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Local atomic structure of CoB-based glassy alloys: Ab initio molecular dynamics simulations
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Local atomic structure of CoeB-based glassy alloys: Ab initio molecular dynamics simulations ⁎
Yaxin Dia, Jianfeng Wanga, , Shijie Zhua, Liguo Wanga, Shaokang Guana, Tao Zhangb a b
School of Materials Science and Engineering, Zhengzhou University, Zhengzhou 450001, PR China School of Materials Science and Engineering, Beihang University, Beijing 100191, PR China
A R T I C L E I N F O
A B S T R A C T
Keywords: Cobalt alloy Glassy alloy Ab initio molecular dynamic simulation Atomic structure
The first principle molecular dynamics simulations based on the density functional theory were performed to study the local structure of CoeB-based glassy alloys. It was evidenced that the B-centered non-distorted (regular) Kasper polyhedra with a coordination number (CN) of 9–10, i.e. < 0, 3, 6, 0 > and < 0, 2, 8, 0 > , are primary structure-forming clusters in CoeB-based glassy alloys. The formation of these regular clusters can be attributed to the efficient dense packing as well as the strong chemical interaction indicated by the results of chemical short range order parameter and electronic charge density. Compared with the Co65B35 glassy alloy, the Ta-bearing Co57B35Ta8 alloy has a higher fraction of Z9 and Z10 (Z = CN) Kasper polyhedra. A higher fraction of these regular Kasper polyhedra and their efficient and stable packing over medium range are likely to constitute the relatively stable regions which may compete with the corresponding crystals, and thus reduce atomic diffusivity and increase the viscosity of liquid/glassy structures. This result is in favor of higher thermal stability and better resistance to plastic flow. Therefore, the Co57B35Ta8 glassy alloy possesses a larger glassforming ability and a higher mechanical strength than the Ta-free glassy alloy.
1. Introduction Bulk glassy alloys have attracted an intensive attention due to its excellent mechanical properties including high yield strength, fracture toughness and elastic limit [1]. A reliable description of the atomiclevel structure is of importance especially to understand the properties of glassy alloys, which has attracted more and more attentions in recent years. Many studies have reported that the atomic structure associated with the composition of glassy alloys has a great influence on their properties [2–11]. In some metal–metal-type glassy alloys, such as ZreCu [4,5] and ZreCueAl [5–7], the predominant icosahedral local order is generally regarded as the structural origin for various properties including relaxation dynamics, glass-forming ability (GFA) and mechanical properties. For example, Cheng et al. [5,7] and Fang et al. [6] found out that the addition of a relatively small amount of alloying element Al in CueZr significantly enhances the fivefold environment and fractions of Cu-centered and Al-centered icosahedra. The increase in stable icosahedral clusters is responsible for the dramatic slowing down of relaxation dynamics, which induces the changes in the viscosity/fragility and GFA. Lee et al. [8] studied the effect of icosahedral clusters (ICOIs) on the toughness of CueZr amorphous alloy. The result shows that, compared with Cu65Zr35 alloy, the coverage rate of ICOIs
⁎
and network structure of icosahedra in Cu50Zr50 is lower, and thus the proportion of loose areas is higher, which leads to better shear deformation ability of alloy. However, icosahedral order is not universally the dominant short-range order (SRO) especially in transition-metal–metalloid type glassy alloys, such as FeeC [11], FeeB [12], NieB [13], and NieP [13]. As reported in the literatures, the dominant SRO in these alloys is presumably the regular Z clusters. They can also play a key role in controlling the properties of glassy alloy. However, the study on the atomic structures of glassy alloys is relatively limited and the structure-property relationship is still unclear. Very recently, we systematically studied the effect of Ta addition on the glass forming ability (GFA) and mechanical properties in CoeBbased glassy alloys [14,15]. Obviously, the appropriate addition of Ta element is very effective to improve GFA and mechanical properties. The results show that CoeBeTa BMGs exhibit good GFA as well as ultrahigh strength of up to 6000 MPa and high hardness of 15–16 GPa. The mechanical strength is higher than other bulk metal materials reported so far. Therefore, it is intriguing to understand how the local structure of CoeB glassy alloy is changed by alloying with Ta. In this paper, we investigated the atomic structure of Co65B35 and Co57B35Ta8 glassy alloys by using ab initio molecular dynamics simulations. The effect of composition on the atomic structure and the relationship of
Corresponding author. E-mail address: [email protected] (J. Wang).
https://doi.org/10.1016/j.jnoncrysol.2018.01.011 Received 8 November 2017; Received in revised form 28 December 2017; Accepted 8 January 2018 0022-3093/ © 2018 Elsevier B.V. All rights reserved.
Please cite this article as: Di, Y., Journal of Non-Crystalline Solids (2018), https://doi.org/10.1016/j.jnoncrysol.2018.01.011
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interaction of different atoms in the system. From Fig. 1, a splitting of the first peak into two sub-peaks around at r ≈ 2.00 Å and r ≈ 2.39 Å, respectively, could be observed in the total PDF of Ta-free CoeB glassy alloy. Both the first and second sub-peaks shift to the larger r ranges for the addition of element Ta in CoeB alloy, which implies that CoeB and CoeCo interatomic distances increase. This is validated by the result of partial PDFs for CoeB and CoeCo atomic pairs as shown in Fig. 2(a) and (b). There exists a pre-peak at r ≈ 1.78 Å which is approximately equal to the interatomic distance of BeB atomic pair. As can be seen from Fig. 2(c), the first peak of BeB atomic pairs becomes higher and narrower for the Ta-bearing alloy, which demonstrates that the number of the neighboring atoms as well as the bonding probability increases, and as a result the atomic ordering becomes more intensive. In addition, the location of the first peak shifts to the lower r range due to the alloying of Ta. This result means that the interatomic distance of BeB atomic pairs decreases. Previous studies [22–26] reported that, in crystalline and amorphous materials, bond shortening is likely related to electron hybridization.
structure with properties were also discussed. 2. Methods Ab initio molecular dynamics (AIMD) calculations based on density functional theory (DFT) were performed to investigate the local atomic structure of Co65B35 and Co57B35Ta8 glassy alloys by using the Vienna ab initio simulation package (VASP) [16] with the generalized gradient approximation to the exchange-correlation functional according to Perdew-Wang 91 [17]. The AIMD experiments were carried out in the canonical (NVT) ensembles using Nosé thermostats to control temperature. Outer electron wave functions were expanded using a planewave basis set with the kinetic energy cutoff of 400 eV. Only Γ point was used to sampling the Brillouin zone. Cubic simulation boxes with periodic boundary conditions contain 100 atoms, and the box size was determined by the experimental density of CoeB-based glassy alloys at room temperature. The density was measured by Archimedes' method using a Sartorius balance (Readability: 10 μg). To obtain the equilibrium lattices of quenched multi-composition amorphous alloys, the configurations were first melted and equilibrated at 3000 K for 9 ps to remove the memory effects from the initial configuration, then quenched to 300 K at a cooling rate of 2 × 1014 K/s. The simulation boxes were subsequently equilibrated at 300 K for 12 ps. The atomic coordinates were subsequently relaxed at 300 K until the dynamic thermal equilibrium state. The energy convergence accuracy was 1 × 10−5 eV in all stages. The atomic coordinates and length of the cell lattices were relaxed with an atomic force tolerance of 0.01 eV/Å. The electronic structures were calculated with 2 × 2 × 2 k-mesh and an energy cutoff of 600 eV in order to ensure the accuracy. The simulated structures were statistically analyzed using pair distribution function, coordination number, Warren-Cowley chemical short range order parameter [18], Honeycutt and Andersen bond-type index [19] and Voronoi tessellation [20,21]. Structure data was collected from 2000 configurations to ensure the statistical precision.
