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Structurally ordered nanoporous Pt–Co alloys with enhanced mechanical behaviors in tension
Microporous and Mesoporous Materials 295 (2020) 109955
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Microporous and Mesoporous Materials journal homepage: http://www.elsevier.com/locate/micromeso
Structurally ordered nanoporous Pt–Co alloys with enhanced mechanical behaviors in tension Jiejie Li a, Yuhang Zhang a, Chenyao Tian a, Hongjian Zhou a, Guoming Hu a, Re Xia a, b, * a b
Key Laboratory of Hydraulic Machinery Transients (Wuhan University), Ministry of Education, Wuhan, 430072, China Hubei Key Laboratory of Waterjet Theory and New Technology, Wuhan University, Wuhan, 430072, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Nanoporous alloys Ordered structure Mechanical properties Molecular dynamics Deformation behaviors
An ordered bimetallic nanoporous structure might be preferable and promising for catalytic applications due to the decreased Pt loading and the enhanced stability. Understanding the mechanical behaviors is the prerequisite for enhancing and prolonging the durability performance of catalysts. Herein, nanoporous (NP) Pt–Co alloys with three–dimensional stochastic bi–continuous structures are created by simulating the spinodal evolution. Mo lecular dynamics (MD) simulations have been utilized to research the mechanical behaviors of structurally or dered nanoporous Pt–Co alloys (NP Pt3 Co, NP PtCo3 and NP PtCo ) under uniaxial tension. The mechanical properties of three tested nanoporous Pt–Co alloys are significantly enhanced compared with NP–Pt, and NP Pt3 Co behaves with the superior mechanical properties due to its unique atomic arrangements. The dominating plastic deformation in the ligaments of nanoporous Pt–Co alloys is the axial yielding, and materials primarily fail through plastic necking and rupture of those ligaments in the loading direction, similar to that of NP–Au. Not only the modulus but also the strength scales a linear or exponential relation with relative density. The present results will provide insights for the mechanical optimization of nanoporous alloys as well as a new design strategy for more stable catalysts. Subjectareas: material science, computational material.
1. Introduction Nanoporous metals (NPMs) present novel and superior structures and properties, such as ultrahigh specific surface area and superior electrocatalytic performance, showing numerous promising applica tions in technological areas, including but not limited to, chemical cat alysts [1,2], proton exchange membrane fuel cells (PEMFCs) [3], biosensors [4], actuation [5], micro–nano devices [6] and tissue engi neering [7]. The functional applications, in turn, put forward the cor responding requirements on the mechanical properties of NPMs, such as strength, hardness, ductility, stability. Hence, to explore the basic me chanical behaviors and improve the mechanical properties will further accelerate the functional applications of NPMs. Many efforts have been devoted to exploring the mechanical prop erties of NPMs, including experimental [8–12], theoretical [13–18] and simulation studies [19–22]. The basic mechanical properties of nano porous (NP) materials have been evaluated and size effects on me chanical behaviors have been discussed by various experimental methods under tension [8], compression [9], nanoindentation [10] and
bending [11]. By considering the surface effects, Feng et al. [13] explored the size–dependence elastic modulus of nanoporous materials. Xia et al. [14,15] and Wang et al. [16] theoretically investigated the effective elastic properties of NP–Au with hierarchical structures. Modelling NPMs by four–coordinated spherical nodes interconnected by cylindrical struts, Huber et al. [17] and Roschning et al. [18] carried out a systematic theoretical investigation on the microstructure and macroscopic mechanical behavior, particular in size effect. With a bicontinuous open–cell porous microstructure, Sun et al. [19] investi gated the uniaxial tensile deformation of nanoporous gold and devel oped the scaling laws between mechanical properties and characteristic size. Using MD simulations, Xian et al. [20] and Li et al. [21] discussed the mechanical properties and deformation behaviors of nanocrystalline NPMs. So far, many effective measures have been developed to improve the mechanical adaptability and stability of NPMs. Aiming to the dealloying methods, pre–treatment of precursor alloy or post–treatment of as–dealloyed sample, controlling the dealloying conditions, and changing dealloying method [23–25] are adopted. Injecting a polymer
* Corresponding author. Key Laboratory of Hydraulic Machinery Transients (Wuhan University), Ministry of Education, Wuhan, 430072, China. E-mail address: [email protected] (R. Xia). https://doi.org/10.1016/j.micromeso.2019.109955 Received 18 September 2019; Received in revised form 31 October 2019; Accepted 11 December 2019 Available online 16 December 2019 1387-1811/© 2019 Elsevier Inc. All rights reserved.
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into pore space [26–28] and coating platinum on the surface [29] have also been utilized to enhance the mechanical properties of NPMs. Ac cording to the theory that alloying improves the mechanical properties of materials, the mechanical properties of nanoporous alloys might be also shown excellent enhancement compared to nanoporous countparts. The deformation mechanisms and mechanical properties of nanoporous alloys need to be clarified and relevant studies are urged to be further investigated. Several recent studies have proven that PtM (M ¼ transition metal) alloys in ordered intermetallic nanocrystals [30–32] showed great cat alytic performance enhancement. For example, the highly ordered intermetallic Pt3Co nanoparticle catalyst [31] showed superior mass activity, much better durability and no obvious activity loss under the specific fuel cell testing. An ordered bimetallic nanoporous structure might be preferable and promising for catalytic applications in PEMFCs due to the decreased Pt loading and the enhanced stability [33–35]. Because of the relative excellent performance (high catalytic activity and good stability), PtCo catalysts have been widely considered as the most attractive and promising ORR catalysts in PEMFCs among PtM catalysts [36]. In the meantime, Pt–Co alloy is a binary alloy based on platinum, whose structure can be in the long–range order when the ratio of platinum atoms to cobalt atoms are 3:1, 1:3 and 1:1. Therefore, nanoporous Pt–Co alloys (NP Pt3 Co, NP PtCo3 and NP PtCo) with ordered structures are chosen as the typical material for this study. In the present paper, nanoporous alloys with stochastic bicontinuous structures are constructed. Molecular dynamics (MD) simulations are performed to investigate the mechanical behaviors of nanoporous Pt–Co alloys under uniaxial tension. The deformation mechanisms of three structurally ordered nanoporous Pt–Co alloys are discussed, and the
scaling laws for the mechanical properties in terms of relative density are developed based on the simulation results. 2. Methodology 2.1. Model Fig. 1(a)–(d) shows the corresponding typical Face Center Cubic (FCC) lattices of structurally ordered Pt3 Co , PtCo3 and PtCo , respec tively. Noteworthy, the lattice of PtCo is anisotropy, shown in Fig. 1(c) and (d), which will result in the structure and properties anisotropy of PtCo alloy. To distinguish the difference in the present work, PtCo–x represents that the tensile direction is perpendicular to the layers of individual cobalt atoms while PtCo–y is parallel. The stochastic bi–continuous structures are often used to simulate the nanoporous structures and some efficient methods have been developed to generate the structures [19–22,37]. A phase field method named spinodal evolution is adopted in this paper and the spinodal decomposition can be described by the Cahn–Hilliard equation [38]. � � ∂u df ðuÞ θ 2 r2 u (1) ¼ r2 du ∂t where uðx; y; z; tÞð 1 � u � 1Þ is the difference in concentration of the two phases, t is the evolutionary time of the system, fðuÞ is the free energy function, and θ is the width of the transition region between the 2
two phases. In this study, fðuÞ ¼ 14 ðu2 1Þ , θ ¼ 0:01 are utilized and the further details of nanoporous sample preparation can be available in our previous studies [20–22]. The relative density ρ is defined as the Fig. 1. Illustration of nanoporous Pt and Pt–Co alloys model. The typical Face Center Cubic (FCC) lattices of structurally ordered (a) Pt3 Co , (b) PtCo3 , (c) PtCo x and (d) PtCo y , (e) NP–Pt with the relative density ρ of 0.40 and the average ligament diameter d of 4.7 nm, (f) a corresponding slab of NP–Pt sample between planes z ¼ 25:6 nm and z ¼ 23:1 nm, and the detailed atomic arrangement of (g) NP–Pt, (h) NP Pt3 Co, (i) NP PtCo3 , (j) NP PtCo x and (k) NP PtCo y marked in (f).
2
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ratio of ligament atoms to atoms of full dense with the same volume, in which the ligament atoms are the atoms that make up the whole nanoporous sample structure and the atoms of full dense are those that make up the whole simulation box. Fig. 1 (e) shows the atomic models of nanoporous platinum (NP–Pt) by solving the aforementioned equation and Fig. 1(f) gives a corresponding slab between planes z ¼ 25:6 nm and z ¼ 23:1 nm, in which the ligament diameter d is 4.7 nm and the relative density ρ is 0.40. Replacing certain platinum atoms in nano porous platinum by cobalt atoms, the structures of nanoporous Pt–Co alloys can be generated and obtained. All models of nanoporous alloys are generated based on the structure of NP–Pt, so the microstructures of nanoporous alloys are similar to each other and NP–Pt. Fig. 1(g) gives the detailed atomic arrangement of nanoporous platinum circled in Fig. 1(f) and the corresponding images of ordered nanoporous Pt–Co alloys are depicted in Fig. 1(h)–(k), respectively. It can be seen that the layers of individual platinum atoms and individual cobalt atoms are arranged alternatively in the tensile direction, x [100], shown in Fig. 1 (j).
