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The deformation and transformation of icosahedron in Mg70Zn30 metallic glasses
Accepted Manuscript Research paper The deformation and transformation of icosahedron in Mg70Zn30 metallic glasses Yongchao Liang, Yuehong Zhang, Bangyi Yu, Rangsu Liu, Quan Xie, Zean Tian PII: DOI: Reference:
S0009-2614(18)30382-8 https://doi.org/10.1016/j.cplett.2018.05.017 CPLETT 35633
To appear in:
Chemical Physics Letters
Received Date: Revised Date: Accepted Date:
5 March 2018 17 April 2018 9 May 2018
Please cite this article as: Y. Liang, Y. Zhang, B. Yu, R. Liu, Q. Xie, Z. Tian, The deformation and transformation of icosahedron in Mg70Zn30 metallic glasses, Chemical Physics Letters (2018), doi: https://doi.org/10.1016/j.cplett. 2018.05.017
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
The deformation and transformation of icosahedron in Mg70Zn30 metallic glasses Yongchao Liang 1, Yuehong Zhang 1, Bangyi Yu 1, Rangsu Liu 2, Quan Xie 1, Zean Tian 1,* 1 2
School of Big Data and information engineering, Guizhou University, Guiyang 550025, China School of Physics and Electronics, Hunan University, Changsha 410082, China
Abstract: A molecular dynamics simulation is performed to investigate the icosahedron in Mg70Zn30 metallic glass during solidification at the cooling rate of 1×1013 K/s. It is found that the 1551, 1541 and 1431 bond-types are closely related to 13-atom icosahedron-like clusters. Two kinds of clusters are very similar to full icosahedron in geometry. The three clusters can transform into each other by changing one bond between a pair of outer atoms. One distorted icosahedron act as the intermediate between the two others. This work provides an insight into the glass formation in alloy from the cluster-level structural viewpoint and will shed light on developing more metallic glasses.
Keywords: Deformed icosahedron, Transformation, Amorphous bond-types, The relative rate, Molecular dynamics simulation. PACS:
61.20.Ja, 61.25.Mv, 64.70.pe, 71.15.Pd
____________________________________________________________ *Corresponding author. E-mail address: [email protected]
1. Introduction The atomic structures of metallic glasses is a long-standing scientific problem [1]. Unlike crystalline metals in which atoms arrange orderly, metallic glasses (MGs) and their parent liquids are amorphous in structure, including different kinds of short- and middle-order, but no long-range order [2]. The internal structure of such materials, therefore, needs to be understood at the atomic level. More than half a century ago, Frank proposed that the icosahedron is the most favorable local order in monatomic metallic liquids because of its high packing fraction [3], successfully explaining the feasibility of achieving undercooling below the melting point. However, icosahedron is difficult to grow, owing to the geometrical frustration opposite to the translational periodicity [4]. Icosahedral clusters in MGs or liquids are found to be distorted in diverse configurations [5]. In fact in a real system, for the atoms in an icosahedron the center-to-shell atomic size ratio is not exactly 0.902, and the glass/liquid is often a concentrated alloy such that the shell is composed of both A and B atoms with different sizes [6]. Previous studies revealed that in amorphous Cu-Zr alloys, the Cu-centered icosahedron was found to be a key structural motif, characterized by high packing density [7] and high shear resistance. But inside shear bands icosahedral backbone is defective because of the high degree of plastic deformation; whereas Zr-centered <0, 2, 8, 5> clusters could be a key structural motif [8]. The fivefold rotational symmetry in MGs clusters recently become one of the focuses in modern models in which the disordered icosahedrons were included (called as icosahedral-like clusters) [9], and icosahedral-like clusters have been reported to play an important role in the glass transition [10] and plasticity [11]. At present, it is still difficult in experiment to obtain the structural details of disordered systems such as liquids, super-cooled liquids, and amorphous solids. Molecular dynamics (MD) simulation is an efficient remedy. With MD simulation, this paper firstly identified two deformations of icosahedron caused by slight displacement of a pair of coordination atoms in Mg70Zn30 alloy, and investigated the transformation pathways between them and their stability. It is found that relative to icosahedron, the more the deformation degree is, the more unstable the structures.