3.2. Coordination number and Warren-Cowley chemical short range order parameter Coordination number (CN) of the atom was calculated directly by integrating the PDF from 0 to the cutoff radius (rcut), and the rcut value was set to the position of the first minima in the pair distribution function. The first shell of Co57B35Ta8 alloy has a higher CN (about 13.13) than that of Co65Ta8 alloy (about 12.40), which indicates the structure of Co57B35Ta8 alloy is denser. The partial coordination number (Nij) and total coordination number (Ni) around element i could also be obtained by the same method. The results calculated are listed in Table 2. It was seen that the total coordination number around Co (NCo) increases for the addition of 8 at.% Ta element, although the NCoeCo and NCoeB values decrease from 10.004 to 8.697 and from 4.419 to 4.114, respectively. In contrast, the variation of NB value is relatively small, which suggests the distribution of B atoms is rather homogeneous. However, the NBeB value increases slightly from 0.923 to 1.047, which accounts for the number of neighboring contact between solute B increases. To determine if the atoms in the amorphous structure are distributed randomly or they have a tendency to form specific clusters, the degree of chemical short range order (CSRO) in the first coordination shell of Co, B and Ta atoms was estimated using the Warren-Cowley CSRO parameter (αij) which is written as [18]:
3. Results 3.1. Pair distribution function Figs. 1 and 2 show the total and partial pair distribution functions (PDFs) of CoeB-based glassy alloys, respectively. The interatomic distance of different atomic pairs is summarized in Table 1. As one of the main parameters describing the amorphous structures, PDF gives the possibility of finding another atom at a distance (r) from the selected atom. The partial PDF describes the relative spatial distribution and
αij = 1–Nij /(cj Ni ),
(1)
where cj is the atomic fraction of the element j. Negative αij (i ≠ j) value indicates the total concentration of j atom in the first coordination shell exceed their total average concentration in the alloy. For a random solution, αij is equal to zero. The αij value of CoeB-based glassy alloys is given in Table 3. It was shown that αij value of Co tends to increase (i.e., αCoCo varies from −0.068 to −0.046) for the addition of Ta element. The result suggests that the fraction of Co-centered chemical short range clustering (CSRC) for the CoeB glassy alloy is larger than Tabearing alloy. Pronounced CSRO parameter was also detected near B atoms, showing that these local regions are enriched with Co and Ta. In addition, the negative αTaCo and positive αTaB values indicate an enrichment of Co and a deficit of B in Ta-centered clusters, respectively. 3.3. Honeycutt-Andersen bond-type index To obtain more detailed information about the local atomic structures of the amorphous alloys, the common-neighbor analysis by using Honeycutt and Andersen (HA) index was performed. The HA index is characterized by four indices (i, j, k and l). The first index i is used to identify the bonding of two given atoms (i = 1 for bonded pairs and i = 2 for non-bonding atoms); the second index j is the number of
Fig. 1. Total pair distribution functions of Co65B35 and Co57B35Ta8 glassy alloys.
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Fig. 2. Partial pair distribution functions of Co65B35 and Co57B35Ta8 glassy alloys.
be characterized by different HA indices [27]. For example, the full icosahedra short range order is characterized by the 1551 index, and the deformed icosahedra short range order is generally characterized by the 1541 and 1431 indices. The indices of 1421 and 1422 represent the
nearest neighbors shared in common by the two atoms; the third index k is the number of bonds among the shared neighbors; and the fourth index l is needed in case the first three numbers are the same but the bond geometries are different. Usually, different local structures could Table 1 The interatomic distance of different atomic pairs (in Å). Alloy
CoeCo
CoeB
BeB
CoeTa
BeTa
TaeTa
Co65B35 Co57B35Ta8
2.391 ± 0.001 2.485 ± 0.001
1.995 ± 0.003 2.040 ± 0.003
1.805 ± 0.003 1.783 ± 0.002
– 2.614 ± 0.002
– 2.510 ± 0.001
– 3.202 ± 0.001
3
10.004 ± 0.003 8.687 ± 0.003
Co65B35 Co57B35Ta8
4.419 ± 0.001 4.114 ± 0.002
NCoeB
NCo 14.416 ± 0.003 14.569 ± 0.001
NCoeTa – 1.770 ± 0.001
4
CoeB
0.124 ± 0.001 0.193 ± 0.001
CoeCo
−0.068 ± 0.002 −0.046 ± 0.002
Alloy
Co65B35 Co57B35Ta8
– −0.519 ± 0.001
CoeTa
Table 3 Warren-Cowley chemical short range order parameter (αij) of CoeB-based amorphous alloys.
NCoeCo
Alloy – 1.429 ± 0.001
NBeTa
0.711 ± 0.003 0.674 ± 0.002
BeB
8.210 ± 0.001 6.692 ± 0.001
NBeCo
−0.383 ± 0.002 −0.281 ± 0.001
BeCo
0.923 ± 0.002 1.047 ± 0.002
NBeB
Table 2 Partial coordination number (Nij) and total coordination number (Ni) around element i in CoeB-based glassy alloys.
– −0.948 ± 0.001
BeTa
9.133 ± 0.005 9.168 ± 0.002
NB – 4.252 ± 0.001
NTaeB
– 0.276 ± 0.001
TaeB
– 11.636 ± 0.002
NTaeCo
– −0.216 ± 0.002
TaeCo
– 0.894 ± 0.004
NTaeTa
– 0.334 ± 0.003
TaeTa
– 16.785 ± 0.003
NTa
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Fig. 3. Fractions of the dominated Honeycutt and Andersen bond-type index in Co65B35 and Co57B35Ta8 glassy alloys. The error bars are smaller than the graph markers and are masked by them.
face-centered cubic and hexagonal close-packed ordering. In addition, 1441 and 1661 indices reflect the body-centered cubic ordering, while 1311 and 1321 indices represent the rhombus ordering. The results of the HA index analyses for the CoeB-based glassy alloys are shown in Fig. 3. It was seen that, the population of 1551 bond pairs significantly increases from 13.26% to 19.74% as 8 at.% Ta was added into Co65Ta8 alloy. The similar trend was also observed in 1661 and 1441 bond pairs. However, the 142X (1421 + 1422), 1541, 1431, 1311 and 1321 bond pairs show a converse variation trend.
