Computational Materials Science 184 (2020) 109895 Contents lists available at ScienceDirect Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci Structural and mechanical behaviors of Mg-Al metallic glasses investigated by molecular dynamics simulations ⁎ ⁎ A Samiri , A Khmich , H Haouas, A Hassani, A Hasnaoui T ⁎ LS3M Laboratory, Polydisciplinary Faculty of Khouribga, Sultan Moulay Slimane University of Beni Mellal, B.P 145, 25000 Khouribga, Morocco A R T I C LE I N FO A B S T R A C T Keywords: Metallic glasses Molecular dynamics Coordination numbers Strain-rate Using molecular dynamics simulations with the embedded atomic method (EAM) to describe interatomic interactions, structural and mechanical properties of Mg-Al metallic glasses (MG) have been investigated for different compositions The atomic structure is characterized using various techniques such as the Radial Distribution Function (RDF), the Voronoi Tessellation Analysis (VTA) and coordination number (CN) distribution The results confirmed that the Mg-Al glass formation is accompanied by a splitting of the RDF second peak upon cooling process The glass transition temperature is determined using different method involving a new suggested way consisting of the cross-over between low and high coordination numbers curves during cooling process This last technique gives approximate results that converge to those given by classical methods On the other hand, we applied a strain-rate of 1010 s−1 at 300 K and showed that with the increase of Al composition, the maximal stress increases as a function of strain For a fixed composition of Mg-Al MG, the yield strength increases with the increase of strain-rate between 109 s−1 and 1010 s−1 The impact of temperature on the mechanical behaviour of Mg-Al under various strain-rates has been investigated and the result suggests that for the same applied strain-rate, the ultimate tensile strength decreases as a function of temperature Finally, the annealing effect has led to a softening of elastic moduli especially the Young modulus (E) which has been determined through both elastic constants Cij and from the stress–strain curve Introduction Metallic glasses (MG) are amorphous alloys obtained by quenching from the liquid phase This method relays on fast cooling of a premelted alloy without leaving the necessary time for the alloy to retrieve its crystalline state [1] The final shape of the produced objects is greatly conditioned by the quenching method because during quenching, the liquid solidifies and the machining of this fragile material is difficult However, the amorphous material once solidified, can be heated and then possess plastic properties of interest for shaping MGs are elaborated by several methods or techniques among which: quenching on wheel, elaboration of ribbons, casting in a mould cooled and quenched by water The glass-forming ability (GFA) is one of the important scientific terminologies in studying MGs; it is defined as the ease or difficulty of the MG to form [2] In the years 1970–2000, two ( ) Tg GFA indicators were commonly used [3]: ΔTX (=TX − Tg ) andTrg = T l where Tg is the glass transition temperature, TX is the crystallization temperature and Tl the melting point (Liquidus) However, with the development of new metallic glass compositions, both indicators ⁎ showed unsatisfactory correlations [4,5] By observing a variation of volume that is almost null during the crystallization of amorphous liquids, Yavari et al [4,5] has demonstrated the importance of the high compactness of the liquid alloy for the kinetics of amorphization: a small volume change during solidification is a general property of alloys with good GFA At the atomic scale, the MG structure is amorphous and lacks crystalline order which infers these materials specific properties that may cover a wide range of variety Knowing that most thermodynamic and mechanical properties of materials result from their structure, the atomic structural characterization of MG is a very important and non-straightforward task due to the complex nature of their amorphous phase Many studies have shown that, at the shortrange order (SRO), the icosahedral type of structure is the fundamental unit in the building of MG [6,7] From another side, several researches [8,9] confirmed that icosahedral clusters are linked to each other by well-defined modes: Intercross Sharing (IS), Face Sharing (FS), Edge Sharing (ES) and Vertex Sharing (VS) In the present study we will focus on the evolution of the structure of Mg-Al binary MG during the cooling process using molecular dynamics (MD) simulations These methods have been shown to be very efficient in investigating the atomic scale Corresponding authors E-mail addresses: samiriabdelali1@gmail.com (A Samiri), abderrahim.khmich@gmail.com (A Khmich), hasnaoui59@hotmail.com (A Hasnaoui) https://doi.org/10.1016/j.commatsci.2020.109895 Received 29 March 2020; Received in revised form 16 June 2020; Accepted 18 June 2020 0927-0256/ Published by Elsevier B.V Computational Materials Science 184 (2020) 109895 A Samiri, et al behaviour of thin film growth [10,11], and modified silicate glasses [12,13] The atomic structure is also characterized using the Radial Distribution Function (RDF), the Voronoi Tessellation Analysis (VTA) and coordination number (CN) distribution Note also that the clustertype index method (CTIM) established by Liu et al [14–16] on the basis of Qi and Wang's research work [17], has been widely used to analyse the evolution mechanisms of local microstructures in the liquid and amorphous metallic systems These last methods (RDF, VAT and CN) have also been used to determine structural changes during cooling These techniques have been extensively used for the investigation of the structural behaviour of monatomic [18], binary [19] and multicomponent (such as Mg60 Ce10 Ni20 Cu5 X5 (X = Co, Zn) MGs [20] At the crystalline phase, Al–Mg alloy is one of the most widely used structural materials owing to its appreciable properties, such as low density, high specific strength and so on [21] However, its properties may be greatly influenced by the formation of different alloy phases For example, the formation of Al12Mg17 phase on grain boundaries will result in poor creep strength [22] The vitrification of Mg-Al alloys would lead to avoid this problem since MGs don’t have grain boundaries So, in order to improve mechanical properties of Al–Mg alloy, it is necessary to have a good understanding of the formation mechanism of microstructures, especially of the atomic cluster structures during the solidification processes In the following, we will give details of the simulation in Section 2, the third part is devoted to discuss and analyze the simulation results Finally, we will summarize our work by a conclusion Fig presents the variation of volume as a function of temperature during the heating–cooling process We observe that during the heating process the volume increases almost linearly as a function of temperature and then shows a sudden jump that corresponds to the melting point which depends on the composition During cooling process, the volume decreases with temperature up to 300 K without a significant jump in the curve and shows a volume excess generated after the solidification This volume difference between the beginning of the heating and the end of solidification is called free volume and its presence suggests that no crystallization has occurred in the alloy that is to say the alloy structure became amorphous [18] The intersection between the linear fits of the upper part and the lower one of the cooling curves allows estimating the glass transition temperature Tg These values are estimated for the three compositions of the system in Table From these results, we see clearly that, as Al-composition increases, Tg increases This variation in terms of Tg is due to the difference in atomic radii between the two elements and can be explained by the suggested idea that the increase in Al-composition hinders atomic vibrations in the whole system and atomic mobility can be prevented at the beginning of cooling process Simulation details 3.1 Glass transition temperature Tg Molecular dynamics (MD) simulations via the Large Scale Atomic/ Molecular Massively Parallel Simulator (LAMMPS) software [23] are used to study the structure of the binary metallic glasses Mgx Al100 − x with x = 10, 20and25 at% Our simulations have been restricted to these compositions because the used interatomic potential describes (and has been developed for) this region of the phase diagram Simulation samples have been prepared by distributing 4000 atoms in threedimensional box according to an fcc lattice Periodic boundary conditions in the three directions are used to mimic bulk properties Firstly, the system is heated from 300 K up to 1300 K (which is well above the melting temperature) to obtain the liquid phase under an NPT statistical ensemble (particle number N, pressure P and temperature T are constant) The heating rate is taken to be 1012K / s Once the Mg-Al melt is obtained, we relaxed the system in an NVT (particle number N, volume V and temperature T are constant) statistical ensemble for a duration of 100 ps to allow the system to forget its crystalline structure Finally, we cooled the alloy down to 300 K in a NPT statistical ensemble using a very high cooling rate of 1013K / s This cooling rate is high enough to avoid atoms to rearrange and form the crystalline phase This value is very high compared to experimental values but it is dictated by the well-known time limitation problem in MD simulations and has been proven to produce metallic glasses [24] We note that lowering the cooling rate by an order of magnitude would increase considerably the computational effort and results in a decrease of glass transition temperature without a drastic change in the alloy structure [18] Fig shows a schematic diagram that summarizes this heating–cooling process To describe the atomic interactions between Mg and Al atoms, we used force field functions within the embedded-atom method (EAM) framework with the parameterization developed by Mendelev et al [25] This potential interaction is a function of the electronic density where the total energy is written as follows [26–28], The intersection method described before does not provide a welldefined value of Tg, another technique uses the evolution of the radial distribution function (also called pair correlation function) g (r) This g (r) function is a very useful property in analyzing amorphous alloys and structural changes as those observed in metallic glasses [10] It represents the average distribution of atoms around a given atom in the system This information can be used to calculate the number of coordination, crystallinity, etc… This function is also defined as the probability of finding an atom at a distance from another which in the center is given by the following expression [12,18,29,30]: Etot = ∑ Ei = ∑ Fi (ρh,i ) + i i the atom i in the total site h, and Uij is a pair interaction potential between atoms i and j separated by a distance rij Results and discussion g (r ) = j N n (r ) ∑ 4πr 2Δr > (2) r=1 With V stands for the volume of the system, N the number of atoms and n(r) is the number of atoms situated between distances r and r + Δr of a central atom Fig presents the radial distribution function g(r) of Mg-Al glasses for the three compositions (Mg25Al75, Mg20Al80 and Mg10Al90) We observe that the first peak is well defined (the function g (r) is more intense), which means that there is a short-range order in Mg-Al MG The second peak undergoes a split into two sub-peaks signifying the beginning of the formation of metallic glass as suggested in references [8,31,32] So, the separation of the second peak into two sub-peaks is another criterion which proves that the glassy state has been reached As a function of the increase of cut-off, the peaks become less pronouncing until null which suggest an absence of long-range order Our results are in a far agreement with several theoretical and experimental works [18,19,30] To determine the glass transition temperature, we used the Wendtg Abraham parameter [33] defined as the ratio R = g with gmin and max gmax are the relative intensities of the first minimum and the first maximum of the radial distribution function (RDF) The plot of this ratio versus temperature (during cooling) shows a small break that determines the glass transition temperature More specifically, we use the intersection between two fits, one at low temperatures and the other at high temperatures (Fig 4) The results led to the estimative transition temperature which to be equal to Tg = 747 K, 750 K and 760 K for 75%, ∑ ∑ Uij (rij) i V < N2 (1) With Fi (ρh, i ) is a function that takes into account the environment of the atom i, ρh, i = ∑i ≠ j ρj (rij ) is the contribution of the electron density of Computational Materials Science 184 (2020) 109895 A Samiri, et al Fig Schematic diagram of the heating and cooling process used in the present simulation Fig Variation of the system volume as a function of temperature during the heating and cooling processes for the three considered compositions Fig Parameter of Wendt Abraham as a function of temperature for each component of Mgx Al100 − x Curves are shifted for clarity Table The glass transition temperature Tg during cooling for different compositions Tg (K) Mg25 Al75 Mg20 Al80 Mg10 Al 90 740 760 770 80% and 90% of Al-composition, respectively It looks like Tg increases with the increasing of the amount of Al concentration, but we should mention that the difference between the three values is very weak and may be within the error margin of the method Globally, we can observe that the obtained results produce the