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.

Polymorphic transitions in single crystals: A new molecular dynamics method

With use of a Lagrangian which allows for the variation of the shape and size of the periodically repeating molecular-dynamics cell, it is shown that different pair potentials lead to different crystal structures.

Crystal structure and pair potentials: A molecular-dynamics study

It is demonstrated that stability criteria derived using elastic stiffness coefficients which govern stress-strain relations at finite deformation give quantitative predictions of crystal instability, as observed in direct molecular dynamics simulations. With the aid of such analysis we show that instabilities can be triggered in succession; as a consequence, the limit of metastability in the superheating of a defect-free crystal can be predicted.

Crystal instabilities at finite strain.

Most metallic elements have a crystal structure that is either body-centered cubic (bcc), face-centered close packed, or hexagonal close packed. If the bcc lattice is the thermodynamically most stable structure, the close-packed structures usually are dynamically unstable, i.e., have elastic constants violating the Born stability conditions or, more generally, have phonons with imaginary frequencies. Conversely, the bcc lattice tends to be dynamically unstable if the equilibrium structure is close packed. This striking regularity essentially went unnoticed until ab initio total-energy calculations in the 1990s became accurate enough to model dynamical properties of solids in hypothetical lattice structures. After a review of stability criteria, thermodynamic functions in the vicinity of an instability, Bain paths, and how instabilities may arise or disappear when pressure, temperature, and/or chemical composition is varied are discussed. The role of dynamical instabilities in the ideal strength of solids and in metallurgical phase diagrams is then considered, and comments are made on amorphization, melting, and low-dimensional systems. The review concludes with extensive references to theoretical work on the stability properties of metallic elements.

https://perssongroup.lbl.gov/papers/rmp2012-instabilities.pdf

Lattice instabilities in metallic elements

Materials with negative Poisson's ratio attract considerable attention due to their underlying intriguing physical properties and numerous promising applications, particularly in stringent environments such as aerospace and defense areas, because of their unconventional mechanical enhancements. Recent progress in materials with a negative Poisson's ratio are reviewed here, with the current state of research regarding both theory and experiment. The inter-relationship between the underlying structure and a negative Poisson's ratio is discussed in functional materials, including macroscopic bulk, low-dimensional nanoscale particles, films, sheets, or tubes. The coexistence and correlations with other negative indexes (such as negative compressibility and negative thermal expansion) are also addressed. Finally, open questions and future research opportunities are proposed for functional materials with negative Poisson's ratios.

Negative Poisson's Ratio in Modern Functional Materials

It is shown by theoretical arguments and lattice-model computations that when an fcc crystal is loaded uniaxially in tension along a [100] direction, a path of minimum energy (under strict [100] uniaxial load) takes the crystal into unstressed bcc.

Theoretical fcc-->bcc Transition under [100] Tensile Loading

A distinction is made between the theoretical mechanical behaviour of cubic crystals in [100] loading (i.e. transverse stresses are zero) and [1001 deformation (i.e. transverse stretches are zero). In the former, a primary loading path passes through thee zeros (the unstressed f.c.c., b.c.c. and b.c.t. states); in the latter, three corresponding states of hydrostatic loading are reached (one of which is unstressed). Detailed computations are made of the mechanical behaviour in both [100] loading and deformation for lattice models of Cu and Ni. In Cu, the elastic instability associated with the invariant eigenstate C22 = C23 occurs in tensile [100] loading at about 20% of the maximum theoretical stress, thus lowering the estimate of the ‘theoretical tensile strength’ of Cu to within the range of experimentally based estimates. The stress and energy barriers for f.c.c. → b.c.c. and b.c.c. → f.c.c. transitions are computed (within the framework of the lattice models) along a path of [100] loading.

On the theoretical strength of copper

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Theoretical fcc-->bcc Transition under [100] Tensile Loading

On the theoretical strength of copper