A lightweight strain-glass alloy showing nearly temperature-independent low modulus and high strength

Chang Liu Xi’an Jiaotong University Jingxian Tang Xi’an Jiaotong University Yuanchao Ji Xi’an Jiaotong University Kazuhiro Otsuka National Institute for Materials Science Yu Wang MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, School of Science, Xi’an Jiaotong University, Xi’an, 710049 Mengrui Hou Xi’an Jiaotong University Yanshuang Hao Xi’an Jiaotong University Shuai Ren Xi’an Jiaotong University Xiaobing Ren (  Ren.Xiaobing@nims.go.jp ) National Institute for Materials Science https://orcid.org/0000-0002-4973-2486

Here we report a surprising nding that with a slightly higher Sc doping by 0.8 at. %, a Mg-21.3Sc alloy shows a completely different performance as compared with the Mg-20.5Sc SMA. It exhibits desired properties of low density (~2 g/cm 3 ), near-constant low Young's modulus (~19.7-22.6 GPa) but high yield strength (~200-270 MPa) from ambient to cryogenic temperatures (298-123 K), which yield the highest elastic energy density (U ~0.5 kJ/kg) at a moderate stress of 200 MPa among known engineering elastic materials ( Fig. 1a) 5,6,8,26,[29][30][31][32][33] . Thus, it overcomes the trade-off relation between low modulus and high strength and forms a virgin region in a modulus-strength chart of Mg-alloys (Fig. 1b) [14][15][16][17][18][19][20][21][22][23][24][25][26] . Moreover, this lightweight elastic material has a high fatigue life of over 1 million cycles (Fig. 1c). Such a performance makes it a promising material for lightweight elastic components in the aerospace and space applications. In the following, we shall rst show the detailed mechanical properties of Mg-21.3Sc alloy, and then reveal that they originate from a strain-glass transition, which explains why the performance changes dramatically with such a small Sc concentration change from Mg-20.5Sc to Mg-21.3Sc.
Herein the inset of Fig. 1a shows stress-strain curves of the Mg-21.3Sc alloy at ambient temperature: the cold-rolled (CR) Mg-21.3Sc alloy exhibits a higher yield strength (σ s ~270 MPa) and a higher elastic strain limit, as well as a slightly increase of Young's modulus (E ~22.6 GPa), as compared with the waterquenched (WQ) one (σ s ~200 MPa, E ~19.7 GPa). The amount of elastic storage energy in Mg-21.3Sc alloy and gum metal under a moderate stress level of 200 MPa was also demonstrated in the inset of Fig.  1a. Fig. 1a further shows a comparison of the elastic energy density among various metallic and organicbased elastic materials including steels, Al-alloys, Ti-alloys, Mg-alloys, GFRP, carbon ber reinforced plastic (CFRP), and our strain glass Mg-21.3Sc alloy 5,6,8,26,[29][30][31][32][33] . The low density, low Young's modulus and high yield strength of Mg-21.3Sc alloy make it possess the highest elastic energy density U= ~0.5 kJ/kg for a given stress of 200 MPa. Fig. 1b shows that the Mg-21.3Sc alloy has an unusual combination of low modulus (19.7-22.6 GPa) and high strength (200-270 MPa) among known Mg-alloys [14][15][16][17][18][19][20][21][22][23][24][25][26] , and thus it overcomes the commonly observed trade-off relation between modulus and strength, which is well known in all structural materials 29 . The data of other Mg-alloys are from the literature and summarized in Supplementary Table   S1. The combination of low modulus and high strength in the Mg-21.3Sc alloy also indicates that it has a higher elastic strain limit compared with other Mg-alloys (see Supplementary Fig. S1). Fig. 1c shows that the CR Mg-21.3Sc alloy presents a fatigue-resistant performance over 1 million cycles, which is superior to GFRP and high-strength aluminum alloys (2024Al T3) 34,35 .
