Deformation Behavior of Pure Titanium With a Rare HCP/FCC Boundary: An Atomistic Study

The compressive and tensile behaviors in a Ti nanopillar with a biphasic hexagonal close-packed (HCP) /face-centered cubic (FCC) phase boundary are theoretically researched using classic molecular dynamic simulation. The results indicate that the HCP/FCC interface and free surface of the nanopillar are the sources of dislocation nucleation. The plastic deformation is mainly concentrated in the metastable FCC phase of the biphasic nanopillar. Under compressive loading, a reverse phase transformation of FCC to the HCP phase is induced by the dislocation glide of multiple Shockley partial dislocations 1 6 <121> under compressive loading. However, for tensile loading a large number


Introduction
Ti and its alloys are used in a wide variety of engineering sectors, including aerospace, automotive, scientific instrumentation, chemical engineering and bioengineering due to their high strength and toughness, excellent resistance to fatigue and corrosion, low thermal conductivity, high temperature performance and biocompatibility 1 . Pure Ti and its majority alloys exhibit a hexagonal close-packed (HCP) crystal structure (α-phase) at room temperature and a body-centered cubic structure (β-phase) above the transus temperature (>882 ± 2°C) 2 . Hydrostatic pressure, shock loading or high-pressure torsion processing can induce transformation from the HCP α-phase to hexagonal ω-phase in α-Ti 3-6 . A transformation from the ω-phase to the orthorhombic γ-phase was observed in Ti under an external pressure of 116 GPa 7 .
In addition to these typical structures, the possible occurrence of a phase with a face-centered cubic (FCC) crystal structure has been widely observed in Ti and its alloys, which is phase that does not exist in the conventional pressure-temperature phase diagrams of Ti. Experimental observations showed that the presence of the FCC phase was associated with thin films, interfaces, powders, high levels of plastic deformation, and heat-treated Ti alloys. Recent work shows that the small FCC precipitates formed in freestanding thin foils during in situ transmission electron microscope (TEM) heating 8 . Experimental results indicate that the stability of FCC Ti in thin films is related to the film thickness, surface orientation, and temperature [9][10][11][12][13][14] . The HCP to FCC phase transformation in Ti is dominated by the high density of dislocations and twins introduced by ball milling but not stacking faults 15 . Another experiment observed small amounts of FCC Ti after ball milling Ti-Al powders. The transformation was induced thermally by the energy provided from the ball milling process 16 . The formation of FCC Ti in heat-treated Ti-6Al-4V alloy caused by adding Zr, which can decrease the basal stacking fault energy 17 . The tress-induced HCP to FCC phase transformation was attributed to the gliding of Shockley partial dislocations 18 . First principles calculations and Gibbs free energy calculation demonstrated the possible occurrence of an FCC phase in pure Ti [19][20][21] . Gibbs free energy calculations showed that the Gibbs free energy decreases with the shape factor and increases with decreasing particle size 18 . Therefore, HCP to FCC phase transformation not only exists in bulk material but also occurs on the nanometer scale. This prediction is consistent with the experimental result of the presence of FCC phase in thin films or under high strains, which has been explained by the minimization of Gibbs free energy. In our previous work 22 , the phase transformation in the {1012}<1011> twinning region was also predicted in α-Ti *e-mail: luxuefeng1979@163.com single-crystal nanopillars by molecular dynamics (MD) simulations. This rare phase transformation is induced by the dislocation glide of multiple Shockley partial dislocations under the condition of size restriction and is strongly affected by temperature and strain rate 23 .
The stress-induced HCP to FCC phase transformation was related to the gliding of Shockley partial dislocations, and the orientation relation between the two phases has been characterized as <0001> HCP ||<001> FCC , <1010> HCP ||<110> FCC and <1120> HCP ||<110> FCC 17 ,The mechanical behavior and deformation mechanism of commercial pure titanium foils and a detailed mechanism of phase transformation with orientation are proposed, to including the three stages of slip, adjustment and expansion by means of first principles calculations and experiments 24 . Different from the phase transition mechanism caused by the gliding of Shockley partial dislocations, the nucleation of FCC-Ti is accomplished via a pure-shuffle mechanism and the growth via shear-shuffle mechanis was studied by combining transmission electron microscopy and density functional theory calculations 23 . The orientation relation of FCC-Ti and HCP-Ti are 〈 0001〉 HCP || 〈 001〉 FCC and {1010} HCP || {110} FCC . Both two distinctive orientation relations between HCP phase and FCC phase were observed simultaneously in cold-rolled pure Zr 25 .
It has been widely accepted that sample size may exert a significant influence on the mechanical properties and deformation mechanism of materials on the micron-and submicron scales. In addition, the HCP to FCC phase transformation which does not exist in bulk material may occur on nanometer scale 18 . This prediction is consistent with experimental result that Ti with an FCC structure is formed under ambient conditions 10,22 . Therefore, a nanopillar model with free boundary conditions was established in this work to study the deformation behavior of pure titanium with a rare HCP/FCC boundary. Although many experimental and simulation works have demonstrated the HCP to FCC phase transformation in pure Ti at ambient temperature under extreme pressure, temperature, high levels of plastic deformation and size restriction conditions, the effect of FCC phase on the deformation mechanism of Ti is not clear thus far. By means of MD calculations, the present study is dedicated to proposing a detailed deformation behavior for Ti nanopillars containing an HCP/FCC phase boundary with the orientation relation of <0001> HCP ||<001> FCC , <1010> HCP ||<110> FCC and <1120> HCP ||<110> FCC . In addition, the stability of the FCC phase has been systematically studied.

