# How can I calculate the lattice parameter for building Argon atoms using LAMMPS?

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In summary: The reference [1] states that the usual formula for the mean free path is given by\ell = \frac {k_{\text{B}}T}{{\sqrt {2}}\pi d^{2}p}where ##k_B## is the Boltzmann constant. Comparing this with your equation it seems that ##n_0=\frac{p}{k_B T}=\frac{N}{V}##. However, this number density is not the mass density of Argon, which is 1.6 ##kg \over {m^3}##.
TL;DR Summary
I try to model Poiseuille flow of Argon gas confined between two parallel Platinum plates. However, I am not able to obtain the density of Ar at the end of my simulation. So, probably, I am doing something wrong and I need help to calculate lattice parameter.
Hello everyone. I am newbie at MD. I started with Poiseuille flow.

I try to model 3D Poiseuille flow of Argon gas confined between two parallel Platinum plates by using LAMMPS. I have one reference paper, as given in [1] below. I built my Platinum structure correctly and I placed Ar atoms and run my simulation. At the end of simulation, I checked the density and it was totally wrong. I suspect that, I am not able to build sufficient number of atoms in my model. I try to use equations given below to obtain number of atoms but I couldn't decide the number of Ar atoms in my model, still. So, I need your help.

In the paper, they obtain the number of atoms by using Knudsen number. So, from the definition of Knudsen,

$$Kn = {\lambda \over D}$$

and

$$\lambda = {1 \over \sqrt{2} \Pi d^2 {n_0}}$$

where ## {n_0} ## is bulk number density. The two things that I know are D, which is 103 Angstrom and the bulk density of Argon, which is 1.6 ## kg \over {m^3} ## .

I want to build Ar atoms using lattice fcc command of Lammps and for that, I need lattice parameter. How can I calculate it and match the number of atoms that I expect and that I get from Lammps?

I would be very happy if you can help me which means a lot for me as I am stuck at this point.

Thanks for your help, indeed.The reference that I use:

[1] https://doi.org/10.1080/15567265.2016.1215364

Last edited:
Usual formula for mean free path is
$${\displaystyle \ell ={\frac {k_{\text{B}}T}{{\sqrt {2}}\pi d^{2}p}},}$$
where ##k_B## is the Boltzmann constant. Comparing it with your fomula it seems
$$n_0=\frac{p}{k_B T}=\frac{N}{V}$$
Does it meet your "bulk density" though its dimension is ##L^{-3}## number density not ##ML^{-3}## mass density?

Last edited:

## 1. How do I determine the lattice parameter for building Argon atoms?

The lattice parameter for building Argon atoms can be determined by using the LAMMPS software, which is a molecular dynamics simulation tool. The lattice parameter is defined as the distance between identical atoms in a crystal structure. In LAMMPS, the lattice parameter can be calculated by running a simulation with a specified number of Argon atoms and using the lattice command to define the lattice type and spacing.

## 2. What is the importance of calculating the lattice parameter for Argon atoms?

Calculating the lattice parameter for Argon atoms is important because it provides information about the structure and stability of the material. It can also be used to study the mechanical and thermal properties of the material, such as its melting point and elastic modulus.

## 3. Can the lattice parameter be calculated for different types of Argon atoms?

Yes, the lattice parameter can be calculated for different types of Argon atoms, such as isotopes or ions. This can be done by specifying the mass and charge of the atoms in the LAMMPS simulation.

## 4. How does the lattice parameter affect the behavior of Argon atoms?

The lattice parameter can affect the behavior of Argon atoms in several ways. For example, a smaller lattice parameter may result in a denser and more stable crystal structure, while a larger lattice parameter may lead to a more disordered and less stable structure. Additionally, the lattice parameter can affect the thermal expansion and mechanical properties of the material.

## 5. Are there any limitations to calculating the lattice parameter for Argon atoms using LAMMPS?

Yes, there are some limitations to using LAMMPS to calculate the lattice parameter for Argon atoms. These include the accuracy of the interatomic potential used in the simulation and the size of the simulation cell, which may not accurately represent the behavior of a bulk material. It is important to validate the results obtained from LAMMPS with experimental data or other simulation methods.

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