Powder diffraction and synchrotron radiation

(1)

Powder diffraction and

synchrotron radiation

Gilberto Artioli

Dip. Geoscienze UNIPD

(2)

(3)

single xl

diffraction

powder

diffraction

(4)

Ideal powder

Powder averaging

Textured sample

(5)

ODF = f(g) = orientation

distribution function



f (g)



g





V (g)

V

P

_k

(



,



)



f (g,



)d





Graphical representation:

Polar figures

(6)

P

_k

(



,



)



f (g,



)d





We collect the whole powder spectra using different sample

(7)

(8)

(9)

(10)

Unit cell parameters

Space group symmetry

Atomic coordinates

Atomic displacement parameters

(11)

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

(12)

radiation

source

sample

(goniometer)

(chamber)

detector

optics

(13)

Available X-ray sources

Rotating anodes /

microsources

Synchrotron

bending magnets

Synchrotron

Insertion devices

X-ray tubes

(14)

X-ray

detectors

Point detectors

Linear detectors

Area detectors

(15)

(16)

X-ray detectors

gas

ionization

phosphors

semi-

conductors

other

spot

0-D

proportional

counters

scintillators

solid state

Si(Li), Ge(Li)

linear

1-D

gas

linear PSD

photo-diode

arrays

area

2-D

multiwires

phosphors

IP

CCD

films

(17)

True 2D detector (with

some energy discrimination)

(18)

CMOS hybrid-pixel

technology Pilatus

2M detectors

(19)

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(23)

Angle

dispersive



monochromatic

2 

measured

- X-ray tubes

- thermal neutrons

- synchrotron radiation

Energy

dispersive



polychromatic

2 

fixed

- synchrotron radiation

- pulsed neutrons

Experimental geometries

(24)

n



2d = ---

sin



n



2d = ---

sin



polychromatic

beam

sample

detector

2θ

polychromatic

beam

monochromatic

beam

sample

detector

2θ

polychromatic

beam

analyzer

sample

detector

2θ

angle dispersive

configuration

energy dispersive

configuration

(25)

Experimental geometries

probed sample volume

geometry

commonly implemented instruments

cylindrical

Debye-Scherrer

or

cylindrical

geometry

laboratory Debye cameras

parallel- or focusing-beam laboratory

goniometers with capillary sample

high resolution parallel-beam

configurations at synchrotron sources

flat-plate

Bragg-Brentano

or

parafocusing geometry

diverging-beam Bragg-Brentano

diffractometers

curved

Guinier

or

focusing geometry

Guinier cameras

Seeman-Bohlin cameras

(26)

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

(27)

Peter Debye

[Petrus Josephus Wilhelmus Debije]

1884-1966

(28)

Debye-Scherrer

geometry

(29)

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MYTHEN II

detector

SLS-MS

powder diffraction

station

(32)

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(34)

(35)

translating cylindrical

image plate chamber

MCX station

(36)

André Guinier

(37)

focusing geometry

S

D

2 

(38)

parafocusing

(39)

(40)

(41)

(42)

Remind:

The Bragg-Brentano diffractometer only samples a small

portion of the Debye cone !!!! Beware !!!

(43)

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(45)

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

(46)

(47)

(48)

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 °

(49)

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CuO tenorite

(52)

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(54)

(55)

(56)

Monoclinic phase

(57)

2D detectors

high resolution

instruments

fast

(58)

Non

Ambient

Studies

-

Time resolved

studies

(59)

time scale of experiments

(60)

Non ambient XRD has been performed in the last 10-15 years in

several operating modes:

“slow”

(tr > 1 sec)

“fast”

(tr < 1 sec)

kinetic studies

(i.e. qualitative

and quantitative

phase info)

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

state of the art in the

lab

routine @ SR and

neutron facilities

(61)

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(66)

 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

(67)

(68)

simultaneous

SAXS-WAXS-FTIR

exp.

(69)

simultaneous

SAXS-WAXS-Raman

exp.

(70)

(71)

(72)

simultaneous

XRD-DLS exp.

GILDA

ESRF

(73)

simultaneous

XRD-XRF exp.

2D XRD

mapping

(74)

(75)

high energy X-ray scanning

ID15B

ESRF

(76)

Diffraction-contrast tomographic techniques for 3D

crystal phase mapping:

 Box beam setup (DCT)

 Pencil beam tomographic scan (XRD-CT)

(77)

X-ray diffraction contrast

(78)

(79)

Energy dispersive

(80)

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Sample2_slice1_glass capillary

ROI

(86)

(87)

ettringite

C-S-H