surface_energy_static calculation style

Lucas M. Hale, lucas.hale@nist.gov, Materials Science and Engineering Division, NIST.

Introduction

The surface_energy_static calculation style evaluates the formation energy for a free surface by slicing an atomic system along a specific plane.

Version notes

  • 2018-07-09: Notebook added.

  • 2019-07-30: Description updated and small changes due to iprPy version.

  • 2020-05-22: Version 0.10 update - potentials now loaded from database.

  • 2020-09-22: Calculation updated to use atomman.defect.FreeSurface class. Setup and parameter definition streamlined.

  • 2022-03-11: Notebook updated to reflect version 0.11.

Additional dependencies

Disclaimers

  • NIST disclaimers

  • Other atomic configurations at the free surface for certain planar cuts may have lower energies. The atomic relaxation will find a local minimum, which may not be the global minimum. Additionally, the material cut is planar perfect and therefore does not explore the effects of atomic roughness.

Method and Theory

First, an initial system is generated. This is accomplished by

  1. Starting with a unit cell system.

  2. Generating a transformed system by rotating the unit cell such that the new system’s box vectors correspond to crystallographic directions, and filled in with atoms to remain a perfect bulk cell when the three boundaries are periodic.

  3. All atoms are shifted by a fractional amount of the box vectors if needed.

  4. A supercell system is constructed by combining multiple replicas of the transformed system.

Two LAMMPS simulations are then performed that apply an energy/force minimization on the system, and the total energy of the system after relaxing is measured, \(E_{total}\). In the first simulation, all of the box’s directions are kept periodic (ppp), while in the second simulation two are periodic and one is non-periodic (ppm). This effectively slices the system along the boundary plane creating two free surfaces, each with surface area

\[A = \left| \vec{a_1} \times \vec{a_2} \right|,\]

where \(\vec{a_1}\) and \(\vec{a_2}\) are the two lattice vectors corresponding to the periodic in-plane directions.

The formation energy of the free surface, \(E_{f}^{surf}\), is computed in units of energy over area as

\[E_{f}^{surf} = \frac{E_{total}^{surf} - E_{total}^{0}} {2 A}.\]

The calculation method allows for the specification of which of the three box dimensions the cut is made along. If not specified, the default behavior is to make the \(\vec{c}\) vector direction non-periodic. This choice is due to the limitations of how LAMMPS defines triclinic boxes. \(\vec{c}\) vector is the only box vector that is allowed to have a component in the Cartesian z direction. Because of this, the other two box vectors are normal to the z-axis and therefore will be in the cut plane.