2. Simulation methods The simulation is conducted under the NVT ensemble [12] with 3D periodic boundary condition in a cubic box containing 7×106 Mg atoms and 3×106 Zn atoms. The box size determined by both the number of atoms and the mean volume of each atom at each given temperature at a constant pressure. The interatomic potentials of Mg70Zn30 alloy used here are the effective pair potential that is derived from the generalized nonlocal model pseudo-potential (GNMP). The GNMP potential is based
Vij (r )
Z eff ,i Z eff , j r
{1 (
1
0
dq[ Fi , j (q) Fj ,i (q)]
sin(rq) }, q
where Zeff and F(q) are, respectively, the effective ionic valence and the normalized energy wave number characteristic, which were defined in detail in Refs. 13, 14. The pair-wise potentials are cut off at 20 a.u. (atomic unit). The time step is 5 1015 s. For the simple metals and their alloys, the accuracy and reliability of this potential have been extensively demonstrated by computing their structural, dynamic, and thermodynamics properties [13-15]. First of all, let the system run 20000 time steps to obtain equilibrium liquid state. The damped force method [16-18] is adopted to control the temperature of the system decreasing linearly from 873 to 273 K at the cooling rate of 1×1013 K/s. This cooling rate is much higher than that can be conducted in experiment, however it is proper for the investigation upon icosahedrons, not only it is high enough to vitrify almost all pure metals and alloys and hence favours the formation of amorphous (icosahedron-like) microstructures [19], but also it is acceptable in computational time for the huge system (totally including 107atoms) [20]. At each given temperature, the instantaneous spatial coordinates of each atom are recorded for the analyses of microstructure.
3. Results and discussion
Since the pair distribution function (PDF) is a Fourier transformation of the structure factor S(q) obtained from diffraction experiment, it can be used to verify the simulation. Fig. 1 displays the PDF curves at different temperatures during the cooling process of liquid Mg70Zn30 alloy, in which the experimental results of the PDFs at 673 K (liquid) and 293 K (glass) come from a conversion of the reduced PDF in Ref. 21 measured by neutron diffraction. It can be found that the simulation results agree well with the experiment. Therefore the simulation method described here is correct and the results are reliable. From Fig.1, it is clearly seen that the splitting of the second peak of the total PDF becomes pronounced with the decreasing of temperature, which indicates the formation of Mg70Zn30 metallic glass and the enhancement of SRO during the quenching processes.
Fig. 1. Pair distribution function curves at different temperatures during the cooling process of liquid Mg70Zn30 alloy. Experimental points are taken from Ref. 21 measured by neutron diffraction. The HA bond-type index method [22] has been proved to be successful in describing the local configurations of the liquid, amorphous, and crystal structures. In this method, a set of four integers ijkl is designed to describe the different local configurations. The first integer i is to identify the bonding of two given atoms (root pair), i is 1 when they are bonded for the root pair, otherwise i is 2. The second integer j is the number of near neighbor atoms shared by the root pair. The third integer k is the number of bonds among the shared neighbors. The fourth integer l is
needed to distinguish configurations that have the same first three indices but are different in bonding geometries. Different structures have different HA indices and general observations are as follows: the fcc structure has only 12×1421 bond-type; the hcp structure has 6×1421 bond-type and 6×1422 bond-type; the bcc structure has 6×1441 bond-type and 8×1661 bond-type; while the 1551, 1541 and 1431 bond-types are characteristic bond-types of typical liquid and amorphous states.
Fig. 2. (a) The 1551 and 1541 bond-types geometries with the five-fold symmetry, 1431 are also five-fold symmetrical if the deviated atom (the dotted atom) is considered together; (b) Evolutions of relative number of various bond-types during the rapid quenching processes of Mg70Zn30 alloy.
Fig 2(a) shows the 1551 and 1541 bond-types with the five-fold symmetry, as well as the 1431 bond-types that usually are also five-fold symmetrical if the deviated atom is considered together, closely related to the icosahedron or disordered
icosahedron. It is emphasized that the icosahedra dominates only in a limited number of alloys (at certain MG compositions), while the five-fold symmetry are always preferred across the board for all MGs and liquids [2]. So, the fivefold bonds as obtained from the HA index generically are populous in various types of MGs clusters. For the Mg70Zn30 metallic glass obtained, the 1551, 1541, and 1431 bond-types, amount to over 75% of the total number as shown in Fig 2(b). Whereas the small percentage of 1421, 1422, 1441 and 1661 bond-types are related to the hcp, fcc, and bcc crystalline orders are insignificant. Moreover, only the 1551 bond-type increases remarkably with decreasing temperature, while others change only a little. This suggests that the five-fold local symmetry in the simulated systems increases during the rapid quenching. In order to concisely characterize clusters in the system, based on the work of Qi and Wang [23], the authors have proposed a cluster-type index method (CTIM), as shown in detail in Refs. 24. In CTIM, a basic cluster is defined as composed of a center atom and its surrounding atoms. At present, for deep understanding the specific structure characteristics of this system, based on our previous works, a new cluster-type index method (CTIM-3) have been proposed. In CTIM-3, a basic cluster is expressed by nine (integer) index of (N, n1, n2, n3, n4, n5, n6, n7, n8), where N is the number of surrounding atoms of the central atom in the basic cluster, namely, the coordination number(CN), and n1, n2, n3, n4, n5, n6, n7, n8 in turn denote the numbers of 1441, 1551, 1661, 1421, 1422, 1541, 1431 and 1321 bond-types (expressed by Honeycutt-Anderson (HA) bond-type index method [22]) connected surrounding atoms to the central atom. For example, the icosahedron basic cluster can be expressed by (12 0 12 0 0 0 0 0 0); similarly, the BCC, FCC, HCP basic clusters expressed in turn by (14 6 0 8 0 0 0 0 0), (12 0 0 0 12 0 0 0 0) and (12 0 0 0 6 6 0 0 0) respectively [25]. Fig. 3 shows an icosahedron and two disordered icosahedron selected from the Mg70Zn30 system. An icosahedron basic cluster that is composed of one central atom and 12 neighbor atoms (they all form 1551 bond-type with the central atom). When one bond between a pair of outer atoms in an icosahedron is broken, four of these
1551 bond-types transform into two 1541 bond-types and two 1431 bond-types. After such transformation, (12 0 8 0 0 0 2 2 0) is formed and here defined as Disordered Icosahedron I (DI), which consists of eight 1551 bond-types, two 1541 bond-types and two 1431 bond-types. As the two un-bonded atoms continue to pull apart further, two 1431 bond-types get transformed into two 1441 bond-types and the two 1541 bond-types into two 1661 bond-types; a (12 2 8 2 0 0 0 0 0) is formed, defined as Disordered Icosahedron II (DII), which consists of eight 1551 bond-types, two 1441 bond-types and two 1661 bond-types. It shows that the DII has characteristics of fourand six-fold symmetry. Hirata indicates that the distorted icosahedra are in an intermediate state between two densely packed configurations: the ideal icosahedron and the fcc cluster in Zr80Pt20 alloy [4].
Fig. 3. Three basic clusters in Mg70Zn30 system: An icosahedron (12 0 12 0 0 0 0 0 0) with center atom of 8543126; A disordered icosahedron (12 0 8 0 0 0 2 2 0) with central atom of 7708405; A disordered icosahedron (12 2 8 2 0 0 0 0 0) with central atom 8002347. (Light color (green) is for Mg atom, dark color (blue) is for Zn atom).
For further deeply understanding the microstructure evolution in this system, we
have obtained the numbers of various main basic clusters in Mg70Zn30 alloy as shown in Fig. 4. At 273 K, there are thousands of kinds of basic clusters that can be described by CTIM-3 in the system. For simplicity, only the top 10 cluster-types (in number) are shown in Fig. 4. One can find that the icosahedral and DI clusters are the first two basic clusters, and the DII clusters also appear in the top 10 cluster-types. So, three typical clusters have representability in this system. With decreasing temperature, the icosahedral cluster and the DI cluster increase remarkably while others increase slightly. This demonstrates that the two basic clusters play a critical role in the microstructure transition during rapid solidification process. It can be clearly seen that the DI cluster is the most prominent in the liquid region. The percentage of the icosahedral cluster exceeds that of DI clusters at T<500 K.
Fig. 4. Relations of the percentage of major basic clusters with temperature.
In order to deeply understand the formation mechanism of three typical clusters during the rapid solidification of Mg70Zn30 alloy, the heredity and evolution of the clusters are further investigated by means of an inverse tracking method. The heredity of basic clusters is defined as follows. When temperature decreases from T to T-ΔT, if the geometry of basic clusters and IDs of the atoms keep unchanged, the evolution of basic clusters will be called as the self-inheritance [26, 27], including ICO-ICO,
DI-DI and DII-DII; if the geometry of an ICO at temperature T has changed into DI at temperature T-ΔT, this evolution is called as ICO-DI transformation; Similarly all such transformations include ICO-DII, DI-ICO, DI-DII, DII-ICO and DII-DI as shown in Fig. 5. The descendible fraction of ICOs is marked as follows: when temperature decreases from T to T-ΔT, if x of N ICOs are unchanged, the percentage of ICO-ICO self-inheritance is defined as fICO-ICO= (x/N) × 100%; and if y of N ICOs has changed into DIs, then the percentage of ICO-DI is fICO-DI= (y/N) × 100%; and if z of N ICOs has changed into DIIs, then the percentage of ICO-DII is fICO-DII=(z/N)×100%; obviously (fICO-ICO + fICO-DI + fICO-DII)≤100% at any temperature.