3.4. Voronoi tessellation analysis It is well known that different combination of bond pairs could form different clusters. Therefore, the HA indices only describe the characteristic bond type required to construct a certain local structure. In order to obtain more direct information on local atomic clusters, the CoeB-based glassy alloys were further analyzed by Voronoi tessellation method. In this method, the perpendicular bisectors between a central atom and all of its neighboring atoms will form a polyhedron around the central atom, which can be differentiated by specific Voronoi indices < n3, n4, n5, … > , where ni denotes the number of i-edged faces of the Voronoi polyhedron. The total number of the faces of the Voronoi polyhedron equals to the CN of central atom. Fig. 4 shows the fractions of different types of B-, Co-, and Ta-centered clusters in CoeB-based glassy alloys. Although many types of coordination polyhedra are present in the amorphous structures, some certain polyhedra with relatively high frequency could be identified. In the B-centered clusters, the predominant polyhedra are non-distorted (regular) Kasper polyhedra with indices of < 0, 3, 6, 0 > and < 0, 2, 8, 0 > , as shown in Fig. 4(a). Obviously, the total fraction of them increases from 16.5% to 18.8% due to the addition of alloying solute Ta element. For the Co-centered clusters, the distribution of polyhedra is dispersive and most of them are distorted Kasper polyhedra with a CN of 12–14 (Fig. 4(b)). In the case of the Ta-centered clusters, the dominant polyhedra are those with a larger CN of 14–17 (Fig. 4(c)), i.e., < 0, 2, 8, 6 > and < 0, 2, 9, 4 > . However, the fraction of these Ta-centered distorted Kasper clusters is much lower than that of B-centered and Co-centered clusters owing to the relatively low content of Ta. Here, it is considered that the B-centered clusters are the primary structure-forming clusters, whereas Coor/and Ta-centered clusters are secondary clusters resulting from specific arrangements of atoms in the vertices of and voids between the Bcentered clusters. The main reason is that they possess more stability caused by very strong covalent-like BeCo bonds (see Section 3.5).
Fig. 4. Distribution of different types of (a) B-centered, (b) Co-centered, and (c) Tacentered clusters in Co65B35 and Co57B35Ta8 glassy alloys. The error bars are smaller than the graph markers and are masked by them.
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Fig. 5. Charge density distribution (in e/Å3) of (A) Co65B35 and (b) Co57B35Ta8 glassy alloys. The blue (middle), purple (large), and pink (small) bullets indicate Co, Ta, and B atoms, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
4. Discussion
Table 4 Average charge (in e) of Co, B and Ta in CoeB-based glassy alloys. Alloy
Co
B
Ta
Co65B35 Co57B35Ta8
8.926 ± 0.018 9.023 ± 0.006
3.138 ± 0.023 3.260 ± 0.002
– 9.700 ± 0.010
4.1. Formation of B-centered Kasper polyhedral clusters For the CoeB-based glassy alloys, the predominant polyhedra < 0, 3, 6, 0 > and < 0, 2, 8, 0 > correspond to the tri-capped trigonal prism packing (TTP) and bi-capped square Archimedean antiprism (BASP), which are similar to those in corresponding crystalline compounds Co3B and Co2B [13,28], respectively. The formation of these B-centered Z9 (Z = CN) and Z10 clusters can be understood from two aspects. Firstly, the relative size ratio between the solute and solvent atoms plays a key role. As suggested by Miracle et al. [29,30], the effective solute-tosolvent radius ratio (R*) controls the preference of a particular type in binary alloys. With a decrease in R*, the preferred polyhedra varies from Frank-Kasper type to the icosahedra type (R* ≈ 0.902), then to the BASP type (R* ≈ 0.835), and finally to TTP type (R* ≈ 0.732). As to the CoeB-based alloy system, the R* values is about 0.69 (B/Co), which predicts the preferred formation of TTP and BASP in glassy structures. The result is also in good agreement with the previous studies on FeeB and NieB binary glassy alloys [12,13]. Secondary, chemical interaction is another important factor on the formation of these local orders. According to the αij values listed in Table 2, there is an attractive interaction of BeCo. The interatomic interactions between the elemental components are represented by the heats of mixing of the corresponding binary alloys. As indicated by the negative heat of mixing, the interaction between Co and B is very strong, which is in favor of the result of Warren-Cowley CSRO parameter. In addition, the large chemical affinity is also validated by the covalent-like CoeB bonds (see Section 3.4), which renders these Z9 and Z10 clusters more stable. It was reported that the predominance of 1551 bond pairs has been taken as evidence of < 0, 0, 12, 0 > full icosahedra local order in some glassy alloys [31,32]. Apparently, the full icosahedra do not dominate in the present CoeB-based glassy alloys, although they have a high fraction of 1551 bond pairs. Here, it should be pointed out that the regular Kasper polyhedra in glassy structures, such as < 0, 3, 6, 0 > , < 0, 2, 8, 0 > , < 0, 2, 8, 1 > , < 0, 2, 8, 2 > and so on, have also high fraction of fivefold bonds as well as high fraction of 1551 bond pairs. As can be seen in Fig. 4(a), the addition of Ta element encourages the development of the regular Z9 and Z10 Kasper local orders. The increase in the total fraction of the Kasper polyhedral clusters is consistent with the variation of the 1551 bond pairs as shown in Fig. 3.
3.5. Electronic charge density It is evident from the above results that the presence of Ta in CoeBbased amorphous alloys leads to different bonding characters. Further, we studied the electronic charge densities for two different composition alloys, especially the differences associated with the Ta element. Fig. 5 shows the charge density distribution in Co65B35 and Co57B35Ta8 glassy alloys. For both two alloys, one can clearly see the overlap of the charge densities between Co and B, indicating the electron orbital hybridization between Co 3d and B 2p states. As shown in Table 1, the CoeB bond length is close to the summation of their covalent atomic radii. These results seem to be consistent and imply the covalent component of CoeB bonds. Also, the covalent-like BeB bonds were found in the glassy structures. However, the charge around Ta is distributed spherically and shows no obvious overlap with the charge of neighboring B atoms, which suggests the ionic character of TaeB bonds. The results of the charge densities are consistent with the previous study [15]. The average charge and charge state for element Co, Ta, and B are listed in Tables 4 and 5, respectively. Because of the addition of Ta element, the average charge of elements Co and B increases from 8.926 e to 9.023 e and 3.138 e to 3.260 e, respectively. For the Co65B35 alloy, the charge state of Co varies from +0.202 e to −0.054 e according to its neighboring environments. All B atoms attract electrons, resulting in a net charge of −0.052 e to −0.223 e. For the Ta-bearing Co57B35Ta8 alloy, all Ta atoms in glassy structure donate electrons to other parts, leading to its ionic characteristic. This also causes a significant change in charge state of Co and B. As can be seen in Table 5, the net state of Co and B is in the range of +0.218 to −0.209 e and −0.123 e to −0.443 e, respectively. The variation of atomic charge can be explained by the electronegative of Co (1.88), Ta (1.5), and B (2.04). The tendency to lose electrons is the highest of Ta among these three elements due to it's the lowest electronegative. Thus, the addition of Ta to replace Co would cause more electrons transfer to the surrounding space of B and Co atoms.
