06 Geometry, Detectors

8/11/2019 06 Geometry, Detectors

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Diffractometer

GeometryOpticsDetectors


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Diffractometers

Debye Scherrer Camera

V.K. Pecharsky and P.Y. Zavalij Fundamentals of Powder Diffractionand Structural Characterization of Materials.


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Diffractometers

Powder Diffractometer

V.K. Pecharsky and P.Y. Zavalij Fundamentals of Powder Diffractionand Structural Characterization of Materials.


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PANalytical XPert Materials Research Diffractometer

Diffractometers


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According to Euclid: the angles in the same segment of a circle are equal toone another and the angle at the center of a circle is double that of the angleat the circumference on the same base, that is, on the same arc.For any two points S and D on the circumference of a circle, the angle x isconstant irrespective of the position of point P.

X-ray Diffraction from PolycrystallineMaterials

2180 = ox

=>


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Diffractometers

Goniometer for Powder Diffraction -scan


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Diffractometers

Goniometer for Powder Diffraction -2scan


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X-ray Powder DiffractometerParafocusing geometry of theBragg-Brentano diffractometer. Sisthe sample, Ris the radius of thegoniometer circle, ris the radius ofa focusing circle and is the Braggangle. The x-ray beam is emitted

from pointAand is focused at thedetection point D.


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Powder Diffraction of MgB2sample.

X-ray Powder Diffractometer


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Diffractometers

Sample Size

+

+

=+=

2sin

2sin

2sin

2sin

21

RR

llL

Irradiated length:

l1 l2

21 llL +=

Divergence SlitFocus

R


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Diffractometers

Irradiated Length

0

5

10

15

20

25

30

35

40

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160

2 (deg)

IrradiatedlengthL(mm)

1/8 1/4 1/2 1 2

Diffractometer radius:R = 320 mm


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X-ray Optics


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Collimators

Simplest collimation is achieved by placing a slit between x-ray sourceand the sample

L

SD +

S

L

DSource

Divergence Slit

Collimated Beam

if DL >>


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Collimators

Second slit can be added to provide additional collimation

Source

Divergence Slit 1

Collimated Beam

Divergence Slit 2


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Diffractometers

Fixed Slits

Divergence Slit: Match the diffraction geometry and sample size At any angle beam does not exceed sample size

R

L

sin (rad)

Receiving Slit: As small as possible to improve the resolution Very small slit size reduces diffracted beam intensity


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Diffractometers

Variable Slits

Vary aperture continuously during the scan Length of the sample is kept constant


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Soller Slits

Soller slits used to limit the axial(vertical / out-of-plane) divergence ofthe incident & diffracted X-ray beamsUsing soller slits improves peak shapeand the resolution in 2-type scans,especially at low scattering angles.

d

l

l

d2


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Beta-filtersA beta-filters are used tokeep as much as possible ofthe characteristic Kradiation from the tube whilstsuppressing K and whiteradiation.

)exp(0 xIIt =


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Beam AttenuatorsThe beam attenuator is an absorber whichis placed in the x-ray beam to reduce itsintensity by a specific factor.

Attenuation factors: Copper (0.1 mm) 100 Combined copper + nickel (0.2 mm / 0.02

mm) 10,000

Automatic beam attenuator

)exp(0 xIIt =

I0 It

x

dx


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Crystal MonochromatorX-ray beam monochromatization can be achieved by diffraction from singlecrystals: Si, Ge, LiCl, and graphite.

PolychromaticBeam

DivergenceSlit

Monochromator

Slit

Monochromator

12 12

=sin2d

Sufficient to separate Kand K Not sufficient to separate K1and K2


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The focusing geometry can be used to provide a monochromatic source of x-rays.Used in Bragg-Brentano geometry and consist of a curved (Johann) pyrolitic graphitecrystal.

Curved Crystal Monochromator


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Three different sample-monochromatorgeometries used in powder diffraction:

Flat diffracted beam monochromator Curved diffracted beam monochromator Flat primary beam monochromator

Crystal Monochromator


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Incident Beam: X-ray Mirror

Parallel Beam Geometry

Mirror

Sample

F

= 0.5o

< 0.04o

Parabola


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Incident Beam: X-ray Mirror

Parallel Beam Geometry

Sample

Parallel Plate Collimator

Detector

d

l

l

d2

Detector

Flat GraphiteMonochromator


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High Resolution Geometry

High resolution double-axis diffractometer: Open detector mode

BeamConditioner

Sample

Detector

2

X-ray

Focus


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High resolution triple-axis diffractometer:

BeamConditioner

Sample

Detector

2

X-rayFocus

AnalyzerCrystal


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Bartels Monochromator


X-ray

Focus


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Incident Beam: X-ray Hybrid Monochromator


Mirror

Sample

F

= 0.5o

< 19 arcsec

Parabola

Ge(220) Crystal


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An incident beam collimator is a device that combines a divergence slit and a beamwidth mask in one optical module. It is used in combination with the point focus x-ray tube.

