relax_dynamic calculation style
Lucas M. Hale, lucas.hale@nist.gov, Materials Science and Engineering Division, NIST.
Introduction
The relax_dynamic calculation style dynamically relaxes an atomic configuration for a specified number of timesteps. Upon completion, the mean, \(\langle X \rangle\), and standard deviation, \(\sigma_X\), of all thermo properties, \(X\), are computed for a specified range of times. This method is meant to measure equilibrium properties of bulk materials, both at zero K and at various temperatures.
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: Setup and parameter definition streamlined.
2022-03-11: Notebook updated to reflect version 0.11. Restart capability added in.
Additional dependencies
Disclaimers
The calculation reports the standard deviation, \(\sigma_X\) of the measured properties not the standard error of the mean, \(\sigma_{\langle X \rangle}\). The two are related to each other according to \(\sigma_{\langle X \rangle} = \sigma_X \sqrt{\frac{C}{N}}\), where \(N\) is the number of samples taken of \(X\), and \(C\) is a statistical inefficiency due to the autocorrelation of the measurements with time. Obtaining a proper estimate of \(\sigma_{\langle X \rangle}\) requires either estimating \(C\) from the raw thermo data (not done here), or only taking measurements sporadically to ensure the samples are independent.
Good (low error) results requires running large simulations for a long time. The reasons for this are:
Systems have to be large enough to avoid issues with fluctuations across the periodic boundaries.
Runs must first let the systems equilibrate before meaningful measurements can be taken.
The standard deviation, \(\sigma\), of thermo properties is proportional to the number of atoms, \(N_a\) as \(\sigma \propto \frac{1}{\sqrt{N_a}}\).
The standard error, \(\sigma_x\) of thermo properties is proportional to the number of samples taken, \(N\) as \(\sigma_x \propto \frac{1}{\sqrt{N}}\).
Method and Theory
An initial system (and corresponding unit cell system) is supplied with box dimensions, \(a_i^0\), close to the equilibrium values. A LAMMPS simulation then integrates the atomic positions and velocities for a specified number of timesteps.
The calculation script allows for the use of different integration methods:
nve integrates atomic positions without changing box dimensions or the system’s total energy.
npt integrates atomic positions and applies Nose-Hoover style thermostat and barostat (equilibriate to specified T and P).
nvt integrates atomic positions and applies Nose-Hoover style thermostat (equilibriate to specified T).
nph integrates atomic positions and applies Nose-Hoover style barostat (equilibriate to specified P).
nve+l integrates atomic positions and applies Langevin style thermostat (equilibriate to specified T).
nph+l integrates atomic positions and applies Nose-Hoover style barostat and Langevin style thermostat (equilibriate to specified T and P).
Notes on the different control schemes:
The Nose-Hoover barostat works by rescaling the box dimensions according to the measured system pressures.
The Nose-Hoover thermostat works by rescaling the atomic velocities according to the measured system temperature (kinetic energy). Cannot be used with a temperature of 0 K.
The Langevin thermostat works by modifying the forces on all atoms with both a dampener and a random temperature dependent fluctuation. Used at 0 K, only the force dampener is applied.
Notes on run parameter values. The proper time to reach equilibrium (equilsteps), and sample frequency to ensure uncorrelated measurements (thermosteps) is simulation dependent. They can be influenced by the potential, timestep size, crystal structure, integration method, presence of defects, etc. The default values of equilsteps = 20,000 and thermosteps = 100 are based on general rule-of-thumb estimates for bulk crystals and EAM potentials, and may or may not be adequate.