Tasks part 1
Answers part 1
Tasks part 2
Answers part 2
Tasks part 3
Answers part 3
Lets reproduce the intensity distributions:
Why are the two diffraction patterns different?
- The left image was calculated for X-ray diffraction. Note
that the intensities drop with increasing distance from
the center of reciprocal space.
- The right image was calculated for neutron diffraction.
Atoms can be treated like point scatterers in this case.
Accordingly the intensities do not decrease with increasing
distance from the origin of reciprocal space.
- The atomic form factors increase with the number of
electrons, while the neutron scattering length do not
show this systematic distribution. Accordingly the same
reflection can have totally different intensity as can be
seen in the diffraction patterns.
What information can you extract from the diffraction patterns?
- By applying Bragg's law you can calculate the d-spacing for the
There are many different ways to get the lattice constants from
a list of d-spacings. Since the diffraction pattern in these
examples are undistorted representations of reciprocal space,
the lattice constants can be obtained directly from the patterns.
The two base vectors of reciprocal space are normal to each
other, of equal length. Base vector a is horizontal,
base vector b is vertical. The lattice constants are:
a=b=5.0 A, alpha=90.
- The second information available directly from the diffraction
pattern is their symmetry. Both diffraction patterns show
symmetry mm4. There are no systematic extinctions, thus
the plane group is pmm4. Note that the X-ray pattern
shows a pseudo c-centering. All reflections hk, h+k=2n+1 are
What, if any, information do you need beyond the diffraction patterns
to solve the crystal structure?
- First we need the chemistry of the substance: Zr Ti O4
- In order to calculate the number of molecules per unit we should
measure the density of the material.
- Physical properties such as the piezoelectric effect will give
insight into the presence of a center of symmetry.
What type of calculations can you perform to solve the structure?
- Direct methods provide the most powerful and usually easiest
way to solve the structure. They are, however, very much
black box methods, and beyond the scope of this tutorial.
- A Patterson synthesis can be calculated directly from the
Now you are ready for the next step towards a solution of the given