Received 16 September 2019; Revised 16 September 2019; Accepted 16 September 2019

DOI: xxx/xxxx

MINI-REVIEW

Experimental methods in chemical engineering: X-ray diffraction

spectroscopy—XRD †
Hayat Khan1 | Aditya S. Yerramilli2 | Adrien D’Oliveira1 | Terry L. Alford2 | Daria C.
Boffito*1 | Gregory S. Patience1

1 Chemical Engineering, Polytechnique

Montréal, C.P. 6079, Succ. “CV”, Summary
Montréal, H3C 3A7 Québec, Canada
2 School for Engineering of Matter, Transport X-ray diffraction (XRD) analysis identifies the long-range order (that is, the structure)
and Energy, Arizona State University, of crystalline materials and the short-range order of non-crystalline materials. From
Tempe, 85287-9106 Arizona, USA this information we deduce lattice constants and phases, average grain size, degree of
Correspondence crystallinity, and crystal defects. Advanced XRD provides information about strain,
*Corresponding author D. C. Boffito, texture, crystalline symmetry, and electron density. When radiation impinges upon
Polytechnique Montreal. Email:
daria-camilla.boffito@polymtl.ca a solid, coherent scattering of the radiation by periodically spaced atoms results in
scattered beams that produce spot patterns from single crystalline samples and ring
patterns from polycrystalline samples. The pattern, intensities of the diffraction max-
ima (peaks or lines), and their position (Bragg angle 𝜃 or interplanar spacing 𝑑hkl ),
correlate to a specific crystal structure. In 2016 and 2017 close to 100 000 articles
mention XRD—more than any other analytical technique and it was the top analytical
technique of researchers that publish in Can. J. Chem. Eng. A bibliographic analy-
sis based on the Web of Science groups articles referring to XRD into 5 clusters: the
largest cluster includes research on nanoparticles, thin films, and optical properties;
composites, electro-chemistry, and synthesis are topics of the second largest cluster;
crystal morphology and catalysis are next; photocatalysis and solar cells comprise
the fourth largest cluster; and, waste water is among the topics of the cluster with the
least number of occurrences. Researchers publishing in Can. J. Chem. Eng. focus
most of the XRD analyses to characterize polymers, nanocomposite materials, and
catalysts.

KEYWORDS:
XRD, nanoparticle, crystallinity, Debye-Scherrer method, limit of quantification

1 INTRODUCTION form that reflect its structural physico-chemical characteristics.

According to Hull (1919), [2] “every crystalline substance gives
The Debye and Scherrer method, [1] known as x-ray pow- a pattern; the same substance always gives the same pattern;
der diffraction is a non-destructive, quick qualitative and and in a mixture of substances, each produces its pattern inde-
quantitative analysis of pure and multi-component mixtures pendently of the others.” It identifies crystal structure, degree
that requires minimal sample preparation. When an x-ray of crystallinity, crystallite size and atomic spacing, crystalline
beam impinges upon crystalline material, diffraction patterns phase, transition and their quantitative proportion, microstruc-
ture, quantitative resolution of chemical species, isomorphous

† This
is an example for title footnote.
This article has been accepted for publication and undergone full peer review but has not been
through the copyediting, typesetting, pagination and proofreading process which may lead to
differences between this version and the Version of Record. Please cite this article as doi:
10.1002/cjce.23747
This article is protected by copyright. All rights reserved.
2 Khan ET AL

substitutions, unknown crystalline materials, and solids. [3] X-

ray diffraction patterns are like fingerprints that identify crys-
talline samples by matching the pattern with the Joint Commit-
tee on Powder Diffraction Standards library (JCPDS). [4] Since 2ࣄ

it produces independent patterns of components in mixtures, ࣄ

it is a prevalent analytical technique in forensics, nanomateri- Incident ࣄ
als, catalysis, and geochemical materials. In 2016 and 2017, 90 beam ࣄ
Crystalline
X-ray
articles in Can. J. Chem. Eng. mention XRD to characterize source
sample

