Re-equilibration after quenches in athermal martensites: Conversion delays for vapor-to-liquid domain-wall phases

Shankaraiah, N.; Murthy, K. P. N.; Lookman, Turab; Shenoy, Subodh R.

doi:10.1103/physrevb.91.214108

Cited by 6 publications

(14 citation statements)

References 43 publications

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“…As the transition is approached T T 4 (<< T 0 ), n m (t) shows incubation behaviour and t m ∼ 10 3 −10 4 MCS where the golf-course edge is small 26 . For T > T 4 , the four petaled golf-course topology provides an infinite entropy barrier for conversions 26 . The temperature dependence of conversion times 21 t m (T ) and conversion success-fraction φ m for a fixed elastic stiffness A 1 and different Hamiltonian energy scales E 0 is plotted in Fig.…”

Section: Resultsmentioning

confidence: 99%

“…At t = t m , when the entropy barrier is crossed, the distribution enters into the golf-course and the occupancy moves into the negative (g L (T ) < (T ) < 0) energy funnel. In TCR, SO, and TO transitions, the final 'equilibrium' distribution (not shown) is an inverse-energy falloff in the excitation energy above the bulk Landau term,˜ ≡ − g L > 0 as in the SR case 26 ,…”

Section: B Evolution Of Strain Textures In Fourier Spacementioning

confidence: 99%

“…In the athermal martensite regime, golf-course and funnel energy landscapes that appear in Fourier space naturally in a simple 3-state strain-pseudospin clock-zero model Hamiltonian for scalar-OP (N OP = 1) squarearXiv:1710.11183v1 [cond-mat.stat-mech] 31 Oct 2017 rectangle transition are used to study the rapid and slow austenite-to-martensite conversions and re-equilibration under systematic temperature-quench MC simulations 26 . Energy landscape concepts in martensites are used in other contexts [27][28][29][30][31][32] .…”

Section: Energy Landscape Conceptsmentioning

confidence: 99%

“…We define conversion time t = t m when n m (t m ) = 0.5 or 50% 17,20,21,26 . On quenching to different temperatures, we find the conversion success-fraction 17 φ m that is the number of successful conversion pathways to martensite out of N runs .…”

Section: Strain-pseudospin Clock-zero Model Hamiltoniansmentioning

confidence: 99%

“…where d¯W (t) = dF LM F (t) is the work done by the domain walls and d¯Q(t) = T dS entr (t) is the heat release by the spins at bath temperature 26 . One can track the relative changes of d¯Q, d¯W through an effective temperature…”

Section: Textural Thermodynamics and Acceptance Fractionsmentioning

confidence: 99%

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Golf-course and funnel energy landscapes: Protein folding concepts in martensites

Shankaraiah

2017

Phys. Rev. E

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We use protein folding energy landscape concepts such as golf-course and funnel to study reequilibration in athermal martensite parameter regime of triangle-to-centered rectangle, squareto-oblique, and triangle-to-oblique transitions under systematic temperature-quench Monte Carlo simulations. On quenching below a transition temperature, the seeded high-symmetry parent-phase austenite that converts to the low-symmetry product-phase martensite, through autocatalytic twinning or elastic photocopying, has both rapid conversions and incubation-delays in the temperaturetime-transformation phase diagram. We find the rapid (incubation-delays) conversions at low (high) temperatures arises from the presence of large (small) size of golf-course edge that has funnel inside for negative energy states. In the incubating state, the strain structure factor enters into the Brillouin zone golf-course through searches for finite transitional pathways which closes off at the transition temperature with Vogel-Fulcher divergences that are insensitive to Hamiltonian energy scales and log-normal distributions, as signatures of dominant entropy barriers. The crossing of the entropy barrier is identified through energy occupancy distributions, Monte Carlo acceptance fractions, heat emission and internal work. The above ideas had previously been presented for the scalar order parameter case. Here we show similar results are also obtained for vector order parameters.