same behavior as that found using the previous method (V = f(T)) where we have seen that Tg increases as a function of Al-composition Nevertheless, we believe that values obtained using the WA method are more reliable and should be considered in any further consideration 3.2 Structural characterization To study the evolution of different local atomic structures during cooling process, and to characterize the vitreous state of Mg-Al MGs, we will use the VTA method that allows determining the nature of different polyhedrons in the metallic glasses This technique characterizes each atom by four integer indices called Voronoi indices < n3, n4 , n5, n6 > [34] For each location i of this vector ni corresponds to the number of edges that can have a face of the cell In this description [35], the icosahedral cluster, for example, corresponds to the Voronoi index vector: < 0, 0, 12, 0> [31,36] In other words, this vector describes a cell formed of a polyhedron with 12 faces (n5 = 12 ) and that each of these faces consists of edges It can be concluded that the Voronoi index vector can be considered as a characteristic fingerprint of the coordination structure of a particle In Fig we draw an histogram which shows the fractions of the dominant Voronoi polyhedrons present in the Fig Radial distribution functions of Mg-Al alloy for the three considered compositions (Mg25Al75, Mg20Al80 and Mg10Al90) Curves are shifted for clarity Computational Materials Science 184 (2020) 109895 A Samiri, et al Fig Fractions of various Voronoi polyhedra at the end of cooling process MG at the end of cooling process(at 300 K) for the three compositions of Mgx Al100 − x with × = 10, 20 and 25 We observe that the top Voronoi polyhedra are < 0, 0, 12, > , < 0, 1, 10, 2> and < 0, 2, 8, 4> with high values of their percentage in the total system These clusters represent icosahedral-like structures that are considered to be responsible for the formation of the vitreous state and behave as a barrier to nucleation and crystalline growth Similar results have been found in another MD study of binary MGs by Wang et al [33] and also by Khmich et al [37] in Ta monatomic metallic glass Our finding is another criterion which confirms the glass formation We mention that the index n5 gives the number of five-edge faces in each cluster and then this index is an indication of the five-fold symmetry [37] Hwang et al [38] have grouped these Voronoi polyhedrons into three types: crystal-like, icosahedral-like and mixed-like clusters and showed that the icosahedral-like clusters are more abundant in ZrCu metallic glasses According to this classification, the icosahedral-like clusters are those with n5 exceeding In the present work, we cumulated the numbers of these clusters (with n5 ≥ ) and plotted the result in Fig 6, which presents the evolution of the fraction of this group of Voronoi polyhedrons as a function of temperature during the cooling process for the three considered compositions The results show that the fraction of the five-fold symmetry (icosahedral-like clusters) increases considerably during the cooling process and becomes dominant with an amount exceeding 70% of all atoms at low temperatures where MGs form Five-fold symmetry has been also highlighted by Li et al [39]in their research of five-fold local symmetry in metallic liquids and glasses From that, we can suggest also that the amorphous state has been reached for the three compositions Another way to analyze the structure of amorphous materials is the distribution of coordination numbers (CN), which presents the number of nearest neighbors to a central atom In the following, we will focus on the evolution of the different coordination numbers versus temperature during cooling Fig 7a) and b) show an example of the evolution of the most abundant coordination numbers found in Mg10Al90MGs We observe that the fractions of 9, 10 and 11-coordinated atoms decrease (Fig 7a) while those of 12, 13, 14 and 15- Fig The amount of five-fold symmetry (Voronoi index n5 ≥ 6) as a function of temperature during cooling process coordinated atoms increase during the cooling process (Fig 7b) A similar behavior has been found in Mg25 Al 75 MG (not shown here), while Mg20 Al80 showed a slight difference where fraction of 12-coordinated atoms decreases as those of low-coordinated ones This small variation can be interpreted by the high composition of Al The main result in these curves is that the amount of low-coordinated atoms decreases while that of high-coordinated atoms increases as temperature decreases towards vitrification This motivated us