polymers, [5,6] composite materials, [7,8] catalysts, [9,10,11] mem-

branes, [12,13,14] minerals, [15,16] and medicinal drugs, [17] , which
makes it one of the most used spectrometries. FIGURE 1 XRD instrument schematic. An incident x-ray
In the early 20th century, physicists developed single crys- beam shines on the surface and a film or electronic detector
tal x-ray diffraction (SCXRD) to derive crystal and molecular captures the signal as it completes an arc
structures and they were frequently awarded Nobel prizes—
Laue (1914), Bragg and Bragg (1915), Siegbhan (1924),
Debye (1936 - chemistry), and Davisson and Thomson (1937). energy of the incident radiation should be equal to the energy
While nuclear magnetic resonance (NMR), mass spectrometry of the scattered radiation.
(MS), and infrared spectroscopy (IR) are more suited for liq- One of, it not, the simplest of x-ray analyses for powders
uids and gases (and solids in the case of NMR), XRD resolves uses a sealed cathode ray tube. An applied voltage of 10 kV
crystal structure directly (Table 1). to 60 kV across a hot filament accelerates electrons towards a
metal anode (e.g., Cu, Cr, Fe, Co, Mo, or Ag). Electrons decel-
erating produce white or background x-ray radiation. [3] When
2 THEORY the bias is such that an electron removes an electron from a
specific energy level, an electron from a specific high level
Crystalline materials have three dimensional regularity of transitions down to that shell and emits a characteristic x-ray.
atoms that form a crystal structure; based on one of the 14 The emission only occurs if the electron level involved satisfies
Bravais lattices. When a monochromatic X-ray beam impinges the Dipole Selections Rule 9. [4]
onto the surface of a material, the atoms interact with the radi- The binding energies of the electrons involved in the elec-
ation to transmit, refract, scatter, and absorb it. [18,19] Unlike tronic transition define the x-ray wavelength. For example, in
raindrops in the sky that diffract light to form a rainbow, Cu, an electronic transition of an electron from the L3 sub-
diffraction requires coherent scattering of the radiation by the shell to K subshell results in K𝛼1 radiation. The energy of
solid. [4] In this uniqure form of elastic scattering, there is no the emitted radiation is the difference in the binding energies.
change in the energy of the x-ray after scattering. For Cu K𝛼1 radiation, ΔE is the difference in the K-subshell
Coherent scattering of radiation occurs due to the dimen- binding energy (8.98 keV) and L3 binding energy (0.94 keV)
sional regularity of unit cells. The directions of the scattered and equals 8.04 keV. This energy corresponds to a monochro-
beam depend on the interatomic spacing (𝑑hkl ) of the plane matic beam of 0.1541 nm radiation. Typically, the Cu anode
and the radiation wavelength. The intensity of the scattered in a sealed tube emits the Cu K𝛼1 and Cu K𝛼2 and Cu K𝛽. A
beam depends on the orientation of the crystal relative to the monochromator allows only the K𝛼1 to pass. The Soller slits
direction of the incident x-ray and the position of each atom produce a narrow band of wavelengths of collimated x-rays, 𝜆
inside the unit cells. Two ways in which the waveforms over- and directs it to the sample (Figure 1). The sample diffracts the
lap in scattering are the constructive and destructive manner radiation at angles that obeys Bragg’s Law [18] :
resulting in allowed reflections with non-zero intensity and 𝑛𝜆 = 2𝑑 sin 𝜃 (1)
disallowed reflections with minimal intensity. Diffraction cri-
teria require the wavelength of the incident radiation, 𝜆, to be where 𝑛 is an integer (1, 2, 3, 4,. . . ), 𝑑hlk marks the interplanar
smaller than the distance between scattering sites and that the spacing generating the diffraction, and 𝜃 is the x-ray incident
scattering occurs in a coherent manner. Given that the atomic angle.
spacing is in the order of lattice constants (0.2 nm to 0.4 nm), This law accounts for the relationship between the wave-
radiation with a wavelength smaller than 0.2 nm is required to length of the produced electromagnetic radiation to the lattice
meet diffraction criteria. Only x-rays and high energy electrons spacing of the crystalline sample and diffraction angle. The
meet this range of wavelength. For coherent scattering, the radiation diffracts at discrete directions in space and an area

