Molecular Dynamics Simulations of Aluminium Foams under Tension

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C: Physical Processes in Nanomaterials and Nanostructures

Molecular Dynamics Simulations of Aluminium Foams under Tension: Influence of Oxidation Nina Gunkelmann, Eduardo M. Bringa, and Yudi Rosandi J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b07146 • Publication Date (Web): 24 Oct 2018 Downloaded from http://pubs.acs.org on October 30, 2018

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The Journal of Physical Chemistry

Molecular Dynamics Simulations of Aluminium Foams under Tension: Influence of Oxidation Nina Gunkelmann,∗,† Eduardo M. Bringa,‡ and Yudi Rosandi¶ †Chair of Computational Material Sciences/Engineering, Institute of Applied Mechanics, Technische Universität Clausthal, Arnold-Sommerfeld-Straße 6, 38678 Clausthal-Zellerfeld, Germany ‡CONICET and Facultad de Ingenier´ıa, Universidad de Mendoza, Mendoza, 5500 Argentina ¶Department of Geophysics, Universitas Padjadjaran, Jatinangor, Sumedang 45363, Indonesia E-mail: [email protected] October 24, 2018 Abstract For materials with high surface-to-volume ratio and high oxygen affinity, oxide layers will significantly change the material properties. However, oxidation effects have not been studied for metal nanofoams which have many applications because of their light weight and high stiffness. We use molecular dynamics simulations to show that oxidized Aluminum nanofoams possess significantly improved ductility without reduction in tensile strength. The Al-O interface leads to an increased defect nucleation rate at the oxide interface preventing localized deformation. At the same time, the enthalpy of mixing between Aluminiun and oxygen decreases for increasing O concentrations, reaching a minimum at the stoichiometric ratio of Al2 O3 , resulting in stabilized bonds and increased strength.

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Introduction Metal foams have many technological applications. They are widely used as shock absorbers due to their light weight and high stiffness. 1–3 They are used for industrial and energy-storage applications, 4 and can be applied as radiation shields in space science. 5 There are experimental and simulation studies dealing with macroscopic metal or plastic foams. 6–8 On the other hand, experiments on foams with nanoscale porosity show large yield strength, 9 and nanoporous metals have been widely used for functional nanostructures such as sensors 10–12 and nanophotonic devices. 13 Molecular Dynamics (MD) simulations can often be used to investigate their response. For instance, many authors have reported results on uniaxial deformation and compression of nanofoams at the atomic level. 14–17 The evolution of foamed aluminium at high rate tension was recently investigated by Mayer et al. using a mechanical model based on molecular dynamics simulations. 18 Zhao et al. 19 studied shock induced melting, finding internal jetting from pores. Xiang et al. investigated the shock response of nanoporous Aluminum and revealed two mechanisms for void collapse: the plasticity mechanism and the internal jetting mechanism. 20 Gunkelmann et al. 21 also studied the compaction and plasticity in an Al nanofoam. Simulations focus on pure, single-element foams but, in atmospheres with oxygen content, oxide layers will change the material properties. For materials with high surface-to-volume ratio and high oxygen affinity this effect is especially pronounced. At aluminum surfaces, an oxide layer may form in seconds, even under vacuum conditions. 22 However, the mechanics describing oxidation behavior are still not fully understood. An efficient oxygen reduction catalysis was found for subnanometer Pt alloy nanowires prepared by a new experimental approach. 23 Recently, foaming of aluminum was investigated under oxidizing and non-oxidizing gas atmospheres using X-ray radioscopy to study the structure and distribution of the oxides. 24 Despite the importance of oxidation to determine the properties of materials, only rela2


