X-Ray Scattering EquipmentReading: X-Ray: Warren, Chapters 5-7

Common Geometries:

• Laue: continuous white source, single crystals

forward and back reflected, Warren Fig. 6.1-5

Program to analyse data: QLaue

(http://mac.softpedia.com/get/Math-Scientific/QLaue.shtml)

• Debye-Scherrer: monochromatic source, polycrystalline sample.

• Monochromatic source, single crystals.

Example:

1

Example:

Pulsed Synchrotron (white spectrum)

Laue diffraction pattern from photo-

active yellow protein (single crystal).

3700 usable reflections that were used

to calculate the structure. From M.

Wulff, ESRF, and B. Perman, U. of

Chicago.

Fig. 4.12 Als-Nielsen/McMorrow.

Example: Debye-Scherrer or Powder diffraction from polycrystalline InSb, (a)

image from 2-d areal detector. (b) integrated intensity of data in (a). Structure

changes from cubic to orthorhombic at high pressure.

2

Elements of Modern X-ray Physics, Jens Als-Nielsen, Des McMorrow, Fig. 4.26, 27

Experimental Equipment and Techniques

X-ray generation:

• Electrons emitted from hot filament accelerated into cooled target eject core electrons;

target emits x-rays upon relaxation.

• Electrons are accelerated around a storage ring giving off continuous spectrum

radiation: eg. Canadian Light Source (CLS), Advanced Light Source (APS), European

Synchrotron Radiation Facility (ESRF), Cornell (CHESS), Wisconsin (Adladin), etc.

Synchrotron

3Elements of Modern X-ray Physics, Jens Als-Nielsen, Des McMorrow, Fig. 2.1, 2.2

45 kV

35 mA

Canadian Light Source, Saskatoon, Sask. (http://www.lightsource.ca/)

4

Fixed Tube Sources:

Target core electrons ejected from atom can result in light emission when atom relaxes following

allowed quantum mechanical transitions. Strong peaks at wavelengths characteristic of element.

Listed in Warren, App. II. eg. Cu Kα1 = 0.154051 nm; Kα2 = 0.154433 nm Kβ= 0.139217 nm

5

( ) ( )( )bandwidth unitarea sourceangle solidbeam

cphotons/se inIntensity Brilliance

2=

Brilliance of a synchrotron source is about 10 orders of magnitude higher at Cu Kα

than for a rotating anode, which is about 6 times that of a fixed tube source.

Emax

λmin

Diagram of x-ray tube (Cullity Fig. 1-15.)

Characteristic radiation

• Monochromatic Intensity, I : where E is electron beam energy and Ec is

energy of characteristic x-ray emitted

Bremsstralung radiation

• Besides the characteristic radiation, a continuous spectrum called Bremsstralung occurs

• Electrons are de-accelerating in the target.

• Maximum deposited into x-ray can be total e energy = eV where V is the accelerating

voltage of the tube. Depends on how close the e passes each nucleus.

Maximizing the characteristic radiation intensity with respect to the continuum spectrum:

5.1)(.)( cEEcharI −∝

22.)( ZVBremI ∝

6

Maximizing the characteristic radiation intensity with respect to the continuum spectrum:

Optimum ratio of V to Vc is 3-4

“take-off angle” = 3-6° produces a line source

Diagram of a diffractometer

• Bragg-Brentano geometry allows divergent

beams with finite angle defined by collimation

slits provide similar incident angles for a powder sample. tube detector

goniometer

circle

Sample

focussing circle

Slits, Monochromation, Filters

• Diffraction from single crystals, single or multiple reflections monochromate

• Filters consist of thin foils of absorbing material to attenuate Kβ radiation from tube

or fluorescence from the sample, eg. Ni filter for Cu Kβ

7

http://physics.nist.gov/Divisions/Div842/Gp5/instdeva.html

Simple slit collimation and beam “conditioning” via multiple single crystal diffractions

monochromate and collimate.

Detectors

Diffractometer Resolution

• Differentiating Bragg’s law assuming small angles bewteen peaks:

• ∆λ between Kα1 and Kα2 is for Cu tubes = 0.004 nm, λave= 0.154 nm

∴ ∆θ = tanθB*∆λ/0.154 = 0.002 to 0.02 rad or 0.1 to 1° for θB = 5 - 40°

• Slits determine signal to noise, level of background from stray x-rays, fluorescence

• Instrument resolution is measured using large grain polycrystalline reference

d

d

θ

∆=

∆−=

∆

tan

θ

λ

λ

8

• Proportional counters (106 cps, efficiency < 50%):

Rare gas in grounded can with charged wire in center,

hν → Xe → Xe+ → negative wire, current pulse

• Scintillation counter (efficiency 5%): eg, NaI doped with Tl, poor resolution, high count rates.

hν + phosphor → optical hν → photomultiplier tube

• Solid state detector (104 cps) good energy resolution: eg. Ge or Si(Li) pin diode.

• Position sensitive detectors (lower energy resolution but fast data collection):

cross-wire gas proportional counters,

image plate (BaFI with Eu long lasting excitation from Eu2+ to Eu3+; readout using He-Ne

laser to photostimulate blue emission) highly linear

CCD (low flux).