A. Composition design

We develop Sr-based BMGs with ultralow glass transition temperature based on the elastic moduli criterion.Reference Wang^13–Reference Wang¹⁵ Extensive data on elastic moduli and T_g of BMGs exhibit that there is clear correlation between the elastic moduli and T_g. That is, the lower the value of elastic modulus of a BMG is, lower is the value of T_g. It is also found that the elastic constants M of BMGs show a correlation with a weighted average of the elastic constants M_i for the constituent elements as: $M^{ - 1} = \sum \,\,{f_i } \cdot M_i ^{ - 1} $, where f_i denotes the atomic percentage of the constituent. The established correlation between elastic moduli and T_g is our guidelines for the development of the BMGs with much lower T_g by appropriate composition selection of components. Table I lists the shear modulus of Sr and other BMG base elements. Strontium has low elastic constants. Its shear modulus (G: 6.1 GPa) is even lower than that of cerium (Ce), calcium (Ca) and ytterbium (Yb) (The shear moduli of Ce, Ca, and Yb are 14, 7.4, and 9.9 GPa, respectively), which are typical metallic plastic base elements.Reference Li, Wang, Liu, Zhao, Bai, Pan and Wang¹⁶ So the strontium is chosen as base element for developing the BMGs with low T_g.

TABLE I.

Heat of mixing, atomic size and eutectic temperature of elements with strontium.

Inoue’s three empirical rules offer useful guideline for alloy design and have been used widely for developing new BMG compositions.Reference Inoue² Deep eutectic is another empirical rule, which was used widely for developing new metallic glasses.Reference Cohen and Turnbull¹⁷Table I lists the heat of mixing, atomic radius, and eutectic temperature of other components with strontium. For simplicity’s sake, only elements, which have negative heat of mixing with Sr, are given. Strontium has large atomic radius and significantly different atomic size with listed elements. All the elements listed meet the requirements of Inoue’s empirical rules. Zinc has the deepest eutectic with strontium, and the eutectic temperature is only 369 °C, so, zinc is chosen as one of the doping elements. Magnesium is chosen as another doping element because it has significantly different atomic size ratio with both Sr and Zn, and Mg also has deep eutectic with Sr.

Figure 1(a) shows XRD pattern of the as-cast Sr₆₀Mg₁₈Zn₂₂ alloy. The broad diffraction peaks without any clearly sharp diffraction peaks corresponding to crystalline phases indicate that the as-cast sample is in amorphous state within the detectable limit of the XRD, although there could be some crystalline phase (less than 5%) in it. Figure 1(b) presents the DSC trace of the as-cast Sr₆₀Mg₁₈Zn₂₂BMG, and the heating rate is 10 K/min. It can be seen that an obvious endothermic characteristic of the glass transition followed by crystallization peaks is exhibited. The distinctive glass transition and sharp crystallization event confirmed the glassy state. The endothermic peak corresponds to the melting of the alloy. The shape of the melting peak indicates that the alloy is close to the eutectic point, which is one of the reasons behind its good GFA.

It is notable that the purity of Sr element is 99% (atomic percent). Inclusions or dissolved impurities in the melt are one of the important extrinsic factors, for they may influence the heterogeneous nucleation during solidification.Reference Louzguine-Luzgin, Miracle and Inoue¹⁸ The impurities might affect the reproducibility of the results.

B. Composition range

Minor addition provides a powerful tool for the BMG-forming alloys development and design.Reference Wang¹⁹ The GFA and properties of the BMGs are quite sensitive to the composition, and the addition technique has already played an effective and important role in GFA, improvement of thermal stability and properties of BMGs since the advent of BMGs. The addition method is applied to explore new Sr-based BMGs composition. Yb, Ca, Li, and Cu can be doped into the Sr-based BMG to improve the properties of the alloy. For example, the Yb can significantly enhance the corrosion resistance of the alloy, while Li addition can further lower the T_g of the alloy. Figure 2 shows the XRD patterns of the Sr-based BMGs with different additions. The broad diffraction peaks without appreciable sharp crystalline peaks in the XRD curves indicate the full amorphous phase of these alloys.

FIG. 1.

(a) XRD pattern of the as-cast Sr₆₀Mg₁₈Zn₂₂ BMG. (b) DSC curve of the as-cast Sr₆₀Mg₁₈Zn₂₂BMG.

