3.5.4. Analyzing Crystals

Space constraints also result in the spectrometers having mechanical limits in Bragg angle range. In the Cameca MBX and SX-50 microprobes, 2q ranges from 25° to 112°, and in the JEOL 733 microprobe, from 25° to 130°. Thus, crystals with different d-spacings are necessary to cover the entire range of wavelengths of interest. The most commonly used crystals are:

• Lithium fluoride 200 (LIF), 2d = 4.028 Å

• Potassium acid pthalate 1011 (KAP), 2d = 26.6 Å

• Ammonium dihydrogen phosphate 011 (ADP), 2d = 10.648 Å

• Rubidium acid pthalate (RAP), 2d = 26.1 Å

• Pentaerythritol 002 (PET), 2d = 8.742 Å

• Thallium acid pthalate 1011 (TAP), 2d = 25.75 Å, and

• Lead sterate or Lead octodecamoate (ODPB), 2d = 100 Å.

LIF is an ionic solid, PET, a KAP, RAP and TAP are organic crystals, and ODPB is a pseudo-crystal, in which Pb atoms are interlayered with a fatty-acid salt to produce regularly spaced planes equivalent to interplanar crystal spacing; it is periodic in only one direction. The approximate range of analyzable elements for Cameca MBX microprobes are:

 

For example, Fe-Ka with a wavelength of 1.937 Å, is located at 2q of 57.5° on LIF, 25.6° on PET, and 8.6° on TAP. Fe-Ka radiation is at or outside the mechanical limits of the MBX spectrometers (2q from 25^o to 112^o) for PET and TAP. The table below shows the crystals and sinq values for most geologically important elements.

SINQ POSITIONS

The efficiency of an X-ray spectrometer, in part, depends on the crystal design and crystals are bent and/or ground to improve their efficiency. This can be done in two ways (Figure 3.5.4a):

• Johann optics, where the dispersing crystal is bent to a radius equal to the diameter of the Rowland circle, R. This results in some broadening and asymmetry of the focusing 'point'.
• Johannsen optics, where the crystal is also ground to a radius of R/2, resulting in focusing over the entire range of angles.

Unfortunately, it is not possible to grind all types of crystals, so the use of Johann optics is more common.

Figure 3.5.4a. The essential geometry of fully focusing Johannson (left) and semi-focusing Johann (right) X-ray spectrometer optics. These diagrams are not drawn to scale and exaggerate the loss of resolution in a semi-focusing spectrometer. The effect is much less pronounced than they suggest, and semi-focusing spectrometers are commonly used in microprobes (after Williams 1987).

A number of characteristics are required for a good spectrometer crystal. Some are more obvious than others:

• A crystal must be chemically stable. Although NaCl has useful 2d-spacing, it dissolves in humid air.
• A crystal should not be too perfect. If the peaks produced are too sharp, the peak position is difficult for the spectrometer drives to reproduce.
• A crystal should have good dispersion efficiency, i.e., the ability to separate adjacent spectral lines. Dispersion efficiency can be expressed as:

Note that higher order reflections are better dispersed and that the 2d-spacing of the crystal is an important factor. Where high resolution is desired, it is best to avoid low q and wide 2d-spacings even at the loss of intensity. Such conditions pertain when analyzing trace amounts of V in Ti-bearing materials and the analysis of rare earth elements.

• A crystal should have low X-ray absorption. The analyzing crystal is constantly bombarded with X-rays. While much radiation is diffracted, some is absorbed and re-emitted as secondary fluorescence radiation, which may reach the detector.
• A crystal should have a high reflection efficiency because correct functioning requires a crystal to diffract X-rays from the sample. The reflection efficiency depends on the number of electrons in the orbits of the atoms of the crystal, the angle of diffraction and the wavelength of the X-rays.
• Ideally, a crystal should not be sensitive to temperature fluctuations, although this is not always possible. The magnitude of the effect of thermal expansion is most pronounced at higher diffraction angles (Figure 3.5.4b). The PET crystal is particularly sensitive; at 120° the 2q value will shift by 0.025° for each 1°C. Most microprobe laboratories are maintained at a constant temperature to avoid problems with temperature-sensitive crystals.

Figure 3.5.4b. Curves of temperature coefficient of linear expansion for some common crystals (after Jenkins & de Vries, 1967).