Vibrational Spectroscopy

Transcription

1 Vibrational Spectroscopy Keith Refson STFC Rutherford Appleton Laboratory August 28, 2009 Density Functional Methods for Experimental Spectroscopy 2009: Oxford 1 / 22

2 Two similar structures Zincblende and diamond dispersion LO/TO splitting DFPT with LO/TO splitting in NaCl LO/TO splitting in non-cubic systems The non-analytic term and Born Charges Electric Field response in CASTEP Ionic and Electronic Dielectric Permittivity Example: NaHF2 Dynamical charges in NaHF2 Density Functional Methods for Experimental Spectroscopy 2009: Oxford 2 / 22

3 Two similar structures Two similar structures Zincblende and diamond dispersion LO/TO splitting DFPT with LO/TO splitting in NaCl LO/TO splitting in non-cubic systems The non-analytic term and Born Charges Electric Field response in CASTEP Ionic and Electronic Dielectric Permittivity Example: NaHF2 Dynamical charges in NaHF2 Zincblende BN Diamond Density Functional Methods for Experimental Spectroscopy 2009: Oxford 3 / 22

4 Zincblende and diamond dispersion Two similar structures Zincblende and diamond dispersion LO/TO splitting DFPT with LO/TO splitting in NaCl LO/TO splitting in non-cubic systems The non-analytic term and Born Charges Electric Field response in CASTEP Ionic and Electronic Dielectric Permittivity Example: NaHF2 Dynamical charges in NaHF2 Phonon dispersion curves BN-zincblende ω (cm -1 ) Γ X Γ L W X ω (cm -1 ) diamond 0 Γ X Γ L W X Cubic symmetry of Hamiltonian predicts triply degenerate optic mode at Γ in both cases. 2+1 optic mode structure of BN violates group theoretical prediction. Phenomenon known as LO/TO splitting. Density Functional Methods for Experimental Spectroscopy 2009: Oxford 4 / 22

5 LO/TO splitting Two similar structures Zincblende and diamond dispersion LO/TO splitting DFPT with LO/TO splitting in NaCl LO/TO splitting in non-cubic systems The non-analytic term and Born Charges Electric Field response in CASTEP Ionic and Electronic Dielectric Permittivity Example: NaHF2 Dynamical charges in NaHF2 Dipole created by displacement of charges of long-wavelength LO mode creates induced electric field. For TO motion E q E.q = 0 For LO mode E.q 0 and E-field adds additional restoring force. Frequency of LO mode is upshifted. Lyndane-Sachs-Teller relation for cubic case: ωlo 2 ω T 2 O = ǫ 0 ǫ LO frequencies at q = 0 depend on dielectric permittivity Density Functional Methods for Experimental Spectroscopy 2009: Oxford 5 / 22

6 DFPT with LO/TO splitting in NaCl Two similar structures Zincblende and diamond dispersion LO/TO splitting DFPT with LO/TO splitting in NaCl LO/TO splitting in non-cubic systems The non-analytic term and Born Charges Electric Field response in CASTEP Ionic and Electronic Dielectric Permittivity Example: NaHF2 Dynamical charges in NaHF2 LO modes can be seen in infrared, INS, IXS experiments, but not raman. ω (cm -1 ) NaCl phonon dispersion 300 Exper: G. Raunio et al Γ X Γ L W X ( ) (Σ) q ( ) (Q) (Z) Density Functional Methods for Experimental Spectroscopy 2009: Oxford 6 / 22

7 LO/TO splitting in non-cubic systems Two similar structures Zincblende and diamond dispersion LO/TO splitting DFPT with LO/TO splitting in NaCl LO/TO splitting in non-cubic systems The non-analytic term and Born Charges Electric Field response in CASTEP Ionic and Electronic Dielectric Permittivity Example: NaHF2 Dynamical charges in NaHF2 ω (cm -1 ) Γ K M Γ A In systems with unique axis (trigonal, hexagonal, tetragonal) LO- TO splitting depends on direction of q even at q = 0. LO frequency varies with angle in α-quartz Zone Center Frequency (1/cm) Approach Angle Density Functional Methods for Experimental Spectroscopy 2009: Oxford 7 / 22

