# Elastic Calculation and dipole tensor calculation using VASP

I am a beginner in learning DFT calculation with VASP. I have just done a relaxation calculation. I want to learn calculating two properties of materials, using VASP. One is the elastic properties (elastic constants, stress strain relation etc), and the other is calculating the dipole tensor. I am currently considering silicon as a test material.

Can anyone suggest me how to calculate the elastic properties in VASP? Also it would be great to know how to calculate the dipole tensor (provided that we have $$P_{ij}=-V_{cell}\sigma_{ij}$$, where $$V_{cell}$$ is the volume of the simulation cell, $$\sigma_{ij}$$ is the difference bteween the average macroscopic stress in the cell, and $$P_{ij}$$ is the dipole tensor)?

A step by step suggestion would be greatly appreciated.

Any resource link, python file etc (along with the steps for a beginner) would be very helpful.

We already have lot of discussion on calculations of elastic constants using stress-strain relationship or energy-strain relationship

For calculating elastic-dipole tensor there is two major general procedure can be adopted

1. Fixed cell method

Insert a defect such as self interstitial atom in your simulation cell and allow atoms to relax with fix dimension of unit cell. Calculate the average stress on unit cell (in VASP : grep 'in kB' OUTCAR). The dipole tensor can be calculated as:

$$P_{ij} = \int_{V_{cell}} \sigma dV$$ = -$$V_{cell}\langle\sigma\rangle$$

2. Applied strain

Relax the simulation box fully (both atomic position and cell vectors) such that macroscopic stress $$\langle\sigma\rangle$$ vanishes. This as same effect as application of external strain on unrelaxed system. One can even calculate equivalent applied strain from relaxed configuration

$$P_{ij} = -V_{cell}(C_{ijkl}\epsilon_{kl}^{ext}-\langle\sigma\rangle)$$

Reference