Proposed correlation of structure network inherited from producing techniques and deformation behavior for Ni-Ti-Mo metallic glasses via atomistic simulations.

Based on the newly constructed n-body potential of Ni-Ti-Mo system, Molecular Dynamics and Monte Carlo simulations predict an energetically favored glass formation region and an optimal composition sub-region with the highest glass-forming ability. In order to compare the producing techniques between liquid melt quenching (LMQ) and solid-state amorphization (SSA), inherent hierarchical structure and its effect on mechanical property were clarified via atomistic simulations. It is revealed that both producing techniques exhibit no pronounced differences in the local atomic structure and mechanical behavior, while the LMQ method makes a relatively more ordered structure and a higher intrinsic strength. Meanwhile, it is found that the dominant short-order clusters of Ni-Ti-Mo metallic glasses obtained by LMQ and SSA are similar. By analyzing the structural evolution upon uniaxial tensile deformation, it is concluded that the gradual collapse of the spatial structure network is intimately correlated to the mechanical response of metallic glasses and acts as a structural signature of the initiation and propagation of shear bands.


Construction of Ni-Ti-Mo interatomic potential
To develop an atomistic approach, the construction of a realistic interatomic potential of an alloy system is of critical importance. To the best of the authors' knowledge, no interatomic potential has been published for the Ni-Ti-Mo system. In the present study, a set of the Ni-Ti-Mo interatomic potentials are constructed under a formulism proposed recently by the authors' group, i.e., the new long-range empirical potential (LREP) scheme 1 .
The proposed potential could distinguish the energy differences between stable and hypothetic structures of bcc, fcc and hcp metals. In particular, it can distinguish the energy difference between the fcc and hcp structures. Moreover, the total energy and force derived from the proposed potential could keep continuous and smooth in the entire calculation range. Thus, it can properly resolve the cutoff problem without a truncation function 2 . According to the potential, the potential energy E i of atom i can be calculated as follows: where the whole second term of Eq. S1 is the cohesive part and ij r is the distance between atoms i and j of the system at equilibrium. ( The six sets of potential parameters are summarized in Table S1. As shown in Table   S2, it lists the lattice constants, bulk modulus and elastic modulus of B2 and D0 3 Ti-Mo compounds derived from the potential and the first-principle calculation developed by Ikehata et al 10 . It can be seen that the potential derived lattice constants, bulk modulus and elastic modulus of Ti-Mo compounds match well with the previous study. Table S3 shows the lattice constants, formation energies, and bulk moduli of related intermetallic compounds in the Ti-Mo binary system derived from potential.
Comparing with the first-principle calculation, the maximum error of the cohesive energies and lattice constants is less than 4%, confirming that the constructed potential could well derive the structure and energy of these compounds in the systems.
To further evaluate the validity of the constructed potential, another approach is to check whether the potential can describe atomic interactions under non-equilibrium states. Therefore, we obtain the equation of state (EOS) from the constructed potential and then compared it with the Rose equation, which has been proved to be universal for most categories of solids 11 . Fig. S1(a) and Fig. S1(b) plot the pair parts, the cohesive parts and the potential energies as a function of the lattice constants calculated from the constructed potential, and the corresponding Rose equations for Meanwhile, we varied x and y with a composition interval of 5% to construct the Ni x Ti y Mo 1-x-y solid solution models over the entire composition triangle of the system.

Glass formation region of Ni-Ti-Mo system
Considering the total structure factor S(q) and

Optimization of glass formation compositions
According to the MD simulation results, one can conveniently predict the possibility of metallic glass formation in the Ni-Ti-Mo system at a given composition. Based on the results from the MD and MC simulations, the contour map of the amorphization driving force for Ni-Ti-Mo system is plotted in Fig. S3(a), as well as the driving force for the (NiTi) 100-x Mo x alloys along the HG line is shown in Fig. S3(b).
From the Fig. S3(a), the ΔE am-s.s is negative over the whole GFR, indicating that the energy of the amorphous phase is lower than that of the solid solution, thus formation of the amorphous phase is energetically favored. Besides, the larger the energy difference, the stronger the driving force for glass formation. Further inspecting Fig.   S3(a), it can be found that the alloy composition represented by red dots features a lower ΔE am-s.s than any other composition regions, indicating that their driving forces for amorphization are stronger. We define this composition sub-region as the optimal compositions for Ni-Ti-Mo metallic glass formation, within which the alloys have greater GFA than those alloys located outside the sub-region. Therefore, it provides basic guidelines to design appropriate alloy compositions for producing Ni-Ti-Mo metallic glasses. As shown in Fig. S3(b), it is found that the driving force of the (NiTi) 100-x Mo x alloys first increases gradually by adding the appropriate Mo concentration, and then after reaching the peak value, decreases with further increasing of Mo. Once the addition of Mo is higher than 66 at.%, the solid solution could maintain its crystalline lattice and no unique amorphous phases would be formed, indicating that the GFR of (NiTi) 100-x Mo x is 0-66 at.%.

Size-dependence of simulated stress-strain curves
As shown in Fig. S4, the stress-strain curves of the nanopillars with a length of 30 nm and diameter of 4, 6, 8, 10 nm are displayed, respectively. For the nanopillar of 8 nm and 10 nm diameter, the σ over value of (NiTi) 80 Mo 20 MGs obtained by LMQ is larger than that obtained by SSR. When the diameter becomes 6 nm, the stress-strain curves obtained by both producing methods are almost the same. However, the sample obtained by SSR becomes more brittle after the diameter decreases to 4 nm.
Therefore, the reduction diameter of the nanopillar can result in material brittleness.
However, the understanding of size-dependent/independent deformation behavior of BMGs at low temperature still needs further researches. It has been reported that the decreasing specimen size can even induced tensile ductility and enhancing yield strength [14][15][16] , which can be attributed to the smaller sample size than the shear-band spacing and the equivalent critical shear offset 17 . On the contrary, some other literature [18][19][20][21] reported size-independent deformation behavior for the BMGs at room temperature, namely the yield strengths and the plastic deformation modes are insensitive to the specimen sizes and initial structural states.

Schematic diagram of spatial connectivity between the dominant clusters
The spatial structure networks are made of dominant clusters that interconnect to neighbor dominant clusters by sharing their vertex, edge, face or volume. As shown in