X-ray methods for nanoscience
Ritva Serimaa
Department of Physics
University of Helsinki
Nanoscience III
X-rays and matter
• wavelength of the order of 0.1 nm
x-ray beam
elastic scattering
absorption
fluorescence
inelastic scattering
Why structural studies?
Understanding the relationship of structure, properties
and function of a system Monitoring the system during its formation for tuning the
structure and properties Dependence of the structure and properties on
environmental conditions like temperature or pressure
HU Course 2013:
Synchrotron radiation in materials research
http://www.helsinki.fi/~serimaa/index-xraypk.html
How to produce x-rays?
Large scale facilities
Synchrotron
http://www.lightsources.org/cms/?pid=1001328
European facilities: ESRF,
MaxLab, Petra III, Soleil, …
ESRF
First x-ray free electron lasers: Flash,
LCLS http://www-ssrl.slac.stanford.edu/lcls/index.html The European XFEL is constructed in Hamburg http://xfel.eu/
Example of new synchrotrons: Petra III Hamburg
Ring was built for particle physics
Diameter about 3 kmGerman synchrotronEMBL beam lines
2015 Max IV Lund, Sweden
Sketch of synchrotron from Wikipedia
XFEL
Tiny samples Coherent diffraction and imaging Chemical reactions
http://www.xfel.eu/research/examples/nanoworld/
Free electron laser (FEL)
FELs are usually based on the combination of a linear accelerator
followed by a high-precision insertion device. The accelerated electrons in the insertion device bunch together more
tightly than usual. Over the length of the insertion device, the electrons in the
microbunches begin to oscillate in step (coherently).
http://www.lightsources.org/cms/?pid=1001328
FEL
http://en.wikipedia.org/wiki/Free_electron_laser
X-ray lithography (XRL) with table top and ordinary synchrotrons and lasers
patterned films
achieved in GGe by
XRL structures with
resolutions of the order
of 100 nm
•G Brusatin et al. Design of hybrid sol–gel films for direct x-ray and electron beam nanopatterning. Nanotechnology 19 (2008) 175306•D Minkov et al. Targets emitting transition radiation for performing X-ray lithography by the tabletop synchrotron MIRRORCLE-20SX. Nucl Instr and Meth in Phys Res A: Accelerators… Vol 590, Iss 1-3, 2008, 110-113 •M.C. Marconia and P.W. Wachulak. Extreme ultraviolet lithography with table top lasers. Progress in Quantum Electronics Vol 34, Iss 4, 2010, 173-190
XFEL experimental stations 2014
FXE femtosecond xray experiments: diffraction … GED high energy density matter experiments, diffraction,
inelastic scattering, spectroscopy SPB single particles clusters biomolecules, coherent
diffraction, resolution < 1 nm MID materials imaging and dynamics, coherent
diffraction, resolution around 10 nm SQS small quantum systems, high resolution
spectroscopy SCS spectroscopy and coherent scattering, coherent
imaging, photon correlation spectroscopy
http://www.xfel.eu/research/experiment_stations/scs/
FLASH, small version of the European XFEL at DESY since 2005
FLASH is 260 m long soft X-rays down to a
wavelength of 6 nm A coherent diffraction
pattern
http://hasylab.desy.de/facilities/flash/research/a_perfect_image_from_a_single_fel_shot/index_eng.html
Coherent x-ray imaging (CXDI)
gold particles (diameter 10 nm) on a Si3N4
membrane
The diffraction pattern was
used to reconstruct the gold
particle using the hybrid
input-output (HIO) method
together with the so-called
shrink-wrap algorithm.
Image with 5 nm spatial
resolution.
C. G. Schroer et al. Coherent X-Ray Diffraction Imaging with Nanofocused Illumination. PRL 101, 090801 (2008) (at ESRF ID 13)J. R. Fienup, Appl. Opt. 21, 2758 (1982).S. Marchesini et al., Phys. Rev. B 68, 140101(R) (2003).
SEM diffraction pattern reconstruction
Absorption needs to be taken into account and gives information on the sample
X-rays are absorbed into the
material or scattered.
