R. W. Balluffi, S. Allen, and W. C. Carter, Kinetics of materials, 2005.

D. A. Young, Phase diagrams of the elements, 1991.

S. Banerjee and P. Mukhopadhyay, Phase transformations: examples from titanium and zirconium alloys, vol.12, 2010.

D. Srivastava, K. Madangopal, S. Banerjee, and S. Ranganathan, Self accomodation morphology of martensite variants in zr 2.5 wt% nb alloy, Acta metallurgica et materialia, vol.41, issue.12, pp.3445-3454, 1993.

G. Lütjering and J. C. Williams, , 2007.

D. A. Molodov, Microstructural design of advanced engineering materials, 2013.

F. Roters, P. Eisenlohr, L. Hantcherli, D. D. Tjahjanto, T. R. Bieler et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, vol.58, issue.4, pp.1152-1211, 2010.

A. Finel, Y. L. Bouar, A. Gaubert, and U. Salman, Phase field methods: Microstructures, mechanical properties and complexity, Comptes Rendus Physique, vol.11, issue.3-4, pp.245-256, 2010.

M. A. Miodownik, A review of microstructural computer models used to simulate grain growth and recrystallisation in aluminium alloys, Journal of Light Metals, vol.2, issue.3, pp.125-135, 2002.

B. Devincre and L. Kubin, Mesoscopic simulations of dislocations and plasticity, Materials Science and Engineering: A, vol.234, pp.8-14, 1997.

E. B. Tadmor and R. E. Miller, Modeling materials: continuum, atomistic and multiscale techniques, 2011.

M. S. Daw and M. I. Baskes, Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals, Physical Review B, vol.29, issue.12, p.6443, 1984.

M. Baskes, Modified embedded-atom potentials for cubic materials and impurities, Physical review B, vol.46, issue.5, p.2727, 1992.

A. F. Voter, Hyperdynamics: Accelerated molecular dynamics of infrequent events, Physical Review Letters, vol.78, issue.20, p.3908, 1997.

A. Laio and M. Parrinello, Escaping free-energy minima, Proceedings of the National Academy of Sciences, vol.99, issue.20, pp.12-562, 2002.

K. Elder, M. Katakowski, M. Haataja, and M. Grant, Modeling elasticity in crystal growth, Physical review letters, vol.88, issue.24, p.245701, 2002.

A. B. Bortz, M. H. Kalos, and J. L. Lebowitz, A new algorithm for monte carlo simulation of ising spin systems, Journal of Computational Physics, vol.17, issue.1, pp.10-18, 1975.

S. Yip, Handbook of materials modeling, 2007.

F. El-mellouhi, N. Mousseau, and L. J. Lewis, Kinetic activation-relaxation technique: An off-lattice self-learning kinetic monte carlo algorithm, Physical Review B, vol.78, issue.15, p.153202, 2008.

L. K. Béland, P. Brommer, F. El-mellouhi, J. Joly, and N. Mousseau, Kinetic activation-relaxation technique, Physical Review E, vol.84, issue.4, p.46704, 2011.

N. G. Van-kampen, Stochastic processes in physics and chemistry, vol.1, 1992.

M. Parrinello and A. Rahman, Polymorphic transitions in single crystals: A new molecular dynamics method, Journal of Applied physics, vol.52, issue.12, pp.7182-7190, 1981.

J. H. Jeans, The dynamical theory of gases, 1921.

D. Pigozzi, Appunti di meccanica razionale, 2009.

B. Diu, B. Roulet, C. Guthmann, and D. Lederer, Eléments de physique statistique, 1989.

D. Tsai, The virial theorem and stress calculation in molecular dynamics, The Journal of Chemical Physics, vol.70, issue.3, pp.1375-1382, 1979.

R. J. Swenson, Comments on virial theorems for bounded systems, American Journal of Physics, vol.51, issue.10, pp.940-942, 1983.

M. J. Louwerse and E. J. Baerends, Calculation of pressure in case of periodic boundary conditions, Chemical physics letters, vol.421, issue.1-3, pp.138-141, 2006.

R. Toral and P. Colet, Stochastic numerical methods: an introduction for students and scientists, 2014.

Z. Schuss, Theory and applications of stochastic processes: an analytical approach, vol.170, 2009.

Q. Bronchart, Y. L. Bouar, and A. Finel, New coarse-grained derivation of a phase field model for precipitation, Physical review letters, vol.100, issue.1, p.15702, 2008.

K. Ito, Proc. Imp. Acad.(Tokyo), vol.20, p.519, 1944.

R. Stratonovich, A new representation for stochastic integrals and equations, SIAM Journal on Control, vol.4, issue.2, pp.362-371, 1966.

P. Kloeden and E. Platen, Numerical methods for stochastic differential equations, Stochastic Hydrology and Hydraulics, vol.5, issue.2, pp.172-172, 1991.

L. Verlet, Computer" experiments" on classical fluids. i. thermodynamical properties of lennard-jones molecules, Physical review, vol.159, issue.1, p.98, 1967.

R. Hockney, S. Goel, and J. Eastwood, Quiet high-resolution computer models of a plasma, Journal of Computational Physics, vol.14, issue.2, pp.148-158, 1974.

A. Rollett, F. Humphreys, G. S. Rohrer, and M. Hatherly, Recrystallization and related annealing phenomena, 2004.

L. Priester, Grain boundaries: from theory to engineering, vol.172, 2012.

J. Burgers, Geometrical considerations concerning the structural irregularities to be assumed in a crystal, Proceedings of the Physical Society, vol.52, issue.1, p.23, 1940.

F. Frank, Report of the symposium on the plastic deformation of crystalline solids, pp.150-154, 1950.

B. Bilby, R. Bullough, and E. Smith, Continuous distributions of dislocations: a new application of the methods of non-riemannian geometry, Proc. R. Soc. Lond. A, vol.231, pp.263-273, 1955.

G. Gottstein and L. S. Shvindlerman, Grain boundary migration in metals: thermodynamics, kinetics, applications, 2009.

D. Gianola, S. Van-petegem, M. Legros, S. Brandstetter, H. Van-swygenhoven et al., Stress-assisted discontinuous grain growth and its effect on the deformation behavior of nanocrystalline aluminum thin films, Acta Materialia, vol.54, issue.8, pp.2253-2263, 2006.

K. Harris, V. Singh, and A. King, Grain rotation in thin films of gold, Acta materialia, vol.46, issue.8, pp.2623-2633, 1998.

J. W. Cahn and Y. Mishin, Recrystallization initiated by low-temperature grain boundary motion coupled to stress, International Journal of Materials Research, vol.100, issue.4, pp.510-515, 2009.

L. Margulies, G. Winther, and H. Poulsen, In situ measurement of grain rotation during deformation of polycrystals, Science, vol.291, issue.5512, pp.2392-2394, 2001.

P. Liu, S. Mao, L. Wang, X. Han, and Z. Zhang, Direct dynamic atomic mechanisms of strain-induced grain rotation in nanocrystalline, textured, columnar-structured thin gold films, Scripta Materialia, vol.64, issue.4, pp.343-346, 2011.

C. Rae and D. Smith, On the mechanisms of grain boundary migration, Philosophical Magazine A, vol.41, issue.4, pp.477-492, 1980.

J. W. Cahn and J. E. Taylor, A unified approach to motion of grain boundaries, relative tangential translation along grain boundaries, and grain rotation, Acta Materialia, vol.52, issue.16, pp.4887-4898, 2004.

D. Caillard, F. Mompiou, and M. Legros, Grain-boundary shear-migration coupling. ii. geometrical model for general boundaries, Acta Materialia, vol.57, issue.8, pp.2390-2402, 2009.

Y. Liu, X. Zou, and B. I. Yakobson, Dislocations and grain boundaries in two-dimensional boron nitride, ACS nano, vol.6, issue.8, pp.7053-7058, 2012.

Z. Trautt and Y. Mishin, Grain boundary migration and grain rotation studied by molecular dynamics, Acta Materialia, vol.60, issue.5, pp.2407-2424, 2012.

M. L. Falk and J. S. Langer, Dynamics of viscoplastic deformation in amorphous solids, Physical Review E, vol.57, issue.6, p.7192, 1998.