to group these clusters in two classes: low- and high–coordination numbers and plot the evolution of these fractions versus temperature Fig shows an example of these curves for Mg20 Al80 MG We observe that there is a cross-over between the two curves around a specific temperature which is very close to the glass transition temperature Computational Materials Science 184 (2020) 109895 A Samiri, et al Fig Distribution of (a) low-coordinated atoms and (b) high-coordinated atoms in Mg10 Al 90 MG as a function of temperature during cooling process 1012, 2.51012, 51012and1013K / s for Mg20 Al80 In Table 2, we present Tg values obtained using intersection between low and high-coordinated curves together with those resulting from the Wendt-Abraham Method (WAM) We can see from Table that Tg increases with increasing cooling rate for both used methods and that the two methods produced values in good agreement Indeed, values of Tg found by the Wendt-Abraham parameter (WAM) are almost equal to those obtained by the coordination curves intersection We suggest then that this method of intersection between the low-and high-coordinated curves provides another way to estimate the glass transition temperature 3.3 Mechanical properties In the previous part, we used several techniques (RDF, transition temperature Tg, Voronoi polyhedra, coordination analysis) to confirm that the obtained samples have a vitreous state for the three considered compositions In the following, we will investigate the mechanical response of these MGs under tensile mechanical stresses Fig An example showing the crossover between low and high- coordinated atoms during cooling process 3.3.1 Tensile deformation Fig shows the stress–strain curve for the different compositions Mgx Al100 − x with × = 10, 20 and 25, with a strain rate equal to 1010s−1 We should mention that this strain rate remains orders of magnitude larger than what is used experimentally, but again this is linked to the MD time scale that limits the investigations to high strain rates Furthermore, MD simulations have employed strain rates from 107s−1 to 1010s−1 [40,41] We observe from this figure that the stress–strain curves present quasi-linear parts extending up to critical values depending on composition, but which can be estimated around 4%–6% of strain This region corresponds to the elastic regime where deformation is reversible upon unloading Beyond this regime when the deformation increases the slope of the stress–strain curve decreases first and then the stress reaches a maximum after which it decreases This maximum value of stress is known as the ultimate tensile strength (or mechanical resistance) However, no clear behavior can be extracted as to the composition variation The mechanical behavior of Mg-Al MGs suggests that ductility can be reached in this system Table Glass transition temperature Tg obtained using the coordination crossover compared to that obtained by the WAB method for different cooling rates Cooling rate (K/s) Tg (K) by WAM Tg (K) by coordination crossover 1012 2.5°1012 5°1012 620 635 660 700 750 670 720 770 1013 computed using the Wendt-Abraham technique We note that the same conclusion could be drawn for the other two compositions Furthermore, we investigated the quenching rate effect on the coordination number distribution and the resulting glass transition temperature using four different quenching rates, namely Computational Materials Science 184 (2020) 109895 A Samiri, et al Fig Stress versus strain curves for different compositions of Mg-Al MGs Fig 10 Stress versus strain at three different temperatures for Mg 25Al75 MG To deeply investigate this property, we deformed the samples with the same strain rate (1010s−1) at different temperatures (300 K, 500 K and 600 K) below the glass transition Tg The results are shown in Fig 10, for the example of Mg25 Al 75 composition We observe clearly that when temperature increases the stress needed to induce a certain level of strain decreases in both the elastic and plastic regimes which means that the glass softens under heat Both yield strength and mechanical resistance decrease when heating up Mg-Al MGs We should note that this has been observed for the three studied compositions This effect has been observed in other MGs [40] Otherwise, to understand the effect of the strain rate on the MG mechanical behavior, we deformed the three samples at 300 K with three different strain rate values (109s−1, 5.109s−1and1010s−1 and) The results are illustrated in Fig 11 for the example of Mg25 Al 75 MG It is observed that when the strain rate increases