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Khan ET AL 3

TABLE 1 Comparing XRD with other analytical techniques; G= gas, L= liquid, S = solid

Characteristic XRD NMR MS IR

Sample form Crystal L, S G, L, S G, L, S
Destructive No No Yes No
Atomic type measured All Limited All All
Determines configuration Yes indirect No No
Resolves absolute structure Yes indirect No No
Establishes crystal structure Yes No No No
Sample preparation Easy Middle Easy Easy
Data interpretation Direct Indirect Indirect Indirect

() = plane

A (101)
A = anatase
B = brookite

Intensity

A (200)
Crystal R= rutile

A (004)

A (211)
A (105)

A (204)
X-rays

R (121)
B (110)

A (220)

A (215)
A (116)
reflections Fourier e- density Atomic
transform map model
20 25 30 35 40 45 50 55 60 65 70 75 8
2θ (degree)
FIGURE 2 Single crystal XRD reflections. [20] A crystal
diffracts an x-ray beam and a film or electronic detector record
reflections on a 2-D surface. A Fourier transform of the pattern FIGURE 3 XRD diffractogram of TiO2
and intensity of the reflections produces an electron density
map from which we derive an atomic model This approach requires that the component has the essential
absorption coefficient when a standard is unavailable:
detector or film records the reflections as the x-ray source com-
𝑘B 𝐼B
pletes an arc over the sample. The position and intensity of the 𝑋B = = 0.14, brookite (3)
reflection relate to the identity and position of the atoms in the 𝑘A 𝐼A + 𝑘B 𝐼A + 𝐼R
unit cell [21] (Figure 2).
𝐼R
Powder x-ray diffraction has a wider applicability com- 𝑋R = = 0.05, rutile (4)
𝑘A 𝐼A + 𝑘B 𝐼A + 𝐼R
pared to single crystal analysis (SCXRD), but peaks overlap
substantially more in the diffractogram compared to SCXRD Although the peak intensity of the anatase is almost 20× higher
of multicomponent samples, which obscures the position and than rutile, its mass fraction is only 6× higher. The peak inten-
intensities of the diffraction maxima (Figure 3). [22,23] In pow- sities correlate with composition, the peak position identifies
der diffraction XRD, a large number of individual crystallites the phase, unit cell parameters, group spacing, stress-strain
intercept the incident x-rays and the individual beams of inten- analysis, and crystal system. The software completes the find
sity become cones; the detector individual spots generate rings and match procedure and identifies crystallographic planes—
of varying intensity. We compare the peak intensity and d- ((101), for example). The peak width (FWHM: full width
spacing against the JCPDS library to identify crystals. at half maximum) correlates with crystal size, lattice distor-
The mass fraction of each phase, 𝑋𝑖 , in the mixture is based tion, and structural dislocation. The Williamson-Hill plot of
on the Zhang and Benfield equation that considers the peak 𝛽 cos 𝜃∕𝜆 versus sin 𝜃 gives a straight line with the slope equal
intensity, 𝐼𝑖 , and a coefficient derived for each component, 𝑘𝑖 to 𝜂∕𝜆 and the intercept is 1∕𝑑p :
(𝑘A = 0.884, 𝑘B = 2.721, 𝑘R = 1) [24] : 𝛽 cos 𝜃 1 𝜂 sin 𝜃
= + (5)
𝑘A 𝐼A 𝜆 𝑑p 𝜆
𝑋A = = 0.81, anatase (2)
𝑘A 𝐼A + 𝑘B 𝐼A + 𝐼R where 𝛽 = FWHM (in radians), 𝑑p is the effective crystallite
size, and 𝜂 is the effective strain. We derive the crystallite size

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4 Khan ET AL

TABLE 2 TiO2 crystallographic parameters derived from the x-ray diffractogram (Figure 3). We assign the peak with the highest
intensity 1000 and other peak heights are ratios of this value † Full width at half maximum

