Stress-assisted structural phase transformation enhances ductility in

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Stress-assisted structural phase transformation enhances ductility in Mo/Cu bicontinuous intertwined composites Lijie He, and Niaz Abdolrahim ACS Appl. Nano Mater., Just Accepted Manuscript • DOI: 10.1021/acsanm.8b02219 • Publication Date (Web): 05 Feb 2019 Downloaded from http://pubs.acs.org on February 10, 2019

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ACS Applied Nano Materials

Stress-assisted Structural Phase Transformation Enhances Ductility in Mo/Cu Bicontinuous Intertwined Composites Lijie Hea, Niaz Abdolrahim*a,b,

a

Materials Science Program, University of Rochester, Rochester, NY, USA,14627

b

Department of Mechanical Engineering, University of Rochester, Rochester, NY, USA,14627

Author Information Corresponding Authors *E-mail: [email protected]

KEYWORDS: Structural phase transformation; Bicontinuous intertwined composite; Nano structure; Ductility enhancement; Dislocation movement suppression; Nanomechanics

ABSTRACT: We use molecular dynamics simulations to demonstrate a homogenous two-step structural phase transformation in the Molybdenum (Mo) phase of a Mo/Cu bicontinuous

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intertwined composite during tensile loading. The Mo atoms first transform from a oriented body-centered cubic structure to a -oriented face-centered cubic structure via the Bain transformation. Then they further transform to a -oriented body-centered cubic via the Pitsch transformation. This homogenous transformation results in a novel stress-strain behavior with extended plastic deformation of the whole material. Stress state analysis indicates that the driving force for this structural phase transformation is the large tensile stress induced by interfaces in the bicontinuous intertwined structure. Our results suggest new strategies for improving the ductility of ultra-strong nanocomposite metals.

I. Introduction:

As technology such as in situ TEM developed quickly during the past decade 1-8, the fundamental mechanisms of plastic deformation in nanoscale materials are revealed to be substantially different from bulk materials 9-13. Dislocation mediated mechanisms are mainly limited to nucleation of single-ended dislocation/twinning sources from interfaces or free surfaces and forest dislocation dynamics are almost absent due to small volumes 14. Other mechanisms such as structural phase transformation in transformation-induced plasticity 2


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(TRIP) steels 15-17, shape memory alloys 18, 19, and pseudoelastic nanostructures 20-22 under specific conditions of high temperature, large applied stresses, or constrained geometry (e.g. one-dimensional nanowires with small cross section) have also been observed in nanoscale materials. Suppression of common plastic deformation mechanisms leads to ultrahigh mechanical strength but low ductility (low elongation before failure).

Here, we use atomistic simulations to study the activation of a novel, two step structural phase transformation of Molybdenum (Mo) from body-centered cubic (BCC) to face-centered cubic phase (FCC), and back to BCC. BCC is the stable phase for Mo at low temperature/pressure (below ~700 GPa) and transformations to FCC usually only occur under high temperature and pressure 23. In our composites, the BCC-to-FCC phase transformation arises due to the high stresses induced at interfaces between Mo and the second component, Copper (Cu), and occurs uniformly in the bicontinuous intertwined material. The resulting FCC Mo phase has much higher energy than BCC Mo and is metastable 24, driving a second phase transformation from FCC back to BCC. The final BCC Mo has a different crystallographic orientation with respect to the tensile axis than in the initial composite structure. This series of

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structural phase transitions imparts a substantial improvement in ductility to the composite while retaining its ultra-high strength. As a result, these bicontinuous intertwined materials are excellent candidate for applications that require better strength and durability, such as actuators 25, 26, electrodes 27 and sensors 26.

Room temperature BCC to FCC phase transformations are very rare in Mo and only occur under high applied stresses. Wang et al. 23 first reported a 2-step BCC -> FCC -> BCC structural phase transformation of single crystal Mo via the Nishiyama-Wassermann (N-W) 28 and Kurdjumov-Sachs (K-S) path 29. The phase transformation occurred only locally at the tip of a crack due to extremely large stresses induced at the front of the crack tip. Lu et al. 30 also reported a BCC->FCC structural phase transformation of via the Bain path 31 during tensile loading of Mo nanowires. However, in their case the phase transformation proceeded by dislocation nucleation and annihilation at free surfaces along the nanowires and only occurred at locations close to fracture points, implying that the transformation is highly localized. By contrast, we report uniform BCC -> FCC -> BCC structural transformation throughout the entire volume of our nanocomposite model.

