Figure 1 shows the temperature evolution of total and partial pair correlation functions (PCFs) in Ce₇₀Al₃₀ and La₇₀Al₃₀ metallic glass-forming alloys in the quenching process, respectively. As temperature decreases, the height of the first peak in total PCFs increases, but the peak position does not change much, as shown in Figs. 1(a) and 1(e). This indicates an increasing degree of short-range order in both glass-forming alloys during cooling. For the second peak, the magnitude also increases slightly. However, it does not show the splitting as observed in CuZr metallic alloy system with decreasing temperature.^[15] In addition, a small pre-peak around 2.8 Å in total PCFs is emerging with decreasing temperature, which corresponds to the Al–Al pair and indicates that the short-range order around Al atoms becomes stronger as temperature decreases. As shown in Figs. 1(b) and 1(f), Ce–Ce and La–La partial PCFs are similar to the respective total PCFs. For Ce–Al and La–Al PCFs, however, the first peak becomes much narrower and sharper, as temperature decreases. Moreover, the second peak is getting wider and exhibits splitting at low temperatures. In Al–Al PCFs in both glass-forming alloys, the first peak is located around 2.8 Å, corresponding to the pre-peak in total PCFs shown in Figs. 1(a) and 1(e), respectively. The splitting of the second peak is also observed and becomes more obvious in Al–Al PCFs. Furthermore, more peaks beyond the second peak are developed in both MGs at 300 K. This indicates that significant medium-range order between Al atoms is developed in the cooling process. It can be seen from Figs. 1(d) and 1(h) that Al–Al PCFs in both glass-forming alloys show similar peaks. However, the peak positions are slightly different, which could imply that the medium-range atomic packing of Al atoms in two MGs is different. This will be further characterized and analyzed in Section 3.3.

Fig. 1.

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	Fig. 1. (color online) Total and partial PCFs in (a)–(d) Ce70Al30 and (e)–(h) La70Al30 glass-forming alloys at various temperatures in the cooling process, respectively.

To investigate the local atomic structures beyond the PCFs in both Ce₇₀Al₃₀ and La₇₀Al₃₀ systems, the Voronoi tessellation method was employed, which divides space into close-packed polyhedra around atoms by construction of bisecting planes along the lines joining the central atom and all its neighbors.^[16–18] Each Voronoi polyhedron can be identified with the Voronoi index to designate the character of the atomic cluster surrounding an atom, where n_i (i = 3, 4, 5, 6) denotes the number of i-edged faces in the Voronoi polyhedron. In the Voronoi analysis, atoms sharing faces in their polyhedra are the nearest neighbors, so that the total number of faces in a polyhedron can be used to determine the coordination number (CN) of the central atom. Thus, we first analyzed the average CNs as a function of temperature. Figure 2 shows the distributions of total and partial CNs in both Ce₇₀Al₃₀ and La₇₀Al₃₀ glass-forming alloys at 1200 K and 300 K, respectively. It can be seen that CN distributions show a slight difference in two systems. As shown in Fig. 2(a), CNs around 13, 14, and 15 are different in two systems. The distributions of CN=13 in two alloys at 1200 K are almost the same. However, the distribution of CN=13 in La₇₀Al₃₀ MG at 300 K significantly decreases, but that in Ce₇₀Al₃₀ MG at 300 K only decreases a little. The situation is reversed in the distribution of CN=14. It can be seen that the distribution of CN=14 in Ce₇₀Al₃₀ alloy decreases more than in La₇₀Al₃₀ alloy, as temperature decreases. For the distributions of CN=15, while it decreases in Ce₇₀Al₃₀ alloy with decreasing temperature, it increases in La₇₀Al₃₀ alloy. From the distributions of partial CNs shown in Figs. 2(b) and 2(c), it can be concluded that the difference in total CN distributions in two alloys is essentially related to the partial CNs around Ce and La atoms in Ce₇₀Al₃₀and La₇₀Al₃₀ glass-forming alloys, respectively. For the distributions of partial CNs around Al atoms in both alloys, only the distributions of CN=10 and CN=13 at 300 K show the obvious difference. The above results indicate that the local structures in Ce₇₀Al₃₀ and La₇₀Al₃₀ glass-forming alloys are a little different, although Ce and La elements are similar and the two glass-forming alloys exhibit almost the same averaged structure features as shown in Fig. 1.