Simulation Model and Method
The schematic of bicrystal Ti with an HCP/FCC phase boundary under compression and tension loading conditions is depicted in Figure 1. The initial configuration of the HCP/FCC bicrystal consists of approximately 201933 atoms and the dimensions of the samples in X -, Y -and Z -are 12 nm, 24 nm and 12 nm, respectively. Free boundary conditions are applied in the x, y and z directions to simulate the configuration of nanocrystal. The crystallographic orientations of the HCP phase and the FCC phase are as follows: x: <2110> HCP ||<011> FCC , y: <0110> HCP ||<011> FCC , and z: <0001> HCP ||<100> FCC , as shown in Figure 1a,b. In the HCP phase, the crystal structure has a known lattice constants of a = 0.2951 nm and c = 0.4683 nm (c/a = 1.587), whereas in the FCC phase, a = 0.4174 nm, corresponding to the minimum cohesive energy (E coh = -4.839 eV). All the MD simulations are performed with a time step of 1.0 fs. The conjugate gradient (CG) algorithm is used for energy minimization to obtain equilibrium configurations before uniaxial tensile (or compressive) loading. Then, the Nosé-Hoover thermostat 26,27 is used to further equilibrate the Ti bicrystal systems. The canonical ensemble(NVT), i.e., constant atom number(N), volume(V), and temperature(T), is applied to keep the system temperature at a constant 300 K. The relaxed bicrystal nanopilars are then loaded along the y-direction, with the atoms at the ends fixed to replicate loading grips. The strain rate during loading is 1×10 8 s -1 . The MD calculations were carried out using the large-scale parallel molecular dynamics program LAMMPS 28 and visualized with the visualization program AtomEye 29 . Common neighbor analysis(CNA) 30,31 is used to distinguish a variety of defects and the simple local lattice structure. The CNA pattern is a useful measure of the local crystal structure around an atom in the simulation system. There are five kinds of CNA patterns that LAMMPS recognizes (FCC = 1, HCP = 2, BCC = 3, icosahedral = 4, and unknown = 5). The CNA calculation can be sensitive to the specified cutoff value, and the following formula can be used to obtain a good cutoff distance: where a=2.951 is the lattice constant for the crystal structure concerned and in HCP-Ti, x = (c/a) =1.587, where 1.587 is the ideal c/a for HCP-Ti crystals.
The Finnis-Sinclair many-body potential in the MD simulation was developed by Ackland 32 , which is adopted to describe Ti-Ti ineratomic interactions in the simulation models. The Finnis-Sinclair many-body potential function can be expressed by where V is a pairwise function between neighbouring atoms i and j. ϕ is the electronic density function. r ij is the distance between atom i and one of the neighbouring atoms j. The potential has been used extensively in various MD studies, including those for Ti single crystals 33-37 and nanocrystals 38 . The transition of the FCC phase to the HCP phase in a pure Ti nanopillar was successfully observed using this potential function under applied stress 21 . In addition, the effect of temperature and strain rate on the HCP-FCC phase transition was also successfully simulated by using the potential 22 . The lowest energy state of the FCC phase exists when the lattice constant is 0.4174 nm.