relative density of 0.40 at 300 K. The NP–Pt samples with the similar relative density to ordered nanoporous Pt–Co alloys are also presented for comparison. Pt–Co alloys are a binary alloy based on platinum with FCC lattice, and the overall tendency of RDF for three ordered Pt–Co alloys is similar to platinum, despite the difference of peak position and probability. The crystal lattice is determined by the second sharp peak of RDF, and it is observed that the lattice parameter of Pt is maximum value, followed by Pt3 Co and PtCo, and PtCo3 is the smallest. The phenomenon can be attributed to the size difference of platinum atom and cobalt atom. More specifically, the diameter of platinum atom, 0
0
1:39 A, is larger than that of cobalt atom, 1:26 A, and the higher proportions of cobalt atom in Pt–Co alloys result in lower lattice con stant. Moreover, Pt3 Co have the largest probability of radial distribution while Pt is the smallest, as depicted in Fig. 2. The difference of peak probability may reveal a more stable structure for Pt3 Co and a relatively less stable structure for Pt compared with Pt3 Co and PtCo. 3.2. Mechanical behaviors
2.2. Computational method
The typical engineering stress–strain curves of three ordered nano porous Pt–Co alloys are shown in Fig. 3 and the curve of NP–Pt is also presented for comparison. The deformation stages are in good consis tency for three ordered nanoporous Pt–Co alloys, as well as NP–Pt, which is attributed to their similar microstructures. In order to analyze the deformation mechanism of nanoporous Pt–Co alloys, we apply the NP Pt3 Co sample with a relative density of 0.40 in the process of tension. The relative variations in the fractions of surface atoms and defect atoms are used to discuss the microstructural evolution quanti tatively. The relative fraction of surface atoms ζ is determined as the ratio of the increased surface atoms during deformation to all surface atoms at the initial state (ε ¼ 0). The fraction of hcp atoms η is defined as the ratio of hcp atoms to the total atoms. Dislocation density ρ is calculated by the total length of dislocation lines contained per unit volume. The formation of stacking faults usually results in an increase of η and ρ [47]. Fig. 4 gives a deformation characteristic of NP–Pt3Co samples as a function of the applied strain, including ζ, η and ρ. The corresponding microstructural evolution is also displayed in Fig. 5. According to the trends, the stress–strain curve can be divided into four regimes, AB, BC CD, and DE, and the tensile deformation can be distinguished by the same four stages. In the first stage (AB), the stress increases linearly with strain and atoms undergo the elastic movements around. There are few stacking faults in the ligament and junction at the initial state, as shown
For this work, MD simulations based on the open–source code Large–scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [39] are performed to investigate the mechanical behaviors of ordered nanoporous Pt–Co alloys. Embedded Atom Method (EAM) potentials developed by Foiles et al. [40] and Passianot et al. [41] are adopted for the individual elements of Pt and Co, respectively. Following the pro cedure of Zhou et al. [42], the interatomic potentials are created to describe the interactions between the element types of Pt and Co, and the corresponding alloy potentials for Pt–Co alloys are calculated and utilized. For all simulations, the initial dimension of box is fixed to 80 a0 � 80 a0 � 80 a0 , in which a0 denotes the lattice constant of platinum and a0 ¼ 0:392 nm for 300 K. All simulations are performed using the Velocity–Verlet algorithm with a constant time step δt ¼ 1 fs . Periodic boundary conditions are imposed in the x, y and z directions to emulate an infinite material. To create a well–equilibrated sample, the nano porous structure is initially relaxed to the minimum energy configura tion by conjugate gradient method, and then equilibrated using a Nos� e–Hoover thermostat at 300 K and a Nos�e–Hoover barostat at 0 atm through isothermal–isobaric ensemble (NPT) for 4 ps. Next, uniaxial tension is applied to the sample with a constant strain rate of 109/s in the x direction, [100]. The tensile deformation is applied on the box through the fix/deform procedure in LAMMPS and the samples will follow the deformation of box. The loading method adopts the stepwise straining method, which has been commonly used in MD simulations of metals and alloys [19,21,22,43]. In each load step, uniaxial tension is applied with an engineering strain of ～0.001 and the whole system is relaxed for another 1 ps at a constant temperature of 300 K using a Berendsen thermostat. All visualization of the model and the microstructure deformation evolution information are constructed from the atomic configuration viewer OVITO software [44]. The common–neighbor–analysis tech nique (CNA) is applied to analyze the deformation processes in the atomistic domain [45], in which green for face–center–cubic (fcc) atoms, blue for body–center–cubic (bcc) atoms, red for hexagonal closepacked (hcp) atoms, and grey for non 12–coordinated–atoms. 3. Results and discussions 3.1. Morphology Radial distribution function (RDF) g(r), an important structural characteristic, is used to describe the distribution of distances between pairs of particles contained within a shell of certain volume [46]. Fig. 2 displays the RDF of three ordered nanoporous Pt–Co alloys with a
Fig. 2. Radial distribution function of NP NP–Pt at 300 K. 3
Pt3 Co, NP
PtCo3 , NP
PtCo and
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Fig. 3. Strain–stress curves of (a) NP–Pt and three ordered nanoporous Pt–Co alloys with a relative density of 0.40; and (b) NP–Pt, (c) NP (e) NP–PtCo–x, (f) NP–PtCo–y with different relative densities of 0.30, 0.35, 0.40, 0.45 and 0.50, respectively.
in Fig. 5(a). No obvious increase of ζ, η and ρ may be attributed to no obvious dislocations activity and negligible surface deformation in the elastic domain, shown in Fig. 5(b). In the second stage (BC), the stress still increases but shows a nonlinear relation with the increased strain until the ultimate stress. As the applied strain increases, more and more stacking faults and partial dislocations are generated, as circled in Fig. 5 (c). The accumulation of dislocations leads to increasing η and ρ. The ligaments and junctions undergo the plastic deformation and new sur faces are generation, resulting in an increase of ζ. In the third stage (CD), the stress decreases as the applied strain further increases, and all η, ζ and ρ continue to grow. The structures of NP Pt3 Co begin to deform greatly and some weak ligaments show necking even rupture (see Fig. 5 (d)). After the strain of 0.168, the remaining ligaments in the necking
Pt3 Co, (d) NP
PtCo3 ,
cross–sectional area undergo successive plastic deformation, depicted in Fig. 5(e), and the whole sample fails as the total applied strain exceeds 0.323 (see Fig. 5(f)). In the last stage (DE), ζ remains nearly constant. In the meantime, η and ρ in the region DE show an obvious downward trend with the applied stain, as shown in Fig. 4(b). Once the dislocation is generated, it will quickly slide through a whole ligament and disap pear into the opposite free surface, leaving behind the stacking fault in the interior of ligament (see Fig. 6 (a)). However, as depicted in Fig. 6 (b) and (c), the stacking fault will disappear immediately if a secondary dislocation follows at the same location, resulting the decrease of hcp atom fraction and dislocation density. Considering the whole deforma tion process, the material breakage mainly occurs in the ligament do mains and it primarily fails through plastic necking and rupture of those 4
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Due to the identical microstructure characteristics between three Pt–Co alloys and NP–Pt, the phenomenons mentioned above may be attributed to the difference of atomic arrangements and its bonding strength between Pt atoms and Co atoms. Furthermore, those differences do not influence the major deformation mechanism of nanoporous Pt–Co alloys. It might be concluded from Fig. 7 that the dominating plastic deformation in the ligaments of ordered nanoporous Pt–Co alloys is the axial yielding rather than the bending, and materials primarily fail through plastic necking and rupture of those ligaments in the loading direction. 3.3. Scaling laws of mechanical parameters As is known that the relative density of porous materials is a key factor to influence the mechanical properties of porous materials [48]. The effect of relative density on the mechanical properties of ordered nanoporous Pt–Co alloys has been discussed in this subsection. Fig. 2 (b)–(d) show the stress–strain curves for NP–Pt and ordered nanoporous Pt–Co alloys with different relative densities. It can be seen that the modulus E, yield stress σ y and ultimate strength σ u vary significantly with the relative density. For further qualitative discussion, the me chanical parameters are derived by the following methods and sum marized in Table 1. The maximum stress in the tension deformation is determined as the ultimate strength σu . The Young’s Modulus, E, is taken from the initial linear loading stage with strain up to 2% and the yield stress, σ y , is calculated by the 0.2% offset strain. Gibson and Ashby [48] indicated that the Young’s modulus of porous materials is strongly depended on their relative density with the following equation [48]: E ¼ C E ρn Eb
(2)
where ρ denotes the relative density, E is the Young’s modulus of nanoporous material and Eb is the Young’s modulus of its bulk phase. CE and n are constants that depend on microstructure and to be determined by experiments. The value of n generally lies in the range 1 < n < 4 and the widely–accepted value of n for open foams at low relative density is 2, giving that their main deforming mechanism is bending of beams. Fig. 9(a) plots the Young’s Modulus of NP Pt3 Co, NP PtCo x , NP PtCo y ,NP PtCo3 and NP–Pt as a function of the relative density with double logarithmic scales. The suitable fitting line reveals that the Young’s modulus of order nanoporous Pt–Co alloys is propor tional to its relative density. The fitting procedure shows the exponents n are 2.14, 1.94, 2.16, 1.98 and 2.12 for NP Pt3 Co,NP PtCo3 NP PtCo x, NP PtCo y, and NP–Pt, respectively. All exponents n are around 2, indicating the bending of beams is their main elastic deforming mechanism. The deviation may be attributed to the geometric characteristics [49]. Noteworthy, the rela tion between Young’s modulus and relative density is linear when we replot the results in isometric scales, depicted in Fig. 9(b). In fact the bending often happens at joining points (see Figs. 5 and 6) and the tensile deformation is not the dominating deformation mechanism. Therefore, we would prefer to formulate the Young’s modulus of nanoporous Pt–Co alloys with relative density in terms of exponential relation rather than linear relation. Considering the deformation mechanisms of nanoporous metals at the nanoscale, Sun et al. [19] suggested that relation between modulus and relative density should be modified to
Fig. 4. Deformation characteristics of the NP Pt3 Co sample with a relative density of 0.40 in the process of tension. Variation of (a) stress (left, red), surface atom fraction (right, blue) and (b) hcp atom fraction (left, red), dislo cation density (right, blue) with the applied strain. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
ligaments in loading direction, similar to NP–Au [19]. The plastic properties of NP Pt3 Co mainly depend on the ligaments and the axial yield of ligament dominates in the yielding behavior. For monocrystalline NP–Pt, NP PtCo3 and NP PtCo, the whole deformation processes are basically the same, as illustrated in Fig. 7. Comparing the details of the deformation, the subtle difference among Pt–Co alloys can be observed, such as the variations of surface atoms fraction ζ and defect atom fraction η. Fig. 8 summarises the ζ, the hcp atom fraction at the initial state η0 and the maximum hcp atom fraction during deformation η1 for samples with the relative density of 0.40. It is evident that the increments of ζ during the deformation for alloy sam ples are higher than NP–Pt, revealing that nanoporous Pt–Co alloys are deformed to a greater extent and more new surfaces are generated during deformation. The initial defect atoms in the NP Pt3 Co sample are significantly less than other alloys, showing fewer intrinsic stacking faults and a relatively stable structure of NP Pt3 Co sample at the initial state. The stacking faults gradually accumulate during plastic defor mation, resulting in an increase of η (from η0 to η1 ). Meanwhile, the fracture strain varies with the type of nanoporous Pt–Co alloys and the major failing cross–sections are not the same. The fraction strain of NP Pt3 Co , NP PtCo3 , NP PtCo x ,NP PtCo y and NPPt are 38.9%, 36.2%, 45.9%, 22% and 30.9%, respectively. The bonding pattern and its strength between Pt atoms and Co atoms strongly affect the microstructure evolution, leading to the difference of fraction strain and major failing cross–section.
E ¼ Cb ρ2 þ Ct ρ Eb
(3)
where the two terms on the right side of Eq. (3) correspond to the bending and tensile deformation, respectively. The value of Cb= pre Ct sents the ration of bending deformation to tensile deformation in a way. The MD simulation results are in accordance with the fitting curves of 5
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Fig. 5. Snapshots of deformation microstructure in the NP Pt3 Co sample with a relative density of 0.40 under the applied strains of (a) ε ¼ 0, (b) ε ¼ 0:030, (c) ε ¼ 0:051, (d) ε ¼ 0:094 (e) ε ¼ 0:246, and (f) ε ¼ 0:323. A slice between planes z ¼ 25:0 nm and z ¼ 30:1 nm is shown. The atoms are colored by the CNA method.
Fig. 6. Schematic diagram of the stacking fault disappearance. (a) A stacking fault left behind by the dislocation movement, (b) a secondary dislocation follows at the same position, and (c) the stacking fault disappears caused by secondary dislocation movement.
Eq. (3) (see Fig. 9(c)), and the extreme ratio of Eb Cb= , 148.90/–3.66, Eb Ct 77.09/4.38, 84.77/0.06 and 109.40/2.36 and 60.12/0.76 for NP Pt3 Co, NP PtCo3 , NP PtCo x , NP PtCo y ,and NP–Pt, respectively. The specific ratio also reveals that bending deformation is the dominating elastic behavior of nanoporous Pt–Co alloys in tension. This finding is consistent with the observed phenomenon that the ex ponents n are around 2. As for the yield stress, the Gibson–Ashby model [48] pointed out that σ y =σby ∝ρ if the yielding of the axial beam dominates in the tension, where σ y and σby are the yield stress of porous materials and bulk ma terials, respectively. The yield stress of all samples is plotted against the
relative density in Fig. 10(a). Note that our numerical results match the scaling law very well, indicating the plastic behavior of ordered nano porous Pt–Co alloys is dominated by the axial yielding of ligaments. The finding is consistent with the deformation mechanisms observed and described in subsection 3.2. Fig. 10(b) displays the MD results of ulti mate strength σ u as a function of relative density ρ and shows an approximately linear relation between σu and ρ. The discussion of ulti mate strength should be similar to that of yield stress. With the similar microstructures for four tested samples, the changing trend of strength compared with the fitted curves is basically the same as each other. For example, the ultimate stress for 0.5 relative density is invariable higher 6
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Fig. 7. Deformation processes with increasing strains of (a) NP the atoms are colored according to the CNA method.
Microporous and Mesoporous Materials 295 (2020) 109955
PtCo3 ; (b) NP
PtCo
than the fitted curve while the ultimate stress for 0.45 relative density is invariable lower than fitted curve, as shown in Fig. 10(b).
x; (c) NP
PtCo
y; (d) NPPt under uniaxial tension. A slab is shown and
with Pt atoms itself. More specifically, the bond length of Co–Co is shorted than that of Pt–Pt and the bond energy of Co–Co is higher than that of Pt–Pt [50,51]. Similarity, the yield stress and ultimate strength of nanoporous alloys are still higher than those of NP–Pt (see Fig. 10). Among three structurally ordered nanoporous Pt–Co alloys, the modulus of NP Pt3 Co is the highest, followed by NP PtCo y, NP PtCo x and NP PtCo3 are the lowest. The obvious difference of modulus be tween NP PtCo x and NP PtCo y is observed in Fig. 9 and Table 1. The individual atomic layers perpendicular to loading direction produce the weaker interatomic bond force, leading to a easily
3.4. Comparison of mechanical properties As seen in Fig. 9 and indicated in Table 1, the Young’s modulus of three nanoporous alloys is higher than that of NP–Pt, indicating that ordered nanoporous Pt–Co alloys are more difficult to produce elastic deformation compared with NP–Pt. The phenomenon may be attributed to the stronger bond strength between Pt atoms and Co atoms compared 7
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Fig. 8. Increments of surface atoms fraction ζ during deformation, the defect atom fraction at the initial state η0 and the maximum atom fraction during deformation η1 for the nanoporous Pt–Co alloys and NP–Pt samples with a relative density of 0.40. Table 1 Mechanical properties of NP–Pt and three ordered nanoporous Pt–Co alloys. Sample
Tensile direction
Relative density
Young’s modulusE (GPa)
Yield stress σy (GPa)
Ultimate strengthσu (GPa)
NP
Pt3 Co
x, [100]
NP
PtCo3
x, [100]
NP
PtCo
x, [100]
0.30 0.35 0.40 0.45 0.50 0.30 0.35 0.40 0.45 0.50 0.30 0.35 0.40 0.45 0.50 0.30 0.35 0.40 0.45 0.50 0.30 0.35 0.40 0.45 0.50
11.48 17.84 23.05 27.67 35.61 7.54 12.04 14.17 16.85 21.74 6.83 10.62 13.82 18.46 20.24 9.63 16.19 18.71 20.69 29.81 4.97 8.04 10.32 12.65 15.09
0.4721 0.5761 0.8154 0.9349 1.3060 0.3428 0.4837 0.5682 0.7422 0.8616 0.2741 0.3952 0.4878 0.6923 0.7175 0.3130 0.5343 0.6592 0.7487 1.1080 0.1740 0.3143 0.4103 0.5307 0.6249
0.5005 0.6843 0.8890 1.0471 1.4801 0.4490 0.6226 0.7769 0.9119 1.3050 0.4452 0.6776 0.8097 0.9573 1.3843 0.4686 0.6194 0.7896 0.9775 1.3979 0.2789 0.4154 0.5355 0.6588 0.8840
y, [010]
NP–Pt
x, [100]
movement of atoms and further a lower modulus of NP PtCo x As for the strength, NP Pt3 Co is maximum and other alloys are relatively close to each other. Compared with NP PtCo and NP PtCo3 , the mechanical proper ties of Pt3 Co seem to be more stable due to its higher modulus and strength. Because the bond lengths of Pt–Pt and Pt–Co are larger than that of Co–Co, the internal pressure of the cluster with cobalt atoms in the center and platinum atoms in the surface is relieved and the corre sponding structure is more stable in the clusters [52,53]. The surface energy of platinum atoms is lower than that of cobalt atoms and the cohesive energy of cobalt is higher than that of platinum [50,51]. The total system energy tends to be minimized if atoms with lower surface energy and higher cohesive energy occupy the structural surface [54]. As depicted in Fig. 1 (a) and (b), the lattice of Pt3 Co can be viewed as the
Fig. 9. Fitting of Young’s modulus E with relative density ρ (a) by exponential relation in logarithmic scale; (b) by linear relation in isometric scale; (c) by Eq. (3) in isometric scale.
structure of cobalt atoms surrounded by platinum atoms while the lat tice of PtCo3 is the exact opposite. As a result, the structure of Pt3 Co tend to be more stable compared with PtCo3 . In the meantime, there are more Pt–Pt or Pt–Co bonds in the lattice of Pt3 Co and the total interaction between atoms in ordered Pt3 Co are higher than that of PtCo and PtCo3 , due to the higher binding energy of Co–Co (Pt–Co) compared with Pt–Pt. Furthermore, the spatial utilization of Pt3 Co, PtCo3 and PtCo unit cell, shown in Fig. 1(a)–(c), are 80.0%, 69.1%, and 67.77%, respectively. For a certain crystal lattice, the structure with higher spatial utilization 8
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the mechanical behaviors and deformation mechanism of nanoporous Pt–Co alloys under uniaxial tension. The strategy of making nanoporous alloys offers a new design strategy for more stable catalysts, promoting the commercial application of fuel cells. Furthermore, relevant experi mental researches on the mechanical stability and catalytic activity of nanoporous alloys may be of great interest and will be conducted in our future work. 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. Acknowledgments We wish to acknowledge the financial support from the National Natural Science Foundation of China (Grant Nos. 11102140 and 51575404). References [1] Y. Ding, Z. Zhang, Nanoporous Metals for Advanced Energy Technologies, Springer, Berlin, 2016. [2] A. Wittstock, V. Zielasek, J. Biener, C.M. Friend, M. B€ aumer, Nanoporous gold catalysts for selective gas–phase oxidative coupling of methanol at low temperature, Science 327 (2010) 319–322. [3] L.Y. Chen, T. Fujita, Y. Ding, M.W. Chen, A Three–Dimensional gold–decorated nanoporous copper core–shell composite for electrocatalysis and nonenzymatic biosensing, Adv. Funct. Mater. 20 (2010) 2279–2285. [4] C. Wu, H. Sun, Y. Li, X. Liu, X. Du, X. Wang, P. Xu, Biosensor based on glucose oxidase–nanoporous gold co–catalysis for glucose detection, Biosens. Bioelectron. 66 (2015) 350–355. [5] A. Quintana, J. Zhang, E. Isarain–Ch� avez, E. Men�endez, R. Cuadrado, R. Robles, Ma D. Bar� o, M. Guerrero, S. Pan�e, B.J. Nelson, C.M. Müller, P. Ordej� on, J. Nogu� es, E. Pellicer, J. Sort, Voltage–induced coercivity reduction in nanoporous alloy films: a boost toward energy–efficient magnetic actuation, Adv. Funct. Mater. 27 (2017) 1701904. [6] M. Heiden, S. Huang, E. Nauman, D. Johnson, L. Stanciu, Nanoporous metals for biodegradable implants: initial bone mesenchymal stem cell adhesion and degradation behavior, J. Biomed. Mater. Res. A 104A (2016) 1747–1758. [7] H.J. Qiu, H.T. Xu, L. Liu, Y. Wang, Correlation of the structure and applications of dealloyed nanoporous metals in catalysis and energy conversion/storage, Nanoscale 7 (2015) 386–400. [8] N. Badwe, X. Chen, K. Sieradzki, Mechanical properties of nanoporous gold in tension, Acta Mater. 129 (2017) 251–258. [9] H.J. Jin, L. Kurmanaeva, J. Schmauch, H. R€ osner, Y. Ivanisenko, J. Weissmüller, Deforming nanoporous metal: role of lattice coherency, Acta Mater. 57 (2009) 2665–2672. [10] Y.C. Kim, E.J. Gwak, S.M. Ahn, J.I. Jiang, H.N. Han, J.Y. Kim, Indentation size effect in nanoporous gold, Acta Mater. 138 (2017) 52–60. [11] E.J. Gwak, J.Y. Kim, Weakened flexural strength of nanocrystalline nanoporous gold by grain refinement, Nano Lett. 16 (2016) 2497. [12] N. Mameka, K. Wang, J. Markmann, E.T. Lilleodden, J. Weissmüller, Nanoporous gold—testing macro–scale samples to probe small–scale mechanical behavior, Mater. Res. Lett. 4 (2016) 27–36. [13] X.Q. Feng, R. Xia, X. Li, B. Li, Surface effects on the elastic modulus of nanoporous materials, Appl. Phys. Lett. 94 (2009), 011916. [14] R. Xia, X. Li, Q. Qin, J. Liu, X.Q. Feng, Surface effects on the mechanical properties of nanoporous materials, Nanotechnology 22 (2011) 265714. [15] R. Xia, X.Q. Feng, G.F. Wang, Effective elastic properties of nanoporous materials with hierarchical structure, Acta Mater. 59 (2011) 6801–6808. [16] X.S. Wang, R. Xia, Size–dependent effective modulus of hierarchical nanoporous foams, Europhys. Lett. 92 (2010) 16004. [17] N. Huber, R.N. Viswanath, N. Mameka, N. Mameka, J. Markmann, J. Weißmüller, Scaling laws of nanoporous metals under uniaxial compression, Acta Mater. 67 (2014) 252–265. [18] B. Roschning, N. Huber, Scaling laws of nanoporous gold under uniaxial compression: effects of structural disorder on the solid fraction, elastic Poisson’s ratio, Young’s modulus and yield strength, J. Mech. Phys. Solids 92 (2016) 55–71. [19] X.Y. Sun, G.K. Xu, X. Li, X.Q. Feng, H. Gao, Mechanical properties and scaling laws of nanoporous gold, J. Appl. Phys. 113 (2013), 023505. [20] Y. Xian, J. Li, R. Wu, R. Xia, Softening of nanocrystalline nanoporous platinum: a molecular dynamics simulation, Comput. Mater. Sci. 143 (2018) 163–169. [21] J. Li, Y. Xian, H. Zhou, R. Wu, G. Hu, R. Xia, Mechanical properties of nanocrystalline nanoporous gold complicated by variation of grain and ligament: a molecular dynamics simulation, Sci. China Technol. Sci. 61 (2018) 1353–1363.
