Magnesium and its alloys exhibit the lowest density of all engineering metals and continue to play an increasingly significant role in aerospace, automotive, consumer electronics and biomedical applications as a result of their high specific strength, stiffness and biocompatibility. Compared to crystalline alloys, amorphous alloys (metallic glasses) possess superior strength, elastic limits and corrosion resistance as a result of their homogeneous glassy structure^{1, 2}. They also exhibit a broad range of fracture toughness properties, ranging from extremely brittle to some of the toughest materials known to date^3–5.

Since their discovery in 1977⁶ numerous Mg-based amorphous alloys and subsequent multi-component bulk metallic glasses (BMGs) have been developed. The majority of these are based on Mg–TM–RE or Mg–TM–Ca ternary systems (where TM = transition metals Cu, Ni, Zn, Ag and RE = Y, Gd, La, Nd, Ce, etc.)^7–14. Some show exceptional glass-forming ability with critical casting sizes up to 27 mm¹⁵, placing them amongst the highest glass-forming alloy families. However, Mg-based BMGs have yet to realise their full potential in long-term load bearing or functional applications due to their intrinsically brittle nature and relatively short structural relaxation times^{16, 17}. To date, modest Mg-based ‘bulk’ glass ductility has only been observed in Mg-rich Mg–Ni–[Gd,Nd]^{9, 10}, and Mg–Ni–Ca¹⁴ alloy systems. It has been postulated that the degree of electronic charge transfer between constituent elements (i.e. the degree of covalency in atomic bonds) needs to be minimised to improve ductility^{16, 18, 19}, and the glass transition temperature raised in order to slow ambient-temperature structural relaxation which also leads to embrittlement¹⁶.

In comparison, plasticity in pure or low-solute polycrystalline alloys results from atoms easily gliding past one another via dislocation-type mechanisms²⁰. From an electronic bonding perspective this atomic translation is relatively easy, as the core charges of the metal ions are uniform and generally only involve outer shell electrons, with little charge transfer or bond directionality (covalency). Hence, atoms need to only move from one crystal lattice site to the next by overcoming a low-energy barrier before reaching an identical neighbouring site^20–22. In a multi-component metallic glass, plasticity occurs via local shear transformations^{23, 24} (similarly, atoms must glide past one another to neighbouring structural sites). However, depending on the atoms present, complex intra-electron orbital bonding between dissimilar constituents may occur. This often results in considerably stronger and/or more directional (covalent) bonding between atoms through electron band hybridisation^{18, 19, 25}. It is well-known that as the number of electrons involved in a hybridised bond increases, the energy/strength of this bond increases (i.e. in the order s-, p-, d- and f-electron bands) and in the case of p-, d- and f-bands, bonding is highly directional. Hence when atoms of different ion-core charges in a multicomponent metallic glass try to glide past one another during shear, the energy required is much higher and often directionally dependent. This results in a considerably altered mechanical response in glasses during deformation when compared to pure (crystalline) metals and is expected to be more closely akin to that of high-strength (covalent) intermetallics^{21, 22}.

In this study we have applied a novel approach to developing Mg-based BMGs with high glass-forming ability and ductility. We implemented a predictive topological model^{26, 27} to locate the maximum glass-forming region of Mg-rich metallic systems of interest. This was combined with the anticipated electronic bonding states/interactions between constituents that minimise bond directionality, allowing atoms to be sheared more uniformly during deformation^{21, 22} in order to maximise glass ductility.

It has been shown that a higher solvent content minimises covalent bonding and improves ductility in Mg-based glasses^{16, 19}, hence higher Mg-contents are preferred. Despite their relatively high density and costs, precious metals exhibit exceptional properties with respect to ductility in BMGs. Some of the toughest materials known are Pd- and Pt-rich metallic glasses^{4, 5}. When alloyed with another metal, elements that have a completely- or near-filled d-band require few if any electrons to fill the band and hence it tends to remain closer to the core of the atom (below the Fermi level, see ref. 28 for band locations of individual elements), contributing less to bonding²². Bonding in these alloys is primarily due to s-band interactions, which have no directionality and lower bond energy, thus during deformation atoms can glide past one another with relative ease leading to ‘more metallic’ or ductile behaviour. This bonding nature is also responsible for the bulk and shear moduli of these elements (i.e. their high Poisson’s ratio: Ag = 0.37, Au = 0.4, Pd = 0.39, Pt = 0.38), which are critical to shear-band branching and crack-shielding mechanisms in metallic glasses^{4, 5, 23, 29}.

Recently, Laws et al. reported bulk glass-formation in the Mg–Ag–Ca ternary system in the Mg-rich region¹³, highlighting this as a potential precious-metal-containing composition space for ductile Mg-based glasses. Further, it has been found that the MgAg intermetallic compound exhibits considerable ductility, shown to be due to the full d-electron shell of Ag remaining below the Fermi level when bound to Mg²². The Mg–Pd binary alloy system³⁰ exhibits similar attributes to Mg–Ag, with an eutectic reaction at ~17 at.% Pd (the same concentration as the Mg-rich Mg–Ag eutectic reaction³¹). Glass formation has also been reported in the binary Mg–Pd system for a composition range of 10–35 at.% Pd³². Based on this, Ag and Pd were selected as precious-metal additions with minimal d-band electron interactions for ductile glass development.

