This discussion focuses on the impact of strain on on-site energy in materials, particularly in the context of quantum mechanics and 2D materials. It establishes that strain affects the energy of individual atoms in a lattice, which can be analyzed using Density Functional Theory (DFT). The conversation highlights the importance of modeling the lattice with matched boundary conditions and optimizing atomic positions to determine site energy. Additionally, it mentions work hardening and annealing as relevant concepts in understanding internal energy in materials.
PREREQUISITESResearchers in material science, quantum physicists, and engineers focused on the mechanical properties of materials, particularly those working with 2D materials and atomic-scale energy calculations.
Thank youBaluncore said:I guess by “on-site energy”, you mean “internal energy”?
As stress increases, the strain increases, and energy is stored in the elastic material.
There is a yield point, where the stress is partially relieved by plastic deformation.
If the stress is then removed the elastic strain will be reduced, but there will be some energy remaining in plastic strain where adjacent grains in the material have undergone different plastic deformation.
“Work hardening” is associated with remaining internal energy.
https://en.wikipedia.org/wiki/Work_hardening
“Annealing” can relieve the remaining internal energy.
The internal energy that remains will depend on the state of the grains within the material.
What is that material and what do you know about the internal grain structure?
Yes this problem is related to the Quantum mechanic and is about 2D materials.Baluncore said:OK, so my mind reading skills are sadly lacking.
What sort of strain are you referring to here ?
Is this Quantum Theory, or strength of materials ?
If you actually specify the subject, you may get a better answer.
Thank you so much.crashcat said:If I understand what you are asking, the answer is yes. Strain will affect the energy of an individual atom in the lattice. There is no simple formula I know of, it has to be solved with DFT. The typical method is to model the lattice with matched boundary conditions, but your unit cell is actually several unit cells large. You allow the atomic positions to migrate to the lowest energy position. Then take your optimized lattice and model again with one atom popped out, without allowing atoms to migrate. The difference is the "site energy" you're looking for. When you do this kind of modeling, you'll see it converge to a value as you increase the number of unit cells, i.e. 3x3 then 4x4 then 5x5. It doesn't take much to get rid of edge effects.
Hi @crashcat , can you provide an example of this from the literature? Whenever I see strain treated via tight binding, I only ever see it entering in the hopping Hamiltonian, rather than the on-site Hamiltonian (example: https://arxiv.org/abs/1511.06254).crashcat said:If I understand what you are asking, the answer is yes. Strain will affect the energy of an individual atom in the lattice. There is no simple formula I know of, it has to be solved with DFT. The typical method is to model the lattice with matched boundary conditions, but your unit cell is actually several unit cells large. You allow the atomic positions to migrate to the lowest energy position. Then take your optimized lattice and model again with one atom popped out, without allowing atoms to migrate. The difference is the "site energy" you're looking for. When you do this kind of modeling, you'll see it converge to a value as you increase the number of unit cells, i.e. 3x3 then 4x4 then 5x5. It doesn't take much to get rid of edge effects.