Fig. 10. (a) Yield stress σ y , and (b) ultimate strength σ u of NP–Pt and three ordered nanoporous Pt–Co alloys as a function of the relative density in iso metric scale.
might be more stable due to the relatively difficult movement between atoms. In a word, the excellent performance of NP Pt3 Co may relate to the unique atom arrangements of the ordered Pt3 Co beneficial for me chanical behavior enhancement and strong stabilization against applied load. 4. Conclusion In summary, nanoporous Pt–Co alloys with 3D stochastic bi–continuous structures and controllable compositions were created by adopting a phase field method named spinodal decomposition. The tensile deformation behaviors of three ordered nanoporous Pt–Co alloys have been investigated using MD simulations. Similar to nanoporous gold, the axial yielding of ligaments is the principal deformation mechanism of ordered nanoporous Pt–Co alloys and it fails through plastic necking and rupture of those ligaments in the loading direction. The Young’s modulus shows a power relation with the relative density of ordered nanoporous Pt–Co alloys while the yield stress and the ultimate strength display linear relations. It is observed that the mechanical properties of nanoporous Pt–Co alloys are significantly enhanced compared with NP–Pt. Due to the special atomic arrangements between Co atoms and Pt atoms, NP Pt3 Co shows the superior mechanical properties among three ordered nanoporous alloys. The present results shall provide atomistic insights for understanding 9
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[22] J. Li, Y. Xian, H. Zhou, R. Wu, G. Hu, R. Xia, Microstructure–sensitive mechanical properties of nanoporous gold: a molecular dynamics study, Model. Simul. Mater. Sci. Eng. 26 (2018), 075003. [23] J. Zhu, E. Seker, H. Bart–Smith, M.R. Begley, R.G. Kelly, G. Zangari, W.K. Lye, M. L. Reed, Mitigation of tensile failure in released nanoporous metal microstructures via thermal treatment, Appl. Phys. Lett. 89 (2006) 133104. [24] Y. Wang, Y.Z. Wang, C. Zhang, T.Y. Kou, Z.H. Zhang, Tuning the ligament/channel size of nanoporous copper by temperature control, CrystEngComm 14 (2012) 8352–8356. [25] I.C. Cheng, A.M. Hodge, Morphology, oxidation, and mechanical behavior of nanoporous Cu foams, Adv. Eng. Mater. 14 (2012) 219–226. [26] K. Wang, J. Weissmüller, Composites of nanoporous gold and polymer, Adv. Mater. 25 (2013) 1280–1284. [27] E. Griffiths, S. Bargmann, B.D. Reddy, Elastic behavior at the nanoscale of innovative composites of nanoporous gold and polymer, Extreme Mech. Lett. 17 (2017) 16–23. [28] J. Li, C. Tian, B. Lu, Y. Xian, R. Wu, G. Hu, R. Xia, Deformation behavior of nanoporous gold based composite in compression: a finite element analysis, Comp. Struct. 211 (2019) 229–235. [29] Y.O. Yildiz, M. Kirca, Compression and shear behavior of ultrathin coated nanoporous gold: a molecular dynamics study, J. Appl. Phys. 124 (2018) 184301. [30] M. Oezaslan, F. Hasch�e, P. Strasser, PtCu3, PtCu and Pt3Cu alloy nanoparticle electrocatalysts for oxygen reduction reaction in alkaline and acidic media, J. Electrochem. Soc. 159 (2012) B444–B454. [31] X.X. Wang, S. Hwang, Y.T. Pan, K. Chen, Y. He, S. Karakalos, H. Zhang, J. S. Spendelow, D. Su, G. Wu, Ordered Pt3Co intermetallic nanoparticles derived from metal–organic frameworks for oxygen reduction, Nano Lett. 18 (2018) 4163–4171. [32] M. Luo, Y. Sun, L. Wang, S. Guo, Tuning multimetallic ordered intermetallic nanocrystals for efficient energy electrocatalysis, Adv. Energy Mater. 7 (2017) 1602073. [33] Q. Zhou, C. Xu, Stratified nanoporous PtTi alloys for hydrolysis of ammonia borane, J. Colloid Interface Sci. 496 (2017) 235–242. [34] Q. Zhou, L. Qi, H. Yang, C. Xu, Hierarchical nanoporous platinum–copper alloy nanoflowers as highly active catalysts for the hydrolytic dehydrogenation of ammonia borane, J. Colloid Interface Sci. 513 (2018) 258–265. [35] L. Liu, E. Pippel, R. Scholz, U. Gosele, Nanoporous Pt–Co alloy nanowires: fabrication, characterization, and electrocatalytic properties, Nano Lett. 9 (2009) 4352–4358. [36] E. Antolini, J.R.C. Salgado, E.R. Gonzalez, The stability of Pt–M (M¼ first row transition metal) alloy catalysts and its effect on the activity in low temperature fuel cells: a literature review and tests on a Pt–Co catalyst, J. Power Sources 160 (2006) 957–968.
[37] C. Liu, P.S. Branicio, Efficient generation of non–cubic stochastic periodic bicontinuous nanoporous structures, Comput. Mater. Sci. 169 (2019) 109101. [38] J.W. Cahn, J.E. Hilliard, Free energy of a nonuniform system. I. interfacial free energy, J. Chem. Phys. 28 (1958) 258–267. [39] S. Plimpton, P. Crozier, A. Thompson, LAMMPS–large–scale atomic/molecular massively parallel simulator, Sandia Natl. Lab. 18 (2007). [40] S. Foiles, M. Baskes, M.S. Daw, Embedded–atom–method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys, Phys. Rev. B 33 (1986) 7983–7991. [41] R. Passianot, E.J. Savino, Embedded–atom–method interatomic potentials for hcp metals, Phys. Rev. B 45 (1992) 12704. [42] X.W. Zhou, R.A. Johnson, H.N.G. Wadley, Misfit–energy–increasing dislocations in vapor–deposited CoFe/NiFe multilayers, Phys. Rev. B 69 (2004) 144113. [43] A.C. To, J. Tao, M. Kirca, L. Schalk, Ligament and joint sizes govern softening in nanoporous aluminum, Appl. Phys. Lett. 98 (2011), 051903. [44] A. Stukowski, Visualization and analysis of atomistic simulation data with OVITO–the open visualization tool, Model. Simul. Mater. Sci. Eng. 18 (2009), 015012. [45] H. Tsuzuki, P.S. Branicio, J.P. Rino, Structural characterization of deformed crystals by analysis of common atomic neighborhood, Comput. Phys. Commun. 177 (2007) 518–523. [46] C. Zhu, X. Liu, X. Yu, N. Zhao, J. Liu, J. Xu, A small–angle X–ray scattering study and molecular dynamics simulation of microvoid evolution during the tensile deformation of carbon fibers, Carbon 50 (2012) 235–243. [47] F. Sansoz, Atomistic processes controlling flow stress scaling during compression of nanoscale face–centered–cubic crystals, Acta Mater. 59 (2011) 3364–3372. [48] L.J. Gibson, M.F. Ashby, Cellular Solids: Structure and Properties 2nd, Cambridge University Press, Cambridge, 1997. [49] A.P. Roberts, E.J. Garboczi, Elastic properties of model random three–dimensional open–cell solids, J. Mech. Phys. Solids 50 (2002) 33–55. [50] Q.L. Lu, L.Z. Zhu, L. Ma, G.H. Wang, Magnetic properties of Co/Cu and Co/Pt bimetallic clusters, Chem. Phys. Lett. 407 (2005) 176–179. [51] Q.L. Lu, L.Z. Zhu, L. Ma, G.H. Wang, Structural transition and magnetic properties of ComPtn (m þ n ¼ 38) clusters, Phys. Lett. A 350 (2006) 258–262. [52] S. Darby, T.V. Mortimer–Jones, R.L. Johnston, C. Roberts, Theoretical study of Cu–Au nanoalloy clusters using a genetic algorithm, J. Chem. Phys. 116 (2002) 1536–1550. [53] G. Rossi, A. Rapallo, C. Mottet, A. Fortunelli, F. Baletto, R. Ferrando, Magic polyicosahedral core–shell clusters, Phys. Rev. Lett. 93 (2004) 105503. [54] K. Yuga, A. Seko, A. Kuwabara, F. Oba, I. Tanaka, First–principles study of bulk ordering and surface segregation in Pt–Rh binary alloys, Phys. Rev. B 74 (2006) 174202.