Table 5 Charge variation (in e) of Co, B and Ta in CoeB-based glassy alloys. Alloy
Co
B
Ta
Co65B35 Co57B35Ta8
+0.202 ± 0.010 to −0.054 ± 0.008 +0.218 ± 0.003 to −0.209 ± 0.011
−0.052 ± 0.003 to −0.223 ± 0.012 −0.123 ± 0.003 to −0.443 ± 0.002
– +1.397 ± 0.005–+1.210 ± 0.014
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likely to constitute the relatively stable regions. It is expected that the MROs of these regions in liquid may compete with the corresponding crystals, and thus reduce atomic diffusivity and increase the viscosity. This is responsible for the high thermal stability (i.e., glass transition temperature Tg or crystallization onset temperature Tx) and GFA of Co57B35Ta8 alloy. On the other hand, the rigid clusters and stable regions formed in glasses are anticipated to better resist to plastic flow. This is also the structure origin of ultra-high mechanical strength of CoeB-based glassy alloys. Accordingly, Tg value is a good macroscopic to gauge the mechanical strength. The relevant researches to build a quantitative scaling relation between yield strength and Tg have been done by Johnson and Samwer [38] and Liu et al. [39].
4.2. Relationships between local atomic structure and properties Previous experimental research [10] has reported that Co57Ta8B35 glassy alloy exhibits higher thermal stability and GFA as well as better mechanical strength than Co65B35 alloy. Here, the relationships of properties with local atomic structures were discussed. As well known, in some glassy alloys with non-directional metallic bonds, e.g., CueZr [4,33,34], CueZreAl [5,6,35], ZreNi [36], ZrePd [37], etc., icosahedra which are structurally different from typical crystalline units can stabilize the liquids. In the case of the present CoeB-based glassy alloys, the primary structure-forming clusters are B-centered Z9 and Z10 Kasper polyhedra which have a relatively lower potential energy and higher stability than other solute-centered clusters because of their strong covalent-like bonding as well as minimum disclinations. In particular, the increase in the fivefold environment and total fraction of these favored SRO clusters caused by the appropriate addition of Ta is conducive to the structural stability in liquid/glass. Since these SROs are very similar to the local motifs in the competing crystals, the stability of structure is also considered to originate from their efficient packing over medium range. Miracle et al. [29] reported an efficient cluster packing (ECP) model and suggested that the crystal-like packing of clusters is efficient and stable. According to this model, the B–centered clusters in binary Co65B35 glassy alloy form a simple cubic (sc) array represented as < 9 > sc with B solutes fully occupying α and β sites. The αΩ anti-site defects are also presented, which is in good agreement with the calculated BeB nearest neighbor peak as shown in Fig. 1. The replacement of Co with Ta in Co65B35 alloy would produce a face-centered cubic (fcc) cluster packing structure written as < 16, 9 > fcc. As the primary cluster-forming solute species α, the concentration of Ta element (CTa) is predicted by:
CTa =
100STa , ∑S
5. Conclusions In summary, the local atomic structures of Co65B35 and Co57B35Ta8 glassy alloys were studied by using AIMD method. The first shell of the Co57B35Ta8 alloy has a higher CN, which indicates a denser amorphous structure. The HA index shows that the population of 1551 bond pairs is higher for the Ta-bearing glassy alloy. The Voronoi tessellation analysis shows that the B-centered Z9 and Z10 Kasper polyhedra are primary structure-forming clusters in CoeB-based glassy alloys. The formation of these regular clusters can be attributed to the efficient dense packing as well as the strong chemical interaction indicated by the results of CSRO parameter and electronic charge density. Compared with the Co65B35 glassy alloy, the Co57B35Ta8 alloy has a higher fraction of Bcentered Z9 and Z10 Kasper polyhedral clusters. This is in good agreement with the fact that the fivefold environment is increased by the addition of Ta element as shown by HA index. According to the ECP model, the optimal concentration of Ta element to produce a fcc cluster packing structure is about 7.6 at.%. The result indicates that the structure of Co57B35Ta8 which is in favor of the ECP model is efficient and stable within the typical range of MRO. Higher fraction of B-centered Z9 and Z10 Kasper polyhedra as well as their efficient and stable packing over medium range is responsible for a higher thermal stability and a better resistance to plastic flow. As a result, Co57B35Ta8 glassy alloy exhibits a larger GFA and higher yield strength than Ta-free glassy alloy.
(2)
where STa represents the total number of Ta element per α site. ∑S is the total number of structural sites which is given by the following equation:
∑ S = ∑j
Sj.
(3)
Acknowledgements
For fcc packing, there is 1 β site and 2 γ sites for α site, so that Sβ = 1 and Sγ = 2. The total number of solvent (Ω) sites per α site (SΩ ) is obtained by:
⎡ Nα − Ω SΩ = ⎢ φ ⎢1 + Nα − Ω ⎣
( )
⎤ ⎥, ⎥ ⎦
This work was financially supported by the National Natural Science Foundation of China (Grant No. 51501166), National Key Research and Development Program of China (Grant No. 2017YFB0702504), Foundation of Henan Educational Committee (Grant Nos. 13A430668 and 15A430002), and Outstanding Young Talent Research Fund of Zhengzhou University (Grant No. 1421320046).
