skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Lattice instability during phase transformations under multiaxial stress: Modified transformation work criterion

Abstract

A continuum/atomistic approach for predicting lattice instability during crystal-crystal phase transformations (PTs) is developed for the general loading with an arbitrary stress tensor and large strains. It is based on a synergistic combination of the generalized Landau-type theory for PTs and molecular dynamics (MD) simulations. The continuum approach describes the entire dissipative transformation process in terms of an order parameter, and the general form of the instability criterion is derived utilizing the second law of thermodynamics. The feedback from MD allowed us to present the instability criterion for both direct and reverse PTs in terms of the critical value of the modified transformation work, which is linear in components of the true stress tensor. It was calibrated by MD simulations for direct and reverse PTs between semiconducting silicon Si i and metallic Si ii phases under just two different stress states. Then, it describes hundreds of MD simulations under various combinations of three normal and three shear stresses. Finally, in particular, the atomistic simulations show that the effects of all three shear stresses along cubic axes on lattice instability of Si i are negligible, which is in agreement with our criterion.

Authors:
 [1];  [2];  [2]
  1. Iowa State Univ., Ames, IA (United States). Dept. of Aerospace Engineering, Mechanical Engineering, and Material Science and Engineering; Ames Lab., Ames, IA (United States)
  2. Iowa State Univ., Ames, IA (United States). Dept. of Aerospace Engineering
Publication Date:
Research Org.:
Ames Laboratory (AMES), Ames, IA (United States)
Sponsoring Org.:
National Science Foundation (NSF); USDOE; US Army Research Office (ARO)
OSTI Identifier:
1418498
Grant/Contract Number:  
CMMI-1536925; DMR-1434613; W911NF-17-1-0225; N00014-16-1-2079
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 96; Journal Issue: 5; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS

Citation Formats

Levitas, Valery I., Chen, Hao, and Xiong, Liming. Lattice instability during phase transformations under multiaxial stress: Modified transformation work criterion. United States: N. p., 2017. Web. doi:10.1103/PhysRevB.96.054118.
Levitas, Valery I., Chen, Hao, & Xiong, Liming. Lattice instability during phase transformations under multiaxial stress: Modified transformation work criterion. United States. doi:10.1103/PhysRevB.96.054118.
Levitas, Valery I., Chen, Hao, and Xiong, Liming. Tue . "Lattice instability during phase transformations under multiaxial stress: Modified transformation work criterion". United States. doi:10.1103/PhysRevB.96.054118. https://www.osti.gov/servlets/purl/1418498.
@article{osti_1418498,
title = {Lattice instability during phase transformations under multiaxial stress: Modified transformation work criterion},
author = {Levitas, Valery I. and Chen, Hao and Xiong, Liming},
abstractNote = {A continuum/atomistic approach for predicting lattice instability during crystal-crystal phase transformations (PTs) is developed for the general loading with an arbitrary stress tensor and large strains. It is based on a synergistic combination of the generalized Landau-type theory for PTs and molecular dynamics (MD) simulations. The continuum approach describes the entire dissipative transformation process in terms of an order parameter, and the general form of the instability criterion is derived utilizing the second law of thermodynamics. The feedback from MD allowed us to present the instability criterion for both direct and reverse PTs in terms of the critical value of the modified transformation work, which is linear in components of the true stress tensor. It was calibrated by MD simulations for direct and reverse PTs between semiconducting silicon Si i and metallic Si ii phases under just two different stress states. Then, it describes hundreds of MD simulations under various combinations of three normal and three shear stresses. Finally, in particular, the atomistic simulations show that the effects of all three shear stresses along cubic axes on lattice instability of Si i are negligible, which is in agreement with our criterion.},
doi = {10.1103/PhysRevB.96.054118},
journal = {Physical Review B},
number = 5,
volume = 96,
place = {United States},
year = {2017},
month = {8}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 14 works
Citation information provided by
Web of Science

Figures / Tables:

Figure 1 Figure 1: Phase transformation process for Si I→Si II under uniaxial loading. (A) heterogeneous nucleation of Si II due to stress fluctuation. (B) and (C) due to internal stresses caused by the transformation strain, complete Si II and residual Si I reshape into bands. Note that Si I bands aremore » formed through the reverse PT. (D) Final stable state of Si II.« less

Save / Share:

Works referenced in this record:

