Rocks Minerals and Crystals By Guest Scientist Dr. David Walker LDEO-Columbia University

Rocks are made of minerals This pallasite meteorite rock came from the edge of the core of an unknown asteroid in our solar system. This thin slab is lit from both the front and back. Magnesium silicate olivine forms amber-colored crystal windows through iron crystals of kamacite and taenite ( the polished metal).

Minerals Are Crystalline Geometrical crystal shapes suggest ordered structures.

Periodic 3D atomic order = crystals External morphology in regular geometric shapes suggests internal periodic structure, such as for: Layered silicate chlorite Ring silicate beryl (gem=emerald)

How to Learn the Atomic Order? Put X-ray beams through crystals. X-rays are short electromagnetic waves of wavelength ( ) between 0.1 and 10 Angstroms. If waves hit periodic array with spacing d  then COOPERATIVE SCATTERING occurs ( = DIFFRACTION ). This is NOT the same as taking an X-ray picture in a medical lab and magnifying it.

Cooperative Scattering Waves on Pond with Array of Duck Decoys Ripple train approaches line of ducks d d d

Map View of Pond Surface d As the ripple train passes, each duck bobs up and down sending out new waves. Those waves interfere with one another. Both + & -

d  wave no wave Condition for Scattering: =d sin   ) sin   = /d To keep parallel beams at angle  1 in phase must be 

d   n = 1 n = 2 wave no wave Condition for Scattering: n =d sin  For small  [ >> d  get many beams. Large n resembles continuous scatter. 1 =d sin   2 =d sin   )   wave no wave

n = d sin  means sin  =n /d Maximum  is 90 o – diffraction directly sideward - for which sin  1 Giving n /d  1 or n  d Smallest n when n = 1 The  easiest to satisfy for n = 1 So  d to keep sin  1  Otherwise no diffraction! d  = 90 o Wavelength must be shorter than d

n = d sin  is satisfied both forward and backward from the array, as well as on either side. d n=2 n=1     NOTICE for fixed, smaller d gives bigger  Spots or wave beams spread as ducks become closer. Spots or wave beams spread as you move away from ducks. n = d sin 

XRD is not like medical X-ray imagery! Medical X-ray XRD Spots spread as fingers spread Spots spread as duck converge. Spread grows with distance from ducks.

Laser/grid diffraction demonstration )  d S s LASER Spots absent in nonperiodic fabric Spot symmetry same as that of grid Spots rotate with grid rotation but not XY Spots spread with grid tilt or smaller d Spot spacing s grows with S

Mineral Crystals Diffract X-rays Therefore: X-rays are waves ! Crystals are periodic arrays !  d ! This 1912 demonstration won Max von Laue the Nobel Prize in physics for X-ray beam

For Mineralogists 1.Symmetry of spots  symmetry of array 2.Spacing of spots  array spacing of scattering atoms 3.Intensity of spots  atomic weight occupancy distribution. This makes possible crystal structure analysis. Library of patterns is reference resource of ‘fingerprints’ for mineral identification! Chain silicate diopside (along chains)

1915 Nobel Prize to the Braggs Father and son team showed that XRD could be more easily used if diffraction spots treated as cooperative scattering “reflections” off planes in the crystal lattice. Planes separated in perpendicular direction by d hkl Angle of beam and reflection from lattice plane is  Braggs’ Law: n  d hkl sin  XRD Mineral identification done from tables of the characteristic Bragg d hkl which are calculated from and  observations.

Powder XRD for mineral ID 2  = 0 2  = 90 X-ray beam in Powdered sample 2  hkl d hkl Make list of d hkl from measured 2  hkl using n  d hkl sin  Compare with standard tables d d d d

Exercise 1.Measure screen to image distance ( S ). 2.Measure distance from middle of pattern to first spot (s). 3.Measure spacing of grid (d). )  d S s LASER Compute wavelength of laser light from n = d sin  Use derived to measure the d of a larger or small grid spacing = d s S

Website References Commercial library of the JCPDS powder patterns of over 60,000 crystal structures. XRD applications freeware and tutorials. Fun resource for mineralogy, especially crystal shapes. Mineralogical Society of America’s site including “Ask A Mineralogist”.