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Polymorphic transitions in single crystals: A new molecular dynamics method

Why this mattered

Parrinello and Rahman’s 1981 paper changed molecular dynamics from a method for following atoms inside a fixed simulation box into a method for following matter whose shape and volume could themselves respond dynamically to stress. By introducing a Lagrangian in which the simulation cell vectors were dynamical variables, the paper made it possible to simulate finite-temperature crystals under general externally applied stress, not just idealized constant-volume or hydrostatic conditions. This was a conceptual shift: phase transformations, elastic instabilities, and stress-driven structural changes could now emerge from the coupled motion of atoms and the boundary conditions, rather than being imposed by hand or inferred from zero-temperature static calculations.

The importance of the method was immediately visible in the nickel example. Under uniaxial loading, Parrinello and Rahman showed that finite-temperature molecular dynamics could reproduce some static predictions while also invalidating others, especially aspects of the stress-strain relation. Their observed bifurcation linking cubic close packing and hexagonal close packing demonstrated that a simulation could expose a pathway through configuration space between crystal structures. That made molecular dynamics a tool not merely for measuring fluctuations around a known structure, but for discovering mechanically driven transformations and possible transition mechanisms under extreme conditions such as shock.

The broader consequence was the foundation of what became variable-cell and constant-stress molecular dynamics, central to later simulations of polymorphism, martensitic transformations, melting, mineral physics, high-pressure phases, and materials under load. The Parrinello-Rahman framework helped establish the modern idea that atomistic simulations could explore phase behavior under realistic thermodynamic and mechanical constraints. Subsequent breakthroughs in ab initio molecular dynamics, high-pressure materials modeling, and computational crystal-structure studies all relied on this expanded view: the simulation cell is not just a container, but part of the physical system being modeled.

Abstract

A new Lagrangian formulation is introduced. It can be used to make molecular dynamics (MD) calculations on systems under the most general, externally applied, conditions of stress. In this formulation the MD cell shape and size can change according to dynamical equations given by this Lagrangian. This new MD technique is well suited to the study of structural transformations in solids under external stress and at finite temperature. As an example of the use of this technique we show how a single crystal of Ni behaves under uniform uniaxial compressive and tensile loads. This work confirms some of the results of static (i.e., zero temperature) calculations reported in the literature. We also show that some results regarding the stress-strain relation obtained by static calculations are invalid at finite temperature. We find that, under compressive loading, our model of Ni shows a bifurcation in its stress-strain relation; this bifurcation provides a link in configuration space between cubic and hexagonal close packing. It is suggested that such a transformation could perhaps be observed experimentally under extreme conditions of shock.

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