X-ray diffraction (XRD)

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X-ray diffraction (XRD) is a non-destructive technique that operates on the nanometre scale based on the elastic scattering of X-rays from structures that have long range order (i.e. an organised structure of some sort, e.g. periodicity, such as in a crystal or polymer).

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X-ray diffraction (XRD):

X-ray diffraction (XRD) Dr. Prafulla Kumar Sahu M.Pharm ., Ph.D.

Introduction/ Principle :

Introduction/ Principle X-ray diffraction (XRD) is a non-destructive technique that operates on the nanometre scale based on the elastic scattering of X-rays from structures that have long range order (i.e. an organised structure of some sort, e.g. periodicity, such as in a crystal or polymer ). It can be used to identify and characterise a diverse range of materials, such as metals, minerals, polymers , catalysts , plastics, pharmaceuticals, proteins, thin-film coatings, ceramics and semiconductors .

Crystalline materials are characterized by the orderly periodic arrangements of atoms.:

Crystalline materials are characterized by the orderly periodic arrangements of atoms. The unit cell is the basic repeating unit that defines a crystal . Parallel planes of atoms intersecting the unit cell are used to define directions and distances in the crystal. These crystallographic planes are identified by Miller indices . The (200) planes of atoms in NaCl The (220) planes of atoms in NaCl

The atoms in a crystal are a periodic array of coherent scatterers and thus can diffract light.:

The atoms in a crystal are a periodic array of coherent scatterers and thus can diffract light. Diffraction occurs when each object in a periodic array scatters radiation coherently, producing concerted constructive interference at specific angles. The electrons in an atom coherently scatter light. The electrons interact with the oscillating electric field of the light wave. Atoms in a crystal form a periodic array of coherent scatterers. The wavelength of X rays are similar to the distance between atoms. Diffraction from different planes of atoms produces a diffraction pattern, which contains information about the atomic arrangement within the crystal X Rays are also reflected, scattered incoherently, absorbed, refracted, and transmitted when they interact with matter.

X-Ray Powder Diffraction (XRPD) uses information about the position, intensity, width, and shape of diffraction peaks in a pattern from a polycrystalline sample.:

X-Ray Powder Diffraction (XRPD) uses information about the position, intensity, width, and shape of diffraction peaks in a pattern from a polycrystalline sample. The x-axis, 2theta, corresponds to the angular position of the detector that rotates around the sample.

Bragg’s law is a simplistic model to understand what conditions are required for diffraction. :

Bragg’s law is a simplistic model to understand what conditions are required for diffraction. For parallel planes of atoms, with a space d hkl between the planes, constructive interference only occurs when Bragg’s law is satisfied. In our diffractometers, the X-ray wavelength l is fixed. Consequently, a family of planes produces a diffraction peak only at a specific angle q . 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. q q d hkl d hkl

Our powder diffractometers typically use the Bragg-Brentano geometry.:

Our powder diffractometers typically use the Bragg-Brentano geometry. q w 2q X-ray tube Detector

Our powder diffractometers typically use the Bragg-Brentano geometry.:

Our powder diffractometers typically use the Bragg-Brentano geometry. The incident angle, w , is defined between the X-ray source and the sample. The diffracted angle, 2 q , is defined between the incident beam and the detector angle. The incident angle w is always ½ of the detector angle 2 q . In a q :2 q instrument (e.g. Rigaku RU300), the tube is fixed, the sample rotates at q ° /min and the detector rotates at 2 q ° /min. In a q : q instrument (e.g. PANalytical X’Pert Pro), the sample is fixed and the tube rotates at a rate - q ° /min and the detector rotates at a rate of q ° /min. q w 2q X-ray tube Detector

A single crystal specimen in a Bragg-Brentano diffractometer would produce only one family of peaks in the diffraction pattern.:

A single crystal specimen in a Bragg-Brentano diffractometer would produce only one family of peaks in the diffraction pattern. 2 q At 20.6 °2 q , Bragg’s law fulfilled for the (100) planes, producing a diffraction peak. The (110) planes would diffract at 29.3 °2 q ; however, they are not properly aligned to produce a diffraction peak (the perpendicular to those planes does not bisect the incident and diffracted beams). Only background is observed. The (200) planes are parallel to the (100) planes. Therefore, they also diffract for this crystal. Since d 200 is ½ d 100 , they appear at 42 °2 q .

A polycrystalline sample should contain thousands of crystallites. Therefore, all possible diffraction peaks should be observed.:

A polycrystalline sample should contain thousands of crystallites. Therefore, all possible diffraction peaks should be observed. 2 q 2 q 2 q For every set of planes, there will be a small percentage of crystallites that are properly oriented to diffract (the plane perpendicular bisects the incident and diffracted beams). Basic assumptions of powder diffraction are that for every set of planes there is an equal number of crystallites that will diffract and that there is a statistically relevant number of crystallites, not just one or two.

PowerPoint Presentation:

Powder Diffraction is more aptly named polycrystalline diffraction Samples can be powder, sintered pellets, coatings on substrates, engine blocks, If the crystallites are randomly oriented, and there are enough of them, then they will produce a continuous Debye cone. In a linear diffraction pattern, the detector scans through an arc that intersects each Debye cone at a single point; thus giving the appearance of a discrete diffraction peak.

Diffraction patterns are best reported using dhkl and relative intensity rather than 2q and absolute intensity.:

Diffraction patterns are best reported using d hkl and relative intensity rather than 2 q and absolute intensity. The peak position as 2 q depends on instrumental characteristics such as wavelength. The peak position as d hkl is an intrinsic, instrument-independent, material property. Bragg’s Law is used to convert observed 2 q positions to d hkl . 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 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.

Powder diffraction data consists of a record of photon intensity versus detector angle 2q.:

Powder diffraction data consists of a record of photon intensity versus detector angle 2 q . Diffraction data can be reduced to a list of peak positions and intensities Each d hkl corresponds to a family of atomic planes {hkl} individual planes cannot be resolved- this is a limitation of powder diffraction versus single crystal diffraction hkl d hkl (Å) Relative Intensity (%) {012} 3.4935 49.8 {104} 2.5583 85.8 {110} 2.3852 36.1 {006} 2.1701 1.9 {113} 2.0903 100.0 {202} 1.9680 1.4 Position [°2 q ] Intensity [cts] 25.2000 372.0000 25.2400 460.0000 25.2800 576.0000 25.3200 752.0000 25.3600 1088.0000 25.4000 1488.0000 25.4400 1892.0000 25.4800 2104.0000 25.5200 1720.0000 25.5600 1216.0000 25.6000 732.0000 25.6400 456.0000 25.6800 380.0000 25.7200 328.0000 Raw Data Reduced dI list

Types of XRD:

Types of XRD The two main types of XRD are: X-ray crystallography X-ray powder diffraction

X-ray crystallography:

X-ray crystallography X-ray crystallography, also known as single crystal diffraction, is a technique that is used to examine the whole structure of a crystal. The crystal is hit with X-rays and, in a typical experiment, the intensity of the X-rays diffracted from the sample is recorded as a function of angular movement of both the detector and the sample. The diffraction pattern of intensity versus angle can also be converted into its more useful form of probability distribution versus distance.

X-ray crystallography cont…:

X-ray crystallography cont… The diffraction pattern produced can be analysed to reveal crystal details such as the spacing in the crystal lattice, bond lengths and angles. It can be difficult to obtain a pure crystal but, if achieved, the data obtained with this method can be very informative. Many compounds can be subjected to X-ray crystallography, such as macromolecules, small inorganic materials, biological compounds such as proteins and even small pharmaceuticals.

