phonopy workshop

7/25/2019 Phonopy Workshop

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Introduction to phonopy


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Run examples

Suppose phonopy's /binis in the list of the execution path.Examples are found at

http://phonopy.sourceforge.net/examples.html

% cd example/NaCl% phonopy -p -nac band.conf

% cd example/Si% phonopy -p mesh.conf


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Installation

Download phonopy http://sourceforge.net/projects/phonopy/

Install phonopy

dd the phonopy li!rary directory"e.g.# ~/phonopy-1.1/lib/python) to PY!"NP#!#may!e in .bash$c# .shen etc.

% s'do apt-(et install python-de& python-n'mpy

python-matplotlib python-t* python-lxml python-yaml

% ta$ x&f phonopy-1.1.ta$.(% cd phonopy-1.1% python set'p.py install home+.

expo$t PY!"NP#!+,PY!"NP#!~/phonopy-1.1/lib/python


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$honopy is

phonon calculation tool!ox Easily installed on recent systems

$honopy re%uires force calculators# e.g.# it wor&togather with firstprinciples calculations# or anycalculation that can calculate forces on atoms.

$rocesses of phonopy and force calculations are

completely separated. (herefore phonopy can !eapplied to any force calculator with small effort. )ritten mainly in $ython

$honopy $ython module is prepared.


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*alculation steps

+orces

Displacement

supercell with a displacement,. $repare a unit cell

-. Relax the structure

. uild a set of supercells with

displacements

0. *alculate forces on atoms ofthe set of supercells

1. *ollect sets of forces

2. *alculate phonon fre%uencies


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)or& flow of phonopy

$repare a crystal structure at e%uili!rium in 3S$P"SC#format

*reate supercells with displacements

+orce calculation !y a force calculator# e.g. 3S$ +orce collection

*ollect sets of forces on atoms of the supercells

$honon analysis

Density of states# and structure# (hermal properties# etc. +urther analysis from a set of phonon calculations

(hermal expansion# etc.


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$reprocess 4 +orce collection

Input structure "P"SC#5

Supercell si6e "--dim5

7utput files- Supercell with

displacements"P"SC#-5

- Displacement directions"disp.yaml5

0isp.yaml

&asp$'n.xml's

7utput file Sets of forces 2"C34S3S)

used in the postprocess.

$reprocess

% phonopy -d -dim+56 6 65

"supercell si6e 8 -x-x-5

+orce collection

% phonopy -f #774&aps$'n.xml


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P"SC#

SP"SC#8 P"SC#-

disp.yaml

$honopyprocess

09:tag

3S$ calculations3S$ D+$( calculations


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$ost process

file containing sets of forces and atomicdisplacements "2"C34S3S5 is transformed tosupercell force constants.

Dynamical matrices at ar!itrary qpoint are !uilt from

the supercell force constants. Dynamical matrices are sol9ed# and phonon fre%uency

and polari6ation 9ectors are o!tained. D7S# $D7S# !and structure# and thermal properties at

constant 9olume are o!tained following a setting file"xxx.conf5 and commandline options.

% cat mesh.conf09: + 6 6 6:P + 6; 6; 6;% phonopy -p -t mesh.conf

(hermal properties are calculated and plotted.


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$honopy postprocess

the$mal4p$ope$ties.yaml total4dos.dat pa$tial4dos.dat

mesh.yamlband.yaml

P"SC#09: tag or--dimoption P9:99


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*omputing system

$* *lusters& force calculation

)or& station

s& phonon analysis"9ia ; forwarding5

Recent $*s are enough strong that usually $* can !e )or& station.

$lot


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(ips of force calculation in 3S$

+ -1.;e-;?Set

and relax as much as possi!le watching the recidual forces

Recidual forces of =,e0 e3/> may !e accepta!le# !ut depends on systems.

+orce calculations of supercells9@9"N + -1Set

P3C + #cc'$ate73#7 + .2#7S3.#00>90 + .A3.30922 + 1.;e-;?

9NC#of phonon calculation

i.e. no relaxation is allowed.

9@9"N + 6B 9S92 + ?ay!e


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n example set of 9NC#s

P3C + #cc'$ate 3NCA + D;; 9@9"N + 6

9S92 + NSE + 6; N37:9N + D 30922 + 1.;e-;? 30922> + -1.;e-;? 9#7>" + ? 9S:3# + ;B S9>:# + ;.1

73#7 + .2#7S3.#00>90 + .A3. 7E# + .2#7S3.

P3C + #cc'$ate 3NCA + D;; 9@9"N + -1

N37:9N + D 30922 + 1.;e-;? 9#7>" + ? 9S:3# + ;B S9>:# + ;.1 73#7 + .2#7S3.#00>90 + .A3. 7E# + .2#7S3.


