Stanford Synchrotron Radiation Lightsource Introduction to Synchrotron X-ray Scattering Techniques Mike Toney, SSRL

1. Why do x-ray scattering? 2. Basics of an x-ray scattering experiment 3. Some examples ¾ SAXS: porous films ¾ Powder: Pd nanoparticles ¾ Textured films: ZnO nanostructures 4. Summary Why do SR X-ray scattering? ¾ Materials properties are caused or affected by their physical structure and morphology ¾ Improve your materials by understanding the structure.

fcc • Phase identification & quantify hcp • Where are the atoms: Atomic or molecular arrangement, crystal & surface structure • Strain, lattice parameters (unit cell size) • Grain/crystallite size (diffraction) • Pore/particle size (SAXS) • Other defects & disorder (faults, positional disorder) • Crystallite orientation or texture SR Scattering Experiment

slits (horz or vert) sample • variable aperture • define beam shape and acceptance beam

monochromator • double crystal M0 mirror • Si(111) or Si(220) • cylindrical or toroidal source • LN or water cooled • Rhodium-coated silicon • selects wavelength • harmonic rejection, power filter, collimating or focusing

2θ scattered Area detector k’ incident k Point detector Q = k’ - k

collect I(Q) All you care about is Q SR Scattering Experiment

2θ scattered Area detector k’ incident k Point detector Q = k’ - k

Diffraction: 5 All you care about is Q 10 peaks collect I(Q)

4 Scattering: 104 the rest 3 103 At SSRL: 2 102

1 101 • Area detector: 11-3

0 I(Q) (arb. units) I(Q) 10 • Point detectors: 2-1, 7-2, 10-2

10-1 • SAXS: 1-4

10-2 0 1 2 3 4 Q (Å) SR Scattering Experiment

Beamline 2-1 7-2 & 10-2 11-3 Detector Point Point Area High resolution High resolution Fast measurement Accurate peak Accurate peak Collect (nearly) whole position and shape position and shape pattern Advantages Weak peaks Weak peaks Variable energy Variable energy Reflectivity 4 degrees of motion Fixed wavelength Slow Slow Dis- Low resolution Only 2 axes of Can be difficult to find advantages motion textured peaks Peak shape and position inaccurate Complicated Weak peaks difficult Powders Single crystals Texture Phase determination Grazing-incidence Real time experiments Used for Reflectivity Anomalous diffraction Polycrystalline, small θ-2θ grains (e.g. soils) Surface studies Anomalous diffraction Thin films SR Scattering Experiment Advantages Area detector (11-3) ¾ Fast measurement ¾ Collect whole pattern Detector Disadvantages ¾ Fixed wavelength ¾ Low resolution Q ¾Peak shape & position inaccurate incident ¾ Weak peaks difficult scattered

Used for ¾ Texture (crystallite orientation) ¾ Real time experiments (electrochemistry, stress-strain) 2θ = scattering angle ¾ Polycrystalline, small grains (e.g. Q = (4π/λ) sin θ soils) ¾ Thin films SR Scattering Experiment Advantages Point detector (2-1) ¾ High resolution ¾Accurate peak position & shape ¾ Weak peaks ¾ Variable energy diffracted x-rays ¾ Reflectivity Disadvantages 2θ ¾ Slow θ ¾ Only 2 degrees of motion (θ, 2θ) incident x-rays θ Used for sample ¾ Powders ¾ Phase determination 2θ = scattering angle ¾ Reflectivity Q = (4π/λ) sin θ ¾ Anomalous diffraction ¾ θ-2θ measurements SR Scattering Experiment Advantages Point detector (7-2/ 10-2) ¾ High resolution ¾ Accurate peak position & shape ¾ Weak peaks ¾ Variable energy ¾ 4 degrees of motion (θ, 2θ, χ, φ) Disadvantages ¾ Slow ¾ Complicated ¾ Can be difficult to find peaks Used for ¾ Single crystals ¾ Grazing-incidence 2θ = scattering angle ¾ Anomalous diffraction ¾ Thin films Q = (4π/λ) sin θ ¾ Surface studies Types of scattering experiments

• Small Angle X-ray Scattering (SAXS) – probes structures 1-100 nm • Powder Diffraction, including in-situ – random or isotropic; nanoparticles – poor crystalline order • Thin Films: random, textured, epitaxial – wide variety • Surface Scattering/monolayers – atomic structure at surface or interface

Fe oxide iron metal Lengths Accessed by Probes USAXS SAXS XRD EXAFS

1 μm 1 nm Summary: SR Scattering

SR Scattering: What can we learn: • Phase identification & quantify • Q is important variable: • Where are the atoms: crystal & measure I(Q) surface structure • choose Q to match • Strain, lattice parameters length scale • Grain/crystallite size • Pore/particle size • variety of materials • Other defects & disorder • Crystallite orientation or texture

Fe oxide fcc hcp iron metal Small Angle Scattering

scattered Q = k’ - k k’ incident k Q |Q| = (4π/λ)sin θ 2θ

• Measure I(Q) with Q ∼ 0.0001 – 1 Å-1 • Scattering from 1-100 nm density inhomogeneities Small Angle Scattering Scattering from density inhomogeneities with sizes 1-100 nm • nanoparticles (catalysts, bio- oxides, geo-oxides) • nanoporous materials • co-polymers • dendimers • supramolecular assemblies • micelles • colloids • metallic glasses Small Angle Scattering

