Powder diffraction and synchrotron radiation Gilberto Artioli Dip. Geoscienze UNIPD CIRCe Center for Cement Materials
single xl diffraction powder diffraction
Ideal powder Powder averaging Textured sample Preferred orientation
how do we describe texture? ODF = f(g) = orientation distribution function f (g) g V(g) V Graphical representation: Polar figures P k (, ) f (g, )d
We collect the whole powder spectra using different sample orientation, and then we fit directly a functional form of the ODF P k (, ) f (g, )d
Crystal structure analysis Unit cell parameters Space group symmetry Atomic coordinates Atomic displacement parameters
XRPD measurements we want to measure the intensity profile in reciprocal space position of diffraction peaks (2, E, ToF d hkl ) intensity ( I hkl F hkl 2 ) peak profile shape ( H(2 ) = f(2 ) g(2 ) ) a correct measurement assumes: the homogeneous spatial distribution of the crystallites in the sample the homogeneous probing of the material by the beam the statistically correct measurement of intensity
radiation source sample (goniometer) (chamber) detector optics optics
Available X-ray sources Synchrotron Insertion devices Synchrotron bending magnets X-ray tubes Rotating anodes / microsources
X-ray detectors Point detectors Linear detectors Area detectors
X-ray detectors gas phosphors semi- other ionization conductors spot proportional scintillators solid state 0-D counters Si(Li), Ge(Li) linear 1-D gas linear PSD photo-diode arrays area multiwires phosphors CCD films 2-D IP
True 2D detector (with some energy discrimination) Empyrean: PIXcel ESRF: FRELON camera
CMOS hybrid-pixel technology Pilatus 2M detectors
X-ray detectors: IP
http://www.esrf.eu/computing/scientific/fit2d/
Experimental geometries Angle dispersive monochromatic 2 measured - X-ray tubes - thermal neutrons - synchrotron radiation Energy dispersive polychromatic 2 fixed - synchrotron radiation - pulsed neutrons
angle dispersive configuration n 2d = ------ sin polychromatic beam monochromatic beam sample 2θ 2θ detector detector energy dispersive configuration n 2d = ------ sin polychromatic beam polychromatic beam sample sample 2θ analyzer 2θ 2θ detector
Experimental geometries probed sample volume geometry commonly implemented instruments laboratory Debye cameras cylindrical Debye-Scherrer or cylindrical geometry parallel- or focusing-beam laboratory goniometers with capillary sample high resolution parallel-beam configurations at synchrotron sources flat-plate curved Bragg-Brentano or parafocusing geometry Guinier or focusing geometry diverging-beam Bragg-Brentano diffractometers Guinier cameras Seeman-Bohlin cameras thin-film focusing-beam goniometers
In terms of practical instrumental performance, the parameters to be optimized for specific applications are: Δd/d resolution, that is the ability to separate two contiguous Bragg peaks in reciprocal space. The resolution is generally measured by the Bragg-peak broadening in terms of angular full-width at half maximum (FWHM) as a function of q. Signal/noise ratio, that is the statistical significance of the Bragg-peak intensity over the instrumental background. The signal to noise ratio is commonly greatly enhanced in synchrotron experiments because of the intrinsic collimation of the source beam. Measurement time. The total time of the measurement depends on a number of factors including: the scattering power of the sample, the probed volume of sample, the incident flux, the type and efficiency of the detectors,.
Peter Debye [Petrus Josephus Wilhelmus Debije] 1884-1966 Nobel Prize for Chemistry 1936
Debye- Scherrer geometry
Debye geometry at ESRF: ID31
MYTHEN II detector SLS-MS powder diffraction station
X-ray detectors: translating IP
translating cylindrical image plate chamber MCX station Elettra
André Guinier [1911-2000]
focusing geometry S D 2 2
parafocusing geometry
Remind: The Bragg-Brentano diffractometer only samples a small portion of the Debye cone!!!! Beware!!!
parafocusing geometry
the exp peak profile shape the measured peak profile is the convolution of all instrumental and sample parameters common exp aberrations: axial divergence sample shift asymmetry absorption/transparency
Smaller Crystals Produce Broader XRD Peaks
ideal peak profile shape ID31-ESRF is the closest we get to ideal: incident flux from undulator monochromator band pass: 10-4 collection time: minutes optimal signal/noise ratio instrumental peak broadening: FWHM<0.001 how does it compare to laboratory data?
CuO tenorite monoclinic C2/c
CuO monoclinic C2/c
Framework Type MFI
Monoclinic phase Orthorhombic phase
fast measurements high resolution instruments 2D detectors
Non Ambient Studies - Time resolved studies
time scale of experiments equilibrium time-resolved
Non ambient XRD has been performed in the last 10-15 years in several operating modes: kinetic studies (i.e. qualitative and quantitative phase info) slow (tr > 1 sec) routine in the lab fast (tr < 1 sec) state of the art in the lab routine @ SR and neutron facilities equilibrium studies (i.e. direct refinement of structure details) state of the art in the lab routine @ SR and neutron facilities state of the art @ SR and neutron facilities
HT apparatuses
LT apparatuses
HP apparatuses
HP apparatuses
HP apparatuses
combined experiments = the sample is measured at different times using different techniques and experimental settings in sequence. simultaneous measurements = the sample is excited and different signals produced by the sample are measured at the same time
simultaneous SAXS-WAXS exp.
simultaneous SAXS-WAXS-FTIR exp. W. Bras archive, ESRF
simultaneous SAXS-WAXS-Raman exp. W. Bras archive, ESRF
simultaneous XRD-XAS exp.
simultaneous XAS-UV Vis exp.
simultaneous XRD-DLS exp. GILDA ESRF
simultaneous XRD-XRF exp. 2D XRD mapping
GRC West Dover - 2012
high energy X-ray scanning ID15B ESRF
Diffraction-contrast tomographic techniques for 3D crystal phase mapping: Box beam setup (DCT) Pencil beam tomographic scan (XRD-CT) Energy dispersive diffraction imaging (TEDDI)
X-ray diffraction contrast tomography (DCT) (grain mapping)
Energy dispersive diffraction imaging (TEDDI)
Pencil beam tomographic scan
Sample2_slice1_glass capillary ROI Sinogram Back projection
ettringite C-S-H portlandite