Fig. 5. The transformation regulation among three typical clusters：(a) the evolution of ICO, (b) the evolution of DI, (c) the evolution of DII.
The transformation regulation among three typical clusters is shown in Fig. 5. During the rapid solidification, at T>Tm (The melting point of Mg70Zn30 alloy is about 616 K [28]) neither self-inheritance nor transformation can be found. At T<600 K, The evolution has three characteristics: (1) The percentages of ICO-ICO, DI-DI, DII-DII self-inheritance are in turn 56.03%, 24.18%, 9.15% at 273 K. The higher
percentage of self-inheritance, the more stable atomic structure is. Sorting by the stability of atomic structure, predicts that ICO is the most stable; (2) At 273 K, 8.65%-(ICO-DI) > 0.77%-(ICO-DII), 18.55%-(DI-ICO) > 2.16%-(DI-DII), and 12.21%-(DII-DI) > 4.94%-(DII-ICO). A careful analysis reveals that the available evolution is ICO↔DI←DII, where DI is the intermediate state between ICO and DII clusters. (3) The ico-targeted transformation of DI-ICO and DII-ICO falls over at low-temperature regions, as shown in Figs. 5(b) and (c). Because at low temperature, the kinetic energy of atoms is much lower, and the energy fluctuation is also much less, hence it is more difficult to go over the energy barrier for the transformation of DI-ICO and DII-ICO. The stability of clusters is critical for their formation during the rapid solidification. To this end, we proposed a parameter called as the relative rate M that is defined as
M
r rT2 1 ncluster CN T1 , 1 ncluster CN 1 rT1
where ncluster is the number of a certain kind of cluster, CN is the coordination number, r is the distance from coordination atom to the center, and T1/T2 are two neighbouring temperatures (or record points). M is a simple but effective index to measure the structure change degree between two temperatures, and obviously the lower the value of M, the more stable the structure. The value of M for three clusters at several temperatures is shown in Fig. 6, and three points can be obtained. (1) For the three kinds of clusters, M decreases with the decrease of temperature, indicating that the atomic motion in the liquid state is more active than that in the solid state, and the lower the temperature is, the more stable the clusters are. (2) M for ICOs is always the lowest, followed by DI and DII in order, therefore in Mg70Zn30 alloys ICO is most stable, DII is most unstable, and DI is in-between. This stability order is consistent with the highest ICO-ICO self-inheritance and the transformation pathway of ICO↔DI←DII. (3) M for DII is much higher than the other two and with temperature decreasing decreases much more rapidly, thus the stability of DII is not only worst but also affected most remarkably by temperature.
Fig. 6. The relative rate M of the three structures v.s. temperature.
4. Conclusions We have systematically studied the icosahedra and two icosahedral-like clusters in Mg70Zn30 metallic glasses by employing classical MD simulations with generalized nonlocal model pseudo potential. The following conclusions are obtained. (1) The differences and relationship among icosahedra and two icosahedral-like clusters are discussed by the 1551, 1541 and 1431 bond-types with the five-fold symmetry. When one bond between a pair of outer atoms in a cluster changes, the three clusters can transform into each other. (2) The transformation regulation among three typical clusters is shown that in the evolution of ICO↔DI←DII, where DI act as an intermediate state between ICO and DII clusters during the rapid solidification. (3) The comparative results of the three relative rate M have shown that the structure of ICO is the most stable, followed by DI and DII in order.
Acknowledgements This work has been supported by the National Natural Science Foundation of China (Grant Nos. 51661005, U1612442 and 51771033). The authors are grateful to the Natural Science Foundation of Guizhou Province of China (Grant No. [2017]1025), Sci-Tech Cooperation Program of Guizhou Province of China (grant no. [2015]7645), and the funds for the talents introduction program of
Guizhou University of China (Grant No. [2014]34).
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Highlights . Two kinds of deformed icosahedrons are identified based on slight change of one pair. . The transforming pathways between icosahedron and the two deformed icosahedrons are discussed. . The structure of icosahedron is the most stable by measuring the relative rate M.