(4)
where Nα − Ω is specified by R* [29]. φ is equal to 12 in fcc structure. If we assume that the α (Ta) solutes completely occupy α sites, the CTa value was calculated as about 7.6 by combining Eqs. (2), (3) and (4). This result indicates that the structure of Co57B35Ta8 glassy alloy which is in favor of the ECP model is efficient within the typical range of medium range ordering (MRO). In addition, as indicated by the partial PDF of BeB (Fig. 2(c)), neighbor contact between solute B becomes unavoidable. As suggested by Sheng et al. [13], such a string-like interconnection would reduce the numbers of like bonds, leading to the reduction of energy. The higher NBeB value for the Co57B35Ta8 also makes a contribution to the increase in structural stability. Moreover, due to the lower electronegative of Ta, the addition of Ta to replace Co would cause more electrons transfer to the surrounding space of B atoms. By accepting electrons transferred from Ta, BeB bonds would become much stronger as revealed by the charge density distribution of B atoms (see Section 3.4), and hence the connection of B-centered clusters would become more stable. Above all, the higher content of regular Z9 and Z10 clusters and their efficient and stable packing for the Co57B35Ta8 glassy alloy are
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Local atomic structure of CoeB-based glassy alloys: Ab initio molecular dynamics simulations ⁎
Yaxin Dia, Jianfeng Wanga, , Shijie Zhua, Liguo Wanga, Shaokang Guana, Tao Zhangb a b
School of Materials Science and Engineering, Zhengzhou University, Zhengzhou 450001, PR China School of Materials Science and Engineering, Beihang University, Beijing 100191, PR China
A R T I C L E I N F O
A B S T R A C T
Keywords: Cobalt alloy Glassy alloy Ab initio molecular dynamic simulation Atomic structure
The first principle molecular dynamics simulations based on the density functional theory were performed to study the local structure of CoeB-based glassy alloys. It was evidenced that the B-centered non-distorted (regular) Kasper polyhedra with a coordination number (CN) of 9–10, i.e. < 0, 3, 6, 0 > and < 0, 2, 8, 0 > , are primary structure-forming clusters in CoeB-based glassy alloys. The formation of these regular clusters can be attributed to the efficient dense packing as well as the strong chemical interaction indicated by the results of chemical short range order parameter and electronic charge density. Compared with the Co65B35 glassy alloy, the Ta-bearing Co57B35Ta8 alloy has a higher fraction of Z9 and Z10 (Z = CN) Kasper polyhedra. A higher fraction of these regular Kasper polyhedra and their efficient and stable packing over medium range are likely to constitute the relatively stable regions which may compete with the corresponding crystals, and thus reduce atomic diffusivity and increase the viscosity of liquid/glassy structures. This result is in favor of higher thermal stability and better resistance to plastic flow. Therefore, the Co57B35Ta8 glassy alloy possesses a larger glassforming ability and a higher mechanical strength than the Ta-free glassy alloy.
1. Introduction Bulk glassy alloys have attracted an intensive attention due to its excellent mechanical properties including high yield strength, fracture toughness and elastic limit [1]. A reliable description of the atomiclevel structure is of importance especially to understand the properties of glassy alloys, which has attracted more and more attentions in recent years. Many studies have reported that the atomic structure associated with the composition of glassy alloys has a great influence on their properties [2–11]. In some metal–metal-type glassy alloys, such as ZreCu [4,5] and ZreCueAl [5–7], the predominant icosahedral local order is generally regarded as the structural origin for various properties including relaxation dynamics, glass-forming ability (GFA) and mechanical properties. For example, Cheng et al. [5,7] and Fang et al. [6] found out that the addition of a relatively small amount of alloying element Al in CueZr significantly enhances the fivefold environment and fractions of Cu-centered and Al-centered icosahedra. The increase in stable icosahedral clusters is responsible for the dramatic slowing down of relaxation dynamics, which induces the changes in the viscosity/fragility and GFA. Lee et al. [8] studied the effect of icosahedral clusters (ICOIs) on the toughness of CueZr amorphous alloy. The result shows that, compared with Cu65Zr35 alloy, the coverage rate of ICOIs
⁎
and network structure of icosahedra in Cu50Zr50 is lower, and thus the proportion of loose areas is higher, which leads to better shear deformation ability of alloy. However, icosahedral order is not universally the dominant short-range order (SRO) especially in transition-metal–metalloid type glassy alloys, such as FeeC [11], FeeB [12], NieB [13], and NieP [13]. As reported in the literatures, the dominant SRO in these alloys is presumably the regular Z clusters. They can also play a key role in controlling the properties of glassy alloy. However, the study on the atomic structures of glassy alloys is relatively limited and the structure-property relationship is still unclear. Very recently, we systematically studied the effect of Ta addition on the glass forming ability (GFA) and mechanical properties in CoeBbased glassy alloys [14,15]. Obviously, the appropriate addition of Ta element is very effective to improve GFA and mechanical properties. The results show that CoeBeTa BMGs exhibit good GFA as well as ultrahigh strength of up to 6000 MPa and high hardness of 15–16 GPa. The mechanical strength is higher than other bulk metal materials reported so far. Therefore, it is intriguing to understand how the local structure of CoeB glassy alloy is changed by alloying with Ta. In this paper, we investigated the atomic structure of Co65B35 and Co57B35Ta8 glassy alloys by using ab initio molecular dynamics simulations. The effect of composition on the atomic structure and the relationship of
Corresponding author. E-mail address: [email protected] (J. Wang).
https://doi.org/10.1016/j.jnoncrysol.2018.01.011 Received 8 November 2017; Received in revised form 28 December 2017; Accepted 8 January 2018 0022-3093/ © 2018 Elsevier B.V. All rights reserved.
Please cite this article as: Di, Y., Journal of Non-Crystalline Solids (2018), https://doi.org/10.1016/j.jnoncrysol.2018.01.011
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interaction of different atoms in the system. From Fig. 1, a splitting of the first peak into two sub-peaks around at r ≈ 2.00 Å and r ≈ 2.39 Å, respectively, could be observed in the total PDF of Ta-free CoeB glassy alloy. Both the first and second sub-peaks shift to the larger r ranges for the addition of element Ta in CoeB alloy, which implies that CoeB and CoeCo interatomic distances increase. This is validated by the result of partial PDFs for CoeB and CoeCo atomic pairs as shown in Fig. 2(a) and (b). There exists a pre-peak at r ≈ 1.78 Å which is approximately equal to the interatomic distance of BeB atomic pair. As can be seen from Fig. 2(c), the first peak of BeB atomic pairs becomes higher and narrower for the Ta-bearing alloy, which demonstrates that the number of the neighboring atoms as well as the bonding probability increases, and as a result the atomic ordering becomes more intensive. In addition, the location of the first peak shifts to the lower r range due to the alloying of Ta. This result means that the interatomic distance of BeB atomic pairs decreases. Previous studies [22–26] reported that, in crystalline and amorphous materials, bond shortening is likely related to electron hybridization.
structure with properties were also discussed. 2. Methods Ab initio molecular dynamics (AIMD) calculations based on density functional theory (DFT) were performed to investigate the local atomic structure of Co65B35 and Co57B35Ta8 glassy alloys by using the Vienna ab initio simulation package (VASP) [16] with the generalized gradient approximation to the exchange-correlation functional according to Perdew-Wang 91 [17]. The AIMD experiments were carried out in the canonical (NVT) ensembles using Nosé thermostats to control temperature. Outer electron wave functions were expanded using a planewave basis set with the kinetic energy cutoff of 400 eV. Only Γ point was used to sampling the Brillouin zone. Cubic simulation boxes with periodic boundary conditions contain 100 atoms, and the box size was determined by the experimental density of CoeB-based glassy alloys at room temperature. The density was measured by Archimedes' method using a Sartorius balance (Readability: 10 μg). To obtain the equilibrium lattices of quenched multi-composition amorphous alloys, the configurations were first melted and equilibrated at 3000 K for 9 ps to remove the memory effects from the initial configuration, then quenched to 300 K at a cooling rate of 2 × 1014 K/s. The simulation boxes were subsequently equilibrated at 300 K for 12 ps. The atomic coordinates were subsequently relaxed at 300 K until the dynamic thermal equilibrium state. The energy convergence accuracy was 1 × 10−5 eV in all stages. The atomic coordinates and length of the cell lattices were relaxed with an atomic force tolerance of 0.01 eV/Å. The electronic structures were calculated with 2 × 2 × 2 k-mesh and an energy cutoff of 600 eV in order to ensure the accuracy. The simulated structures were statistically analyzed using pair distribution function, coordination number, Warren-Cowley chemical short range order parameter [18], Honeycutt and Andersen bond-type index [19] and Voronoi tessellation [20,21]. Structure data was collected from 2000 configurations to ensure the statistical precision.
