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Page 6 of 15 Hu et al. J Mater Inf 2023;3:1 I http://dx.doi.org/10.20517/jmi.2022.28

0.0

0.1
)
A
A
+ 0.2
B
B
(
/ 0.3
)
A
A
0.4
B
B
(
film
0.5
ribbon
bulk
0.6
0.6 0.8 1.0 1.2 1.4 1.6
BB / AA

Figure 2. Data exploration of experimental binary alloys grouped by the glass type. The geometrical parameter and the energetic parameter
are considered for comparison.

neighbors of each particle are obtained by radical Voronoi tessellation [21] . We calculate the bond orientational
order parameter 6 ( ) for each particle :

∑

6 ( ) = 6 ( (r ), (r )), (2)

=1 tot
where is the number of nearest Voronoi neighbors of particle , 6 ( (r , (r )) is the spherical harmonic
function of degree 6 and order , and and are the polar and azimuthal angles. The contribution from
the spherical harmonics of each neighbor of particle is weighted by the fraction / of the area of the

tot

Voronoifaceseparatingthetwoparticlestothetotalareaofallfaces ofthepolyhedronsurroundingparticle
tot
. Wedeterminethenumberofcrystal-likeatomsbycalculatingthecorrelationsinthebondorientationalorder
parameter:
6
∑
6 ( ) ∗ ( )
=−6 6
6 ( , ) = √ , (3)
6 6
∑ 2 ∑ 2
| 6 ( )| | 6 ( )|
=−6 =−6
where ∗ 6 ( ) is the complex conjugate of 6 ( ). If 6 ( , ) > 0.7, we treat the bond as crystal-like [22] . If the
total number of crystal-like bonds for a given particle is larger than 10, the particle is considered to be in a
crystallineenvironment. Thesensitivityofthethresholdsfor 6 ( , ) andthenumberofcrystal-likebondshave
been studied previously [22,23] . For each set of size ratios and energetic parameters, we calculate the fraction of
crystalline particles xtal as a function of the cooling rate . Then we use the following function to model the
rate-dependent xtal and estimate the critical cooling rate when xtal = 0.5.

1 ( [ − ])
xtal = 1 − tanh log ( / ) , (4)
10
2
where 0 < < 1 is the stretching exponent [13,14,16] .