GA
The full icosahedron and two slightly disordered icosahedrons are identified in the Mg70Zn30 system. The transform and heredity between such three structures have been discussed. The stability of them is measured and full icosahedron is the most stable.
S0009-2614(18)30382-8 https://doi.org/10.1016/j.cplett.2018.05.017 CPLETT 35633
To appear in:
Chemical Physics Letters
Received Date: Revised Date: Accepted Date:
5 March 2018 17 April 2018 9 May 2018
Please cite this article as: Y. Liang, Y. Zhang, B. Yu, R. Liu, Q. Xie, Z. Tian, The deformation and transformation of icosahedron in Mg70Zn30 metallic glasses, Chemical Physics Letters (2018), doi: https://doi.org/10.1016/j.cplett. 2018.05.017
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
The deformation and transformation of icosahedron in Mg70Zn30 metallic glasses Yongchao Liang 1, Yuehong Zhang 1, Bangyi Yu 1, Rangsu Liu 2, Quan Xie 1, Zean Tian 1,* 1 2
School of Big Data and information engineering, Guizhou University, Guiyang 550025, China School of Physics and Electronics, Hunan University, Changsha 410082, China
Abstract: A molecular dynamics simulation is performed to investigate the icosahedron in Mg70Zn30 metallic glass during solidification at the cooling rate of 1×1013 K/s. It is found that the 1551, 1541 and 1431 bond-types are closely related to 13-atom icosahedron-like clusters. Two kinds of clusters are very similar to full icosahedron in geometry. The three clusters can transform into each other by changing one bond between a pair of outer atoms. One distorted icosahedron act as the intermediate between the two others. This work provides an insight into the glass formation in alloy from the cluster-level structural viewpoint and will shed light on developing more metallic glasses.
Keywords: Deformed icosahedron, Transformation, Amorphous bond-types, The relative rate, Molecular dynamics simulation. PACS:
61.20.Ja, 61.25.Mv, 64.70.pe, 71.15.Pd
____________________________________________________________ *Corresponding author. E-mail address: [email protected]
1. Introduction The atomic structures of metallic glasses is a long-standing scientific problem [1]. Unlike crystalline metals in which atoms arrange orderly, metallic glasses (MGs) and their parent liquids are amorphous in structure, including different kinds of short- and middle-order, but no long-range order [2]. The internal structure of such materials, therefore, needs to be understood at the atomic level. More than half a century ago, Frank proposed that the icosahedron is the most favorable local order in monatomic metallic liquids because of its high packing fraction [3], successfully explaining the feasibility of achieving undercooling below the melting point. However, icosahedron is difficult to grow, owing to the geometrical frustration opposite to the translational periodicity [4]. Icosahedral clusters in MGs or liquids are found to be distorted in diverse configurations [5]. In fact in a real system, for the atoms in an icosahedron the center-to-shell atomic size ratio is not exactly 0.902, and the glass/liquid is often a concentrated alloy such that the shell is composed of both A and B atoms with different sizes [6]. Previous studies revealed that in amorphous Cu-Zr alloys, the Cu-centered icosahedron was found to be a key structural motif, characterized by high packing density [7] and high shear resistance. But inside shear bands icosahedral backbone is defective because of the high degree of plastic deformation; whereas Zr-centered <0, 2, 8, 5> clusters could be a key structural motif [8]. The fivefold rotational symmetry in MGs clusters recently become one of the focuses in modern models in which the disordered icosahedrons were included (called as icosahedral-like clusters) [9], and icosahedral-like clusters have been reported to play an important role in the glass transition [10] and plasticity [11]. At present, it is still difficult in experiment to obtain the structural details of disordered systems such as liquids, super-cooled liquids, and amorphous solids. Molecular dynamics (MD) simulation is an efficient remedy. With MD simulation, this paper firstly identified two deformations of icosahedron caused by slight displacement of a pair of coordination atoms in Mg70Zn30 alloy, and investigated the transformation pathways between them and their stability. It is found that relative to icosahedron, the more the deformation degree is, the more unstable the structures.