L. A. Barrales-mora, J. Brandenburg, and D. A. Molodov, Impact of grain boundary character on grain rotation, Acta Materialia, vol.80, pp.141-148, 2014.

L. A. Barrales-mora and D. A. Molodov, Capillarity-driven shrinkage of grains with tilt and mixed boundaries studied by molecular dynamics, Acta Materialia, vol.120, pp.179-188, 2016.

J. Brandenburg, L. Barrales-mora, and D. Molodov, On migration and faceting of low-angle grain boundaries: Experimental and computational study, Acta Materialia, vol.77, pp.294-309, 2014.

K. Wu and P. W. Voorhees, Phase field crystal simulations of nanocrystalline grain growth in two dimensions, Acta Materialia, vol.60, issue.1, pp.407-419, 2012.

M. Upmanyu, D. J. Srolovitz, A. Lobkovsky, J. A. Warren, and W. Carter, Simultaneous grain boundary migration and grain rotation, Acta Materialia, vol.54, issue.7, pp.1707-1719, 2006.

M. Upmanyu, R. Smith, and D. J. Srolovitz, Atomistic simulation of curvature driven grain boundary migration, Interface Science, vol.6, issue.1-2, pp.41-58, 1998.

Z. Trautt and Y. Mishin, Capillary-driven grain boundary motion and grain rotation in a tricrystal: a molecular dynamics study, Acta Materialia, vol.65, pp.19-31, 2014.

B. B. Rath, M. Winning, and J. Li, Coupling between grain growth and grain rotation, Applied physics letters, vol.90, issue.16, p.161915, 2007.

F. Mompiou, M. Legros, T. Radetic, U. Dahmen, D. Gianola et al., In situ tem observation of grain annihilation in tricrystalline aluminum films, Acta Materialia, vol.60, issue.5, pp.2209-2218, 2012.

T. Radetic, C. Ophus, D. Olmsted, M. Asta, and U. Dahmen, Mechanism and dynamics of shrinking island grains in mazed bicrystal thin films of au, Acta Materialia, vol.60, issue.20, pp.7051-7063, 2012.

S. Nosé, A molecular dynamics method for simulations in the canonical ensemble, Molecular physics, vol.52, issue.2, pp.255-268, 1984.

W. G. Hoover, Constant-pressure equations of motion, Physical Review A, vol.34, issue.3, p.2499, 1986.

J. W. Cahn, Y. Mishin, and A. Suzuki, Coupling grain boundary motion to shear deformation, Acta materialia, vol.54, issue.19, pp.4953-4975, 2006.

P. Clapp and J. Rifkin, Nucleation of a martensite in a computer, pp.1165-1169, 1981.

, Simulated martensitic transformations, MRS Online Proceedings Library Archive, vol.21, 1983.

J. P. Rifkin, J. G. Kenyon, and L. Tanner, Computer study of tweed as a precursor to a martensitic transformation of a bcc lattice, Metallurgical Transactions A, vol.19, issue.4, pp.783-787, 1988.

S. Rubini and P. Ballone, Quasiharmonic and molecular-dynamics study of the martensitic transformation in ni-al alloys, Physical Review B, vol.48, issue.1, p.99, 1993.

R. Meyer and P. Entel, Martensite-austenite transition and phonon dispersion curves of fe 1-x ni x studied by molecular-dynamics simulations, Physical Review B, vol.57, issue.9, p.5140, 1998.

P. Entel, R. Meyer, and K. Kadau, Molecular dynamics simulations of martensitic transitions, Philosophical Magazine B, vol.80, issue.2, pp.183-194, 2000.

P. Entel, R. Meyer, K. Kadau, H. Herper, and E. Hoffmann, Martensitic transformations: first-principles calculations combined with moleculardynamics simulations, The European Physical Journal B-Condensed Matter and Complex Systems, vol.5, issue.3, pp.379-388, 1998.

M. Grujicic and P. Dang, Computer simulation of martensitic transformation in fe-ni face-centered cubic alloys, Materials Science and Engineering: A, vol.201, issue.1-2, pp.194-204, 1995.

, Atomic-scale analysis of martensitic transformation in titanium alloyed with vanadium part ii: molecular dynamics simulations, Materials Science and Engineering: A, vol.205, issue.1-2, pp.153-165, 1996.

