Our XRD interpretation includes: 
1. Phase determination 
2. Determination of diffracted planes
 3- Calculation of crystalline size and microstrain
 4- Whatever your request
 Its cost is only 12$ 
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XRD is a non-destructive test method used to analyze the structure of crystalline materials. XRD analysis, by way of the study of the crystal structure, is used to identify the crystalline phases present in a material and thereby reveal The chemical composition information. JCPDS does not exist now. It has not existed since 1978. It is now known as ICDD. These particular files have never been, are not, and never will be free; it a commercial only database. There are other free databases, however. Vikas has given you a starting point.

Powder Diffraction File is a trademark of the “JCPDS (Joint Committee on Powder Diffraction Standards)-International Centre for Diffraction Data”.In 1978, the name of the organization was changed to the “International Centre for Diffraction Data” in order to highlight the global commitment of this scientific endeavor. Here, you need to purchase the database.

Some free databases are collected:

1. COD (Crystallography Open Database):

COD is an open-access database, and you can freely obtain all data contained in it. You can download cif files and then you can use mercury to plot structure models and save reflection list and xrd calculated pattern.http://www.crystallography.net/cod/search.html

2. The American Mineralogist Crystal Structure Database:

This site is an interface to a crystal structure database that includes every structure published in the American Mineralogist, The Canadian Mineralogist, European Journal of Mineralogy and Physics and Chemistry of Minerals, as well as selected datasets from other journals. The database is maintained under the care of the Mineralogical Society of America and the Mineralogical Association of Canada, and financed by the National Science Foundation.http://rruff.geo.arizona.edu/AMS/amcsd.php

3. DASH: (Cambridge Structural Database System (CSDS)):DASH is a versatile and interactive package for solving crystal structures from powder diffraction data. DASH solves structures by simulated annealing of structural models to indexed diffraction data and features a helpful wizard to guide you through the entire structure solution process.https://www.ccdc.cam.ac.uk/solutions/csd-materials/components/dash/

Some of Paid databases:

1. The International Centre for Diffraction Data® (ICDD®):

ICDD (JCPDS is now called ICDD) is a non-profit scientific organization dedicated to collecting, editing, publishing, and distributing powder diffraction data for the identification of materials. The membership of the ICDD consists of worldwide representation from academe, government, and industry. The Powder Diffraction File™ (PDF®) is the only crystallographic database that is specifically designed for material identification and characterization. It is an analysis system that is comprised of crystallographic and diffraction data. The only crystallographic database organization in the world with its Quality Management System ISO 9001:2015 certified by DEKRA.http://www.icdd.com/

2. HighScore Plus:The ideal tool for crystallographic analysis and more. Whether you are interested in improved process control, or doing research and development, understanding your materials starts very often with understanding the powder diffraction pattern. After identification of all phases present in your sample with Malvern Panalytical’s HighScore, this all-in-one software suite with the Plus option continues to support you with your analysis. Whether your focus is on quantification with or without the Rietveld method, profile fitting, or pattern treatment; HighScore Plus is the solution and helps you performing your daily analyses.https://www.malvernpanalytical.com/en/products/category/software/x-ray-diffraction-software/highscore-with-plus-option

Our XRD interpretation includes:
1. Phase determination
2. Determination of diffracted planes
3- Calculation of crystalline size and microstrain
4- Whatever your request
Its cost is only 12$
Payment Upon Completion

Send your patterns...

1. Profex

What is Profex?

Profex is a graphical user interface for Rietveld refinement of powder X-ray diffraction data with the program BGMN. It provides a large number of convenience features and facilitates the use of the BGMN Rietveld backend in many ways.

