BRAGG WAVEGUIDE AND ITS DESCRIPTION

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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!



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



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





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



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



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





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)



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



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



• 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



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



Spectroscopy

• Exactly how light is absorbed andreflected, transmitted, or refractedchanges the info and is determined bydifferent techniques

sample

Reflectedspectroscopy

Transmittance

spectroscopy

Raman

Spectroscopy



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



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)



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



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



Spectroscopy

• Exactly how light is absorbed andreflected, transmitted, or refractedchanges the info and is determined bydifferent techniques

sample

Reflectedspectroscopy

Transmittance

spectroscopy

Raman

Spectroscopy





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



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BRAGG WAVEGUIDE AND ITS DESCRIPTION

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