Glass Structure by Synchrotron Techniques Sabyasachi Sen Dept. of Materials Science University of California, Davis Glass Structure by Synchrotron Techniques • Knowledge of structure is • Practically all atomic-scale important in glass science structural characterization and technology techniques are based on in: – Understanding and – Elastic scattering controlling physical and (e.g. neutron scattering, chemical properties SAXS, WAXS, AXS) – Leads to optimization of – Spectroscopy (XAS, magnetic processing resonance, Raman/IR, UV/VIS, XPS, QENS, XPCS, IXS etc.) How do synchrotrons work? • A Synchrotron accelerates electrons using magnets and RF waves, into an orbit at almost the speed of light. When electrons are deflected through magnetic fields they emit extremely bright light, million times brighter than sunlight. • Basic parts of synchrotron – 1. Electron gun – 2. LINAC – 3.Booster Ring – 4. Storage Ring – 5. & 6. Beamline- End Station Why Synchrotron ? Brilliance / Intensity Up to 12 orders of magnitude Brighter than laboratory source 45 synchrotron sources worldwide 11 in the USA SPRING8 in Japan is the brightest Neutron Sources • Reactor sources Neutrons produced from fission of 235U. Moderated to thermal energies (5 to 100 meV corresponding to wavelengths of 1 to 4 Å) e.g. with D2O. These are continuous sources. • Spallation sources Proton acclerator and heavy metal target (e.g. W or U) Higher energy neutrons, comes in pulses, wider range of incident neutron energies Neutron vs. x-ray: properties Neutron Photon • Mass = 1.675x10-27 • Mass = 0 kg • Spin = 1 • Charge = 0; spin = ½ • Charge =0 • Has magnetic dipole • Magnetic Moment = 0 moment • High-energy x-ray (40 • Wavelength can vary to 100 keV) provides over a wide range wavelength range of (e.g. 1 to 30 Ǻ) 0.125 to 0.3 Ǻ Neutron vs. x-ray: advantages & disadvantages Neutron X-ray = inter-atomic spacing Penetrates bulk matter = inter-atomic spacing Strong isotopic contrast High brilliance. High resolution possible Needs small sample Magnetic order can be probed Low brilliance, needs large Weak scattering from light sample elements Not suitable for some No isotopic contrast elements e.g. B (needs Radiation damage to samples isotopic replacement) Scattering Techniques X-ray and Neutron Scattering Theory of elastic x-ray (and neutron) scattering Elastic (Thomson) scattering of photon by one electron: d = # of scattered photons into unit solid angle/ # of incident photons per unit time d 2 2 2 d e 1 cos 2 r0 P d mc 2 2 r0 = 2.82 fm is the Thomson scattering length, P is the polarization factor. Atom has many electrons in the form of an electron cloud around the nucleus. Theory of elastic scattering (contd.) Atomic form factor or scattering factor f is the ratio of amplitude of wave scattered by an atom to that by an electron f (Q ) (r)e iQ.r dr 0 FT of the spatial distribution of electron cloud, considered to spherically symmetric. A wave has a momentum p = ħk . Momentum transfer due to scattering is Q = kf − ki. d ** Neutrons are scattered by nuclei; b 2 for single atom d b= nuclear scattering cross section (Q-independent !) X-ray and Neutron scattering lengths Theory of elastic scattering (contd.) For many atoms with spherical electron clouds centered around each atom : add up phases of the wavelets scattered from all the electron clouds (atoms) in the sample. Theory of elastic scattering (contd.) d 2 (elastic ) c f (Q ) I x (Q ) d Self Distinct Measured experimentally (plus inelastic/Compton scattering) Distinct scattering contains structural information !! It is related to structure factor S(Q), the FT of the pair distribution function g(r): ' iQ .( r r ') S (Q ) V drdr e N ( r ) N ( r ' ) positional correlation of atoms Theory of elastic scattering (contd.) Theory of elastic scattering (contd.) Theory of elastic scattering (contd.) How to obtain G(r) from I(Q) ? How to obtain DFs from I(Q) ? corrections Effect of cutoff on resolution As4O6 molecule J. Non-Cryst. Sol 111 (1989) 123. Physical meaning of RDF First Coordination shell g(r) Second Coordination shell 1.0 0 2 3 Types of Disorder Dense Plastic fluid Crystals Liquids Glasses Nanoparticles Defects Orientational Disorder Orientational Perfect Quasicrystals Crystals Translational Disorder Glass structure at various length scales Glass structure at various