25 °C in Fe_86−xB₁₄Nb_x and Fe₈₈B_12−xNb_x amorphous alloys with the decrease of per 1% of niobium, but only increased by ∼14 °C in Fe₈₃B_17−xY_x amorphous alloys with the decrease of per 1% of yttrium.²⁷ The above phenomena could be attributed to the much lower T_c of the Fe–Nb binary compounds (−223 ∼ −73 °C)²⁸ than that of the Fe–Y (47 ∼ 84.4 °C)^29,30 binary compounds. The Fe–Y and Fe–Nb pairs form short-range order in the base Fe_68.352B_23.04Y_4.608Nb₄ alloy (amorphous), which were verified by in situ synchrotron-based high-energy x-ray diffraction,^22,23 and they very likely inherit the characteristic of Fe–Y and Fe–Nb from binary compounds in the crystalline form. T_c of amorphous alloys thus increases more quickly with the decrease of niobium than the decrease of yttrium, regardless of the substitution of niobium and yttrium by silicon or iron, as shown by the Fe–B–Y–Nb–Si, Fe–B–Y, and Fe–B–Nb alloys in Fig. 7.

The Invar effect is a characteristic of weak magnets.^1,3,5,9 When the compositional adjustment brings in an elevation of T_c, it also results in an increase of α, as indicated in this work and all previous reports.^{9,19,22,23,26,31–35} The difficulty is how to increase T_c quickly and meanwhile to slow down the increase of α. As shown in Fig. 8, when adding silicon to substitute boron, T_c did not increase so much but α did, which is not ideal. On the contrary, when silicon was added to substitute yttrium or niobium, T_c increased significantly while α did not increase so much, which is desirable. When 3% of niobium was substituted by silicon, i.e., Fe_68.352B_23.04Y_4.608Nb₁Si₃, T_c reached the maximum value of 296 °C and α only increased 34% when comparing to the base alloy, thus achieving a decent balance between low thermal expansion and high operating temperature.

As shown by the DSC trace in Fig. 9, the Fe_68.352B_23.04Y_4.608Nb₁Si₃ BMG has a high crystallization temperature T_x of 648 °C and thus good thermal stability. Before crystallization, there is a prolonged endothermic glass transition process, which begins at the onset temperature T_g-on of 559 °C and ends at T_g-end of 580 °C. On the other hand, α increases with the glass transition due to the free volume generation and then drops quickly due to softening.³⁶ The α peak temperature of 582 °C is very close to T_g-end, since at this point the alloy is completely transformed from the solid state to the soft super-cooled liquid state. When the temperature further elevates to T_x, the alloy begins to shrink and releases the heat very fast, manifested as the synchronous sharp peaks of the DSC and α traces.

The long-range atomic rearrangement during crystallization brings a great change in the distribution of Fe–Fe nearest neighbors' distance, and thus deteriorates the Invar effect.^9,37 As shown in Fig. 10(a), the sample is first heated above T_x to 720 °C, cooled down, and then reheated. The α trace has a step-type transition,⁹ which signalizes the Invar effect, in the first heating process. The steepest point of the step-type α transition is T_c, corresponding to the inflection point in the DIL trace. In the cooling and reheating processes, the step-type α transition at 300 °C disappears, indicating the vanishing of the Invar effect. On the other hand, as shown in Fig. 10(b), after first heating to 600 °C (T_g-end< 600 °C < T_x), the Invar effect almost remains the same, in spite of a slightly increased T_c, in the following cooling and reheating processes. Therefore, as long as crystallization does not occur, the Invar effect stays.

Note that the cooling α trace of Fig. 10(a), and the first heating and cooling α traces of Fig. 10(b), are not fully displayed, due to the inaccurate values when the program switches from heating to cooling. Similarly, the first heating α trace of Fig. 10(a) and the reheating α trace of Fig. 10(b) are also not fully displayed, due to the α value runout in softening and crystallization. As indicated by the shaded circles, the α peak shown in Fig. 10(b) is higher than that shown in Fig. 10(a). This phenomenon is attributed to more free volume generation during glass transition for the deeply annealed sample, i.e., the sample first heated to 600 °C that is in the super-cooled liquid region, and then cooled down with a slow heating rate of 5 K/min. According to the free volume theory,^38,39 the less free volume annihilation in the structural relaxation, the more free volume generation in the glass transition, and vice versa. This regularity is universally applied in several scenarios that cause the free volume difference, including cooling rate in sample preparation,^36,40,41 annealing temperature or annealing time,^42,43 heating rate used in measurements,^36,44 etc.

