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X-RAY DIFFRACTOMETER: X-rays is a form of electromagnetic radiation. X-rays have a wavelength in the range of 10 to 0.01 nanometers, corresponding to frequencies in

the range 30 petahertz to 30 exahertz (3 1016 Hz to 3 1019 Hz) and energies in the range

120 eV to 120 keV. X-rays have shorter wavelengths than ultraviolet light but longer

wavelengths than gamma rays.

a method of determining the arrangement of atoms within a crystal, in which a beam of X-ray

strikes a crystal and diffracts into many specific directions.

this method determined the size of atoms, the lengths and types of chemical bonds, and the

atomic-scale differences among various materials, especially minerals and alloys

A crystal consists of a periodic arrangement of the unit cell into a lattice. The unit cell

can contain a single atom or atoms in a fixed arrangement.

Crystals consist of planes of atoms that are spaced a distance d apart, but can be resolved

into many atomic planes, each with a different d-spacing.

a,b and c (length) and a, b and g angles between a,b and c are lattice constants orparameters which can be determined by XRD.

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Why XRD?

Measure the average spacings between layers or rows of atoms

Determine the orientation of a single crystal or grain

Find the crystal structure of an unknown material

Measure the size, shape and internal stress of small crystalline regions

Specimen Preparation:Double sided tape Glass slide Powders: 0.1mm < particle size

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Braggs law is a simplistic model to understand

what conditions are required for diffraction.

For parallel planes of atoms, with a space dhkl between the planes, constructiveinterference only occurs when Braggs law is satisfied.

In our diffractometers, the X-ray wavelength is fixed.

Consequently, a family of planes produces a diffraction peak only at a specific angle .

Additionally, the plane normal must be parallel to the diffraction vector Plane normal: the direction perpendicular to a plane of atoms

Diffraction vector: the vector that bisects the angle between the incident and diffracted beam

The space between diffracting planes of atoms determines peak positions.

The peak intensity is determined by what atoms are in the diffracting plane.

sin2hkl

d dhkl

dhkl

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Our powder diffractometers typically use the

Bragg-Brentano geometry.

The incident angle, , is defined between the X-ray source and the sample.

The diffracted angle, 2 , is defined between the incident beam and thedetector angle.

The incident angle is always of the detector angle 2 .

In a :2 instrument (e.g. Rigaku RU300), the tube is fixed, the samplerotates at /min and the detector rotates at 2 /min.

In a : instrument (e.g. PANalytical XPert Pro), the sample is fixed and the

tube rotates at a rate - /min and the detector rotates at a rate of /min.

X-ray

tube

Detector

The peak position as 2q depends on instrumental characteristics such as wavelength.

The peak position as dhkl is an intrinsic, instrument-independent, material

property. Braggs Law is used to convert observed 2q positions to dhkl.

The absolute intensity, i.e. the number of X rays observed in a given peak, can vary due

to instrumental and experimental parameters.

The relative intensities of the diffraction peaks should be instrument independent.

To calculate relative intensity, divide the absolute intensity of every peak

by the absolute intensity of the most intense peak, and then convert to a

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percentage. The most intense peak of a phase is therefore always called

the 100% peak.

Peak areas are much more reliable than peak heights as a measure of intensity.

Application of XRD:

Phase Composition of a Sample Quantitative Phase Analysis: determine the relative amounts of phases in a

mixture by referencing the relative peak intensities

Unit cell lattice parameters and Bravais lattice symmetry

Index peak positions

Lattice parameters can vary as a function of, and therefore give you information

about, alloying, doping, solid solutions, strains, etc.

Residual Strain (macrostrain)

Crystal Structure

By Rietveld refinement of the entire diffraction pattern

Epitaxy/Texture/Orientation Crystallite Size and Microstrain

Indicated by peak broadening

Other defects (stacking faults, etc.) can be measured by analysis of peak shapes

and peak width

We have in-situ capabilities, too (evaluate all properties above as a function of time,

temperature, and gas environment).

Typical applications for XRD include analysis of coal ash, exploration drill cores, mill

circuit head, tail, rougher, and concentrate samplings, power plant corrosion deposits,

boiler tube scale, clay minerals, waste streams, mineral products, crystalline phases in

fused silica, contaminants in tungsten carbide, swelling minerals in soils, and industrial

by-products.

Identification of bulk mineralogy (Silicates, Carbonates, Sulfates, Oxides and etc). Identification of clay minerals. Semi-quantitative estimation of clays mineral Measurement of Illite crystallite in order to estimate thermal maturity Indirect assessment of level of organic matter maturation by using Illaite crystality data Determination of Sedimentary environments by using identification and Semi-

quantitative estimation information and data. Temperature and time dependent processes determine the conversion of organic matter to

oil and gas and the extent of most digenetic mineral reactions. Thermal history andmaturity reconstructions are, therefore, a key factor for the exploration strategy. Such

simulations become meaningful for exploration purposes if the complex interaction of allinvolved factors is analyzed.

Subsidence and burial history of single wells or basins Down hole mineral and lithotype logs which allow improved calibration and

interpretation of geophysical wireline logs; cross-well correlation; improved source, seal

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and reservoir characterization; in-situheavy mineral provenance studies which preservestextural context and enhances interpretation.

The resulting high resolution digital images allow classification of cuttings and cores intoquantitative lithotypes. This classification is based on mineralogy and micro-texture.

Suspected cavings can be digitally removed and the data renormalized caving-free.

In-situ XRD allows the laboratory-scale examination of mineral processing reactions

under operating conditions, which is useful in determining reaction mechanisms and

kinetics