X-Ray CrystallographyX-Ray Crystallography

The most important technique for The most important technique for mineralogymineralogy Direct measurement of atomic Direct measurement of atomic

arrangementarrangement Direct measurement of what was Direct measurement of what was

originally deduced from crystal facesoriginally deduced from crystal faces

X-RaysX-Rays

Electromagnetic radiation – similar to Electromagnetic radiation – similar to visible lightvisible light = 0.02 to 100 Å= 0.02 to 100 Å = 0.002 to 10 nm= 0.002 to 10 nm Visible light = 400 to 750 nmVisible light = 400 to 750 nm

Fig. 6-6Fig. 6-6

Visible light Visible light spectrumspectrum

Full range of electrom

agnetic radiationF

ull range of electromagnetic radiation

(nm) f (hertz)

1 nm = 101 nm = 10-9-9 m m

} X-Rays

X-Ray generationX-Ray generation

Heat filament, which discharges electrons

Electron accelerated with 20 to 100 kV toward “target”

Target is Cu or Mo (also Co, Fe and Cr)

Very hot – requires continuous circulation of cooling water

Fig. 8-2

Full spectrum of X rays

X-Ray generatedX-Ray generated

Continuous spectrum of X-Continuous spectrum of X-ray energy (wavelengths) ray energy (wavelengths) are produced without are produced without electrons changing shellselectrons changing shells

Characteristic spectrum Characteristic spectrum when incoming electrons when incoming electrons dislodge electrons from dislodge electrons from outer shellsouter shells

Electrons drop from either Electrons drop from either M shell (KM shell (K) or L shell (K) or L shell (K))

KK the most intense (highest the most intense (highest energy)energy)

X-rays

Target material - Cu

Electrons K

K

Fig. 8-3

Use of X-rays requires single wavelengthUse of X-rays requires single wavelength Similar to monochromatic visible lightSimilar to monochromatic visible light Wavelength critical for measurementWavelength critical for measurement Acts like a “ruler”Acts like a “ruler”

Must filter out the continuous spectrum, Must filter out the continuous spectrum, and leave only one of the characteristic and leave only one of the characteristic spectrumspectrum

Typically KTypically K peak – most intense peak – most intense Referred to as Cu – KReferred to as Cu – K radiation radiation

FilteringFiltering Use a monochrometerUse a monochrometer Typically a thin piece of Ni or Be foilTypically a thin piece of Ni or Be foil

Foil allows most Cu-KFoil allows most Cu-K radiation to pass radiation to pass Blocks most wavelengths except KBlocks most wavelengths except K

Absorption Absorption edge, Ni edge, Ni filters out filters out these these wavelengthswavelengths

X-rays pass through filter

X-rays blocked by filter

= 1.5418 Å= 1.5418 Å

DetectionDetection Variety of detectorsVariety of detectors

Scintillation counters (light flashes)Scintillation counters (light flashes) Gas proportional countersGas proportional counters

Detectors are arranged so that X-Detectors are arranged so that X-rays reflected off of mineral surfaces rays reflected off of mineral surfaces can be recordedcan be recorded

DetectorDetector

SampleSample

Arrangement Arrangement of X-Ray of X-Ray

diffractometdiffractometerer

X-ray X-ray generatigenerationon

X-Ray diffractionX-Ray diffraction

Wavelength of X rays 1 to 2 ÅWavelength of X rays 1 to 2 Å Cu KCu K = 1.5418 Å = 1.5418 Å

About the same length as spacing of About the same length as spacing of atoms in mineralsatoms in minerals

Typically 1 to 2 ÅTypically 1 to 2 Å

Called d spacingCalled d spacing

= 1.5418 Å

X-Ray diffractionX-Ray diffraction

pqr = npqr = n

pq = d sin pq = d sin

Reflects waves in phase, Reflects waves in phase, only if angle only if angle is such at is such at that the additional distance that the additional distance pqr traveled by wave 2 is pqr traveled by wave 2 is an integer number of an integer number of wavelengths (here 1 wavelengths (here 1 wavelength) wavelength)

Bragg Bragg EquationEquation

pqr = npqr = n

pq = d sin pq = d sin

pqr = 2pq = pqr = 2pq =

2d sin 2d sin = n = n

Bragg Equation

Planes of atoms

ExampleExample

Halite – {111} planes have d spacing Halite – {111} planes have d spacing of 3.255 Åof 3.255 Å

Cu KCu K radiation, radiation, = 1.5418 Å = 1.5418 Å Solving Bragg equation showsSolving Bragg equation shows

= 13.70º for n = 1= 13.70º for n = 1 = 28.27º for n = 2= 28.27º for n = 2 = 45.27º for n = 3= 45.27º for n = 3 = 71.30º for n = 4= 71.30º for n = 4

When X-rays reflect off mineral at these angles, they will interfere constructively – cause a peak in energy at the detector

Multiple possible atomic planes {110}, Multiple possible atomic planes {110}, {100}, {001} etc.{100}, {001} etc.

Orienting a single grain unlikely to reflect Orienting a single grain unlikely to reflect X-rays off of any of these planes X-rays off of any of these planes

Better to use multiple grains with random Better to use multiple grains with random orientationsorientations With enough planes (1000’s), there will be With enough planes (1000’s), there will be

enough parallel to create reflections.enough parallel to create reflections. Powder Diffraction methodPowder Diffraction method

Powder DiffractionPowder Diffraction

Sample crushed to small size, Sample crushed to small size, typically < 0.05 mmtypically < 0.05 mm

Placed on glass slide or hollow holderPlaced on glass slide or hollow holder Sample placed in X-Ray Sample placed in X-Ray

diffractometerdiffractometer Blasted with X-rays as sample and Blasted with X-rays as sample and

detector rotate from around 2º to 70ºdetector rotate from around 2º to 70º

Degrees 2

Intensity of reflection

Strip recorder records intensity of signal from detector

Data reductionData reduction

Powder Powder diffraction filesdiffraction files Cards with the Cards with the

intensity and d intensity and d spacing for all spacing for all mineralsminerals

4 major peaks, d spacing

All peaks, d spacings relative intensity, reflecting plane

Take rock, sediment, mineral sampleTake rock, sediment, mineral sample Grind sampleGrind sample MountMount Measure all d spacingsMeasure all d spacings Compare with the powder diffraction Compare with the powder diffraction

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