Fig. 2.

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	Fig. 2. (color online) Total (a) and partial ((b), (c)) coordination numbers in Ce70Al30 and La70Al30 glass-forming alloys at 1200 K and 300 K, respectively.

To get more detailed structural information for the local atomic arrangement, we analyzed the bond–angle distribution, the so-called three-body correlation,^[18] which characterizes the angles between two bonds connecting the central atom to any two neighboring atoms. Figure 3 shows the total bond-angle distributions for Ce₇₀Al₃₀ and La₇₀Al₃₀ glass-forming alloys at various temperatures. Both systems exhibit quite similar bond-angle distributions. There are two main peaks located at 55° and 105°. Previous studies have shown that for the icosahedral short-range order, the bond angles are 63.5° and 116.5°,^[18] quite different from the two main peak angles shown in Fig. 3. This indicates that the local structure ordering in Ce₇₀Al₃₀ and La₇₀Al₃₀ glass-forming alloys would not be icosahedral dominated, but quite complex.

Fig. 3.

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	Fig. 3. (color online) Total bond-angle distributions in Ce70Al30 (a) and La70Al30 (b) glass-forming alloys at various temperatures, respectively.

We also investigate the partial bond–angle distributions at various temperatures in Ce₇₀Al₃₀ and La₇₀Al₃₀ glass-forming alloys, respectively. As shown in Fig. 4(a), the bond angle distribution of Ce–Ce–Ce exhibits a similar behavior to that in the total bond-angle distribution. This indicates that the bond-angle distribution of Ce–Ce–Ce is dominant. On the other hand, another peak located around 150° in Ce–Ce–Ce becomes more obvious as temperature decreases. For Ce–Ce–Al, as temperature decreases, the first peak increases and shifts toward larger angles, from about 51° to 54°. The second and third peaks are located at 100° and 146°, respectively. Although the peak positions in Ce–Ce–Al are different from those in Ce–Ce–Ce, the shape of bond-angle distributions is similar. For Al–Ce–Al, the first and second peaks are located around 48 and 98, shifting towards smaller angles compared to those in Ce–Ce–Al. The third peak located around 150° is getting more pronounced in the distribution of Al–Ce–Al. For La atoms in the La₇₀Al₃₀ alloy, the bond angle distributions are similar to those around Ce atoms in the Ce₇₀Al₃₀ alloy, as shown in Figs. 4(g), 4(h), and 4(i). In contrast, bond–angle distributions around Al atoms exhibit different behaviors in Ce₇₀Al₃₀ and La₇₀Al₃₀ glass-forming alloys. For Ce–Al–Ce in the Ce₇₀Al₃₀ glass-forming alloy shown in Fig. 4(d), the first peak increases, but the peak position does not change. The two main peaks are located at around 65° and 118°, respectively, which are quite close to the icosahedral bond angles^[18]. This indicates that the Ce atoms around Al atoms are arranged in an icosahedral-like fashion. The bond angles of La–Al–La in La₇₀Al₃₀ alloy show similar distributions. For Al–Al–Ce, the first peak splits into two peaks with decreasing temperature, located at around 49° and 63°, respectively. However, the intensities of these two peaks do not change monotonically with temperature, but show fluctuation with temperature. Finally, in Ce₇₀Al₃₀ MG at 300 K, two peaks are formed. This implies that the arrangement of Al and Ce atoms around Al atoms is affected significantly by temperature in glass formation. This is totally different in bond-angle distributions of Al–Al–La in La₇₀Al₃₀ alloy. As shown in Fig. 4(k), the distribution at 1200 K exhibits the main peak around 60° with a shoulder on the left. As temperature decreases, the main peak becomes narrower and shifts to around 63°, and the intensity increases continuously with decreasing temperature. Meanwhile, a small peak on the left is gradually formed, and the intensity increases with temperature decrease. This indicates that the arrangements of Al and La atoms around Al atoms in theLa₇₀Al₃₀ alloy are relatively stable, so that the bond-angle distribution of Al–Al–La changes continuously in the cooling process. Such features are also reflected in the bond-angle distributions of Al–Al–Al. As shown in Fig. 4(f), the distribution of Al–Al–Al in the Ce₇₀Al₃₀ alloy does not change monotonically with temperature, either. At some temperatures, there is only a main peak around 60° with a shoulder on the left. At some other temperatures, there are two small peaks located around 42° and 60°, respectively. In La₇₀Al₃₀ alloy, however, two small peaks around 42° and 60° are formed gradually with decreasing temperature, as shown in Fig. 4(l). In addition, a peak located around 170° becomes more obvious, which is not observed in the Ce₇₀Al₃₀ alloy. Although Ce and La atoms are similar, the local atomic configurations of Al atoms in these two systems show a significant difference.