X-ray powder diffraction:

X-ray powder diffraction When a single pure crystal cannot be obtained, X-ray powder diffraction can be used instead. It can still yield important information about the crystalline structure, such as crystal size, purity and texture, but the data set may not be as complete as X-ray crystallography. The sample under investigation is usually ground down to a fine microcrystalline powder first. Sometimes the sample must be rotated to obtain the optimal diffraction pattern.

Instrumentation:

Instrumentation The instrument used is called a diffractometer. Schematic diagram o f a x-ray diffractometer

Overview of the Diffractometer:

Overview of the Diffractometer

Essential Parts of the Diffractometer:

Essential Parts of the Diffractometer X-ray Tube: the source of X Rays Incident-beam optics: condition the X-ray beam before it hits the sample The goniometer: the platform that holds and moves the sample, optics, detector, and/or tube The sample & sample holder Receiving-side optics: condition the X-ray beam after it has encountered the sample Detector: count the number of X Rays scattered by the sample

Most of our powder diffractometers use the Bragg-Brentano parafocusing geometry.:

Most of our powder diffractometers use the Bragg-Brentano parafocusing geometry. A point detector and sample are moved so that the detector is always at 2 q and the sample surface is always at q to the incident X-ray beam. In the parafocusing arrangement, the incident- and diffracted-beam slits move on a circle that is centered on the sample. Divergent X rays from the source hit the sample at different points on its surface. During the diffraction process the X rays are refocused at the detector slit. This arrangement provides the best combination of intensity, peak shape, and angular resolution for the widest number of samples. F: the X-ray source DS: the incident-beam divergence-limiting slit SS: the Soller slit assembly S: the sample RS: the diffracted-beam receiving slit C: the monochromator crystal AS: the anti-scatter slit

Source:

Source The source is the sealed X-ray tube or a synchrotron (with much higher photon flux).

X-radiation for diffraction measurements is produced by a sealed tube or rotating anode.:

X-radiation for diffraction measurements is produced by a sealed tube or rotating anode. Sealed X-ray tubes tend to operate at 1.8 to 3 kW. Rotating anode X-ray tubes produce much more flux because they operate at 9 to 18 kW. A rotating anode spins the anode at 6000 rpm, helping to distribute heat over a larger area and therefore allowing the tube to be run at higher power without melting the target. Both sources generate X rays by striking the anode target wth an electron beam from a tungsten filament. The target must be water cooled. The target and filament must be contained in a vacuum.

The wavelength of X rays is determined by the anode of the X-ray source.:

The wavelength of X rays is determined by the anode of the X-ray source. Electrons from the filament strike the target anode, producing characteristic radiation via the photoelectric effect. The anode material determines the wavelengths of characteristic radiation. While we would prefer a monochromatic source, the X-ray beam actually consists of several characteristic wavelengths of X rays. K L M

Wavelengths for X-Radiation are Sometimes Updated:

Wavelengths for X-Radiation are Sometimes Updated Often quoted values from Cullity (1956) and Bearden, Rev. Mod. Phys. 39 (1967) are incorrect. Values from Bearden (1967) are reprinted in international Tables for X-Ray Crystallography and most XRD textbooks. Most recent values are from H ö lzer et al. Phys. Rev. A 56 (1997) Has your XRD analysis software been updated? Copper Anodes Bearden (1967) Holzer et al. (1997) Cobalt Anodes Bearden (1967) Holzer et al. (1997) Cu K a 1 1.54056Å 1.540598 Å Co K a 1 1.788965Å 1.789010 Å Cu K a 2 1.54439Å 1.544426 Å Co K a 2 1.792850Å 1.792900 Å Cu K b 1.39220Å 1.392250 Å Co K b 1.62079Å 1.620830 Å Molybdenum Anodes Chromium Anodes Mo K a 1 0.709300Å 0.709319 Å Cr K a 1 2.28970Å 2.289760 Å Mo K a 2 0.713590Å 0.713609 Å Cr K a 2 2.293606Å 2.293663 Å Mo K b 0.632288Å 0.632305 Å Cr K b 2.08487Å 2.084920 Å

The X-ray Shutter is the most important safety device on a diffractometer:

The X-ray Shutter is the most important safety device on a diffractometer X-rays exit the tube through X-ray transparent Be windows. X-Ray safety shutters contain the beam so that you may work in the diffractometer without being exposed to the X-rays. Being aware of the status of the shutters is the most important factor in working safely with X rays.

