Abstract
Strain glass is a new structural state in ferroelastic materials, which offers unique transition behavior and properties. In this chapter, we introduce a phase field model of strain glass systems and study their transition behavior and the associated properties by computer simulations. Local stresses associated with randomly distributed defects, including point defects and extended defects (dislocations and concentration modulations), are found to play the most important role in the formation of strain glass, by suppressing autocatalysis in nucleation and confining the growth of martensitic domains. A broad distribution of defect strength leads to continued nucleation and growth of martensitic domains in a broad temperature or stress range and renders the otherwise sharp first-order martensitic transformation into a broadly smeared “diffuse” strain glass transition with slim hysteresis, nearly linear superelasticity, ultralow elastic modulus and Invar and Elinvar anomalies. New strategies for designing strain glass systems with large recoverable strain are discussed.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
K. Ōtsuka, C.M. Wayman, Shape Memory Materials (Cambridge University Press, Cambridge, 1998)
A.R. Pelton et al., Nitinol medical devices. Adv Mater Process 163, 63–65 (2005)
T.W. Duerig, A.R. Pelton, An overview of superelastic stent design. Mater Sci Forum 394-3, 1–8 (2001)
T.W. Duerig, Engineering Aspects of Shape Memory Alloys (Butterworth-Heinemann, Oxford, 1990)
S. Sarkar, X.B. Ren, K. Otsuka, Evidence for strain glass in the ferroelastic-martensitic system Ti50-xNi50 + x. Phys Rev Lett 95, 205702 (2005). https://doi.org/10.1103/Physrevlett.95.205702
Y. Wang, X.B. Ren, K. Otsuka, Shape memory effect and superelasticity in a strain glass alloy. Phys Rev Lett 97, 225703 (2006). https://doi.org/10.1103/Physrevlett.97.225703
X.B. Ren et al., Strain glass in ferroelastic systems: Premartensitic tweed versus strain glass. Philos Mag 90, 141–157 (2010). https://doi.org/10.1080/14786430903074771
L.-Q. Chen, Phase-field models for microstructure evolution. Annual Review of Materials Research 32, 113–140 (2002). https://doi.org/10.1146/annurev.matsci.32.112001.132041
A.G. Khachaturȋân, Theory of Structural Transformations in Solids (Wiley, Hoboken, 1983)
D. Raabe, Continuum Scale Simulation of Engineering Materials: Fundamentals, Microstructures, Process Applications (Wiley-VCH, Hoboken, 2004), pp. 271–296
Y. Wang, J. Li, Phase field modeling of defects and deformation. Acta Materialia 58, 1212–1235 (2010). https://doi.org/10.1016/j.actamat.2009.10.041
I. Steinbach, Phase-field model for microstructure evolution at the mesoscopic scale. Annual Review of Materials Research 43, 89–107 (2013). https://doi.org/10.1146/annurev-matsci-071312-121703
K. Elder, H. Gould, J. Tobochnik, Langevin simulations of nonequilibrium phenomena. Computers in Physics 7, 27–33 (1993). https://doi.org/10.1063/1.4823138
A. Artemev, Y. Jin, A.G. Khachaturyan, Three-dimensional phase field model of proper martensitic transformation. Acta Materialia 49, 1165–1177 (2001). https://doi.org/10.1016/S1359-6454(01)00021-0
Y. Wang, A.G. Khachaturyan, Three-dimensional field model and computer modeling of martensitic transformations. Acta Materialia 45, 759–773 (1997). https://doi.org/10.1016/S1359-6454(96)00180-2
Y.L. Li, S.Y. Hu, Z.K. Liu, L.Q. Chen, Phase-field model of domain structures in ferroelectric thin films. Applied Physics Letters 78, 3878–3880 (2001). https://doi.org/10.1063/1.1377855
J. Wang, S.-Q. Shi, L.-Q. Chen, Y. Li, T.-Y. Zhang, Phase-field simulations of ferroelectric/ferroelastic polarization switching. Acta Materialia 52, 749–764 (2004). https://doi.org/10.1016/j.actamat.2003.10.011
L.Q. Chen, Phase-field method of phase transitions/domain structures in ferroelectric thin films: A review. J Am Ceram Soc 91, 1835–1844 (2008). https://doi.org/10.1111/j.1551-2916.2008.02413.x
L.J. Li, C.H. Lei, Y.C. Shu, J.Y. Li, Phase-field simulation of magnetoelastic couplings in ferromagnetic shape memory alloys. Acta Materialia 59, 2648–2655 (2011). https://doi.org/10.1016/j.actamat.2011.01.001
Y.M. Jin, Domain microstructure evolution in magnetic shape memory alloys: Phase-field model and simulation. Acta Materialia 57, 2488–2495 (2009). https://doi.org/10.1016/j.actamat.2009.02.003
Y.Z. Wang, A.G. Khachaturyan, Multi-scale phase field approach to martensitic transformations. Mat. Sci. Eng. A 438, 55–63 (2006). https://doi.org/10.1016/j.msea.2006.04.123
D. Wang et al., Superelasticity of slim hysteresis over a wide temperature range by nanodomains of martensite. Acta Materialia 66, 349–359 (2014). https://doi.org/10.1016/j.actamat.2013.11.022
Y.P. Gao, R.P. Shi, J.F. Nie, S.A. Dregia, Y.Z. Wang, Group theory description of transformation pathway degeneracy in structural phase transformations. Acta Materialia 109, 353–363 (2016). https://doi.org/10.1016/j.actamat.2016.01.027
J.W. Cahn, J.E. Hilliard, Free energy of a nonuniform system. I. Interfacial free energy. The Journal of Chemical Physics 28, 258–267 (1958). https://doi.org/10.1063/1.1744102
C. Shen, J.P. Simmons, Y. Wang, Effect of elastic interaction on nucleation: II. Implementation of strain energy of nucleus formation in the phase field method. Acta Materialia 55, 1457–1466 (2007). https://doi.org/10.1016/j.actamat.2006.10.011
C.-J. Huang, D.J. Browne, S. McFadden, A phase-field simulation of austenite to ferrite transformation kinetics in low carbon steels. Acta Materialia 54, 11–21 (2006). https://doi.org/10.1016/j.actamat.2005.08.033
S. Semenovskaya, A.G. Khachaturyan, Coherent structural transformations in random crystalline systems. Acta Materialia 45, 4367–4384 (1997). https://doi.org/10.1016/S1359-6454(97)00071-2
D. Wang, Y.Z. Wang, Z. Zhang, X.B. Ren, Modeling abnormal strain states in ferroelastic systems: the role of point defects. Phys Rev Lett 105, 205702 (2010). https://doi.org/10.1103/Physrevlett.105.205702
A.P. Levanȋȗk, A.S. Sigov, Defects and Structural Phase Transitions (Gordon and Breach Science Publishers, Philadelphia, 1988)
P. Lloveras, T. Castan, M. Porta, A. Planes, A. Saxena, Influence of elastic anisotropy on structural nanoscale textures. Phys Rev Lett 100, 165707 (2008). https://doi.org/10.1103/Physrevlett.100.165707
D. Wang, X.B. Ren, Y.Z. Wang, Nanoscaled martensitic domains in ferroelastic systems: strain glass. Curr Nanosci 12, 192–201 (2016). https://doi.org/10.2174/1573413711666150523001617
K. Otsuka, X. Ren, Physical metallurgy of Ti–Ni-based shape memory alloys. Progress in Materials Science 50, 511–678 (2005). https://doi.org/10.1016/j.pmatsci.2004.10.001
E.K.H. Salje, Phase Transitions in Ferroelastic and Co-Elastic Crystals: An Introduction for Mineralogists, Material Scientists, and Physicists (Cambridge University Press, Cambridge, 1990)
S.M. Shapiro, J.Z. Larese, Y. Noda, S.C. Moss, L.E. Tanner, Neutron-scattering study of premartensitic behavior in Ni-Al alloys. Phys Rev Lett 57, 3199–3202 (1986). https://doi.org/10.1103/PhysRevLett.57.3199
D. Shindo, Y. Murakami, T. Ohba, Understanding precursor phenomena for the R-phase transformation in Ti-Ni-based alloys. Mrs Bull 27, 121–127 (2002). https://doi.org/10.1557/Mrs2002.48
Y. Wang, X. Ren, K. Otsuka, A. Saxena, Evidence for broken ergodicity in strain glass. Phys Rev B 76, 132201 (2007). https://doi.org/10.1103/Physrevb.76.132201
D. Wang et al., Strain glass in Fe-doped Ti-Ni. Acta Materialia 58, 6206–6215 (2010). https://doi.org/10.1016/j.actamat.2010.07.040
Y. Wang et al., Strain glass transition in a multifunctional beta-type Ti alloy. Sci Rep 4, 3995 (2014). https://doi.org/10.1038/Srep03995
Z. Zhang et al., Phase diagram of Ti50-xNi50 + x: Crossover from martensite to strain glass. Phys Rev B 81, 224102 (2010). https://doi.org/10.1103/Physrevb.81.224102
Y. Zhou et al., Strain glass in doped Ti50(Ni50 − xDx) (D = Co, Cr, Mn) alloys: Implication for the generality of strain glass in defect-containing ferroelastic systems. Acta Materialia 58, 5433–5442 (2010). https://doi.org/10.1016/j.actamat.2010.06.019
Y.M. Zhou et al., High temperature strain glass in Ti-50(Pd50-xCrx) alloy and the associated shape memory effect and superelasticity. Applied Physics Letters 95, 151906 (2009). https://doi.org/10.1063/1.3249580
Q. Liang et al., Novel B19\ensuremath{'} strain glass with large recoverable strain. Phys. Rev. Mater. 1, 033608 (2017)
