Contrasting Bonding Interaction Induced Distinct Relaxation in

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B: Fluid Interfaces, Colloids, Polymers, Soft Matter, Surfactants, and Glassy Materials

Contrasting Bonding Interaction Induced Distinct Relaxation in La Ni and La Al Glass-Forming Alloys 65

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Hua-Ping Zhang, Fang-Ru Wang, and Mao-Zhi Li J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b09188 • Publication Date (Web): 09 Jan 2019 Downloaded from http://pubs.acs.org on January 10, 2019

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The Journal of Physical Chemistry

Contrasting Bonding Interaction Induced Distinct Relaxation in La65Ni35 and La65Al35 Glass-Forming Alloys H. P. Zhang, F. R. Wang, and M. Z. Li* Department of Physics, Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Renmin University of China, Beijing 100872, China Corresponding Author *E-mail: [email protected]

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ABSTRACT α and β relaxation are two fundamental processes in glass-forming materials, and quite important on many of the properties. While intensive studies have found that α and β relaxation can be tuned by changing the constituent elements, the underlying structural basis is still elusive. Here we explored the effect of two key elements of Al and Ni on distinct β and α relaxation in La65Al35 and La65Ni35 glass-forming alloys via classical and ab initio molecular dynamics simulations combined with dynamical mechanical spectroscopy. Unexpected coupling of relaxation in both β and α relaxation time scales is observed for La and Al atoms in La65Al35 system, which drastically suppresses the relaxation dynamics. It is revealed that the dynamic coupling of La and Al results from the covalent-like bonding interaction between Al atoms, which connect Al together, forming a network-like structure. The bonding network not only drastically slows down the dynamics of Al, but also couples the motion of La and Al together. This finding elucidates the underlying basis of Al and Ni elements for distinct β and α relaxation, and shed light on tuning the formation and properties of metallic glasses by minor alloying.


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

INTRODUCTION From the microscopic point of view, atoms in a glass-forming liquid do not always vibrate

within the cages formed by the nearest-neighbor atoms, but break their cages and diffuse. In this process, two fundamental relaxation processes, the so-called β relaxation and α relaxation are involved. Specifically, α relaxation is directly related to viscous flow in supercooled liquids, responsible for vitrification, and fully inhibited after glass transition.1,2 However, β relaxation still exists in glass, which is initiated at high temperatures, and mainly responsible for the dynamics in the glassy state.3-7 So far, numerous findings have revealed that β relaxation is crucial to many of the properties of glass-forming materials.7,8 For instance, β relaxation has an essential influence on the stability and crystallization of metallic glasses (MGs).9 Some studies also show that β relaxation affects mechanical properties such as brittleness in glassy solids and closely correlates to the mechanism of plastic deformation, which is an important issue in the developments and applications of MGs.8,10 In addition, β relaxation is also correlated with the fragility or α relaxation in glass-forming liquids.8,11,12 It has been shown that the more fragile the glass-forming liquids, the stronger the β relaxation is.11,12 Generally, these two relaxation processes can be responsible for understanding many fundamental issues in glassy physics and materials science. Although much effort has been devoted, the intrinsic understanding of both α and β relaxation and their relationship with atomic structures or interactions remain elusive.13-17 So far, it has been revealed in experiments that some specific elements play important roles in β relaxation in metallic glasses.8,14,17,18 For example, it is reported that replacing Ni with Al will suppress β relaxation in LaNiAl MGs, and that binary La65Ni35 MG exhibits much stronger β relaxation than La65Al35 MG.18 These findings indicate that Ni and Al elements play significantly different roles in β relaxation in La-based MGs. However, the physical origin is still



unclear. On the other hand, α relaxation is also found to be significantly influenced by the elements in multicomponent glass-forming liquids.19,20 It is not clear either whether the element dependent relaxation in α and β relaxation time scales has the same fundamental structural basis. More generally, Ni and Al are two key elements for minor addition to improve and even tune the formation and properties of MGs.21-23 It has been shown that while minor addition of Al often enhances glass-forming ability of metallic alloys and yield strength of MGs,22,23 Ni addition can induce super plasticity at room temperature in ZrCuNiAl MGs.24 The plasticity of Fe-based MGs can also be significantly improved through substitution of Fe by Ni.25,26 Therefore, elucidating the effect of Al and Ni elements on both α and β relaxations may also be quite useful for understanding the underlying physical basis of minor alloying of Al and Ni elements on the formation and properties of MGs, as well as the nature of α and β relaxations in metallic glass-forming alloys. In this work, we systematically characterized the β and α relaxation in La65Ni35 and La65Al35 metallic liquids and glasses via classical and ab initio molecular dynamics simulations combined with dynamical mechanical spectroscopy (MD-DMS). Atomic motion of each element was analyzed for clarifying its effect on the relaxation dynamics, and very different behavior was observed. The physical origin was explored by analyzing the atomic and electronic structures in two MGs, and it is found that the covalent-like bonds formed between Al atoms play key role in the distinct relaxation behavior. These findings provide a new understanding for the relaxation dynamics from the electronic characteristic of elements, hence are useful for deeper insight into the mechanism of minor addition of Al and Ni elements for tuning the formation and properties of MGs. 