2. Simulation methods The simulation is conducted under the NVT ensemble [12] with 3D periodic boundary condition in a cubic box containing 7×106 Mg atoms and 3×106 Zn atoms. The box size determined by both the number of atoms and the mean volume of each atom at each given temperature at a constant pressure. The interatomic potentials of Mg70Zn30 alloy used here are the effective pair potential that is derived from the generalized nonlocal model pseudo-potential (GNMP). The GNMP potential is based
Vij (r )
Z eff ,i Z eff , j r
{1 (
1
0
dq[ Fi , j (q) Fj ,i (q)]
sin(rq) }, q
where Zeff and F(q) are, respectively, the effective ionic valence and the normalized energy wave number characteristic, which were defined in detail in Refs. 13, 14. The pair-wise potentials are cut off at 20 a.u. (atomic unit). The time step is 5 1015 s. For the simple metals and their alloys, the accuracy and reliability of this potential have been extensively demonstrated by computing their structural, dynamic, and thermodynamics properties [13-15]. First of all, let the system run 20000 time steps to obtain equilibrium liquid state. The damped force method [16-18] is adopted to control the temperature of the system decreasing linearly from 873 to 273 K at the cooling rate of 1×1013 K/s. This cooling rate is much higher than that can be conducted in experiment, however it is proper for the investigation upon icosahedrons, not only it is high enough to vitrify almost all pure metals and alloys and hence favours the formation of amorphous (icosahedron-like) microstructures [19], but also it is acceptable in computational time for the huge system (totally including 107atoms) [20]. At each given temperature, the instantaneous spatial coordinates of each atom are recorded for the analyses of microstructure.
3. Results and discussion
Since the pair distribution function (PDF) is a Fourier transformation of the structure factor S(q) obtained from diffraction experiment, it can be used to verify the simulation. Fig. 1 displays the PDF curves at different temperatures during the cooling process of liquid Mg70Zn30 alloy, in which the experimental results of the PDFs at 673 K (liquid) and 293 K (glass) come from a conversion of the reduced PDF in Ref. 21 measured by neutron diffraction. It can be found that the simulation results agree well with the experiment. Therefore the simulation method described here is correct and the results are reliable. From Fig.1, it is clearly seen that the splitting of the second peak of the total PDF becomes pronounced with the decreasing of temperature, which indicates the formation of Mg70Zn30 metallic glass and the enhancement of SRO during the quenching processes.
Fig. 1. Pair distribution function curves at different temperatures during the cooling process of liquid Mg70Zn30 alloy. Experimental points are taken from Ref. 21 measured by neutron diffraction. The HA bond-type index method [22] has been proved to be successful in describing the local configurations of the liquid, amorphous, and crystal structures. In this method, a set of four integers ijkl is designed to describe the different local configurations. The first integer i is to identify the bonding of two given atoms (root pair), i is 1 when they are bonded for the root pair, otherwise i is 2. The second integer j is the number of near neighbor atoms shared by the root pair. The third integer k is the number of bonds among the shared neighbors. The fourth integer l is
needed to distinguish configurations that have the same first three indices but are different in bonding geometries. Different structures have different HA indices and general observations are as follows: the fcc structure has only 12×1421 bond-type; the hcp structure has 6×1421 bond-type and 6×1422 bond-type; the bcc structure has 6×1441 bond-type and 8×1661 bond-type; while the 1551, 1541 and 1431 bond-types are characteristic bond-types of typical liquid and amorphous states.
Fig. 2. (a) The 1551 and 1541 bond-types geometries with the five-fold symmetry, 1431 are also five-fold symmetrical if the deviated atom (the dotted atom) is considered together; (b) Evolutions of relative number of various bond-types during the rapid quenching processes of Mg70Zn30 alloy.
