Chapter 1340 - Density Functional Method
Chapter 1340: Density Functional Method
Young’s modulus > 2.1TPa, breaking strength ≥ 80N/m…
Judging from the series of required parameters, Lu Zhou first thought of a rope with high tensile strength, then he thought of impact-resistant coatings used in automobiles or aerospace equipment.
As for where this material could be used…
There were a ton of uses.
It could be used as cables on the space station or as towing ropes for fixing heat sink and solar panels. It could be used as a suspension material for engineering equipment or as arresting gear on the deck of an aircraft carrier.
All of these uses could save a ton of money.
And these were just a few uses for this kind of material.
Lu Zhou believed that this kind of material with a high Young’s modulus and a high breaking strength could have countless applications that he never even would have thought of.
Back to research.
For the technical standards given by the system, the best option Lu Zhou could think of was to have a carbon-based material with high tensile strength, light in weight, and strong plasticity.
Such as carbon fiber and a series of graphite-derived reinforced composite materials.
This kind of material not only had a broad scope for development, but it was also his original field of research in computational materials science. When he started his research on computational materials, he started with carbon materials.
Therefore, for him, this task was not difficult at all.
It was as easy as a piece of cake!
After leaving Professor Wang Qingping’s laboratory, Lu Zhou did not stay at the Jinling Institute for Advanced Study. Instead, he went straight back to his home.
When modifying the mathematical model based on the experimental results, some ideas about computational materials research suddenly appeared in his mind.
Perhaps because of the fact that he had reached level 10 in both mathematics and physics, Lu Zhou found that his sensitivity to numbers and physical phenomena had reached a new level.
Even a clue that was so small that it was almost negligible was enlarged infinitely in his eyes; it turned into a key that he could see with his mind.
Regardless of where the inspiration came from, there was only one thought in his mind at this moment.
Which was to record this inspiration before it disappeared.
Lu Zhou went upstairs to the study room. After instructing Xiao Ai to make a cup of coffee for him, Lu Zhou sat at the desk and spread out the draft paper he brought back from the laboratory.
“According to material A synthesized in the experimental process designed by the model, a soft mass forms after deposition, and the diameter of the carbon nanotubes is extremely uneven…
“The reason for this result should be that the monomer acrylonitrile undergoes inadequate free radical polymerization, and a large amount of intermediate product is formed. This leads to the insufficient progress of the third-stage reaction… Then, the soft foamy mixture forms.
“Hmm, interesting.”
The soft foamy mixture wasn’t what Lu Zhou felt to be interesting; it was the phenomena he discovered when he revised the calculation model.
After thinking seriously for a while, he picked up his pen and wrote a line of text on a blank draft paper neatly.
[Implicit density functional method]
When Lu Zhou saw his inspiration form into words, he couldn’t help but smile.
Generally speaking, when a problem was clearly written down, it was already half-way to being solved.
At least for him!
The implicit functional density was a computational materials science method for the explicit functional density; it was a popular research area in the theoretical field of computational materials science.
As we all knew, the exchange-correlation energy function was an explicit function that was directly represented by an electron density function. And by using a Kohn-Sham orbital wave function as a direct variable representation, the function would become implicit.
The simplest implicit function was the Fock commutative energy function, which was often called the exact correlation function in the context of density functional theory.
For molecular systems, the use of implicit functionals could achieve an accuracy equivalent to the second-order multi-body perturbation theory, with a relatively small amount of calculation. Therefore, the implicit density functional method was widely regarded as a high potential computational materials science method.
However, although there were obvious advantages, its disadvantages were also obvious. For example, the accuracy was limited, as well as the inability to accurately describe van der Waals interactions, etc. This was crucial for the study of solid materials.
Therefore, the implicit density functional method had relatively few applications in the research of solid materials, and only some progress had been made in certain fields, despite the tremendous development in computing power.
So far, the implicit correlation functional method was based on the adiabatic correlation fluctuation and dissipation theorem that had attracted widespread attention in the academic community. This was widely regarded as a breakthrough in the research to overcome the shortcomings of implicit functional density.
However, the sizes of these functions were huge, and even the most powerful traditional computers would struggle with the huge amount of calculations. Thus the current research area was still stuck in the exploratory research of simple systems.
What Lu Zhou had to do at the moment was to extend this method from a simple system to complex carbon materials research!
Once this research was a success, it would be of great help to the entire research field of carbon composite materials. Its significance could even surpass the “Young’s modulus ≥ 2.1 TPa, breaking strength ≥ 80N/m” material itself!
The pen in his hand did not stop for one bit. After writing the title, Lu Zhou quickly went deep into the exploration of the proposition itself.
[According to the HK theorem, the ground state energy functional of the system can be expressed as: EG{P(r)}=E{P(r)}+∫V(r)ρ(r)dr…]
[The function E{P(r)} can be expressed as: E{P(r)}=T{ρ(r)}+1/2∫∫{ρ(r){ρ(r)drdr+Exc{ P(r)}…]
[…]
The lines of calculations flowed out under the pen tip, like a trickling stream, together with the burst of inspiration, and they formed into rivers and flowed into the sea!
All of his inspiration were manifested as numbers.
All of the materials forces and physical properties were included and abstracted into mathematical language by rigorous logic!
“Then, introduce Schrodinger equation…”
The pen by Lu Zhou’s fingertips was like a sharp dagger, piercing through the thick branches in the foggy forest.
Lu Zhou looked at the result on the paper. His pupils lit up, and his eyebrows finally loosened, showing a smile on his face.
There was still a long way to go.
However, his intuition on science told him that he was very close to the end!
Time slowly passed by.
The sun gradually moved across the sky.
The sky outside the windows turned completely dark; the street lights on both sides of the tree-lined path began to light up. Lu Zhou finally raised his head and let out a sigh of relief. He put down the pen from his hand.
“… The implicit density functional method also has broad prospects for the research of carbon composite materials. It is now much more applicable.
“At the same time, this can also be regarded as a breakthrough in extending the method from a simple system to a complex system.
“Although there is still room for further exploration behind this.
“But… let’s stop here for now.”
Lu Zhou smiled and put the pen in his hand aside.
The second he put down the pen, a line of light blue text appeared in front of his eyes.
Lu Zhou blinked, thinking it was an illusion.
However, the light blue text remained there…
[Congratulations, User, for mission completion!]