SIMULATION METHODS


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1. Classical molecular dynamics simulation Classical molecular dynamics (MD) simulations were performed in binary La65Ni35 and La65Al35 metallic glass-forming alloys within LAMMPS27 package. In our simulations, the metallic system contains 4 000 atoms in a cubic box with periodic boundary conditions applied in three directions. The interatomic interactions in two alloys were described by the realistic embedded-atom method (EAM) potential developed by Sheng et al.28 Samples were first equilibrated at 1200 K for 2.0 ns, followed by hyper-quenching to 300 K with cooling rate of 1.0×1012 K/s in NPT (constant particle number, pressure, and temperature) ensemble, in which the pressure was adjusted to be zero. At each temperature of interest, after the samples were annealed for 2.0 ns in NPT ensemble, the ensemble was switched to NVT (constant particle number, volume, and temperature) ensemble and the samples were further annealed for 2.0 ns. The final configurations were used for the dynamical mechanical spectroscopy simulation. 2. Dynamical mechanical spectroscopy based on MD simulation To investigate the dynamical mechanical spectroscopy, MD-DMS29-32 simulations combined with isoconfigurational ensemble33,34 were employed. A sinusoidal strain 𝜀(𝑡) = 𝜀𝐴 sin(2𝜋𝑓𝐴 𝑡) was applied to the samples along xy direction, where 𝑓𝐴 is the frequency and selected as 100 GHz, and 𝜀𝐴 is fixed at 2%. For statistics, 100 independent sinusoidal shear deformation simulations were performed, in which the same initial configuration was employed with initial momenta randomly assigned according to the Maxwell−Boltzmann distribution at each temperature. For each MD-DMS loading, 10 cycles were used. We fitted the stress as 𝜎(𝑡) = 𝜎0 + 𝜎𝐴 sin(2𝜋𝑓𝐴 𝑡 + 𝛿), where 𝜎0 is a constant term and 𝛿 is the phase difference between stress and strain (see the Supplementary Information Figure S1 for more details). Loss modulus 𝐸" are calculated according to 𝐸" = 𝜎𝐴 /𝜀𝐴 sin(𝛿). We also performed MD-DMS



Simulations with much lower loading frequency of 𝑓𝐴 =1 GHz for comparison (see the Supplementary Information for more details). 3. Ab initio MD simulation and electronic structure calculations To accurately describe the interatomic interactions in La65Al35 and La65Ni35 alloys and achieve reliable atomic configurations of the liquids and glasses, ab initio MD simulations were also performed with the Vienna ab initio simulation package (VASP).35 The projector augmented-wave method within the density-functional theory was used to describe the interactions between ions and electrons, and the atomic forces can be determined without using any experimental input or empirical potentials.36 In specific, PW9137 functional under the general gradient approximation and a plane-wave cutoff of 270 eV were used for both alloys. Each modeled system contains 200 atoms in a cubic box with periodic boundary conditions applied in three dimensions. In ab initio MD simulations, NVT ensemble was performed with the temperature controlled by Nose-Hoover thermostat, and the time step was 3fs. First, the two alloys were equilibrated at 1200 K well above the melting temperatures. They were then quenched to 300 K with a cooling rate of 3.33×1013K/s. In quenching process, the atomic configurations in each temperature interval of 100K were stored. At each temperature, the corresponding atomic configuration was further relaxed for 30ps and the box size was adjusted to have zero pressure. Here only Γ-point was considered to sample the Brillouin zone in ab initio MD simulations. For the accurate electronic structure calculations, the Brillouin zone was sampled with 3×3×3 k-point mesh. 