length scales ‘First sharp diffraction peak’ 1 S(Q) 0 Total -1 Intra-molecular 8 Inter-molecular 0 5 10 15 6 -1 Q (Å ) ) r ( 4 T Sine Fourier 2 intra inter Transformation 0 S(Q) T(r) = 4 r.g(r) 0 2 4 6 8 r (Å) Intermediate-range order B C A case study of molecular Ge-doped BAsData 1 -3:37:50S PMglasses: 11/13/2008 8 1 8 0 7 1 6 0 B a n d -1 6 1 4 0 5 1 2 0 T g (° C ) 4 1 0 0 3 80 2 60 1 40 Relative Intensity0 of 273 cm 20 30 35 40 45 50 55 60 65 70 Atom % Ge+As (x+y) S. Soyer-Uzun et al. , 2009, JPC-C Intermediate-range order-contd. B C D a t a 1 D E F A case study of molecularG Ge-doped As-S glasses: H D a t a 1 8 1 .2 6 1 .4 S =35 N e u tr o n 7 1 .2 4 X - r a y N e u tr o n S=37.5 ) 1 .2 6 -1 1 .2 2 X - r a y FSDP Intensity S = 40 5 1 .2 1 S = 45 (Q) 4 1 .1 8 X S S = 57 0 .8 3 1 .1 6 S = 60.5 2 1 .1 4 Position of FSDP (Å 0 .6 S = 65 1 1 .1 2 0 1 .1 0 .4 0 5 10 15 20 30 35 40 45 50 55 60 65 70 -1 Q (Å ) Atom % Ge+As (x+y) S. Soyer-Uzun et al. , 2009, JPC-C Intermediate-range order-contd. N e u tro n X -ra y D a t a 1 Data 1 1:50:58 PM 9/23/2008 A case study of molecular Ge-doped As-S glasses: 0 .3 2 34 1 .3 1 32 1 .2 0 .3 0 .9 X-ray FSDP Intensity ) 30 1 .1 2 -1 0 .2 8 0 .8 / 28 1 N e u t r o n 0 .2 6 Q X - r a y 26 FSDP 0 .9 0 .7 N e u t r o n 0 .2 4 X - r a y (Å ) 0 .8 24 0 .6 0 .2 2 0 .7 FSDP W idth (Å 22 Neutron FSDP Intensity 0 .5 0 .2 0 .6 20 0 .5 0 .4 0 .1 8 18 -2 0 2 4 6 8 30 35 40 45 50 55 60 65 70 -1 Relative Intensity of 273 cm B a n d Atom % Ge+As (x+y) S. Soyer-Uzun et al. , 2009, JPC-C Partial Pair Distribution Functions: The Holy Grail 1 Remember : S (Q ) 1 c f (Q ) c f (Q ) S (Q ) 1 2 , c f (Q ) For a material with n different types of atoms there are n(n+1)/2 partial structure factors S (Q) and hence, that many partial pair distribution functions g (r). A complete structural description at the short-range requires this information. Need to vary the weighting factors of S (Q) in the above equation: combined neutron & x-ray, isotope substitution for neutron and anomalous x-ray scattering (AXS) Partial Structure Factors: vitreous GeO2 Partial Pair Distribution Functions: vitreous SiO2 Experiment Molecular Dynamics SSiSi(Q) 15 10 S (Q) (Q) SiO S 5 SOO(Q) 0 0 5 10 15 Q (Å -1) Nat 2 2 2 2 I N (Q ) c Si Nat b Si 2 c Si c O Nat b Si b O c O b O S SiSi (Q ) 1 29 2 2 2 2 I N (Q ) c Si 29 b Si 2 c Si c O 29 b Si b O c O b O S SiO (Q ) 1 2 2 2 2 I X (Q ) c Si f Si (Q ) 2 c Si c O f Si (Q ) f O (Q ) c O f O (Q ) S OO (Q ) 1 Anomalous x-ray scattering (AXS) Marked change in atomic form factor near absorption edge: Kramers-Krönig Dispersion Relation f” f’ E (keV) E (keV) Anomalous x-ray scattering (AXS): contd. • Limited applicability but powerful technique • Good for heavy elements • Longer range than EXAFS • Depends on very small differences between S(Q) collected near and away from the absorption edge: hence requires sufficient statistics and careful data processing • Absorption and fluorescence corrections are critical AXS on Rb2O-GeO2 glasses Ge-Rb third neighbor D.L. Price et al., PRB, 55, 11249 (1997) Diffraction + Simulation (MD/RMC) • Often a combined analysis is the best way to obtain structural information • Most useful for multi- component systems (will discuss later) • Use SRO as constraint and Grandinetti and coworkers investigate IRO PRB, 70, 064202, 2004 (will discuss later) Small-Angle X-ray Scattering (SAXS) • X-rays (and neutrons) are also scattered at very small angles (0.001 to 0.5 Å-1) from large scale (bigger than individual atoms- e.g. 1-100 nm) fluctuations in electron/nuclear density • For glasses small-angle scattering originates typically from density and/or concentration fluctuations related or unrelated to phase separation • For glass-ceramics the coexistence of glass and crystal with different densities is important • Particle shape, size distribution, crystallinity SAXS-Fundamentals d 2 Differential Scattering Cross-section = 2 (Q ) 1 2 V 1 nP (Q ) S (Q ) d N A d ( b i / M i ) V1 = scattering particle volume n= concentration of particles d= density of particles bi,Mi = scattering length and atomic weights of elements in the particle NA = Avogadro’s number 1, 2 = scattering length density of particle and matrix P(Q) = form factor (intra-particle atomic arrangement) S(Q)= structure factor (inter-particle correlations) SAXS-Fundamentals: Contd.