phonopy-workshop

声子计算介绍文档

Introduction to phonopy

声子计算介绍文档

Run examplesSuppose phonopy's/bin is in the list of the execution path. Examples are found at /examples.html% cd example/Si% phonopy -p mesh.conf% cd example/NaCl% phonopy -p–-nac band.conf

声子计算介绍文档

Installation●

Download phonopy●

/projects/phonopy/

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Install phonopy% sudo apt-get install python-dev python-numpy\ python-matplotlib python-tk python-lxml python-yaml% tar xvfz phonopy-1.1.tar.gz% cd phonopy-1.1% python setup.py install–home=.

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Add the phonopy library directory (e.g.,~/phonopy-1.1/lib/python) to maybe in .bashrc, .zshenv, etc.

PYTHONPATH,

export PYTHONPATH=$PYTHONPATH:~/phonopy-1.1/lib/python

声子计算介绍文档

Phonopy is●

A phonon calculation toolbox Easily installed on recent systems Phonopy requires force calculators, e.g., it work togather with first-principles calculations, or any calculation that can calculate forces on atoms. Processes of phonopy and force calculations are completely separated. Therefore phonopy can be applied to any force calculator with small effort. Written mainly in Python●

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Phonopy Python module is prepared.

声子计算介绍文档

Calculation stepsA supercell with a displacement

1. Prepare a unit cell 2. Relax the structure 3. Build a set of supercells with displacements 4. Calculate forces on atoms of the set of supercells 5. Collect sets of forces

Forces Displacement

6. Calculate phonon frequencies

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Work flow of phonopy●

Prepare a crystal structure at equilibrium in VASP POSCAR format Create supercells with displacements Force calculation by a force calculator, e.g. VASP Force collection●

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Collect sets of forces on atoms of the supercells Density of states, Band structure, Thermal properties, etc. Thermal expansion, etc.

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Phonon analysis●

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Further analysis from a set of phonon calculations●

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Pre-process& Force collectionPre-process●

Force collection●

Input structure (POSCAR) Supercell size (--dim)% phonopy -d–-dim=”2 2 2” (supercell size= 2x2x2)

Disp.yaml vasprun.xml's% phonopy -f ALL_vapsrun.xml

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Output files- Supercell with

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Output file●

displacements (POSCAR-*)- Displacement directions

Sets of forces (FORCE_SETS) used in the post-process.

(disp.yaml)

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POSCAR DIM tag

Phonopy process

SPOSCAR, POSCAR-* disp.yamlVASP calculations VASP DFPT calculations

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Post process●

A file containing sets of forces and atomic displacements (FORCE_SETS) is transformed to supercell force constants. Dynamical matrices at arbitrary q-point are built from the supercell force constants. Dynamical matrices are solved, and phonon frequency and polarization vectors are obtained. DOS, PDOS, band structure, and thermal properties at constant volume are obtained following a setting file (xxx.conf) and command-line options.% cat mesh.conf DIM= 2 2 2 MP= 20 20 20% phonopy -p -t mesh.conf

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← Thermal properties are calc

ulated and plotted.

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Phonopy post-processPOSCAR DIM tag or --dim option FORCE_SETS or FORCE_CONSTANTS PRIMITIVE_AXIS tag

band.yaml

mesh.yaml

thermal_properties.yaml total_dos.dat partial_dos.dat

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Computing system

PC

Ask force calculation

Cluster

Plot

Ask phonon analysis (via X forwarding)

Work station

Recent PCs are enough strong that usually PC can be Work station.

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Tips of force calculation in VASPINCAR of phonon calculation PREC= Accurate LREAL= .FALSE. ADDGRID= .TRUE. EDIFF= 1.0e-08 Geometry optimization of unit cellSet

EDIFFG= -1.0e-08

and relax as much as possible watching the recidual forces Recidual forces of~1e-4 eV/Å may be acceptable, but depends on systems. Maybe

IBRION= 2; ISIF= 3

Force calculations of supercells Set IBRION= -1i.e. no relaxation is allowed.

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An example set of INCARsGeometry optimizationPREC ENCUT IBRION ISIF NSW NELMIN EDIFF EDIFFG IALGO ISMEAR LREAL ADDGRID LWAVE LCHARG============== Accurate 500 2 3 20 5 1.0e-08 -1.0e-08 38 0; SIGMA= 0.1 .FALSE. .TRUE. .FALSE. .FALSE.

Force calculationPREC ENCUT IBRION NELMIN EDIFF IALGO ISMEAR LREAL ADDGRID LWAVE LCHARG=========== Accurate 500 -1 5 1.0e-08 38 0; SIGMA= 0.1 .FALSE. .TRUE. .FALSE. .FALSE.

You may need to relax several times by, mv CONTCAR POSCAR.

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Tips of k-point sampling mesh in electronic structure calculationsReal space Reciprocal space

Unit cell

2×2 supercell

½×½

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Brief introduction to phonon theory

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Harmonic oscillatorHarmonic potential well

V

Spring constant Mass

k m x x

Equation of motion

F=ma=-kxA solution is

frequency

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1D-lattice connected with N.N.Nearest neighbor

a

Mass

m

n-1un-1

nun

n+1un+1

n+2un+2

Let displacement be superposition of traveling waves

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Dispersion relationSolving equation of motion, frequency is

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Transverse waveq

Atomic modulation is orthogonal to wave vector.

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Longitudinal waveq

Atomic modulation is parallel to wave vector.

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Interaction among atoms

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We don't know how far it reaches and how strong it is. Furthermore interaction is not only in pairs.