Query Regarding Temporal Variation of Mean Square Displacement

[amithac]

Hello,

This is not a question strictly related to LAMMPS but I am open to any inputs. I am using LAMMPS version dated 23 June 2022 to plot the temporal variation of mean squared displacement (MSD) at three temperatures (500, 600, and 700 K) for the iodine ion in an ABI3 crystal (A and B are metal ions). The domain comprises of approximately 1000 atoms with 12 iodine vacancies. The input code is as follows:

Initialization

read_restart

Potential Parameters

pair_style buck/coul/long 12
kspace_style pppm 1e-5
List of Pair Coeffs

Simulation Specifics

timestep 1e-3 # in PICOSECONDS
neigh_modify every 5 delay 0 check yes
restart 500000 restart.perov
group iodine type 2
fix 1 all npt temp 700 700 0.01 aniso 0 0 1
compute m iodine msd com yes average no
fix sq_disp iodine ave/time 200 1 200 c_m[*] file dump.msd
thermo 200
run 10000000

The temporal variation of MSD at the three temperatures is obtained as shown below:

While the MSD at 600K and 700K have a linear temporal variation, the MSD at 500 K shows a stepped variation instead of a smooth linear variation (A magnified image is shown below).

What can be the possible reason for this change in behaviour at lower temperatures? Any suggestions would be helpful. Could it be due to insufficient domain size?

Thanks!

[srtee]

When a crystal is cold enough that, on average, only zero or one particles are hopping between sites at any given time, how will the MSD change over time?

When a crystal is hot enough that, on average, a dozen or more particles are hopping between sites at any given time, how will the MSD change over time?

[amithac]

Thanks for your inputs. I also wondered if it is the very low hopping rate at low temperatures that causes the stepped variation in MSD. However, I was also confused by the fact that another study recorded a linear variation in MSD at 500 K in the same material with just two iodine vacancies (see image below). Obviously, the interatomic potential used in this study, which is different from mine, can significantly influence results and thus can explain the difference in results. Even so, I was wondering if there are other factors that may be influencing my results. Thanks for your time!

Source: https://doi.org/10.1021/acs.jpclett.1c01192