We further present the temperature independence of mechanical behaviors of the Mg-21.3Sc alloy. Fig. 2a shows stress-strain curves of Mg-21.3Sc and Mg-19.5Sc alloys at different temperatures. During cooling, the elasticity of Mg-21.3Sc alloy becomes better, manifested by better recoverability. By contrast, the Mg- 19.5Sc alloy exhibits quasi-linear elasticity with lower yield strength and lower Young's modulus at ambient temperature (see dashed line in Fig. 2a). Interestingly, with cooling this quasi-linear elasticity disappears. Instead a nonlinear elastic behaviour with high recoverable strain and large hysteresis emerges, which is known as superelasticity and was also reported in Mg-20.5Sc alloy 27 . Later, these different mechanical behaviors of Mg-Sc alloys will be explained in a uni ed framework of strain-glass. Fig. 2b shows the comparison between the Mg-21.3Sc alloy and normal non-transforming Mg alloys. For the non-transforming Mg-alloys of AZ91 and LA141, the modulus increases with decreasing temperature, which is a normal elastic hardening behavior with cooling; for the Mg-21.3Sc alloy, the modulus exhibits a nearly invariant behavior with lowering temperature. This will also be explained based on the strain-glass.
In the following, we shall reveal that the Mg-21.3Sc alloy is not a martensitic alloy, rather it undergoes a strain-glass transition proved by four sets of evidence 36-39 : (i) an invariance of average structure with varying temperature, (ii) frequency dependence of both elastic modulus and internal friction, (iii) nonergodicity, and (iv) the formation of nano-domains.
Firstly, we present data of the invariance of average structure. Fig. 3a shows differential scanning calorimetry (DSC) results, which reveal an absence of the temperature-induced martensitic transformation from 350 to 123 K 33,40,41 . In-situ X-ray diffraction (XRD) patterns in Fig. 3b show almost no change from 298 to 123 K, keeping a bcc (β) structure with a negligible amount of hcp (α) phase. Note that the presence of α-phase is due to the metastability of β-phase, and thus the α-phase can be formed during water-quenching 27 (see elements distribution analysis in Supplementary Fig. S2).
Although there is no temperature-induced martensitic transformation in the Mg-21.3Sc alloy, we present the frequency dependence of both elastic modulus and internal friction, which reveals a gradual slowingdown of dynamics of a strain-glass transition 36 . Fig. 3c shows that both the storage modulus and internal friction (tan δ) curves exhibit the frequency dispersion, which can be demonstrated by a decrease of peak temperature (T g ) in internal friction curves with decreasing frequency from 20 to 0.2 Hz.
Moreover, this frequency-dependent anomaly obeys a Vogel-Fulcher relation 42 where ω is the frequency, ω 0 the frequency pre-factor, E a the activation energy, k B the Boltzmann constant, T g the strain glass transition temperature, and T 0 the ideal freezing temperature (~198 K, see inset of Fig. 3c). The frequency-dependent behavior at T g is a key feature of the strain-glass transition 36,37,43 .
Another critical feature of strain-glass transition is the nonergodicity or history-dependence, which can be demonstrated through zero-eld-cooling (ZFC)/ eld-cooling (FC) measurements 38 . The detailed experimental procedures can be found in Supplementary Fig. S3. Fig. 3d shows that upon heating the difference between ZFC and FC curves becomes smaller and gradually coincides at high temperatures. The large deviation in ZFC/FC curves below T g (peak temperature in the ZFC curve) demonstrates the history-dependence of strain state, a direct evidence for the nonergodicity [37][38][39] .
Finally, we show microscopic evidence of the strain glass in WQ Mg-21.3Sc alloy in Fig. 4 and 5. At ambient temperature, a tweed-like or cross-hatched microstructure was observed in Fig. 4a. Moreover, two kinds of diffused 1/2(002) and 1/2(112) superlattice re ections appear in diffraction patterns along [110] b and [111] b zone axes (marked by green cycle and yellow triangles in insets of Fig. 4a and b). In the equilibrium phase diagram of Mg-Sc alloy 27 , the β-phase is metastable at ambient temperature and it will transform into a chemically ordered bcc structure, i.e., B2 phase, which produces the 1/2(002) re ections. Therefore, the diffused 1/2(002) superlattice re ections in the diffraction patterns should stem from the chemical ordering during water-quenching. On the other hand, the appearance of 1/2(112) re ections is known to result from the orthorhombic symmetry of martensitic phase in Mg-Sc SMA 27,44 (also see Supplementary Fig. S4). Thus, the diffused 1/2(112) superlattice re ections indicate local orthorhombic symmetry of strain-glass nano-domains.
