Symmetry mode analysis in the Bilbao Crystallographic Server: The program AMPLIMODES

Transcription

1 Symmetry mode analysis in the Bilbao Crystallographic Server: The program AMPLIMODES

2 AMPLIMODES Symmetry Modes Analysis

3 Modes in the statics of low-symmetry distorted phases: Distorted Structure = High-symmetry Struct frozen modes distortion mode = Amplitude x polarization vector Description of a mode : e 2 e 1 e 3 e 4 u(atoms) = Q e amplitude polarization vector e = ( e 1,e 2,e 3,e 4 ) normalization: e 1 2 e 2 2 e e 4 2 =1 (within a unit cell) AMPLIMODES calculates the amplitudes and polarization vectors of all distortion modes with different symmetries (irreps) frozen in a distorted structure.

4 We can compare the amplitudes of different frozen distortion modes: Q 2 e 2 Q 1 e 1 Q 1 and Q 2 have the same dimensions and their values can be compared

5 The orthorhombic Amm2 structure of BaTiO 3 ( Kwei et al. (1993) neutron-powder 190 K ) b c max. atomic displ. : 0.13 Ǻ Mode decomposition of distortion: Q GM4- x Q GM5- x GM4- mode GM5- mode polar ferroelectric mode Q GM4- >> Q GM5-

6 Example of input of AMPLIMODES: Amm2 phase of BaTiO 3 Pm-3m b Amm2 c 4 parameters Transf.

7 Example of output of AMPLIMODES:

8 Example of output of AMPLIMODES: amplitude of the GM4- distortion basis for this 4dim vector polarization vector in two forms crystallographic form

9 The orthorhombic Amm2 structure of BaTiO 3 ( Kwei et al. (1993) neutron-powder 190 K ) b Perovskite in Amm2 setting c δx δy δz Ba Ti O O polarization vector GM4- polarization vector GM5- δx δy δz δx δy δz Q GM4- Ba Ti O O Q GM5- Ba Ti O O Q GM4- = Å Q GM5- = Å

10 The orthorhombic Amm2 structure of BaTiO 3 ( Kwei et al. (1993) neutron-powder 190 K ) Amm2 b c 4 parameters

11 The orthorhombic Amm2 structure of BaTiO 3 Orthorhombic Distortion Polar (ferroelectric) mode T 1u δx δy δz Q T1u >> Q T2u Non-polar mode T 2u δx δy δz Q T1u x Ba Ti O Q T2u x Ba Ti O O O Symmetry T 1u : δy O1 δz O1 - δz O12 = 0 zero global translation : 2δz Ba1 2δz Ti11 4δz O12 2δz O12 = 0 Symmetry T 1u : δy O1 δz O1 δz O12 = 0 δy O1 = δz O1 normalization normalization 3 parameters 1 parameter

12 Leucite KAlSi 2 O 6 I4 1 /a Palmer et. (Amer. Miner. 82 (1997) 16 max. atomic displ. : 1.04Ǻ Ia-3d Γ 3 Γ 4 I4 1 /acd I4 1 /a DISTORTION AMPLITUDES VS. TEMPERATURE: Q Γ 3 Γ 4 I4 1 /a Induced effect : 2 Q Γ3 = α Q Γ4 T (K)

13 Sequence of transitions in SrZrO 3 (Howard et al & data from B. Kennedy) 20 C Pnma Pm3m P4/mmm M 2 P4/mbm M 3 P4/mbm Cmmm Pbam X 5 Cmcm R 4, R 5 Imma two primary modes necessary Q M2 = Å Q M3 = Å Q X5 = Å Q R4 = Å Q R5 = Å Pnma Pnma - Each primary mode is a different instability mechanism - each primary mode condenses in general at different temperatures : two phase transitions Expected transition sequence: T > Pnma Imma Pm3m ( M 3, R 4 ) R 4

14 Sequence of transitions in SrZrO 3 R M 4 3 X 5 R 5 M Å 0.79 Å Å 0.07 Å Å (Howard et al & data from B. Kennedy) They deform the octahedra. X 5 has significant amplitude Q R 4 M 3 [ (1,1,0) direction] Pnma Imma I4/mcm R 4 [ (1,1,0) direction] Pm-3m X 5 R 4 [ (1,0,0) direction] R 5 M 2 T(C)

15 PrNiO 3 P2 1 /n11(p2 1 /c) instead of Pnma? Medarde et al. PRL (2007) R 1 Fm-3m Amplitudes SrZrO3 PrNiO3 R4 (Imma) M3 (P4/mbm) X5 (Cmcm) R (Imma) 0.06 (C2/m) M2 (P4/mbm) ?? R1 (Fm-3m) R3 (I4/mmm) M5 (Pmna) P2 1 /n11

16 Polarization vectors in Leucite I4 1 /a Palmer et. (Amer. Miner. 82 (1997) 16 Ia-3d Γ 3 KAlSi 2 O 6 Γ 4 I4 1 /ac I4 1 /a Q Γ 3 Γ 4 I4 1 /a dot product e(4k).e(t) Γ 4 Γ 1 Γ 3 Induced effect : 2 Q Γ3 = α Q Γ4 T (K)

17 Polymorphism: nephelines Na 8-r Al 8-r Si 8r O 4 (r 0) Virtual arystotype: P6 3 mc P6 3 Ampl. (Ǻ) Dim. GM2 (P63): M1(P63mc,2x2x1): M2(P63,2x2x1): (max. atomic displ. : 1.34Ǻ)

18 Mode decomposition vs. ab-initio calculations SrAl 2 O 4 (Larsson et al. 2008) P P2 1 P two different displacive instabilities: Γ 4 P312 C222 1 Γ 5 (b) M 3-1q Γ 6 Γ 6 C2 M 3-1q P P M 2-1q E(mRy) M 2-1q P2 1

19 SrAl 2 O 4 Comparison of mode decomposition of experimental and ab-initio structures Amplitudes and dot products of polarization vectors : irrep M 2-1q Γ 6 M 3-1q Γ 5 Γ 4 dim Amp. prod. Amp. prod. Amp. prod. Amp. prod. Amp. prod. Exp. Struct ab-initio

20 Mode decomposition in "collapse" high pressure phase transitions Lillianite: Pb3Bi2S6 Olsen et al., Inorg. Chem. 2008,47 6/56 0 GPa Bbmm 4.7 GPa Pbnm

21 Mode decomposition in "collapse" high pressure phase transitions Lillianite: Pb 3 Bi 2 S 6 Mode decomposition of High-pressure phase: Active irrep distortion but also large fully symmetric distortion Fully symmetric distortion: irrep GM1 symmetry breaking distortion: active irrep Y2-

22 Symmetry-mode coordinates in the structure refinement, instead of the individual atomic coordinates: AMPLIMODES FullProf (Juan Rodriguez-Carvajal) (for powder or single crystal diffraction refinement) One expects: a natural hierarchy of parameters less correlations with atomic (thermal) displacement parameters better control of the refinement

23 Example of PCR file for FullProf corresponding to the compound LaMnO 3! Polarisation Vectors of Symmetry Modes for each atom V_MODES 12 Symbols of the Irreducible representations! Nm Atm Irrep Vx Vy Vz Coeff 1 O1 R O2 R La R O1 R Polarisation. vectors components 7 O2 M ! Amplitudes of Symmetry Modes A_MODES Q1_R Q2_R Q3_R Q4_X Q5_X Q6_M Q7_M ! > Profile Parameters for Pattern # 1 Keyword, # of modes, output for FST Names of amplitudes, values and refinement codes (allowing constraints)! Scale Shape1 Bov Str1 Str2 Str3 Strain-Model E

24 Example of direct refinement of mode amplitudes with FullProf: Symmetry Mode amplitudes have very different amplitudes and their standard deviations may differ in orders of magnitude => Amplitudes of symmetry modes ==> Name Value Sigma Q1_GM Q2_GM Q3_GM Q4_GM Q5_GM Q6_GM Q7_GM Q8_X Q9_X Q10_X Q11_X Q12_X dominant irrep distortions with much smaller standard deviations

25 Other programs: