Research & Reviews: Journal of Physics

ISSN: 2278-2265(online), ISSN: 2347-9973(print)

Volume 4, Issue 3
www.stmjournals.com

An Overview on Powder X-Ray Diffraction and

Its Current Applications
Gunashekar GS*, Krishna M
Department of Mechanical Engineering, RVCE, Bangalore, Karnataka, India

Abstract
Industries and research centres are continuously developing novel materials with light weight,
higher strength and which can retain their properties at environmental temperatures. The
cited properties mainly depend upon micro-structure and chemical composition of materials.
Many research works focused to characterize the materials by different experiment
techniques. Among them powder x-ray diffraction (XRD) is a most prominent, non-destructive
technique used for investigation, characterization, and quality control of crystalline materials.
Numerous fundamental XRD techniques and software packages are available for analyzing
the crystal structure, crystallite size, degrees of crystallinity and other structural parameters
of materials. In this work the brief description of XRD techniques employed in quantitative
analysis and its current applications have been discussed.

Keywords: XRD, crystal structures, crystallite size, degrees of crystallinity, quantitative

analysis

*Author for Correspondence E-mail: gunashekar.gs2@gmail.com

INTRODUCTION beam of known wavelength λ is illuminated. A

The micro-structure and chemical composition scattered beam of similar wavelength of
of crystalline materials are characterized by incident beam is diffracted at angle 2θ with
different experiment techniques such as respect to the lattice planes based on Bragg’s
scanning electron microscope (SEM), law [2]. Bragg’s law determines the
transmission electron microscope (TEM), relationship between the wavelength of x-ray
dynamic light scattering (DLS), photon (λ), distance between the lattice planes (d) and
correlation spectroscopy (PCS), scanning diffracted angle (θ) as described in the Eq. (1):
probe microscope (SPM), neutron diffraction 𝑛𝜆 = 2𝑑 𝑠𝑖𝑛𝜃 (1)
(ND), electron backscatter diffraction (EBSD), Where; n is an integer which represents the
x-ray diffraction (XRD) and selected area order of reflections,
electron diffraction (SAED). Powder x-ray
diffraction is one of the primary analytical The XRD machine generates only intensity
techniques employed in characterizing the plot as a function of 2θ, identification of
crystalline, amorphous and thin film materials. material is based on Bragg’s law and miller
XRD is a unique technique applicable in indices (h k l). Diffraction patterns recorded
determining the crystal structure, crystalline by XRD machine is like a “fingerprint” of
phases, crystalline orientation and other crystalline materials, where it can be compared
structural properties such as crystallite size, with standard patterns for identification of
lattice parameters, strain, stress, energy unknown materials. According to BCC
density, expitaxy, phase composition, research the global market for spectroscopy
preferred orientation, order-disorder equipments were valued at $8.5 billion in 2012
transformation and thermal expansion. It can and is expected to grow at compound annual
be also used to measure the thickness of thin growth rate (CAGR) of 11.7% from 2012 to
films, multi-layers as well as to determine the 2017 [3]. X-ray diffraction is one of the
atomic arrangement of solid materials [1]. prominent spectrometry used for
characterization of crystalline materials. The
In XRD analysis the powder sample is placed market of spectrometry is dominated in North
on a sample holder where a collimated x-ray America followed by Europe, Asia and rest of

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Powder X-Ray Diffraction Gunashekar and Krishna

the world. The global x-ray diffraction width at half maximum or integral breadth
analytical market has been dominated by many (IB)) after correcting with instrument
companies such as Brucker AXS, PANalytic broadening (βhkl) and K is the Scherrer’s
B.V, Thermo Fisher Scientifics, Riguku, constant (0.9). According to Uvarov, K value
AMETEK etc., [4]. Besides, increasing depends upon the type of definition of peak’s
investigation in the fields of solid state width, the crystallite size distribution, the
chemistry, material science, forensic science, crystalline shape and the indexes of diffraction
pharmaceuticals and environmental science line [7]. K value actually varies from 0.62 and
the demand for XRDs are growing further for 2.08, in absence of crystalline shape
research and development of advanced information, it is accepted to use K as 0.89–1.
materials. In current scenario many software The first definition of peak’s breadth used in
packages are developed on the basis of XRD Scherrer’s equation is the full width at half
techniques with ICDD database for profile height of diffraction peak. The second
fitting of diffraction data. The main objective definition of peak’s width is an integral
of this work is to investigate the powder XRD breadth, which is measured as the ratio of total
techniques for identification and quantification area of diffraction peak by the maximum peak
of materials and its current applications. intensity of particular diffraction peak. Ahmad
described that K=1 when an integral breadth
BRIFE DESCRIPTION OF definition is used for calculation of crystallite
TECHNIQUES AND SOFTWARE size [8].
PACKAGES FOR QUANTITATIVE
ANALYSIS OF SAMPLE Williamson-Hall Analysis
XRD analysis techniques and software Williamson-Hall (W-H) analysis is an X-ray
packages are used for full-profile fitting of peak broadening analysis and a simplified
measured diffraction pattern with observed integral breadth method used to calculate the
diffraction pattern. Numerous fundamental crystallite size and lattice strain of crystalline
mathematical functions and softwares are materials. The physical parameters such as
employed in quantitative analysis of strain, stress and energy density of crystalline
crystalline materials. Quantitative analysis materials are calculated by using the W-H
usually involves determination of phase analysis models, viz., uniform deformation
composition, lattice parameters, crystallite size model (UDM), uniform deformation stress
and degree of crystallinity etc., of bulk, nano model (UDSM) and uniform deformation
and thin film materials [5–6]. Among the energy density model (UDEDM) as
available techniques for quantitative analysis represented in Eq. (3)–(5).
𝐾𝜆
of materials are the Scherrer’s equation, 𝛽ℎ𝑘𝑙 𝑐𝑜𝑠𝜃 = + 4𝜀𝑠𝑖𝑛𝜃 (3)
𝐷
Williamson-hall method, Rietveld refinement
method, pseudo-Voigt function, Warren- 𝐾𝜆 𝑠𝑖𝑛𝜃𝜎
𝛽ℎ𝑘𝑙 𝑐𝑜𝑠𝜃 = 𝐷
+4 𝐸ℎ𝑘𝑙
(4)
Averbach analysis, direct comparison method,
absorption-diffraction method and internal
𝐾𝜆 2𝑢 1/2
standard method [7–13]. In this present work 𝛽ℎ𝑘𝑙 𝑐𝑜𝑠𝜃 = + 4 𝑠𝑖𝑛𝜃 (𝐸 ) (5)
three such techniques are explained in brief as 𝐷 ℎ𝑘𝑙

follows: Where; 𝜀 is the lattice strain, 𝜎 is the lattice

Scherrer’s Equation stress, Ehkl is the Young’s modulus in the
The Scherrer’s equation is used to estimate the perpendicular direction to the set of crystal
nano-crystallite size more accurately using lattice planes (hkl) and u is the energy density
XRD. This equation was published by (energy per unit volume). According to Mote,
Scherrer in 1918 for calculation of the the crystallite size obtained from UDM,
crystallite size of nano crystalline bulk UDSM and UDEDM are in good agreement
materials as described in Eq. (2): with the values obtained by Scherrer’s
K×λ equation and TEM analysis [9].
D= (2)
β ×cosθ
Where; D is the crystallite size, λ is the Rietveld Refinement Analysis
wavelength of x-ray beam, θ is the diffraction The Rietveld refinement analysis is a full-
angle, β (in radian) is the peak width (full profile fitting approach employed in

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Research & Reviews: Journal of Physics
Volume 4, Issue 3
ISSN: 2278-2265(online), ISSN: 2347-9973(print)

refinement of crystal structures using XRD solid state materials. Today about 291,440
[11–13]. This method is based on least-squares inorganic, 34,212 mineral and 370,844
refinement fit between step-scan data of inorganic standard diffraction patterns have
calculated XRD pattern and observed XRD been collected and stored in PDF database by
pattern, the refinement procedure is continued ICDD. The above mentioned software
until the best fit is obtained. The least-squares packages allows the application of the
fitting method leads to minimal residual Rietveld refinement method, pseudo-Voigt
quantity Sy described in Eq. (6): functions and fundamental parameters
𝑆𝑦 = ∑𝑖 𝑊𝑖 (𝑦𝑜𝑖 − 𝑦𝑐𝑖 )2 (6) approach (FPA) for full-profile fitting of
th diffraction data. It also makes use of
Where; yoi= observed intensity at i step,
yci= calculated intensity at ith step and Williamson-Hall method and the Scherrer’s
Wi=1/yci. equation for the calculation of crystallite size.

The calculated profile of diffraction pattern CURRENT APPLICATIONS OF

can be described by Eq. (7): POWDER X-RAY DIFFRACTION
𝑦𝑐𝑖 = 𝑆∑𝑘 𝐿𝑘 |𝐹𝑘 |2 𝜙(2𝜃𝑖 − 2𝜃𝑘 )𝑂𝑘 𝐴 + 𝑦𝑏𝑖 (7) Most recent applications of powder x-ray
Where; S is the scale factor, K is the miller diffraction are as follows [13]:
indices (hkl) of diffracted peaks, Lk contains Mineralogy
the polarization, Lorentz and multiplicity Powder XRD is a primary technique used by
factors, 𝜙 is the reflection profile function, Ok mineralogist and geologist to identify minerals
is the preferred orientation function, A is the - in museums, mineral and mining industries
absorption factor, Fk is the structure factor for etc., According to Post, powder XRD is a non-
the Kth Bragg reflection and ybi is the destructive techniques used for quantitative
background intensity at ith step. analysis of birnessite, a manganese oxide with
layer structure present in many soils [14].
The fitting quality of diffraction pattern can be
estimated by using Rwp factor that is measured Space Exploration
by the following Eq. (8): Bish described that recently NASA sent a
∑𝑖−1,𝑛 𝑤𝑖 |𝑦𝑜𝑖 −𝑦𝑐,𝑖 |2 miniaturized XRD instrument to the MARS
𝑅𝑤𝑝 = ∑𝑖=1,𝑛 𝑤𝑖 𝑦𝑜𝑖 2
(8)
planet named as CheMin, which is employed
According to AL-Dhahir, the Rietveld in analyzing the soils and rocks on Mars
refinement has numerous advantages surface and it has sent a diffraction data which
compared with other x-ray diffraction method unravels that the sample contains clay
such as having better accuracy, no need of minerals and amorphous materials [15].
additional internal standards/pure-phase
standards for the Rietveld method Energy Storage Materials
analysis [12]. Powder XRD and the Rietveld refinement
methods are used in investigating MOF74
Computer-Based Expert Systems sorbents which is an efficient solid storage and
The peak indexing and refinement ofcrystal capture materials [16].
structures of diffraction data are carried out
using the commercial/freeware software Pharmaceuticals
packages such as International centre for Powder x-ray diffraction is a prominent
diffraction data (ICDD) in the name of PDF technique used in the field of pharmaceuticals
4+, EVA, PCW, TOPAS, Win-XRD, Crystal in analysis and discovery of drugs. XRD
Diffract, X’Pert High Score, played a major role in discovery of
DAJUST_Software, MAUD, FullProfSuite, Atomoxetine drug used for the treatment of
MATCH Software and Reflex Plus software attention deficit hyperactivity disorder
package etc. The ICDD is a non-profit (ADHD) [17].
scientific institute dedicated in collecting,
editing, publishing and distributing powder Construction
diffraction data in the name of PDF (powder Powder XRD is used to examine the cement-
diffraction file) for quantitative analysis of phases, atomic structures for optimal use in

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Powder X-Ray Diffraction Gunashekar and Krishna

construction. XRD allows for analyzing and CONCLUSION

monitoring the composition of cement during Powder x-ray diffraction is a most significant
production [18]. characterization tool applicable in quick
analysis of single crystal, polycrystalline and
Superconductors amorphous materials. The diffracted pattern
Powder XRD is used to characterize the purity recorded by XRD machine is like a finger-
in the synthesis of superconducting materials. print of atomic structures used for
Many new superconductors such as Hg-based identification and characterization of material.
superconductor materials are developed by the Many software packages and XRD techniques
application of XRD and Rietveld refinement. are available for quantitative analysis of
According to Antipov, power XRD is used in materials.
refinement of Bi2 Sr2 Eu1.3 Ce0.7 Cu2 O10.17
structure [19]. XRD finds many applications in the fields of
solid state chemistry and material science in
Nano-Composites development of advanced materials, it can also
Using XRD, researchers can follow the be ideal with in-situ studies. Thus, x-ray
process involved in manufacturing of diffraction is a powerful technique used to
nanocomposites, determine composition of examine physico-chemical properties of
nanocomponents and can predict the unknown materials. However, XRD
performance of nanocomposites in different techniques need to be developed for analysis
environmental conditions. XRD is used to of mixed-layer clay minerals and pure
determine the interlayer distance and amorphous materials.
intercalation or exfoliation in lattice structure.
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