1. Nanotechnology congress & Expo August 11-13, 2015, Frankfurt, Germany Application of a Difference Electron Nanoscope (DEN): Correlation between 3D Magnetical Structures of Synthetic Fayalite with Synchrotron and Neutron Diffraction and Mössbauer Spectroscopy Part II Lottermoser W, Steiner K, Grodzicki M, Kirfel A, Amthauer G Lottermoser W, Steiner K, Grodzicki M, Kirfel A, Amthauer G Dep. of Materials Engineering and Physics/Univ. of Salzburg

2. Overview Spectroscopy Diffractometry Mössbauer/NQR X-ray, synchrotron,n 0 Mössbauer/NQR X-ray, synchrotron,n 0 semi-quant. semi-quant. experimental DEN DFT full- quant. experimental DEN DFT full- quant. EFG/H(0)/µ EFG/H(0)/µ Example: synth. Fe 2 SiO 4 Example: synth. Fe 2 SiO 4

3. The electric field gradient (EFG) V xx V xy V xz EFG =  V = - V yx V yy V yz V zx V zy V zz...with V ij =   V/  i  j (i,j = x,y,z) Choice of the main axes components: | V zz |  | V yy |  | V xx | Geometrically: EFG = tensor ellipsoid Asymmetry parameter:  = (V xx - V yy )/ V zz 2 main contrib. to the EFG at the nucleus: 1. the own e-shell (electronic contrib.) 2. the ligands (lattice contrib.)

4. Experimental determination of the EFG Mößbauer spectroscopy Mößbauer spectroscopy Quantity to be measured:   Quadrupole splitting QS = 1/2 e Q V zz  1 +  2 /3 Asymmetry parameter  (V xx – V yy )/ V zz With SCMBS additionally: Angle  betw. k-vector of the inc.  -rays (=crystal axis) and V zz Angle  betw. proj. of k to the (V xx,,V yy )-plane and V xx I=1/2 I=3/2

5. Example : synth. fayalite Fe 2 SiO 4 Synth. fayalite  -Fe 2 SiO 4, orthorhombic, SG Pnma, Z=4 a = 1.0459(3), b = 0.6074(1), c = 0.4815(1) nm Fe 2+ -cations: M1(4a, PS -1) M2 (4c,PS m) -->amazing structural u. magn. properties -->amazing structural u. magn. properties

6. Stereogram EFG + H(0) Lottermoser W, Forcher K, Amthauer G, Treutmann W, Hosoya S: Phys Chem Miner 23 No. 7, 432 - 438 (1996) M2 M1 H(0)

7. Semi-quantitative method/Nanoscope  (x,y,z) =  hkl e -2  i (h*x/a + k*y/b + l*z/c)  (x,y,z) =  hkl e -2  i (h*x/a + k*y/b + l*z/c) h k l h k l A = Structure amplitude A = Structure amplitude |  hkl | = 1/V Z * |F hkl | |  hkl | = 1/V Z * |F hkl |  (F obs ) -  (F cal,spherical ) =  (F obs ) -  (F cal,spherical ) =  aspherical (Difference fourier)  aspherical (Difference fourier) Idea: Aspherical densities-->EFG calc. Idea: Aspherical densities-->EFG calc. Special software (Comp. tomography, DEDLOT under IDL ® ): Special software (Comp. tomography, DEDLOT under IDL ® ): EFG as wire frame graphics, EFG as wire frame graphics, calculated from difference electron densities (DEDs) on a Mac G5 ® calculated from difference electron densities (DEDs) on a Mac G5 ®

8. Problem, especially on higher symmetric sites like M2: series termination errors („Fourier ghosts“) Solution: Fourier- „ghost-buster- program“ Jean Baptiste Joseph Fourier (1768-1830)

9. DEN images: M2 at 0.22| 0.75 |0.48: [001] DEDs + EFG | Oct.

10. DEN images: M2 at 0.22| 0.75 |0.48: [100] DEDs + EFG | Oct.

11. DEN images: M2 at 0.22| 0.75 |0.48 : [010] DEDs + EFG | Oct.

12. DEN images: M2 at 0.22| 0.75 |0.48: [001] DEDs + H(0), T ≤ 50K

13. DEN images: M2 at 0.22| 0.75 |0.48: [100] DEDs + H(0), T ≤ 50K

14. DEN images: M2 at 0.22| 0.75 |0.48 : [010] DEDs + H(0), T ≤ 50K

15. DEN images: M1 at 1/2 1/2 1/2: [001] DEDs + MO

16. Conclusions By application of the difference electron nanoscope (DEN) the electric field gradient (EFG) can be determined with high accuracy By application of the difference electron nanoscope (DEN) the electric field gradient (EFG) can be determined with high accuracy The EFG constitutes the link between (synchrotron-) diffractometry and spectroscopy (SCMBS or NQR/NMR) The EFG constitutes the link between (synchrotron-) diffractometry and spectroscopy (SCMBS or NQR/NMR) Essential for success is a multitude of exquisite structure factors preferably stemming from synchrotron diffraction measurements in order to widely avoid Essential for success is a multitude of exquisite structure factors preferably stemming from synchrotron diffraction measurements in order to widely avoid series termination errors series termination errors The difference electron densities (DEDs) within the unit cell may be viewed 3D with a wire frame model of the EFG The difference electron densities (DEDs) within the unit cell may be viewed 3D with a wire frame model of the EFG

17. Conclusions It is possible to see amazing details like DED maxima around certain oxygens reponsible for superexchange coupling (also on M2!) It is possible to see amazing details like DED maxima around certain oxygens reponsible for superexchange coupling (also on M2!) It should be possible to establish the DEN-method (semi- quant.) as another procedure to derive an EFG and direction of magnetic moments besides Mössbauer /NQR (exp.), neutron diffraction and DFT (full-quant.) It should be possible to establish the DEN-method (semi- quant.) as another procedure to derive an EFG and direction of magnetic moments besides Mössbauer /NQR (exp.), neutron diffraction and DFT (full-quant.)