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II. Methods:

The morphological properties for the nano-sized Cu/Mo bicontinuous material studied in this research is similar to the product of spinodal decomposition. Cu and Mo are separated into two continuous phases (no isolated clusters of Cu in Mo and vice versa) that are intertwined with each other. The Monte Carlo (MC) method has been commonly used for constructing models of porous structures from a template generated by spinodal decomposition 32, 33 and is adopted in this study. We performed a MC simulation on a 36nm×36nm×36nm cubic structure with full periodic boundary conditions. The initial configuration and simulation time were carefully controlled to ensure that the resulting structure has a volume ratio of ~50%:50% between phases as well as an average feature size of 2.6nm for both phases. The details of the MC method can be found in our previous paper 33. The resulting morphology possesses similarities to the structures obtained by physical vapor deposition by Cui et al. 34. A surface mesh of the resulting structure is shown in Supplementary Fig. S1. The next step is to populate the MC model with lattices of Cu and Mo with specific interface relationships and lattice orientations. As observed by Cui et al. 34, in Mo/Cu

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nanocomposites, Cu either takes the FCC structure and adopts a Kurdjumov–Sachs (K- S) orientation relation with respect to BCC Mo, or takes the BCC structure and forms coherent interfaces with Mo. Structural phase transformations are sensitive to the loading direction, e.g. the structural phase transformation reported here occurs when Mo is loaded along the [001] direction 23, 30, but not along [111] direction 35. With both the interface structure and loading direction taken into consideration, we constructed the four different structures listed in Table 1:

Table 1. Simulation setup

Setup

1)

Phase 1

BCC Mo

Phase 2

FCC Cu

Orientation relation between Cu and Mo

K-S

Crystal

Crystal

Crystal

Phase

Orientation of

Orientation of

Orientation of

transform

Mo along z

Mo along x

Mo along y

ation

directiona

directiona

directiona

Mo

[001]

[100]

[010]

Yes

[110]

[112]

[111]

No

[001]

[100]

[010]

Yes

[110]

[112]

[111]

No

in

(110)𝑀𝑜//(111)𝐶𝑢 𝑎𝑛𝑑[111]𝑀𝑜//[110]𝐶𝑢 2)

BCC Mo

FCC Cu

K-S (110)𝑀𝑜//(111)𝐶𝑢 𝑎𝑛𝑑[111]𝑀𝑜//[110]𝐶𝑢

3)

BCC Mo

BCC Cu

Coherent (001)𝑀𝑜//(001)𝐶𝑢 𝑎𝑛𝑑[100]𝑀𝑜//[100]𝐶𝑢

4)

BCC Mo

BCC Cu

Coherent (001)𝑀𝑜//(001)𝐶𝑢 𝑎𝑛𝑑[100]𝑀𝑜//[100]𝐶𝑢

a

An illustration of the x,y,z direction is shown as the tripod in Fig. 2 A), z is the loading direction.

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1) K-S interface, loaded along [001] direction of Mo; 2) K-S interface, loaded on [110] direction of Mo; 3) coherent interface, loaded on [001] direction of Mo; 4) coherent interface, loaded on [110] direction of Mo. Details on how phases were filled with crystals of set orientation may also be found in our previous paper 33. Because we used the same MC template to construct all of these models, the morphology of the interpenetrating phases is identical in all of them. To investigate the mechanical response of the structures under tensile loading, we perform molecular dynamics (MD) simulations using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) code 36. The embedded atom method potential developed by Gong et al. 37 was applied in our CuMo models. The simulation is divided into three stages. First, the energy of the structure is minimized using the conjugate gradient method with a maximum force tolerance of 10-27 eV/Angstrom. Then the structure is further equilibrated at room temperature for 100 picoseconds (ps) in a Nose-Hoover isothermal-isobaric NPT ensemble. Finally, uniaxial tensile loading was applied to the structure in strain increments of 0.1% at each loading step (1 femtosecond) and followed by relaxation for 1 ps at room temperature using the same NPT ensemble. This


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process corresponds to a constant engineering strain rate of 109/s. It is worth mentioning that albeit strain rate in MD simulation is much higher than that in real experiment, it generally yields accurate result when describing deformation process where thermal activated events (e.g. diffusion) is minimum. Specifically, MD simulations were proven to be able to capture structural phase transformations in Mo 23. Atomic stresses are calculated based on the virial theorem 14. Macroscopic stress is then obtained by averaging the sum of the atomic stresses over the last 100 time steps of the relaxation period after each loading step.

During loading, setup 1) and 3), in which Mo has a [001] BCC crystal orientation along the loading direction, exhibit similar structural phase transformation in Mo, while the other two setups show no structural transformation at all. This suggests that structural phase transformations in Mo are closely related to the Mo crystal orientation with respect to the loading direction. Recognizing that the K-S relationship is the most commonly observed interfacial relationship in Cu/Mo nanocomposites 34, the results reported in this paper will be from setup


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Figure 1 A). Stress strain curve of the Mo/Cu bicontinuous intertwined structure with KS interface relationship loaded along [001]𝑀𝑜. B). Structure analysis of Mo and C). Cu.

1), where the structure with a K-S interface is loaded along the [001] direction of Mo. Readers can refer to the supplementary materials for the results of other settings.