RESULTS AND DISCUSSION First, the MD-DMS simulations were performed to calculate the loss modulus for

characterizing β and α relaxations in two MGs. The details of MD-DMS simulations were


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presented in Simulation Methods. Briefly, at temperature T, a sinusoidal shear strain 𝜀(𝑡) = 𝜀𝐴 sin(2𝜋𝑓𝐴 𝑡) was applied to the generated samples along xy direction, so that the resulting stress 𝜎(𝑡) was measured. The loss modulus 𝐸" can be calculated based on 𝜀(𝑡) and 𝜎(𝑡). MD-DMS simulations were conducted at various temperatures between 300 and 1200 K, covering both glass and liquid states. The frequency 𝑓𝐴 is fixed at 100 GHz, and the strain amplitude 𝜀𝐴 is fixed at 2%. Figure 1a shows 𝐸" as a function of T, and the loss peaks of α relaxation at high T can be clearly seen. The corresponding temperatures (Tp) are about 760 and 840 K in La65Ni35 and La65Al35 metallic liquids, respectively. The lower Tp means that α relaxation is easier to be activated in La65Ni35 system. For different metallic glasses, β relaxation can be compared by normalizing the temperature and loss modulus with the peak position and amplitude, respectively. As shown in Figure 1a, La65Ni35 MG exhibits larger reduced 𝐸" at low temperatures than La65Al35 MG, indicative of stronger β relaxation in La65Ni35 MG, which can be seen more clearly in Figure S2 in the Supplementary Information. This is qualitatively consistent with experimental observations.18 From the microscopic point of view, the existence of non-zero loss modulus in low temperature MGs infers that atoms do not always vibrate within cages formed by their nearest neighbor atoms. Some faster atoms can break their cages and relax to new positions during cyclic loading, which make contributions to β relaxation in MGs. In previous studies, Yu et, al.28-30 found that the relaxation (or internal friction) in MGs is governed by these faster atoms. Wang et, al.31 also proved that the intrinsic connectivity and spatial heterogeneity of these faster atoms is the key factor that determines the low temperature relaxation behavior of MGs. Therefore, atoms with large displacements are highly responsible for β relaxation in MGs. Here, to investigate the role of different elements in β relaxation, we calculated the atomic displacement distribution



function p(u)28-32 (see the Supplementary Information Figure S3 for more details) for each element in two systems during each cycle of loading at 400K and 800K. As shown in Figure 1b, while the displacement distributions of Ni and La in La65Ni35 system are slightly different, Ni atoms showing larger displacement, p(u)s of Al and La atoms in La65Al35 system are almost identical, even at higher temperatures. This clearly shows that in La65Ni35 system, La and Ni atoms make different contributions to β relaxation, while the dynamics of La and Al atoms in La65Al35 system in β relaxation are intimately coupled. In addition, La65Ni35 system exhibits larger atomic displacements, indicating that β relaxation this system is more significant. For the loading frequency of 𝑓𝐴 =1 GHz, similar behavior was also observed, indicative of the intrinsic relaxation behavior in two MGs (see the Supplementary Information Figure S4 for more details). We also performed MD-DMS simulations for a very long time with 10000 periods at 400K to investigate whether the distinct relaxation behavior persists in longer time scale. Similarly, the frequency 𝑓𝐴 is fixed at 100 GHz. Here, the self-intermediate scattering function (SISF)38 of each element was calculated to characterize the dynamics according to 𝐹𝑠𝛼 (𝐪, 𝑡) = 𝑁𝛼 𝛼 𝛼 𝛼 〈exp[𝑖𝐪 ∙ (𝐫𝑗,𝑡 𝑁𝛼−1 ∑𝑗=1 − 𝐫𝑗,0 )]〉, where 𝑁𝛼 is the number of atoms of element α, 𝐫𝑗,𝑡 is the

coordinate vector of atom j of element α at time t, 𝐪 is the wave vector fixed at |𝐪| = 𝑞𝑚𝑎𝑥 which corresponds to the first peak position of the structure factor, and < > denotes the ensemble average. As shown in Figure 1c, while the SISF of Ni decays faster than that of La in La65Ni35 MG, the SISFs of La and Al in La65Al35 MG are still coupled together even in very long time scale. To provide further evidence of the relaxation behavior of different elements in two systems in α relaxation time scale, we performed MD simulations in liquid regions. Here ab initio MD simulations were carried out for La65Ni35 and La65Al35 metallic liquids at


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various temperatures, in which the interatomic interactions can be precisely determined for accurately describing atomic motions and electronic structures can be calculated as well. The simulation details can be found in Simulation Methods. Figure 2a shows the SISFs of elements in La65Ni35 and La65Al35 metallic liquids at 800K. A typical two-step relaxation behavior6 can be seen in both La65Ni35 and La65Al35 liquids at 800 K. It can be seen that the relaxations of Al and Ni atoms in La65Ni35 liquid in all time scale are different. The SISF of Ni decay faster than La. However, the SISFs of Al and La in La65Al35 liquid are quite different in very short time scale (

Contrasting Bonding Interaction Induced Distinct Relaxation in

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