Fig 2(a) shows the 1551 and 1541 bond-types with the five-fold symmetry, as well as the 1431 bond-types that usually are also five-fold symmetrical if the deviated atom is considered together, closely related to the icosahedron or disordered
icosahedron. It is emphasized that the icosahedra dominates only in a limited number of alloys (at certain MG compositions), while the five-fold symmetry are always preferred across the board for all MGs and liquids [2]. So, the fivefold bonds as obtained from the HA index generically are populous in various types of MGs clusters. For the Mg70Zn30 metallic glass obtained, the 1551, 1541, and 1431 bond-types, amount to over 75% of the total number as shown in Fig 2(b). Whereas the small percentage of 1421, 1422, 1441 and 1661 bond-types are related to the hcp, fcc, and bcc crystalline orders are insignificant. Moreover, only the 1551 bond-type increases remarkably with decreasing temperature, while others change only a little. This suggests that the five-fold local symmetry in the simulated systems increases during the rapid quenching. In order to concisely characterize clusters in the system, based on the work of Qi and Wang [23], the authors have proposed a cluster-type index method (CTIM), as shown in detail in Refs. 24. In CTIM, a basic cluster is defined as composed of a center atom and its surrounding atoms. At present, for deep understanding the specific structure characteristics of this system, based on our previous works, a new cluster-type index method (CTIM-3) have been proposed. In CTIM-3, a basic cluster is expressed by nine (integer) index of (N, n1, n2, n3, n4, n5, n6, n7, n8), where N is the number of surrounding atoms of the central atom in the basic cluster, namely, the coordination number(CN), and n1, n2, n3, n4, n5, n6, n7, n8 in turn denote the numbers of 1441, 1551, 1661, 1421, 1422, 1541, 1431 and 1321 bond-types (expressed by Honeycutt-Anderson (HA) bond-type index method [22]) connected surrounding atoms to the central atom. For example, the icosahedron basic cluster can be expressed by (12 0 12 0 0 0 0 0 0); similarly, the BCC, FCC, HCP basic clusters expressed in turn by (14 6 0 8 0 0 0 0 0), (12 0 0 0 12 0 0 0 0) and (12 0 0 0 6 6 0 0 0) respectively [25]. Fig. 3 shows an icosahedron and two disordered icosahedron selected from the Mg70Zn30 system. An icosahedron basic cluster that is composed of one central atom and 12 neighbor atoms (they all form 1551 bond-type with the central atom). When one bond between a pair of outer atoms in an icosahedron is broken, four of these
1551 bond-types transform into two 1541 bond-types and two 1431 bond-types. After such transformation, (12 0 8 0 0 0 2 2 0) is formed and here defined as Disordered Icosahedron I (DI), which consists of eight 1551 bond-types, two 1541 bond-types and two 1431 bond-types. As the two un-bonded atoms continue to pull apart further, two 1431 bond-types get transformed into two 1441 bond-types and the two 1541 bond-types into two 1661 bond-types; a (12 2 8 2 0 0 0 0 0) is formed, defined as Disordered Icosahedron II (DII), which consists of eight 1551 bond-types, two 1441 bond-types and two 1661 bond-types. It shows that the DII has characteristics of fourand six-fold symmetry. Hirata indicates that the distorted icosahedra are in an intermediate state between two densely packed configurations: the ideal icosahedron and the fcc cluster in Zr80Pt20 alloy [4].
Fig. 3. Three basic clusters in Mg70Zn30 system: An icosahedron (12 0 12 0 0 0 0 0 0) with center atom of 8543126; A disordered icosahedron (12 0 8 0 0 0 2 2 0) with central atom of 7708405; A disordered icosahedron (12 2 8 2 0 0 0 0 0) with central atom 8002347. (Light color (green) is for Mg atom, dark color (blue) is for Zn atom).
For further deeply understanding the microstructure evolution in this system, we
have obtained the numbers of various main basic clusters in Mg70Zn30 alloy as shown in Fig. 4. At 273 K, there are thousands of kinds of basic clusters that can be described by CTIM-3 in the system. For simplicity, only the top 10 cluster-types (in number) are shown in Fig. 4. One can find that the icosahedral and DI clusters are the first two basic clusters, and the DII clusters also appear in the top 10 cluster-types. So, three typical clusters have representability in this system. With decreasing temperature, the icosahedral cluster and the DI cluster increase remarkably while others increase slightly. This demonstrates that the two basic clusters play a critical role in the microstructure transition during rapid solidification process. It can be clearly seen that the DI cluster is the most prominent in the liquid region. The percentage of the icosahedral cluster exceeds that of DI clusters at T<500 K.
Fig. 4. Relations of the percentage of major basic clusters with temperature.
In order to deeply understand the formation mechanism of three typical clusters during the rapid solidification of Mg70Zn30 alloy, the heredity and evolution of the clusters are further investigated by means of an inverse tracking method. The heredity of basic clusters is defined as follows. When temperature decreases from T to T-ΔT, if the geometry of basic clusters and IDs of the atoms keep unchanged, the evolution of basic clusters will be called as the self-inheritance [26, 27], including ICO-ICO,
DI-DI and DII-DII; if the geometry of an ICO at temperature T has changed into DI at temperature T-ΔT, this evolution is called as ICO-DI transformation; Similarly all such transformations include ICO-DII, DI-ICO, DI-DII, DII-ICO and DII-DI as shown in Fig. 5. The descendible fraction of ICOs is marked as follows: when temperature decreases from T to T-ΔT, if x of N ICOs are unchanged, the percentage of ICO-ICO self-inheritance is defined as fICO-ICO= (x/N) × 100%; and if y of N ICOs has changed into DIs, then the percentage of ICO-DI is fICO-DI= (y/N) × 100%; and if z of N ICOs has changed into DIIs, then the percentage of ICO-DII is fICO-DII=(z/N)×100%; obviously (fICO-ICO + fICO-DI + fICO-DII)≤100% at any temperature.
