Evgeny Blokhin

Chelyabinsk SUSU’2013 summer workshop

Max-Planck Institute for Solid State Research

Stuttgart, Germany

Theory and practice of ab initiomaterials modeling

Part II

Outlook

1. Considering temperature from ab initio

2. Atomic vibrations and phase transitions

3. Example of four perovskites

4. And example of strontium titanate surface

How to deal with temperature at 0°K?

1. Symmetry constrains

2. Elastic properties and equation of state, e.g.

3. Configurational disorder entropy

4. Vibrational entropy (phonons)

Symmetry constrains

[1] Kennedy et al., PRB 59, 4023 (1999) (experiment)

T, K

Volu

me,

Å^3

200 1600600 1200

6972

Ortho-I

Ortho-II

Tetrag.

Cubic

Pm-3mI4/mcmCmcmPbnm

0−40−177−241

CubicTetrag.Ortho-IIOrtho-I

Calc. ∆Etot, meV

Phase

[1] [2]

[2] Evarestov et al., Phys.Stat.Sol.(b) 242, R11 (2005) (calculation)

SrZrO3

Calculating phonons

Brillouin zone of cubic SrTiO3

Cubic SrTiO3

primitive cell

( )( )

0

( )!

nni

i in

EE Rn

δ δ∞

=

∂= −∑

Calculating phonons

Brillouin zone of cubic SrTiO3

Cubic SrTiO32x2x2 supercell

( )( )

0

( )!

nni

i in

EE Rn

δ δ∞

=

∂= −∑

Cubic SrTiO3 phonon dispersion over the BZ

T, K37 1050

“Tetragonal FE” Tetragonal AFD Cubic

R4+Г4- Sr

OTi

Soft-mode driven phase transitionsin perfect SrTiO3

9

...

triperiodic (3D) diperiodic (2D), LG61

Soft-mode driven phase transitionsin perfect SrTiO3 surface

z

Γ

Γ

M

3-dimensional Brillouin zone

2-dimensional Brillouin zone

548517B1g

447439B1g460, 447454Eg

394421Eg

175180Eg235, 229157B2g

162155Eg

147153A1g

129129A1g143, 144142Eg

4848Eg48, 5285A1g

37133iEg15, 4017Eg

Expt.TheoryIrrepExpt.TheoryIrrep

Surface AFD STOBulk AFD STO

Soft-mode driven phase transitionsin perfect SrTiO3 surface

SrTiO3 (2 phases):T > 105 K Pm-3m (221),T < 105 K I4/mcm (140)

SrZrO3 (4 phases):T > 1343 K Pm-3m (221),T < 1343 K I4/mcm (140),T < 1113 K Cmcm (63),T < 1000 K Pbnm (62)

14

BaTiO3 (4 phases):T > 403 K Pm-3m (221),T < 403 K P4mm (99),T < 278 K Amm2 (38),T < 183 K R3m (160)

BaZrO3 (1 phase):Pm-3m (221)

Example of four perovskites

Image by Amisi et al., PRB85, 064112 (2012)

SrZrO3 ab initio predicted phase transitions

}

}

}

cubic

tetragonal

orthorhombic

Symmetry constrains

[1] Kennedy et al., PRB 59, 4023 (1999) (experiment)

T, K

Volu

me,

Å^3

200 1600600 1200

6972

Ortho-I

Ortho-II

Tetrag.

Cubic

Pm-3mI4/mcmCmcmPbnm

0−40−177−241

CubicTetrag.Ortho-IIOrtho-I

Calc. ∆Etot, meV

Phase

[1] [2]

[2] Evarestov et al., Phys.Stat.Sol.(b) 242, R11 (2005) (calculation)

SrZrO3

Summary

1. Group-theory analysis allows finding: (a) symmetry of phonons for the high symmetry phase, (b) the set of low symmetry subgroups and possible symmetry of phonons responsible for 2nd order phase transitions

2. The phonon calculations for the high symmetry phase give the soft modes symmetry and define the possible low symmetry phases

3. The phonon calculations for the found low symmetry phases allows one to define the most stable phase