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(ips of kpoint sampling mesh inelectronic structure calculations

Real space Reciprocal space

-A-supercell

Bnit

cell

CAC


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rief introduction to phonon theory


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armonic oscillator

armonic potential wellV

m

k

fre%uency

?ass

Spring constant

F8ma8-kx

x

x

E%uation of motion

solution is


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,Dlattice connected with ..

n nF, nF-n,

earest neigh!or

un, un unF, unF-

a?ass m

Get displacement !e superposition of tra9eling wa9es


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Dispersion relation

Sol9ing e%uation of motion# fre%uency is


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(rans9erse wa9e

q

tomic modulation is orthogonal to wa9e 9ector.


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Gongitudinal wa9e

tomic modulation is parallel to wa9e 9ector.

q


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Interaction among atoms

H H

H

H

)e don't &now how far it reaches and how strong it is.

+urthermore interaction is not only in pairs.


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$otential energy expansion

amiltonian 8 &inetic F potential

$otential energy is expaned with respect to

atomic displacements "U5.

i#j# k# H : *artesian components

?# # $# H : Gattice points

"?onatomic unit cell5

: +orce constants

"+*s5


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$honon from classical mechanics

7mit higher terms than ndorder armonic approximation

Diagonali6ation is needed.

$honon is found to diagonali6e harmonic amiltonian:

(his is reduced to eigen9alue pro!lem of dynamical matrix.

JM: mass#NK: num!er of atoms# R: positon 9ector

?ultiple atoms in a unit cell are considered.Indices LMN... are used for internal atomic la!eling.

$honon fre%uencies are o!tained as s%uare roots of

eigen9alues of the dynamical matrix.


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It is con9enient for sol9ing eigen9alue pro!lem using computer toconstruct a matrix of in the form li&e "two atom in unit cell5:

Diagonali6ation using computer

eigvals, eigvecs = numpy.linalg.eigh( dynmat )

D: dynamical matrix# w: eigen9ector# s: !and index


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Eigen9ector w

Jere indices i#jrun o9er the *atesian components and atom indices.

w"qs5 are eigen9ectors in the output files of phonopy.

7rthonormality

*ompleteness


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Imaginary mode

"aOK# bPK5

Sometimes it relates to phase transition# or may !eused to chec& if 9irtual crystal structure is sta!le or not.

ormal mode coordinate

Imaginary fre%uency appears when crystal structureis dynamically unsta!le through the imaginary mode.

JIn phonopy output# imaginary fre%uency is gi9en as negati9e fre%uency.


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Supercell approach

H H

H

H

ssume interaction range is confined in supercell si6e.

E.g.# -x- supercell is used to calculate force constans.


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+inite difference method

+orce on an atom "Fi5

tomic displacement "Qrj5

Displace one atom# and measure forces on all atoms


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(hermal properties

elmholt6 free energy

(hermal properties are calculated from fre%uencies.

Entropy

eat capacity at constant 9olume

uantum mechanics is necessary to deri9e them.


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*rystal symmetry


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*rystal symmetry

*I+ data!ase may ha9e small num!er of decimalse.g. ,/ K.

3S$ geometry optimi6ation may result in !rea&ing symmetryin hexagonal case# etc.

*rystal symmetry gi9es high %uality results and reducescomputational demands.

% phonopy -symmetry --tolerance=1e-8

Detailed crystal symmetry is chec&ed !y

*rystal structure has to !e correctly symmetri6edaccording to the space group type.


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*entrings of crystals

In space group type names in international ta!le#

starting withF#I# C#A# andBmeans thatcrystal has centring.

F: face centreI: !ody centreC#A#B: !ase centre

In these cases# the con9entional unit cell is ,# -# or0fold larger than the primiti9e cell.

Gattice parameters of the con9entional and primiti9ecells are related !y transformation matrix."I(-KK- Sec. 1.,5 JI(: International ta!le 9olume


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Fmm"e.g. Silicon5

*on9entional unit cell to

primiti9e cell

PRIMITIVE_AXIS = 1!" 1!" 1!" 1!" 1!" 1!"


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rillouin 6ones for space groups


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rillouin 6one ofFmm

*oordinates wrt. reciprocalprimiti9e lattice 9ectors

(his is to !e written in #Iand #$tags.


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?ore on phonopy


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Running modes of phonopy

and structure

?esh sampling

Gist of qpoints

Sample qpoints along specified paths

Sample qpoints on a uniform mesh

Sample %points listed in FP"9NSfile

*alculations of D7S# $D7S# thermal properties !elong to this mode.


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and structure mode

qpoint sampling paths:

um!er of sampling points in a path:

@#N0 + ; ; ; 1/6 ; ; 1/6 1/6 ;

@#N04P"9NS + D1 JEnd points are counted.

",5 "-5 "5

(he output file is band.yaml.


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bandplot

Replot !and structure from !and.yaml !y

% bandplot

*ommand options can !e shown !y

% bandplot -h

(o print out fre%uencies in gnuplot data format

% bandplot --(n'plot

If you want to cut !elow K#

% bandplot --fmin+;


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?esh sampling mode

Reciprocal lattice are sampled !y a uniform mesh.:P + 1; 1; 1;

In phonopy# a mesh point samples the point when the

num!er is odd. 7ptionally# the sampling mesh can !eshifted with respect to grid space.

