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 WLottermoser W, Steiner K, Grodzicki M, Kirfel A, Amthauer G, Steiner K, Grodzicki M, Kirfel A, Amthauer G

Dep. of Materials Engineering and Physics/Univ. of Salzburg Dep. of Materials Engineering and Physics/Univ. of Salzburg

Zur Anzeige wird der QuickTime™ Dekompressor „“

benötigt.

OverviewOverview

SpectroscopySpectroscopy DiffractometryDiffractometry Mössbauer/NQRMössbauer/NQR X-ray, synchrotron,n X-ray, synchrotron,n00

semi-quant.semi-quant. experimentalexperimental DEN DEN DFT full- DFT full-

quant.quant.

EFG/H(0)/µEFG/H(0)/µ

Example: synth. FeExample: synth. Fe22SiOSiO44

The electric field gradient (EFG)The electric field gradient (EFG)

Vxx Vxy Vxz

EFG = V = - Vyx Vyy Vyz

Vzx Vzy Vzz

...with Vij = V/ ij (i,j = x,y,z)Choice of the main axes components: | Vzz| | Vyy| | Vxx|Geometrically: EFG = tensor ellipsoid Asymmetry parameter: = (Vxx - Vyy )/ Vzz

2 main contrib. to the EFG at the nucleus:1. the own e-shell (electronic contrib.)1. the own e-shell (electronic contrib.)2. the ligands (lattice contrib.)2. the ligands (lattice contrib.)

Experimental determination of the Experimental determination of the EFGEFG

Mößbauer spectroscopyMößbauer spectroscopy Quantity to be measured: Quadrupole splitting QS = 1/2 e Q Vzz 1 + 2/3 Asymmetry parameter (Vxx – Vyy)/ Vzz

With SCMBS additionally:Angle betw. k-vector of the inc. -rays (=crystal axis) and Vzz

Angle betw. proj. of k to the (Vxx, ,Vyy)-plane and Vxx

I=1/2

I=3/2

Example : synth. fayalite FeExample : synth. fayalite Fe22SiOSiO44

Synth. fayalite -Fe2SiO4, orthorhombic, SG Pnma, Z=4

a = 1.0459(3), b = 0.6074(1), c = 0.4815(1) nm Fe2+ -cations: M1(4a, PS -1) M2 (4c,PS m)

-->amazing structural u. magn. properties-->amazing structural u. magn. properties

a

b

c

x

yz

Stereogram EFG + H(0)Stereogram EFG + H(0)

Lottermoser W, Forcher K, Amthauer G, Treutmann W, Hosoya S: Phys Chem Miner 23 No. 7, 432 - 438 (1996)

M2M1

H(0)

Semi-quantitative Semi-quantitative method/Nanoscopemethod/Nanoscope

(x,y,z) = (x,y,z) = hklhkl e e-2-2ii (h*x/a + k*y/b + l*z/c)(h*x/a + k*y/b + l*z/c)

h k lh k l

A = Structure amplitude A = Structure amplitude ||hklhkl| = 1/V| = 1/VZZ * |F * |Fhklhkl||

(F(Fobsobs) - ) - (F(Fcal,sphericalcal,spherical) =) = asphericalaspherical (Difference fourier) (Difference fourier) Idea: Aspherical densities-->EFG calc.Idea: Aspherical densities-->EFG calc. Special software (Comp. tomography, Special software (Comp. tomography,

DEDLOT under IDLDEDLOT under IDL®® ): ): EFG as wire frame graphics,EFG as wire frame graphics, calculated from difference electron calculated from difference electron

densities (DEDs) on a Mac G5densities (DEDs) on a Mac G5®®

Problem, especially on higher symmetric sites like M2:series termination errors („Fourier ghosts“)

Solution:Fourier-„ghost-buster-program“

Jean Baptiste Joseph Fourier (1768-1830)

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

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

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

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

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

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

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

ConclusionsConclusions

By application of the difference electron nanoscope By application of the difference electron nanoscope (DEN) the electric field gradient (EFG) can be (DEN) the electric field gradient (EFG) can be determined with high accuracydetermined with high accuracy

The EFG constitutes the link between (synchrotron-) The EFG constitutes the link between (synchrotron-) diffractometry and spectroscopy (SCMBS or NQR/NMR) diffractometry and spectroscopy (SCMBS or NQR/NMR)

Essential for success is a multitude of exquisite structure Essential for success is a multitude of exquisite structure factors preferably stemming from synchrotron diffraction factors preferably stemming from synchrotron diffraction measurements in order to widely avoidmeasurements in order to widely avoid

series termination errorsseries termination errors The difference electron densities (DEDs) within the unit The difference electron densities (DEDs) within the unit

cell may be viewed 3D with a wire frame model of the cell may be viewed 3D with a wire frame model of the EFGEFG

ConclusionsConclusions

It is possible to see amazing details like DED It is possible to see amazing details like DED maxima around certain oxygens reponsible for maxima around certain oxygens reponsible for superexchange coupling (also on M2!)superexchange coupling (also on M2!)

It should be possible to establish the DEN-It should be possible to establish the DEN-method (semi-quant.) as another procedure to method (semi-quant.) as another procedure to derive an EFG and direction of magnetic derive an EFG and direction of magnetic moments besides Mössbauer /NQR (exp.), moments besides Mössbauer /NQR (exp.), neutron diffraction and DFT (full-quant.)neutron diffraction and DFT (full-quant.)