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Page 1: Bragg’s Law

Bragg’s Law

• n=2dsinΘ• Just needs some




These 2 constructivelyInterfere good signal!



These 2 destructivelyInterfere bad signal!

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X-Ray Diffraction (XRD) equipment

• n=2dsinΘ

• nd=sinΘ• Solution ‘satisfied’ at

specific angles (n MUST be an integer)

X-ray source

Sample holderX





Orientation of diffracting hkl planes in sampleA number of these are possible

Detector typically moves over range of 2 Θ angles

Typically a Cu or Mo target1.54 or 0.8 Å wavelength

XRD machines vary angle as 2Θ because that angle is always relative to incident X-ray beam trajectory

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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 results• Diffraction pattern• Higher symmetry fewer, more intense lines

because multiple planes are complimentary (identical d-spacings for different planes yields identical diffraction)

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XRD extinctions

• Some forms exhibit extinctions – when planes should 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, face centered 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 a

powder• Single Crystal must be careful about orienting

the crystal so Bragg’s Law is satisfied, use several different techniques, advanced machines manipulate the sample in 3 axes (x,y,z) to ‘catch’ all the peaks required for structural determination

• Powder has many particles with planes at many different orientations many orientations satisfy Bragg’s Law, intensities and locations (2Θ) are characteristic of specific minerals. Technique primarily used for identification

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Powder XRD analyses• With a single crystal, alignment of planes

which give strong diffraction returns is very exact – requires precise alignment

• With a fine powder, idea is to have crystals at a wide variety of orientations so hitting that exact alignment is possible without manipulating the sample – i.e. in a powder we figure a few grains are lined up correctly

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Powder X-ray Analyses

• XRD analysis of a powder is a common, quick, and relatively easy way to identify minerals.

• Having a mixture of minerals can be tricky, so grains are first separated if possible (small amounts of other minerals will give other peaks, but intensities are low enough that it is not a big deal)

• Do lose the ability to ‘see’ the details of the structure of the mineral however as the precise alignment of the mineral giving the peak is unknown and not changeable

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Analytical Techniques for Minerals

• XRD (X-ray diffraction) is one of the most powerful 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 which we will also study in detail (both lecture and lab)

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More analytical techniques

• Electron microscopy – look at techniques which utilize how electrons (shot through a sample of mineral) interact with minerals – imaging possible to very small sizes

• Scanned-proximity probe microscopy techniques – look at forces between probe tip and sample to measure a property (height, optical absorption, magnetism, etc)

• Spectroscopy – different methods of studying how different parts of the electromagnetic spectrum (of which visible light is a small part) are affected by minerals

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More analytical techniques

• Sychrotron – Different techniques (including many spectroscopic techniques) that utilize particles accelerated to very high speeds and high energies

• Magnetic – different techniques that utilize the 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 interaction of some part of the electromagnetic spectrum with a material

• Each technique provides different information about the chemistry, structure, and physics of the material

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Spectroscopic Techniques

• Utilize the absorption or transmittance of electromagnetic radiation (light is part of this, as is ~UV, IR) for analysis

• Governed by Beer’s Law (or Beer-Lambert-Bouger law, but everyone likes Beer…)A=abcWhere: A=Absorbance, a=wavelength-

dependent absorbtivity coefficient, b=path length, c=analyte concentration

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• Exactly how light is absorbed and reflected, transmitted, or refracted changes the info and is determined by different techniques





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Light Source• Light shining on a sample can come from

different places (in lab from a light, on a plane from a laser array, or from earth shining on Mars with a big laser)

• Can ‘tune’ these to any

wavelength or range of


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 at a specific frequency only specific bonds can absorb IR though (IR active)

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Vibrational spectroscopy

• Another name applied to absorption spectroscopy in IR range and for Raman spectroscopy

• Sensitive to the vibrational modes of bonds between atoms rather than of the ions themselves

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Optical Spectroscopy

• Techniques concerned with how light reflects, absorbs, or transmits through minerals 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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• Exactly how light is absorbed and reflected, transmitted, or refracted changes the info and is determined by different techniques





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Reflectance Spectroscopy• Can be optical or vibrational• Non-destructive form of analysis, used to ‘see’

some of the chemistry, bonding• Spectroscopy is particularly good at detecting

water and OH groups in minerals (especially in IR)• Good at differentiating between different clays

because it detects OH groups well

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Raman Spectroscopy

• Another kind of spectroscopy which looks at a scattering effect and what that tells us about the chemistry, oxidation state, and relative proportions of different ions

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Mössbauer Spectroscopy• Special effect, restricted to specific isotopes

of certain elements which causes a very characteristic emission (after getting hit with a beam of gamma radiation) which is sensitive to the bonding environment of that isotope (only 57Co, 57Fe, 129I, 119Sn, 121Sb)

• Generally used to study Fe – tells us about how Fe is bonded and it’s oxidation state