FIG. 2.

XRD patterns of Sr-based BMGs.

A topological structural model has been developed recently to interpret the composition of the BMG-forming alloys.Reference Senkov, Miracle and Mullens^20–Reference Miracle²² Amorphization occurs when local atomic strains generated by size differences between solute and solvent elements attain a critical level. It is supposed that the solute occupies substitutional lattice site in the crystalline lattice of the solvent element. In this case, the critical level of lattice instability is achieved at a lower concentration of a solute element as the difference in atomic size between the solvent and the solute elements increased. However, as the solute atom becomes increasingly smaller relative to the solvent atom, a substitutional occupancy is no longer stable and the smaller solute atoms may occupy alternate sites in the crystalline lattice, such as interstices. For Sr-based BMGs, the solute elements (Li, Mg, Zn, and Cu) are smaller than the solvent atoms (Sr, Ca, and Yb), so the interstitial atoms produce a positive lattice strain and the substitutional atoms create a negative lattice strain. In this case, the concentration of the substitutional atoms (Li and Mg) is the least in the glass-forming alloy, while the concentration of interstitial atoms (Zn and Cu) increases a little. The Sr-based BMGs can be described by the formula:

(1)$${\rm( \bf Sr,\rm Ca,Yb)}_A ({\rm{Li}},{\rm{Mg}})_B ({\rm{Zn}},{\rm{Cu}})_C ,$$

with A = 40 to 70, B = 5 to 25, C = 10 to 35, and A + B + C = 100. A strong topological basis exists for the compositions represented in Eq. (1).Reference Senkov, Miracle, Keppens and Liaw²³ The concentration of the elements and their atomic size are consistent with the densely packed solute-centered cluster model proposed by Miracle et al. Such atomic-concentration arrangement in the Sr-based BMGs provides efficient atomic cluster packing, and this may be another reason why the Sr-based BMGs are good glass-formers.

C. Fragility

The fragility concept, as introduced by Angell, describes the different temperature dependencies of viscosity.Reference Angell²⁴ The change in viscosity or relaxation time reflects an intrinsic property of glass-forming liquids, and classifies liquids between two extremes: the strong extreme, where viscosity and relaxation time behave in an Arrhenius fashion with respect to temperature; and the fragile extreme, where these properties tend toward more non-Arrhenius behavior.Reference Evenson, Gallino and Busch²⁵ Metallic glasses display intermediate or strong fragility strength, as indicated by the fragility parameter, m.Reference Penera²⁶ From the Vogel–Fulcher–Tammann (VFT) fit, the m at a particular T_g can be calculated fromReference Böhmer, Ngai, Angell and Plazek²⁷

(2)$$m = {{DT_0 T_g } \over {(T_g - T_0 )^2 \ln 10}},$$

where D and T ₀are fitting parameters derived from VFT equation.

Figure 3(a) shows the DSC curves of the Sr₆₀Mg₁₈Zn₂₂glass with heating rate over three orders of magnitude. The heating rates were 2, 5, 10, 20, 40, 80, 120, and 160 K/min, respectively. The corresponding glass transition temperatures were 332, 328, 331, 336, 341 K, 347, 349, and 352 K, respectively. A functional form of VFT type, which is suitable for fitting the present results, isReference Brüning and Samwer²⁸

(3)$$\ln \phi \, = \,\ln B - {{DT_0 } \over {T_g - T_0 }},$$

FIG. 3.

(a) DSC curves of Sr₆₀Mg₁₈Zn₂₂ BMG at different heating rate and (b) VFT relation between glass transition temperature T_g and heating rate ϕ of Sr₆₀Mg₁₈Zn₂₂BMG.

where $\phi $ is the heating rate, and T_g is the glass transition temperature. B, D, and T ₀ are adjustable parameters. From the VFT fit [Fig. 3(b)], D and T ₀ of Sr₆₀Mg₁₈Zn₂₂ are determined to be 12.4 and 205 K, respectively. When the heating rate is 20 K/min, the glass transition temperature T_g is 336 K. The value m calculated from Eq. (2) is 21. It can be classified to the strong liquids in the framework of fragility, and the value m is smaller than other common BMGs such as Zr- (m ∼ 34–39), Fe- (m ∼ 32–37), Mg- (m ∼ 39–46), and RE- (m ∼ 21–53) based BMGs.Reference Böhmer, Ngai, Angell and Plazek^27, Reference Borrego, Conde, Roth and Eckert^29–Reference Luo, Zhao, Pan, Wang and Wang³⁴ It is notable that some values of m are not determined from some of these methods, and it may cause some discrepancy.

It has been reported that the fragility of metallic glass is correlated with the number of components in the alloy.Reference Shadowspeaker and Busch³⁵ In most cases, the metallic glass-forming liquids become stronger with increase in the number of elements. Metallic glass ribbons with two or three elements are more fragile compared with BMGs with three or more elements.Reference Park, Na and Kim³⁰ The value m of the new developed Sr₆₀Mg₁₈Zn₂₂alloy indicates that the Sr-based glass-forming liquids are rather strong. If more elements are added to the alloy, even stronger liquids are to be expected. The metallic glass-forming system is one of the simplest systems where the microstructure units are composed of metallic atoms. The strong metallic glass-forming liquid may facilitate the study of some fundamental issues such as glass transition and relaxation in glass.

High-mixing entropy is a new route for designing novel BMGs.Reference Takeuchi, Chen, Wada, Yokoyama, Kato, Inoue and Yeh^36, Reference Gao, Zhao, Ke, Ding, Wang and Bai³⁷ The Sr₂₀Ca₂₀Yb₂₀Mg₂₀Zn₂₀ alloy was determined from the prototype Sr₆₀Mg₁₈Zn₂₂ BMG in accordance with strategic alloy design. The fragility of Sr₂₀Ca₂₀Yb₂₀Mg₂₀Zn₂₀ BMG was determined using the same method as used for Sr₆₀Mg₁₈Zn₂₂. The adjustable parameters D and T ₀ were 107 and 80.6 K, respectively. The fragility index m was 17 calculated from Eq. (2) (T_g = 357 K, heating rate 20 K/min). It is the lowest value recorded among known metallic glasses.

D. Low elastic constant and low glass transition temperature

The longitudinal (v_l) and transverse (v_s) velocities, densities, elastic constants, Poisson’s ratio, and Debye temperature of Sr-based BMGs are listed in Table II. The Sr-based BMGs have relatively low density (ρ ∼ 3.5 g/cm³). The density of Sr-based BMGs is just higher than that of Ca-based BMGs,Reference Senkov, Miracle, Keppens and Liaw²³ but much lower than other conventional BMGs such as Zr-, Cu-, and Pd-based BMGs.Reference Wang¹³ The Sr-based BMGs have the lowest elastic constant among all the known BMGs. For Sr₂₀Ca₂₀Yb₂₀Li₁₁Mg₉Zn₂₀ BMG, the Young’s modulus is as low as 16.1 GPa, which is comparable to the human bone (2–18 GPa). The Sr-based BMGs have small value for Poisson’s ratio. For Sr₆₀Mg₁₈Zn₂₂, the Poisson’s ratio ν is just 0.276. Brittleness is expected in metallic glasses with smaller values of Poisson’s ratio.Reference Lewandowski, Wang and Greer³⁸ However, due to the low glass transition temperature, uncommon room temperature rheology is observed. The Sr-based BMGs have low Debye temperature θ_D. Debye temperature is indicative of the relative strength of the atomic bond. The low Debye temperature implies weak bonding of the alloy atoms, which is consistent with the low elastic constants.Reference Wang¹³

TABLE II.

Acoustic velocity, density, elastic constant, Poisson’s ratio, and Debye temperature of Sr-based BMGs.

The thermodynamic parameters of Sr-based BMGs derived from DSC curves are listed in Table III. The BMGs have the lowest glass transition temperature among all the known BMGs. For Sr₆₀Li₁₁Mg₉Zn₂₀, the T_g is just 26 °C, which is at room temperature. However, due to the ultralow T_g, it is unstable at room temperature. It begins to crystallize at about 1 h after being cast, and will achieve fully crystallized phase in 24 h as indicated by x-ray diffraction. The Sr₆₀Li₅Mg₁₅Zn₂₀ with a little higher T_g (42 °C) is much more stable. It remains in amorphous state after 1 wk at room temperature. The Sr-based BMGs was designed by elastic correlations, which also confirm the elastic criterion well. The Li (Young’s modulus E: 4.9 GPa) have the lowest elastic moduli among all BMG-forming elements. The glass transition temperature can be tuned by Li content (Fig. 4). As the Li content increases, the T_g of the BMGs shifts to lower temperature, and finally reaches to room temperature.

