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Solid-solid phase transitions in Fe-nanowires Solid-solid phase transitions in Fe-nanowires Presentation Transcript

  • Solid-solid phase transitions in Fe-nanowires L. Sandoval and H. M. Urbassek Fachbereich Physik und Forschungszentrum OPTIMAS Universit¨t Kaiserslautern a Erwin-Schr¨dinger-Straße, D-67663 Kaiserslautern o Germany
  • Abstract In this work we investigate the solid-solid phase transition from a bcc to a close-packed crystal structure in cylindrical iron nanowires. Using classical molecular dynamics, we study the martensite (and austenite) transition and discuss its dependence on the nanowire diameter, the heating/cooling rate and an applied axial stress. The interatomic potential employed has been shown to be capable of describing the martensite-austenite phase transition in iron [1], which reproduces qualitatively the bcc-fcc phase transition [2-4]. Additionally we study the stress vs strain curves for different temperatures and show that for a range of temperatures it is possible to induce a solid-solid phase transition by axial strain before the elasticity is lost; these transition temperatures are below the bulk transition temperature. The two phases have different (non-linear) elastic behavior: the bcc phase softens, while the close-packed phase stiffens with temperature. Our results [4-7] are of predictive nature and may bear consequences on the design of nanoelectromechanical systems, since nanowires with novel properties might be included as interconnectors, sensors or actuators.
  • Methodology and Results Phase transformation induced by heating/cooling: The nanowires have a cylindrical shape with diameters D in the range of 2.5 nm to 4 nm. By using periodic boundary conditions along the cylinder axis, we mimic infinitely long wires. The total number of atoms in our simulation cell thus varies between 11,000 and 40,000 atoms. The nanowires have their cylinder axis oriented along the 111 orientation. Temperature is controlled via a Nose-Hoover thermostat. We also control the stress along the nanowire axis using a barostat. The nanowires were prepared in bcc crystal structure at 0 K. After 50 ps of equilibration time, the temperature was increased at a constant rate Q up to 1000 K. Cooling proceeds by the same rate until we reach 0 K. We study heating and cooling rates in the range of 0.5 − 4 K/ps. The simulations were performed with the LAMMPS code.
  • Methodology and Results 1400 900 (a) 1300 (b) 1200 800 1100 1000 Tc (K) Tc (K) 700 900 800 600 700 D = 2.5 nm 600 0GPa D = 3.0 nm 1GPa 500 D = 3.5 nm 500 2GPa D = 4.0 nm 3GPa 400 0 0.5 1 1.5 2 2.5 3 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Stress (GPa) 1/D (1/nm) Fig.1 bcc → fcc/hcp transformation temperature Tc vs axial stress (a) and vs the inverse of the diameter D (b). The transition temperature increases inversely proportional to the wire diameter. A tensile axial stress lowers the transition temperature, and may – above a critical stress value – inhibit the backtransformation.
  • Methodology and Results Phase transformation induced by axial strain: We focus on cylindrical nanowires with diameter D = 3 nm and 111 axial orientation in their ground-state bcc phase. The strain is established by changing the length of the simulation box. We investigate the relation between the axial (tensile) stress σ and the strain ǫ = (L − L0 )/L0 , in the elastic regime, for 5 strain rates ǫ (67, 33, 6.7, 3.3, and 1.7 × 10−5 /ps) and 7 temperature ˙ values ranging from 0 K to 600 K. The data are presented for ǫ = 6.7 × 10−5 /ps; smaller strain rates produce within our statistical ˙ error bars identical results. We chose a value of L0 /D = 5 for all simulations presented for this case; this corresponds to 9048 atoms.
  • Methodology and Results 14 14 12 0K 100K 12 (b) 200K 10 300K 400K 10 8 500K ¢c(GPa) 600K 8 Critical axial stress ¡(GPa) 6 Axial stress 6 4 2 4 0 2 0 2 4 6 8 10 12 14 00 100 200 300 400 500 600 700 800 Strain (%)-2   Temperature T (K) Fig.2 (a) Axial stress as a function of the applied strain (strain rate ǫ = ˙ 6.7 × 10−5 /ps) for various temperatures. (b) Critical axial tensile stress σc vs temperature. Cylindrical nanowires can exhibit, for a range of temperatures, a solid-solid phase transition from the bcc to a cp phase induced by axial strain.
