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Bragg’s Law
• nl=2dsinΘ • Just needs some
satisfaction!!
d
Θ Θ
l These 2 constructivelyInterfere good signal!
d
Θ Θ
l
These 2 destructivelyInterfere bad signal!
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X-Ray Diffraction (XRD) equipment
• nl=2dsinΘ
• nl 2d=sinΘ • Solution ‘satisfied’ at
specific angles (n MUST
be an integer)
X-ray source
Sample holder
Orientation of diffracting hkl planes in sample A number of these are possible
Detector typicallymoves over range of
2 Θ angles
2Θ
Typically a Cu or Mo target1.54 or 0.8 Å wavelength
XRD machines vary angle as 2Θ becausethat angle is always relative to incident X-raybeam trajectory
2Θ
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XRD Part II• Theoretically, almost an infinite number of planes
can exist, but certain ones diffract more strongly• Related to the atomic density – both of ## of atoms
and in those ions’ atomic density
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XRD extinctions
• Some forms exhibit extinctions – when planesshould be present (i.e. satisfy Bragg’s Law) but
are not due to destructive interference with
another plane’s diffraction. • Useful for determining special conditions of
symmetry in a single crystal – ID for body, facecentered minerals as well as ones with screw
axes and glide planes method to ‘see’differences between space groups
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XRD analyses
• Can look at minerals as single crystals or as apowder• Single Crystal must be careful about orienting
the crystal so Bragg’s Law is satisfied, use several
different techniques, advanced machinesmanipulate the sample in 3 axes (x,y,z) to ‘catch’all the peaks required for structuraldetermination
• Powder has many particles with planes at manydifferent orientations many orientations satisfyBragg’s Law, intensities and locations (2Θ) arecharacteristic of specific minerals. Techniqueprimarily used for identification
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Powder XRD analyses• With a single crystal, alignment of planes
which give strong diffraction returns is veryexact – requires precise alignment
• With a fine powder, idea is to have crystals ata wide variety of orientations so hitting thatexact alignment is possible withoutmanipulating the sample – i.e. in a powder we
figure a few grains are lined up correctly
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Analytical Techniques for Minerals
• XRD (X-ray diffraction) is one of the mostpowerful tools for mineral identification,structural/chemical refinement, and size
determination• Microscopy – Optical techniques are another
very powerful tool for mineral identification,identification of physical/ chemical ‘history’ of
minerals/rocks, and mineral association whichwe will also study in detail (both lecture and lab)
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More analytical techniques
• Electron microscopy – look at techniques whichutilize how electrons (shot through a sample ofmineral) interact with minerals – imagingpossible to very small sizes
• Scanned-proximity probe microscopy techniques – look at forces between probe tip and sample tomeasure a property (height, optical absorption,magnetism, etc)
• Spectroscopy – different methods of studyinghow different parts of the electromagneticspectrum (of which visible light is a small part)are affected by minerals
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More analytical techniques
• Sychrotron – Different techniques (includingmany spectroscopic techniques) that utilizeparticles accelerated to very high speedsand high energies
• Magnetic – different techniques that utilizethe magnetic properties of minerals• Size – techniques to determine the sizes of
different minerals• Chemistry/isotopes – techniques to probe
chemical and isotopic signatures in minerals
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• Spectroscopic techniques investigate the interactionof some part of the electromagnetic spectrum with amaterial
• Each technique provides different information aboutthe chemistry, structure, and physics of the material
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Spectroscopic Techniques
• Utilize the absorption or transmittance ofelectromagnetic radiation (light is part ofthis, as is ~UV, IR) for analysis
• Governed by Beer’s Law (or Beer -Lambert-Bouger law, but everyone likesBeer…)
A=abcWhere: A=Absorbance, a=wavelength-dependent absorbtivity coefficient, b=pathlength, c=analyte concentration
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Spectroscopy
• Exactly how light is absorbed andreflected, transmitted, or refractedchanges the info and is determined bydifferent techniques
sample
Reflectedspectroscopy
Transmittance
spectroscopy
Raman
Spectroscopy
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Light Source• Light shining on a sample can come from
different places (in lab from a light, on aplane from a laser array, or from earthshining on Mars with a big laser)
• Can ‘tune’ these to any
wavelength or range of
wavelengths
IR image of MarsOlivine is purple
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Causes of Absorption
• Molecular or atomic orbitals absorb light,kicks e- from stable to excited state
• Charge transfer or radiation (color centers)
• Vibrational processes – a bond vibrates ata specific frequency only specific bondscan absorb IR though (IR active)
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Vibrational spectroscopy
• Another name applied to absorptionspectroscopy in IR range and for Ramanspectroscopy
• Sensitive to the vibrational modes ofbonds between atoms rather than of theions themselves
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Optical Spectroscopy
• Techniques concerned with how lightreflects, absorbs, or transmits throughminerals from near UV to mid-infrared
(250 – 3000 nm wavelengths)• Dealing with energy which excited
electrons from a standard to an excited
state
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Spectroscopy
• Exactly how light is absorbed andreflected, transmitted, or refractedchanges the info and is determined bydifferent techniques
sample
Reflectedspectroscopy
Transmittance
spectroscopy
Raman
Spectroscopy
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Raman Spectroscopy
• Another kind of spectroscopy which looksat a scattering effect and what that tells usabout the chemistry, oxidation state, and
relative proportions of different ions