• Various options and output formats to create publication-quality graphs
• Main window
• Display hkl line positions from the internal reference structure database
• Powerful text editors support syntax highlighting and various convenience features
• A context help provides descriptions of all refinement parameters
• After the refinement, results are summarized (bottom right)
• Show the refined chemical composition (bottom right)
• A powerful search-match module for phase identification
• CIF / XML import editor to convert CIF or ICDD XML structure files to the native STR format
• Compute electron density maps (Fobs, Fcalc, or difference fourier maps)
• Graphical instrument editor to edit the fundamental parameters
• Generic non-linear curve fitting module
• Various options and output formats to create publication-quality graphs
• Main window

Key features

• Support for a variety of raw data formats, including all major instrument manufacturers (Bruker / Siemens, PANalytical / Philips, Rigaku, Seifert / GE, and generic text formats)
• Export of diffraction patterns to various text formats (ASCII, Gnuplot scripts, Fityk scripts), pixel graphics (PNG), and vector graphics (SVG)
• Batch conversion of raw data scans
• Automatic control file creation and output file name management
• Conversion of CIF and ICDD PDF-4+ XML structure files to BGMN structure files
• Export of refined crystal structures to CIF and Castep CELL format
• Internal database for crystal structure files, instrument configuration files, and predefined refinement presets
• Computation of chemical composition from refined crystal structures
• Batch refinement
• Export of refinement results to spreadsheet files (CSV format)
• Context help for BGMN variables
• Syntax highlighting
• Enhanced text editors for structure and control file management and editing
• Generic support for FullProf.2k as an alternative Rietveld backend to BGMN
• And many more…

Profex runs on Windows, Linux, and Mac OS X operating systems and is available as free software licensed under the GNU General Public License (GPL) version 2 or any later version.

Video tutorials

August 12, 2020. Check out our brand new YouTube channel Profex Tutorials. We will periodically publish new tutorials for selected topics. The first episode explains installation and setup of Profex on three different platforms:https://www.youtube.com/embed/vaWBjTNWG7U?feature=oembed

Profex 4.2 released

August 05, 2020. Profex, our software for Rietveld refinement of powder X-ray diffraction data (XRD), continues to gain popularity and is now established worldwide in the material and earth sciences communities. With the new version 4.2, it has received some long-awaited features that make it easier to use for new and experienced users. As always, Profex remains available as open-source software and is free for academic and commercial use. Visit the What’s new page for an overview of the new features, and download the latest version for Windows, Mac OS or Linux from the Download page.

Feature highlights in version 4.2

Import of CIF structure files has further been improved. Most CIF files require no user input anymore. Wyckoff symbols are determined automatically.

Creating instrument configurations has always been a major obstacle for new users. A brand new graphical instrument editor is easier and more attractive to use. It guides users through the process of creating configuration files for their own devices.

The search-match module for phase identification was introduced with Profex 4.0. With version 4.2, it supports chemical restrictions, which gives more control over the search process and improves the match rate and processing speed

See https://www.profex-xrd.org/

2. OpenXRD

OpenXRD is a program for the analysis of X-ray diffraction data.It will comprise scan treatment (background substraction, peak hunting) as well as mineral identification. OpenXRD will read almost any available data format. OpenXRD is free software and published under the GPL.

We will try to establish a free file with mineral data, fed by scientists and given back to scientists. OpenXRD will be available for Linux/Unix, Windows, and, perhaps Macintosh computers.

Released under GNU General Public License version 2.0 (GPLv2) 

OpenXRD is a free software application from the Other subcategory, part of the Graphic Apps category. The app is currently available in English and it was last updated on 2001-12-27. The program can be installed on All 32-bit MS Windows (95/98/NT/2000/XP) All POSIX (Linux/BSD/UNIX-like OSes) OS X Linux.
OpenXRD (version ) is available for download from our website. Just click the green Download button above to start. Until now the program was downloaded 13911 times. We already checked that the download link to be safe, however for your own protection we recommend that you scan the downloaded software with your antivirus.

See: https://openxrd.soft112.com/

3. FullProf

What is FullProf?

The FullProf program has been mainly developed for Rietveld analysis (structure profile refinement) of neutron (constant wavelength, time of flight, nuclear and magnetic scattering) or X-ray powder diffraction data collected at constant or variable step in scattering angle 2theta. The program can be also used as a Profile Matching (or pattern decomposition using Le Bail method) tool, without the knowledge of the structure. Single crystal refinement can also be performed alone or in combination with powder data. Time of flight (TOF) neutron data analysis is also available. Energy dispersive X-ray data can also be treated but only for profile matching.