3.2. Coordination number and Warren-Cowley chemical short range order parameter Coordination number (CN) of the atom was calculated directly by integrating the PDF from 0 to the cutoff radius (rcut), and the rcut value was set to the position of the first minima in the pair distribution function. The first shell of Co57B35Ta8 alloy has a higher CN (about 13.13) than that of Co65Ta8 alloy (about 12.40), which indicates the structure of Co57B35Ta8 alloy is denser. The partial coordination number (Nij) and total coordination number (Ni) around element i could also be obtained by the same method. The results calculated are listed in Table 2. It was seen that the total coordination number around Co (NCo) increases for the addition of 8 at.% Ta element, although the NCoeCo and NCoeB values decrease from 10.004 to 8.697 and from 4.419 to 4.114, respectively. In contrast, the variation of NB value is relatively small, which suggests the distribution of B atoms is rather homogeneous. However, the NBeB value increases slightly from 0.923 to 1.047, which accounts for the number of neighboring contact between solute B increases. To determine if the atoms in the amorphous structure are distributed randomly or they have a tendency to form specific clusters, the degree of chemical short range order (CSRO) in the first coordination shell of Co, B and Ta atoms was estimated using the Warren-Cowley CSRO parameter (αij) which is written as [18]:
3. Results 3.1. Pair distribution function Figs. 1 and 2 show the total and partial pair distribution functions (PDFs) of CoeB-based glassy alloys, respectively. The interatomic distance of different atomic pairs is summarized in Table 1. As one of the main parameters describing the amorphous structures, PDF gives the possibility of finding another atom at a distance (r) from the selected atom. The partial PDF describes the relative spatial distribution and
αij = 1–Nij /(cj Ni ),
(1)
where cj is the atomic fraction of the element j. Negative αij (i ≠ j) value indicates the total concentration of j atom in the first coordination shell exceed their total average concentration in the alloy. For a random solution, αij is equal to zero. The αij value of CoeB-based glassy alloys is given in Table 3. It was shown that αij value of Co tends to increase (i.e., αCoCo varies from −0.068 to −0.046) for the addition of Ta element. The result suggests that the fraction of Co-centered chemical short range clustering (CSRC) for the CoeB glassy alloy is larger than Tabearing alloy. Pronounced CSRO parameter was also detected near B atoms, showing that these local regions are enriched with Co and Ta. In addition, the negative αTaCo and positive αTaB values indicate an enrichment of Co and a deficit of B in Ta-centered clusters, respectively. 3.3. Honeycutt-Andersen bond-type index To obtain more detailed information about the local atomic structures of the amorphous alloys, the common-neighbor analysis by using Honeycutt and Andersen (HA) index was performed. The HA index is characterized by four indices (i, j, k and l). The first index i is used to identify the bonding of two given atoms (i = 1 for bonded pairs and i = 2 for non-bonding atoms); the second index j is the number of
Fig. 1. Total pair distribution functions of Co65B35 and Co57B35Ta8 glassy alloys.
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Fig. 2. Partial pair distribution functions of Co65B35 and Co57B35Ta8 glassy alloys.
be characterized by different HA indices [27]. For example, the full icosahedra short range order is characterized by the 1551 index, and the deformed icosahedra short range order is generally characterized by the 1541 and 1431 indices. The indices of 1421 and 1422 represent the
nearest neighbors shared in common by the two atoms; the third index k is the number of bonds among the shared neighbors; and the fourth index l is needed in case the first three numbers are the same but the bond geometries are different. Usually, different local structures could Table 1 The interatomic distance of different atomic pairs (in Å). Alloy
CoeCo
CoeB
BeB
CoeTa
BeTa
TaeTa
Co65B35 Co57B35Ta8
2.391 ± 0.001 2.485 ± 0.001
1.995 ± 0.003 2.040 ± 0.003
1.805 ± 0.003 1.783 ± 0.002
– 2.614 ± 0.002
– 2.510 ± 0.001
– 3.202 ± 0.001
3
10.004 ± 0.003 8.687 ± 0.003
Co65B35 Co57B35Ta8
4.419 ± 0.001 4.114 ± 0.002
NCoeB
NCo 14.416 ± 0.003 14.569 ± 0.001
NCoeTa – 1.770 ± 0.001
4
CoeB
0.124 ± 0.001 0.193 ± 0.001
CoeCo
−0.068 ± 0.002 −0.046 ± 0.002
Alloy
Co65B35 Co57B35Ta8
– −0.519 ± 0.001
CoeTa
Table 3 Warren-Cowley chemical short range order parameter (αij) of CoeB-based amorphous alloys.
NCoeCo
Alloy – 1.429 ± 0.001
NBeTa
0.711 ± 0.003 0.674 ± 0.002
BeB
8.210 ± 0.001 6.692 ± 0.001
NBeCo
−0.383 ± 0.002 −0.281 ± 0.001
BeCo
0.923 ± 0.002 1.047 ± 0.002
NBeB
Table 2 Partial coordination number (Nij) and total coordination number (Ni) around element i in CoeB-based glassy alloys.
– −0.948 ± 0.001
BeTa
9.133 ± 0.005 9.168 ± 0.002
NB – 4.252 ± 0.001
NTaeB
– 0.276 ± 0.001
TaeB
– 11.636 ± 0.002
NTaeCo
– −0.216 ± 0.002
TaeCo
– 0.894 ± 0.004
NTaeTa
– 0.334 ± 0.003
TaeTa
– 16.785 ± 0.003
NTa
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Fig. 3. Fractions of the dominated Honeycutt and Andersen bond-type index in Co65B35 and Co57B35Ta8 glassy alloys. The error bars are smaller than the graph markers and are masked by them.
face-centered cubic and hexagonal close-packed ordering. In addition, 1441 and 1661 indices reflect the body-centered cubic ordering, while 1311 and 1321 indices represent the rhombus ordering. The results of the HA index analyses for the CoeB-based glassy alloys are shown in Fig. 3. It was seen that, the population of 1551 bond pairs significantly increases from 13.26% to 19.74% as 8 at.% Ta was added into Co65Ta8 alloy. The similar trend was also observed in 1661 and 1441 bond pairs. However, the 142X (1421 + 1422), 1541, 1431, 1311 and 1321 bond pairs show a converse variation trend.