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tively few simulation studies exist on this topic. There are detailed studies of oxidation of Al nanoparticles, starting with the seminal study by Campbell et al., 25 including the study of Hong et al., 26 and more recent studies. 27,28 Recently, Sun et al. analyzed the oxidation of Fe nanoparticles in solution by small- and wide-angle x-ray scattering and molecular dynamics simulations. 29 They observed the formation of voids within the nanoparticles accompanied by mass diffusion into and out of the nanoparticles. Sen et al. showed with MD simulations that oxidation leads to increased ductility for Al nanowires as a consequence of increased dislocation nucleation due to increased activation volume and increased number of dislocation sites. 22 There are even fewer structures on the role of oxidation in porous structures. The shock Hugoniot of full-density and porous CeO2 was investigated in the liquid regime using ab initio and classical molecular dynamics. 30 The study points to the necessity of acquiring data in the porous regime to increase the reliability of equation of state models. In the present paper we use MD simulations to study tension of an Al nanofoam in an oxygen atmosphere. We characterize the stress-strain response of Al foams: pure, covered by an oxide layer, and in an O2 environment, showing that oxidized foams display increased ductility. We also calculate the mixing enthalpy which is minimal for the stoichiometric ratio of Al2 O3 . Our results are relevant for understanding the behavior of nanoporous structures at ambient conditions.

Methods We construct foams with initial filling factor of φ0 = 0.5. The construction algorithm takes advantage of the non-simply connected structure of atoms of fixed temperature in a liquid and is described in. 21 In brief, we first create a template for the foam structure by starting with an fcc crystal with periodic boundary condition using a simple LennardJones (LJ) potential. The target crystal is then heated above the melting temperature for

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several thousand time steps. The atoms do not all have the same temperature because of equilibrium fluctuations. From the melt we delete atoms with temperature above a certain value, until the desired filling factor is reached. We obtain a spongy structure, which serves as a template for our nanofoam. Thus, we create the crystalline Al foam by using it as a spatial filter to remove all superfluous atoms from an fcc Al crystal. Note that some atoms are isolated inside voids. We relax the structure using a short-ranged LJ potential with a strongly increased binding energy to attach them to filaments. In a final step, all non-connected atoms and clusters are removed by using a cluster detector 31 which isolates the largest interconnected structure. This structure is used as as template to create the crystalline Al foam by using it as a spatial filter to remove all superfluous atoms from an fcc Al crystal. Another often applied procedure to generate Au nanofoams makes use of a phase-field model simulating the spinodal decomposition of a binary alloy. 32,33 The authors found that the obtained microstructure is similar to a microstructure obtained using the Berk analysis based on small angle neutron scattering data taken for porous gold. Our generation procedure leads to similar foam structures.

Figure 1: Different simulation configurations. From left to right: Foam in an O2 environment filling the voids of the foam (‘O2’), oxidized Al in vacuum and Al nanofoam. Red: O; blue: Al. The number of oxygen atoms in the initial cubic box was 64000. The foams have a cubic shape with a side length of 13 nm and the total number of Al atoms amounts to 69367. The foam was placed in a cubic box with a number of O atoms varying from 32000 to

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80000 in increments of 16000 atoms using the software PACKMOL. 34 The oxygen density was varying between 0.23 and 0.60 g/cm3 , several hundred times that of ambient conditions. We deleted all O atoms overlapping with the Al nanofoam. In detail, pairs of O and Al atoms whose distance of separation is smaller than the sum of their radii are searched for, and O atoms are deleted. After 100 ps relaxation in a NPH ensemble an amorphous oxide layer has formed at the Al surface. According to Hong et al. , oxidation of nanoparticles reaches a limiting thickness after approximately 100 ps, for T < 570 K, 26 and this thickness compares well with experimental thickness meassured after several 100 seconds. Sun et al. 29 compared oxidation kinetics from MD at the ns scale, with experimental kinectics at the minute scale. Both of these simulations use relatively high oxygen gas pressure in order to achieve comparable oxidation at available simulation time scales (initial oxygen density of 0.48g/cm3 compared to approximately 1e-4 g/cm3 in experiments). Kinetics depends on a number of factors, including structure, diffusivities and temperature. 35 Regarding mechanical deformation, we are carrying simulations at high strain rate, where it takes 100 ps to reach 10 % deformation (more details see below), and it takes the same time to reach a steady oxide layer thickness. This might compare well with experiments, where both of these processes take minutes. Plasticity would be controlled by dislocation nucleation and propagation, and by bond-breaking, which take a much shorter time than oxidation reaching a steady thickness. From mean square displacement (MSD) calculations, for instance in, 28 O and Al atoms would move more than 2 nm after 100 ps, traversing the filaments in our simulated foam and allowing partial healing during necking. We removed the atoms outside the simulation box of the Al nanofoam to ensure that both the Al foam and the oxidized foam have the same stress state and strain rate upon deformation. The number of O atoms after this step amounts to [15039, 21678, 29391, 31911], for [32000, 48000, 64000, 80000] starting atoms. To evaluate the difference between oxidized Al in vacuum (in the following denoted as ‘O2 layer’) and in an O2 environment