Attenuation is described by
mass attenuation constant
μ/ρ [cm2/g], where ρ is the
density.
I = I0 exp(-(μ/ρ) ρt),
where t is the
thickness.
X-ray
I0 I
t
X-ray microtomography
In X-ray tomography a series of radiographs are recorded for different angular positions of the sample which rotates around an axis perpendicular to the beam.
Laboratory setups: cone beam, polychromatic radiation
Synchrotron: parallel beam and
monochromatic radiation
The number of radiographs is the order of 1000 and the data is several Gigabytes.
X-ray source sample detector
http://laskin.mis.hiroshimau.ac.jp/Kougi/08a/PIP/
X-ray microtomography setup at Department of Physics, Helsinki University
Phoenix nanotom 180 NF Tungsten x-ray tube Hamamatsu flat panel
detector
One experiment 1,440 projections The measurement time
for a single image 750 ms
Absorption as a function of energy
An x-ray photon is absorbed by the atom and the excess
energy is transferred to an electron, which may be
expelled from the atom, leaving the atom ionized
X-ray
http://physics.nist.gov/PhysRefData/XrayMassCoef/ElemTab/z28.html
X-ray absorption spectroscopy XAS
If x-ray energy is suitable, a
photoelectron will be ejected. X-ray absorption fine structure: The
outgoing electron scatters from
nearest atoms. This causes
oscillations in the linear absorption
coefficient.
Extended x-ray absorption fine
structure EXAFS X-ray absorption near edge structure
XANES
X-ray
photoelectron
XAS tutorials http://xafs.org/
XANES X-ray absorption near edge structure
XANES gives information on the electronic state of the absorbing atom and the local structure surrounding it.
Data base for XANES spectra by Farrel Lyttle (http://www.esrf.fr/computing/scientific/dabax)
XANES EXAFS
Normalized absorption
EXAFS Extended x-ray absorption fine structure
Studies on the average
environment of a
selected type of atom by
its absorption
coefficient.
EXAFS gives
information of distances
and numbers of nearest
neigbours of the chosen
atom type.
8800 9000 9200 9400 96000.2
0.4
0.6
0.8
1
E (eV)
No
rma
liz
ed
ab
so
rpti
on
Fluoresence analysis
Elemental analysis Sample is irradiated by x-rays The emitted fluorescence radiation is
detected. The elements are regognized on the
basis of the energies of the x-ray
fluorescence emittion lines.
http://en.wikipedia.org/wiki/X-ray_fluorescence
Example: J. Szlachetko et al. Application of the high-resolution grazing-emission x-ray fluorescence method for impurities control in semiconductor nanotechnology. J Appl Phys 105, 086101, 2009
X-ray microcopy and XANES at ESRF
2-7 keV Spot size 0.3 – 1 micrometer
http://www.esrf.eu/UsersAndScience/Experiments/Imaging/ID21/http://www-cxro.lbl.gov/BL612/index.php?content=research.html
XAS: Sulfur in King Henry VIII's warship Mary Rose and Gustav II Adolf’s warship Vasa
Marine-archaeological oak timbers XANES and synchrotron-based x-ray microspectroscopy Iron sulfides and elemental sulfur occur in separate
particles.
Sandström M et al. PNAS 102 (40): 14165-14170 OCT 4 2005
Synchrotron radiation X-ray microscopy since 2000
X-ray fluorescence analysis (XRF):
elemental composition
X-ray diffraction (XRD): crystalline
impurities
X-ray Absorption Near Edge
Structure (XANES): the chemical
state of the sulfur or iron atom
Extended X-ray absorption fine
structure (EXAFS): bonding of the
sulfur or iron atom
EXAFS
XRD
XANES
e-
X-ray
Scanning experiments with a small beam
Large amounts of reduced sulfur compounds abound in lignin-
rich parts such as the middle lamella between the cell walls,
mostly as thiols and disulfides
Y Fors, M Sandström: Sulfur and iron in shipwrecks cause conservation concerns. Chem. Soc. Rev. 2006, 35, 399-415
SO42-
(2.483 eV)
Elemental sulfur (2.473 eV)
ESRF ID21, beam size 0.5 μm
Nanoparticle de-acidification of the Mary Rose
SrCO3 nanoparticles were dispersed into 2-
propanol and sonicated for 1 hour.
