Introduction to MineralogyDr. Tark Hamilton

Chapter 14: Lecture 27-29Analytical & Imaging Methods

in Mineral Science

Camosun College GEOS 250

Lectures: 9:30-10:20 M T Th F300

Lab: 9:30-12:20 W F300

Analytical Techniques in Mineralogy• XRD: X-Ray Diffraction of single crystals or powders in

cameras or slide mounts (structure)• XRF: X-Ray Fluorescence of bulk mineral or rock powders or

during Microprobe analyses (chemistry)• SEM: Scanning Electron Microscopy for surface imagery of

micrometer size mineral crystals and textures• TEM: Transmission Electron Microscopy of micrometer thick

mineral films & crystal slices for imagery of phase boundaries & electron diffraction patterns

• EMPA: Electron Microprobe Analyses, Quantitative or qualitative chemical analyses down to 1 micron sizes of polished mineral surfaces WDA, EDA spectroscopy (major & minor elements down to ~0.1%)

• SIMS: Secondary Ion Mass Spectrometry using O- or Cs+ beams of trace elements down to ppb concentrations

• AFM: Based on Scanning Tunnelling Microscopy of Metals and Conductive Sulphide Minerals, used for imaging Insulators on Atomic Scale

Electromagnetic Spectrum

fig_14_01

1.0 nm > Xray λ > 0.01 nm(~the size of atoms)

10 Å = 10-9 m

Generation of X-Rays• Energetic electron transmission & elastic

collision preserves Kinetic Energy (most)

• Inelastic ejects inner shell electrons (few)

• Outer shell electrons (N O P Q) are weakly held & closely spaced in energy levels so these generate IR or Visible Light Photons

• Inner Shell Electrons (K, L, M) are close to the nucleus & feel the full atomic number so they generate hard UV or X-Ray photons

• Cascade from adjacent shells is most common, e.g. L K making a Kα photon

Sealed Vacuum X-Ray Source Tube

fig_14_02

Common Sources:Mo, Cu, Co, Fe, Cr, W

Soft X-RayExclusion

Filter

Usually 15 to 30 KeV

Continuous & Characteristic X-Ray Spectra

fig_14_03

W @ EnergiesMo Source

&Transitionsto K shell

Kα = 0.7107Kβ = 0.6308Absorbtion

Edge

X-Ray Absorbtion Edges• As the optical excitation of a core level electron

requires the binding energy EB as a minimum photon energy, exceeding this energy will coincide with an increased absorption coefficient. This leads to the formation of absorption edges, which may be indexed by their atomic subshells (K,L,M...). Beyond the absorption edge the intensity of a monochromatic X-ray passing through a medium of thickness d will follow the absorption law

• I = exp (-μd) where μ = Z2 / (hv)2

• whereby μ depends the atomic number Z of the medium and decreases with increasing photon energy hv

Production of K L & M Characteristic X-Ray Spectra

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K lines transit to K Shellα is from the L shellβ is from the M Shell

L lines transit to L Shellα is from the M shellβ is from the N Shell

X-Ray Source• Schematic Diagram of an X-ray

Generator. The heated filament boils off electrons, which then accelerate toward the positively charged Cu anode. ~99% just collide and heat up the target. ~1% generate X-Rays. The photons are absorbed by shielding and collimators (not shown), except those headed along the main beam axis. (After Piccard and Carter, 1989.)

X-Ray K Wavelengths for Common Sources

Source Wavelength Filter Abs. Edge.

Molybdenum 0.7107 Niobium 0.66

Copper 1.5418 Nickel 1.49

Cobalt 1.7902 Iron 1.743

Iron 1.9373 Manganese

Chromium 2.2909 Vanadium

Tungsten Tantalum

X-Ray Diffraction Effects• Incident X-Ray beam of photons causes

electrons in lattice atoms to resonate & emit new wave fronts of the same wavelength

• Usually these new wavefronts distructively interfere

• When the spacing between atoms is a regular trigonometric function of the X-Ray wavelength, constructive interference occurs

• This reinforced scattering of relatively intense X-rays is termed “Diffraction”