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filling the voids of the foam (‘O2’) we removed the oxygen atoms inside the holes which were not attached to the surface by using a cluster detector. The number of O atoms for the oxidized sample is [11523, 17319, 20978, 23962] referring to [32000, 48000, 64000, 80000] O atoms in the initial cubic box. The concentration of O atoms for this configuration thus amounts to c =[0.14, 0.20, 0.23, 0.26]. The different structures are shown in Fig. 1. We relax the samples using high-temperature annealing at 80 % of the melting temperature with a Nosé/Hoover isenthalpic ensemble (NPH) during 100 ps. 36 The samples were then cooled back to 10 K followed by 2 ps in a microcanonical NVE ensemble. The heating and cooling ramps were performed during 2 ps. The simulations are conducted at a temperature of 10 K in an NVT ensemble in order to minimize thermal noise. The open-source MD code LAMMPS 37 is used in this work to perform the simulations. We apply periodic boundary conditions. For our simulations we employ the reactive force field ReaxFF, including charge transfer between aluminum and oxygen molecules, 38,39 with the implementation by Aktulga et al. 40 The charge is equilibrated instantaneously at each molecular dynamics timestep to minimize the Coulomb energy. An elaborated force field potential equation can be derived in terms of different interactions factors as:

Epot = Ebond + Eover + Eangle + Etors +EvdWaals + ECoulomb + Especific .

(1)

Here, the bonding interaction represents ionic and covalent components, while van-der-Waals interactions are attributed to non-bonding terms. Eangle represents the deviation of the bond angle from equilibrium described by a harmonic term, Etors describes the four-body torsional angle strain. Ebond is a continuous function of interatomic distance and describes the energy associated with forming bonds between atoms. Eover describes an energy penalty term preventing the over coordination of atoms. The non-bonding interactions ECoulomb and EvdWaals

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are electrostatic and dispersive contributions quantifying long-range interaction between neutral atoms, while Especific represents specific energy contributions of the system, capturing properties particular to the system of interest. The potential we use was fit to describe Al2 O3 , but some Alx Oy clusters were included in the fit. 39 Zeng et al. describe simulations with the same potential used in this work, and the presence of sub-oxides in Al nanoparticles compares favorably with experiments. 28 Douglas-Gallardo et al. recently found good agreement between ReaxFF and DFT for different oxidation degrees in Al nanoclusters. 41 The simulations were carried out by performing uniaxial tension tests along the z axis at a strain rate of 109 s−1 for 320 ps.

Results The shear stress describing the onset of plasticity is defined as 1 pshear = − (pzz − ptrans ), 2

(2)

where pij denote the components of the stress tensor, and the transverse stress is defined as 1 ptrans = (pxx + pyy ). 2

(3)

For tensile stresses the shear stress definition above is equal to the von Mises stress if offdiagonal terms are ignored 42 and it is often used for the analysis of MD simulations. 43 In our simulation, non-diagonal stress components are small. Fig. 2 shows the shear stress in the tension experiment versus strain for pure Al, with oxide layer and in an O2 environment. For pure Al foams the shear stress shows a narrow linear elastic regime up to 3 % strain until dislocation emission leads to a maximum in the stress and subsequent plastic relaxation after 11 % strain. We observe increased ductility for Al covered with an oxide layer as well as for foams in an oxygen environment. In contrast to