the stress–strain curves shift to high stresses in both the elastic and plastic regimes We should note that this has been observed for the three studied compositions We can see clearly that both yield strength and mechanical resistance of Mg-Al MGs increase with increasing strain rate This can be interpreted by the difficulty for atoms to relax the stress in the sample when the strain rate is very high leaving no time for atoms to move and Fig 11 Stress versus strain under different strain rate for Mg 25Al75 MG Computational Materials Science 184 (2020) 109895 A Samiri, et al obtained MGs sample showed that the increase in the deformation rate and also the increase in the percentage of aluminum increase the yield strength and the maximum stress at the same temperature, while increasing temperature induces a decrease in the yield strength and maximum stress Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper Acknowledgement We would like to thank Act4Community (OCP Khouribga) for providing simulation resources References [1] A Inoue, Stabilization of metallic supercooled liquid and bulk amorphous alloys, Acta Mater 48 (2000) 279–306 [2] A Inoue, High strength bulk amorphous alloys with low critical cooling rates (overview), Mater Trans 36 (1995) 866–875 [3] H.A Davies, B.G Lewis, Generalized kinetic approach to metallic glass formation, Scripta Met (1975) 1107–1112 [4] A.R Yavari, Small volume change on melting as a new criterion for easy formation of metallic glasses, Phys Lett A 95 (1983) 165–168 [5] A.R Yavari, J.L Uriarte, A Inoue, Volume effects in amorphization by rapid solidification and solid-state reaction and 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plotted as a function of the annealed temperature in Fig 12 were therefore calculated as a function of the annealing From Fig 12, it can be seen that elastic moduli B, G and E decrease with increasing annealing temperature It is known that a longitudinal deformation produces a change of volume without change of shape [42] Note that we also computed the anisotropic factor defined by 2C A = C −44C and found that it remains constant around (A ≈ 1) re11 12 gardless of the annealing temperature, which means that the material is isotropic We note that this isotropic behavior is necessary to compute elastic moduli out of elastic constants It is noted that the behavior of the elastic moduli and elastic constants as a function of annealing temperature found in the present work is similar to what has been obtained by Hasanzadeh [43] and Boufadi [42] Conclusion Embedded atom method combined to molecular dynamics simulations have been used to investigate structural and mechanical properties of Mg-Al binary metallic glasses for three compositions (Mg25Al75, Mg20Al80 and Mg10Al90) Firstly, we used various structural analyzing techniques (RDF, VNA …) that allowed confirming the obtaining of the glassy state Our results showed that upon cooling process, a split in the second peak in the RDF occurs, which led to conclude that the glassy state has been formed Furthermore, the < 0,1,10,2 > , < 0,0,12,0 > and < 0,2,8,4 > clusters have been depicted as the top dominant clusters in the considered system for the considered compositions This suggests that these icosahedral-like clusters appear in a large amounts after solidification and behave as a barrier to nucleation and crystalline growth Secondly, we adopted a new method to determinate the glass transition temperature using the crossover between low and high-coordinated atoms populations versus temperature during cooling process This method provides estimative results in terms of Tg which are closer to those obtained by classical 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Hamedani, G Alahyarizadeh, A Minuchehr, M Aghaei, The role of chromium and nickel on the thermal and mechanical properties of FeNiCr austenitic stainless steels under high pressure and temperature: A molecular dynamics study, Mol Simul 45 (2019) 672–684 ... investigate structural and mechanical properties of Mg -Al binary metallic glasses for three compositions (Mg2 5Al7 5, Mg2 0Al8 0 and Mg1 0Al9 0) Firstly, we used various structural analyzing techniques... in the Fig Radial distribution functions of Mg -Al alloy for the three considered compositions (Mg2 5Al7 5, Mg2 0Al8 0 and Mg1 0Al9 0) Curves are shifted for clarity Computational Materials Science 184... distances r and r + Δr of a central atom Fig presents the radial distribution function g(r) of Mg -Al glasses for the three compositions (Mg2 5Al7 5, Mg2 0Al8 0 and Mg1 0Al9 0) We observe that the first