Fig. 5. The transformation regulation among three typical clusters：(a) the evolution of ICO, (b) the evolution of DI, (c) the evolution of DII.
The transformation regulation among three typical clusters is shown in Fig. 5. During the rapid solidification, at T>Tm (The melting point of Mg70Zn30 alloy is about 616 K [28]) neither self-inheritance nor transformation can be found. At T<600 K, The evolution has three characteristics: (1) The percentages of ICO-ICO, DI-DI, DII-DII self-inheritance are in turn 56.03%, 24.18%, 9.15% at 273 K. The higher
percentage of self-inheritance, the more stable atomic structure is. Sorting by the stability of atomic structure, predicts that ICO is the most stable; (2) At 273 K, 8.65%-(ICO-DI) > 0.77%-(ICO-DII), 18.55%-(DI-ICO) > 2.16%-(DI-DII), and 12.21%-(DII-DI) > 4.94%-(DII-ICO). A careful analysis reveals that the available evolution is ICO↔DI←DII, where DI is the intermediate state between ICO and DII clusters. (3) The ico-targeted transformation of DI-ICO and DII-ICO falls over at low-temperature regions, as shown in Figs. 5(b) and (c). Because at low temperature, the kinetic energy of atoms is much lower, and the energy fluctuation is also much less, hence it is more difficult to go over the energy barrier for the transformation of DI-ICO and DII-ICO. The stability of clusters is critical for their formation during the rapid solidification. To this end, we proposed a parameter called as the relative rate M that is defined as
M
r rT2 1 ncluster CN T1 , 1 ncluster CN 1 rT1
where ncluster is the number of a certain kind of cluster, CN is the coordination number, r is the distance from coordination atom to the center, and T1/T2 are two neighbouring temperatures (or record points). M is a simple but effective index to measure the structure change degree between two temperatures, and obviously the lower the value of M, the more stable the structure. The value of M for three clusters at several temperatures is shown in Fig. 6, and three points can be obtained. (1) For the three kinds of clusters, M decreases with the decrease of temperature, indicating that the atomic motion in the liquid state is more active than that in the solid state, and the lower the temperature is, the more stable the clusters are. (2) M for ICOs is always the lowest, followed by DI and DII in order, therefore in Mg70Zn30 alloys ICO is most stable, DII is most unstable, and DI is in-between. This stability order is consistent with the highest ICO-ICO self-inheritance and the transformation pathway of ICO↔DI←DII. (3) M for DII is much higher than the other two and with temperature decreasing decreases much more rapidly, thus the stability of DII is not only worst but also affected most remarkably by temperature.
Fig. 6. The relative rate M of the three structures v.s. temperature.
4. Conclusions We have systematically studied the icosahedra and two icosahedral-like clusters in Mg70Zn30 metallic glasses by employing classical MD simulations with generalized nonlocal model pseudo potential. The following conclusions are obtained. (1) The differences and relationship among icosahedra and two icosahedral-like clusters are discussed by the 1551, 1541 and 1431 bond-types with the five-fold symmetry. When one bond between a pair of outer atoms in a cluster changes, the three clusters can transform into each other. (2) The transformation regulation among three typical clusters is shown that in the evolution of ICO↔DI←DII, where DI act as an intermediate state between ICO and DII clusters during the rapid solidification. (3) The comparative results of the three relative rate M have shown that the structure of ICO is the most stable, followed by DI and DII in order.
Acknowledgements This work has been supported by the National Natural Science Foundation of China (Grant Nos. 51661005, U1612442 and 51771033). The authors are grateful to the Natural Science Foundation of Guizhou Province of China (Grant No. [2017]1025), Sci-Tech Cooperation Program of Guizhou Province of China (grant no. [2015]7645), and the funds for the talents introduction program of
Guizhou University of China (Grant No. [2014]34).
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Highlights . Two kinds of deformed icosahedrons are identified based on slight change of one pair. . The transforming pathways between icosahedron and the two deformed icosahedrons are discussed. . The structure of icosahedron is the most stable by measuring the relative rate M.
GA
The full icosahedron and two slightly disordered icosahedrons are identified in the Mg70Zn30 system. The transform and heredity between such three structures have been discussed. The stability of them is measured and full icosahedron is the most stable.