FIG. 4.

DSC curves of Sr-based BMGs with different Li content.

TABLE III.

Thermodynamic parameters of Sr-based BMGs.

E. Room temperature rheology

We note that brittleness is expected in metallic glasses with small values of Poisson’s ratio or large values of the ratio of shear modulus to bulk modulus.Reference Lewandowski, Wang and Greer³⁸ The Poisson’s ratio is regarded as indicator of the plastic character for BMGs and this idea was verified in various BMGs. The Sr-based BMGs have small Poisson’s ratio, and it should be attributed to the class of brittle BMGs. However, the BMG could show superplasticity at room temperature due to the ultralow T_g. It is well known that the deformation behavior of metallic glasses scales with glass transition temperature T_g. The transition from inhomogeneous to homogeneous flow occurs at approximately 0.8 T/T_g. For this alloy, room temperature lies within the homogeneous flow regime (T/T_g = 0.93). Figure 5 shows the imprinted pattern on the BMGs. The BMG was under a pressure of 50 MPa for 24 h, and the smooth surface emerged as square array. The imprinting for other BMGs is usually carried out in the supercooled liquid region with much higher temperature, but this BMG can be imprinted at room temperature. The polymer-like thermoplastic behavior is convenient for micro- and nanomanufacture.Reference Kumar, Tang and Schroers^6, Reference Kumar and Schroers³⁹

FIG. 5.

SEM image of square array on the surface of Sr-based BMG imprinted at room temperature.

Figure 6(a) shows the stress–strain curves of the Sr₂₀Ca₂₀Yb₂₀Li₁₁Mg₉Zn₂₀ BMG. When the strain rate is 1 × 10⁻³ /s, the sample breaks into pieces just after elastic deformation, which resembles Mg- and Ca-based BMGs.Reference Wang, Yu and Bai^40, Reference Wang, Liaw, Senkov, Miracle and Morrison⁴¹ The inset on the left shows the SEM image of the pieces. However, when the strain rate decreases to a slightly lower value of 1 × 10⁻⁴ /s, the BMG exhibits a complete change in deformation behavior. It shows elastic strain limit of ∼2% before yielding, and then displays superplasticity as observed in the supercooled liquid state for other BMGs.Reference Kato, Kawamura, Inoue and Chen^42–Reference Harmon, Demetriou, Johnson and Tao⁴⁴ The sample can be compressed to 70% of its original height without cracking, and further compression is still possible to extend the deformation. The XRD examination verifies that the severe deformed sample remains fully amorphous state. The scanning electron microscopy (SEM) shows that the severe deformed specimen keeps smooth surface. No primary shear band and other observable shear bands can be found, which confirms the uniform deformation and homogeneous flow of metallic glass at room temperature.Reference Zhao, Xia, Bai, Zhao and Wang⁴⁵

FIG. 6.

(a) Different deformation type of Sr₂₀Ca₂₀Yb₂₀Li₁₁Mg₉Zn₂₀ BMG at room temperature. The inset at left shows that the BMG is brittle at high strain rate, while the inset at right shows that the BMG is superplastic at low strain rate. (b) Stress–strain curves of Sr₂₀Ca₂₀Yb₂₀Li₁₁Mg₉Zn₂₀BMG at different strain rate.

For homogeneous flow in metallic glass, the flow stress changes with different strain rate. Figure 6(b) shows the stress–strain curves of the Sr₂₀Ca₂₀Yb₂₀Li₁₁Mg₉Zn₂₀ with wide strain rate region. The yield stress and steady flow stress increase with strain rate. It belongs to Non-Newtonian fluid, which is the characteristic of BMG for homogeneous deformation. The compression behavior of this BMG can be expressed by free volume theory. Spaepen gives the stress–strain relation in metallic glass based on free volume theory. The original equation is written in shear stress and shear strain rate.Reference Spaepen⁴⁶ For normal stress and normal strain rate, the equation changes to Reference Bletry, Guyot, Blandin and Soubeyroux⁴⁷:

(4)$${{ \dot\varepsilon}} = 2c_f v_D \exp \left( { - {{\Delta G^m } \over {kT}}} \right)\sinh \left( {{{{\rm{\sigma }}V} \over {2\sqrt 3 kT}}} \right),$$

where ${{\dot \varepsilon }}$ is the normal strain rate, c_f is the concentration of defect, v_D is the Debye frequency, ΔG^m is the activation free energy migration, σ is the normal stress, and V is the activation volume.

The experiments were carried out at room temperature. If relatively small variation of the flow defect concentration with strain is assumed, the defect concentration depends only on temperature. Since the experiments were carried out near the glass transition temperature for long duration, the defect concentration when deformation starts is supposed to be equal to its equilibrium value.Reference Bletry, Guyot, Blandin and Soubeyroux⁴⁷ In such a framework, Eq. (4) can be rewritten:

(5)$${{\dot \varepsilon }} = {{\dot \varepsilon }}_{\rm{0}} \sinh (a{\rm{\sigma }}),$$

where ${{\dot \varepsilon }}_{\rm{0}} = 2c_f v_D \exp \left( { - {{\Delta G^m } \over {kT}}} \right)$ and $a = {V \over {kT}}$. Both of them are constant based on the supposition above.

The strain rate and the maximum flow stress follow Eq. (5). At low strain rate, the maximum flow stress grows with strain rate. However, the maximum flow stress will not exceed the fracture stress, which is regarded as the intrinsic character of BMGs at strain rate covering the entire quasistatic range.Reference Schuh, Hufnage and Ramamurty⁴⁸ When the maximum flow stress reaches fracture stress (for this BMG, the critical strain rate is 1 × 10⁻³/s and the critical stress is 400 MPa as indicated by experiment), the sample breaks into pieces. The deformation behavior of the Sr-based BMGs changes at a critical strain rate, and the transition from homogeneous deformation to inhomogeneous deformation occurs.

F. Corrosion behavior

Strontium is friendly to human body, and it is useful for the treatment and prevention of osteoporosis. However, crystalline Sr is extremely reactive. It reacts with water strongly. The reaction gives a lot of heat, and produces large amounts of gas. Metallic glasses usually have much more desirable corrosion resistance than their crystalline counterparts.Reference Dahlman, Senkov, Scott and Miracle⁴⁹ Mg- and Ca-based BMGs glasses are regarded as promising biodegradable materials.Reference Zberg, Uggowitzer and Löffler^4, Reference Gu, Zheng, Zhong, Xi, Wang and Wang^50, Reference Wang, Xie, Li, Wang, Zhao, Zhang, Bai, Zheng and Qing⁵¹ Strontium-based BMGs constitute a new class of alkaline earth-based BMGs. The stability of Sr-based BMGs in aqueous environment determines whether the material is suitable for biodegradable application.

The water degradation of Sr-based BMGs in water can be modulated by minor addition. Figure 7(a) shows the weight change of Sr-based BMGs in deionized water, where m₀ represents the original alloy weight, and m represents the weight that the alloy has been immersed in water for some time. For Yb-free Sr-based BMGs, bubbles are produced immediately after the BMGs are immersed in water. The solid alloys dissolved in water in less than 1 min and the water became muddy black due to the violent reaction.Reference Zhao, Li, Zhao, Pan and Wang⁵² The Yb-doped Sr-based BMGs show totally different behavior in water. They are much more stable than the Yb-free ones in deionized water. They could stay in water for more than a week without observable weight change.

FIG. 7.

(a) Weight change of Sr-based BMGs in deionized water. (b) Weight loss of Sr₄₀Mg₂₀Zn₁₅Cu₅Yb₂₀ and Ca₆₀Mg₂₀Cu₁₀Ga₁₀BMGs in Hanks solution.

Hanks solution is a salt solution usually used as simulated body fluids. The degradation behavior of Sr-based BMG in Hanks solution can help us to evaluate the feasibility of it as biodegradable materials. Figure 7(b) shows the weight loss of Sr- and Ca-based BMGs in Hanks solution. The weight loss of the Sr₄₀Yb₂₀Mg₂₀Zn₁₅Cu₅BMG in Hanks solution is much slower than the Ca-based BMG. The slowdown degradation in Hanks solution is favorable for biodegradation materials. Fast degradation rate is harmful to human body because the degradation process is usually accompanied with hydrogen evolution, and it is not conducive for the functional requirement of the human body. The Yb-doped Sr-based BMGs might be potential biodegradation materials, and further studies are needed to prove the supposition.