As you know that BaTiO3 and the other peroviskite [ ABX3 ] have many phase transition with temperature Rhombohedral - Orthorhombic - Tetragonal - Cubic - Hexagonal .
Taking into consideration:
1- The Coordination Number ( CN ) is very important factor to determine the ion radii . for any ion the the ionic radius changed as the CN change. . http://www.geo.arizona.edu/xtal/geos596a/ACB25_925.pdf
http://abulafia.mt.ic.ac.uk/shannon/radius.php
2- Goldschmidt Tolerance Factor ( GTF ) is an important factor to estimate the crystal structure . also many researchers think that the phase transition of peroviskite family is related to the change in the value of GTF. https://en.wikipedia.org/wiki/Goldschmidt_tolerance_factor
3- As a result of 1 & 2 . Any change in the value of CN leads to increase or decrease the Value of GTF which lead to phase transition { rhombohedral - orthorhombic - tetragonal - cubic - Hexagonal .} .
4- The CN in crystaline solids is always a chameleon
5- So 1,2&3 lead to think that CN play an Important factor in the phase transition of perovikite .
The tolerance factor was derived for the tendency of the cubic structure to distort, so it should be calculated using the coordination numbers corresponding to this structure.
Another point is that the distortions predicted by the tolerance factor do not lead to the break of the central symmetry, so it cannot be used for the explanation of the ferroelectric properties. This is because the tolerance factor takes into account only atomic radii while the ferroelectric properties in the perovskites are mainly due to the electronic effects.
I agree with the above given opinions, and I add that an internal stress relaxation in perovskites (namely in PZT) can influence the phase coexistence and consequently their ferroelectrical properties, too.
You can see more in my Article:
Contribution to the study of tetragonal and rhombohedral phase coexistence in the PbZrO3–PbTiO3 system
T. Kala
ABSTRACT: Some new experimental results of the X-ray diffraction analysis of Pb(Zr, Ti)O3 solid solutions with 1.5 mol% of MnO2 additions and the experimental data of other authors are used for the proposal of a new conception of the interpretation of the tetragonal–rhombohedral phase coexistence in the PbZrO3–PbTiO3 system in the vicinity of the morphotropic phase boundary. It suggests the internal stress relaxation as the primary reason of the phase coexistence. The internal stresses may arise due to the contraction or dilatation during temperature changes, due to the influence of external electric or mechanical fields, and probably due to further variables, too.
Es werden einige neue experimentelle Ergebnisse der Röntgen-Diffraktionsanalyse von festen Lösungen Pb(Zr, Ti)O3 mit 1,5 Mol% MnO2-Beimischungen und von anderen Autoren gewonnene Daten für den Entwurf einer neuen Konzeption der Erklärung der Koexistenz der tetragonalen und rhomboedrischen Phasen im System PbZrO3–PbTiO3 in der Nähe der morphotropen Phasengrenze verwendet. Es wird angenommen, daß die Ursache der Phasenkoexistenz, in der Relaxation der inneren Spannung liegt. Die inneren Spannungen können infolge Kontraktion oder Dilatation während der Temperaturänderung, infolge des Einflusses äußerer elektrischer oder mechanischer Felder und wahrscheinlich auch infolge weiterer Veränderlicher entstehen.
physica status solidi (a) 07/1983; 78(1):277 - 282. DOI:10.1002/pssa.2210780133 · 1.21 Impact Factor
I think slight displacement of ions on A-site (12 coordination) may result phase transition/change in crystal structure as compared to B-site (6 fold coordination).
Dear Natheer Basheer Mahmood,
Just at the time of the discovery of the highTc superconductor, I have established the role of interaction of the Xe shell for Ba and rare earths Ln. see for example “On the Phase transformation Ce gama, Ce alpha” and ATOMS AND CRYSTAL STRUCTURES “on my researchgate site. I hope you will find inspiration.
I wish in this spot to tackle a point often do not known, Dirac in is paper giving all the quantum states found that the electron behave as it has a magnetic moment but also an electric moment. Dirac does not expect that the electric moment being a pure imaginary has any physical meaning. In fact we can interpret that the imaginary character is there to separate it from the magnetic moment a classical way to work simultaneously independent quantities.
So this magnetic moment is probably the property observed in compound as in Perovskites [ABX3] having an electric moment? In fact there are not so much ferroelectric compounds as magnetic moment but this must probably the result of the strong interaction of electric dipoles.
Dirac P.A.M. Proc. Roy. Soc., A117, 610-624, 1928. Second part A118, 351-361, 1928.
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Condensed Matter Physics
- Solid State Physics