3.4. Voronoi tessellation analysis It is well known that different combination of bond pairs could form different clusters. Therefore, the HA indices only describe the characteristic bond type required to construct a certain local structure. In order to obtain more direct information on local atomic clusters, the CoeB-based glassy alloys were further analyzed by Voronoi tessellation method. In this method, the perpendicular bisectors between a central atom and all of its neighboring atoms will form a polyhedron around the central atom, which can be differentiated by specific Voronoi indices < n3, n4, n5, … > , where ni denotes the number of i-edged faces of the Voronoi polyhedron. The total number of the faces of the Voronoi polyhedron equals to the CN of central atom. Fig. 4 shows the fractions of different types of B-, Co-, and Ta-centered clusters in CoeB-based glassy alloys. Although many types of coordination polyhedra are present in the amorphous structures, some certain polyhedra with relatively high frequency could be identified. In the B-centered clusters, the predominant polyhedra are non-distorted (regular) Kasper polyhedra with indices of < 0, 3, 6, 0 > and < 0, 2, 8, 0 > , as shown in Fig. 4(a). Obviously, the total fraction of them increases from 16.5% to 18.8% due to the addition of alloying solute Ta element. For the Co-centered clusters, the distribution of polyhedra is dispersive and most of them are distorted Kasper polyhedra with a CN of 12–14 (Fig. 4(b)). In the case of the Ta-centered clusters, the dominant polyhedra are those with a larger CN of 14–17 (Fig. 4(c)), i.e., < 0, 2, 8, 6 > and < 0, 2, 9, 4 > . However, the fraction of these Ta-centered distorted Kasper clusters is much lower than that of B-centered and Co-centered clusters owing to the relatively low content of Ta. Here, it is considered that the B-centered clusters are the primary structure-forming clusters, whereas Coor/and Ta-centered clusters are secondary clusters resulting from specific arrangements of atoms in the vertices of and voids between the Bcentered clusters. The main reason is that they possess more stability caused by very strong covalent-like BeCo bonds (see Section 3.5).
Fig. 4. Distribution of different types of (a) B-centered, (b) Co-centered, and (c) Tacentered clusters in Co65B35 and Co57B35Ta8 glassy alloys. The error bars are smaller than the graph markers and are masked by them.
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Fig. 5. Charge density distribution (in e/Å3) of (A) Co65B35 and (b) Co57B35Ta8 glassy alloys. The blue (middle), purple (large), and pink (small) bullets indicate Co, Ta, and B atoms, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
4. Discussion
Table 4 Average charge (in e) of Co, B and Ta in CoeB-based glassy alloys. Alloy
Co
B
Ta
Co65B35 Co57B35Ta8
8.926 ± 0.018 9.023 ± 0.006
3.138 ± 0.023 3.260 ± 0.002
– 9.700 ± 0.010
4.1. Formation of B-centered Kasper polyhedral clusters For the CoeB-based glassy alloys, the predominant polyhedra < 0, 3, 6, 0 > and < 0, 2, 8, 0 > correspond to the tri-capped trigonal prism packing (TTP) and bi-capped square Archimedean antiprism (BASP), which are similar to those in corresponding crystalline compounds Co3B and Co2B [13,28], respectively. The formation of these B-centered Z9 (Z = CN) and Z10 clusters can be understood from two aspects. Firstly, the relative size ratio between the solute and solvent atoms plays a key role. As suggested by Miracle et al. [29,30], the effective solute-tosolvent radius ratio (R*) controls the preference of a particular type in binary alloys. With a decrease in R*, the preferred polyhedra varies from Frank-Kasper type to the icosahedra type (R* ≈ 0.902), then to the BASP type (R* ≈ 0.835), and finally to TTP type (R* ≈ 0.732). As to the CoeB-based alloy system, the R* values is about 0.69 (B/Co), which predicts the preferred formation of TTP and BASP in glassy structures. The result is also in good agreement with the previous studies on FeeB and NieB binary glassy alloys [12,13]. Secondary, chemical interaction is another important factor on the formation of these local orders. According to the αij values listed in Table 2, there is an attractive interaction of BeCo. The interatomic interactions between the elemental components are represented by the heats of mixing of the corresponding binary alloys. As indicated by the negative heat of mixing, the interaction between Co and B is very strong, which is in favor of the result of Warren-Cowley CSRO parameter. In addition, the large chemical affinity is also validated by the covalent-like CoeB bonds (see Section 3.4), which renders these Z9 and Z10 clusters more stable. It was reported that the predominance of 1551 bond pairs has been taken as evidence of < 0, 0, 12, 0 > full icosahedra local order in some glassy alloys [31,32]. Apparently, the full icosahedra do not dominate in the present CoeB-based glassy alloys, although they have a high fraction of 1551 bond pairs. Here, it should be pointed out that the regular Kasper polyhedra in glassy structures, such as < 0, 3, 6, 0 > , < 0, 2, 8, 0 > , < 0, 2, 8, 1 > , < 0, 2, 8, 2 > and so on, have also high fraction of fivefold bonds as well as high fraction of 1551 bond pairs. As can be seen in Fig. 4(a), the addition of Ta element encourages the development of the regular Z9 and Z10 Kasper local orders. The increase in the total fraction of the Kasper polyhedral clusters is consistent with the variation of the 1551 bond pairs as shown in Fig. 3.
3.5. Electronic charge density It is evident from the above results that the presence of Ta in CoeBbased amorphous alloys leads to different bonding characters. Further, we studied the electronic charge densities for two different composition alloys, especially the differences associated with the Ta element. Fig. 5 shows the charge density distribution in Co65B35 and Co57B35Ta8 glassy alloys. For both two alloys, one can clearly see the overlap of the charge densities between Co and B, indicating the electron orbital hybridization between Co 3d and B 2p states. As shown in Table 1, the CoeB bond length is close to the summation of their covalent atomic radii. These results seem to be consistent and imply the covalent component of CoeB bonds. Also, the covalent-like BeB bonds were found in the glassy structures. However, the charge around Ta is distributed spherically and shows no obvious overlap with the charge of neighboring B atoms, which suggests the ionic character of TaeB bonds. The results of the charge densities are consistent with the previous study [15]. The average charge and charge state for element Co, Ta, and B are listed in Tables 4 and 5, respectively. Because of the addition of Ta element, the average charge of elements Co and B increases from 8.926 e to 9.023 e and 3.138 e to 3.260 e, respectively. For the Co65B35 alloy, the charge state of Co varies from +0.202 e to −0.054 e according to its neighboring environments. All B atoms attract electrons, resulting in a net charge of −0.052 e to −0.223 e. For the Ta-bearing Co57B35Ta8 alloy, all Ta atoms in glassy structure donate electrons to other parts, leading to its ionic characteristic. This also causes a significant change in charge state of Co and B. As can be seen in Table 5, the net state of Co and B is in the range of +0.218 to −0.209 e and −0.123 e to −0.443 e, respectively. The variation of atomic charge can be explained by the electronegative of Co (1.88), Ta (1.5), and B (2.04). The tendency to lose electrons is the highest of Ta among these three elements due to it's the lowest electronegative. Thus, the addition of Ta to replace Co would cause more electrons transfer to the surrounding space of B and Co atoms.
Table 5 Charge variation (in e) of Co, B and Ta in CoeB-based glassy alloys. Alloy
Co
B
Ta
Co65B35 Co57B35Ta8
+0.202 ± 0.010 to −0.054 ± 0.008 +0.218 ± 0.003 to −0.209 ± 0.011
−0.052 ± 0.003 to −0.223 ± 0.012 −0.123 ± 0.003 to −0.443 ± 0.002
– +1.397 ± 0.005–+1.210 ± 0.014
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likely to constitute the relatively stable regions. It is expected that the MROs of these regions in liquid may compete with the corresponding crystals, and thus reduce atomic diffusivity and increase the viscosity. This is responsible for the high thermal stability (i.e., glass transition temperature Tg or crystallization onset temperature Tx) and GFA of Co57B35Ta8 alloy. On the other hand, the rigid clusters and stable regions formed in glasses are anticipated to better resist to plastic flow. This is also the structure origin of ultra-high mechanical strength of CoeB-based glassy alloys. Accordingly, Tg value is a good macroscopic to gauge the mechanical strength. The relevant researches to build a quantitative scaling relation between yield strength and Tg have been done by Johnson and Samwer [38] and Liu et al. [39].
4.2. Relationships between local atomic structure and properties Previous experimental research [10] has reported that Co57Ta8B35 glassy alloy exhibits higher thermal stability and GFA as well as better mechanical strength than Co65B35 alloy. Here, the relationships of properties with local atomic structures were discussed. As well known, in some glassy alloys with non-directional metallic bonds, e.g., CueZr [4,33,34], CueZreAl [5,6,35], ZreNi [36], ZrePd [37], etc., icosahedra which are structurally different from typical crystalline units can stabilize the liquids. In the case of the present CoeB-based glassy alloys, the primary structure-forming clusters are B-centered Z9 and Z10 Kasper polyhedra which have a relatively lower potential energy and higher stability than other solute-centered clusters because of their strong covalent-like bonding as well as minimum disclinations. In particular, the increase in the fivefold environment and total fraction of these favored SRO clusters caused by the appropriate addition of Ta is conducive to the structural stability in liquid/glass. Since these SROs are very similar to the local motifs in the competing crystals, the stability of structure is also considered to originate from their efficient packing over medium range. Miracle et al. [29] reported an efficient cluster packing (ECP) model and suggested that the crystal-like packing of clusters is efficient and stable. According to this model, the B–centered clusters in binary Co65B35 glassy alloy form a simple cubic (sc) array represented as < 9 > sc with B solutes fully occupying α and β sites. The αΩ anti-site defects are also presented, which is in good agreement with the calculated BeB nearest neighbor peak as shown in Fig. 1. The replacement of Co with Ta in Co65B35 alloy would produce a face-centered cubic (fcc) cluster packing structure written as < 16, 9 > fcc. As the primary cluster-forming solute species α, the concentration of Ta element (CTa) is predicted by:
CTa =
100STa , ∑S
5. Conclusions In summary, the local atomic structures of Co65B35 and Co57B35Ta8 glassy alloys were studied by using AIMD method. The first shell of the Co57B35Ta8 alloy has a higher CN, which indicates a denser amorphous structure. The HA index shows that the population of 1551 bond pairs is higher for the Ta-bearing glassy alloy. The Voronoi tessellation analysis shows that the B-centered Z9 and Z10 Kasper polyhedra are primary structure-forming clusters in CoeB-based glassy alloys. The formation of these regular clusters can be attributed to the efficient dense packing as well as the strong chemical interaction indicated by the results of CSRO parameter and electronic charge density. Compared with the Co65B35 glassy alloy, the Co57B35Ta8 alloy has a higher fraction of Bcentered Z9 and Z10 Kasper polyhedral clusters. This is in good agreement with the fact that the fivefold environment is increased by the addition of Ta element as shown by HA index. According to the ECP model, the optimal concentration of Ta element to produce a fcc cluster packing structure is about 7.6 at.%. The result indicates that the structure of Co57B35Ta8 which is in favor of the ECP model is efficient and stable within the typical range of MRO. Higher fraction of B-centered Z9 and Z10 Kasper polyhedra as well as their efficient and stable packing over medium range is responsible for a higher thermal stability and a better resistance to plastic flow. As a result, Co57B35Ta8 glassy alloy exhibits a larger GFA and higher yield strength than Ta-free glassy alloy.
(2)
where STa represents the total number of Ta element per α site. ∑S is the total number of structural sites which is given by the following equation:
∑ S = ∑j
Sj.
(3)
Acknowledgements
For fcc packing, there is 1 β site and 2 γ sites for α site, so that Sβ = 1 and Sγ = 2. The total number of solvent (Ω) sites per α site (SΩ ) is obtained by:
⎡ Nα − Ω SΩ = ⎢ φ ⎢1 + Nα − Ω ⎣
( )
⎤ ⎥, ⎥ ⎦
This work was financially supported by the National Natural Science Foundation of China (Grant No. 51501166), National Key Research and Development Program of China (Grant No. 2017YFB0702504), Foundation of Henan Educational Committee (Grant Nos. 13A430668 and 15A430002), and Outstanding Young Talent Research Fund of Zhengzhou University (Grant No. 1421320046).
(4)
where Nα − Ω is specified by R* [29]. φ is equal to 12 in fcc structure. If we assume that the α (Ta) solutes completely occupy α sites, the CTa value was calculated as about 7.6 by combining Eqs. (2), (3) and (4). This result indicates that the structure of Co57B35Ta8 glassy alloy which is in favor of the ECP model is efficient within the typical range of medium range ordering (MRO). In addition, as indicated by the partial PDF of BeB (Fig. 2(c)), neighbor contact between solute B becomes unavoidable. As suggested by Sheng et al. [13], such a string-like interconnection would reduce the numbers of like bonds, leading to the reduction of energy. The higher NBeB value for the Co57B35Ta8 also makes a contribution to the increase in structural stability. Moreover, due to the lower electronegative of Ta, the addition of Ta to replace Co would cause more electrons transfer to the surrounding space of B atoms. By accepting electrons transferred from Ta, BeB bonds would become much stronger as revealed by the charge density distribution of B atoms (see Section 3.4), and hence the connection of B-centered clusters would become more stable. Above all, the higher content of regular Z9 and Z10 clusters and their efficient and stable packing for the Co57B35Ta8 glassy alloy are
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