1. The document discusses using ab initio methods to model materials at different temperatures, including calculating phonons and predicting phase transitions. 2. Group theory analysis and phonon calculations for high symmetry phases can identify soft modes and possible low symmetry phase subgroups responsible for second-order phase transitions. 3. Phonon calculations for predicted low symmetry phases then determine the most stable phase as temperature decreases.

1. Evgeny Blokhin
Chelyabinsk SUSU’2013 summer workshop
Max-Planck Institute for Solid State Research
Stuttgart, Germany
Theory and practice of ab initio
materials modeling
Part II

2. 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

3. 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)

4. Symmetry constrains
[1] Kennedy et al., PRB 59, 4023 (1999) (experiment)
T, K
Volume,Å^3
200 1600600 1200
6972
Ortho-I
Ortho-II
Tetrag.
Cubic
Pm-3m
I4/mcm
Cmcm
Pbnm
0
−40
−177
−241
Cubic
Tetrag.
Ortho-II
Ortho-I
Calc. ∆Etot,
meV
Phase
[1] [2]
[2] Evarestov et al., Phys.Stat.Sol.(b) 242, R11 (2005) (calculation)
SrZrO3

5. Calculating phonons
Brillouin zone of cubic
SrTiO3
Cubic SrTiO3
primitive cell
( )
( )
0
( )
!
n
ni
i i
n
E
E R
n
δ
δ
∞
=
∂
= −∑

6. Calculating phonons
Brillouin zone of cubic
SrTiO3
Cubic SrTiO3
2x2x2 supercell
( )
( )
0
( )
!
n
ni
i i
n
E
E R
n
δ
δ
∞
=
∂
= −∑

7. Cubic SrTiO3 phonon dispersion over the BZ

8. T, K
37 1050
“Tetragonal FE” Tetragonal AFD Cubic
R4+
Г4- Sr
O
Ti
Soft-mode driven phase transitions
in perfect SrTiO3

9. 9
...

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

12. Soft-mode driven phase transitions
in perfect SrTiO3 surface
z
Γ
Γ
M
3-dimensional Brillouin zone
2-dimensional Brillouin zone

13. 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 transitions
in perfect SrTiO3 surface

14. 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

15. Image by Amisi et al., PRB85, 064112 (2012)
SrZrO3 ab initio predicted phase transitions
}
}
}
cubic
tetragonal
orthorhombic

16. Symmetry constrains
[1] Kennedy et al., PRB 59, 4023 (1999) (experiment)
T, K
Volume,Å^3
200 1600600 1200
6972
Ortho-I
Ortho-II
Tetrag.
Cubic
Pm-3m
I4/mcm
Cmcm
Pbnm
0
−40
−177
−241
Cubic
Tetrag.
Ortho-II
Ortho-I
Calc. ∆Etot,
meV
Phase
[1] [2]
[2] Evarestov et al., Phys.Stat.Sol.(b) 242, R11 (2005) (calculation)
SrZrO3

17. 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