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Section: Resultsmentioning

confidence: 99%

Section: B Evolution Of Strain Textures In Fourier Spacementioning

confidence: 99%

Section: Energy Landscape Conceptsmentioning

confidence: 99%

Section: Strain-pseudospin Clock-zero Model Hamiltoniansmentioning

confidence: 99%

Section: Textural Thermodynamics and Acceptance Fractionsmentioning

confidence: 99%

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Golf-course and funnel energy landscapes: Protein folding concepts in martensites

Shankaraiah

2017

Phys. Rev. E

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Monte Carlo simulations of vector pseudospins for strains: Microstructures and martensitic conversion times

Shankaraiah

2016

Journal of Alloys and Compounds

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We present systematic temperature-quench Monte Carlo simulations on discrete-strain pseudospin model Hamiltonians to study microstructural evolutions in 2D ferroelastic transitions with twocomponent vector order parameters (NOP = 2). The zero value pseudospin is the single hightemperature phase while the low-temperature phase has Nv variants. Thus the number of nonzero values of pseudospin are triangle-to-centered rectangle (Nv = 3), square-to-oblique (Nv = 4) and triangle-to-oblique (Nv = 6). The model Hamiltonians contain a transition-specific Landau energy term, a domain wall cost or Ginzburg term, and power-law anisotropic interaction potential, induced from a strain compatibility condition. On quenching below a transition temperature, we find behaviour similar to the previously studied square-to-rectangle transition (NOP = 1, Nv = 2), showing that the rich behaviour found, is generic. Thus we find for two-component order parameters, that the same Hamiltonian can describe both athermal and isothermal martensite regimes for different material parameters. The athermal/isothermal/austenite parameter regimes and temperature-timetransformation diagrams are understood, as previously, through parametrization of effective-droplet energies. In the athermal regime, we find rapid conversions below a spinodal like temperature and austenite-martensite conversion delays above it, as in the experiment. The delays show early incubation behaviour, and at the transition to austenite the delay times have Vogel-Fulcher divergences and are insensitive to Hamiltonian energy scales, suggesting that entropy barriers are dominant.

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Dynamical scaling for underdamped strain order parameters quenched below first-order phase transitions

et al. 2016

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In the conceptual framework of phase ordering after temperature quenches below transition, we consider the underdamped Bales-Gooding-type 'momentum conserving' dynamics of a 2D martensitic structural transition from a square-to-rectangle unit cell. The one-component or NOP = 1 order parameter is one of the physical strains, and the Landau free energy has a triple well, describing a first-order transition. We numerically study the evolution of the strain-strain correlation, and find that it exhibits dynamical scaling, with a coarsening length L(t) ∼ t α . We find at intermediate and long times that the coarsening exponent sequentially takes on respective values close to α = 2/3 and α = 1/2. For deep quenches, the coarsening can be arrested at long times, with α 0. These exponents are also found in 3D. To understand such behaviour, we insert a dynamical-scaling ansatz into the correlation function dynamics to give, at a dominant scaled separation, a nonlinear kinetics of the curvature g(t) ≡ 1/L(t). The curvature solutions have time windows of power-law decays g ∼ 1/t α , with exponent values α matching simulations, and manifestly independent of spatial dimension. Applying this curvature-kinetics method to mass-conserving Cahn-Hilliard dynamics for a double-well Landau potential in a scalar NOP = 1 order parameter yields exponents α = 1/4 and 1/3 for intermediate and long times. For vector order parameters with NOP ≥ 2, the exponents are α = 1/4 only, consistent with previous work. The curvature kinetics method could be useful in extracting coarsening exponents for other phase-ordering dynamics.

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Re-equilibration after quenches in athermal martensites: Conversion delays for vapor-to-liquid domain-wall phases

Cited by 6 publications

References 43 publications

Golf-course and funnel energy landscapes: Protein folding concepts in martensites

Golf-course and funnel energy landscapes: Protein folding concepts in martensites

Monte Carlo simulations of vector pseudospins for strains: Microstructures and martensitic conversion times

Dynamical scaling for underdamped strain order parameters quenched below first-order phase transitions

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