8 The non-analytic term and Born Charges Two similar structures Zincblende and diamond dispersion LO/TO splitting DFPT with LO/TO splitting in NaCl LO/TO splitting in non-cubic systems The non-analytic term and Born Charges Electric Field response in CASTEP Ionic and Electronic Dielectric Permittivity Example: NaHF2 Dynamical charges in NaHF2 LO-TO splitting at q 0 is automatically included in DFPT. At q = 0 exactly, need to add additional non-analytic term to dynamical matrix C κ,κ α,α (q = 0)(NA) = 4π P γ q γz P κ,γα γ q γ Zκ,γ α P Ω 0 γγ q γ ǫ γγ q γ ǫ γγ Zκ,βα is the dielectric permittivity tensor is the Born Effective Charge tensor Z κ,β,alpha = V P β x κ,α = F κ,α E β Z is polarization per unit cell caused by displacement of atom κ in direction α or force exerted on ion by macroscopic electric field. Zκ,βα and ǫ γγ can both be computed via DFPT response to electric field perturbation. (Dipole-dipole model use for Coulombic tail correction in Fourier interpolation procedure also depends on Z and ǫ. Not included in most supercell calculations be suspicious of convergence in case of polar systems). Density Functional Methods for Experimental Spectroscopy 2009: Oxford 8 / 22

9 Electric Field response in CASTEP Two similar structures Zincblende and diamond dispersion LO/TO splitting DFPT with LO/TO splitting in NaCl LO/TO splitting in non-cubic systems The non-analytic term and Born Charges Electric Field response in CASTEP Ionic and Electronic Dielectric Permittivity Example: NaHF2 Dynamical charges in NaHF2 Can also apply DFPT to electric field perturbation. Need trick to evaluate position operator. Evaluate k φ. See NMR lecture for details. set task = efield or task = phonon+efield Convergence controlled by efield energy tol Computes dielectric permittivity for crystals and polarisability (for molecules) Includes lattice contribution for ω 0 response. Writes additional file seedname.efield containing ǫ γγ (ω) in infrared region. =============================================================================== Optical Permittivity (f->infinity) DC Permittivity (f=0) =============================================================================== =============================================================================== Polarisabilities (A**3) Optical (f->infinity) Static (f=0) =============================================================================== Density Functional Methods for Experimental Spectroscopy 2009: Oxford 9 / 22

10 Ionic and Electronic Dielectric Permittivity Two similar structures Zincblende and diamond dispersion LO/TO splitting DFPT with LO/TO splitting in NaCl LO/TO splitting in non-cubic systems The non-analytic term and Born Charges Electric Field response in CASTEP Ionic and Electronic Dielectric Permittivity Example: NaHF2 Dynamical charges in NaHF2 Pure covalent system - Si Z = 0.009, Ionic system, NaCl. ǫ 0 = 6.95, ǫ = Z (Na) = 1.060, Z (Cl) = α-quartz, SiO 2 : ǫ = (exp: ǫ 0 = 4.64/4.43) Z (O 1 ) = Note anisotropic tensor character of Z. ǫ 0 = Z (Si) = Density Functional Methods for Experimental Spectroscopy 2009: Oxford 10 / 22