:P4shift + ;.D ;.D ;.D

)hen MP_SI$Tis K or K.1# the symmetri6ation of thegrid points is fast# which may !e important when themesh is %uite dense.

(he output file is mesh.yaml.


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?esh sampling/D7S

n: num!er of calculated qpoints# g: function used for !roadening

% phonopy --dos % phonopy -por

"without plot5 "with plot5

(he output file is totalTdos.dat.

(he !roadening function is the


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?esh sampling/$D7S

$artial D7S is o!tained !y

P0"S + 1 68 G D H

s well as total D7S# smearing is controlled !y --si(ma.

% phonopy

)ith -poption# $D7S is plotted.

(he output files is pa$tial4dos.dat# and reploted !y

% pdosplot -i I1 6 G D8 H5

)here num!ers for -ioption correspond to,x# ,y# ,6# -x# -y# -6# H "num!ers are atom indices.5

and


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D7S/(hermal properties

elmholt6 free energy# entropy# heat capacity at constant9olume are calculated from phonon fre%uencies !y

% phonopy -t

)ith -poption# the resutls are plotted.7ptions --tmax8--tmin8--tstepmay !e used together.

(he output file is the$mal4p$ope$ties.yaml.

(hermal properties are replotted !y

% p$opplot c& "or-fe8 --ent$opy5

--(n'plotoption is dummy....5


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onanalytical term correction

Dynamical matrix at q K are corrected !y nonanalytical term correction. R. ?. $ic& et al.# $R ,# U,K# ",UVK5

t general qpoints# force constants are corrected !yinterpolation scheme of )ang et al. (W. $hys.: *ondens.?atter. --# -K--K, "-K,K55

% phonopy --nac

orn effecti9e charge and dielectric tensors arenecessary to use this option and those aresummari6ed in @"Nfile.

JZ: orn effecti9e charge tensor# X: dielectric tensor


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@"Nfile

73PS97"N + .A3.

@"N 3223C93S in e8 c'mm'lati&e o'tp't)

:#C"SC"P9C S#9C 09373C9C 3NS" incl'din( local fieldeffects in 02)

3S$ results are found in "AC#around:

1G.G;;6.;; ;.;; ;.;; ;.;; 6.;; ;.;; ;.;; ;.;; 6.;;1.J? ;.;; ;.;; ;.;; 1.J? ;.;; ;.;; ;.;; 1.J?-;.JJ ;.;; ;.;; ;.;; -;.JJ ;.;; ;.;; ;.;; -;.JJ...

Bnit con9ersion factor X

Z

(hese 9alues may !e o!tained !y 3S$ 1 !y setting

J7nly Y for independent atoms ha9e to !e written. Independent

atoms are found atom4mappin(of output of % phonopy --symmet$y


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uasiharmonic approximation"5

: +re%uencies at 9olumes

Z phonopy%ha p s e9.dat [thermalTpropertiesTyamlTofT9olume, [thermalTpropertiesTyamlTofT9olume- [thermalTpropertiesTyamlTofT9olume ...

(he file e-&.datcontains 9olumes andelectronic total energies U"V5 of unit cells.

1G;.;;;;; -G6.166GH1GG.D;;;;; -G6.H;;JKG1GJ.;H;;;; -G6.JGJ1G6...

3 B


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(hermal expansion of Silicon !y

7rigin of thermal expansion is9olume dependence of fre%uency.

Supercell si6es

l d d f f


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3olume dependence of fre%uencyof Silicon

(his point


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nimation for 9Tsim and else

#N9:3 + ;.D ;.D ;.D

#N9:3 + G D 6; ;.6D ;.6D ;.6D

+or 9Tsim

+or gdis# etc# at only point

and index "from the !ottom5

qpoint

mplitude

um!er of pictures

tomic position shift


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Eigen9ector to displacement

:"0A7#9"N + ; ; ; 1 1 18 G 1

Displaced structure along an eigen9ector is created !y

:P"SC#-;;1is the structure that we want.


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+inite displacements

mplitudeDefault 9alue is K.K, >.

(oo small 9alue enhances error of forces.

(oo large 9alue induces anharmonic contri!ution.

$lusminus displacement

(a&e plusminus as default

7nly plus when symmetric "automatically searched from crystal symmetry5

(his often also compensates residual forces.

*om!ination of these defaults and high enoughenergy con9ergence criteria in force calculation isexpected to gi9e uniform results.


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oo&s and a reference

Introduction to Gattice Dynamics "?artin (. Do9e5 $hysical $roperties of *rystals "W. +. ye5 (hermodynamics of *rystals "Duane *. )allace5 (hermodynamics and an Introduction to

(hermostatistics "er!ert . *allen5 Electrons and $honons "W. ?. Yiman5 $rinciples of uantum ?echanics "R. Shan&ar5

+rom ultrasoft pseudopotentials to the projectoraugmentedwa9e method#

phonopy workshop

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