Second tutorial on aTDEP¶

INP SIMaP

The 3 $^{rd}$ and 4 $^{th}$ order effective Interatomic Force Constants (IFC)¶

This tutorial shows how to build an anharmonic Temperature Dependent Effective Potential (TDEP) using the ABINIT package

In practice, this means to obtain the $3^{rd}$ and 4 $^{th}$ order effective IFC. Many quantities (Gr"uneisen parameter, thermal expansion…) can be derived therefrom.

You will learn:

how to launch aTDEP just after an ABINIT simulation,
the meaning and effects of the main input variables, and
how to exploit the data provided in the output files.

You are supposed to have performed the 1 $^{st}$ aTDEP tutorial and strongly encouraged to read the following documents:

User guide: aTDEP guide
Theory: aTDEP paper corresponding to the article [Bottin2020]

This tutorial should take about 1.5 hour.

Note

Supposing you made your own installation of ABINIT, the input files to run the examples are in the ~abinit/tests/ directory where ~abinit is the absolute path of the abinit top-level directory. If you have NOT made your own install, ask your system administrator where to find the package, especially the executable and test files.

In case you work on your own PC or workstation, to make things easier, we suggest you define some handy environment variables by executing the following lines in the terminal:

export ABI_HOME=Replace_with_absolute_path_to_abinit_top_level_dir # Change this line
export PATH=$ABI_HOME/src/98_main/:$PATH      # Do not change this line: path to executable
export ABI_TESTS=$ABI_HOME/tests/             # Do not change this line: path to tests dir
export ABI_PSPDIR=$ABI_TESTS/Psps_for_tests/  # Do not change this line: path to pseudos dir

Examples in this tutorial use these shell variables: copy and paste the code snippets into the terminal (remember to set ABI_HOME first!) or, alternatively, source the set_abienv.sh script located in the ~abinit directory:

source ~abinit/set_abienv.sh

The ‘export PATH’ line adds the directory containing the executables to your PATH so that you can invoke the code by simply typing abinit in the terminal instead of providing the absolute path.

To execute the tutorials, create a working directory (Work*) and copy there the input files of the lesson.

Most of the tutorials do not rely on parallelism (except specific tutorials on parallelism). However you can run most of the tutorial examples in parallel with MPI, see the topic on parallelism.

1. Summary of the aTDEP method¶

In the previous tutorial, we have considered that the potential energy of a crystal can be rewritten using a Taylor expansion around the equilibrium. If this expansion is truncated at the 4 $^{th}$ order, we obtain: $$ U= U_0 + \sum_{p\ge 1}^4 \frac{1}{p !} \sum_{\substack{\alpha_1…\alpha_p \ i_1…i_p}}\overset{(p)}{\Theta}\vphantom{\Theta}{i_1…i_p}^{{\alpha_1…\alpha_p}\prod_{k=1}}p u^{\alpha_k} $$

In the same way as previously, it is then possible to obtain the 3 $^{rd}$ and 4 $^{th}$ order effective IFC $\overset{(3)}{\Theta}\vphantom{\Theta}$ and $\overset{(4)}{\Theta}\vphantom{\Theta}$ by using a least squares method. These effective IFC are no longer constant and become temperature dependent by taking into account in an effective way all the terms neglected (above the truncation). The anharmonicity comes from both the presence of 3 $^{rd}$ and 4 $^{th}$ order effective IFC and their temperature dependancy.

2. Negative thermal expansion : Si-d¶

This calculation is similar to the one performed in the following article [Bottin2020].

2.0 NetCDF input files¶

2.1 Convergence with respect to Rcut¶

2.2 Etot/FcatMDvsTDEP¶

2.3 The mode Gr"uneisen parameters and the thermal expansion¶

2.4 Another question?¶

3. Temperature effect on the Gr"uneisen parameters : MgO.¶

This calculation is similar to the one performed in the following article [Bouchet2019].

3.1 Convergence with respect to Rcut¶

3.2 The LO-TO splitting¶

3.3 Another question?¶

4. Description of an alloy : UMo- $\gamma$ ¶

This calculation is similar to the one performed in the following article [Castellano2020].

4.1 Convergence with respect to Rcut¶

4.2 The VCA and the SIFC approaches¶

4.3 Another question?¶

5. HOWTO use `qtdep` ?¶

Harmonic Potential