Wood was placed in the nanoparticle
medium and left for 3 days whilst being
sonicated throughout.
Samples were removed from solution and
rinsed with distilled water.
The sulfate is almost entirely converted to
SrSO4
Eleanor J. Schofield et al. Materials Today Volume 14, Issues 7–8, July–August 2011, Pages 354–358
The penetration of SrCO3 nanoparticles in
Mary Rose timbers
(a) SEM micrograph of after treatment with SrCO3; (inset) EDS of strontium
(b) XRF of strontium
(c) Sulfur and strontium profile using EDS; (inset) line analysis throughout the cross-section
X-ray imaging of biological systems
Imaging based on soft x-ray or electron microscopyRadiation damageResolution < 100 nm
SamplesFrozen samplesDehydrated specimens at room temperature.
Example: Scanning transmission X-ray microscopy and
XANES at Carbon K absorption edge on Wood with
resolution of 100 nm. XANES result: Polysaccharides are
susceptible to soft X-ray irradiation induced chemical
transformations
GD Cody et al. Soft X-ray induced chemical modification of polysaccharides in vascular plant cell walls. J El. Spect and Rel. Phen. 170(1-3), March 2009, 57-64
X-ray scattering methods for structural studies
Size range method variations
0.1-1 nm Wide angle x-ray scattering
WAXS,
Crystallography
Element specific anomalous
scattering AWAXS, grazing
incidence x-ray diffraction
GIXD for surfaces
10-100 nm Small angle x-ray scattering
SAXS, crystallography
Element specific ASAXS,
Surfaces GISAXS
>1000 nm Ultra-low angle x-ray scattering
Cullity and Stock: Elements of x-ray diffraction J Als-Nielsen, D McMorrow: Elements of modern x-ray physicsFeigin, Svergun: Structure analysis by small-angle X-ray and neutron scattering. http://www.embl-hamburg.de/ExternalInfo/Research/Sax/reprints/feigin_svergun_1987.pdf
X-rays 2θ
X-ray scattering
SAXS and WAXS
WAXS
Scattering vector q, length q = 4π/λ sin θ where λ is the
wavelength and 2θ the
scattering angle
X-rays
q = k2-k1
q
monochromator sample detector
q
k1 k2
Symmetrical transmission
Symmetrical reflection
ESRF ID2
http://www.esrf.eu/UsersAndScience/Experiments/SoftMatter/ID02/BeamlineLayout
X-ray scattering WAXS, SAXS, USAXS, XRD …
Wavelength of the order of 0.1 nm X-rays scatter from electrons.
Scattering amplitude A(q) is proportional to Fourier transform
of the electron density (x): A(q) = (y) exp(i q·y) d3y
Here q is the scattering vector.
Intensity I(q) = A*A may be presented as a Fourier transform of the
autocorrelation function C(z) of the electron density:
I(q) = C(z) exp(-i q·z) d3z
Here C(z)= (z+y) (y) d3y
Bragg law 2d sin θ = λ
Scattering vector q = k2 - k1 is perpendicular to the lattice
planes. The lenght of the scattering vector |q| = 4π/λ sinθ Bragg law in terms of q: d = 2π/q
Path difference 2x
x/d = sin θ
2x = 2d sin θ = λ
k1
k2
q
dx
Crystallography of macromolecules
Cellulose I The oriented fibrous samples prepared by
aligning cellulose microcrystals from the cell wall of the
freshwater alga Glaucocystis nostochinearum.
Nishiyama Y, Sugiyama J, Chanzy H, Langan P. Crystal structure and hydrogen bonding system in cellulose Ia from synchrotron X-ray and neutron fiber diffraction. J Am Chem
Soc 125(47), 14300-14306, 2003
Isotropic crystalline powder sample
Diffraction pattern
consists of rings Example. Silver behenate
Crystal structure from the
positions of the peaks Crystallite size from the
FWHM’s of the peaks
http://chemistry.library.wisc.edu/subject-guides/x-ray-crystallography.html
Anisotropic crystalline sample
Diffraction pattern may consists of ”spots” Crystal structure Crystallite size Preferred orientation of crystallites from
the azimuthal intensity of one reflection
Example: paper - cellulose and filler
0
100
200
300
400
500
600
700
q
Semicrystalline materials: Crystallinity from WAXS intensity
Crystallinity index =
Intensity of crystalline model--------------------------------------Experimental intensity
Solid bamboo sample Crystalline intensity from
model Amorphous pattern
measured from a lignin
sample.