J. Liu et al., Strain glassy behavior and premartensitic transition in Au${}_{7}$Cu${}_{5}$Al${}_{4}$ alloy. Phys Rev B 84, 140102 (2011)
Y. Nii, T.-h. Arima, H.Y. Kim, S. Miyazaki, Effect of randomness on ferroelastic transitions: Disorder-induced hysteresis loop rounding in Ti-Nb-O martensitic alloy. Phys Rev B 82(214), 104 (2010)
S. Kartha, T. Castan, J.A. Krumhansl, J.P. Sethna, Spin-glass nature of tweed precursors in martensitic transformations. Phys Rev Lett 67, 3630–3633 (1991). https://doi.org/10.1103/PhysRevLett.67.3630
R. Vasseur, T. Lookman, Effects of disorder in ferroelastics: A spin model for strain glass. Phys Rev B 81, 094107 (2010). https://doi.org/10.1103/Physrevb.81.094107
D. Sherrington, S. Kirkpatrick, Solvable model of a spin-glass. Phys Rev Lett 35, 1792–1796 (1975). https://doi.org/10.1103/PhysRevLett.35.1792
D. Sherrington, A simple spin glass perspective on martensitic shape-memory alloys. J. Phys. Condens. Matter 20, 304213 (2008). https://doi.org/10.1088/0953-8984/20/30/304213
Y.C. Ji, X.D. Ding, T. Lookman, K. Otsuka, X.B. Ren, Heterogeneities and strain glass behavior: Role of nanoscale precipitates in low-temperature-aged Ti48.7Ni51.3 alloys. Phys Rev B 87, 104110 (2013). https://doi.org/10.1103/Physrevb.87.104110
J. Zhang et al., Dislocation induced strain glass in Ti50Ni45Fe5 alloy. Acta Materialia 120, 130–137 (2016). https://doi.org/10.1016/j.actamat.2016.08.015
R. Vasseur et al., Phase diagram of ferroelastic systems in the presence of disorder: Analytical model and experimental verification. Phys Rev B 86, 184103 (2012). https://doi.org/10.1103/Physrevb.86.184103
N. Gayathri et al., Electrical transport, magnetism, and magnetoresistance in ferromagnetic oxides with mixed exchange interactions: A study of the La0.7Ca0.3Mn1-xCoxO3 system. Phys. Rev. B 56, 1345–1353 (1997). https://doi.org/10.1103/PhysRevB.56.1345
D. Viehland, J.F. Li, S.J. Jang, L.E. Cross, M. Wuttig, Glassy Polarization Behavior Of Relaxor Ferroelectrics. Phys Rev B 46, 8013–8017 (1992). https://doi.org/10.1103/PhysRevB.46.8013
J.A. Mydosh, Spin Glasses: An Experimental Introduction (Taylor & Francis, Oxfordshire, 1993)
P. Lloveras, T. Castán, M. Porta, A. Planes, A. Saxena, Thermodynamics of stress-induced ferroelastic transitions: Influence of anisotropy and disorder. Phys Rev B 81, 214105 (2010)
D. Wang et al., Defect strength and strain glass state in ferroelastic systems. Journal of Alloys and Compounds 661, 100–109 (2016). https://doi.org/10.1016/j.jallcom.2015.11.095
J. Zhu, Y. Gao, D. Wang, T.-Y. Zhang, Y. Wang, Taming martensitic transformation via concentration modulation at nanoscale. Acta Materialia 130, 196–207 (2017). https://doi.org/10.1016/j.actamat.2017.03.042
D. Wang et al., Integrated computational materials engineering (ICME) approach to design of novel microstructures for Ti-alloys. JOM 66, 1287–1298 (2014). https://doi.org/10.1007/s11837-014-1011-2
S.-J. Qin, J.-X. Shang, F.-H. Wang, Y. Chen, The role of strain glass state in the shape memory alloy Ni50 + xTi50 − x: Insight from an atomistic study. Materials & Design 120, 238–254 (2017). https://doi.org/10.1016/j.matdes.2017.02.011
X.B. Ren, Strain glass and ferroic glass - Unusual properties from glassy nano-domains. Phys. Status Solidi B Basic Solid State Phys. 251, 1982–1992 (2014). https://doi.org/10.1002/pssb.201451351
L. Zhang, D. Wang, X. Ren, Y. Wang, A new mechanism for low and temperature-independent elastic modulus. Sci Rep 5, 11477 (2015). https://doi.org/10.1038/srep11477
J. Cui, X. Ren, Elinvar effect in co-doped TiNi strain glass alloys. Applied Physics Letters 105, 061904 (2014). https://doi.org/10.1063/1.4893003
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Wang, D., Ren, X., Wang, Y. (2018). Phase Field Model and Computer Simulation of Strain Glasses. In: Lookman, T., Ren, X. (eds) Frustrated Materials and Ferroic Glasses. Springer Series in Materials Science, vol 275. Springer, Cham. https://doi.org/10.1007/978-3-319-96914-5_10
Download citation
DOI: https://doi.org/10.1007/978-3-319-96914-5_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-96913-8
Online ISBN: 978-3-319-96914-5
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)