EASA Mineralogy Homepage

Week 9: March 22

USE OF X-RAYS TO STUDY MINERALS

X-Ray Diffraction (XRD) - Used to determine the distances between atomic planes in a crystal ("d-spacings") and hence help identify a mineral

X-rays striking the surface of a crystal at an angle are "reflected" off the upper (let's call this ray 1) and next lower layer of atoms in a crystal (let's call this ray 2)
Because ray 2 must travel to the lower layer then out the upper surface of the crystal, it covers a slightly longer distance than ray 1.
If the difference in distance in the paths of ray 1 and 2 is equal to a whole number of wavelengths of the x-ray being reflected (l, 2l, 3l, etc.) then one will get constructive interference between the two rays as they are reflected off the crystal. Otherwise, there is partial or complete destructive interference.
The path difference between rays 1 and 2 is a function of the angle of incidence and the spacing between the atomic laters (the d-spacing).
The Bragg equation gives the condition for a strong reflection of x-rays off the crystal surface: nl = 2d(sin q), where n is an integer, l is the wavelength of the x-ray, d is the atomic spacing, and q is the angle of incidence of the x-rays on the crystal surface.
Because a known x-ray source is used, l is known, q can be measured precisely, and hence the only unknown is d, which can be solved for.
In the so-called powder method of XRD analysis, the unknown mineral is powdered and hence there are several crystal fragments in various orientations. One therefore gets reflections from a variety of d-spacings in the mineral as q is varied and these d-spacings together are characteristic of a mineral.

XRF and EPMA - x-ray fluoresence (XRF) and electron probe microanalysis (EPMA) exploit the same phenomenon to determine what type of elements and how much of that element are present in a mineral.

Recall that one of the causes of color was electrons jumping between orbitals of the 3d subshell (a subshell of the M electron shell) of transition elements, which led to the selective absortion and emission of visible light. Absoption and emission of light occurred because the light had energies equivalent to the energy difference between the 3d orbitals.
It turns out that the energy difference between the innermost electron shells of atoms (the K, L, and M shells) is in the range of energies for x-rays (at the higher energy end of the electromagnetic spectrum)
In the XRF and EPMA techniques, electrons from the innermost shell (the K shell) are knocked out by incident x-rays and electrons, respectively. Electrons from the L and M shells then drop down into the vacancy in the K shell and in doing so, emit x-rays.
The wavelengths of the emitted x-rays are characteristic of the particular element being excited, and the intensity of the emitted x-rays is proportional to the concentration of the particular element in the mineral.
The XRF technique is usually used to analyze whole rock samples and the EPMA technique is used to analyze individual minerals. The EPMA technique has the advantage that the electrons used to bombard or excite the sample can be focused on a very small area (down to a circle a micron or so in diameter) and therefore one can analyze small areas in individual minerals, which is useful for detecting zoning in a single mineral, for example.