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the curve for pure Al, for both the foam with the oxide layer and in the oxygen cloud, the shear stress only slowly decreases after the maximum at around 17 % strain and still has a magnitude of 4 GPa at 60 % strain. In addition, the strength is increased in both cases. Note that the strength is higher in the O2 environment because the number of O atoms is higher in this sample. We note that recent simulations of collision of Al oxide nanoparticles show much smaller maximum shear values, around 5 GPa. 27 The magnitude of the shear stress depends on the number of O atoms. Fig. 3 shows the shear stress versus strain for an Al nanofoam covered by amorphous oxide (‘O2 layer’) with different numbers of O atoms, thus different O concentrations. Although the shear stress increases for increasing number of oxygen atoms, the curves do not change qualitatively for c ≥ 0.14. We observe a maximum at around 12 % strain and subsequent plastic relaxation. If we increase the number of O atoms further the concentration will not increase anymore because the surface contacts are saturated. Only for small oxygen concentrations, c = 0.02, the behavior is similar to the pure Al foam showing decreasing shear stress after 7 % strain. For visualization of the atomistic configurations we use the adaptive common-neighbor analysis together with the dislocation extraction algorithm (DXA) 44 within the free software tool OVITO. 45 We display in Fig. 4 the tension behavior of the pure Al foam, the stress induced changes in our foam covered with an oxide layer and in an oxygen environment. The oxide layer has a thickness of 2 nm. Up to 31 % strain the structure of all foams does not change significantly during tension. Then, we observe fracture occurring in the center of the foam. For the pure Al foam, we observe a defined fracture surface. On the contrary, for the oxidized foam we do not have a complete rupture of the material but chains of Al-O atoms stick the material together, even up to 50 % strain. This effect is even more pronounced for the foam in an oxygen environment. Here, the foam appears to be stable up to 41 % strain. At 51 % strain chains of Al-O connect the upper and lower part of the foam similar to the foam covered by an oxide layer. A reason could be that strain energy is absorbed through

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breaking of bonds between highly coordinated atoms (see Fig. 7, below). This finding was also observed by Gao et al. for silica and alumina coated Silicon nanowires. 46 From Fig. 5 we see that many Shockley partial dislocations nucleate at the Al-O interface for oxidized foams; 73 % of the detected dislocations are Shockley partials. The reason is the small size of the filaments which cannot accommodate a full stacking fault ribbon. The disordered structure at the Al-O interface eases dislocation nucleation so that they mainly originate at the interface. Further dislocation pictures showing nucleation at the interfaces and stacking faults at different strains for the sample covered by the oxide layer can be seen in the Supplemental Material. The dislocation evolution is in agreement with the results by Sen et al. 22 where it was shown that the oxide shell decreases the aluminum dislocation nucleation stress by increasing the activation volume and the number of nucleation sites in Al nanowires. By increasing the defect nucleation rate at the interface, localized strains at the glide planes of dislocations are reduced and toughness is increased. In contrast, for pure Al dislocations do not only nucleate at the surface of the foam but are homogeneously distributed inside the filaments. Here, stair-rod dislocations cross the filaments. Although the total amount of dislocations is comparable for both samples the dislocation analysis is more reliable for pure Al. The reason is that the detector cannot sufficiently analyze the structure at the Al-O interface resulting in a smaller defect surface for the oxidized foam. Slices of the oxidized sample at different strains colored by their lattice types can be found in the Supplemental material showing that the majority of the foam is detected as disordered (up to 60 %). Our results for Al nanofoam are similar to the results for a single Al nanowire by Sen et al. 22 This is not unexpected, since a nanofoam has often been considered as a collection of connected nanowires. 47 This approach, however, does not take into account plasticity at nanowire junctions, which could control the overall mechanical response. 48 In Fig. 6 we color the atoms of the pure and oxidized foam by the shear strain invariant EvM which can be computed from the components of the atomic strain tensor Ei . For details

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of the calculation of the atomic strain tensor please refer to. 49 r EvM =