Figure 11 compares the thermal expansion behavior and mechanical property of three kinds of alloys. Admittedly, α of the BMG is inferior than the Fe–Ni Invar alloy, but it is much lower than that of the commonly used SUS304 alloy, indicating a considerable low expansion characteristic. It is worth noting that, as shown by the DIL traces of Fig. 11(a), the Fe–Ni alloy has a much gradual transition than the BMG. Technically, this is probable because of the much larger difference in the α value of the ferromagnetic and paramagnetic states, as marked in Fig. 11(a), of the Fe–Ni alloy than that of BMG. In physics, this phenomenon shows the quite different local atomic magnetic structure between the FCC alloy and amorphous Fe-based alloy, which is beyond the topic of this work but deserves further in-depth studies. On the other hand, more importantly, the BMG has two significant advantages over the Fe–Ni Invar alloy, one being T_c is 115 °C higher, and the other being the yield strength, σ_y, is about nine times higher, as shown in Fig. 11(b). Three kinds of alloys exhibit quite different mechanical properties. The BMG is very strong but completely brittle due to the disorder structure and strong Fe–B bonding.⁴⁵ Both SUS304 and the Fe–Ni Invar alloy have an FCC structure and thus a good plasticity but simultaneously a much worse strength than the BMG. Comparatively, the commercial Fe–Ni alloy is even softer, and more importantly its work hardening ability is much weaker than that of SUS304. The Invar alloy containing carbide-forming elements can be strengthened to 1166 MPa by cold drawing,⁸ at the cost of a larger α of 4.9 × 10⁻⁶/K. Even so, the strength cannot be comparable to the BMG. However, the Fe_68.352B_23.04Y_4.608Nb₁Si₃ BMG has also an obvious shortcoming, showing a poor GFA with the critical diameter of 1 mm. Nevertheless, this BMG still has potential in the application scenarios that require a high strength, high operating temperature, and a small thickness, like the thermal bimetal plate.

In conclusion, it was found that the Curie temperature, T_c, determined by thermal expansion tests was close to the ending temperature of the ferromagnetic transition determined by thermomagnetic tests. Yttrium and niobium, especially the latter, were the main reason of the low T_c of (Fe_71.2B₂₄Y_4.8)₉₆Nb₄. When silicon partially substituted boron, T_c did not increase significantly but α did, which is not preferred; when silicon partially substituted yttrium and niobium and especially niobium, T_c increased significantly while α only increased mildly, which is desirable. When 3% of niobium was substituted by silicon, i.e., Fe_68.352B_23.04Y_4.608Nb₁Si₃, T_c reaches the maximum value of 296 °C and α remains a small value of 7.4 × 10⁻⁶/K. This BMG has a high T_x of 648 °C, and as long as crystallization does not occur, the Invar effect stays. Comparing to the traditional Fe-Ni Invar alloy, this BMG has an inferior α, but has 115 °C higher T_c and about 9 times higher strength, exhibiting a potential for application as a new Invar material with moderate (low) thermal expansion, high operating temperature, and high strength.

The authors acknowledge financial support from the National Natural Science Foundation of China (NSFC, No. 52061016) and fundings from the Jiangxi Academy of Sciences (Nos. 2021YSBG21002, 2022YSBG10001, and 2023YSBG21013).

The authors have no conflicts to disclose.

Z. R. Wang: Data curation (lead); Investigation (lead); Methodology (lead); Validation (lead); Writing – original draft (lead). T. Yang: Investigation (equal); Methodology (equal). D. Wu: Formal analysis (equal). C. M. Wang: Investigation (equal). H. Guo: Investigation (equal). Q. Hu: Conceptualization (lead); Funding acquisition (lead); Supervision (lead); Writing – original draft (equal); Writing – review & editing (equal). S. Guo: Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.