Geos 306, Lecture 11
Crystallography III, X-ray Diffraction

Opal, SiO2·nH2O
Cristobalite, SiO2


Coordinate systems

nl = 2d sin(q),
where l is the wavelength of the X-ray, d is the spacing between planes, and q is the angle of incidence that the incident X-ray beam makes with the plane of atoms (hkl).


  • You should be able to derive Bragg's equation using this drawing. He won the Nobel prize for figuring this out while a first-year grad student at the tender age of 22.


  • Indexing a diffraction pattern

    Refining the cell parameters

     ******************************************************************************
           **Program REFINE Version 3.0**  Kurt Bartelmehs and Bob Downs, 1998
     ******************************************************************************
    
      quartz: Kihara: E. J. Mineral. 2 (1990) 63-77
    
     Symmetry constraint is: HEXAGONAL
    
     Wavelength #1 =  1.541838
     Wavelength #2 =  1.540562
     Wavelength #3 =  1.544390
    
     Refinement after correcting for machine error
    
     MACHINE ERROR:   -0.010
    
             OBSERVED                         CALCULATED          DIFFERENCE
        2theta      d     h  k  l  Wave#  2theta       d      2theta       d
        20.850  4.26043   1  0  0    1    20.886   4.25314     0.036   0.00729
        20.900  4.24683   1  0  0    2    20.869   4.25314    -0.031  -0.00631
        26.630  3.34738   0  1  1    1    26.677   3.34156     0.047   0.00583
        26.700  3.33600   0  1  1    2    26.655   3.34156    -0.045  -0.00555
        26.630  3.34738   1  0  1    1    26.677   3.34156     0.047   0.00583
        26.700  3.33600   1  0  1    2    26.655   3.34156    -0.045  -0.00555
        36.530  2.45976   1  1  0    1    36.595   2.45555     0.065   0.00421
        36.630  2.45124   1  1  0    2    36.563   2.45555    -0.067  -0.00431
        39.460  2.28360   1  0  2    1    39.527   2.27989     0.067   0.00371
        39.560  2.27618   1  0  2    2    39.493   2.27989    -0.067  -0.00372
        39.460  2.28360   0  1  2    1    39.527   2.27989     0.067   0.00371
        39.560  2.27618   0  1  2    2    39.493   2.27989    -0.067  -0.00372
        40.280  2.23899   1  1  1    1    40.348   2.23539     0.068   0.00360
        40.380  2.23183   1  1  1    2    40.313   2.23539    -0.067  -0.00357
    
     rmse = 0.00053932607
    
         A =    4.9110(39)         B =    4.9110(39)          C =    5.4013(57)
     Alpha =   90.0             Beta =   90.0             Gamma =  120.0
    
     Volume =   112.82(16)
    


    Reading:
    Wenk and Bulakh, chapter 7