Discriminator:

Discriminator The discriminator is a crystal monochromator such as graphite. Soller slits after the monochromator keep divergence of the beam to a minimum.

The X-ray beam produced by the X-ray tube is divergent. Incident-beam optics are used to limit this divergence:

The X-ray beam produced by the X-ray tube is divergent. Incident-beam optics are used to limit this divergence X Rays from an X-ray tube are: divergent contain multiple characteristic wavelengths as well as Bremmsstrahlung radiation Neither of these conditions suit our ability to use X rays for analysis The divergence means that instead of a single incident angle q, the sample is actually illuminated by photons with a range of incident angles. The spectral contamination means that the sample does not diffract a single wavelength of radiation, but rather several wavelengths of radiation. Consequently, a single set of crystallographic planes will produce several diffraction peaks instead of one diffraction peak. Optics are used to: Limit divergence of the X-ray beam Refocus X rays into parallel paths Remove unwanted wavelengths

Divergence slits are used to limit the divergence of the incident X-ray beam.:

Divergence slits are used to limit the divergence of the incident X-ray beam. The slits block X-rays that have too great a divergence. The size of the divergence slit influences peak intensity and peak shapes. Narrow divergence slits: reduce the intensity of the X-ray beam reduce the length of the X-ray beam hitting the sample produce sharper peaks the instrumental resolution is improved so that closely spaced peaks can be resolved.

One by-product of the beam divergence is that the length of the beam illuminating the sample becomes smaller as the incident angle becomes larger. :

One by-product of the beam divergence is that the length of the beam illuminating the sample becomes smaller as the incident angle becomes larger. The length of the incident beam is determined by the divergence slit, goniometer radius, and incident angle. This should be considered when choosing a divergence slits size: if the divergence slit is too large, the beam may be significantly longer than your sample at low angles if the slit is too small, you may not get enough intensity from your sample at higher angles The width of the beam is constant: 12mm for the Rigaku RU300.

Other optics::

Other optics: limit divergence of the X-ray beam Divergence limiting slits Parallel plate collimators Soller slits refocus X rays into parallel paths “parallel-beam optics” parabolic mirrors and capillary lenses focusing mirrors and lenses remove unwanted wavelengths monochromators K b filters Parallel Plate Collimator & Soller Slits block divergent X-rays, but do not restrict beam size like a divergent slit Göbel Mirrors and capillary lenses collect a large portion of the divergent beam and refocus it into a nearly parallel beam

Monochromators remove unwanted wavelengths of radiation from the incident or diffracted X-ray beam.:

Monochromators remove unwanted wavelengths of radiation from the incident or diffracted X-ray beam. Diffraction from a crystal monochromator can be used to select one wavelength of radiation and provide energy discrimination. An incident-beam monochromator might be used to select only Ka1 radiation for the tube source. A diffracted-beam monochromator, such as on the Rigaku RU300, may be used to remove fluoresced photons, Kb, or W-contimination photons from reaching the detector. Without the RSM slit, the monochromator removes ~75% of unwanted wavelengths of radiation. When the RSM slit is used, over 99% of the unwanted wavelengths of radiation can be removed from the beam.

Detector:

Detector The position-sensitive detector registers the diffraction pattern of the sample by moving around the sample. The detector is usually a scintillation counter or more recently an array of X-ray detectors (CCD), which allows more data to be collected simultaneously.