J. Morris and K. Ho, Molecular dynamic simulation of a homogeneous bcc ? hcp transition, Physical Review B, vol.63, issue.22, p.224116, 2001.

M. Zelazny, R. Richardson, and G. Ackland, Twinning hierarchy, shape memory, and superelasticity demonstrated by molecular dynamics, Physical Review B, vol.84, issue.14, p.144113, 2011.

U. Pinsook and G. Ackland, Simulation of martensitic microstructural evolution in zirconium, Physical Review B, vol.58, issue.17, p.11252, 1998.

, Atomistic simulation of shear in a martensitic twinned microstructure, Physical Review B, vol.62, issue.9, p.5427, 2000.

G. J. Ackland, A. Jones, and R. Noble-eddy, Molecular dynamics simulations of the martensitic phase transition process, Materials Science and Engineering: A, vol.481, pp.11-17, 2008.

K. R. Morrison, M. J. Cherukara, K. G. Vishnu, and A. Strachan, Role of atomic variability and mechanical constraints on the martensitic phase transformation of a model disordered shape memory alloy via molecular dynamics, Acta Materialia, vol.69, pp.30-36, 2014.

K. R. Morrison, M. J. Cherukara, H. Kim, and A. Strachan, Role of grain size on the martensitic transformation and ultra-fast superelasticity in shape memory alloys, Acta Materialia, vol.95, pp.37-43, 2015.

X. Ding, T. Suzuki, X. Ren, J. Sun, and K. Otsuka, Precursors to stressinduced martensitic transformations and associated superelasticity: Molecular dynamics simulations and an analytical theory, Physical Review B, vol.74, issue.10, p.104111, 2006.

L. Gao, X. Ding, H. Zong, T. Lookman, J. Sun et al., Diffuse scattering as an indicator for martensitic variant selection, Acta Materialia, vol.66, pp.69-78, 2014.

J. Ren, Q. Sun, L. Xiao, X. Ding, and J. Sun, Phase transformation behavior in titanium single-crystal nanopillars under [0 0 0 1] orientation tension: A molecular dynamics simulation, Computational Materials Science, vol.92, pp.8-12, 2014.

H. Zong, T. Lookman, X. Ding, C. Nisoli, D. Brown et al., The kinetics of the ? to ? phase transformation in zr, ti: Analysis of data from shock-recovered samples and atomistic simulations, Acta Materialia, vol.77, pp.191-199, 2014.

G. Ma, S. Qin, J. Shang, F. Wang, and Y. Chen, Atomistic study on the phase transformation in niti under thermal cycling, Journal of Alloys and Compounds, vol.705, pp.218-225, 2017.

Y. Li, J. Li, and B. Liu, Homogeneous shear-driven reversible ?-to-? phase transformation and superelasticity of titanium investigated by molecular dynamics simulations, Acta Materialia, vol.93, pp.105-113, 2015.

W. Ko, S. B. Maisel, B. Grabowski, J. B. Jeon, and J. Neugebauer, Atomic scale processes of phase transformations in nanocrystalline niti shape-memory alloys, Acta Materialia, vol.123, pp.90-101, 2017.

W. Ko, B. Grabowski, and J. Neugebauer, Development and application of a ni-ti interatomic potential with high predictive accuracy of the martensitic phase transition, Physical Review B, vol.92, issue.13, p.134107, 2015.

W. Petry, A. Heiming, J. Trampenau, M. Alba, C. Herzig et al., Phonon dispersion of the bcc phase of group-iv metals. i. bcc titanium, Physical Review B, vol.43, issue.13, p.10933, 1991.

M. Pitteri and G. Zanzotto, Continuum models for phase transitions and twinning in crystals, 2002.

W. Burgers, On the process of transition of the cubic-body-centered modification into the hexagonal-close-packed modification of zirconium, Physica, vol.1, issue.7-12, pp.561-586, 1934.

R. Shi and Y. Wang, Variant selection during ? precipitation in ti-6al-4v under the influence of local stress-a simulation study, Acta Materialia, vol.61, issue.16, pp.6006-6024, 2013.

