Detecting Pseudosymmetries with PSEUDO J.M. Perez-Mato, E. Tasci - - PowerPoint PPT Presentation

Detecting Pseudosymmetries with PSEUDO

Bilbao Crystallographic Server (http://www.cryst.ehu.es)

J.M. Perez-Mato, E. Tasci

Bilbao Crystallographic Server

http://www.cryst.ehu.es

(Main developers of the program: Emre S. Tasci, Cesar Capillas, E. Kroumova)

Problem

Given a structure with space group H, finding/ predicting if there is a compatible high symmetry structure of space group G

G + small (symmetry-breaking) distortion = H

Structure Structure

known

?

Pseudosymmetry Search

Initial Structure

H H

Low Symmetry

Structural Pseudosymmetry

↔

Distortion

If the distortion is small enough, one can infer a symmetry change at high temperature

↓

Phase Transition

Prototype Structure

G G

High Symmetry

PSEUDO

• Prediction of phase transitions
• Search for ferroic materials
• Prediction of the symmetry and structure of some
• ther phase of a material
• Detection of false symmetry assignments

(overlooked symmetry)

• Space group determination of a theoretically

determined structure (e.g. ab initio calculations)

• Determination of an optimized virtual parent

structure (paraphase)

Atomic Displacements Method

Assumption: The high symmetry phase is described by a supergroup of the initial space group

G = H + g2H + … + gmH

Supergroups of Space Groups

G > H G > H → G > … > Z G > … > Z2 > Z > Z1 > H > H

Any group – supergroup relation can be represented by a chain of minimal supergroups. Stepwise detection of pseudosymmetry for successive minimal supergroups.

Supergroups of Space Groups

G > H G > H → G > … > Z G > … > Z2 > Z > Z1 > H > H

Any group – supergroup relation can be represented by a chain of minimal supergroups. If a structure of symmetry H is pseudosymmetric for a supergroup G, it will be pseudosymmetric for all intermediate subgroups Zi Zi.

Structural Data Search

• ptions

Tolerance

Example: NaSb3F10

Example from the PSEUDO tutorial

Space group C2221

Wyckoff Splitting Compatibility

WYCKSPLIT

C2221 example from the PSEUDO tutorial

Exercise

Polar groups… some additional care

uBa = 0 uTi uO1 uO2 uO2 uTi uO1

u'Ti

Polar groups… some additional care

u'Ba = δ u’Ti=uTi + δ u’O1=uO1 + δ

u’O2 u’O1

u’O2=uO2+ δ

uBa = δ u’O1

Pseudosymmetry

BaTiO3

Example: NaSb3F10

Example: NaSb3F10

Example: NaSb3F10

P63 / mmc P63 P63 / m P6322 P63mc

Example: NaSb3F10

P63 / mmc P63 P63 / m P6322 P63mc P63 P63mc u=0.45Å P6322 u=0.70Å P63/m u=0.70Å P63/mmc Sb Na F

Example: NaSb3F10 P63 → P63mc → P63/mmc

Sb Na F

• Max. Displacement : 0.70Å

Exercise 3

Search of ferroelectrics as pseudosymmetric polar structures

Two necessary conditions to be a ferroelectric:

• Polar symmetry group (it should allow non-zero polarization)
• Pseudosymmetry with respect to a non-polar symmetry group

(the polar distortion should be small and “multistable”)

Known Ferroelectrics with space group Pna21

Possible Ferroelectrics with space group Pna21

Search of ferroelectrics as pseudosymmetric polar structures

BaHgS2 (Kroumova et al. 2002)

“complex” Phase II Ga under pressure

104 atoms per unit cell Space group C2221

• Phys. Rev. Lett.93, 205502 (2004))

(divisible by 2, 4, 8 and 13)

Acknowledgements:

The past and present rest of the team in Bilbao of the… past:

• D. Orobengoa
• C. Capillas
• E. Kroumova
• S. Ivantchev

Present:

• M. I. Aroyo
• J.M. Perez-Mato
• G. Madariaga
• E. Tasci
• G. de la Flor
• S. Vidal