Slide 1 by Y33R7e

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									  The fundamental role of secondary
 modes in perovskite phase transitions

                   Ross Angel, Di Wang, Yonggang Yu
                Virginia Tech Crystallography Laboratory

                          Michael Carpenter
                        University of Cambridge
rangel@vt.edu                                     www.crystal.vt.edu


  Work supported by NSF grant EAR-0738692


  Thanks to Harold T. Stokes. Branton J. Campbell, and Dorian
  M. Hatch for Isodisplace




                                                                       VTX
Perovskites
 Corner-linked octahedral
  framework
    Octahedra can tilt
    Octahedral cations can
     displace
 Extra-framework cations




       Cubic                  Orthorhombic
                                             VTX
    Tilt transitions in perovskites




                    Pm3m
                                   Temperature

P4/mbm      I4/mcm         Imam   R-3c


         Cmcm

                     Pbnm




                                                                            Glazer (1972a,b)
                                                                            Woodward (1997)


    Transitions with rigid octahedra (except Pmmn)
                      Octahedral deformation allowed but not essential
                      Analysis in terms of rigid units, soft modes, Q=tilt angle


                                                                                       VTX
Rigid octahedra and tilt transitions


                         Pressure


                         Temperature




    No tilts:                       Tilted structure:
          Volume = a3                    Volume = a(acosq)2


If the octahedra are rigid, volume reduction can only be
     achieved through increasing tilts
      = decreasing B-O-B angles
Pressure must lead to lower symmetry structures

                                                                VTX
Rigid octahedra


 No change in octahedral
  volume

 All volume reduction results
  from tilting

 Tilts increase with pressure

 Phase transition to lower
  symmetry:
      DV < 0
      DS < 0
      dTc/dP > 0




                                 VTX
CaTiO3: Temperature and Pressure
           Tet Ortho



            Cubic Ortho




                Cubic Tet




                                   VTX
LaAlO3 perovskite: high temperature

 R-3c at room conditions
    a-a-a- tilt system
    Effective single order parameter

 Transforms to Pm3m at high T
    Boysen et al (2000)
    Hayward et al. (2005)

 Tilts decrease on increasing
  temperature




                                        Hayward et al. (2005)




                                                           VTX
LaAlO3 perovskite: high pressure
 R-3c: Cell parameters
  trend towards cubic

 Tilt angle decreases with                                                      a/ 2
  increasing P
      Extrapolates to zero at ~15
       GPa                                                               c/2 3


 Octahedra are not rigid


                               30

                               25

                               20
                          2




                               15

                               10

                               5
                                                                     Zhao et al. (2004)
                               0
                                    0   2   4   6 8 10 12 14 16 18
                                                Pressure(GPa)

                                                                                        VTX
LaAlO3 perovskite: high temperature

 The octahedral compression is also apparent in
  the high-temperature data:




                                        Pm3m




                R-3c

                               Hayward et al. (2005)




                                                       VTX
LaGaO3




                                             Pseudo-cubic cell volume: A3
                                                                            5 9.0
Low pressure phase is Pbnm                                                 5 8.5
                                                                            5 8.0
                                                                            5 7.5
                                                                            5 7.0
GaO6 octahedra compress                                                    5 6.5




                                                           me: A3
                                                                            1 0.2

Distortion decreases with increasing




                                            Octahedr a volu
                                                                                             R-3c
                                                                            1 0.0
pressure in Pbnm




                                                      l
                                                                                    Pbnm
   B-O-B angles increase                                                    9.8

   Tilt angles decrease




                                                           gle: deg
                                                                            162




                                                  Ga-O-Gaan
                                                                            160

Phase transition Pbnm -> R-3c at 2.3 GPa                                   158
                                                                                    Angel et al (2005) PRL

                                                                                    0   2     4     6        8
                                                                                        Pressure: GPa
DV from compression of octahedra
                                                                                                  VTX
Role of Octahedral Compression

 The compressibility of the octahedra plays an essential
  role in perovskite tilt transitions
 The relative compressibility of A and B sites controls the
  high-pressure behavior and dTtr/dP

          Octahedra less                   Octahedra more
       compressible than A site         compressible than A site

  P                                 P
      Low symmetry                                        High symmetry
         phase                                                phase
                 High symmetry
                     phase                                 DV < 0


                                        L aG a O 3
                                        L aAlO 3
                                                           DS > 0
      MgSiO3



               CaSiO3




                                                       Tilts decrease
                                                     Low symmetry
                                                        phase

                          T                                             T VTX
LaAlO3: simulations

 DFT calculations from Di Wang (2010)




                                         VTX
LaAlO3: octahedral compression

 Which mode?
     Pm3m  R-3c
     Strain modes: G1+ , isotropic volume strain
                    G5+ : hexagonal strain, no volume strain
     Octahedral rotation: a-a-a- tilt system: q1 = q2 = q3
     One structural mode R4+

                                              VA  VB 6 cos 2   1)
                                                      
                                                  VB k R4  1
                                                                2
                                                                    )
                                               Differential
                                                compression of
                                                B octahedra
                                                comes from R4+

                                                                    VTX
YAlO3: DFT simulations of Pnma

                   Increasing B-O-B
                   Decreasing tilts
                   Octahedron compresses more
                    than A site




                                            VTX
YAlO3: mode amplitudes

    Continuous transition Pnma (a+b-b-) = Imma (a0b-b-)

                              R4+ : Oxygen only, tilt mode
                                    b-b- tilt.


                              M3+ : Oxygen only, tilt mode
                                    a+ tilt: zero in Imma

                              X5+: octahedral shear
                                    zero in Imma
                                    No volume effect


                              R5+: oct. rotation plus A shift
                                    Oct rotation component is weak
                                    No volume effect


                                                                 VTX
Conclusions: It’s the tilts, dummy!

   V0 reference state
                                      VA VB  5
     G1+: isotropic strain



   V compressed state                VA VB  5
   G3+,5+: anisotropic strain

   V: strained state
                                      VA VB  5
     R4+,M3+: tilts

   V: strained state             Tilts increase VB
      Plus tilts                 And decrease VA
                                      VA VB  5
                                              VTX
Source of octahedral compression


                    Strains do not affect VA/VB :
                     both compress

                    Decrease in tilt at compressed
                     volume:
                         VA increases
                         VB decreases




                                                 VTX
Landau test: Imma YAlO3




Carpenter et al (2005)


                                                                       -0.025


                   etx Imma                                                        50GPa                                e4 Imma
      -0.015
                                                                       -0.030




      -0.020                                                           -0.035                                     100GPa
                                                                  e4
etx




                                                                       -0.040

      -0.025
                                                                                                                                  700GPa
                                                                       -0.045
                                                                                -0.0030   -0.0025         -0.0020     -0.0015     -0.0010
          0.001   0.002           0.003           0.004   0.005
                                                                                                      2       0
                              2           0       0                                                 -q4 / C
                          2q4 / (1/2)(C   11
                                               - C 12)                                                        44




                                                                                                                                      VTX
Mode coupling: Pnma YAlO3


   X5+ coupled to M3+   R5+ coupled to R4+

                        M3+,X5+ not coupled
                           to R4+




                                              VTX
Conclusions

 The relative compressibility of A and B sites plays an
  essential role in perovskite tilt transitions and controls the
  high-pressure behavior and dTtr/dP

 The relative compressibility arises not from strains, but
  from the tilts:
    Decreasing tilts lead to relative compression of octahedra
    Increasing tilts lead to relative expansion of octahedra


 The relative compressibility is associated with the primary
  M3+ and R4+ modes

 The R5+ and X5+ modes
    Are secondary
    Follow the primary modes
    Contribute to octahedral distortion but not compression
                                                                  VTX
VTX
LaCrO3 at high temperature

 Pbnm  R-3c at 280C

 Xray powder diffraction

 At transition:
      DV < 0
      Tilts increase
      Octahedron compresses




  Hashimoto et al. (2000)
  Solid State Ionics 132:183
                               VTX
Further examples

 NdNiO3
      Powder neutron diffraction
      Pbnm R-3c
      Medrade et al (1997) Physica
       B




 NdAlO3
      Ab-initio calculations
      R-3c  Pm3m
      Tohei et al (2005) PRL


 Octahedra cannot be rigid



                                      VTX

								
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