Fig. 4.

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	Fig. 4. (color online) Partial bond–angle distributions in Ce70Al30 ((a)–(f)) and La70Al30 ((g)–(l)) glass-forming alloys at various temperatures, respectively.

According to the above analysis, the local atomic arrangements related to Al atoms change significantly as temperature decreases. In addition, the local structures around Al atoms are also different in Ce₇₀Al₃₀ and La₇₀Al₃₀ glass-forming alloys. To get a deeper insight into the local atomic structure features, we analyzed the distributions of the major populated atomic clusters in Ce₇₀Al₃₀ and La₇₀Al₃₀ glass-forming alloys at various temperatures. It is found that Ce (La) and Al atoms in Ce₇₀Al₃₀(La₇₀Al₃₀) alloy rarely share the same types of atomic clusters, so that only the major populated Ce (La)-centered and Al-centered atomic clusters were presented, respectively, as shown in Fig. 5. It can be seen that the major atomic clusters are slightly different for Ce and La atoms, as shown in Figs. 5(a) and 5(c), respectively. For Ce atoms, is the only type of 12-coordinated cluster. For La atoms, however, as well as are 12-coordinated clusters. The population of both Ce-centered and La-centered clusters is very small. However, the fraction of La-centered clusters is much larger. On the other hand, Ce-centered clusters also contain 13-coordinated and 16-coordinated clusters, but no such clusters are major populated around La atoms. In addition, La atoms in La₇₀Al₃₀ alloy contain one more type of 14-coordinated clusters, . For Al-centered clusters, only the 13-coordinated clusters are different in these two systems. In Ce₇₀Al₃₀ alloy, the 13-coordinated cluster is , while in La₇₀Al₃₀ alloy the 13-coordinated cluster is . The fraction of is much more than that of . Therefore, in the La₇₀Al₃₀ alloy, Al atoms tend to form and , which are often regarded as icosahedral-like clusters.^[18] For other types of clusters, they are all major populated in both alloys. Although their fractions show a little difference, the temperature dependent behaviors are similar. In both alloys, most clusters are Al-centered. However, the fraction of icosahedral clusters is very small in these two systems, indicating that icosahedral clusters are not dominated local structures, consistent with the above analysis. This is in contrast to CuZr metallic glass-forming alloy where the population of is dominant. The Voronoi analysis further demonstrates that the local atomic structures show a little difference, although Ce and La atoms are quite similar.

Fig. 5.

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	Fig. 5. (color online) Fraction of the major populated atomic clusters in Ce70Al30 ((a), (b)) and La70Al30 ((c), (d)) glass-forming alloys at various temperatures, respectively.

As mentioned above, in partial PCFs of the Al–Al pair in Ce₇₀Al₃₀ and La₇₀Al₃₀ alloys, the peak positions show a slight difference, indicative of different atomic packing in medium-range structures in two MGs. To further characterize the medium-range atomic packing features in two MGs, we analyzed the partial PCFs with the distance scaled by the first peak position R₁. Previous studies show that the oscillation in the PCFs is an indication that a certain order does exist in amorphous solids, and the values of (i = 1, 2, 3, 4, 5) in PCFs correspond to several characteristic constants of , , , , and .^[19] Further studies reveal that the scaled peak positions of partial PCFs in MGs reflect medium-range atomic packing orders.^[20,21] For multicomponent MGs, the scaled peak positions of partial PCFs may correspond to different sequences of characteristic constants, indicative of different medium-range topological orders, which are found to directly correlate with the glass-forming ability.^[18] Therefore, we analyzed the scaled partial PCFs in Ce₇₀Al₃₀ and La₇₀Al₃₀ MGs to investigate the medium-range atomic packing feature.

Figure 7 shows the scaled partial PCFs for Ce–Ce, Ce–Al, and Al–Al in Ce₇₀Al₃₀ MG and La–La, La–Al, and Al–Al in La₇₀Al₃₀ MG, respectively. It can be seen that the scaled PCFs of Ce–Ce and La–La are quite similar. The peak positions are almost the same. However, the scaled PCFs of Ce–Al and La–Al, Al–Al (Ce₇₀Al₃₀) and Al–Al (La₇₀Al₃₀) are significantly different. For Ce–Al and La–Al pairs, the second and third peak positions are almost the same. However, the fourth peak positions are quite different, located at and in Ce–Al and La–Al pairs, respectively. For La–Al pair, the fifth peak is not obvious, while it still exhibits significant ordering in Ce–Al pair. This indicates that the medium-range atomic packing for Ce–Al and La–Al is different, and medium-range order between Ce and Al in Ce₇₀Al₃₀ MG is more significant than that between La and Al in La₇₀Al₃₀ MG. Furthermore, the scaled Al–Al partial PCFs in both MGs are also quite different in both peak positions and peak number. It can be seen that at , there is a small shoulder in Al–Al of Ce₇₀Al₃₀ MG, but no peak or shoulder shows up in Al–Al of La₇₀Al₃₀ MG. On the contrary, at , there is a small shoulder in Al–Al of La₇₀Al₃₀ MG. As is close to and , the scaled Al–Al partial PCFs in both MGs show two peaks, respectively. However, the peak intensities in La₇₀Al₃₀ MG are higher. There are even two more peaks at and in Al–Al of Ce₇₀Al₃₀ MG. However, there is only one peak located at in Al–Al of La₇₀Al₃₀ MG, which is also different from the peak of in Al–Al of Ce₇₀Al₃₀ MG. Therefore, the medium-range atomic packing related to Al atoms in two MGs is significantly different, although Ce and La are similar elements and the compositions in two MGs are the same. This is different from the MGs with a large atomic size mismatch.

Recently, similar element substitution enhanced GFA was observed by substitution of Ce for La in (La_0.7Ce_0.3)₆₅Co₂₅Al₁₀ bulk MGs.^[3] It was found that more icosahedral-like clusters may be one of the structural origins of the higher GFA enhanced by similar element substitution.^[9] This is consistent with the above local structure analysis in terms of the Voronoi tessellation method. The substitution of Ce for La will introduce more and icosahedral-like atomic clusters, since such clusters tend to form around Ce atoms, which may play different roles in dynamical properties as liquids are quenched into glassy states.^[22] More importantly, the medium-range atomic packing analysis shows that the substitution of Ce will introduce more different atomic packing in medium range structures. Although Ce and La atoms are similar, their medium-range atomic packing with Al is quite different, as shown in Fig. 6. In addition, the substitution of Ce atoms will also lead to the more complicated atomic packing of Al atoms in medium-range structures. More diverse medium-range atomic packing introduced by the substitution of Ce for La will enhance GFA in this system. Although Ce and La are similar, the Ce element contains 4f electrons, which could be the physical reason for the distinctive short- to medium-range atomic packing in Ce₇₀Al₃₀ and La₇₀Al₃₀MGs and enhanced GFA by similar element substitution. This also implies that a slight difference may lead to a significant difference in short- to medium-range atomic packing.

Fig. 6.

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	Fig. 6. (color online) Scaled partial pair correlation functions in Ce70Al30 and La70Al30 MGs at 300 K, respectively.