• For fixed λ, lattice d-spacings relate to the angle

Constructive Diffraction: 1 Atomic Row

fig_14_06

AB = nλ = c cos Φ

Constructive Interference from Atomic Lattices

fig_14_05

fig_14_07

Successive Diffraction Conesfrom a Row of Atoms

AB = nλ = c Cos Φ

fig_14_08

Scattering from 3D Intersecting Atomic Rows

Solution to3 Laue equations

= 1 line, 1 spot

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The Bragg Equation: Reflections from Planes of Atoms in a Crystal Lattice

nλ = 2d Sin θ , θ = 90°- Φ

fig_14_10

Laue X-Ray Diffraction Photographof Vesuvianite 4/m 2/m 2/m

Ca19 (Al,Fe,Mg)13 (Si2O7)4 (SiO4)10 (O,OH,F)10

Contact Metamorphism Impure Limestones

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Precession Photograph About C-Axisof Vesuvianite 4/m 2/m 2/m

Determination of a Crystal Structure

• I = k [ Σ f exp(i2π(hx+ky+lz))]2 = kF2hkl

• Intensity of a diffracted beam for (hkl)

• k is a combined experimental constant

• f is the scattering factor for an atom, depending on Z, scattering angle θ, & thermal motion

• Fhkl is the Structure Factor, depending on atom types & positions in unit cell

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P4-Single Crystal Diffractometer

X-Ray TubeX-Ray Detector

4 Circle Goniometer

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Electron Density Map for Diopside on (010) from Fourier Sums & Atomic Positions

2/m cut obliqueTo (110) Cleavage

Derivation of Crystal Structure from Stoichiometry & Unit Cell

• NaCl: Space Group 4/m 3 2/m• a = 5.64 Å, unit cell edge (V=a3)• 39.4% Na & 60.6% Cl by weight• (39.4 / 22.99) / (60.6 / 35.453) = 1.71/1.71 = 1• ρ = 2.165 g/cm• Since density & unit cell volume are known, the

number of formula units per cell are:• Z = (n D V)/M where Z is formula units, D is density, V

is molar volume, M is formula weight & n is Avogadro’s number

• For NaCl : Z = (6.022 x 1023 per mol) x (2.165 g/cm3) (5.64 x 10-8 cm)3 / 58.443 g/mol = 4.002 formulae per unit cell

• Na+/Cl- =1.02/1.81 = 0.564, 0.41 < .564 < 0.73 FCC

Other Spectroscopic Techniques for Determining Crystal Structures

• Neutron or Electron Diffraction: wave behaviour of particle beams

• Infrared: energy absorbtion bands related to bonds, strengths & atomic masses, stretching, bending, torsion of bonds; molecular ions

• Mossbauer: Distinguishes positions & valences of Iron, Fe2+ versus Fe3+, e.g. M1 versus M2

• Nuclear Magnetic Resonance: useful for Hydrogen & other elements with unpaired nuclear spins. Good for O-2 versus OH-

fig_14_14

X-Ray Powder Diffraction

For Randomly Oriented Crystals, AllBragg Angles are solved Simultaneously

nλ = 2d sin θ

Flat Plate MethodWorks only for small 2θ

fig_14_15

X-Ray Powder Camera:Straumanis Method

Pb Beam Catcher

Powder Spindle

Film Strip, Low 2θ

fig_14_16

X-Ray Powder Diffractometer

Sample & Detector RotateRespectively by θ & 2θ

fig_14_17

Powder Diffractometer Scan for α-Quartz 32

Peak Intensity is Scaled Relative to (101)=1,(or whatever is the strongest peak)

What kind of a form is thestrongest diffraction for low Quartz?