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Contents lists available at ScienceDirect
Microporous and Mesoporous Materials journal homepage: http://www.elsevier.com/locate/micromeso
Structurally ordered nanoporous Pt–Co alloys with enhanced mechanical behaviors in tension Jiejie Li a, Yuhang Zhang a, Chenyao Tian a, Hongjian Zhou a, Guoming Hu a, Re Xia a, b, * a b
Key Laboratory of Hydraulic Machinery Transients (Wuhan University), Ministry of Education, Wuhan, 430072, China Hubei Key Laboratory of Waterjet Theory and New Technology, Wuhan University, Wuhan, 430072, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Nanoporous alloys Ordered structure Mechanical properties Molecular dynamics Deformation behaviors
An ordered bimetallic nanoporous structure might be preferable and promising for catalytic applications due to the decreased Pt loading and the enhanced stability. Understanding the mechanical behaviors is the prerequisite for enhancing and prolonging the durability performance of catalysts. Herein, nanoporous (NP) Pt–Co alloys with three–dimensional stochastic bi–continuous structures are created by simulating the spinodal evolution. Mo lecular dynamics (MD) simulations have been utilized to research the mechanical behaviors of structurally or dered nanoporous Pt–Co alloys (NP Pt3 Co, NP PtCo3 and NP PtCo ) under uniaxial tension. The mechanical properties of three tested nanoporous Pt–Co alloys are significantly enhanced compared with NP–Pt, and NP Pt3 Co behaves with the superior mechanical properties due to its unique atomic arrangements. The dominating plastic deformation in the ligaments of nanoporous Pt–Co alloys is the axial yielding, and materials primarily fail through plastic necking and rupture of those ligaments in the loading direction, similar to that of NP–Au. Not only the modulus but also the strength scales a linear or exponential relation with relative density. The present results will provide insights for the mechanical optimization of nanoporous alloys as well as a new design strategy for more stable catalysts. Subjectareas: material science, computational material.
1. Introduction Nanoporous metals (NPMs) present novel and superior structures and properties, such as ultrahigh specific surface area and superior electrocatalytic performance, showing numerous promising applica tions in technological areas, including but not limited to, chemical cat alysts [1,2], proton exchange membrane fuel cells (PEMFCs) [3], biosensors [4], actuation [5], micro–nano devices [6] and tissue engi neering [7]. The functional applications, in turn, put forward the cor responding requirements on the mechanical properties of NPMs, such as strength, hardness, ductility, stability. Hence, to explore the basic me chanical behaviors and improve the mechanical properties will further accelerate the functional applications of NPMs. Many efforts have been devoted to exploring the mechanical prop erties of NPMs, including experimental [8–12], theoretical [13–18] and simulation studies [19–22]. The basic mechanical properties of nano porous (NP) materials have been evaluated and size effects on me chanical behaviors have been discussed by various experimental methods under tension [8], compression [9], nanoindentation [10] and
bending [11]. By considering the surface effects, Feng et al. [13] explored the size–dependence elastic modulus of nanoporous materials. Xia et al. [14,15] and Wang et al. [16] theoretically investigated the effective elastic properties of NP–Au with hierarchical structures. Modelling NPMs by four–coordinated spherical nodes interconnected by cylindrical struts, Huber et al. [17] and Roschning et al. [18] carried out a systematic theoretical investigation on the microstructure and macroscopic mechanical behavior, particular in size effect. With a bicontinuous open–cell porous microstructure, Sun et al. [19] investi gated the uniaxial tensile deformation of nanoporous gold and devel oped the scaling laws between mechanical properties and characteristic size. Using MD simulations, Xian et al. [20] and Li et al. [21] discussed the mechanical properties and deformation behaviors of nanocrystalline NPMs. So far, many effective measures have been developed to improve the mechanical adaptability and stability of NPMs. Aiming to the dealloying methods, pre–treatment of precursor alloy or post–treatment of as–dealloyed sample, controlling the dealloying conditions, and changing dealloying method [23–25] are adopted. Injecting a polymer
* Corresponding author. Key Laboratory of Hydraulic Machinery Transients (Wuhan University), Ministry of Education, Wuhan, 430072, China. E-mail address: [email protected] (R. Xia). https://doi.org/10.1016/j.micromeso.2019.109955 Received 18 September 2019; Received in revised form 31 October 2019; Accepted 11 December 2019 Available online 16 December 2019 1387-1811/© 2019 Elsevier Inc. All rights reserved.
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into pore space [26–28] and coating platinum on the surface [29] have also been utilized to enhance the mechanical properties of NPMs. Ac cording to the theory that alloying improves the mechanical properties of materials, the mechanical properties of nanoporous alloys might be also shown excellent enhancement compared to nanoporous countparts. The deformation mechanisms and mechanical properties of nanoporous alloys need to be clarified and relevant studies are urged to be further investigated. Several recent studies have proven that PtM (M ¼ transition metal) alloys in ordered intermetallic nanocrystals [30–32] showed great cat alytic performance enhancement. For example, the highly ordered intermetallic Pt3Co nanoparticle catalyst [31] showed superior mass activity, much better durability and no obvious activity loss under the specific fuel cell testing. An ordered bimetallic nanoporous structure might be preferable and promising for catalytic applications in PEMFCs due to the decreased Pt loading and the enhanced stability [33–35]. Because of the relative excellent performance (high catalytic activity and good stability), PtCo catalysts have been widely considered as the most attractive and promising ORR catalysts in PEMFCs among PtM catalysts [36]. In the meantime, Pt–Co alloy is a binary alloy based on platinum, whose structure can be in the long–range order when the ratio of platinum atoms to cobalt atoms are 3:1, 1:3 and 1:1. Therefore, nanoporous Pt–Co alloys (NP Pt3 Co, NP PtCo3 and NP PtCo) with ordered structures are chosen as the typical material for this study. In the present paper, nanoporous alloys with stochastic bicontinuous structures are constructed. Molecular dynamics (MD) simulations are performed to investigate the mechanical behaviors of nanoporous Pt–Co alloys under uniaxial tension. The deformation mechanisms of three structurally ordered nanoporous Pt–Co alloys are discussed, and the
scaling laws for the mechanical properties in terms of relative density are developed based on the simulation results. 2. Methodology 2.1. Model Fig. 1(a)–(d) shows the corresponding typical Face Center Cubic (FCC) lattices of structurally ordered Pt3 Co , PtCo3 and PtCo , respec tively. Noteworthy, the lattice of PtCo is anisotropy, shown in Fig. 1(c) and (d), which will result in the structure and properties anisotropy of PtCo alloy. To distinguish the difference in the present work, PtCo–x represents that the tensile direction is perpendicular to the layers of individual cobalt atoms while PtCo–y is parallel. The stochastic bi–continuous structures are often used to simulate the nanoporous structures and some efficient methods have been developed to generate the structures [19–22,37]. A phase field method named spinodal evolution is adopted in this paper and the spinodal decomposition can be described by the Cahn–Hilliard equation [38]. � � ∂u df ðuÞ θ 2 r2 u (1) ¼ r2 du ∂t where uðx; y; z; tÞð 1 � u � 1Þ is the difference in concentration of the two phases, t is the evolutionary time of the system, fðuÞ is the free energy function, and θ is the width of the transition region between the 2
two phases. In this study, fðuÞ ¼ 14 ðu2 1Þ , θ ¼ 0:01 are utilized and the further details of nanoporous sample preparation can be available in our previous studies [20–22]. The relative density ρ is defined as the Fig. 1. Illustration of nanoporous Pt and Pt–Co alloys model. The typical Face Center Cubic (FCC) lattices of structurally ordered (a) Pt3 Co , (b) PtCo3 , (c) PtCo x and (d) PtCo y , (e) NP–Pt with the relative density ρ of 0.40 and the average ligament diameter d of 4.7 nm, (f) a corresponding slab of NP–Pt sample between planes z ¼ 25:6 nm and z ¼ 23:1 nm, and the detailed atomic arrangement of (g) NP–Pt, (h) NP Pt3 Co, (i) NP PtCo3 , (j) NP PtCo x and (k) NP PtCo y marked in (f).
2
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ratio of ligament atoms to atoms of full dense with the same volume, in which the ligament atoms are the atoms that make up the whole nanoporous sample structure and the atoms of full dense are those that make up the whole simulation box. Fig. 1 (e) shows the atomic models of nanoporous platinum (NP–Pt) by solving the aforementioned equation and Fig. 1(f) gives a corresponding slab between planes z ¼ 25:6 nm and z ¼ 23:1 nm, in which the ligament diameter d is 4.7 nm and the relative density ρ is 0.40. Replacing certain platinum atoms in nano porous platinum by cobalt atoms, the structures of nanoporous Pt–Co alloys can be generated and obtained. All models of nanoporous alloys are generated based on the structure of NP–Pt, so the microstructures of nanoporous alloys are similar to each other and NP–Pt. Fig. 1(g) gives the detailed atomic arrangement of nanoporous platinum circled in Fig. 1(f) and the corresponding images of ordered nanoporous Pt–Co alloys are depicted in Fig. 1(h)–(k), respectively. It can be seen that the layers of individual platinum atoms and individual cobalt atoms are arranged alternatively in the tensile direction, x [100], shown in Fig. 1 (j).
