relax_liquid calculation style
Lucas M. Hale, lucas.hale@nist.gov, Materials Science and Engineering Division, NIST.
Introduction
The relax_liquid calculation style is designed to generate and characterize a liquid phase configuration for an atomic potential based on an initial configuration, target temperature and target pressure. The calculation involves multiple stages of relaxation and computes the mean squared displacement and radial distribution functions on the final liquid.
Version notes
2022-10-12: Calculation created
Additional dependencies
Disclaimers
No active checks are performed by this calculation to ensure that the system is liquid. Be sure to check the final atomic configurations. The thermo output can also provide a rough guideline in that you should see convergence of volume but not of the individual lx, ly, lz dimensions for a liquid phase.
If starting with a crystalline configuration, be sure to use an adequately high melt temperature and number of melt steps.
The temperature and volume equilibrium stages are designed to get the final nve system close to the target temperature and pressure, but they will not be exact. Be sure to check that the measured temperature and pressure are close to the targets.
Method and Theory
This performs five stages of simulations to create and analyze a liquid phase at a given temperature and pressure.
A “melt” stage is performed using npt at the target pressure and an elevated melt temperature.
A “cooling” stage is performed using npt in which the temperature is linearly reduced from the melt to the target temperature.
A “volume equilibrium” stage is performed using npt at the target temperature and pressure. Following the run, the system’s dimensions are equally scaled to the average volume.
A “temperature equilibrium” stage is performed using nvt at the target temperature. Following the run, the atomic velocities are scaled based on the expected total energy at the target temperature.
An “nve analysis” stage is performed in which the mean squared displacements of the atoms and the radial distribution function are measured.
Melt stage
The melt stage subjects the initial configuration to an npt simulation at the elevated melt temperature. This stage is meant to transform initially crystalline system configurations into amorphous liquid phases. As such, the melt temperature should be much higher than the melting temperature of the initial crystal, and the number of MD steps during this stage should be sufficiently high to allow for the phase transformation to occur.
If the initial atomic configuration is already amorphous, this stage can be skipped by setting meltsteps = 0. Also, if the initial configuration already has velocities assigned to the atoms, you can use those velocities by setting createvelocities = False. These two options make it possible to run a single melt simulation that can be used as the basis for all target temperatures. Note that createvelocities = True is needed if you want to measure statistical error from multiple runs.
Cooling stage
The cooling stage runs npt and linearly scales the temperature from the melt temperature to the target temperature. The larger the number of coolsteps, the more gradual the change from melt to target temperatures will be. This can be important if the target temperature is much smaller than the melt temperature.
Similarly to the melt stage, this stage can be skipped by setting coolsteps = 0. If meltsteps = coolsteps = 0 and createvelocities = True, the atomic velocities will be created for the system at the target temperature rather than the melt temperature. This allows for a generic amorphous state to be used as the starting configuration.
Volume equilibration stage
The volume equilibration stage runs npt at the target temperature and pressure. It is meant to allow for the system to equilibrate at the target temperature, then to obtain a time-averaged measurement of the system’s volume. The average volume is computed from a specified number of samples (volrelaxsamples) taken every 100 timesteps from the end of this stage. The max value allowed for volrelaxsamples is volrelaxsteps / 100, but practically it should be noticeably smaller than this to ignore measurements at the beginning of the stage where the system has not yet equilibrated.
When this stage finishes, the volume of the configuration cell is adjusted to the average volume computed by scaling each box length and tilt by the same factor, s
Temperature equilibration stage
The temperature equilibration stage runs nvt at the target temperature for the system fixed at the computed average volume. This allows for the system to equilibrate at the fixed volume and target temperature, and to compute a target total energy, \(E_{target}\), that corresponds to the system in equilibrium at the target temperature. \(E_{target}\) is computed based on time-averaged energy values from a specified number of samples (temprelaxsamples) taken every 100 timesteps from the end of this stage. The max value allowed for temprelaxsamples is temprelaxsteps / 100. Unlike the previous stage, the equilibration portion of this stage is likely negligible, therefore it is less important to ignore the initial measurements.
In LAMMPS, the adjustment is made by scaling all atomic velocities to a temperature \(T_s\) such that the current potential energy, \(E_{pot}\), plus the kinetic energy for \(T_s\) equals \(E_{target}\)
Two alternate methods for computing \(E_{target}\) are implemented and can be accessed with the temprelaxstyle option.
For temprelaxstyle = ‘te’, the target total energy is taken as the computed mean total energy
For temprelaxstyle = ‘pe’, the target total energy is taken as the computed mean potential energy plus kinetic energy for the target temperature, \(T\)
Limited tests show the two methods to result in mean temperatures in the final stage that have roughly the same variation from the target temperature, with ‘pe’ style giving slightly better results. As such, both methods are included as options and ‘pe’ is set as the default.
Analysis stage
The analysis stage runs nve with the system that has been adjusted to the target volume and total energy from the last two stages. During this stage, mean squared displacements and radial distribution function calculations are performed that can be used to analyze the liquid phase at the target temperature and pressure.
In addition to the analysis calculations, the average measured temperature and pressure are reported, which can be used as verification that the volume and temperature equilibration stages and adjustments worked properly.