  • Methodology and Results The elastic behavior of the wire can be quantified by fitting a non-linear Young’s modulus E as a function of the strain ǫ to the data, E (ǫ) = E0 − E1 ǫ . (1) The bcc phase softens progressively with temperature, while the cp phase stiffens. These pronounced effects have their origin in the contribution of the surface stress to the Young’s modulus.
  • Methodology and Results 80 500 0K bcc Young's modulus E ( <111 >) (GPa) 70 400K 450 fcc+hcp bulk bcc (0 K) 60 400 exp. bcc(0 K) bulk fcc (0 K) 50 350 CNA (%) 0 40 300 30 250 20 200 10 150 0 2 4 6 8 10 12 1000 100 200 300 400 500 600 Strain (%)0 £ Temperature T (K) Fig.3 (a) Common neighbor analysis (CNA) of wires strained at two tem- peratures. Circles: bcc crystal structure; squares: cp phase (fcc+hcp). (b) Young’s modulus E0 along 111 for different dominant crystal structures in the nanowire as a function of temperature. We also include the exper- imental data and the theoretical data for the fcc and the bcc crystal for our potential; these apply for bulk material at 0 K.
  • Snapshots Fig.4(a) Local structure in the wire strained at 600 K. Elastic regime in bcc phase (ǫ = 0%). Colors: local crystal structures as determined from the CNA: violet: bcc, green: fcc, cyan: hcp and red: unknown.
  • Snapshots Fig.4(b) Local structure in the wire strained at 600 K. Elastic regime in cp phase (ǫ = 4%). Colors: local crystal structures as determined from the CNA: violet: bcc, green: fcc, cyan: hcp and red: unknown.
  • Snapshots Fig.4(c) Local structure in the wire strained at 600 K. Non-elastic regime (ǫ = 10%). Colors: local crystal structures as determined from the CNA: violet: bcc, green: fcc, cyan: hcp and red: unknown.
  • Conclusions • The transition temperature increases inversely proportional to the wire diameter. A tensile axial stress lowers the transition temperature, and may – above a critical stress value – inhibit the backtransformation. • Cylindrical nanowires can exhibit, for a range of temperatures, a solid-solid phase transition from the bcc to a cp phase induced by axial strain. • These two solid phases exhibit different non-linear elastic behaviors: with increasing temperature, the bcc phase softens, while the cp phase stiffens.
  • References [1] R. Meyer and P. Entel, Martensite-austenite transition and phonon dispersion curves of Fe1−x Nix studied by molecular-dynamics simulations, Phys. Rev. B 57, 5140 (1998). [2] C. Engin, L. Sandoval and H. M. Urbassek, Characterization of Fe potentials with respect to the stability of the bcc and fcc phase, Modelling Simul. Mater. Sci. Eng. 16, 035005 (2008). [3] L. Sandoval, H. M. Urbassek and P. Entel. The Bain versus Nishiyama-Wassermann path in the martensitic transformation of Fe. New J. Phys. 11, 103027 (2009). [4] L. Sandoval, H. M. Urbassek and P. Entel. Solid-solid phase transitions and phonon softening in an embedded-atom method model for iron. Phys. Rev. B 80, 214108 (2009).
  • References [5] L. Sandoval and H. M. Urbassek. Finite-size effects in Fe-nanowire solid-solid phase transitions: a molecular dynamics approach. Nano Lett. 9, 2290 (2009). [6] L. Sandoval and H. M. Urbassek. Solid-solid phase transitions in Fe-nanowires induced by axial strain. Nanotechnology 20, 325704 (2009). [7] L. Sandoval and H. M. Urbassek. Transformation pathways in the solid-solid phase transitions of iron nanowires. Appl. Phys. Lett. 95, 191909 (2009).