Main applications: Texture analysis -stress analysis

Point Source Geometry

Crossed slits collimator


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X-ray Lens


X-rayCapillary Lens

X-rayFocus

Quasi-parallelBeam


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X-ray Mono-capillary Used for microdiffraction Beam sizes 1 mm 10m


X-rayMono-capillary

X-rayFocus


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The x-ray detector is the last item in the x-ray beam path.It is used to count numbers of photons, that is, the intensity of the diffracted beamat a certain 2position of the goniometer

Detectors

single photon detectors

scintillation detectors

(gas-filled) proportional counters

semiconductor detectors

linear (position-sensitive) detectors

gas-filled (wire) detectors

charge-coupled devices (CCDs)

area detectors

2-D wire detectors

CCD area detectors

X-ray film (should be obsolete)


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Quantum counting efficiencynumber of photons detected bythe detector to the number ofphotons entering the detector.

Desired Properties of X-ray Detectors

( )( )[ ][ ]lossesdabswabsdetabs

fff

EEE

=

=

11 ,,


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Linearity the ability ofthe detector to provide anoutput that is in directproportion to the intensity ofthe x-ray beam (number ofx-ray photons entering thedetector).



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Energy resolution the ability of the detector to distinguish between energies. resolution input photon of energy E produces an output pulse of height V V


V

WR = Smaller R better resolution


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Energy proportionality the ability of the detector to produce a pulse with aheight proportional to the energy of the x-ray photon detected.Sensitivity the ability of the detector to detect low intensity levels.



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A proportional counter consists of the following main components: a gas-filled cylindrical envelope (usually Ar, Kr, or Xe) a central anode wire a grounded coaxial cylinder (the cathode) an X-ray transparent window

Gas-filled Proportional Counter


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When an X-ray photon ionizesa gas molecule, the ejectedphotoelectrons are acceleratedto the anode low voltages photoelectrons

dont have enough energy toionize other molecules

intermediate voltages gasamplification occurs (photo-electrons ionize gas moleculeson the way to the anode

high voltages dischargeoccurs throughout the gasvolume

Gas-filled Proportional Counter


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Proportional counter Each X-ray photon causes multiple ionizations (29 eV for argon >300 ion/electron pairs

with CuK) In the gas amplification regime (gain of 103 to 105), a pulse of a few millivolts is produced Pulse amplitude proportional to photon energy Much better energy resolution (15% to 20%) than scintillation detectors

Geiger-Mller counter no longer proportional entire chamber light up with UV large pulse amplitude (~volts) so no amplification needed; good for survey meters slow to relax, so maximum count rate is limited

Aspects of Proportional Counters


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The detector has two basic elements: a crystal that fluoresces visible light (scintillates) when struck by X-ray photons a photomultiplier tube (PMT) that converts the light to electrical pulses

The Scintillation Detector

NaI(Tl) scintillator(very sensitive tomoisture) emitsaround 4200

CsSb photocathode ejects electrons

gain ~5per dynode(total gain with tendynodes is 510107)


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Aspects of Semiconductor Detectors


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Semiconductor detectors are solid-state proportional counters each photonproduces electron-hole (e/h) pairsThe detection of e/h pairs would not be possible if the semiconductor has freecarriers (n-type or p-type) so it must be intrinsic this can be done by lithiumdrifting

Semiconductor Detectors

p--SiLi+

Li

+

lithium

heat apply

lightly p-dopedSi has Li plated

heat to havethe Li diffuse

apply a reverse bias tocause Li+ions to drift

np np

i

a wide centralintrinsic region

is formed


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Originally: Si(Li) and Ge(Li) silly and jellyNow intrinsic Si and intrinsic Ge are available (Ge better due to higher absorption andbetter energy resolution)Energy resolution about 2%Small signal requires a charge-sensitive preamp integrated with the detector

due to thermal e/h generation and noise in the preamp, cooling to 77K is neededNew detectors use Si p-i-n photodiodes and large bandgap materials (CdTe andCdZnTe) for room-temperature operation

Aspects of Semiconductor Detectors


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Detectors

Scint.

Prop.

Si(Li)


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PIXcel Detector

Resolution better than 0.04o2ThetaEfficiency: > 94 % for Cu radiationMaximum count rate: > 25,000,000 cpsDetector noise: < 0.1 cpsScan range: from 1oto more than 160oin 2Theta

Large active length: ~2.5o2ThetaCan be used for static measurements


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PIXcel Detector

DivergenceSlit

Sample

1D detector


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PIXcel Detector

Bragg-Brentano geometry 2:30:00 h:m:sXCelerator detector 0:28:28 h:m:s


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Two Dimensional Detector

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06 Geometry, Detectors