Features:

• X-ray diffraction data: laboratory and synchrotron sources
• X-ray diffraction data: laboratory and synchrotron sources
• One or two wavelengths (eventually with different profile parameters)
• Scattering variables: 2theta (in degrees), TOF (in microseconds), energy (in KeV)
• Background: fixed, refinable points or polynomial coefficients, Fourier filtering
• Choice of peak shape for each phase: Gaussian, Lorentzian, modified Lorentzian, pseudo-Voigt, Pearson-VII, Thompson-Cox-Hastings (TCH) pseudo-Voigt, numerical, split pseudo-Voigt, convolution of a double exponential with a TCH pseudo-Voigt for TOF
• Multi-phase (up to 16 phases)
• Preferred orientation: two functions available
• Absorption correction for different geometries. Micro-absorption for Bragg-Brentano set-up
• Choice between three weighting scheme: standard least-square, maximum likelihood and unit weights
• Choice between automatic generation of hkl and/or symmetry operators and file given by user
• Magnetic structure refinement (crystallographic and spherical representation of the magnetic moment). Two methods: describing the magnetic structure in the magnetic unit cell or making use of the propagation vectors using the crystallographic unit cell. This second method is necessary for incommensurate magnetic structures
• Automatic generation of reflections for an incommensurate structure with up to 24 propagation vectors. Refinement of propagation vectors components in reciprocal lattice units
• hkl-dependence of FWHM for strain and size effects
• hkl-dependence of the position shifts of Bragg reflections for special kinds of defects
• Profile Matching: the full profile can be adjusted without prior knowledge of the structure (needs only good starting cell parameters and profile parameters)
• Quantitative analysis withour need of structure factor calculations
• Chemical (distances and angles) and magnetic (magnetic moments) slack constraints. They can be generated automatically by the program
• The instrumental resolution function (Voigt function) may be supplied in a file. A microstructural analysis is then performed
• Form factor refinement of complex objects (plastic crystals)
• Structural or magnetic model could be supplied by an external subroutine for special purposes (rigid bodies TLS is the default, polymers, small angle scattering of amphifilic crystals, description of incommensurate structure in real direct space, etc)
• Single crystal data or integrated intensities can be used as observations (alone or in combination with a powder profile)
• Neutron (or X-ray) powder patterns can be mixed with integrated intensities of X-ray (or neutron) for single crystal or powder data
• Full multi-pattern capabilities. The user may mix several powder diffraction patterns (eventually heterogeneous: X-rays, TOF neutrons, etc.) with total control of the weighting scheme
• Montecarlo/Simulated Annealing algorithms have been introduced to search the starting parameters of a structural problem using integrated intensity data

See: https://www.ill.eu/sites/fullprof/php/programs.html

4. PowDLL

PowDLL is a .NET dynamic link library used for the interconversion procedure between variable formats of Powder X-Ray files. The DLL is capable of handling the most common file formats (binary and ASCII). The library can be used as a reusable component with any .NET language or as a standalone utility.

See: http://users.uoi.gr/nkourkou/powdll/

5. Software Ic

The software packages currently developed at IC are:

• Sir: a widely used package for the solution and refinement of macro and small  molecules using either X-ray or electron diffraction single-crystal data.
• EXPO2014/EXPO2013: an integrated package for the indexation of a powder diffraction pattern, the extraction of integrated intensities, the space group determination, the crystal structure solution viaDirect Methods and/or by a direct-space approach, and the structure refinement by the Rietveld technique.
• QualX2.0/QualX: a computer program for phase identification using powder diffraction data.
• Quanto: a Rietveld program for quantitative phase analysis of polycrystalline mixtures from powder diffraction data.
• SunBIM: a suite of programs for the supra- and sub-molecular X-ray imaging of nano and bio materials with SAXS, WAXS, GISAXS and GIWAXS techniques
• RootProf: An interactive, general purpose tool for processing unidimensional profiles with specific applications to X-ray diffraction measurements
• OChemdb: an on-line portal, using an appropriately designed database of already solved crystal structures, for searching and analysing crystal-chemical information of organic, metal-organic and inorganic structures, and providing statistics on desired bond distances, bond angles, torsion angles, and space groups.

The software is free for academic and non-profit research institutions, while it requires the payment of a license fee to commercial users.

To download the software packages, academic and no-profit users must first register to the web site, choosing the software packages of their interest and accepting all the terms and conditions of the on-line Academic License Agreement. After completing the registration, users will receive a confirmation e-mail and will be allowed tologin to download the selected packages.

Registered users can download freely the previous versions of our packages (such as Sir97, Sir2004, EXPO2004, EXPO2009, EXPO2013 and QualX) for non-commercial use from the Old Software section of the web site.

Commercial users must fill the Order Form and send it by email or fax to our office, together with a signed copy of the Commercial License Agreement.

The license covers the use of all the requested programs under all the supported operating systems for an unlimited time on an unlimited number of computers.

See: http://www.ba.ic.cnr.it/softwareic/

X-ray diffraction, abbreviated as XRD, is an old and well-known technique for studying the structure and properties of crystals. The basis of the XRD method is single-color X-ray diffraction by atoms of a substance. Diffraction generally occurs when light strikes an obstacle. When it hits an obstacle, the light beam either bends and propagates or passes through tiny pores on the obstacle. The diffraction phenomenon is visible for all electromagnetic rays, including X-rays. Interference between the X-ray electric vector and the electrons of the material through which the beam passes can be constructive or destructive. In constructive interference, the X-ray diffraction pattern is characterized by a pattern of atomic arrangement in a regular crystal structure. In fact, when an X-ray is shone on a crystal, its diffraction occurs according to the structural characteristic pattern of the crystal.

Bragg’s Law

Due to the regular structure in a crystal, it can be assumed to be regular plates with specified intervals. Diffraction occurs because the distance between the regular layers of a crystal is close to the X-ray wavelength. The X-ray strikes the angle θ with the surface, causing part of the initial beam to propagate at the same angle θ and the other part to enter the inner plates of the crystal. This process is repeated for many pages of a crystal. The distance traveled by X-rays in contact with surface atoms is less than the distance traveled in contact with the inner layer of the crystal. The distance traveled depends on the distance between the two layers and the angle of X-ray radiation.

X-ray diffraction – XRD – analium
Figure 1 X-ray collision and its diffraction method in XRD method

Figure 1 shows that the difference in path traveled between the first and second layers is equal to:

BG = BC = dSinθ (1)

Constructive diffraction occurs when the difference in the length of the X-ray path is an exact multiple of the wavelength. Therefore, for the total distance traveled, it is equal to:

(2) nλ = 2dSinθ

This equation is known as the Bragg relation. In this relation λ the wavelength of the source d is the distance between the crystal plates and θ is the angle of incidence and n is an integer. Note that based on this equation, the X-ray will only be reflected at specific angles obtained from the rearrangement of Equation 1:

   (3) Sinθ = nλ / 2d

An XRD spectrum is obtained by plotting the intensity in θ. By changing θ and knowing the wavelength of the source λ, d is obtained at any moment.

XRD device
Similar to many XRD component analyzers, they include a source, a wavelength selector, a sample location, a detector, and a signal converter. Figure 2 shows an overview of an X-ray diffraction device (XRD).

X-ray diffraction device (XRD) – analium
Figure 2 Overview of an X-ray diffraction device (XRD)

X-ray tubes with tungsten filament are commonly used as sources. Source intensity can be adjusted by adjusting the current flowing through it. The beam wavelength can also be controlled by applying applied voltage control.

A monochromator or filter is used to create a monochromatic beam. A variety of scintillation and semiconductor gas-filled detectors are used in XRD devices.

Preparation of XRD samples
The sample must be well ground to obtain a homogeneous powder from the crystalline sample. In this case, it is possible to place a large number of crystalline particles in the desired direction and in accordance with the Bragg equation. The samples are mixed with a suitable adhesive and then molded.

Crystallization is a very important step in the preparation of XRD samples and requires special skills and expertise.

In powder X-ray diffraction, the diffraction pattern is obtained from the powder form of the sample. XRD powder is usually lighter and simpler than crystalline diffraction. Because in powder form, there is no need to prepare single crystal. In the powder method, the mass pattern (bulk) of the sample is also obtained.

