Brief introduction to X-ray diffraction theory

Powder X-ray diffraction is a rapid, non-destructive analytical technique commonly used in mineralogy to identify and quantify various phases of crystalline materials. X-ray diffraction is based on constructive interference of monochromatic X-rays and a crystalline sample. These X-rays are generated inside a cathode ray tube, filtered to produce monochromatic radiation, collimated to concentrate and are directed toward the sample. When electromagnetic X-rays encounter any obstacle, they are scattered (elastic) by the electrons of the object. The electrons oscillate at the same frequency as that of the incoming X-rays and hence generate secondary radiations of the same frequency and wavelength. These waves are superimposed on each other and when constructive interference occurs, it gives rise to a diffraction pattern.The diffracted X-ray are detected, processed and counted. The wavelength of X-rays is in the range of inter-atomic distances or unit cell sizes, and therefore diffraction can be produced by the elastic interaction of X-rays with matter having some degree of ordering. For constructive interference to occur, Bragg’s law must be satisfied.

Bragg’s law

The general relationship between the wavelength of the incident X-rays, angle of incidence and spacing between the crystal lattice planes of atoms is known as Bragg’s Law, expressed as
n λ =2dsinΘ
where n (an integer) is the “order” of reflection, λ is the wavelength of the incident X-rays, d is the interplanar spacing of the crystal and Θ is the angle of incidence.


To illustrate this feature, consider a crystal with crystal lattice planar distances d (above). Where the travel path length difference between the ray paths ABC and A’B’C’ is an integermultiple of the wavelength, constructive interference will occur for a combination of that specific wavelength, crystal lattice planar spacing and angle of incidence (Θ).

XRD instrumentation

X-ray diffractometer consists of three basic elements: an X-ray tube, a sample holder, and an X-ray detector. X-rays are generated in a cathode ray tube by heating a filament, generally made of tungsten, to produce high energy electrons. These electrons are accelerated toward the target anode by applying a voltage. The moment they hit the target material, the electrons are decelerated. When electrons have sufficient energy to dislodge inner shell electrons of the target material, characteristic X-ray spectra are produced. These spectra consist of several components, the most common being Kα and Kβ. Kα consists, in part, of Kα1 and Kα2. Kα1 has a slightly shorter wavelength and twice the intensity as Kα2. The specific wavelengths are characteristic of the target material (Cu, Fe, Mo, Cr, etc.). These X-rays are collimated and directed onto the sample. As the sample and detector are rotated, the intensity of the reflected X-rays is recorded. When the geometry of the incident X-rays impinging the sample satisfies the Bragg equation, constructive interference occurs and a diffraction peak is generated. A detector records and processes this X-ray signal and converts the signal to a count rate. The geometry of an X-ray diffractometer is such that the sample rotates in the path of the collimated X-ray beam at an angle θ while the X-ray detector is mounted on an arm to collect the diffracted X-rays and rotates at an angle of 2θ. The instrument used to maintain the angle and rotate the sample is termed a goniometer. For typical powder patterns, data is collected at 2θ from ~5° to 80°.

Applications of powder XRD in mineralogy

X-ray powder diffraction is mostly used for the identification and quantification of unknown crystalline material.

  1. Identification of different phases of silica: Silica exists as quartz, crystoballite or amorphous silica which can easily be distinguished from the unique diffraction pattern of each of these phases in a mixture. 
  2. Identification of different phases in iron ore – determination of FeO content from magnetite: FeO content in iron ore sinter is an important parameter for blast furnace operations and can easily be determined using powder XRD from the magnetite content.


  1. Determination of purity of Gypsum:The different phases present in a gypsum sample can be identified and quantified using powder XRD. An anhydrite sample can also be easily distinguished form a pure gypsum sample using the powder diffraction pattern.

  1. Analysis of cement and clinker phases: The major clinker phases namely alite & belite (silicate phases), aluminate and ferrite (aluminate phases) can be identified and quantified using powder XRD. Accurate quantification of the major phases in clinker is important for the manufacture of cement as the quantity of gypsum to be added is determined from the quantity of these phases (mainly aluminate phases). The different phases present play a significant role in the hydration process, with the major contribution from the silicate phases forming the main hydration product, calcium silicate hydrate gel.

Commodity Phases Concentration (%)
Clinker Alite 59.86
Belite 24.14
Aluminate 8.20
Ferrite 7.81
Cement Alite 33.68
Belite 30.88
Aluminate 23.97
Periclase 0.39
Gypsum 11.08

Different phases in a clinker sample

Estimation of available alumina and reactive silica in Bauxite: The available alumina and reactive silica contents, the main parameters for grade control of bauxite, are related to gibbsite/boehmite and kaolinite respectively. Powder XRD is used to determine the concentration of different alumina phases and aluminosilicate phases present in a bauxite sample and subsequently available alumina and reactive silica contents are calculated.

% Gibbsite = 1.5295 (% Av Al2O3)

% Kaolinite = 2.1478 (% Rx SiO2)


XRD is the key tool in mineral exploration. In mineralogy, powder XRD data gives qualitative and quantitative information about the different mineral phases present in a crystalline geological sample. Each mineral type is defined by a characteristic crystal structure, which will give a unique x-ray diffraction pattern, allowing rapid identification of minerals present within a rock or soil sample.XRD can be used as a stand-alone method, or used in conjunction with other tools to provide a comprehensive, integrated approach to petrologic evaluation.