This projects illustrates the use of LAMMPS for simulation of elastic constant of Si (diamond lattice) at absolute zero temperature.

Elastic constants characterize the stiffness of a material. The formal definition is provided by the linear relation that holds between the stress and strain tensors in the limit of infinitesimal deformation. In tensor notation, this is expressed as s_ij = C_ijkl * e_kl, where the repeated indices imply summation. s_ij are the elements of the symmetric stress tensor. e_kl are the elements of the symmetric strain tensor. C_ijkl are the elements of the fourth rank tensor of elastic constants. In three dimensions, this tensor has 3^4=81 elements. Using Voigt notation, the tensor can be written as a 6x6 matrix, where C_ij is now the derivative of s_i w.r.t. e_j. Because s_i is itself a derivative w.r.t. e_i, it follows that C_ij is also symmetric, with at most 7*6/2 = 21 distinct elements.

At zero temperature, it is easy to estimate these derivatives by deforming the simulation box in one of the six directions using the *change_box* command and measuring the change in the stress tensor. A general-purpose script that does this is given in the examples/elastic directory described in *this section*.

## Model New Results

## Software Used

### LAMMPS

LAMMPS is a classical molecular dynamics code, and an acronym for Large-scale Atomic/Molecular Massively Parallel Simulator.

LAMMPS has potentials for solid-state materials (metals, semiconductors) and soft matter (biomolecules, polymers) and coarse-grained or mesoscopic systems. It can be used to model atoms or, more generically, as a parallel particle simulator at the atomic, meso, or continuum scale.

LAMMPS runs on single processors or in parallel using message-passing techniques and a spatial-decomposition of the simulation domain. Many of its models have versions that provide accelerated performance on CPUs, GPUs, and Intel Xeon Phis.

### Using LAMMPS on Kogence

## Using LAMMPS on Kogence

You can either fork and modify an existing LAMMPS public project or alternatively you can also start from scratch and create a new LAMMPS project.

- In order to fork an existing project
- Make sure you fist click "Copy" button to create a personal copy to modify.
- Then click Settings -> Machine to choose a machine and
- Click Settings -> Software and choose LAMMPS from the dropdown menu. In the empty text box, type the name of the input script.

- In order to create a new project from scratch
- Click on Model Library -> My Models
- Click on + button on top left corner. Provide name and short description for your new project.
- Click on + button again in the next project screen and either create or upload an existing LAMMPS input file.
- Click Settings -> Software and choose LAMMPS from the dropdown menu. In the empty text box, type the name of the input script.

- Access to command terminal with installed LAMPPS environment
- Click Settings -> Software and choose LAMMPS from the dropdown menu. In the empty text box, type "xterm" (without quotes).

To see detailed step-by-step instructions on how to use LAMMPS on Kogence free cloud supercomputing platform [click here].

## LAMMPS Versions on Kogence

- 11 Aug, 2017 (runs with only MPI threads and no openMP threads even on single node)
- 31 Mar, 2017 (runs with openMP threads on single node)

For more details see LAMMPS .

## Related Models

Following are some related models available for cloning/copying by anyone: