mirror of https://github.com/abinit/abinit.git
78 lines
3.0 KiB
Markdown
78 lines
3.0 KiB
Markdown
---
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authors: FB & JB
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---
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# Second tutorial on aTDEP
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## The 3$^{rd}$ and 4$^{th}$ order **effective** Interatomic Force Constants (IFC)
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This tutorial shows how to build an anharmonic **Temperature Dependent Effective Potential** (TDEP) using the ABINIT package
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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.
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You will learn:
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1. how to launch aTDEP just after an ABINIT simulation,
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2. the meaning and effects of the main input variables, and
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3. how to exploit the data provided in the output files.
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You are supposed to have performed the [1$^{st}$ aTDEP tutorial](/tutorial/atdep1) and strongly encouraged to read the following documents:
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* User guide: [[pdf:aTDEP_Guide| aTDEP guide]]
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* Theory: [[pdf:aTDEP_Paper|aTDEP paper]] corresponding to the article [[cite:Bottin2020]]
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This tutorial should take about 1.5 hour.
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[TUTORIAL_README]
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## 1. Summary of the aTDEP method
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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:
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$$
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U= U_0 +
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\sum_{p\ge 1}^4 \frac{1}{p\ !} \sum_{\substack{\alpha_1...\alpha_p \\ i_1...i_p}}\overset{(p)}{\Theta}\vphantom{\Theta}_{i_1...i_p}^{\alpha_1...\alpha_p}\prod_{k=1}^p
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u_{i_k}^{\alpha_k}
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$$
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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.
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## 2. Negative thermal expansion : Si-d
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This calculation is similar to the one performed in the following article [[cite:Bottin2020]].
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### 2.0 NetCDF input files
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### 2.1 Convergence with respect to Rcut
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### 2.2 Etot/FcatMDvsTDEP
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### 2.3 The mode Gr\"uneisen parameters and the thermal expansion
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### 2.4 Another question?
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## 3. Temperature effect on the Gr\"uneisen parameters : MgO.
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This calculation is similar to the one performed in the following article [[cite:Bouchet2019]].
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### 3.1 Convergence with respect to Rcut
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### 3.2 The LO-TO splitting
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### 3.3 Another question?
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## 4. Description of an alloy : UMo-$\gamma$
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This calculation is similar to the one performed in the following article [[cite:Castellano2020]].
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### 4.1 Convergence with respect to Rcut
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### 4.2 The VCA and the SIFC approaches
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### 4.3 Another question?
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## 5. HOWTO use `qtdep` ?
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