Ca is a large, chemically active alkaline metal (atomic radius ~197 pm) with an electronic configuration 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² (no d-electron band in its ground state), effective in improving glass-forming ability in Mg-based glasses^12–14. Yb is a unique rare earth/lanthanide metal that can exhibit a full f-electron shell and the stable oxidation state of +2 ([Xe] f¹⁴6s²), making it more closely akin to Ca. The 4d-electron band of Yb resides beneath the 5s, 5p and 4f-bands, respectively, and is not expected to interact in these alloys (the 5d band is empty). It is also known that 4f electrons have a high probability of being close to the nucleus of an atom or ion, resulting in little overlap between the orbitals of lanthanides and binding ions³³. Similar to Ca, Yb has a large atomic radius of ~194 pm when adopting the full f-electron shell state and Yb has been shown to behave similarly to Ca with respect to glass-forming ability in other Mg-based systems³⁴. Based on this, Ca and Yb were selected as potential alloying elements.

The efficient packing of atoms in an amorphous structure is known to hinder atomic diffusion upon cooling, retarding crystallisation kinetics, leading to greater glass-forming ability^{13, 26, 27}. A predictive topological model (method described in detail in ref. 27) that determines composition space where efficient packing around each atom is achieved was utilised for alloy development. This model uses a ‘hard sphere’ approximation where, based on the alloy composition and the radii of the elements present, every atom in a given atom’s first coordination shell touches that central atom and its nearest neighbours, hence achieving global packing efficiency. Based on these concepts, a range of Mg-rich ternary alloys from the Mg–Ag–Ca, Mg–Ag–Yb, Mg–Pd–Ca and Mg–Pd–Yb systems were prepared and analysed.

Figure 1(a–d) shows the Mg-rich composition space tested within this study for the Mg–Ag–Ca, Mg–Ag–Yb, Mg–Pd–Ca and Mg–Pd–Yb ternary alloy systems. Red crosses indicate the compositions of the alloys produced, and their size indicates their relative glass-forming ability. From binary system information^{30, 31, 35, 36} and DSC data generated from this work, a ternary liquidus iso-surface was produced for each system. Liquidus lines are indicated in black and ternary eutectics in hollow black circles. Also indicated are the precise efficient packing zones/compositions for each atomic centre. The atomic radii used for these calculations were Mg = 160 pm, Ag = 144 pm, Pd = 139 pm, Ca = 197 pm, and Yb = 194 pm^{37, 38}.Figure 1

Ternary liquidus iso-surfaces of the Mg-rich regions in the (a) Mg–Ag–Ca, (b) Mg–Ag–Yb, (c) Mg–Pd–Ca, and (d) Mg–Pd–Yb alloy systems, determined using DSC data and binary phase diagram information^{30, 33, 35, 36}. Also shown are the glass-forming alloy compositions tested, their relative glass-forming abilities (critical casting diameters) and the efficiently-packed cluster regions determined, where blue indicates Ag- or Pd-centred clusters, green Mg-centred clusters and red Ca- or Yb-centred clusters.

A range of ductile Mg-rich BMGs from the Mg–Ag–Ca, Mg–Ag–Yb, Mg–Pd–Ca, and Mg–Pd–Yb ternary systems was discovered using a topologically efficient packing model and electron band theory. The Pd-containing alloy systems exhibit glass-forming ability superior to that of the Ag-containing alloys. The Mg–Pd–Ca BMGs exhibit high ductility and the highest thermal stability of any Mg-based BMGs to date, while the Mg–Pd–Yb BMGs exhibit high glass-forming ability and the highest compressive plastic strain to failure reported for a Mg-based BMG. Based on these results, our observations and theoretical analysis, it is expected that ductility will be significantly improved in these and other BMGs if d- and f- band electron interactions can be constrained in participating alloy elements.

Nominal alloy compositions (shown in Tables 1–4) were prepared using pure metals: Mg (99.95 wt.%), Ag (99.95 wt.%), Pd (99.95 wt.%), Ca (99.8 wt.%) and Yb (99.99 wt.%). These metals were alloyed in graphite crucibles using an induction furnace in an argon-purged (99.997 wt.%) atmosphere by completely dissolving the solute elements in the molten Mg balance at 750 °C. Samples were produced for each composition by tilt casting the alloys into a wedge-shaped (10:1 taper) copper mould at temperatures of 100 to 150 °C above the liquidus. Compositions of good glass-forming ability were vacuum cast into rods of varying thickness, from 1–4 mm, in 0.5 mm incremental steps where appropriate. The relative glass-forming ability of each alloy was initially determined using electron-based microscopy (Hitachi SU70 SEM) and verified on the central sections of castings using X-ray diffraction (XRD) with a Phillips MRD instrument equipped with a 0.5 mm micro-capillary tube and a Cu Kα radiation source. Thermophysical data were determined by differential scanning calorimetry (DSC) using a Mettler Toledo DSC1 calorimeter at a heating rate of 20 °C min⁻¹. For compression testing, samples of 1.7 and 3 mm in diameter with a height-to-diameter ratio of 2:1 were fabricated from as-cast rods. Compression testing was carried out at room temperature using a screw-driven Schenck mechanical testing machine with a compliance of ∼10 nm/N at a strain rate of 10⁻⁴ s⁻¹.