Reflection mode Transmission mode
Crystallite size from the width of the reflections
Scherrer formula L = K λ/(B(2θ) cosθ), where K is a constant,
B(2θ) is the the full width at half maximum of the reflection, 2θ is the scattering angle and λ the wavelength.
Instrumental broadening of the reflection should be considered.
Extraction of a diffraction peak from the intensity curve.
FWHM
Crystallite size vs grain size
Grain size from electron microscopy, microtomography Crystallite size using x-ray diffraction Grains can contain several crystallites
Small-angle x-ray scattering and diffraction
Crystal structures in length scales 1-100 nm
Macromolecules in solution: shape and size Fractal structures: fractal dimension Two-phase systems with sharp interfaces: spesific
surface
Feigin LA, Svergun DI. Structure analysis by small-angle X-ray and neutron scattering. http://www.embl-hamburg.de/ExternalInfo/Research/Sax/reprints/feigin_svergun_1987.pdfGlatter O, Kratky O (1982). Small Angle X-ray Scattering. http://physchem.kfunigraz.ac.at/sm/
Small-angle diffraction: nanoporous silica
Two-dimensional Hexagonal
structure
d-2 = 4/3 (h2 + hk + k2)/a2
Values of h and k for first
peaks:
01, 10
1 1
0 2
Dirk Mter et al. Surfactant Self-Assembly in Cylindrical Silica Nanopores. J. Phys. Chem. Lett., 2010, 1 (9), pp 1442–1446
Mesoporous silica
F Kleitz, S Hei Choi, R Ryoo. Cubic Ia3d large mesoporous silica: synthesis and replication to platinum nanowires, carbon nanorods and carbon nanotubes. Chem. Commun., 2003, 2136-2137
Block co-polymers and surfactants
C16E7–D2O system
BL-15A instrument at the
Photon Factory in KEK,
Japan
M Imaia et al. Kinetic pathway of lamellar \ gyroid transition: Pretransitionand transient states. J. Chem. Phys., Vol. 115, No. 22, Dec 2001, 10525-10531
Electron density
a r
Electron density
Shape of objects in dilute solution using SAXS
Amplitude of a sphere with electron
density ρ and radius a:
F(q) = 4/3 π a3 ρ 3 (sin x –x cos x)/x3,
where x = qa.
Blue: intensity of spheres, a = 30 Å.
Green: Guinier law I ~ exp(-1/3 Rg2 q2)
ρ
http://www.embl-hamburg.de/research/unit/svergun/index.html
http://kur.web.psi.ch/sans1/SANSSoft/sasfit.html
SAXS of hydrophobin protein in a dilute solution
Guinier law. At small q the
intensity can be approxi-
mated with a Gaussian:
I(q) ≈ I(0) exp(-(1/3)(qRg)2 )
The radius of gyration
Rg = ∫ρ(r)r2 dV / ∫ρ(r)dV
Figure:
Rg = 25.1 Å
V = 45475 Å3 ≈ (36)3 Å3
Sphere R = 32 Å
0 0.1 0.2 0.3 0.410
-10
10-5
100
q
I(q
)
Hydrophobin protein and model based on a fit to measured SAXS intensity
Crystalline structure
Hakanpaa JM, Szilvay GR, Kaljunen H, Maksimainen M, Linder M, Rouvinen J. Two crystal structures of Trichoderma reesei hydrophobin HFBI -The structure of a protein amphiphile with and without detergent interaction. Protein Sci. V15, 2129-2140, 2006
http://www.embl-hamburg.de/ExternalInfo/Research/Sax/software.html
Power law behaviour of SAXS intensity from solutions
IN(q) ≈ 4π (ρ- ρ0)2 S/q4 at large q, where S is the total
area of particles and ρ- ρ0 electron density difference
Sheets I(q) ≈ const /q2
Long thin rods I(q) ≈ const /q1
e.g. Teixeira. J.Appl. Cryst. 21 1988, 781-785 and SAXS text books
I ≈ 1/q4
Flexible polymers with Gaussian statistics
Intensity is proportional to
F(q) = 2(exp(-u) + u - 1)/u2
where u = <Rg
2>q2 and <Rg2> is the
average radius of gyration
squared. <Rg
2> = (Lb)/6, where L is
the contour length and b is
the statistical segment
length.