Peak Phase 2𝜃 Intensity FWHM†

1 Anatase 25.3 1000 0.4133
2 Rutile 27.4 67 0.3542
3 Brookite 30.8 55 0.4723
4 Anatase 37.7 186 0.2952
5 Anatase 48 288 0.2952
6 Anatase 53.8 191 0.4723
7 Anatase 55 188 0.4132
8 Anatase 62.6 136 0.4723
9 Anatase 68.6 77 0.7084
10 Anatase 70.2 74 0.2362
11 Anatase 74 118 0.3542

from Scherrer’s equation: extremely bright and monochromatic and produces diffrac-
0.9𝜆 tograms with minimal peak overlap. Electrons enter a stor-
𝑑p = (6)
𝛽 cos 𝜃 age ring several kilometers in circumference at high vacuum
The anatase crystallite size (Figure 3) is 20 nm, which is a lit- (10 Torr to 12 Torr) to minimize particle loss by collision
tle smaller than the rutile (23 nm) but larger that the brookite with residual gas atoms. In the storage ring, a magnetic
(17 nm) based on a copper metal target with 𝜆 = 0.154 18 nm. field changes the direction of the high speed electrons so
Under reaction conditions, catalysts calcine and become they emit electromagnetic radiation because of the angular
more crystalline, which increases the 𝑑p and thereby the acceleration—synchrotron radiation (SR)—that ranges from
intensity as the peaks become narrower (Figure 4). [25,26] In from microwaves (𝜆 > 1 m) to hard x-rays (0.05 nm). [30] A
situ XRD measures changes in catalyst and other materials synchrotron beam line incorporates collimating mirrors (col-
structure during synthesis and reaction to identify structural limates the beam in vertical direction into parallel light to
changes associated with phase transition and chemical reac- improve the energy resolution [31] ), slits, focusing mirrors, and
tions Figure 5. Si (111) or germanium (220) double crystal monochroma-
It has become straightforward to follow changes as a func- tors to create tunable monochromatic x-rays and focus the
tion of temperature, pressure, and gaseous environment while beam in a horizontal direction. [32] The characteristics of syn-
maintaining the signal quality throughout the duration of the chrotron radiation that make it suitable for XRD include [33] :
test. [27,28] he following example shows the usefulness of the (a) bright x-rays that are 100× to 1000× more intense than con-
powder diffractometer with a hot stage that allows for in-situ ventional laboratory analyzers; (b) highly collimated beams
heating and controlled ambient. In this case, we anneal a thin to increase resolution; (c) a wide energy spectrum; and (d) a
bilayer of Al (≈ 10 nm) and Ag (≈ 200 nm) that resides on short pulsed time structure. These characteristics yield high
a SiO2 in an oxygen environment (for safety, Ar is the carrier signal/noise ratios and high angular resolution, while minimiz-
gas). ing peak overlap and improving peak positioning (Figure 7).
At the onset of annealing, Al diffuses into the Ag to form Furthermore, the 𝐾𝛼2 and 𝐾𝛽 diffraction peaks are absent.
a solid-solution that changes the lattice constant (Figure 6) At
725 ◦C, the Ag peak gradually shifts to the original direction
but less at 500 ◦C. This confirms that the high temperature 3 APPLICATIONS
anneal accelerates Al diffusion through Ag films. Also, the
(111) peaks are stronger at 725 ◦C than 500 ◦C at all time peri- Researchers apply x-ray diffraction across a wide range of
ods, which confirms that a higher temperature enhances the materials in dozens of scientific fields (Figure 8): metals and
texture of Ag films. [29] alloys, clays and minerals, catalysts, cement, ceramics, plas-
Synchrotron radiation, generated as charged particles accel- tics, composites, corrosion products, fly ash, asbestos, solar
erate in a straight-line path or travelling in a curved path, is cells, films, and semiconductors. Carbon-based materials—
graphene, diamond, carbon nanotubes, carbon nanobuds, car-
bon nanofoams, and activated carbon—are finding application

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Khan ET AL 5

VHP
Spent
Calcined

VPP
Precursor

VPP

VPP
VHP

VHP
VHP

VHP

VHP
*
*

20 22 24 26 28 30 32 34
2 (degrees)

20 30 40 50 60 70 80
2
(degrees)

FIGURE 4 XRD diffractograms of vanadyl hemihydrate (precursor), calcined vanadium pyrophosphate (VPP), and equilibrated
VPP after over 12 000 h of continuous operation at 400 ◦C [25,26]

Al Al
AlOx
SiO2

O2
SiO2

Ag Ag(Al)

FIGURE 5 Al/Ag bilayer on a SiO2 substrate

in sensors, optoelectronics, green adsorbents for pollutants,

and electrochemical catalysts. [3] These novel materials require
electron microscopy (SEM/TEM/EDX) to image local features
FIGURE 6 XRD: Ag (111) peak shifts as a function of anneal
at the nanometric scale and XRD to characterize the bulk char-
time at 725 ◦C and 500 ◦C
acteristics because of its simplicity and reliability. While the
applications in geology, building materials, and textiles exam-
ine strength, texture, and susceptibility to structural cracking, properties are the other frequent keywords in this cluster that
in forensic sciences, chemistry, and biology, researchers exam- includes 34 of the 107 most often cited keywords. Nanocom-
ine the microstructure and determine the stereochemistry to posites and composites figure prominently in the green cluster
evaluate crystallinity and identify phase composition. In phar- that comprises graphene, facile and hydrothermal synthesis,
maceuticals, it identifies polymorphs to design drugs. [35] nanosheets, and battery type applications. Many of the subjects
A bibliometric analysis of the top 10 000 cited articles in in the blue cluster relate to catalysis and include oxidation,
WoS (2016-2107) mentioning XRD grouped research into 5 reduction, crystal structure, and metal organic frameworks.
clusters. [36,37] Nanoparticles is the most cited research topic The blue and green clusters comprise at least 25 keywords,
associated with XRD (red cluster in Figure 9) - 15 % of the arti- while the yellow cluster and magenta cluster have 13 and 9
cles mention this keyword. Thin films, optical, and mechanical keywords, respectively. The major topics in the yellow cluster

This article is protected by copyright. All rights reserved.

6 Khan ET AL

Ϭ͘ϵϰ;ŝϬ͘ϱEĂϬ͘ϱͿdŝKϯͲϬ͘ϬϲĂdŝKϯ;EdϲͿƐŝŶƚĞƌĞĚĐĞƌĂŵŝĐ and includes basic structures, charge transport properties,

and the classes of compounds for applications. [42] The third
ϮϬϬĐ
ŽŶǀĞŶƚŝŽŶĂůyZ
^LJŶĐŚƌŽƚƌŽŶyZ reveiw, "Recent Progress in Electrode Materials for Sodium-
Ion Batteries" has keywords that fall in the green cluster, like
ϭϭϭĐ
lithium ion and energy storage. [43]
Energy & Environmental Science, Chemical Engineering
Journal, and Applied Catalysis B-Environmental published the
most cited articles in the chemical engineering category of
WoS (145 citations in two-years). "Nickel selenide as a high-
ͮ ͮ ͮ ͮ ͮ ͮ
efficiency catalyst for oxygen evolution reaction" belongs to
the green cluster (electrochemistry). [44] The second most cited
1.90 1.95 2.00 Ě͕ Å 2.20 2.25 2.30

chemical engineering article (141 citations) also belongs to the

FIGURE 7 Synchrotron XRD diffractograms of sintered
green cluster, as it considers electrochemical storage for super-
BNBT6 bulk ceramic compared with conventional XRD: con-
capacitors: "Advanced electrochemical energy storage super-
ventional Cu-cathode x-ray tube (step 0.05 2𝜃 and 5 s counting
capacitors based on the flexible carbon fiber fabric-coated with
time) and synchrotron radiation at MCX beamline Elettra Sin-
uniform coral-like MnO2 structured electrodes." [45] Solar cells
crotrone, Trieste (step 0.005 2𝜃 and 2 s counting time). Peaks
(red cluster) and waste water (magenta cluster) are the focus
are at least 10 % narrower with the synchrotron XRD [34]
of the third and fourth most cited articles: "Structural and
optical properties of methylammonium lead iodide across the
relate to photocatalysis and the environment, which includes tetragonal to cubic phase transition: implications for perovskite
TiO2 , degradation, and water. The subjects in the magenta solar cells" [46] and "In situ synthesis of In2S3@MIL-125(Ti)
cluster deal with waste water, adsorption, aqueous solutions, core-shell microparticle for the removal of tetracycline from
and activated carbon. WoS assigns the journals that publish wastewater by integrated adsorption and visible-light-driven
most of these articles to categories related to chemistry: 3051 photocatalysis," [47] respectively.
articles in physical chemistry, 2881 in multidisciplinary mate-
rials science, 1497 in multidisciplinary chemistry, 1225 in
applied physics, and 1214 in chemical engineering. These cat- 4 UNCERTAINTY
egories are among the categories most related to chemical
engineering. [38] 4.1 Limitations
As of 2018, Science Advances, Parasitology Research, An XRD analyzer costs about 150 k$ and operating and main-
Chemical Reviews, and Advanced Energy Materials published tenance costs are low with respect to other comparable ana-
the most cited articles with 680, 262, 218, and 163 cita- lytical instruments. A complete analysis takes from 30 min to
tions, respectively. The top cited article, "Efficient luminescent 90 min. To produce a uniform and smooth surface, which is
solar cells based on tailored mixed-cation perovskites," syn- essential to maximize peak heights and minimize scattering,
thesized a metal halide perovskite photovoltaic cell. [39] This samples are pulverized. Poorly crystalline materials generate
work belongs mostly to the red cluster. The other three arti- weak signals with broad diffraction peaks and a low intensity.
cles are all reviews, which are more often cited than original For composite materials with standard analyzers, the detec-
contributions. [40] tion limit is about 2 %, but the sensitivity in a synchrotron is
The review entitled "Plant-mediated biosynthesis of much better because of the greater precision of the beamline
nanoparticles as an emerging tool against mosquitoes of med- and higher energy.
ical and veterinary importance: A review" also belongs to the
red cluster, as it describes how effective Ag nanoparticles are
as ovicides, larvicides, pupicides, adulticides, and oviposition 4.2 Sources of error
deterrents. [41] It mentions UV/vis spectroscopy, scanning The major contributions to error of the peak analyses relate to
electron microscopy, transmission electron microscopy, sample type, instrument operation, and preparation.
energy dispersive x-ray photoelectron spectroscopy, and
Fourier transform infrared spectroscopy to characterize the
4.2.1 Sample related errors
nano-particles. Discotic Liquid Crystals cites 675 articles and
describes advances in liquid crystals applied to anisotropic i Preferred orientation: To identify phases based on peak
organic semiconductors in organic field effect transistors, intensities requires a random orientation of the sam-
organic light emitting diodes, and organic photovoltaic devices ple. Plates and crystallites have a preferred orientation
that introduces a systematic error in peak intensities.

This article is protected by copyright. All rights reserved.

Khan ET AL 7

Glass Polymer Geology

• Measures crystallinity • Degree of orientation • Material analysis and
• Assesses coating crystallinity • Thermal stability identification
• Structure factor analysis • Identifies polymorphism • Degree of crystallinity
• Deformation analysis • Opacity and strength • Particle measurement

Forensic sciences
Corrosion • Trace analysis
• Solids phase composition • Qualitative phase analysis &
• Identifies, quantifies compounds composition
• Recognize samples, diluents &
Pharmaceutical adulterant
XRD • Identification of torn specimens
• Resolves complex structures
• Physicochemical properties analysis
• Identifies drug polymorphism
Microelectronics
• Excipient analysis
• Materials characterization
• Temperature gradient & moisture
• Topography defects and imaging
analysis

Material Science Composite Environment

• Mechanical properties • Shape and intensity • Morphology analysis
• Phase transformation • Phase composition • Clay minerals
• Particle size • Localization • Adsorbent surface area
• Residual stress determination • Fabrication determination • Sediment pollutants

