1. Bragg’s Law nl=2dsinΘ Just needs some satisfaction!! d Θ l
These 2 constructively
Interfere  good signal!
Bragg’s Law
nl=2dsinΘ
Just needs some satisfaction!! d Θ l
These 2 destructively
Interfere  bad signal!

2. X-Ray Diffraction (XRD) equipment
XRD machines vary angle as 2Θ because that angle is always relative to incident X-ray beam trajectory
nl=2dsinΘ
nl/2d=sinΘ
Solution ‘satisfied’ at specific angles (n MUST be an integer)
X-ray source
Sample holder
X-ray detector
Orientation of diffracting hkl planes in sample
A number of these are possible
Detector typically moves over range of 2 Θ angles 2Θ
Typically a Cu or Mo target
1.54 or 0.8 Å wavelength 2Θ

3. 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

4. XRD results Diffraction pattern
Higher symmetry  fewer, more intense lines because multiple planes are complimentary (identical d-spacings for different planes yields identical diffraction)

5. 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

6. 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

7. 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

8. 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

9. 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)

10. 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

11. 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

12. 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

13. 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=abc
Where: A=Absorbance, a=wavelength-dependent absorbtivity coefficient, b=path length, c=analyte concentration

14. Spectroscopy
Exactly how light is absorbed and reflected, transmitted, or refracted changes the info and is determined by different techniques
sample
Reflected
spectroscopy
Transmittance
Raman
Spectroscopy

15. 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
wavelengths
IR image of Mars
Olivine is purple

16. 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)

17. 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

18. 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

19. Spectroscopy
Exactly how light is absorbed and reflected, transmitted, or refracted changes the info and is determined by different techniques
sample
Reflected
spectroscopy
Transmittance
Raman
Spectroscopy

20. 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

21. 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

22. 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