Isolated particles Hexagonal packed or pores with cylinders diameter D

π/D

Q-4

• Need large Q range: 1/D ~< Q ~< 10/D Example 1: Nanoporous Films

Matrix: Methyl Silsesquioxane (MSSQ),

CH3SiO1.5 Porogen (thermally labile polymer): copolymer poly(methyl methacrylate-co- dimethylaminoethyl methacrylate) or P(MMA- IBM co-DMAEMA) Elbert Huang Jonathan 1. Spin coat MSSQ/Porogen Hedstrom solution Spin Ho-Cheol Kim Coat Teddie Magbitang Robert Miller 2. Heat to 450°C, at Willi Volksen 5°C/min under argon

Funded by NSF-ATP MSSQ crosslinks at 200°C Δ Argon Poragen fully degrades at 400°C

3. Cool to room temperature ¾ Huang et al, Appl. Phys. Lett. 81, 2232 (2002) ¾ Huang et al., Chem. Mater. 14, 3676 (2002) ¾ Magbitang, Adv. Materials. 17, 1031 (2005) Nanoporous Films: SAXS Results

Find: • reasonably small pores (good) • broad distribution of pore sizes (bad) • size increases with loading => agglomeration (bad) Huang et al, Appl. Phys. Lett. 81, 2232 (2002) Nanoporous Film Morphology

Goal: obtain representative real space picture (correct size scale and extent of interconnection)

Approximations: ¾ morphology is “disordered” or random with no preferred direction ¾ morphology described by cosine waves: with random phase and direction non-random distribution of wavelengths (from SAXS)

• Cahn, J.W., J. Chem. Phys. 42, 93 (1965). • Berk, N.F. Phys. Rev. Lett. 58, 2718 (1987) & Phys. Rev. A 44, 5069 (1991). • Jinnai, H., et al., Phys. Rev. E 61, 6773 (2000). • Teubner, M., Europhys. Lett. 14, 403 (1991). • Hedstrom et al., Langmuir 20, 1535 (2004) Summary: SAXS • Isolated Particles/Pores (not ordered) 9 Obtain average size & particle/pore size distribution (need large Q range)

• (More) Ordered Structures 9 particle/pore spacing and morphology

• Dense Network of Pores/Particles 9 Obtain representative morphology 9 Good for interconnected & bicontinuous morphologies

John Pople, up next! Example 2: Nanoparticles

Motivation: • Pd absorbs hydrogen at an atomic level • Clusters behave differently to bulk • Pd clusters: + – size dependence H2 – surface/volume ratio Nanoparticles: X-ray diffraction

Q = k – k’ Q = k – k’ k’ θ k’ 2θ 2θ kk k θ Transmission Reflection

Point detector (2-1, 7-2) Nanoparticles: X-ray diffraction

Ingham et al., Phys. Rev. B 78 245408 (2008). Summary: Nanoparticles This work: Powder diffraction: • Observe peaks • Phase identification corresponding to fcc Pd • Structure determination • Lattice expansion upon • Strain addition of hydrogen • Crystallite size • Dependence on cluster • Defects size • In situ measurements • Transmission and reflection geometries

Q = k – k’ Q = k – k’ k’ θ k’ 2θ 2θ k k θ

Apurva Mehta, etc : this afternoon Example 3: ZnO Motivation: •ZnO exhibits a wide variety of nanostructures •Electrochemical processing has many advantages •Experimental parameters determine morphology

How does crystallography affect the growth of the nanostructures?

002

100 Thin Film Diffraction Area Detector 2θ incident

Q scattered α ~ 0.1−0.2 deg

Detector

Beam line Q incident 11-3 scattered ZnO: experiments Ex situ:

102 Au 102

Au 002

101 Au

200 100 002

100 ZnO: Summary Summary: Thin films and texture: •Texture increases with • Surfaces, interfaces deposition time • Structure, strain •Nanostructures are • Orientation oriented along 002 direction • Crystallite size in-plane •Films deposited at less and out-of-plane negative electrochemical potentials have poorer MFT, Arturas Vailionis, this epitaxy afternoon

002

100 Summary • Typical SR x-ray scattering experiment & some examples: porous films, nanoparticles, textured films

• To be covered in this workshop: - SAXS - Powder - Poorly ordered - Films: random, textured, epitaxial - Monolayers Bibliography

• B Warren, “X-ray Diffraction”, Dover (1990): $13.16 & eligible for FREE Super Saver Shipping on

• BD Cullity & SR Stock, “X-ray Diffraction”, Prentice Hall (2001): $118.40.

• J Als-Nielsen & D McMorrow, “Elements of Modern X-ray Physics”, Wiley (2001): $84.10. More Bibliography

• M. Tolan, “X-ray Scattering from Soft-Matter: Materials Science and Basic Research”, Springer (1998). • RL Snyder, K. Fiala & HJ Bunge, Eds., “Defect and Microstructure Analysis by Diffraction”, Oxford (1999). • V Holy, U Pietsch, T Baumbach, “High-Resolution X-Ray Scattering: From Thin Films to Lateral Nanostructures”, Springer-Verlag, (2004) • O Glatter, “Small Angle X-Ray Scattering”, Academic (1982). • “Modern Aspects of Small Angle X-Ray Scattering”, H. Brumberger (Editor), Springer (1994). • Int. Union of Crystallography: Links to everything crystallographic. www.iucr.org . See : www.iucr.org/cww-top/edu.index.html and also Teaching and Education in Crystallography: www.minerals.csiro.au/mirror/w3vlc/edu.index.html. • Structural data for thousands of minerals: database.iem.ac.ru/mincryst/ • Lawrence Berkeley: X-ray interactions with matter, data & calculations www- cxro.lbl.gov/optical_constants/ • International Centre for Diffraction Data - purveyors of the Powder Diffraction File (PDF) www.icdd.com