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

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.

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

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

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

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

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.

Example Ca2CoSi2O7 Sequence of phases: Diffraction pattern at RT: HT - Phase IC - Phase C - Phase DT Tc = 155 K - 270 K Tc = 498(1) K Diffraction pattern at RT:

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 300 400 500 Temperature [K] Intensity Satellite-Intensity Phase transition at about 500 K No thermal hysteresis: 2.nd order phase transition

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 0 100 200 300 400 500 Temperature [K] Variation of the q-vector (incommensurate phase) Phase transition between 155 K und 270 K Thermal hysteresis: 1. order phase transition

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

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

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.

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.

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 300 400 500 Temperature [K] Intensity Satellite reflection Superstructure reflection

?  ? 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

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.

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

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).