1 2 + E2 + E2 (Exx − Eyy )2 + (Exx − Ezz )2 + (Ezz − Eyy )2 + 6 · Exy xz yz . 2

We observe that strain is localized in the center of the specimen for the Al foam. In contrast, the shear strain appears less concentrated for the foam covered by the oxide layer. Here, the material has deformed by dislocations nucleated at the Al-O interface. Shear localization is related to bond-breaking, and Al-O bonds have an important role modifying ductility. To quantify this, Fig. 7 shows the number of bonds in the sample. The pure Al sample displays a large localized fracture starting at 20 % strain, leaving only a few connecting thin wires, shown in Fig. 4. This is the reason why there is a significant number of surviving Al-Al bonds (about 99 %), and the number of bonds stabilizes because the upper and bottom part are no longer connected. For the samples with O, O mobility leads to bond-healing, and there is creation of new Al-O bonds which delay fracture, as already noted by Sen et al. for a single nanowire. 22 Note that the creation of new Al-O bonds originates mostly from rearrangement of the AlOx layer while the number of molecular O2 remains almost constant. Bond breaking is not localized in a single region, but spread. For the sample with O2 atmosphere, there is nearly 6 % of Al-Al bond breaking, compensated by 6 % Al-O bond formation. For this sample, the O-O bonds also increase, unlike what happens for the sample without the O2 atmosphere, where Al-O bond formation is also more modest. The underlying mechanism leading to increased ductility without reduction in strength can therefore be understood from two observations. First, oxygen absorbs strain energy through breaking of highly coordinated bonds as explained in Fig. 7. Due to the strong interaction between O and Al atoms, bond breaking is not localized but distributed across a larger volume. Second, localized deformation is prevented by increased defect nucleation rate from the Al-O interface (Fig. 5). To find out the correct concentration of O in the oxidized Al target, we measure the

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mixing enthalpy of the system with varying concentration. We take a mixture of Al and O, ˚3 . To obtain the desired concentration initialized by Alumina structure of size 33x29x26 A we randomly remove Al or O atoms from the target. The system is then relaxed using an NpT ensemble to 1 K. Upon annealing the sample is amorphized due to the breaking of bonds of the corundum structure. The enthalpy of mixing ∆H is measured using a modified formula by Delannay et al. 50 The plot of ∆H is shown in Fig. 8. The figure shows that O atoms only do not mix with Al at very small concentration. At concentrations > 0.15 oxygen atoms are always bounded to Al atoms. The minimum shows the correct stoichiometric ratio of Alumina emphasizing the reliability of the potential used in this study. The increasing ductility, shown in Fig. 3, corresponds to more negative values of the heat of mixing. At these concentrations, it is shown that the bonds between O and Al are preferable and play an important role in modifying ductility as seen in Fig. 7.

Conclusions Using MD simulations we studied the response under uniaxial tension of pure Al nanofoams and Al nanofoams containing different oxygen concentration. Our results show that oxygen helps to increase the ductility without decreasing the tensile strength of Al nanofoams. The total amount of dislocations under strain is comparable for pure Al and oxidized foams, but for Al-O Shockley partials nucleate at the interface bettween the metal and the oxide. The enthalpy of mixing is positive for low oxygen concentrations and its minimum corresponds to the stoichiometric relation of corundum leading to increased stability of the bonds. These results are relevant for designing nanofoams at ambient conditions. The increased toughness could lead to an improved long-term stability of nanodevices.

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O2 O2 layer Al

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Figure 2: Shear stress versus strain for pure Al, an Al nanofoam covered by amorphous oxide (‘O2 layer’) and an Al foam in an oxygen environment (‘O2’). The number of oxygen atoms in the initial cubic box was 64000. The blue arrows mark the linear elastic regime up to 3 % strain and the inversion point for pure Al at 11 % strain where the shear stress starts decreasing. The green arrow shows the maximum shear stress for O2 at 0.17 strain.