XRD Analysis Tips
The sample must have a crystalline structure.
Has little accuracy in quantifying phases (phases with values ​​less than 5% are not detected).
In qualitative analysis, the element does not perform well.
The method is fast and powerful and with convenient access.
XRD Application Background
Determining the crystal structure and accurate measurement of lattice parameters
Determining fuzzy diagrams
Chemical identification and analysis
Determining the quality and direction of plates in single crystals

Our XRD interpretation includes:
1. Phase determination
2. Determination of diffracted planes
3- Calculation of crystalline size and microstrain
4- Whatever your request
Its cost is only 12$
Payment Upon Completion

Send your patterns...

X-ray diffraction (XRD) is a technique used in materials science for determining the atomic and molecular structure of a material. This is done by irradiating a sample of the material with incident X-rays and then measuring the intensities and scattering angles of the X-rays that are scattered by the material. The intensity of the scattered X-rays are plotted as a function of the scattering angle, and the structure of the material is determined from the analysis of the location, in angle, and the intensities of scattered intensity peaks. Beyond being able to measure the average positions of the atoms in the crystal, information on how the actual structure deviates from the ideal one, resulting for example from internal stress or from defects, can be determined.

The diffraction of the X-rays, that is central to the XRD method, is a subset of the general X-ray scattering phenomena. XRD, which is generally used to mean can wide-angle X-ray diffraction (WAXD), falls under several methods that use the elastically scattered X-ray waves. Other elastic scattering based X-ray techniques include small angle X-ray scattering (SAXS), where the X-rays are incident on the sample over the small angular range of 0.1-10⁰typically). SAXS measures structural correlations of the scale of several nanometers or larger (such as crystal superstructures), and X-ray reflectivity that measures the thickness, roughness, and density of thin films. WAXD covers an angular range beyond 10⁰.

CITE THIS VIDEO | REPRINTS AND PERMISSIONS

JoVE Science Education Database. Materials Engineering. X-ray Diffraction. JoVE, Cambridge, MA, (2020).

PRINCIPLES

Relationship between diffracted peak positions and crystal structure:

When light waves of sufficiently small wavelength are incident upon a crystal lattice, they diffract from the lattice points. At certain angles of incidence, the diffracted parallel waves constructively interfere and create detectable peaks in intensity. W.H. Bragg identified the relationship illustrated in Figure 1 and derived a corresponding equation:

nλ = 2d_hkl sin θ [1]

Here λ is the wavelength of the X-rays used, d_hkl is the spacing between a particular set of planes with (hkl) Miller indices*, and θ is the angle of incidence at which a diffraction peak is measured. Finally, n is an integer that represents the ‘harmonic order’ of the diffraction. At n=1, for example, we have the first harmonic, meaning that the path of X-rays diffracted through the crystal (equivalent to 2d_hkl sin ) is exactly 1λ, while at n=2, the diffracted path is 2λ. We can typically assume n=1, and, in general, n=1 for θ < sin^-1(2λ/d_h’k’l’), where h’k’l’ are the Miller indices of the planes that show the first peak (at the lowest 2θ value) in a diffraction experiment. Miller indices are a set of three integers that constitute a notation system for identifying directions and planes within crystals. For directions, the [h k l]Miller indices represent the normalized difference in the respective x, y and z coordinates (in a Cartesian coordinate system) of two points along the direction. For planes, the Miller indices (h k l) of a plane are simply the h k l values of the direction perpendicular to the plane.

In a typical XRD experiment in reflection mode, the X-ray source is fixed in position and the sample is rotated with respect to the X-ray beam over θ. A detector picks up the diffracted beam and has to keep up with the sample rotation by rotating at twice the rate (i.e. for a given sample angle of θ, the detector angle is 2θ). The geometry of the experiment is schematically shown in Figure 1.

Figure 1: Illustration of Bragg’s Law.

When a peak in intensity is observed, equation 1 is necessarily satisfied. Consequently, we can calculate d-spacings based on the angles at which these peaks are observed. By calculating the d-spacings of multiple peaks, the crystal class and the crystal structure parameters material sample can be identified using a database such as the Hanawalt Search Manual or database libraries available with the XRD software being used.

