Understanding the mechanisms of metastable states in CuZr systems with glass-like structures
Wen-Xiong Song1, Shi-Jin Zhao1,a) and Gang Wang2
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Institute of Materials Science, Shanghai University, Shanghai 200072, China
Laboratory for Microstructures, Shanghai University, Shanghai 200444, China
The comparison between the cutoff radius and Voronoi cell methods.
To determine the first coordinate shell, two methods are used and compared. One is the cutoff of pair
correlation function (PCF)1, 2, which is usually not unique. The other is the use of a Voronoi cell,
which is unique. Both of these associations are shown in Fig. S1. The PCF of Cu50Zr50 in a glassy
state is shown in Fig. S1(a). The large full width at half maximum (FWHM) illustrates that it is
heterogeneous in a local region. In Fig. S1(b), the Voronoi cell method is used and the integration of
the related curve gives the average coordinate number, i. e. the number of Cu and Zr atoms that are
around a center atom (Cu or Zr) in a Voronoi cell on average. Comparing Fig. S1(a) and Fig. S1(b),
the shapes of related curves using the two methods are similar in spite of a difference in the tails of
the distributions. The relative intensities of the related curves by the two methods are not consistent
due to the differences of both normalization method and integral value. However, using the Voronoi
cell method to determine the first coordinate shell is reasonable, and thus is used throughout this
paper.
a)
To whom correspondence should be addressed. Email: shijin.zhao@shu.edu.cn.
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Figure S1 The PCFs of Cu-Cu, Cu-Zr and Zr-Zr bonds are shown in (a); the BLDs of Cu-Cu, Cu-Zr
and Zr-Zr bonds are shown in (b), determined by Voronoi cell.
The crystallization process of Cu15Zr85 suppercooled system
The snapshots of the crystallization process of Cu15Zr85 are shown in Fig. S2. The time for critical
nucleation is shorter than the time in Ni50Al503, illustrating that Cu15Zr85 is easier to nucleate because
the composition of Cu15Zr85 is close to pure metal Zr without long-range diffusion. In Cu15Zr85, there
are always two Cu atoms in each polyhedron, as shown in Fig. S3. This results in that polyhedra
could not form stable icosahedron for improper atomic number ratio between Cu and Zr. A basic bcc
unit is drawn on several polyhedra with twelve dotted black lines, as shown in Fig. S3. By breaking
some of the twelve related bonds, the cluster is more like an icosahedron. As a result, (0,5,2,8),
(0,5,2,7) and (0,4,4,6) are bcc-like polyhedra, while (0,1,10,2) and (0,1,10,3) are icosahedron-like
polyhedra. Taking (0,4,4,6) for example, it has one bond broken compared to (0,6,0,8) cluster. Thus,
a polyhedron with large number of the third index K in (I,J,K,L) is more like icosahedron, otherwise
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it is more like bcc cluster. Compared to (0,6,0,8) clusters, other bcc-like clusters are deformed more
or less, and their bond lengths are more heterogeneous, whose structures are determined by both the
local region and surroundings nearby. Nonlinear and asymmetric strain energies of bonds will
magnify the strain energy values of these inhomogeneous polyhedra. Despite the decrease of the
strain energy during crystallization, a large ordered nucleus is needed nearby to cause a disordered
cluster to become an ordered one. Otherwise, this will result in large strain energy in some bonds that
do not match their surroundings. Thereby, the key to nucleation in Cu15Zr85 is to form a large ordered
nucleus.
Fig. S2. Snapshots of (0,6,0,8) nucleus in Zr85Cu15 at 1150 K. I, 0 ps (fluctuation); II, 80 ps (critical
nucleation); III, 200 ps (growth); IV, 400 ps (finished); the rotated and enlarged nucleus between II
and III is critical and the orientation index [100] is perpendicular to the paper and point out.
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Fig. S3. (0,6,0,8), (0,4,4,6), (0,4,4,7), (0,3,6,4), (0,3,6,5), (0,3,6,6), (0,2,8,4), (0,2,8,5), (0,1,10,2),
(0,1,10,3), and (0,0,12,0) clusters are detected in Cu15Zr85 at 1150 K.
We calculate the relative energy of the main polyhedra, as shown in Fig. S4. We found that the
icosahedron is the most stable but there are a few of them, and the next most stable is (0,6,0,8). The
stability of icosahedron arises from lower strain energy when Cu and Zr atoms with different atomic
radii are mixed and the stability of the (0,6,0,8) cluster is due to its homogeneous BLD. Fig. S5
shows the relationship of the polyhedron transformation during the nucleus growth up very passing
0.2 ps. The direction is toward (0,6,0,8). Although (0,6,0,8) is not the most stable cluster, the system
with this cluster in the crystal is stable due to its translational symmetry that results in the
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homogeneous BLD of system. The polyhedra located at the middle of Fig. S5 are unstable, such as
(0,3,6,5) cluster. The number of this cluster is the largest when the system is in a glassy state. They
tend to become stable polyhedra in order to stabilize the system. Without suitable atomic number
ratios between Cu and Zr, these unstable polyhedra become stable (0,6,0,8) clusters, not icosahedra.
Cluster transformation may result in a few atoms diffusing, but no long-range diffusion as in Ni50Al50
crystallization. This difference in diffusion results in a nucleus growth time in Cu15Zr85 that is two
times faster than the time in Ni50Al50, despite of their opposite relative values of diffusion velocity3.
After crystallization, a few icosahedon-like polyhedra are found in system. This is caused by both
lower strain energy for geometrically preferred dense packing, and by ordered dense packing in the
surroundings owing to crystallization.
Fig. S4. The relative energy of the main polyhedra in Cu15Zr85.
Fig. S5. The relationship of polyhedra transformation during the nucleus growth up in Cu15Zr85
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