Dense systems: fractal aggregates
• The SAXS intensity follow a power law
I ≈ 1/qa. • This can be interpreted as arising from fractal structures,
if the characteristic length scale R of a fractal satisfies the condition Rq >>1.
• For surface fractals the power law exponent a is between 3 and 4. It is related to surface fractal dimension Ds as a = 6 - Ds.
• The Porod law, a = 4, is valid for the scattering of a compact particle with a smooth surface (Ds = 2, Dm = 3)
• A power law with a < 3 is caused by a mass fractal for which a = Dm = Ds < 3.
• Continuous charge density transitions can cause a to be larger than 4.
μ-SAXS and microfluidics
T. Pfohl et al.Trends in microfluidics with complex fluids,
Chem. Phys. Chem. 4 (2003), pp. 1273–1274.
Piggee C. Sometimes less is more: microfluidics extends the
capabilities of SAXS. Analytical Chemistry 80(11), 3948-
3948, 2008
Surface structures
PS
D
PS
D
αi
αf
Side view
Film surface
Soller slits
Top view
w1w2
λ = 2π/k, qxy = 2ksinθ, qz ≈ k sinαf
GIXD Grazing incidence x-ray
diffraction
Troika beam line of ESRF
Thin films with GISAXS
Structure in the film statistical information over several square
millimeters probe from surface to buried interfaces various types of environment chemical contrast of a given element can be
enhanced by performing anomalous
scattering close to a specific absorption
edge.
G Renaud, R Lazzari, F Leroy. Probing surface and interface morphology with Grazing Incidence Small Angle X-Ray Scattering. Surf Sci Rep 64 (2009) 255380http://staff.chess.cornell.edu/%7Esmilgies/gisaxs/GISAXS.php
Reflectivity studies using x-rays from laboratory source
20 nm thick film cellulose film using X-ray
tube based system
E Kontturi and Lankinen. Following the
Kinetics of a Chemical Reaction in Ultrathin
Supported Polymer Films by Reliable Mass
Density Determination with X-ray
Reflectivity. J. Am. Chem. Soc., 2010, 132,
3678–3679
18.04.23 53
αr
detectorq || z-axis
Regenerated cellulose films using GISAXS and reflectivity
• Cellulose regenerated from dimethylsilyl cellulose
• Experiments at Hasylab and ESRF
• Small-angle scattering arises from microfibril bundles.
• Electron density profile in z-direction (thickness of film)
18.04.23 54
Rossetti et al. Structures of regenerated cellulose films. Biointerphases vol 3 no 4, Dec 2008
Fast experiments with pink synchrotron beam
Kong Q., Wulff M., Lee J.H., Bratos S., Ihee H., Photochemical reaction pathways of carbon tetrabromide in solution probed by picosecond X-ray diffraction. J Am Chem Soc 129, 13584-13591 (2007)
Structure factor and radial distribution function
Carbon nanotube
Koloczek J, Hawelek L, Burian A, et al. Modelling studies of carbon nanotubes - Comparison of simulations and X-ray diffraction data. Journal of Alloys and Compounds Vol 401 Iss1-2, 46-50 SEP 29 2005
Experiment at high energy x-rays
Large scale facilities vs home laboratory
High intensity – short measurement times Example. SAXS milliseconds (home laboratory minutes)
Tunability – special methods like absorption spectroscopy
or anomalous scattering monochromatic radiation,
pink beam,
white beam
Well-collimated beam: better resolution, easier data
analysis Coherence: special methods