relative density of 0.40 at 300 K. The NP–Pt samples with the similar relative density to ordered nanoporous Pt–Co alloys are also presented for comparison. Pt–Co alloys are a binary alloy based on platinum with FCC lattice, and the overall tendency of RDF for three ordered Pt–Co alloys is similar to platinum, despite the difference of peak position and probability. The crystal lattice is determined by the second sharp peak of RDF, and it is observed that the lattice parameter of Pt is maximum value, followed by Pt3 Co and PtCo, and PtCo3 is the smallest. The phenomenon can be attributed to the size difference of platinum atom and cobalt atom. More specifically, the diameter of platinum atom, 0
0
1:39 A, is larger than that of cobalt atom, 1:26 A, and the higher proportions of cobalt atom in Pt–Co alloys result in lower lattice con stant. Moreover, Pt3 Co have the largest probability of radial distribution while Pt is the smallest, as depicted in Fig. 2. The difference of peak probability may reveal a more stable structure for Pt3 Co and a relatively less stable structure for Pt compared with Pt3 Co and PtCo. 3.2. Mechanical behaviors
2.2. Computational method
The typical engineering stress–strain curves of three ordered nano porous Pt–Co alloys are shown in Fig. 3 and the curve of NP–Pt is also presented for comparison. The deformation stages are in good consis tency for three ordered nanoporous Pt–Co alloys, as well as NP–Pt, which is attributed to their similar microstructures. In order to analyze the deformation mechanism of nanoporous Pt–Co alloys, we apply the NP Pt3 Co sample with a relative density of 0.40 in the process of tension. The relative variations in the fractions of surface atoms and defect atoms are used to discuss the microstructural evolution quanti tatively. The relative fraction of surface atoms ζ is determined as the ratio of the increased surface atoms during deformation to all surface atoms at the initial state (ε ¼ 0). The fraction of hcp atoms η is defined as the ratio of hcp atoms to the total atoms. Dislocation density ρ is calculated by the total length of dislocation lines contained per unit volume. The formation of stacking faults usually results in an increase of η and ρ [47]. Fig. 4 gives a deformation characteristic of NP–Pt3Co samples as a function of the applied strain, including ζ, η and ρ. The corresponding microstructural evolution is also displayed in Fig. 5. According to the trends, the stress–strain curve can be divided into four regimes, AB, BC CD, and DE, and the tensile deformation can be distinguished by the same four stages. In the first stage (AB), the stress increases linearly with strain and atoms undergo the elastic movements around. There are few stacking faults in the ligament and junction at the initial state, as shown
For this work, MD simulations based on the open–source code Large–scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [39] are performed to investigate the mechanical behaviors of ordered nanoporous Pt–Co alloys. Embedded Atom Method (EAM) potentials developed by Foiles et al. [40] and Passianot et al. [41] are adopted for the individual elements of Pt and Co, respectively. Following the pro cedure of Zhou et al. [42], the interatomic potentials are created to describe the interactions between the element types of Pt and Co, and the corresponding alloy potentials for Pt–Co alloys are calculated and utilized. For all simulations, the initial dimension of box is fixed to 80 a0 � 80 a0 � 80 a0 , in which a0 denotes the lattice constant of platinum and a0 ¼ 0:392 nm for 300 K. All simulations are performed using the Velocity–Verlet algorithm with a constant time step δt ¼ 1 fs . Periodic boundary conditions are imposed in the x, y and z directions to emulate an infinite material. To create a well–equilibrated sample, the nano porous structure is initially relaxed to the minimum energy configura tion by conjugate gradient method, and then equilibrated using a Nos� e–Hoover thermostat at 300 K and a Nos�e–Hoover barostat at 0 atm through isothermal–isobaric ensemble (NPT) for 4 ps. Next, uniaxial tension is applied to the sample with a constant strain rate of 109/s in the x direction, [100]. The tensile deformation is applied on the box through the fix/deform procedure in LAMMPS and the samples will follow the deformation of box. The loading method adopts the stepwise straining method, which has been commonly used in MD simulations of metals and alloys [19,21,22,43]. In each load step, uniaxial tension is applied with an engineering strain of ～0.001 and the whole system is relaxed for another 1 ps at a constant temperature of 300 K using a Berendsen thermostat. All visualization of the model and the microstructure deformation evolution information are constructed from the atomic configuration viewer OVITO software [44]. The common–neighbor–analysis tech nique (CNA) is applied to analyze the deformation processes in the atomistic domain [45], in which green for face–center–cubic (fcc) atoms, blue for body–center–cubic (bcc) atoms, red for hexagonal closepacked (hcp) atoms, and grey for non 12–coordinated–atoms. 3. Results and discussions 3.1. Morphology Radial distribution function (RDF) g(r), an important structural characteristic, is used to describe the distribution of distances between pairs of particles contained within a shell of certain volume [46]. Fig. 2 displays the RDF of three ordered nanoporous Pt–Co alloys with a
Fig. 2. Radial distribution function of NP NP–Pt at 300 K. 3
Pt3 Co, NP
PtCo3 , NP
PtCo and
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Fig. 3. Strain–stress curves of (a) NP–Pt and three ordered nanoporous Pt–Co alloys with a relative density of 0.40; and (b) NP–Pt, (c) NP (e) NP–PtCo–x, (f) NP–PtCo–y with different relative densities of 0.30, 0.35, 0.40, 0.45 and 0.50, respectively.
in Fig. 5(a). No obvious increase of ζ, η and ρ may be attributed to no obvious dislocations activity and negligible surface deformation in the elastic domain, shown in Fig. 5(b). In the second stage (BC), the stress still increases but shows a nonlinear relation with the increased strain until the ultimate stress. As the applied strain increases, more and more stacking faults and partial dislocations are generated, as circled in Fig. 5 (c). The accumulation of dislocations leads to increasing η and ρ. The ligaments and junctions undergo the plastic deformation and new sur faces are generation, resulting in an increase of ζ. In the third stage (CD), the stress decreases as the applied strain further increases, and all η, ζ and ρ continue to grow. The structures of NP Pt3 Co begin to deform greatly and some weak ligaments show necking even rupture (see Fig. 5 (d)). After the strain of 0.168, the remaining ligaments in the necking
Pt3 Co, (d) NP
PtCo3 ,
cross–sectional area undergo successive plastic deformation, depicted in Fig. 5(e), and the whole sample fails as the total applied strain exceeds 0.323 (see Fig. 5(f)). In the last stage (DE), ζ remains nearly constant. In the meantime, η and ρ in the region DE show an obvious downward trend with the applied stain, as shown in Fig. 4(b). Once the dislocation is generated, it will quickly slide through a whole ligament and disap pear into the opposite free surface, leaving behind the stacking fault in the interior of ligament (see Fig. 6 (a)). However, as depicted in Fig. 6 (b) and (c), the stacking fault will disappear immediately if a secondary dislocation follows at the same location, resulting the decrease of hcp atom fraction and dislocation density. Considering the whole deforma tion process, the material breakage mainly occurs in the ligament do mains and it primarily fails through plastic necking and rupture of those 4
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Due to the identical microstructure characteristics between three Pt–Co alloys and NP–Pt, the phenomenons mentioned above may be attributed to the difference of atomic arrangements and its bonding strength between Pt atoms and Co atoms. Furthermore, those differences do not influence the major deformation mechanism of nanoporous Pt–Co alloys. It might be concluded from Fig. 7 that the dominating plastic deformation in the ligaments of ordered nanoporous Pt–Co alloys is the axial yielding rather than the bending, and materials primarily fail through plastic necking and rupture of those ligaments in the loading direction. 3.3. Scaling laws of mechanical parameters As is known that the relative density of porous materials is a key factor to influence the mechanical properties of porous materials [48]. The effect of relative density on the mechanical properties of ordered nanoporous Pt–Co alloys has been discussed in this subsection. Fig. 2 (b)–(d) show the stress–strain curves for NP–Pt and ordered nanoporous Pt–Co alloys with different relative densities. It can be seen that the modulus E, yield stress σ y and ultimate strength σ u vary significantly with the relative density. For further qualitative discussion, the me chanical parameters are derived by the following methods and sum marized in Table 1. The maximum stress in the tension deformation is determined as the ultimate strength σu . The Young’s Modulus, E, is taken from the initial linear loading stage with strain up to 2% and the yield stress, σ y , is calculated by the 0.2% offset strain. Gibson and Ashby [48] indicated that the Young’s modulus of porous materials is strongly depended on their relative density with the following equation [48]: E ¼ C E ρn Eb
(2)
where ρ denotes the relative density, E is the Young’s modulus of nanoporous material and Eb is the Young’s modulus of its bulk phase. CE and n are constants that depend on microstructure and to be determined by experiments. The value of n generally lies in the range 1 < n < 4 and the widely–accepted value of n for open foams at low relative density is 2, giving that their main deforming mechanism is bending of beams. Fig. 9(a) plots the Young’s Modulus of NP Pt3 Co, NP PtCo x , NP PtCo y ,NP PtCo3 and NP–Pt as a function of the relative density with double logarithmic scales. The suitable fitting line reveals that the Young’s modulus of order nanoporous Pt–Co alloys is propor tional to its relative density. The fitting procedure shows the exponents n are 2.14, 1.94, 2.16, 1.98 and 2.12 for NP Pt3 Co,NP PtCo3 NP PtCo x, NP PtCo y, and NP–Pt, respectively. All exponents n are around 2, indicating the bending of beams is their main elastic deforming mechanism. The deviation may be attributed to the geometric characteristics [49]. Noteworthy, the rela tion between Young’s modulus and relative density is linear when we replot the results in isometric scales, depicted in Fig. 9(b). In fact the bending often happens at joining points (see Figs. 5 and 6) and the tensile deformation is not the dominating deformation mechanism. Therefore, we would prefer to formulate the Young’s modulus of nanoporous Pt–Co alloys with relative density in terms of exponential relation rather than linear relation. Considering the deformation mechanisms of nanoporous metals at the nanoscale, Sun et al. [19] suggested that relation between modulus and relative density should be modified to
Fig. 4. Deformation characteristics of the NP Pt3 Co sample with a relative density of 0.40 in the process of tension. Variation of (a) stress (left, red), surface atom fraction (right, blue) and (b) hcp atom fraction (left, red), dislo cation density (right, blue) with the applied strain. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
ligaments in loading direction, similar to NP–Au [19]. The plastic properties of NP Pt3 Co mainly depend on the ligaments and the axial yield of ligament dominates in the yielding behavior. For monocrystalline NP–Pt, NP PtCo3 and NP PtCo, the whole deformation processes are basically the same, as illustrated in Fig. 7. Comparing the details of the deformation, the subtle difference among Pt–Co alloys can be observed, such as the variations of surface atoms fraction ζ and defect atom fraction η. Fig. 8 summarises the ζ, the hcp atom fraction at the initial state η0 and the maximum hcp atom fraction during deformation η1 for samples with the relative density of 0.40. It is evident that the increments of ζ during the deformation for alloy sam ples are higher than NP–Pt, revealing that nanoporous Pt–Co alloys are deformed to a greater extent and more new surfaces are generated during deformation. The initial defect atoms in the NP Pt3 Co sample are significantly less than other alloys, showing fewer intrinsic stacking faults and a relatively stable structure of NP Pt3 Co sample at the initial state. The stacking faults gradually accumulate during plastic defor mation, resulting in an increase of η (from η0 to η1 ). Meanwhile, the fracture strain varies with the type of nanoporous Pt–Co alloys and the major failing cross–sections are not the same. The fraction strain of NP Pt3 Co , NP PtCo3 , NP PtCo x ,NP PtCo y and NPPt are 38.9%, 36.2%, 45.9%, 22% and 30.9%, respectively. The bonding pattern and its strength between Pt atoms and Co atoms strongly affect the microstructure evolution, leading to the difference of fraction strain and major failing cross–section.