11 Example: NaHF2 Two similar structures Zincblende and diamond dispersion LO/TO splitting DFPT with LO/TO splitting in NaCl LO/TO splitting in non-cubic systems The non-analytic term and Born Charges Electric Field response in CASTEP Ionic and Electronic Dielectric Permittivity Example: NaHF2 Dynamical charges in NaHF2 Unusual bonding, nominally ionic Na + FHF, with linear anion. Layer structure, R 3 space group. Phase transition to monoclinic form at 0.4 GPa. Phonon spectrum measured at ISIS on TOSCA high-resolution neutron powder spectrometer. No selection rule absences Little or no anharmonic overtone contamination of spectra No control over (q, ω) path - excellent for molecular systems but spectra hard to interpret if dispersion present. Density Functional Methods for Experimental Spectroscopy 2009: Oxford 11 / 22

12 Dynamical charges in NaHF2 Two similar structures Zincblende and diamond dispersion LO/TO splitting DFPT with LO/TO splitting in NaCl LO/TO splitting in non-cubic systems The non-analytic term and Born Charges Electric Field response in CASTEP Ionic and Electronic Dielectric Permittivity Example: NaHF2 Dynamical charges in NaHF2 highly anisotropic Z xy z (H) (F) (Na) charge density n (1) (r) from DFPT shows electronic response under perturbation Charge on F ions moves in response to H displacement in z direction. n (1) (r) response to Hx (blue) and Hz (green) n (1) (r) response to Ex (blue) and Ez (green) Density Functional Methods for Experimental Spectroscopy 2009: Oxford 12 / 22

13 Inelastic Neutron Scattering INS of Ammonium Fluoride Single-crystal infrared Powder infrared Modelling of powder IR Non-resonant raman Raman scattering of t-zro2 Inelastic X-Ray scattering IXS of Diaspore Density Functional Methods for Experimental Spectroscopy 2009: Oxford 13 / 22

14 Inelastic Neutron Scattering Inelastic Neutron Scattering INS of Ammonium Fluoride Single-crystal infrared Powder infrared Modelling of powder IR Non-resonant raman Raman scattering of t-zro2 Inelastic X-Ray scattering IXS of Diaspore To model spectra need to treat scattering dynamics of incident and emergent radiation. In case of INS interaction is between point neutron and nucleus - scalar quantity b depends only on nucleus specific properties. d 2 σ dedω = k f k i b 2 S(Q, ω) Q is scattering vector and ω is frequency - interact with phonons at same wavevector and frequency. Full measured spectrum includes overtones and combinations and instrumental geometry and BZ sampling factors. Need specific spectral modelling software to incorporate effects as postprocessing step following CASTEP phonon DOS calculation. A-Climax : A. J. Ramirez-Cuesta Comput. Phys. Comm (2004)) Density Functional Methods for Experimental Spectroscopy 2009: Oxford 14 / 22

15 INS of Ammonium Fluoride Inelastic Neutron Scattering INS of Ammonium Fluoride Single-crystal infrared Powder infrared Modelling of powder IR Non-resonant raman Raman scattering of t-zro2 Inelastic X-Ray scattering IXS of Diaspore NH 4 F is one of a series of ammonium halides studied in the TOSCA spectrometer. Collab. Mark Adams (ISIS) Structurally isomorphic with ice ih INS spectrum modelled using A-CLIMAX software (A. J. Ramirez Cuesta, ISIS) Predicted INS spectrum in mostly excellent agreement with experiment NH 4 libration modes in error by 5%. Complete mode assignment achieved. Density Functional Methods for Experimental Spectroscopy 2009: Oxford 15 / 22

16 Single-crystal infrared Inelastic Neutron Scattering INS of Ammonium Fluoride Single-crystal infrared Powder infrared Modelling of powder IR Non-resonant raman Raman scattering of t-zro2 Inelastic X-Ray scattering IXS of Diaspore Prediction of reflectivity of optically flat single crystal surface given as function of q - projected permittivity ǫ q (ω) R(ω) = q (ω) 1 q (ω) + 1 ǫ 1/2 ǫ 1/2 with ǫ q defined in terms of ǫ and mode oscillator strength S m,αβ ǫ q (ω) = q.ǫ.q + 4π Ω 0 X m 2 q.s.q = q.ǫ(ω).q ω2 ω 2 m ǫ(ω) is tabulated in the seendname.efield file written from a CASTEP efield response calculation. Example BiFO3 (Hermet et al, Phys. Rev B 75, (2007) Density Functional Methods for Experimental Spectroscopy 2009: Oxford 16 / 22