FIGURE 8 XRD applied in 10 fields of science

ŶĂŶŽƐŚĞĞƚƐ
>ŝŝŽŶ

ŝƌƌĂĚŝĂƚŝŽŶ

ƉŚŽƚŽĚĞŐƌĂĚĂƚŝŽŶ
ĨĂďƌŝĐĂƚŝŽŶ
ƉŚŽƚĐĂƚĂůLJƚŝĐ
,Ϯ ĂĐƚŝǀŝƚLJ
ƉƌŽĚƵĐƚŝŽŶ
ĐŽŵƉŽƐŝƚĞƐ
ŐƌĂƉŚĞŶĞŽdžŝĚĞ
ĚĞƉŽƐŝƚŝŽŶ
ĞĨĨŝĐŝĞŶĐLJĨŝůŵƐ
ĐĂƚĂůLJƐƚƐ
ZĂŵĂŶ
ŵĞĐŚĂŶŝƐŵ ƐŽůĂƌ
ĐĞůůƐ

ĐŽŶǀĞƌƐŝŽŶ ŶĂŶŽĐƌLJƐƚĂůƐ

ĚŝĞůĞĐƚƌŝĐ
ƉƌŽƉĞƌƚŝĞƐ
ĂƋ ƐŽů͛Ŷ ŚĞƚĞƌŽŐĞŶĞŽƵƐ
ĐĂƚĂůLJƐƚƐ ĚĞƐŝŐŶ ŵŝĐƌŽƐƚƌƵĐƚƵƌĞ

ĂĐŝĚ ĞŵŝƐƐŝŽŶ

ĞŶĞƌŐLJ
ƚƌĂŶƐĨĞƌ

FIGURE 9 XRD bibliometric map generated by VOSviewer. [36,37] The data base consists of the top 107 keywords of the 10 000
most cited articles in WoS (2016-2017). The size of the circle represents the number of occurrences of the keyword in the 10 000
articles, while related research is grouped into clusters of the same colour. nanoparticles appears in 1493 articles followed by
performance (1054), oxidation (416), degradation (597), and adsorption (659). The least frequent of the top 100 keywords appear
fewer than 130 times: sol gel method (117), supercapacitor (121), heterogeneous catalysts (115), sensitized solar cells (116),
and sorption (126)

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8 Khan ET AL

! "

FIGURE 10 XRD scans (𝜃 − 2𝜃) of Ag on SiO2 and PEN FIGURE 11 XRD data of encapsulated Ag layers annealed at
substrates 625 ◦C and 725 ◦C

Standards are 100 % crystalline to minimize order/dis- (in radians). For a displacement of 𝑠 = 0.15 mm, the
order variability of amorphous materials. [48] Only the peak shift is 0.08◦ at 2𝜃 = 28.4◦ and 𝑅 = 200 mm.
(111) and (200) reflections appear on the Ag thin film Algorithms, which compensate for sample displacement
diffractograms over SiO2 and the polymer substrate PEN errors, require internal calibration standards. Zero back-
(Figure 10). The major reflections of PEN substrates ground sample holders and parallel-beam optics further
appear at 37◦ and 41◦ (Figure10). Relative intensities of minimize displacement errors.
(200) that are normalized to the intensities of the (111) iv Sample transparency error: X-ray penetration depth
peak were calculated for Ag on SiO2 as I200/I111 = 4.69 depends on the specimen mass absorption coefficient,
and PEN as I200/I111 = 13.19. These values indicated 𝜇, and the incident angle of the x-ray beam. Conse-
that Ag on SiO2 has more (111) planes parallel to the sur- quently, diffracted x-rays arrive from different points,
face than Ag on PEN. The full width at half maximum (dotted lines versus solid lines in Figure 12(B)) and
(FWHM) is inversely proportional to the grain size of the introduce peak position errors and peak asymmetry—
thin film. This implies that the average grain size of Ag the most common error for organic and low absorbing
on SiO2 is higher than on PEN (Figure 10, FWHMPEN (low atomic number) specimens. Thin specimens and
= 0.5341◦ and FWHMSiO2 = 0.5092◦ ). parallel beam optics minimize transparency error.
Figure 11 is another example of the preferred orienta-
v Plate sample error: When the entire surface of the flat
tion during sample processing. X-ray diffraction spectra
sample cannot lie on the focusing circle (Figure 12(C))
(𝜃 − 2𝜃) of Ag (100 nm)/Al (30 nm) bi-layers annealed
the peaks are broader and asymmetric (at low 2𝜃 angles).
at 625 ◦C and 725 ◦C in NH4 form an aluminium-
Narrow divergence slits with a shorter beam and parallel
encapsulation layer on the surface. The as-deposited
beam optics reduce this error.
sample shows a strong (111) texture that increases for
the high temperatures anneal at 725 ◦C. vi Counting statistics: Statistical characterization of pow-
ders is best when the particle size is less than 10 µm.
ii Peak shape: Peaks of amorphous materials are typically
Diffractograms of large crystallite sizes and non-random
broad and asymmetrical, which compromises quantify-
orientations lead to peak intensity variations that are
ing how much is present.
incongruent with an ideal powder (measured for many
iii Sample displacement: If the sample moves (dashed line crystallites randomly oriented) and thus are poorly iden-
above green block Figure 12(A)), the diffracted lines tifiable with reference patterns in the Powder Diffraction
miss the detector aperature (solid lines versus dashed File (PDF) database.
lines). As a result, the instrument incorrectly reports the
vii Axial/vertical divergence error: Soller slits, capillary
peak position. The displacement error, 𝑠, is a function of
lenses, and decreasing the vertical opening of the
the 𝜃 and the goniometer radius, 𝑅:
counter slit maximize the diffracted intensity and reduce
2𝑠 cos 𝜃
Δ2𝜃 = − (7) peak assymetric broadening due the divergence of the
𝑅
x-ray beam in the plane with the sample. [49]

