X-RAY DIFFRACTION ANALYSIS X-Rays and Their Generation

X-ray diffraction is the most widely used method for identification of fine-grained soil minerals and the study of their crystal structure. X-rays are one of sev-eral types of waves in the electromagnetic spectrum (Fig. 3.2). X-rays have wavelengths in the range of 0.01 to 100 A˚ . When high-speed electrons impinge on a target material, one of two phenomena may occur:

1. The high-speed electron strikes and displaces an electron from an inner shell of one of the atoms of the target material. An electron from one of the outer shells then falls into the vacancy to lower the energy state of the atom. An X-ray photon of wavelength and intensity characteristic

X-RAY DIFFRACTION ANALYSIS 71

Figure 3.35 Composite relationship for X-ray intensity as a function of wavelength.

Figure 3.34 X-ray generation by deceleration of electrons in an electric field.

Figure 3.33 X-ray generation by electron displacement. Let-ters designate shells in which electron transfer takes place.

of the target atom and of the particular electronic positions is emitted. Because electronic transfers may take place in several shells and each has a characteristic frequency, the result is a relation-ship between radiation intensity and wavelength as shown in Fig. 3.33.

2. The high-speed electron does not strike an elec-tron in the target material but slows down in the intense electric fields near atomic nuclei. The de-crease in energy is converted to heat and to X-ray photons. X-X-rays produced in this way are independent of the nature of the bombarded at-oms and appear as a band of continuously vary-ing wavelength as shown in Fig. 3.34.

The resulting output of X-rays from these two ef-fects acting together is shown in Fig. 3.35. X-rays are generated using a tube in which electrons stream from a filament to a target material across a voltage drop of 20 to 50 kV. Curved crystal monochrometers can be used to give X-rays of a single wavelength. Alterna-tively, certain materials are able to absorb X-rays of different wavelengths, so it is possible to filter the out-put of an X-ray tube to give rays of only one

wave-length. The wavelengths of monochromatic radiation (usually K_, Fig. 3.33) produced from commonly used target materials range from 0.71 A˚ for molybdenum to 2.29 A˚ for chromium. Copper radiation, which is most frequently used for mineral identification, has a wave-length of 1.54 A˚ .

Diffraction of X-rays

Because wavelengths of about 1 A˚ are of the same order as the spacing of atomic planes in crystalline materials, X-rays are useful for analysis of crystal structures. When X-rays strike a crystal, they penetrate to a depth of several million layers before being ab-sorbed. At each atomic plane a minute portion of the beam is absorbed by individual atoms that then oscil-late as dipoles and radiate waves in all directions. Ra-diated waves in certain directions will be in phase and can be interpreted in simplistic fashion as a wave re-sulting from a reflection of the incident beam. In-phase radiations emerge as a coherent beam that can be de-tected on film or by a radiation counting device. The orientation of parallel atomic planes, relative to the di-rection of the incident beam, at which radiations are in phase depends on the wave length of the X-rays and the spacing between atomic planes.

Figure 3.36 shows a parallel beam of X-rays of wavelengthstriking a crystal at an angleto parallel atomic planes spaced at distance d. If the reflected wave from C is to reinforce the wave reflected from A, then the path length difference between the two waves must be an integral number of wave lengths n. From Fig. 3.36, this difference is distance BC_⫹ CD.

Thus,

BC_⫹ CD _⫽ n

Figure 3.36 Geometrical conditions for X-ray diffraction according to Bragg’s law.

From symmetry, BC _⫽ CD, and by trigonometry, CD _⫽ d sin . Thus the necessary condition is given by

n_⫽ 2d sin (3.3)

This is Bragg’s law. It forms the basis for identification of crystals using X-ray diffraction. Since no two min-erals have the same spacings of interatomic planes in three dimensions, the angles at which diffractions oc-cur (and the atomic spacings calculated from them) can be used for identification. X-ray diffraction is partic-ularly well suited for identification of clay minerals because the (001) spacing is characteristic for each clay mineral group. The basal planes generally give the most intense reflections of any planes in the crystals because of the close packing of atoms in these planes.

The common nonclay minerals occurring in soils are also detectable by X-ray diffraction.

Detection of Diffracted X-rays

Because the small size of most soil particles prevents the study of single crystals, use is made of the powder method and of oriented aggregates of particles. In the powder method, a small sample containing particles at all possible orientations is placed in a collimated beam of parallel X-rays, and diffracted beams of various in-tensities are scanned by a Geiger, proportional, or scin-tillation tube and recorded automatically to produce a chart showing the intensity of diffracted beam as a function of angle 2. As an example, the diffraction pattern for quartz is shown in Fig. 3.37. The powder method works because the very large number of par-ticles in a sample ensures that some will always be properly oriented to produce a reflection.

All prominent atomic planes in a crystal will pro-duce a reflection if properly positioned with respect to

the X-ray beam. Thus, each mineral will produce a characteristic set of reflections at values of  corre-sponding to the interatomic spacings between the prominent planes. The intensities of the different re-flections vary according to the density of atomic pack-ing and other factors.

When the oriented aggregate method is used, platy clay particles are precipitated onto a glass slide, usu-ally by drying from a deflocculated suspension or sep-arated from a suspension on a porous ceramic plate.

With most particles oriented parallel to the slide, the (001) reflections are intensified, whereas reflections from (hk0) planes are minimized.

In the Bragg equation, n may be any whole number.

The reflection corresponding to n _⫽ 1 is termed the first-order reflection. If the first-order reflection for a mineral gives d_{(001) ⫽} 10 A˚ , then for n _⫽ 2 there can be a reflection at 5 A˚ , for n _⫽ 3 there can be a reflec-tion at 3.33 A˚ , and so on. It is common to refer to these as higher-order reflections due to the (002) plane, the (003) plane, and so on, even though atomic planes do not exist at these spacings. They are, in reality, val-ues of d / n_⫽/ (2 sin ) for integer values of n _⬎ 1.