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PDF file for Low Quartz from ICDD

217,000 filesExperimental &

Calculated,for natural &

Syntheticcompounds

Usually <5 peaks< 75° 2θ

Applications of Powder XRD• Minerals with solid solution have variations in

“d-spacings” proportionate to ionic substitutions• Some “d-spacings” are particularly sensitive as

are molar volume and density as with Fe vs Mg• Fine grained minerals like clays, zeolites & Fe,

Mn or Al oxy-hydroxides often occur in mixtures. Comparing patterns of pure end members & known mixtures permit calculation of compostions e.g. illite vs montmorillonite or natrolite vs thompsonite or limonite vs goethite

• The Reitveld refinement method is the main tool for clay mineral structures

Example d-spacing Calculation

• nλ = 2d sinθ or d = λ/2sinθ

• λ = 1.540598 Å for Cu Kα1

• θ(100) = 10.425° for d (100) as measured

• So for α-Quartz:

• d(100) = 1.540598 Å / 2 • (0.18094) = 4.2570 Å

• Data from table 14.18 in Klein & Dutrow (2002)

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Variation in Vmol Å3, β Å & 2θ(1,11,0) for

Monoclinic Amphiboles: Cummingtonite-Grunerite

After Klein &Waldbaum (1967)

Formula Units from Crystal Structure for Unit Cell of Grunerite

• Grunerite: 2/m , Fe7Si8O22(OH)2

• b = 18.44 Å, β = 102°• M = 1001.614 g/mol• ρ = 3.6 g/cm• Since density & unit cell volume are known, the

number of formula units per cell are:• Z = (n D V)/M where Z is formula units, D is density, V

is molar volume, M is formula weight & n is Avogadro’s number

• For Grunerite: Z = (6.022 x 1023 per mol) x (3. 6 g/cm3) (925 x 10-24 cm3) / 1001.614 g/mol = 2.004 formulae per unit cell

XRF: X-Ray FluorescenceEmission Spectroscopy

• Chemical Analyses of Inorganic Compounds, Rocks and Minerals

• Mining, Ceramics, Metallurgy, Mineralogy, Petrology• Compressed powdered sample + binder or flux if

fused• Polychromatic X-ray Source• Absorbtion according to Beer’s Law:• log(Io/I) = KdΔd , I-Intensities, Kd–Constant, Δd-

thickness• Absorbed X-ray photons expel inner shell e- & falling e-

L to K emits characteristic X-rays for each element• Spectra for 2 or more elements need to be resolved

for emission lines proportions

fig_14_20

XRF: X-Ray FluorescenceEmission Spectroscopy

Spectrum for 2Elements

Molybdenum & Copper

BackgroundSpectrum

CharacteristicSpectrum

fig_14_21

X-Ray Fluorescence Spectrometer

Differentelements & λ’s

LIF: LiF, ADP: Ammoniumdihydrogen phosphate

KAP: Potassium biphthalate,Known d-spacings

fig_14_22

XRF Spectrum of a Genuine Bank Note(Counterfeiting is not a way to get ahead)

W is due to X-RayTube Target Metal

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Schematic of Electron Microprobe

Magnetic Lenses

10-7 Torr

or Energy Dispersive Spectrometerw/ Be window & SiLi detector

~30 KeV

SEM’s have detectors forElectrons to image sample

fig_14_25

SEM or EMP Stage

BSE: Backscattered e- sSE: Secondary e- s

CL: Cathodoluminescence

25 Å < Resolution < 50 Å

Cathodoluminescence SEM ImagesGranite Llano Texas

J.Schreiber, IUSandstone Simon Fm Ill

Rob Reed, UofTx

Calcite &K-spar

Quartz &Barite

fig_14_27

TEM Schematic

Magnetic Lenses

Resolution to 0.14 Å(half a small unit cell)

Where are those impurities?

fig_14_30

EMPA & Analytical VolumeVolume is proportional to Average Z

fig_14_32

SIMS: Secondary Ion Mass Spec

Most Elements & Isotopes 1H to 92U

Especially Light Elements

fig_14_33

SHRIMP: Ion Microprobe

U & Pb isotopesOn a 20 μ scale

Zircon growth zones

SHRIMP Analyses for Dating

research.eas.ualberta.ca/rif/mc_icp_ms.html

fig_14_34

AFM: Atomic Force Microscope

Electro-mechanical AmplifierOf the Force Between Atoms

Outgrowth of STEM for conductors

Atomic Topography