E ¼ Cb ρ2 þ Ct ρ Eb
(3)
where the two terms on the right side of Eq. (3) correspond to the bending and tensile deformation, respectively. The value of Cb= pre Ct sents the ration of bending deformation to tensile deformation in a way. The MD simulation results are in accordance with the fitting curves of 5
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Fig. 5. Snapshots of deformation microstructure in the NP Pt3 Co sample with a relative density of 0.40 under the applied strains of (a) ε ¼ 0, (b) ε ¼ 0:030, (c) ε ¼ 0:051, (d) ε ¼ 0:094 (e) ε ¼ 0:246, and (f) ε ¼ 0:323. A slice between planes z ¼ 25:0 nm and z ¼ 30:1 nm is shown. The atoms are colored by the CNA method.
Fig. 6. Schematic diagram of the stacking fault disappearance. (a) A stacking fault left behind by the dislocation movement, (b) a secondary dislocation follows at the same position, and (c) the stacking fault disappears caused by secondary dislocation movement.
Eq. (3) (see Fig. 9(c)), and the extreme ratio of Eb Cb= , 148.90/–3.66, Eb Ct 77.09/4.38, 84.77/0.06 and 109.40/2.36 and 60.12/0.76 for NP Pt3 Co, NP PtCo3 , NP PtCo x , NP PtCo y ,and NP–Pt, respectively. The specific ratio also reveals that bending deformation is the dominating elastic behavior of nanoporous Pt–Co alloys in tension. This finding is consistent with the observed phenomenon that the ex ponents n are around 2. As for the yield stress, the Gibson–Ashby model [48] pointed out that σ y =σby ∝ρ if the yielding of the axial beam dominates in the tension, where σ y and σby are the yield stress of porous materials and bulk ma terials, respectively. The yield stress of all samples is plotted against the
relative density in Fig. 10(a). Note that our numerical results match the scaling law very well, indicating the plastic behavior of ordered nano porous Pt–Co alloys is dominated by the axial yielding of ligaments. The finding is consistent with the deformation mechanisms observed and described in subsection 3.2. Fig. 10(b) displays the MD results of ulti mate strength σ u as a function of relative density ρ and shows an approximately linear relation between σu and ρ. The discussion of ulti mate strength should be similar to that of yield stress. With the similar microstructures for four tested samples, the changing trend of strength compared with the fitted curves is basically the same as each other. For example, the ultimate stress for 0.5 relative density is invariable higher 6
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Fig. 7. Deformation processes with increasing strains of (a) NP the atoms are colored according to the CNA method.
Microporous and Mesoporous Materials 295 (2020) 109955
PtCo3 ; (b) NP
PtCo
than the fitted curve while the ultimate stress for 0.45 relative density is invariable lower than fitted curve, as shown in Fig. 10(b).
x; (c) NP
PtCo
y; (d) NPPt under uniaxial tension. A slab is shown and
with Pt atoms itself. More specifically, the bond length of Co–Co is shorted than that of Pt–Pt and the bond energy of Co–Co is higher than that of Pt–Pt [50,51]. Similarity, the yield stress and ultimate strength of nanoporous alloys are still higher than those of NP–Pt (see Fig. 10). Among three structurally ordered nanoporous Pt–Co alloys, the modulus of NP Pt3 Co is the highest, followed by NP PtCo y, NP PtCo x and NP PtCo3 are the lowest. The obvious difference of modulus be tween NP PtCo x and NP PtCo y is observed in Fig. 9 and Table 1. The individual atomic layers perpendicular to loading direction produce the weaker interatomic bond force, leading to a easily
3.4. Comparison of mechanical properties As seen in Fig. 9 and indicated in Table 1, the Young’s modulus of three nanoporous alloys is higher than that of NP–Pt, indicating that ordered nanoporous Pt–Co alloys are more difficult to produce elastic deformation compared with NP–Pt. The phenomenon may be attributed to the stronger bond strength between Pt atoms and Co atoms compared 7
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Fig. 8. Increments of surface atoms fraction ζ during deformation, the defect atom fraction at the initial state η0 and the maximum atom fraction during deformation η1 for the nanoporous Pt–Co alloys and NP–Pt samples with a relative density of 0.40. Table 1 Mechanical properties of NP–Pt and three ordered nanoporous Pt–Co alloys. Sample
Tensile direction
Relative density
Young’s modulusE (GPa)
Yield stress σy (GPa)
Ultimate strengthσu (GPa)
NP
Pt3 Co
x, [100]
NP
PtCo3
x, [100]
NP
PtCo
x, [100]
0.30 0.35 0.40 0.45 0.50 0.30 0.35 0.40 0.45 0.50 0.30 0.35 0.40 0.45 0.50 0.30 0.35 0.40 0.45 0.50 0.30 0.35 0.40 0.45 0.50
11.48 17.84 23.05 27.67 35.61 7.54 12.04 14.17 16.85 21.74 6.83 10.62 13.82 18.46 20.24 9.63 16.19 18.71 20.69 29.81 4.97 8.04 10.32 12.65 15.09
0.4721 0.5761 0.8154 0.9349 1.3060 0.3428 0.4837 0.5682 0.7422 0.8616 0.2741 0.3952 0.4878 0.6923 0.7175 0.3130 0.5343 0.6592 0.7487 1.1080 0.1740 0.3143 0.4103 0.5307 0.6249
0.5005 0.6843 0.8890 1.0471 1.4801 0.4490 0.6226 0.7769 0.9119 1.3050 0.4452 0.6776 0.8097 0.9573 1.3843 0.4686 0.6194 0.7896 0.9775 1.3979 0.2789 0.4154 0.5355 0.6588 0.8840
y, [010]
NP–Pt
x, [100]
movement of atoms and further a lower modulus of NP PtCo x As for the strength, NP Pt3 Co is maximum and other alloys are relatively close to each other. Compared with NP PtCo and NP PtCo3 , the mechanical proper ties of Pt3 Co seem to be more stable due to its higher modulus and strength. Because the bond lengths of Pt–Pt and Pt–Co are larger than that of Co–Co, the internal pressure of the cluster with cobalt atoms in the center and platinum atoms in the surface is relieved and the corre sponding structure is more stable in the clusters [52,53]. The surface energy of platinum atoms is lower than that of cobalt atoms and the cohesive energy of cobalt is higher than that of platinum [50,51]. The total system energy tends to be minimized if atoms with lower surface energy and higher cohesive energy occupy the structural surface [54]. As depicted in Fig. 1 (a) and (b), the lattice of Pt3 Co can be viewed as the
Fig. 9. Fitting of Young’s modulus E with relative density ρ (a) by exponential relation in logarithmic scale; (b) by linear relation in isometric scale; (c) by Eq. (3) in isometric scale.
structure of cobalt atoms surrounded by platinum atoms while the lat tice of PtCo3 is the exact opposite. As a result, the structure of Pt3 Co tend to be more stable compared with PtCo3 . In the meantime, there are more Pt–Pt or Pt–Co bonds in the lattice of Pt3 Co and the total interaction between atoms in ordered Pt3 Co are higher than that of PtCo and PtCo3 , due to the higher binding energy of Co–Co (Pt–Co) compared with Pt–Pt. Furthermore, the spatial utilization of Pt3 Co, PtCo3 and PtCo unit cell, shown in Fig. 1(a)–(c), are 80.0%, 69.1%, and 67.77%, respectively. For a certain crystal lattice, the structure with higher spatial utilization 8
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the mechanical behaviors and deformation mechanism of nanoporous Pt–Co alloys under uniaxial tension. The strategy of making nanoporous alloys offers a new design strategy for more stable catalysts, promoting the commercial application of fuel cells. Furthermore, relevant experi mental researches on the mechanical stability and catalytic activity of nanoporous alloys may be of great interest and will be conducted in our future work. 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. Acknowledgments We wish to acknowledge the financial support from the National Natural Science Foundation of China (Grant Nos. 11102140 and 51575404). References [1] Y. Ding, Z. Zhang, Nanoporous Metals for Advanced Energy Technologies, Springer, Berlin, 2016. [2] A. Wittstock, V. Zielasek, J. Biener, C.M. Friend, M. B€ aumer, Nanoporous gold catalysts for selective gas–phase oxidative coupling of methanol at low temperature, Science 327 (2010) 319–322. [3] L.Y. Chen, T. Fujita, Y. Ding, M.W. Chen, A Three–Dimensional gold–decorated nanoporous copper core–shell composite for electrocatalysis and nonenzymatic biosensing, Adv. Funct. Mater. 20 (2010) 2279–2285. [4] C. Wu, H. Sun, Y. Li, X. Liu, X. Du, X. Wang, P. Xu, Biosensor based on glucose oxidase–nanoporous gold co–catalysis for glucose detection, Biosens. Bioelectron. 66 (2015) 350–355. [5] A. Quintana, J. Zhang, E. Isarain–Ch� avez, E. Men�endez, R. Cuadrado, R. Robles, Ma D. Bar� o, M. Guerrero, S. Pan�e, B.J. Nelson, C.M. Müller, P. Ordej� on, J. Nogu� es, E. Pellicer, J. Sort, Voltage–induced coercivity reduction in nanoporous alloy films: a boost toward energy–efficient magnetic actuation, Adv. Funct. Mater. 27 (2017) 1701904. [6] M. Heiden, S. Huang, E. Nauman, D. Johnson, L. Stanciu, Nanoporous metals for biodegradable implants: initial bone mesenchymal stem cell adhesion and degradation behavior, J. Biomed. Mater. Res. A 104A (2016) 1747–1758. [7] H.J. Qiu, H.T. Xu, L. Liu, Y. Wang, Correlation of the structure and applications of dealloyed nanoporous metals in catalysis and energy conversion/storage, Nanoscale 7 (2015) 386–400. [8] N. Badwe, X. Chen, K. Sieradzki, Mechanical properties of nanoporous gold in tension, Acta Mater. 129 (2017) 251–258. [9] H.J. Jin, L. Kurmanaeva, J. Schmauch, H. R€ osner, Y. Ivanisenko, J. Weissmüller, Deforming nanoporous metal: role of lattice coherency, Acta Mater. 57 (2009) 2665–2672. [10] Y.C. Kim, E.J. Gwak, S.M. Ahn, J.I. Jiang, H.N. Han, J.Y. Kim, Indentation size effect in nanoporous gold, Acta Mater. 138 (2017) 52–60. [11] E.J. Gwak, J.Y. Kim, Weakened flexural strength of nanocrystalline nanoporous gold by grain refinement, Nano Lett. 16 (2016) 2497. [12] N. Mameka, K. Wang, J. Markmann, E.T. Lilleodden, J. Weissmüller, Nanoporous gold—testing macro–scale samples to probe small–scale mechanical behavior, Mater. Res. Lett. 4 (2016) 27–36. [13] X.Q. Feng, R. Xia, X. Li, B. Li, Surface effects on the elastic modulus of nanoporous materials, Appl. Phys. Lett. 94 (2009), 011916. [14] R. Xia, X. Li, Q. Qin, J. Liu, X.Q. Feng, Surface effects on the mechanical properties of nanoporous materials, Nanotechnology 22 (2011) 265714. [15] R. Xia, X.Q. Feng, G.F. Wang, Effective elastic properties of nanoporous materials with hierarchical structure, Acta Mater. 59 (2011) 6801–6808. [16] X.S. Wang, R. Xia, Size–dependent effective modulus of hierarchical nanoporous foams, Europhys. Lett. 92 (2010) 16004. [17] N. Huber, R.N. Viswanath, N. Mameka, N. Mameka, J. Markmann, J. Weißmüller, Scaling laws of nanoporous metals under uniaxial compression, Acta Mater. 67 (2014) 252–265. [18] B. Roschning, N. Huber, Scaling laws of nanoporous gold under uniaxial compression: effects of structural disorder on the solid fraction, elastic Poisson’s ratio, Young’s modulus and yield strength, J. Mech. Phys. Solids 92 (2016) 55–71. [19] X.Y. Sun, G.K. Xu, X. Li, X.Q. Feng, H. Gao, Mechanical properties and scaling laws of nanoporous gold, J. Appl. Phys. 113 (2013), 023505. [20] Y. Xian, J. Li, R. Wu, R. Xia, Softening of nanocrystalline nanoporous platinum: a molecular dynamics simulation, Comput. Mater. Sci. 143 (2018) 163–169. [21] J. Li, Y. Xian, H. Zhou, R. Wu, G. Hu, R. Xia, Mechanical properties of nanocrystalline nanoporous gold complicated by variation of grain and ligament: a molecular dynamics simulation, Sci. China Technol. Sci. 61 (2018) 1353–1363.