III. Results and Discussion

The two-step phase transformation we observed occurs uniformly in the Mo phase. It includes a [001] BCC Mo (hereafter defined as BCC1 Mo) -> [001] FCC Mo (hereafter defined as FCC Mo) transformation via the Bain path 31 and a FCC Mo -> [101] BCC Mo (hereafter defined as BCC2 Mo) transformation via the Pitsch path 38. This mechanism leads to large homogenous deformation across the whole structure and suppression of stress localization, thus achieving large elongations before reaching the ultimate stress of the composite. Our observation of large homogenous deformation


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are in agreement with the nanoindentation results of Cui et al. 34, who also observed large deformation and no shear band formation in similar structures.

Fig. 1 A) shows the stress-strain curve for setup 1). We have used adaptive common neighbor analysis 39 and polyhedral template matching 40 to characterize the structure type as well as local lattice orientation of atoms. Data from both analyses is further adopted to calculate the structure type fraction for Mo defined as the number of Mo atoms with a specific structure type (FCC, HCP, BCC1, BCC2 and Others) divided by the total number of all Mo atoms, as shown in Fig. 1 B). Similarly, the structure type fraction for Cu is shown in Fig. 1 C). Mo atoms whose local structure is not FCC, BCC, or hexagonal close packed (HCP) were designated as “others.” They include Cu-Mo interfacial atoms, interfacial atoms between different phases of Mo, and dislocation cores 41. In Cu, atoms termed “others” are Cu-Mo interfacial atoms while HCP atoms denote dislocation cores. These atomic structure fractions help us to understand the dynamic of the structural phase transformation quantitatively. For example, at 0% strain, 87% of the Mo atoms are BCC1 and the rest are “others” located at the interface. The


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mechanical behavior of the structure under loading can then be divided into four distinctive regimes:

Regime i. At low strain ( FCC Mo and FCC Mo -> BCC2 Mo), a small cell of the structure containing 35 Mo atoms is studied at 5%, 30% and 60% strain, as shown in Fig. 2. Close examination reveals the following transformation mechanisms:

BCC1 Mo to FCC Mo via the Bain path. Local lattice orientation analysis suggests the following crystallographic orientation relationship during the first structural phase transformation: (001)𝐹𝐶𝐶//(001)𝐵𝐶𝐶1 and [110]𝐹𝐶𝐶//[100]𝐵𝐶𝐶1 , as shown in Fig. 2 B). This implies that the first transformation happened via the Bain path 31, 42. A schematic of this transformation is shown in Fig. 3 A), where yellow lines indicate four adjacent BCC1 unit cells, and pink lines and planes indicate a facecentered tetragonal (FCT) unit cell. During tensile loading, the BCC1 lattice is


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continuously strained: [001]𝐵𝐶𝐶1 is stretched while [010]𝐵𝐶𝐶1 and [100]𝐵𝐶𝐶1 are compressed. Once the lattice constant on x, y and z direction reaches the ratio 𝑐𝑥 : 𝑐𝑦 : 𝑐𝑧 = 1 :1 :√2, which corresponds to a 20% stretching on [001]𝐵𝐶𝐶1, as well as 12% compression on [010]𝐵𝐶𝐶1 and [100]𝐵𝐶𝐶1, the FCT unit cell transforms into FCC unit cell and the BCC1 -> FCC transformation is completed. [001]𝐵𝐶𝐶1 becomes [001]𝐹𝐶𝐶, [010]𝐵𝐶𝐶1 becomes [110]𝐹𝐶𝐶 and [100]𝐵𝐶𝐶1, becomes [110]𝐹𝐶𝐶,. Similar transformations via the Bain path has been observed in Mo nanowires during tensile loading by Lu et al. 30.


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Figure 3. Schematic of the A) Bain transformation and B) Pitsch transformation. The Bain transformation consists of stretching along the [001]𝐵𝐶𝐶1 direction as well as compression along [010]𝐵𝐶𝐶1 and [100]𝐵𝐶𝐶1. The Pitsch transformation consists of a stretching δ along [001]𝐹𝐶𝐶 as well as a rotation α of the atoms along [110]𝐹𝐶𝐶//[121]𝐵𝐶𝐶2 around [001]𝐹𝐶𝐶// [101]𝐵𝐶𝐶2. The unit cell edges are shown as dotted red line and the lattice constants are 𝑎𝐵𝐶𝐶1 = 𝑎𝐵𝐶𝐶2 = 0.3147𝑛𝑚, 𝑎𝐹𝐶𝐶 = 0.4030𝑛𝑚 43.


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FCC Mo to BCC2 Mo via the Pitsch path. As shown in Fig. 2 B), local lattice orientation analysis suggests that the crystallographic orientation relationship for the second phase transformation is: (001)𝐹𝐶𝐶//(101)𝐵𝐶𝐶2, [110]𝐹𝐶𝐶//[121]𝐵𝐶𝐶2 and [110]𝐹𝐶𝐶//[111]𝐵𝐶𝐶2, implying that the second transformation occurs via the Pitsch path [35, 39]. A schematic of this transformation is shown in Fig. 3 B). As illustrated, there is no significant change along the [110]𝐹𝐶𝐶//[111]𝐵𝐶𝐶2direction (no rotation and an interatomic distance change of

Stress-assisted structural phase transformation enhances ductility in

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