Ab initio study of the high-pressure phase transition from the cubic-diamond to the β-tin structure of Si
journal, November 2001


Shear-induced phase transition of nanocrystalline hexagonal boron nitride to wurtzitic structure at room temperature and lower pressure
journal, November 2012

  • Ji, C.; Levitas, V. I.; Zhu, H.
  • Proceedings of the National Academy of Sciences, Vol. 109, Issue 47
  • DOI: 10.1073/pnas.1214976109

Strained Tetragonal States and Bain Paths in Metals
journal, May 1997


Low-pressure phase transformation from rhombohedral to cubic BN: Experiment and theory
journal, February 2002


Lattice instabilities in metallic elements
journal, June 2012

  • Grimvall, Göran; Magyari-Köpe, Blanka; Ozoliņš, Vidvuds
  • Reviews of Modern Physics, Vol. 84, Issue 2
  • DOI: 10.1103/RevModPhys.84.945

On the stability of crystal lattices. I
journal, April 1940


Ab initio calculations of mechanical properties: Methods and applications
journal, August 2015


Theoretical bcc fcc Transitions in Metals via Bifurcations under Uniaxial Load
journal, April 1995


The internal stability of an elastic solid
journal, December 2000


Phase field approach to martensitic phase transformations with large strains and interface stresses
journal, October 2014


Triaxial-Stress-Induced Homogeneous Hysteresis-Free First-Order Phase Transformations with Stable Intermediate Phases
journal, January 2017


Molecular dynamics with coupling to an external bath
journal, October 1984

  • Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.
  • The Journal of Chemical Physics, Vol. 81, Issue 8
  • DOI: 10.1063/1.448118

Kinetics of materials with wiggly energies: Theory and application to the evolution of twinning microstructures in a Cu-Al-Ni shape memory alloy
journal, February 1996


Crystal instabilities at finite strain
journal, December 1993


Atomistic mechanisms governing elastic limit and incipient plasticity in crystals
journal, July 2002

  • Li, Ju; Van Vliet, Krystyn J.; Zhu, Ting
  • Nature, Vol. 418, Issue 6895
  • DOI: 10.1038/nature00865

Fast Parallel Algorithms for Short-Range Molecular Dynamics
journal, March 1995


Polymorphic transitions in single crystals: A new molecular dynamics method
journal, December 1981

  • Parrinello, M.; Rahman, A.
  • Journal of Applied Physics, Vol. 52, Issue 12
  • DOI: 10.1063/1.328693

Twin Boundaries in Ferroelastic Media without Interface Dislocations
journal, September 1984


Visualization and analysis of atomistic simulation data with OVITO–the Open Visualization Tool
journal, December 2009


Comparative study of silicon empirical interatomic potentials
journal, July 1992


Reversible stress-induced martensitic phase transformations in a bi-atomic crystal
journal, February 2011

  • Elliott, Ryan S.; Triantafyllidis, Nicolas; Shaw, John A.
  • Journal of the Mechanics and Physics of Solids, Vol. 59, Issue 2
  • DOI: 10.1016/j.jmps.2010.10.011

Principles of stability analysis of ideal crystals
journal, March 1977


Phase-field theory for martensitic phase transformations at large strains
journal, October 2013


Ideal crystal stability and pressure-induced phase transition in silicon
journal, November 1994


Atomistic basis for the plastic yield criterion of metallic glass
journal, June 2003

  • Schuh, Christopher A.; Lund, Alan C.
  • Nature Materials, Vol. 2, Issue 7
  • DOI: 10.1038/nmat918

Dynamics of viscoplastic deformation in amorphous solids
journal, June 1998


Phase transformations in nanograin materials under high pressure and plastic shear: nanoscale mechanisms
journal, January 2014

  • Levitas, Valery I.; Javanbakht, Mahdi
  • Nanoscale, Vol. 6, Issue 1
  • DOI: 10.1039/C3NR05044K

Theory of Shear Banding in Metallic Glasses and Molecular Dynamics Calculations
journal, January 2007


Continuum interpretation of virial stress in molecular simulations
journal, July 2008


Elastic criterion for dislocation nucleation
journal, January 2004


Molecular dynamics at constant Cauchy stress
journal, May 2016

  • Miller, Ronald E.; Tadmor, Ellad B.; Gibson, Joshua S.
  • The Journal of Chemical Physics, Vol. 144, Issue 18
  • DOI: 10.1063/1.4948711

    Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.