Fig. 10. (a) Yield stress σ y , and (b) ultimate strength σ u of NP–Pt and three ordered nanoporous Pt–Co alloys as a function of the relative density in iso metric scale.
might be more stable due to the relatively difficult movement between atoms. In a word, the excellent performance of NP Pt3 Co may relate to the unique atom arrangements of the ordered Pt3 Co beneficial for me chanical behavior enhancement and strong stabilization against applied load. 4. Conclusion In summary, nanoporous Pt–Co alloys with 3D stochastic bi–continuous structures and controllable compositions were created by adopting a phase field method named spinodal decomposition. The tensile deformation behaviors of three ordered nanoporous Pt–Co alloys have been investigated using MD simulations. Similar to nanoporous gold, the axial yielding of ligaments is the principal deformation mechanism of ordered nanoporous Pt–Co alloys and it fails through plastic necking and rupture of those ligaments in the loading direction. The Young’s modulus shows a power relation with the relative density of ordered nanoporous Pt–Co alloys while the yield stress and the ultimate strength display linear relations. It is observed that the mechanical properties of nanoporous Pt–Co alloys are significantly enhanced compared with NP–Pt. Due to the special atomic arrangements between Co atoms and Pt atoms, NP Pt3 Co shows the superior mechanical properties among three ordered nanoporous alloys. The present results shall provide atomistic insights for understanding 9
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[22] J. Li, Y. Xian, H. Zhou, R. Wu, G. Hu, R. Xia, Microstructure–sensitive mechanical properties of nanoporous gold: a molecular dynamics study, Model. Simul. Mater. Sci. Eng. 26 (2018), 075003. [23] J. Zhu, E. Seker, H. Bart–Smith, M.R. Begley, R.G. Kelly, G. Zangari, W.K. Lye, M. L. Reed, Mitigation of tensile failure in released nanoporous metal microstructures via thermal treatment, Appl. Phys. Lett. 89 (2006) 133104. [24] Y. Wang, Y.Z. Wang, C. Zhang, T.Y. Kou, Z.H. Zhang, Tuning the ligament/channel size of nanoporous copper by temperature control, CrystEngComm 14 (2012) 8352–8356. [25] I.C. Cheng, A.M. Hodge, Morphology, oxidation, and mechanical behavior of nanoporous Cu foams, Adv. Eng. Mater. 14 (2012) 219–226. [26] K. Wang, J. Weissmüller, Composites of nanoporous gold and polymer, Adv. Mater. 25 (2013) 1280–1284. [27] E. Griffiths, S. Bargmann, B.D. Reddy, Elastic behavior at the nanoscale of innovative composites of nanoporous gold and polymer, Extreme Mech. Lett. 17 (2017) 16–23. [28] J. Li, C. Tian, B. Lu, Y. Xian, R. Wu, G. Hu, R. Xia, Deformation behavior of nanoporous gold based composite in compression: a finite element analysis, Comp. Struct. 211 (2019) 229–235. [29] Y.O. Yildiz, M. Kirca, Compression and shear behavior of ultrathin coated nanoporous gold: a molecular dynamics study, J. Appl. Phys. 124 (2018) 184301. [30] M. Oezaslan, F. Hasch�e, P. Strasser, PtCu3, PtCu and Pt3Cu alloy nanoparticle electrocatalysts for oxygen reduction reaction in alkaline and acidic media, J. Electrochem. Soc. 159 (2012) B444–B454. [31] X.X. Wang, S. Hwang, Y.T. Pan, K. Chen, Y. He, S. Karakalos, H. Zhang, J. S. Spendelow, D. Su, G. Wu, Ordered Pt3Co intermetallic nanoparticles derived from metal–organic frameworks for oxygen reduction, Nano Lett. 18 (2018) 4163–4171. [32] M. Luo, Y. Sun, L. Wang, S. Guo, Tuning multimetallic ordered intermetallic nanocrystals for efficient energy electrocatalysis, Adv. Energy Mater. 7 (2017) 1602073. [33] Q. Zhou, C. Xu, Stratified nanoporous PtTi alloys for hydrolysis of ammonia borane, J. Colloid Interface Sci. 496 (2017) 235–242. [34] Q. Zhou, L. Qi, H. Yang, C. Xu, Hierarchical nanoporous platinum–copper alloy nanoflowers as highly active catalysts for the hydrolytic dehydrogenation of ammonia borane, J. Colloid Interface Sci. 513 (2018) 258–265. [35] L. Liu, E. Pippel, R. Scholz, U. Gosele, Nanoporous Pt–Co alloy nanowires: fabrication, characterization, and electrocatalytic properties, Nano Lett. 9 (2009) 4352–4358. [36] E. Antolini, J.R.C. Salgado, E.R. Gonzalez, The stability of Pt–M (M¼ first row transition metal) alloy catalysts and its effect on the activity in low temperature fuel cells: a literature review and tests on a Pt–Co catalyst, J. Power Sources 160 (2006) 957–968.
[37] C. Liu, P.S. Branicio, Efficient generation of non–cubic stochastic periodic bicontinuous nanoporous structures, Comput. Mater. Sci. 169 (2019) 109101. [38] J.W. Cahn, J.E. Hilliard, Free energy of a nonuniform system. I. interfacial free energy, J. Chem. Phys. 28 (1958) 258–267. [39] S. Plimpton, P. Crozier, A. Thompson, LAMMPS–large–scale atomic/molecular massively parallel simulator, Sandia Natl. Lab. 18 (2007). [40] S. Foiles, M. Baskes, M.S. Daw, Embedded–atom–method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys, Phys. Rev. B 33 (1986) 7983–7991. [41] R. Passianot, E.J. Savino, Embedded–atom–method interatomic potentials for hcp metals, Phys. Rev. B 45 (1992) 12704. [42] X.W. Zhou, R.A. Johnson, H.N.G. Wadley, Misfit–energy–increasing dislocations in vapor–deposited CoFe/NiFe multilayers, Phys. Rev. B 69 (2004) 144113. [43] A.C. To, J. Tao, M. Kirca, L. Schalk, Ligament and joint sizes govern softening in nanoporous aluminum, Appl. Phys. Lett. 98 (2011), 051903. [44] A. Stukowski, Visualization and analysis of atomistic simulation data with OVITO–the open visualization tool, Model. Simul. Mater. Sci. Eng. 18 (2009), 015012. [45] H. Tsuzuki, P.S. Branicio, J.P. Rino, Structural characterization of deformed crystals by analysis of common atomic neighborhood, Comput. Phys. Commun. 177 (2007) 518–523. [46] C. Zhu, X. Liu, X. Yu, N. Zhao, J. Liu, J. Xu, A small–angle X–ray scattering study and molecular dynamics simulation of microvoid evolution during the tensile deformation of carbon fibers, Carbon 50 (2012) 235–243. [47] F. Sansoz, Atomistic processes controlling flow stress scaling during compression of nanoscale face–centered–cubic crystals, Acta Mater. 59 (2011) 3364–3372. [48] L.J. Gibson, M.F. Ashby, Cellular Solids: Structure and Properties 2nd, Cambridge University Press, Cambridge, 1997. [49] A.P. Roberts, E.J. Garboczi, Elastic properties of model random three–dimensional open–cell solids, J. Mech. Phys. Solids 50 (2002) 33–55. [50] Q.L. Lu, L.Z. Zhu, L. Ma, G.H. Wang, Magnetic properties of Co/Cu and Co/Pt bimetallic clusters, Chem. Phys. Lett. 407 (2005) 176–179. [51] Q.L. Lu, L.Z. Zhu, L. Ma, G.H. Wang, Structural transition and magnetic properties of ComPtn (m þ n ¼ 38) clusters, Phys. Lett. A 350 (2006) 258–262. [52] S. Darby, T.V. Mortimer–Jones, R.L. Johnston, C. Roberts, Theoretical study of Cu–Au nanoalloy clusters using a genetic algorithm, J. Chem. Phys. 116 (2002) 1536–1550. [53] G. Rossi, A. Rapallo, C. Mottet, A. Fortunelli, F. Baletto, R. Ferrando, Magic polyicosahedral core–shell clusters, Phys. Rev. Lett. 93 (2004) 105503. [54] K. Yuga, A. Seko, A. Kuwabara, F. Oba, I. Tanaka, First–principles study of bulk ordering and surface segregation in Pt–Rh binary alloys, Phys. Rev. B 74 (2006) 174202.
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