X-ray diffraction and minerals

Is this mineral crystalline?

Bragg’s law

Why work on single crystals?

Why work on crystal powder?

The powder X-ray diffraction pattern of an amorphous solid - No sharp peak - Broad hump

Bragg’s law: n = 2 d sin  1) What do we know?, i.e. the wavelenth of the X-ray radiation 2) What do we assume? n = 1 (Peaks for higher “n” are weaker.) 3) What do we want to know? d, i.e. the interplanar spacings of the lattice

X-ray spectra used to be recorded on film strips rolled up within a round chamber.

The distance from the center of each line to the center of the hole (where X-rays entered the chamber) was proportional to the angle 2-theta. The intensities of the lines were originally estimated by a human eye, on a scale of 1 to 100, before detectors became routine.

Ion order-disorder can be detected by X-ray diffraction. This is very different from the lack of order found in an amorphous solid.

Powder X-ray diffraction is a routine technique to measure the amount of crystalline SiO 2 (quartz) present in mineral dust or soil. A chemical analysis will not distinguish the SiO 2 of quartz from the silicate “skeleton” of clays and many other minerals.

Laue diffraction experiment

Laue photographs are used to study the epitaxial relationships between thin films and the material on which they are grown. Large spots: aluminum. Small spots: silicon.

How to solve crystal structures? The electron density ( ) at a point X, Y, Z in a unit cell of volume V is; (X,Y,Z) = 1/V F hkl cos [ 2 (h  X + k  Y + l  Z) - ] Therefore if we know Fhkl and (for each h, k, l) we can compute for all values of X, Y, and Z and plot the values obtained to give a three- dimensional electron density map. Then, assuming atoms to be at the centres of the electron density peaks, we would have the entire structure.

The unit cell is described as being the smallest regular repeat unit in a crystalline lattice. These cells are defined by three unit lengths (a, b, c) along the crystallographic axe,s and the three interaxial angles ( , ,  ).

E: this tube is the X-ray source. Inside it, there is a 40,000 volt difference between a tungsten filament and a copper target.

What radiation does the target metal emit? A spectrum (i.e. many wavelengths) with two sharp peaks.

A cathode filament is heated so that it boils off electrons. A large voltage ( kV) is maintained between the filament and the target (a metal such as Mo, Cu, Co, Fe or Cr). The electrons are accelerated and hit the target metal.

H: scintillation counter which measures the intensity of the diffracted X-ray beams. It is connected to a goniometer which measures the 2-theta angles at which diffracted beams are detected.

G: the sample chamber holds the specimen. Samples are ground to a fine powder before mounting them in the chamber. X-rays enter from the left, are diffracted by the powder, and leave the chamber to the right.

A graphite monochromator is used to let only one specific X-ray wavelength escape the X-ray source.

piezoelectricity: production of electrical polarization in a material by the application of mechanical stress - phonographs - microphones - quartz watches

When a chemical analysis will not tell you what mineral this is.... This Anglo-Saxon brooch contains an inlay of CaCO 3, but is it calcite or aragonite (2 common polymorphs)?

When detecting twinning matters ! Piezoelectric crystals may not display that property if they are twinned. Twinning can show up in - external forms - re-entrant angles (non-convex morphology)

Indices of diffracted X-ray peaks are usually written without parentheses. 111, 222 and 333 correspond to the 1 st, 2 nd and 3 rd order reflections of the (111) planes. 222 is produced when the X-rays of successive planes have a path difference of 2*wavelength (two “lambdas”).

Bragg’s law predicts at which angles the peaks will be diffracted, but not their intensities. Diffraction intensities are influenced by the atomic number (Z) of the atoms in the structure, by the shape and size of the specimen, and by other factors related to the machine. We use the peak intensities to determine where the atoms are in the unit cell.

Structures with lighter elements can be studied using neutron diffraction. Neutrons are scattered by the nucleus, and their scattering varies less from element to element. whereas X-rays are scattered by the electron cloud, and light elements barely re- emit them.

Mineral structure can be destroyed by radiation damage.