We will be assuming that the sample being investigated is not a single crystal. If the sample were a single crystal with a particular (h*k*l*) plane parallel to the sample surface, it would need to be rotated until the Bragg condition for the (h*k*l*) is satisfied in order to see a peak in diffracted intensity (for n=1) with potentially higher harmonic (h*k*l*)peaks (e.g. for n=2) also detectable at higher angles. At all other angles there would be no peaks in a single crystal sample. Instead, let’s assume that the sample is either polycrystalline or that it is a powder, with a statistically significant number of crystalline grains or powder particles illuminated by the incident X-ray beam. Under this assumption, the sample consists of randomly oriented grains, with a similar statistical probability for all possible lattice planes to diffract.

The relationships between the d_hkl and the unit cell parameters are shown below in Equations 2-7 for the 7 crystal classes, cubic, tetragonal, hexagonal, rhombohedral, orthorhombic, monoclinic and triclinic. The unit cell parameters consist of lengths of(a,b,c) and the angles between (α, β, γ) the edges of the unit cells for the 7 crystal classes (Figure 1x shows the example of one of the crystal classes: the tetragonal structure where a=b≠c, and α=β=γ=90⁰). Using multiple diffracted peak positions (i.e. several distinct d_hkl values), the values of the unit cell parameters can be solved uniquely.

Figure 2: The tetragonal structure as one of the seven crystal classes.

Cubic (a = b = c; α = β = γ = 90⁰):

  [2]

Tetragonal (a = b ≠ c; α = β = γ = 90⁰):

  [3]

Hexagonal (a = b ≠ c; α = β = 90⁰; γ = 120⁰):

  [4]

Orthorhombic (a ≠ b ≠ c; α = β = γ = 90⁰):

  [5]

Rhombohedral (a = b ≠ c; α = β = γ = 90⁰):

  [6]

Monoclinic (a ≠ b ≠ c; α = γ = 90⁰≠ β):

  [7]

Triclinic (a ≠ b ≠ c; α ≠ β ≠ γ ≠ 90⁰): 

        [8] 

Relationship between diffracted peak intensities and crystal structure:

Next we examine the factors that contribute to the intensity in an XRD pattern. The factors can be broken down as 1) the contribution to scattering that results directly from the unique structural aspects of the material (the specific types and locations of scattering atoms in the structure) and 2) those that are not specific to the material. In the former, there are two factors: the ‘absorption factor’ and the ‘structure factor’. The absorption factor primarily depends on the ability of the material to absorb X-rays on their way in and out. This factor does not have a θ dependence as long as the samples are not thin (the sample should be > 3 times thicker than the attenuation length of the X-rays). In other words, the contribution by the absorption factor to the intensity of different peaks is constant. The ‘structure factor’ directly affects the intensity of specific peaks as a direct result of the structure. The remaining factors, the ‘multiplicity’, which accounts for all the planes that belong to the same family because they are symmetrically related, and the ‘Lorentz-Polarization’ factor, which comes from the geometry of the XRD experiment, also affect the relative intensity of the peaks but they are not specific to a material and can easily be accounted for with analytical expressions (i.e. XRD analysis software can remove them with analytical functions).

Figure 3: Three diffraction ray paths, of which rays 11′ and 22′ satisfy the Bragg condition, while ray 33′ results from scattering by an atom (red circle) at an arbitrary position.

As the only factor that carries the unique structural contribution of a material to the relative intensities of XRD peaks, the structure factor is very important and requires a closer look. In Figure 2, let us assume that the 1^st order Bragg diffraction condition (remember, that this corresponds to n=1) is satisfied between ray_11′ and ray_22′ which are scattered on two atomic planes in the h00 direction (using the Miller indices notation described earlier) separated by a distance d. Under this condition, the difference in path length between ray_11′ and ray_22′ is δ_{(22′-11′)} = SA + AR = λ. The phase shift between the diffracted rays 1 and 2 is, therefore, Φ_22′-11′ = (δ_{(22′-11′)}/λ) 2π = 2π (assuming a cubic symmetry and, therefore, d = a/h in the h00 direction].

