This is a 2D numerical simulation of atoms based purely on their mutual attraction and their repulsion as their electron cloud overlaps each-other in a zero-gravity environment. The main idea is to demonstrate a (solid) material's behaviour on an atomic level under deformation.
This simulation is designed with a situation where a mentor/instructor is guiding the learner in mind.
This simulation started life as a small javascript script based on the work of Daniel V. Schroeder's (Weber State University) MD simulation, which was published in the American Journal of Physics 83 (3), 210-218 (2015), arXiv: 1502.06169 [physics.ed-ph] and the accompany javascript applet posted at: https://physics.weber.edu/schroeder/md/ . Modifications were made in order to demonstrate the effect of deformation on a solid material.
Atom Generation
Click any where within the red shaded area to add a cluster of atoms, the number of atoms to generate per click can be chosen under the
'Atoms Generation' menu
OR
A large number of atoms can be generated at random locations by using the
Large Scale Random Atom Gen. method
OR
A closed packed 2-D lattice can be generated for any given number of rows and columns by using the
Large Scale Lattice Atom Gen. method.
Click Mode
What happens when the mouse clicks on the canvas can be chosen using the
Click Mode. The default setting is to
add atoms.
Increase atom size and
Decrease atom size allows the atom underneath the pointer to change its radius. This allows for the changing one atom to become a substitutional solute of various size. You can click an atom multiple times to further change its size though there are limits to the available sizes
Remove atom allows the atom underneath the pointer to be removed. This allows for creating a vacancy.
Applying Load
The
loading control panel allows for a load to be applied by the white bar onto the atoms.
The default
loading intensity is 5. This is an arbitrary scale. Note that this force is applied for every timestep (which occurs about 15 times every frame). If you change this value, you must re-click the loading function for it to take into effect.
Note that the higher this value, the higher the load as well as the higher the strain rate.
Speed Factor
On the
Simulation Control panel, there is an option to change the
speed factor. This factor is scale factor to slow down the atoms. This sort of slowing down is a way to simulate a temperature change, more specifically to get the temperature down to below the solidification temperature.
This is a bit iffy, and does not represent temperature that well (see notes on how this simulation work).
The atomic forces are based on the
Lennard-Jones (L-J) potential
which brings about certain limitations in our work. The Lennard-Jones potential is a relatively simple model that is more fitted for approximating van der Waal forces, i.e. secondary bonds, but can be adjusted to somewhat approximate the behaviour of a solid material.
In general, the forces of each atom have to be determined against every other atoms on the field which can be especially taxing on the computer when the number of atoms is high. In an attempt to alleviate this, a spatial partitioning system is in place. That is, the field is divided into a grid where the interactions are only calculated for pair of atoms found within the same cell and the neighbouring cells.
One of the major objectives of this simulation is to help learners to visualize defects and their importance. To make this visualization easier, a color system based on the "energy level" of each individual atom. It is important to note that this is not based on a quantitative energy level that can be calculated, rather a pseudo-scale to make understanding easier.
The lowest energy on this pseudo-scale, i.e. the "ground-state", for an atom is defined to be the scenario where it is surrounded by six other atoms all of which are located a distance equal to the equilibrium distances described by the L-J potential function. The colour scale illustrates the deviation from this state, either due to the surrounding atoms being too far/near or due to having more/less than the ideal six atoms configuration.
Considering the nature of defects in a crystalline solid where the atoms are often displaced from their equilibrium so they will “light up” in a lighter cyan.
For e.g.: the vacancy near the top, both of the smaller and larger substitutional atoms near the center and bottom respectively, and lastly the free surfaces in the picture below.
Dislocations (specifically edge dislocation) will also light up though it is a little different from how we typically see them in textbook. For example, there are two dislocations in the picture below.
This looks vastly different from the textbook treatment of this. For one, textbook tends to use a simple cubic system in their illustration, this simulation on the other hand is of a closed pack plane of a face centered cubic (FCC) or hexagonal closed pack (HCP) system. For your convenience, a set of the closed pack planes are highlighted in the following picture; notice the extra half plane that exist around each of the dislocations. Note the slip plane is at an angle to the closed packed plane highlighted in the picture.
The second difficulty is that the dislocation are almost always moving, due to the nature of the weak attraction in the L-J potential, so they may cause a “trail” (like a comet) of cyan in this similar. A snapshot of such a trail is shown below: This picture to the right is of a dislocation transitioning from one position to the next and does not show multiple dislocations moving together. If you don’t believe it, count the atomic planes involved.
This picture to the right is of a dislocation transitioning from one position to the next and does not show multiple dislocations moving together. If you don’t believe it, count the atomic planes involved.
The use of L-J potential for simulated a solid is dubious at best when accuracy and realistic behaviour is required, but it is good-enough for a simple simulation for visualization purposes albeit with limitations.
For one, tensile loading does not work well under this potential. The atomic attraction is too weak to properly simulate the Poisson’s effect during tensile loading. The second issue is the lack of consideration of surface energy which is also necessary for better approximation of the Poisson’s effect.
The tensile loading in this simulation somewhat works by applying an extra “gravity” force toward the centerline along the vertical in an attempt to mimic the Poisson’s effect in tension. Clearly, this will not work well if the atoms are gathered around the centerline.
However, the Poisson’s effect in compression is fine since atoms will not push into each other under this potential. As a result, atoms are pushed out to increase the width of the solid which sufficiently mimics the Poisson’s effect in compression.
Due to the nature of the weak attraction in the L-J potential, the solids will behave similar to when it is at a relatively high homologous temperature. Unfortunately, there is no quick fix for this without bogging down the simulation.
The atomic forces are based on the
Lennard-Jones (L-J) potential
which brings about certain limitations in our work. The Lennard-Jones potential is a relatively simple model that is more fitted for approximating van der Waal forces, i.e. secondary bonds, but can be adjusted to somewhat approximate the behaviour of a solid material.
In general, the forces of each atom have to be determined against every other atoms on the field which can be especially taxing on the computer when the number of atoms is high. In an attempt to alleviate this, a spatial partitioning system is in place. That is, the field is divided into a grid where the interactions are only calculated for pair of atoms found within the same cell and the neighbouring cells.
