**1.2. X-ray diffraction**

X-ray diffraction (XRD) is another quantitative spectroscopic technique which reveals information about the crystal structure, chemical composition, and physical properties of materials and thin films. These techniques are based on observing the scattered intensity of an X-ray beam hitting a sample as a function of incident and scattered angle, polarization, and wavelength or energy. Similar to the EDS and WDS techniques discussed above X-ray diffraction is dependent on Bragg equation, which describes the condition for diffraction to occur in terms of the wavelength of the x-radiation (λ), the interplanar ("d") spacings of the crystal, and the angle of incidence of the radiation with respect to the crystal planes (θ). As the spacing between atoms is on the same order as X-ray wavelengths crystals can diffract the radiation when the diffracted beams are in-phase.

312 Advanced Aspects of Spectroscopy

qualitative and quantitatively.

**1.2. X-ray diffraction** 

Those which satisfy Bragg's Law; *n dSin*

relationship: E = hν = hc/λ, where ν is the frequency, h is Planck's constant (6.62 x 10-34 joule-second), c is the speed of light (2.998 x 108m/sec), and λ is the wavelength of the radiation (in m). Based on this relationship, two distinct types of x-ray detector systems are used. These two types of detector systems are called Energy-Dispersive x-ray

EDS spectrometer are most frequently attached to electron column instruments such as SEM or (EPMA). As the name implies is a method of x-ray spectroscopy by which x-rays emitted from a sample are sorted out and analyzed based on the difference in their energy level. An EDS system consists of a source of high-radiation; a sample, a solid-state detector (usually from lithium-drifted silicon (Si(Li)); and a signal processing electronics. When the sample atoms are ionized by a high-energy radiation, they emit characteristic x-rays. X-rays that enter the Si(Li) detector are converted into signals (charge pulses) that can be processed by the electronics into an x-ray energy histogram. This x-ray spectrum consists of a series of peaks representative of the type and relative amount of each element in the sample. The number of counts in each peak can be further converted to elemental weight concentration either by comparison standards or standardless calculations. In general, three principal types of data can be generated using an EDS detector: (i) x-ray dot maps or images of the sample using elemental distribution as a contrast mechanism, (ii) line scan data or elemental concentration variation across a given region, and (iii) overall chemical composition, both

As the name implies, WDS is a detection system by which x-rays emitted from the sample are sorted out and analyzed based on differing wavelength (λ) in the WDS, or crystal spectrometry. As in EDS or imaging mode, the beam rasters the sample generating x-rays of which a small portion enters the spectrometer. As the fluorescent x-rays strike the analyzing crystal, they will either past through the crystal, be absorbed, be scattered, or be diffracted.

> .

(where n = an integer, *d* = the interplanar spacing of the crystal, θ = the angle of incidence, and λ = x-ray wavelength) will be diffracted and detected by a proportional counter. The signal from this detector is amplified, converted to standard pulse size in the single channel analyzer and counted with a scalar or displayed as rate vs time on rate meter. By varying the positioning crystal one changes the wavelength that will satisfy Bragg's Law. Therefore one can sequentially analyze different elements. By automating crystal movements one can dramatically speed up the analysis time. Typically the WDS analysis is used to gain the same type of information that the EDS is used for, qualitative and quantitative and

X-ray diffraction (XRD) is another quantitative spectroscopic technique which reveals information about the crystal structure, chemical composition, and physical properties of materials and thin films. These techniques are based on observing the scattered intensity of an X-ray beam hitting a sample as a function of incident and scattered angle, polarization,

2

quantitative information, line scan and dot maps for elemental distribution.

Spectrometry (EDS) and Wavelength-Dispersive x-ray Spectrometry (WDS).

When the incident beam satisfies the Bragg condition, a set of planes forms a cone of diffracted radiation at an angle q to the sample. Since the cone of X-rays intersects the flat photographic filmstrip in two arcs equally spaced from the direct X-ray beam, two curved lines will be recorded on the photographic film. The distance of the lines from the center can be used to determine the angle q, which can then be used to determine the interplanar "d" spacing. X-ray powder diffractometers record all reflections using a scintillation detector (in counts per second of X-rays). The pattern of diffracted X-rays is unique for a particular structure type and can be used as a "fingerprint" to identify the structure type. Different minerals have different structure types, thus X-ray diffraction is an ideal tool for identifying different minerals.
