A universal framework for on-lattice atomistic dynamics simulation

About OpenFerro

OpenFerro is a Python package for on-lattice atomistic dynamics simulation. OpenFerro is based on JAX, a high-performance linear algebra package supporting auto-differentiation and GPU acceleration. OpenFerro is designed to minimize the effort required to build on-lattice Hamiltonian models, and to perform molecular dynamics (MD) and Landau-Lifshitz-Gilbert simulations.

Highlighted features

• GPU supports, highly efficient for large-scale simulations.
• auto-differentiable, will have native support for enhanced sampling and Hamiltonian optimization.
• highly modularized, easy to implement new interaction terms without looking into the codebase.
• highly flexible, supports simultaneous simulation of $R^d$ and SO(3) local order parameters. Fields with other symmetries can also be implemented.

Installation

See documentation for installation instructions.

OpenFerro in a nutshell

Crystalline system and Lattice Hamiltonian

A crystalline system is a periodic arrangement of atoms or molecules in space. In OpenFerro, a crystalline system is defined by a Bravias lattice, local order parameter, global variables of the lattice (such as global strain) and a Hamiltonian describing the energy of the system. See documentation for more details than the outline below.

Bravias lattice

A Bravias lattice is specified by a set of basis vectors. For example, a 3D Bravais lattice is an infinite array of discrete points described by $\mathbf{R} = n_1 \mathbf{a}_1 + n_2 \mathbf{a}_2 + n_3 \mathbf{a}_3$, where $n_1, n_2, n_3$ are integers, and $\mathbf{a}_1, \mathbf{a}_2, \mathbf{a}_3$ are the basis vectors.

Local order parameters

Local order parameters describe the state of each lattice site. They can be vectors in $R^d$ (e.g. atomic displacements, electric dipoles) or elements of SO(3) (e.g. fixed-magnitude magnetic moments, molecular orientations).

Global variables

Global variables describe global properties of the lattice. In OpenFerro, the default global variable is the global strain tensor in the Voigt notation: $\eta = (\eta_1, \eta_2, \eta_3, \eta_4, \eta_5, \eta_6)$.

Lattice Hamiltonian

A lattice Hamiltonian $E$, as a function of all local order parameters and all global variables, is an energy function defined on the crystalline system. It typically consists of terms like dipole-dipole interaction, dipole-strain interaction, elastic energy, etc. OpenFerro provides a flexible framework to construct lattice Hamiltonians by combining these energy terms. The energy terms are implemented as Python classes with a unified interface, making it easy to add new types of interactions.

Relevant materials:

• Ferroelectric materials: perovskites like BaTiO3, PbTiO3, etc.
• Magnetic materials: bcc iron, etc.
• Heterostructures
• ...

Simulate the dynamics

OpenFerro simulates dynamical evolution of local order parameters with molecular dynamics (MD) and Landau-Lifshitz-Gilbert (LLG) equations of motion. See the documentation for equations of motion used in NVE, NVT, NPT, and structure-optimization simulations. The isothermal condition is maintained by the second fluctuation-dissipation theorem.

Integrator

Supported integrators (see documentation for details):

• MD: Leapfrog (NVE), Mid-point Langevin (NVT, NPT, see J. Phys. Chem. A 2019, 123, 28, 6056-6079)
• LLG: Semi-implicit B (SIB) scheme (see J. Phys.: Condens. Matter 22 (2010) 176001)

Use OpenFerro

Overview

A schematic of OpenFerro is shown below. See documentation for introduction to core components of OpenFerro.

Quick start

See documentation for a quick start, where we cover both the basic usage and more advanced features.

Examples

See examples in examples.

Snapshot

Credits

There will be a paper in the near future explaining the technical details of OpenFerro. Before that, please cite this repository for any use of OpenFerro.

The initial development of OpenFerro is done by Pinchen Xie with support from LBNL.

Model configuration

At this point, only a few publicly available model configurations are provided in the model_configs directory. We welcome contributions from the community to add more model configurations.

Contributing

We welcome contributions from the community. Raise an issue or submit a pull request. Also feel free to contact pinchenxie@lbl.gov for any questions.