1. Structural Phase Transitions
IX ECERS, Portorož 2005
Mechanisms at
Structural Phase Transitions
H. Böhm
Institut für Geowissenschaften
Universität Mainz
Germany
V. Kahlenberg, J. Kusz, O. Pawlig, M. Riester

2. Definition Structural Phase Transition:
It occurs in a crystalline solid with a sudden change in symmetry because of a change of pressure and/or temperature.
A change of the symmetry is associated with the change of the structure.

3. classification DV  0 Mechanisms: First order phase transitions.
at the temperature Tc : DS  0
DV  0
Mechanisms:
nucleation and growth,
range of coexisting phases
characteristic features:
thermal hysteresis

4. classification DV = 0 Mechanisms: Second order phase transitions.
at the temperature Tc : DS = 0
DV = 0
Mechanisms:
continuous transition
characteristic feature:
no thermal hysteresis;
Landau Theory is applied

5. Example Sequence of phases Bi2Ti4O11 c0(a) = 2 c0(b) Tc = 233 °C a
C2/m b
195
215
235
T °C
Intensity
 = order parameter
Superstructure reflection

6. continued Bi2Ti4O11 Spontaneous strain Lattice parameter b
200
400
T °C
lattice parameter b [Å]
3.802
3.810
Spontaneous strain
200
400
T °C e1 e3 e2
Tensor components
No thermal hysteresis:
2.nd order phase transition ,
coupling between  and the spontaneous strain

7. continued Bi2Ti4O11 structure : b-Phase Interpretation in terms of
the Landau Theory:
At Tc a continuous shift of the
Bi-atoms begins off the
mirror plane.
structure : a-Phase
Bi - Atome
Comment:
The transition is triggered by
the ordering of the lone
electron pair of Bi.

8. Example Ca2CoSi2O7 Sequence of phases: Diffraction pattern at RT:
HT - Phase
IC - Phase
C - Phase DT
Tc = 155 K K
Tc = 498(1) K
Diffraction pattern
at RT:

9. continued Ca2CoSi2O7 Phase transition at about 500 K
HT - Phase
IC - Phase
C - Phase
300
350
400
450
500
550
600
2000
4000
6000
8000
10000
12000
I [cps]
teperature [K]
Tc= 498 K
Temperature [K]
Intensity
Satellite-Intensity
Phase transition at about 500 K
No thermal hysteresis:
2.nd order phase transition

10. continued Ca2CoSi2O7 Phase transition between 155 K und 270 K
HT - Phase
IC - Phase
C - Phase
0.34
0.33
0.32
0.31
0.30
0.29
Temperature [K]
Variation of the q-vector
(incommensurate phase)
Phase transition
between 155 K und 270 K
Thermal hysteresis:
1. order phase transition

11. a c continued = CoO4 = Si2O7 = Ca HT - Phase Ca2CoSi2O7 IC - Phase

12. continued
Ca2CoSi2O7
C - Phase
3·a
HT - Phase
IC - Phase
C - Phase

13. continued IC - Phase Ca2CoSi2O7 HRTEM picture at RT: Octagonal rings.
HT - Phase
IC - Phase
C - Phase
IC - Phase
Van Heurk et al., 1992
8 nm
HRTEM picture at RT:
Octagonal rings.

14. continued Relationship between the phases Ca2CoSi2O7 IC-Phase:
HT - Phase
IC - Phase
C - Phase
Relationship between the phases
C-Phase:
An ordered superposition of octagonal rings.
IC-Phase:
An arbitrary superposition of octagonal rings.

15. Mechanisms Bi2Ti4O11 Ca2CoSi2O7 Satellite reflection
195
215
235
T °C
Intensity
300
350
400
450
500
550
600
2000
4000
6000
8000
10000
12000
I [cps]
teperature [K]
Tc= 498 K
Temperature [K]
Intensity
Satellite reflection
Superstructure reflection

16. ?  ? Mechanisms Tc = 250 K Tc = 277 K (Ca1-xSrx)2MgSi2O7; x = 0.16
HT - Phase
IC - Phase
?  ?
Transformation temperature
Tc = 250 K
Tc = 277 K

17. continued Relationship between the phases Ca2CoSi2O7 C-Phase:
HT - Phase
IC - Phase
C - Phase
Relationship between the phases
C-Phase:
An ordered
superposition
of octagonal
rings.
IC-Phase:
An arbitrary
superposition
of octagonal
rings.
HT-Phase:
Domains of octagonal rings with short range order.

18. continued Bi2Ti4O11 structure : b-Phase Interpretation :m
Interpretation :
Above Tc the lone pair
of Bi-atoms begins to order in
domains with short range order.
structure : a-Phase
Bi - Atome
Long range order is attained at
the transition point

19. Final question What characterizes a continuous phase transition ?
Answer:
The continuous increase of the range of order until long range order is achieved
(not a continuous shift of atomic positions).