Phase Field Study of Lattice Instability and Nanostructure Evolution in Silicon During Phase Transformation Under Complex Loading

  • H. BabaeiEmail author
  • V. I. Levitas
Conference paper
Part of the The Minerals, Metals & Materials Series book series (MMMS)


An advanced phase-field approach (PFA) to study martensitic phase transformations is developed for finite strains, particularly taking into account crystal lattice instability conditions under complex triaxial compression-tension loading obtained using molecular dynamics (MD) simulations. Calibration of novel phase-field instability criteria with those from MD simulations for Si I \( \leftrightarrow \) Si II phase transformations leads to unexpected interpolation functions for transformation strain and elastic constants. A finite element algorithm and a numerical procedure are developed and implemented using code deal.II. The effect of stress state on lattice instability and nanostructure evolution is studied. Within a specific stress range for which direct and reverse transformation instability stresses coincide, a unique homogeneous, hysteresis-free, and dissipation-free transformation is observed. For such a transformation, a continuum of intermediate phases exists along the transformation path, all in indifferent thermodynamic equilibrium. The absence of interfaces results in the absence of internal stresses and minimizes damage. All these properties are optimal for various PT-related applications.


Phase field approach Martensitic phase transformation Lattice instability conditions 


Support of NSF (CMMI-1536925 and DMR-1434613), ARO (W911NF-17-1-0225), XSEDE (TG-MSS140033), and ISU (Schafer 2050 Challenge Professorship and Vance Coffman Faculty Chair Professorship) is gratefully acknowledged.


  1. 1.
    Jin YM, Artemev A, Khachaturyan AG (2001) Three-dimensional phase field model of low-symmetry martensitic transformation in polycrystal: simulation of ζ′2 martensite in AuCd alloys. Acta Mater 49:2309–2320CrossRefGoogle Scholar
  2. 2.
    Chen LQ (2002) Phase-field models for microstructure evolution. Annu Rev Mater Res 32:113–140CrossRefGoogle Scholar
  3. 3.
    Seol DJ, Hu SY, Li YL, Chen LQ, Oh KH (2003) Cubic to tetragonal martensitic transformation in a thin film elastically constrained by a substrate. Int J Mater Res 9:221–226CrossRefGoogle Scholar
  4. 4.
    Levitas VI, Lee DW (2007) Athermal resistance to an interface motion in phase field theory of microstructure evolution. Phys Rev Lett 99:245701CrossRefGoogle Scholar
  5. 5.
    Idesman AV, Cho J-Y, Levitas VI (2008) Finite element modeling of dynamics of martensitic phase transitions. Appl Phys Lett 93:043102CrossRefGoogle Scholar
  6. 6.
    Levitas VI, Chen H, Xiong L (2017) Triaxial-stress-induced homogeneous hysteresis-free first-order phase transformations with stable intermediate phases. Phys Rev Lett 118:025701Google Scholar
  7. 7.
    Levitas VI (2014) Phase field approach to martensitic phase transformations with large strains and interface stresses. J Mech Phys Solids 70:154CrossRefGoogle Scholar
  8. 8.
    Levitas VI (2013) Phase-field theory for martensitic phase transformations. Int J Plast 49:85CrossRefGoogle Scholar
  9. 9.
    Bangerth W, Hartmann R, Kanschat G (2007) deal.II—a general purpose object oriented finite element library. ACM Trans Math Softw 33(4):1–27CrossRefGoogle Scholar

Copyright information

© The Minerals, Metals & Materials Society 2018

Authors and Affiliations

  1. 1.Department of Aerospace EngineeringIowa State UniversityAmesUSA
  2. 2.Ames Laboratory, Division of Materials Science & Engineering, Departments of Aerospace Engineering, and Mechanical Engineering, and Material Science & EngineeringIowa State UniversityAmesUSA

Personalised recommendations