Analysis of X-ray Patterns

A complete X-ray diffraction pattern consists of a se-ries of reflections of different intensities at different values of 2. Each reflection must be assigned to some component of the sample. The first step in the analysis is to determine all values of d / n for the particular type of radiation (which determines) using Eq. (3.3). The test pattern may be compared directly with patterns for known materials. The American Society for Testing and Materials maintains a file of patterns for many materials indexed on the basis of the strongest lines in the pattern. X-ray diffraction data for the clay minerals and other common soil minerals are given in Grim

X-RAY DIFFRACTION ANALYSIS 73

Figure 3.37 X-ray diffractometer chart for quartz. Peaks occur at specific 2angles, which can be converted to d spacings by Bragg’s law. Numbers in parentheses are the Miller indices for the crystal planes responsible for the indicated peak.

(1968), Carroll (1970), Brindley and Brown (1980), Whittig and Allardice (1986), and Moore and Reyn-olds (1997). The most intense reflections for minerals commonly found in powder samples of soils are listed in Table 3.7. Basal spacings for different clay minerals associated with different pretreatments are listed in Ta-ble 3.8 and shown pictorially in Fig. 3.38.

Criteria for Clay Minerals

The different clay minerals are characterized by first-order basal reflections at 7, 10, or 14 A˚ . Positive iden-tification of specific mineral groups ordinarily requires specific pretreatments. Separation of size fractions re-quires thorough dispersion of the sample. As cement-ing compounds may both inhibit dispersion and adversely affect the quality of the diffraction patterns, their removal may be necessary. To ensure uniform ex-pansion due to hydration for all crystals of a particular mineral, the clay should be made homoionic. Magne-sium and potasMagne-sium are most frequently used for sat-uration of the exchange sites. Detailed procedures for pretreatments useful in X-ray diffraction analysis of clay soils are given by Whittig and Allardice (1986) and Moore and Reynolds (1997).

Kaolinite Minerals The kaolinite basal spacing of about 7.2 A˚ is insensitive to drying or moderate heat-ing. Heating to 500_C destroys kaolinite minerals, but not the other clay minerals. Hydrated halloysite has a basal spacing of 10 A˚ , which collapses irreversibly to 7 A˚ on drying at 110_C. Organic chemical treatments are sometimes used to distinguish dehydrated halloy-site from kaolinite (MacEwan and Wilson, 1980). The electron microscope can also be used to distinguish dehydrated halloysite with its tubular morphology from kaolinite.

Hydrous Mica (Illite) Minerals Illite is character-ized by d₍₀₀₁₎of about 10 A˚ , which remains fixed both in the presence of polar liquids and after drying.

Smectite (Montmorillonite) Minerals The expan-sive character of this group of minerals provides the basis for their positive identification. When air dried, these minerals may have basal spacings of 12 to 15 A˚ . After treatment with ethylene glycol or glycerol, the smectites expand to a d₍₀₀₁₎value of 17 to 18 A˚ . When oven dried, d₍₀₀₁₎drops to about 10 A˚ as a result of the removal of interlayer water.

Vermiculite Although an expansive mineral, the greater interlayer ordering in vermiculite results in less variability in basal spacing than occurs in the smectite minerals. When Mg saturated, the hydration states of vermiculite yield a discrete set of basal spacings, re-sulting from a changing but ordered arrangement of Mg cations and water in the interlayer complex. When fully saturated, the d spacing is 14.8 A˚ , which reduces

to 11.6 A˚ when heated at 70_C. All interlayer water can be expelled at 500_C, but rehydration is rapid on cooling. Permanent dehydration and collapse to 9.02 A˚ can be achieved by heating to 700_C.

Chlorite Minerals The basal spacing of chlorite minerals is fixed at 14 A˚ because of the strong ordering of the interlayer complex. Chlorites often have a clear sequence of four or five basal reflections. The third-order reflection at 4.7 A˚ is often strong. Iron-rich chlo-rites have a weak first-order reflection but strong second-order reflections and, thus, may be confused with kaolinite. The facts that chlorite is destroyed when treated with 1 N HCl at 60_C while kaolinite is unaffected, and that kaolinite is destroyed but chlorite may not be affected on heating to 600_C, are useful for distinguishing the two clay mineral types.

Criteria for Nonclay Minerals

Strong X-ray diffraction reflections for some of the nonclay minerals are listed in Table 3.7. These include feldspar, quartz, and carbonates. More detailed listings of X-ray powder data for specific iron oxide minerals, silica minerals, feldspars, carbonates, and calcium sul-fate minerals are given in Brindley and Brown (1980) as well as in standard reference files.

Quantitative Analysis by X-ray Diffraction

Quantitative determination of the amounts of different minerals in a soil on the basis of simple comparison of diffraction peak heights or areas are uncertain because of differences in mass absorption coefficients of different minerals, particle orientations, sample weights, surface texture of the sample, mineral crys-tallinity, hydration, and other factors. Estimates based on X-ray data alone are usually at best semiquantita-tive; however, in some cases techniques that account for differences in mass absorption characteristics and utilize comparisons with known mixtures or internal standards may give good results. Soils containing only two or three well-crystallized mineral components are more easily analyzed than those with multimineral compositions and mixed layering. For more detailed treatment of X-ray diffraction theory, identification cri-teria, and techniques, particularly as related to the study of clays, see Klug and Alexander (1974), Carroll (1970), Brindley and Brown (1980), Whittig and Al-lardice (1986), and especially Moore and Reynolds (1997).

3.23 OTHER METHODS FOR COMPOSITIONAL