Download - SrTiO 3
SrTiO3Tomáš Bzdušekfor Advanced Solid State Physics
Where are we now?
Structure of SrTiO3
Vertices – SrCube center – TiFacet centers – O
http://hasylab.desy.de/news__events/research_highlights/perovskite_like_crystal_in_an_electric_field/index_eng.html
Notice this octahedron!
Sides (simple cubic)
What happens below critical temperature?
Simple cubic Tetragonalhttp://hasylab.desy.de/news__events/research_highlights/perovskite_like_crystal_in_an_electric_field/index_eng.html
What happens below critical temperature?
http://cst-www.nrl.navy.mil/ResearchAreas/Ferroelectrics/
What happens below critical temperature?
http://hasylab.desy.de/news__events/research_highlights/perovskite_like_crystal_in_an_electric_field/index_eng.html
More about phase transition in SrTiO3(à la outline)
Experimental evidence
What drives the phase transition?
Is case of SrTiO3 exceptional?
EXPERIMENTAL EVIDENCE
High temperature
Loss of symmetry = new Bragg peaks
Loss of symmetry = new Bragg peaks
Destructive interferenc
e!
Loss of symmetry in SrTiO3
Blue octahedraclockwise rotated
Green octahedracounterclockwise
rotated
Loss of symmetry in SrTiO3
High-T phase:
Low-T phase:
real space momentum space
Experimental verification
G. Shirane and Y. Yamada, Lattice-dynamical study of 110 degrees K phase transition in SrTiO3, Phys. Rev. 177, 858 (1969).
• Rising intensity of a new Bragg peak that appers below critical temperature.
Hypothesis of “soft mode”There might exist an optical
phonon with vanishing frequency:
Under Tc, the crystal is unstable against this phonon and „crashes“ into a new structure.
as
Inelastic neutron scattering
Inelastic scattering & “Soft mode”
G. Shirane and Y. Yamada, Lattice-dynamical study of 110 degrees K phase transition in SrTiO3, Phys. Rev. 177, 858 (1969).
Soft mode verification
R. A. Cowley, The Phase Transition of Strontium Titanate, Philos. Trans. R. Soc. Lond. Ser. A-Math. Phys. Eng. Sci. 384, 2799 (1996)
WHAT DRIVES THE PHASE TRANSITION?
Phonon theoryThe simplest phonon theory is
quadraticWidely used, though sometimes
insufficient:◦Phonon frequencies independent of
temperature◦No thermal expansion of a crystal
Higher corrections necessary:Example: To obtain thermal expansion
we need 3rd order expansion of potential.
A “toy model”
M. T. Dove Theory of displacive phase transitions in minerals, Am. Miner. 82, 213, (1997)
To obtain soft mode we need 4th order expansion of potential with specific properties.
Order-disorder limitIf potential depth is much larger than
coupling constant, atoms always sit in one of the minima.
Yet another application of the Ising model!
Displacive limitIf potential depth is much smaller
than coupling constant, atoms’ positions change smoothly
This is the case of SrTiO3.
Theory vs. experiments
Below Tc, the crystal changes structure and new phonon branches appear.M. T. Dove Theory of displacive phase transitions in minerals, Am. Miner. 82, 213, (1997)
Detailed computation predicts soft mode vanishing as .
IS CASE OF STRONTIUM TITANITE EXCEPTIONAL?
And many others (screenshot of part of long list of displacive phase transitions in Dove’s article).
Definitely not!
Example: FerroelectricsAtoms move to create a net dipole moment
SrTiO3 also approaches ferroelectric transition at absolute zero.http://department.fzu.cz/lts/en/res-ferro.htmhttp://en.wikipedia.org/wiki/Ferroelectricity
Used literatureG. Shirane and Y. Yamada, Lattice-dynamical
study of 110 degrees K phase transition in SrTiO3, Phys. Rev. 177, 858 (1969).
R. A. Cowley, The Phase Transition of Strontium Titanate, Philos. Trans. R. Soc. Lond. Ser. A-Math. Phys. Eng. Sci. 384, 2799 (1996)
M. T. Dove Theory of displacive phase transitions in minerals, Am. Miner. 82, 213, (1997)
Some cited images from Internet and even more own ones.