Mechanical response of the bicrystal nanopillars under uniaxial compression and tension
The stress-strain curves of a Ti bicrystal nanopillar oriented in the [0110] HCP || [011] FCC direction subjected to tension and compression are shown in Figure 2. The nonapillars under different loading directions show a similar maximum stress 2.32 GPa (tagged points A and C in Figure 2a and Figure 2b, respectively). The yield stress is the maximum stress at a strain of 3.178% under compressive load. As shown in Figure 1a, after the initial yield peak, the flow stress of the bicrystal nanopillars builds up again to a second stress peak at point B. After the second stress peak, further loading causes an extensive plateau with a constant stress of approximately 1.25 GPa at strain 7%~10% (Figure 1a). However, two stress drops have occurred before the stress reaches its maximum under tensile load, at points A and B in Figure 2b, respectively. The maximum stress at a strain of 3.632% (point C in Figure 2b) is no longer the yield stress. The yield point occurs at a strain of 0.55%.

Deformation mechanism under compression and tension
To better understand the different plasticity behaviors, the substructure variation and dislocation evolution during compression are carefully studied. The dislocation evolution is illustrated in Figure 3a-d, which corresponds to point A in the stress-strain curves in Figure 2. In this and subsequent figures, the atoms are colored according to CNA. The HCP atoms are colored light blue, the FCC atoms are colored dark blue, and the defect and surface atoms are colored red. For clarity, the atoms on the perfect FCC lattice are not shown in Figure 3a-d. As shown in Figure 3a-d, under compression loading, partial dislocations nucleate and grow into dislocation lines at the interface of the HCP-phase and FCC-phase of the nanopillar where stress concentration occurs as plastic deformation progresses.
The Burgers vector was determined to be b 1 = 1 6 [112] on the basis of crystallographic analysis, which indicates that the slip system (111) [112] is activated in the FCC-phase under compression. The partial dislocation glides along  Figure 4a shows the partial dislocations and SFs found in Figure 3. The stacking sequence of {111} planes is perfect outside the partial dislocations (ABCABC…). The SFs formed in the nanopillar can be identified as shown in Figure 4b-c, and the SFs correspond to ABCBCABC…. All the partial dislocations and stacking faults are characterized in the conventional manner with a right handed Burgers circuit in Figure 4 38 . Furthermore, the partial dislocation is determined to be an edge-type Shockley partial dislocation because the dislocation is perpendicular to the Burgers vectors b 1 = 1 6 [112]. These edge partial dislocation lines are initiated and propagated along the slip plane (111) and ultimately disappeared from the nanopillar surfaces. With further compression, the deformation of the nanopillar is primarily controlled by the partial dislocations, as marked by the symbol ''⊥'' in Figure 4b. The continuous accumulation of a high density of deformation faults was caused by the dislocation glide of multiple Shockley partial dislocations, eventually leading to the phase transformation from FCC to HCP, and surface steps are left (Figure 5a). There is no plastic deformation in the HCP phase. As the strain increases further, a partial dislocation with Burgers vector b 1 = [112] on the slip plane (111) nucleates from the corner of the nanopillar at a strain level of 5.6%. The partial dislocation is blocked by the new HCP phase, as indicated by white dotted lines in Figure 6. This site becomes a new dislocation source, and the Shockley partial dislocation is nucleated here. Another partial dislocation with Burgers vector b 2 = 1 6 [ 121 ] nucleates at the free surface or corner and propagates along the (111) plane. Figure 7a-d shows snapshots of the configurations at different tension strains. In contrast to the compression process, the     nucleation location of Shockley partial dislocations increases obviously. It can be seen from Figure 2 that the tensile stress decreases at points A and B, corresponding to the partial activation of the dislocation sources at the HCP/FCC interface of the nanopillar. A significant serrated-like behavior before point C is caused in the stress-strain curve of Figure 2b due to the partial dislocation glide and dislocation reaction in the nanopillar. Atomic snapshots also confirm that a large number of Lomer-Cottrell sessile dislocations are generated before the maximum stress occurs. The HCP/FCC interface and free surfaces or corners of the nanopillars become favorable sites for dislocation nucleation. As shown in Figure 7a   i.e a Lomer -Cottrell dislocation. The dislocation reaction can be expressed as 1 1 1 121 [112] 01 1 6 This dislocation reaction can be expressed by Thompson tetrahedron notation