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c=0.02 c=0.14 c=0.20 c=0.23 c=0.26

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Figure 3: Shear stress versus strain for an Al nanofoam covered by amorphous oxide (‘O2 layer’) with different concentrations c of O atoms. The arrow denotes the maximum of the shear stress. The mechanical behavior of the foam under tension is somewhat similar to the mechanical behavior of a single nanowire, but the sudden failure of a single wire, 22 is replaced by extended ductility, because there is a collection of wires with irregular cross-sections and junctions. It would be interesting to study an oxidation scenario under compression, since there is a large tension-compression asymmetry in foams, 17 which might be modified by oxygen on the foam surface, affecting surface stress. 51 Given that temperature affects significantly oxygen mobility, 28 ductility of the oxidized foam might be enhanced even further with respect to the pure foam as temperature is increased. Al oxide, as well as other metallic oxide materials display reduced ductility when compared to their pure metallic counterparts. Oxide layers fracture and lead to failure, 52 as shown for instance in early work on thin Al films. 53 There must be a critical oxide thickness where there is a transition from this cracking behavior observed at the micron scale, to the assisted-ductility behavior observed at the nano-scale. Our oxide layer is amorphous, while

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Figure 4: Snapshots of the foams at different strains. Top: pure Al nanofoam, middle: Al nanofoam covered by amorphous oxide (‘O2 layer’), bottom: foam in an oxygen environment (‘O2’). Red: O; blue: Al. The number of oxygen atoms in the initial cubic box was 64000.

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Figure 5: Dislocation pictures for the foam covered by an oxide layer (left) and the Al foam (right) at 30 % strain. White: defect surface; dislocations: green: Shockley partials 16 h112i, gray: stair-rod dislocations 16 h110i, red: other dislocations.

Figure 6: Snapshots for the foam covered by an oxide layer (left) and the Al foam (right) at 30 % strain. Atoms are colored by shear strain.

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1.01

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Figure 7: Relative number of bonds versus strain for the pure Al foam and the sample covered by an oxide layer (top) and in an oxygen environment (bottom). Bonds between O-O (rcut =0.4 nm), Al-O (rcut =0.25 nm) and Al-Al (v=0.35 nm). Numbers of bonds have been normalized to the number of bonds at 0 % strain. Under tension, bond breaking is expected and would lead to a decreasing number of bonds, as observed in all samples for Al-Al bonds. However, O mobility leads to formation of an increasing number of Al-O bonds, which allow extended ductility of samples with O, compared to the pure Al sample.

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Figure 8: Mixing enthalpy versus oxygen concentration, calculated using ReaxFF. The minimum at concentration of 0.6 corresponds to the stoichiometric ratio of Alumina .

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macroscopic layers are polycrystalline and fracture is aided by grain boundaries and crystal plasticity in the oxide. Further research is needed to understand the transition and the critical size at which cracking start occurring. Most studies of mechanical degradation of Al samples focus on the influence of hydrogen on embrittlement and failure. H accumulates at the interface between Al and the oxide layer, leading to blistering, 54,55 especially under irradiation conditions. 56 Future simulation studies might consider the early stages of H-bubble formation at the Al-AlOx interface, which under tension would provide additional pathways for H diffusion and bubble growth. Finally, we note that metallic nanofoams have been shown to be radiation resistant, due to their free surfaces acting as defect sink. 47 Indentation of irradiated Au nanofoam leads to hardness increase under irradiation due to defect accumulation 57 and to topology changes. 58 Oxidation would modify foam evolution under irradiation, and competing effects might not lead to hardening. However, it is likely that oxidized nanofoams would provide additional defect sinks at the oxide-metal interface, likely increasing radiation tolerance.

Supporting Information • Additional dislocation pictures for the foam covered by an oxide layer at different strains. • Slices of the oxidized sample at different strains.

Acknowledgement This work has been supported by the Simulation Science Center Clausthal-Göttingen. EMB thanks support from grants PICT2014-0696 and SeCTyP-UNCuyo. The authors acknowledge the North-German Supercomputing Alliance (HLRN) for providing HPC resources that have contributed to the research results reported in this paper.

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Molecular Dynamics Simulations of Aluminium Foams under Tension

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