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

Valery I. Levitas, Hao Chen, and Liming Xiong

Phys. Rev. B 96, 054118 – Published 29 August 2017

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. 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.

Received 15 December 2016
Revised 22 June 2017

DOI:https://doi.org/10.1103/PhysRevB.96.054118

Physics Subject Headings (PhySH)

Phase transitions

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Valery I. Levitas^1,2, Hao Chen³, and Liming Xiong³

¹Departments of Aerospace Engineering, Mechanical Engineering, and Material Science and Engineering, Iowa State University, Ames, Iowa 50011, USA
²Ames Laboratory, Division of Materials Science and Engineering, Ames, Iowa 50011, USA
³Department of Aerospace Engineering, Iowa State University, Ames, Iowa 50011, USA

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 96, Iss. 5 — 1 August 2017

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Phase transformation process for Si i $\to Si$ ii under uniaxial loading. (a) Heterogeneous nucleation of Si ii due to stress fluctuation. (b) and (c) Completely transformed Si ii and residual Si i reshape into bands due to internal stresses caused by the transformation strain. Note that Si i bands are formed through the reverse PT. (d) Final stable state of Si ii.
Reuse & Permissions
Figure 2
Phase transformation process for Si ii $\to Si$ i under uniaxial unloading. (a) Heterogeneous nucleation of Si i due to stress fluctuation. (b) Formation of bandlike structure consisting of almost complete Si i and some intermediate phase, but without Si ii. (c) Final stable state of Si i.
Reuse & Permissions
Figure 3
Stress–Lagrangian-strain $E$ curves for uniaxial compression ( $σ_{1} = σ_{2} = 0$ ) for the Cauchy $σ$ , the first Piola-Kirchhoff $P$ , and the second Piola-Kirchhoff stress $T$ for direct and reverse PTs Si i $\leftrightarrow Si$ ii. Dots mark instability points, which correspond to stresses above (or below for reverse PT), where the crystal cannot be at equilibrium at prescribed $σ$ , or multiple (homogeneous and heterogeneous) microstructures exist. After a loss of stability, the microstructure initially evolves homogeneously, then heterogeneously with stochastic fluctuations, and then with bands consisting of some intermediate phases and, at larger strains, bands with fully formed Si ii. Heterogeneous microstructures in Fig. 3 are obtained from two-phase band structures at larger strains by returning to instability point $I$ . (a) Results obtained for prescribed $σ$ (lines) and $P$ (symbols) are not distinguishable. Microstructures near the $σ$ and $P$ curves are obtained under corresponding prescribed stresses $σ$ and $P$ , respectively. (b) Stress-strain curves for strain-controlled loading (dashed lines), which are the same for direct and reverse PTs, in comparison with curves under controlled stresses for direct (upper lines) and reverse (lower lines) PTs.
Reuse & Permissions
Figure 4
Conformation of the lattice instability criterion (12). (a) Plane in stress space corresponding to the instability criterion (12) for direct Si i $\to Si$ ii PT and instability points from MD simulations, along with projection of each point on $σ_{i} - σ_{j}$ planes. (b) The same plot but rotated until the theoretical plane (12) is visible as a line, to demonstrate how close all simulation points are to the theoretical plane. Parts (c) and (d) are the same but for reverse Si ii $\to Si$ i PT.
Reuse & Permissions
Figure 5
Relationships between stresses $σ_{2}$ and $σ_{3}$ corresponding to the lattice instability for direct ( $D$ ) and reverse ( $R$ ) Si i $\leftrightarrow Si$ ii PTs for (a) $σ_{1} = σ_{2}$ and (b) $σ_{1} = - σ_{2}$ . Bars in (b) show the relative error of the theoretical prediction of the simulation results.
Reuse & Permissions
Figure 6
Modified transformation work in the instability criterion (11) vs maximum shear stress for normal stresses in the ranges $σ_{1} = 1.50 - 2.17, σ_{2} = 1.41 - 1.61$ , and $- σ_{3} = 10.38 - 10.76 GPa$ .
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics