X-Ray Diffraction

Introduction to XRD

X-ray Diffraction (XRD) is a non-destructive technique for analyzing the crystalline structure and composition of materials. It measures how X-rays diffract through atomic planes within a material. X-rays diffract at specific angles, creating a fingerprint that identifies the crystalline phases present.

X-ray wavelengths are similar to interatomic distances in crystals. This makes interference patterns easy to observe.

Chemists call it PXRD (Powder X-ray Diffraction). Physicists call it WAXS (Wide-Angle X-ray Scattering). XRD identifies phases, while EDS identifies elements and their amounts.

A complete material description needs both elemental composition and phase structure. EDS can be replaced by OES or chemical methods for elements. Determining phase structure without XRD is much harder.

In addition to the fingerprint of different phases, XRD allows us to determine the following:

• Phase Identification & Quantification:

The specific crystalline phases present and how much of each phase. We identify phases by matching them against a database and eliminating impossible phases. We could quantify phases with segmentation analysis in SEM images, but we often lack the phase identities. BSE images of stellites show Chromium-rich carbides as bright spots and Tungsten-rich carbides as dark spots. EDS identifies composition but handles carbon poorly.

• Lattice Parameters:

By diving a bit into Bragg's law, we can determine the spacing between atomic planes in a crystal lattice. In particular, we can tell if some atomic planes have been forced closer or further apart from the ideal, which can tell us more about the material

• Crystalline Content

The degree of crystallinity in a sample, or perhaps more realistically, the amount of amorphous phase in the material since just about everything in our (usually metal or ceramic) samples are crystals. Amorphous phases are usually detrimental, although that's not a hard rule.

Fun fact, the International Union of Crystallography defines crystals as substances that produce X-ray diffraction patterns. Which is maybe a little weird, but this definition is better than anything else i've heard.

• Crystal Quality

The size of crystallites and the presence of microstrain or defects. Keep in mind that crystal grain sizes can heavily impact material performance, with smaller crystals generally being better, so being able to determine crystal sizes is great. The broadening of XRD peaks due to small crystals is described by the Scherrer equation. The presence of microstrain is useful if some external stress or phase transformation has caused defects in the crystal structure, and in the determination of SFE.

• Orientation:

The preferred ordering and epitaxial growth of crystallites (texture). This is something that I'm not quite familar with unfortunately as I haven't had the pleasure of dealing with powder XRD, I've only seen bulk specimens under XRD.

X-rays and the basic principles behind XRD

X-rays were discovered in 1895 by German physicist Roentgen. The typical wavelength of X-rays is $1 x 10^{-10}$m (1 angstrom), whereas the wavelength of visible light is typically $1 x 10^{-6}$m (1 µm). This is also why angstroms were initially used in Xray research, even if it's not a standard SI unit prefix.

X-ray Generation in a X-ray vacuum tube

X-rays form in a vacuum tube. High-energy electrons strike a target material. A heated tungsten filament releases electrons. Those electrons travel to anode targets of copper (Cu) or molybdenum (Mo). Other targets include Au, W, Ag, Co, Fe, and Cr.

The target atoms decelerate the incoming electrons. This releases a continuous spectrum of energy called "bremsstrahlung" (braking radiation).

Incident electrons can knock electrons off the atom shells of the target material. An electron from a higher shell fills the vacancy. This transition emits X-ray photons with characteristic wavelengths. The most intense peak comes from electrons falling from the second to the first shell ($K \alpha 1$). This is the wavelength used for XRD. Copper emits at 1.5 Å and molybdenum at 0.7 Å.

X-rays exit the tube through a Beryllium side window. Filters reduce them to a single wavelength. Collimators focus the beam into a single direction. A high-intensity beam on a small focal spot gives greater spatial resolution.

Aiming X-rays onto the sample and measuring angles with receiver

An XRD goniometer aligns the emitter, sample, and receiver. We will discuss X-ray interactions with material soon.

The distance from the X-ray focal spot to the sample equals the distance from the sample to the detector. Moving the sample holder and detector in a 1:2 ratio keeps the reflected beam focused on the detector.

For a THETA:2-THETA goniometer, the X-ray tube is stationary, the sample moves by angle THETA and the detector simulataneously moves by the angle 2-THETA. One disadvantage is that samples may shift or fall off the sample holder at high THETA.

For a THETA:THETA goniometer, the sample is staionary, while the X-ray tube and detector move simultaneously by THETA.

University of Sharjah, a wonderful lab that gives us access to XRD, uses the Bruker D8 Venture, which is a THETA:THETA goniometer. It's quite impressive looking in person.

References: https://www.geo.umass.edu/courses/geo311/xrdbasics.pdf

In short, a goniometer controls the angle of incidence and the detection of X-rays. Why this is necessary will become clearer in the next section.

X-ray Interaction with Matter:

When X-rays interact with a crystalline material, they are diffracted by the atoms in the crystal lattice.

Electrons in an electromagnetic field oscillate at the field's frequency. In most directions, oscillations cancel. They interfere constructively only along specific directions in a crystal. The result resembles reflection at specific angles.

This observation is formalized as Bragg's law, which relates the angle of incidence ($\theta$) of the X-rays, the wavelength of the X-rays ($\lambda$), and the spacing between the crystal lattice planes ($d$):

$$ n\lambda = 2d sin\theta $$

A lattice plane intersects atoms across the 3D crystal lattice. Each plane generates a diffraction peak. Peaks should bear Miller indices.

Parallel crystal planes that cause constructive interference carry h,k,l indices aligned with the unit cell.

Selection rules

Angle measurements determine crystal structure. Lattice spacing follows:

$$\displaystyle d = \frac {a}{\sqrt{h^2+k^2+l^2}} $$

where $a$ is the lattice spacing of the cubic crystal, and $h$, $k$, and $l$ are the Miller indices of the Bragg plane. Combining this relation with Bragg's law gives:

Selection rules define which Miller indices reflect for each cubic Bravais lattice., a few of the selection rules are given in the table below.

References: https://en.wikipedia.org/wiki/Bragg%27s_law

Data Analysis

1. Peak Identification: Identifying the positions and intensities of the diffraction peaks. 2. Phase Identification: Comparing the diffraction pattern to reference patterns in a database. 3. Quantitative Analysis: Determining the relative amounts of different phases in a mixture. 4. Crystallographic Analysis: Refining the crystal structure of a material.

Space Groups

Bravais lattices have finite combinations of rotation, screw axes, mirror, glide planes, and inversion points. These 230 unique symmetry combinations form the 230 space groups. Powder diffraction users need not memorize them all, but should understand their properties. Space groups classify by symmetry type.

Crystallographers use 230 space groups numbered 1 to 230. These group into 7 crystal systems: triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic.

Within each crystal system, the space groups can be ordered by Laue class, crystal class (e.g. 2 < m < 2/m) and, finally, lattice centring (e.g. P < A,B,C < F < I ), as shown in the table below. Further ordering is based largely on the symmetry elements present: In general, rotation axes come before screw axes and mirror planes before glide planes. Note that space groups are not listed here in exact order of their standard space group number, though the order is very similar.

Notation

Each space group is unique. Space group symbols are not always unique to one group. The same symmetry can have different symbols depending on unit cell vector choices. Space group symbols start with the lattice type (e.g. C2). The same space group can carry different symbols under different unit-cell labels (A2, I2, B2, or F2). The table below uses standard settings.

The 230 Crystallographic Space Groups

Space groups with inversion points are centrosymmetric (shown in red). Space groups that cannot change handedness are enantiomorphic (shown in magenta).

https://en.wikipedia.org/wiki/Space_group#Table_of_space_groups_in_2_dimensions_(wallpaper_groups)

SOP for using Bruker d8 from Washington Universoty

https://xraysrv.wustl.edu/web/xrd/brukerd8.html

Bruker D8 Advance @ University of Sharjah

University of Sharjah's Advanced Material Characterization Lab uses the Bruker D8 Advance XRD. This theta-theta instrument analyzes powder samples. It has a Cu x-ray tube, slits, filters, a rotating sample holder, and a Bruker AXS PHOTON II detector.

The diffractometer houses the goniometer, x-ray tube, power supply, cooling circuit, and electronics. On-board electronics or a PC with Measurement Server and Diffrac.Suite software monitor and control everything.

Bruker d8 Software Summary

The Bruker d8 diffractometer offers features summarized here but detailed in the manuals. Download them for full instructions (Bruker PDF Manuals).

• Bruker Measurement Server. The measurement server establishes communication between the PC and the Bruker d8 hardware so that you can run XRD jobs. It runs continuously once established and needs no other input from you.
• Bruker Measurement Suite. This program hosts the software modules that are used to set up an XRD job (Wizard) and then run that job (Jobs). The Commander is used to perform manual aspects of XRD scans (turning the x-ray tube on and off, positioning axes, manually setting up a scan, etc.).
• Bruker Diffrac.Eva. This program is used for processing of XRD scans, including background removal, peakfinding, and search-match procedures.
• Topas. This program performs Rietveld refinement on XRD scans, which can be used for quantitative analysis, structure determination, cell refinement, among other things.

Bruker Diffrac.Eva Program (Evaluation)

The Bruker Diffrac.Eva program is used for the evaluation or processing of xrd data.

There are two manuals for Eva. The Diffrac.Eva manual contains a complete discussion of the components of the program, and the Diffrac.Eva tutorial has some examples of how to use the program, located here: Bruker PDF Manuals.

Capabilities of the Diffrac.Eva program are:

Pattern display. Used to import a raw file or previously processed file saved as an .eva file. Background subtraction. Peak identification and processing, including stripping of Cu Kα2. Pattern processing. Search-match identification. Eva can perform search match procedures using the following database files (one at a time) ICDD PDF5+ subscription database Crystallography Open Database (COD, a special Bruker compiled database file) User-defined database files

Bruker Topas

Topas has a graphical interface and scripted launch mode. Its capabilities include:

• Background fitting and peak modelling
• Structure determination with hkl files
• Rietveld analysis with hkl, known structures, or .cif files
• Quantitative analysis of multiphase mixtures

See the Topas documentation for other capabilities.

Python libraries

xylib

https://github.com/wojdyr/xylib/

Note: Seems like the last update was in 2020

xylib is a portable library for reading files that contain x-y data from powder diffraction, spectroscopy and other experimental methods.

It comes with two programs that can convert supported formats to plain text: command-line xyconv and graphical xyconvert.

Supported formats:

plain text, delimiter-separated values (e.g. CSV) Crystallographic Information File for Powder Diffraction (pdCIF) Siemens/Bruker UXD Siemens/Bruker RAW ver. 1/2/3/4 Philips UDF Philips PC-APD RD raw scan V3/V5 PANalytical XRDML Rigaku DAT Sietronics Sieray CPI DBWS/DMPLOT data file Canberra CNF (from Genie-2000 software; aka CAM format) Canberra AccuSpec MCA XFIT/Koalariet XDD RIET7/LHPM/CSRIET/ILL_D1A5/PSI_DMC DAT Vamas ISO14976 (only experiment modes: SEM or MAPSV or MAPSVDP are supported; only REGULAR scan_mode is supported) Princeton Instruments WinSpec SPE (only 1-D data is supported) χPLOT CHI Ron Unwin's Spectra XPS format (VGX-900 compatible) Freiberg Instruments XSYG (from lexsyg) Bruker SPC/PAR

pyxrd

https://github.com/PyXRD/PyXRD PyXRD

PyXRD is a python implementation of the matrix algorithm for computer modeling of X-ray diffraction (XRD) patterns of disordered lamellar structures. It's goals are to:

provide an easy user-interface for end-users provide basic tools for displaying and manipulating XRD patterns produce high-quality (publication-grade) figures make modelling of XRD patterns for mixed-layer clay minerals 'easy' be free and open-source (open box instead of closed box model)

PyXRD was written with the multi-specimen full-profile fitting method in mind. A direct result is the ability to 'share' parameters among similar phases. This allows for instance to have an air-dry and a glycolated illite-smectite share their coherent scattering domain size, but still have different basal spacings and interlayer compositions for the smectite component. Or play with the di/tri-octahedral composition of a chlorite with ease.

Other features are (incomplete list):

Import/export several common XRD formats (.RD, .RAW, .CPI, ASCII) Simple background subtraction/addition (linear or custom patterns) Smoothing patterns and adding noise to patterns Peak finding and annotating (markers) Peak stripping and peak area calculation tools Custom line colors, line widths, pattern positions, ... Goniometer settings (wavelengths, geometry settings, ...) Specimen settings (sample length, absorption, ...) Automatic parameter refinement using several algorithms, e.g.: L BFGS B Brute Force Covariation Matrix Adapation Evolutionary Strategy (CMA-ES; using DEAP 1.0) Multiple Particle Swarm Optimization (MPSO; using DEAP 1.0) Particle-swarm CMA-ES (PS-CMA-ES; using DEAP 1.0) Scripting support

powerxrd

A Python package made to handle powder XRD (and XRD) data. The only known open-source Github project with a Rietveld refinement method in development. https://github.com/andrewrgarcia/powerxrd

https://gist.github.com/andrewrgarcia/c023c575ad3e9574394578a073986b53

Additional Resources

https://drive.google.com/drive/folders/1WLKDNFwYWb6fndtJovhMejl3V_5Ha4J_

https://enze-chen.github.io/resources/

Emirates Crystallographic Society

Website http://ecs2020.org/ Members http://ecs2020.org/group-and-facility/

On 20 September 2020, researchers from academia and industry in the United Arab Emirates (UAE) established the Emirates Crystallographic Society (ECS). The ECS is the culmination of years of work and represents the only internationally recognized professional body to represent UAE researchers who use diffraction methods. For a country that is only 50 years old, the UAE has made significant investments in scientific research over a short period of time. The establishment of the ECS is another milestone for the growing research community in the UAE.

Emirates Crystallographic Society was founded in 2020, it has gained a string of admittances to a number of international crystallographic bodies. With each admittance to an international body, the ECS and its representatives are working hard to bring better visibility and resources to the growing community of researchers in the UAE.

28 April 2021, the council of the European Crystallographic Association (ECA) voted to admit the ECS as a full national member

13 August 2021, the ECS was admitted to the Asian Crystallographic Association (AsCA)

15 August 2021, the ECS was admitted to the International Union of Crystallography (IUCr) as a Category 1 adhering body, which was formalized at the 25th Congress of the IUCr in Prague

Great article on residual stress method https://www.stressmap.co.uk/residual-stress-measurement-standards/

COMMENT Python

conda create --name pymatgen python
conda activate pymatgen
conda install --yes numpy scipy matplotlib pymatgen

from mp_api.client import MPRester
from pymatgen.analysis.diffraction.xrd import XRDCalculator
from pymatgen.symmetry.analyzer import SpacegroupAnalyzer

#+RESULTS: :RESULTS:

:END:

with MPRester(api_key="v4FBrisymyG7Uh4MafRhXmUMfi068mkW") as mpr:

    # retreive relevant structures
    structure = mpr.get_structure_by_material_id("mp-723")

#+RESULTS: :RESULTS:

:END:

 # important to use the conventional structure to ensure
# that peaks are labelled with the conventional Miller indices
sga = SpacegroupAnalyzer(structure)
conventional_structure = sga.get_conventional_standard_structure()

# this example shows how to obtain an XRD diffraction pattern
# these patterns are calculated on-the-fly from the structure
calculator = XRDCalculator(wavelength="CuKa")
pattern = calculator.get_pattern(conventional_structure)

print(pattern.as_dict())

https://www.youtube.com/watch?v=I-39vMocHKs&t=1s

Sample Preparation

Sample preparation is critical for a good diffraction pattern, especially if you want to use advanced techniques like Rietveld refinement. This is especially true since we test the actual metal itself, and not the milled powder. High energy milling typically causes lattice defects and strain in the crystal structure, as well as peak broadening due to reduction of crystallite size.

General tips:

• Adjust divergence slit and beam mask for largest possible irradiated area.
• Use spinning sample stage for better randomization if possible

Counting time per step >= 1 revolution of sample stage spinner You want the entire sample to rotate withing each time step.