Transformation mechanism of FCC phase to HCP phase in FCC crystal
The transformation mechanism of the FCC phase to the HCP phase in the FCC crystal is illustrated in Figure 8. [112]. The sequence of stacking faults conforms to the atomic sequence of the HCP structure, which liea at lower right angles to the plane of the diagram. The unit cell of the HCP phase liea at the lower left angles of the diagram. The atomic plane shown in yellow in the HCP unit cell is the slip plane {0001}. The phase transition from the metastable FCC phase to the HCP phase completed by Shockley partial edge dislocation nucleation, propagation, and accumulation. The lattice parameter of 0.4174 nm calculated for the FCC phase is almost the same as that reported earlier for 5-min deposited film (0.41638 nm 39 ), mechanically milled polycrystalline Ti powder (0.4237 nm 40  The formation of a Lomer-Cottrell sessile dislocation is illustrated in Figure 9. The Lomer -Cottrell dislocation is a pure edge-type dislocation. The glide plane of the Lomer dislocation is (100), so it is sessile, i.e., the dislocation cannot glide on any of the {111} glide plane. As the plastic deformation progresses, a large number of Lomer-Cottrell sessile dislocations and stacking fault nets are generated in the FCC phase of the nanopillar (Figure 7). These defects acs as a barrier to the glide of further dislocations on the two {111} planes and are known as a Lomer-Cottrell lock. This also leads to a higher tensile stress (Figure 2), and maximum tensile stress is close to the compression stress, which could have an important effect on metal strain hardening and fracture.

Conclusions
Molecular dynamics simulations have been used to study the mechanical behavior and deformation mechanisms of Ti nanopillars containing an HCP/FCC phase boundary. The biphasic crystal yield is controlled by the nucleation and propagation of dislocations from the interface and free surface. Based on this study, the following conclusions can be drawn: (1) The yield stress under tensile loading is much lower than that under compression, but has a similar maximum stress because a large number of Lomer-Cottrell sessile dislocations are produced during tensile loading.
(2) Plastic deformation occurs in the FCC phase and Shockley partial dislocation with Burgers vector 1 6 <121> are the primary deformation mode of the nanopillars during tensile and compressive loading.
The continuous accumulation of the deformation faults caused by the Shockley partial dislocations eventually leads to the FCC to HCP phase transformation in the FCC phase under compression. However, a large number of Lomer-Cottrell sessile dislocations and stacking fault nets are formed when the partial dislocations react during tensile loading, leading to an increase in tensile stress.
(3) The FCC phase can be easily transformed into the HCP phase, which is a metastable phase in biphasic nanopillars.