# Elasticity and piezoelectricity

### This page gives hints on how to compute elastic, piezoelectric and internal strain tensors from DFPT with the ABINIT package.

##### Copyright (C) 2016-2017 ABINIT group (MT)

Mentioned in help_features#6.

### Table of content:

- 1. Introduction.
- 2. Related lesson(s) of the tutorial.
- 3. Related input variables.
- 4. Selected input files.
- 5. References.

### 1. Introduction.

The DFPT theory to compute the elastic, piezoelectric and internal strain tensors is presented in [Hamann2005].

See the generalities about DFPT as well as the tutorial lesson_elastic. For the preliminary runs of ABINIT, see rfstrs, while for ANADDB, see elaflag for the elastic tensor, and piezoflag for the piezoelectric tensor.
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### 2. Related lesson(s) of the tutorial.

- The lesson on the elastic properties presents the computation with respect to the strain perturbation and its responses: elastic constants, piezoelectricity.
- Parallelism of response-function calculations. Additional information to use the DFPT in parallel.
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### 3. Related input variables.

Compulsory input variables:

... rfatpol [Response Function : ATomic POLarisation]
... rfdir [Response Function : DIRections]
... rfstrs [Response Function with respect to STRainS]

Basic input variables:

... elaflag@anaddb [ELAstic tensor FLAG]
... instrflag@anaddb [INternal STRain FLAG]
... piezoflag@anaddb [PIEZOelectric tensor FLAG]
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### 4. Selected input files.

WARNING : as of ABINITv8.6.x, the list of input files provided in the specific section of the topics Web pages is still to be reviewed/tuned. In some cases, it will be adequate, and in other cases, it might be incomplete, or perhaps even useless.
The user can find some related example input files in the ABINIT package in the directory /tests, or on the Web:

tests/v4/Input: t68.in t70.in t83.in

tests/v7/Input: t95.in t96.in
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### 5. References.

[Hamann2005] D. R. Hamann, X. Wu, K. M. Rabe and D. Vanderbilt, "Metric tensor formulation of strain in density-functional perturbation theory", Phys. Rev. B 71, 035117 (2005).

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