Ensure sample height displacement is lowered:

Effect of sample height displacement

• On the isntrument:
  • Focus of diffracted beam is displaced
  • Detector is out of focus
  • Diffracted beam blocked by apertures
• In the XRD pattern
  • 2\theta shift of peaks
  • Diffuse / broad peaks & distorted peak profiles
  • Poor rietveld fits

Effect of surface roughness

• On the instrument
  • Focus of diffracted beam is partially displaced
  • Detector is out of focus
  • Diffracted beam blocked by apertures
• In the XRD pattern:
  • 2θ shift of peaks
  • Diffuse / broad peaks
  • Distorted peak profiles
  • Poor Rietveld fits

How to choose scan parameters

Unfortunately, we have a iron triangle of the following:

• Angular Range (5deg - 100 deg)

Must start before first peak (usually 10 deg) and must avoid primary beam (so avoid 5 deg) End at 60 and above, the higher the better. No need to measure empty background Recommendations: 5 deg to 60/80 deg for phase quantification 5 deg to 80 / 100 / 120 deg for structure refinement

• Step size 0.02 2\theta deg

You want atleast 5 data points per peak Typically 0.01 - 0.02 2\theta size

• Counting Time (0.50 sec / steps)

Counting time determines the number of counts, and the higher the counts, the better the signal/noise ratio For standard measurements, the strongest peak should be atleast 5000 counts For high intensity measurements, the strongest peak should be atleast 10000 counts. Recommendations: Standard S/N ratio can be done by +0.15+ 0.50 sec / step High S/N ratio can be done by +0.5+ > 0.5 sec / step

Tried 0.15 sec/step and it was terrible.

Diffraction Pattern Features

Rietveld Refinement

How to report in Materials and Methods section

Need to match the level of detail to the relevance of XRD

DOs and DON'Ts for manuscripts

• DO show your raw data (as a stacked plot if necessary)
• DO show one full refinement
• DO give details according to the relevance of XRD data

(either Identification, Quantification, Refinement)

• DO NOT spam the manuscript with refinement plots
• DO NOT publish results from non-standard samples
• DO NOT publish results from poor refinements

What's the difference between ICDD and JCPDS?

JCPDS (Joint Committee on Powder Diffraction Standards) is the former name of the ICDD (International Centre for Diffraction Data). They are the same organization, which officially changed its name in 1978. JCPDS results might be a bit old.

Need for more open data in XRD patterns

https://www.crystallography.net/cod/petition/

Petition for Open Data in Crystallography Petition text

It is requested that CSD, ICSD, CRYSTMET and ICDD provide a light version of their content (crystal data or powder patterns) at no cost on the Web. A light version consists of the complete database that is fully searchable on the Web by crystal parameters and references and returns the CIFs. It would not consist of the other value-added possibilities produced by these companies, which would stay inside of the toll versions - unless, of course, they want to give more... The principle defended here is that the atomic positions in natural or synthetic crystal samples of our Universe are not copyrightable.

More than 2000 signatures were collected that supported our petition; 10 signatures were placed against our initiative. We thank everyone who signed the petition, and we are glad that so many scientists around the world supported our action. We will also take the negative comments seriously; we are however convinced that the the COD undertaking is a fair, legal, and very necessary one.

At the moment, the signatures of the petition are no longer accepted. The case for petition is over: no positive answer was obtained from the databases, and, with the invaluable help of the volunteers and CIF contributors, the COD is growing fast.

Please stay tuned for our future initiatives, and in the meantime enjoy the COD CIF collection!

The COD Advisory Board - Dec 2008 More information

The Open Data principles have great supporters in crystallography with mainly the PDB, AMCSD and NDB, all offering full crystal data access at no cost on the Web. The other essential crystallography databases (CSD, ICSD, CRYSMET, ICDD) are available by a fee subscription. The COD expected to produce a minimal database in the same domains as these four last ones. The COD growing depended on the data (CIF) upload of individuals, or laboratories, and it was asked for permission to download the CIF in free access at the IUCr and ACS (etc) websites. These expectations seem to fail, or are not fulfilled fast enough. The IUCr asked for letters of support for the COD from crystallographers unable to obtain a copy of the Cambridge Database (see letters below). Hence this petition, in a slightly different direction (but waiting for an improbable petition effect, you can continue to upload your CIF files to the COD).

PS - As said by DLR, Caltech,"considering all that one can do with a CSD subscription, its hard to imagine why CCDC won't consider a lite version, if only to stimulate users to try and find the funds for a full CSD subscription."

Related

• EDS — chemistry where XRD gives structure
• Metallography — sample preparation overlap
• Optical Microscopy — correlated grain imaging
• Metallurgy — the structure-property context
• Residual Stress — XRD is the standard for measuring it