17 Powder infrared Inelastic Neutron Scattering INS of Ammonium Fluoride Single-crystal infrared Powder infrared Modelling of powder IR Non-resonant raman Raman scattering of t-zro2 Inelastic X-Ray scattering IXS of Diaspore α-quartz IR Intensity (Arb. Units) Phonon Frequency (cm -1 ) Straightforward to compute peak areas. Peak shape modelling depends on sample and experimental variables. Multiphonon and overtone terms less straightforward. Density Functional Methods for Experimental Spectroscopy 2009: Oxford 17 / 22

18 Modelling of powder IR Inelastic Neutron Scattering INS of Ammonium Fluoride Single-crystal infrared Powder infrared Modelling of powder IR Non-resonant raman Raman scattering of t-zro2 Inelastic X-Ray scattering IXS of Diaspore See E. Balan, A. M. Saitta, F. Mauri, G. Calas. First-principles modeling of the infrared spectrum of kaolinite. American Mineralogist, 2001, 86, Spectral shape determined by optical effects and shifted LO modes in specific size/shape of crystallites. Density Functional Methods for Experimental Spectroscopy 2009: Oxford 18 / 22

19 Non-resonant raman Inelastic Neutron Scattering INS of Ammonium Fluoride Single-crystal infrared Powder infrared Modelling of powder IR Non-resonant raman Raman scattering of t-zro2 Inelastic X-Ray scattering IXS of Diaspore Raman scattering depends on raman activity tensor I raman αβ = d 3 E dε α dε β dq m = dǫ αβ dq m i.e. the activity of a mode is the derivative of the dielectric permittivity with respect to the displacement along the mode eigenvector. CASTEP evaluates the raman tensors using hybrid DFPT/finite displacement approach. Raman calculation is fairly expensive and is not activated by default (though group theory prediction of active modes is still performed) Parameter calculate raman = true in a task=phonon calculation. Spectral modelling of IR spectrum is relatively simple function of activity. with the thermal population factor dσ dω = (2πν)4 c 4 e S.I.e L 2 h(n m + 1) 4πω m n m =» «1 ωm exp 1 k B T which is implemented in dos.pl using the -raman flag. Density Functional Methods for Experimental Spectroscopy 2009: Oxford 19 / 22

20 Raman scattering of t-zro2 Inelastic Neutron Scattering INS of Ammonium Fluoride Single-crystal infrared Powder infrared Modelling of powder IR Non-resonant raman Raman scattering of t-zro2 Inelastic X-Ray scattering IXS of Diaspore Density Functional Methods for Experimental Spectroscopy 2009: Oxford 20 / 22

21 Inelastic X-Ray scattering Inelastic Neutron Scattering INS of Ammonium Fluoride Single-crystal infrared Powder infrared Modelling of powder IR Non-resonant raman Raman scattering of t-zro2 Inelastic X-Ray scattering IXS of Diaspore IXS spectrometers at ESRF, Spring-8, APS synchrotrons. Density Functional Methods for Experimental Spectroscopy 2009: Oxford 21 / 22

22 IXS of Diaspore Inelastic Neutron Scattering INS of Ammonium Fluoride Single-crystal infrared Powder infrared Modelling of powder IR Non-resonant raman Raman scattering of t-zro2 Inelastic X-Ray scattering IXS of Diaspore B. Winkler et el., Phys. Rev. Lett (2008) energy [mev] (0.5, 0, 0) to (0, 0, -0.33) wave vector [A -1 ] Density Functional Methods for Experimental Spectroscopy 2009: Oxford 22 / 22