The high-resolution transmission electron microscopy (HR-TEM) images in Fig. 4b and c show various modulated patterns. Then, we tried a technique of an inverse fast Fourier transform (IFFT) 39 , which is similar with the production of dark eld image. Fig. 4d shows the corresponding IFFT image of Fig. 4c, which was obtained via selecting all 1/2(112) superlattice re ections. Many randomly distributed bright nano-regions (~10 nm), i.e., strain-glass nano-domains, were observed in Fig. 4d (more evidence in Fig.  5).
The formation of nano-domains is further con rmed by in-situ TEM observations. Fig. 5 shows the evolution of strain-glass nano-domains with temperature. The dark eld images were obtained through selecting the 1/2(112) superlattice re ection in the diffraction pattern along [110] b zone axis. At 298 K, the morphology of dark eld image shows many nano-sized bright regions (strain-glass nano-domains) in the matrix, which is well consistent with the IFFT result in Fig. 4d. Upon cooling, the size of nanodomains became larger and the volume fraction also increased, as shown in Fig. 5b. Correspondingly, the brightness of 1/2(112) spots in the diffraction pattern also became stronger (see inset of Fig. 5b).
Next, we shall reveal the relationship between the unusual properties and the strain glass in Mg-21.3Sc.
As reported in a typical Ti 50-x Ni 50+x strain-glass system where excess Ni atoms act as the defects 36,37,40 , the mechanical properties change abruptly around a critical composition from the martensite to the strain glass. In alloys with lower defect concentrations (e.g., Ti 48.7 Ni 51.3 ), the martensitic transformation occurs upon cooling or under external stress, and thus the shape-memory effect and superelasticity can be observed. By contrast, due to the high energy barrier caused by the higher concentration of defects, some strain-glass alloys (e.g., Ti 48 Ni 52 ) cannot transform into the martensite through neither cooling nor applying an external stress, thereby leading to the disappearance of shape-memory effect and superelasticity. But the quasi-linear elasticity can be found in these strain-glass alloys, because strainglass nano-domains can respond the external stress 37,40,41 .
Following above analysis, it is easy to understood the sharp change in mechanical behavior from the superelasticity in Mg-19.5Sc to the quasi-linear elasticity in Mg-21.3Sc, where Sc atoms act as the defects (for the CR alloy the defects also include cold-rolling induced dislocations). The low Sc concentration in Mg-19.5Sc with large temperature-induced martensitic domains (see Supplementary Fig S4), explains the superelasticity at a low temperature of 123 K (Fig. 2a). The high Sc concentration in Mg-21.3Sc explains the observation of quasi-linear elasticity (Fig. 2a). The nano-sized strain domains in Mg-21.3Sc can further prevent the movement and development of dislocations and microcracks hence to ensure a long fatigue life under cyclic stress.
The evolution from the martensite to the strain glass also associates with the change of mechanical properties from "soft" to "hard", as manifested by a decrease of recoverable strain and an increase of both stress and modulus. The increase of defect concentration leads to a decreased volume fraction of strain domains and thus a decrease from a large recoverable strain (>1.5%) in Mg-19.5Sc to a small one of ~1% in Mg-21.3Sc (see Fig. 2a). It also leads to a reduction of the elastic instability of austenite towards martensite, and thus yields an enhanced effect on both the modulus and the critical stress at which a stress-induced martensitic transformation occurs. As shown in the Supplementary Fig. S5, the modulus increases in a sequence of WQ Mg-19.5Sc, WQ Mg-21.3Sc, and CR Mg-21.3Sc. Note that for the Mg-21.3Sc the critical stress is even larger than the yield stress. In short, the Mg-21.3Sc alloy, being a strain glass, exhibits a higher critical stress, a higher modulus and a lower recoverable strain compared with the martensitic Mg-19.5Sc.
On the other hand, when we compared the Mg-21.3Sc alloy with normal non-transforming Mg-alloys, the existence and continuous formation of strain-glass nano-domains in Mg-21.3Sc alloy (shown in Fig. 4 and 5) provide an elastic softening mechanism to offset the normal elastic hardening. As a result, the low Young's modulus is achieved and keeps nearly unchanged.
In conclusion, a new type of strain-glass Mg-alloys has been reported in comparison with nontransforming and martensitic Mg-alloys. The strain-glass Mg-21.3Sc alloys exhibit low density, low modulus and high yield strength, thereby leading to a record-high elastic energy density under a moderate stress. Moreover, the performance can persist for 1 million stress cycles and over a wide temperature range from ambient to cryogenic temperatures. Such a property combination has not been achieved before. The lightweight strain glass Mg-21.3Sc alloy may have potential for use as light spring materials in adaptive systems and vibration control for space exploration, together with as implant materials in orthopedic applications due to its modulus proximity to human bones [1][2][3][4][8][9][10] .

Sample preparation
Mg-21.3Sc and Mg-19.5Sc alloys were melted and solidi ed in an induction furnace under Ar atmosphere using pure Mg and Sc (99.99%). The cast ingots with 15 mm in diameter were hot-rolled at 600 o C into sheets with a thickness of 1.5 mm. Then, specimens with different shapes were cut from the sheet, and further heat-treated at 690 o C for 0.5 h, followed by water quenching (termed WQ herein) to obtain a bcc (β) phase. Cold-rolled samples (termed CR herein) with a thickness of 1 mm were made through rolling the annealed sheet (at 600 o C). The chemical composition was determined by Energy Dispersive Spectrometer (EDS) on a Quanta 250 FEG FEI at 20kV and chemical analysis.

Tensile testing
The stress-strain behaviors of hot-rolled and cold-rolled specimens were examined by cyclic tensile testing with a Tension machine. Specimens for tensile testing were cut from the hot-rolled and cold-rolled sheets, with a gauge length and width being 40 mm and 3.6 mm, respectively. The specimens were nally mechanically polished to 0.41 -0.67 mm in thickness using ner graded SiC papers and diamond slurry to remove the surface oxide layer. Cyclic tensile testing was performed at 123, 173, 213, 298 K at a crosshead speed of 0.3 mm/min.

Structural determination
The structures at different temperatures were determined by X-ray diffraction (Shimadzu 7000 XRD) with a Cu-Kα source at 40 kV and 40 mA using the θ/2θ scan mode. The microscopic observations at different temperatures were performed by TEM (JEM 2100F), recorded using a GATAN CCD slow scan camera and analyzed by the Digital Micrograph software. The sheet samples were cut and mechanically polished down to about 100 μm. Subsequently, disk samples of 3 mm in diameter were punched from the thin sheet samples and then further thinned by dimple grinding and Ar-ion milling at 4-5 keV.

Strain glass transition
Heat ow was analyzed with a DSC-Q200 from TA instrument at a heating/cooling rate of 10 K/min. Dynamical mechanical analysis (DMA TA Q800) was employed to measure the storage modulus and internal friction as a function of temperature under different frequencies (0.2, 0.4, 2, 4, 10 and 20 Hz) using a three points bending mode with a constant amplitude of 3 mm and a cooling/heating rate of 2 K/min. Zero-eld-cooling/ eld-cooling (ZFC/FC) experiments were also carried on the DMA using a three point bending mode under the stress of 40 MPa (see Supplementary Fig. S3).  Supplementary Table S1. c, Fatigue test of the Mg-21.3Sc alloy for 1 and 106 cycles.