Detectors:

Detectors point detectors observe one point of space at a time slow, but compatible with most/all optics scintillation and gas proportional detectors count all photons, within an energy window, that hit them Si(Li) detectors can electronically analyze or filter wavelengths position sensitive detectors linear PSDs observe all photons scattered along a line from 2 to 10 ° long 2D area detectors observe all photons scattered along a conic section gas proportional (gas on wire; microgap anodes) limited resolution, issues with deadtime and saturation CCD limited in size, expensive solid state real-time multiple semiconductor strips high speed with high resolution, robust

Sample:

Sample A single crystal can be mounted in a thin glass tube or on a glass fibre using grease or glue to hold it in place. The crystals are often cooled to reduce radiation damage and thermal motion during the expt. The solid sample can be rotated about an axis during exposure to the X-rays to increase the chances of all orientations of the crystals in a powder sample being detected. The crystals act as 3-D diffraction gratings.

Output:

Output The diffraction data is recorded, manipulated and can be plotted at the computer in the form required. The diffraction pattern can be compared to a library of patterns (International Centre for Diffraction Data) and, therefore, a positive identification made.

Information Obtained:

Information Obtained Information such as spacing in the crystal lattice, bond lengths and angles, crystal size, purity and texture can all be obtained using XRD. Information about thermal motion can also be obtained. Overall, a picture of the molecules, unit cells and the crystal can be built up.

You can use XRD to determine:

You can use XRD to determine 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)

Phase Identification:

Phase Identification The diffraction pattern for every phase is as unique as your fingerprint Phases with the same chemical composition can have drastically different diffraction patterns. Use the position and relative intensity of a series of peaks to match experimental data to the reference patterns in the database

Databases such as the Powder Diffraction File (PDF) contain dI lists for thousands of crystalline phases. :

Databases such as the Powder Diffraction File (PDF) contain dI lists for thousands of crystalline phases. The PDF contains over 200,000 diffraction patterns. Modern computer programs can help you determine what phases are present in your sample by quickly comparing your diffraction data to all of the patterns in the database. The PDF card for an entry contains a lot of useful information, including literature references.

Quantitative Phase Analysis:

Quantitative Phase Analysis With high quality data, you can determine how much of each phase is present must meet the constant volume assumption (see later slides) The ratio of peak intensities varies linearly as a function of weight fractions for any two phases in a mixture need to know the constant of proportionality RIR method is fast and gives semi-quantitative results Whole pattern fitting/Rietveld refinement is a more accurate but more complicated analysis

Unit Cell Lattice Parameter Refinement:

Unit Cell Lattice Parameter Refinement By accurately measuring peak positions over a long range of 2theta, you can determine the unit cell lattice parameters of the phases in your sample alloying, substitutional doping, temperature and pressure, etc can create changes in lattice parameters that you may want to quantify use many peaks over a long range of 2theta so that you can identify and correct for systematic errors such as specimen displacement and zero shift measure peak positions with a peak search algorithm or profile fitting profile fitting is more accurate but more time consuming then numerically refine the lattice parameters

Crystallite Size and Microstrain:

23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 2 q (deg.) Intensity (a.u.) 00-043-1002> Cerianite- - CeO 2 Crystallite Size and Microstrain Crystallites smaller than ~120nm create broadening of diffraction peaks this peak broadening can be used to quantify the average crystallite size of nanoparticles using the Scherrer equation must know the contribution of peak width from the instrument by using a calibration curve microstrain may also create peak broadening analyzing the peak widths over a long range of 2theta using a Williamson-Hull plot can let you separate microstrain and crystallite size

Preferred Orientation (texture):

Preferred Orientation (texture) Preferred orientation of crystallites can create a systematic variation in diffraction peak intensities can qualitatively analyze using a 1D diffraction pattern a pole figure maps the intensity of a single peak as a function of tilt and rotation of the sample this can be used to quantify the texture (111) (311) (200) (220) (222) (400) 40 50 60 70 80 90 100 Two-Theta (deg) x10 3 2.0 4.0 6.0 8.0 10.0 Intensity(Counts) 00-004-0784> Gold - Au

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