With a few steps in analytical geometry, it can be shown that the phase shift, Φ_{(33′-11′)}, with ray 3 diffracted by an arbitrary plane of atoms that are spaced an arbitrary distance x, is given by: Φ_{(33′-11′)} = 2πhu, where u=x/a (a is the unit cell parameter in the (h00) direction.) Taking the two other orthogonal directions, (0k0) and (00l), and v=y/a and w=z/a as fractional coordinates in the y- and z-directions, the expression for the phase shift extends to Φ = 2π(hu+kv+lw). Now, the X-ray wave scattered by the j-th atom in a unit cell will have a scattering amplitude of f_j and a phase of Φ_j, such that the function describing it is . The structure factor we seek, therefore, is the sum of all the scattering functions due to all the unique atoms in a unit cell. This structure factor, F, is given as:

  [9]

and the intensity factor contributed by the structure factor is I = F².

Based on the positions (u,v,w) of atoms on particular planes (h,k,l), there is the possibility of interference between scattered waves that is constructive, destructive, or in-between, and this interference directly affects the amplitude of the XRD peaks representing the (hkl) planes.

Now, a plot of intensity, I, versus 2θ is what is measured in an XRD experiment. The determination of the of crystal type and the associated unit cell parameters (a, b, c, α, β, and γ) can be arrived at analytically by observing systematic presence/absence of peaks, using the equations 2-9, comparing values against databases, using deduction and a process of elimination. Nowadays, this is process is fairly automated by a variety of software linked to crystal structure databases.

PROCEDURE

The following procedure applies to a specific XRD instrument and its associated software, and there may be some variations when other instruments are used.

1. We will examine a Ni powder sample on a Panalytical Alpha-1 XRD instrument.
2. First, choose the mask to fix the beam size according to your sample diameter. The beam must not have a footprint larger than the sample at the smallest θ value (typically ~ 7⁰-10⁰). For a sample of width ε, the beam size should be < ε sinθ.
3. Load the sample in the sample spinner stage and lock the sample into position. The sample spinner helps to spatially randomize the exposure of the sample to the X-ray source.
4. Choose the angle range for your XRD scan. For example 15-90 degrees is a typical range.
5. Choose a step size, i.e. the increment in 2θ, and integration (counting) time. Generally a 0.05 degree step size and 4 seconds integration is the default for a wide angle scan.
6. Once all the peak positions are determined through this initial scan, subsequent scans can focus on a narrower scan range around specific peaks using a smaller step size in angle if higher resolution data from those peaks are desired.

RESULTS

In Figure 4 we see the XRD peaks for the Ni powder sample. Note that the peaks that are observed (e.g. {111}, {200}) are for those that have either all even or all odd combinations of h, k, and l. Ni is face-centered cubic (FCC), and in all FCC structures, the peaks corresponding to {hkl} planes where h, k, and l are mixtures of even and odd integers, are absent due to the destructive interference of the scattered X-rays. Peaks corresponding to planes, such as {210} and {211} are missing. This phenomenon is called the systematic presence and absence rules, and they provide an analytical tool for assessing the crystal structure of the sample.

Figure 4: An XRD scan of Ni with a face-centered cubic structure is shown.

APPLICATIONS AND SUMMARY

This is a demonstration of a standard XRD experiment. The material examined in this experiment was in a powder form, but XRD works equally well with solid piece of material as long as the sample has a flat surface that can be set parallel to the plane of the sample stage.

XRD is a fairly ubiquitous method for determining the presence (or absence) of crystallographic order in materials. Beyond the standard application of determining the crystal structure, XRD is often used to obtain a variety of other structural information such as:

1. Whether or not the structure of a material is amorphous (characterized by a broad hump in the diffraction intensity and a lack of discernable crystallographic peaks),
2. Whether the sample is a composite material consisting of multiple crystallographic phases and, if so, determine the fraction of each phase,
3. Determining whether a material is an amorphous/crystalline composite
4. Determining the grain/particle size of the material,
5. Determining the degree of texture (preferred orientation of grains) in material