T. Furuhara, H. Kawata, S. Morito, and T. Maki, Crystallography of upper bainite in fe-ni-c alloys, Materials Science and Engineering: A, vol.431, issue.1-2, pp.228-236, 2006.

K. Bhattacharya, Microstructure of martensite: why it forms and how it gives rise to the shape-memory effect, vol.2, 2003.

P. M. Larsen, S. Schmidt, and J. Schiøtz, Robust structural identification via polyhedral template matching, Modelling and Simulation in Materials Science and Engineering, vol.24, issue.5, p.55007, 2016.

J. Wu, C. Yang, C. Chen, and N. Tsou, The variant identification in molecular dynamics simulations for shape memory alloys

G. J. Ackland, Theoretical study of titanium surfaces and defects with a new many-body potential, Philosophical Magazine A, vol.66, issue.6, pp.917-932, 1992.

S. Wooding, D. Bacon, and W. Phythian, A computer simulation study of displacement cascades in ?-titanium, Philosophical Magazine A, vol.72, issue.5, pp.1261-1279, 1995.

A. Girshick, D. Pettifor, and V. Vitek, Atomistic simulation of titanium. ii. structure of 1/3 1210 screw dislocations and slip systems in titanium, Philosophical Magazine A, vol.77, issue.4, pp.999-1012, 1998.

A. Ready, A. Sutton, P. Haynes, and D. Rugg, Point, linear and planar defects in titanium, Proceedings of the 13th World Conference on Titanium, pp.1029-1034, 2016.

X. Zhou, R. Johnson, and H. Wadley, Misfit-energy-increasing dislocations in vapor-deposited cofe/nife multilayers, Physical Review B, vol.69, issue.14, p.144113, 2004.

M. Mendelev, T. Underwood, and G. Ackland, Development of an interatomic potential for the simulation of defects, plasticity, and phase transformations in titanium, The Journal of chemical physics, vol.145, issue.15, p.154102, 2016.

R. Hennig, T. Lenosky, D. Trinkle, S. Rudin, and J. Wilkins, Classical potential describes martensitic phase transformations between the ?, ?, and ? titanium phases, Physical Review B, vol.78, issue.5, p.54121, 2008.

T. Andersson, One-shot free of energy calculations for techniques crystalline materials, 2012.

S. Goedecker, Optimization and parallelization of a force field for silicon using openmp, 2002.

T. J. Lenosky, B. Sadigh, E. Alonso, V. V. Bulatov, T. D. De-la-rubia et al., Highly optimized empirical potential model of silicon, Modelling and Simulation in Materials Science and Engineering, vol.8, issue.6, p.825, 2000.

K. Madangopal, J. Singh, and S. Banerjee, Self-accommodation in ni ti shape memory alloys, Scripta metallurgica et materialia, vol.25, issue.9, pp.2153-2158, 1991.

Y. Chai, H. Kim, H. Hosoda, and S. Miyazaki, Self-accommodation in ti-nb shape memory alloys, Acta Materialia, vol.57, issue.14, pp.4054-4064, 2009.

V. Pancholi, M. Krishnan, I. Samajdar, V. Yadav, and N. Ballal, Selfaccommodation in the bainitic microstructure of ultra-high-strength steel, Acta Materialia, vol.56, issue.9, pp.2037-2050, 2008.

N. Takayama, G. Miyamoto, and T. Furuhara, Effects of transformation temperature on variant pairing of bainitic ferrite in low carbon steel, Acta Materialia, vol.60, issue.5, pp.2387-2396, 2012.

J. Morris, Y. Ye, K. Ho, C. T. Chan, and M. Yoo, Structures and energies of compression twin boundaries in hcp ti and zr, Philosophical Magazine A, vol.72, issue.3, pp.751-763, 1995.

K. Bhattacharya, Self-accommodation in martensite, Archive for Rational Mechanics and Analysis, vol.120, issue.3, pp.201-244, 1992.

Z. Nishiyama, S. Sato, M. Oka, and H. Nakagawa, Transmission electron microscope study of the martensites in a titanium-3 wt% iron alloy, Transactions of the Japan Institute of Metals, vol.8, issue.2, pp.127-132, 1967.