This article is protected by copyright. All rights reserved.

Khan ET AL 9

viii Microabsorption: This error stems from differences in interact with materials (clays and zeolite minerals, for
the interactions of each material with the x-ray beam, example) and alter their structure.
volume fractions of the components (large particles not
crystallites), and on die geometrical peculiarities of their
distribution. [50] Complex composites such as cements/- 4.3 Detection limits
concretes, coal combustion by-products (CCBs), and Following the rules of a Poisson distribution, for 𝑁 counts at
geologic materials are among the materials that are 2𝜃 the absolute and relative standard deviation 𝜎 and 𝜎rel are:
susceptible to microabsorption errors. Each material √
absorbs x-ray radiation depending on its linear absorp- 𝜎= 𝑋 (8)
tion coefficient for the particular wavelength (energy). √
For example, CCBs have linear absorption coefficients 𝑋 1
𝜎rel = =√ (9)
ranging from 81 cm−1 for quartz to 1153 cm−1 for mag- 𝑋 𝑋
netite using copper radiation. Grinding and milling to a The limit of detection (LOD) of a particular reflection is:
smaller particle size reduces this error.
𝑋ref lection > 𝑋background > 3𝜎background (10)
For example, measuring an 𝑋max of 10 000 counts, the 𝜎rel =
4.2.2 Instrumental errors 0.01, corresponding to a relative error of 1 %, the counting sta-
i Sample fluorescence: Instrumental error in which inci- tistical error. (Note: Suppose we have a background of 100
dent x-ray radiation excite electrons of certain elements counts and a small hump of 120 counts. This cannot be clas-
(V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga). The excited elec- sified as a reflection for the reason that 3𝜎background = 30 is
tron emits a characteristic x-ray and the detector will obviously higher than 20. The only solution is to increase the
record signals that are close to Cu K𝛼—increasing back- measurement time to improve the peak background ratio.)
ground noise but not position or intensity. Monochro-
mators, 𝛽 filters, energy sensitive detectors, and pulse
4.4 Limit of quantification
height distribution levels (PHD) reduce the fluorescence
contribution to the signal. In the analysis of multiphase samples, an important considera-
tion is the question of the lower limit of quantification (LOQ).
ii Equipment misalignment: The error of the “zero” 2𝜃 What is the smallest amount of a given phase that can be iden-
position, ie, the offset of the instrument, introduces a tified by XRD? The LOQ depends on preferred orientation,
systematic peak position error that is proportional to matrix effect crystal symmetry, peak overlap, and amorphous
2𝜃. [51] The source, sample, and detector must all be content. Generally, the LOQ of a phase must be determined by
perfectly in line at 0◦ 𝜃. a calibration curve.
Practitioners cite a lower limit of 5 %, but this value
4.2.3 Compositional variations errors varies with the composition of the constituents. Catalysts, for
example, are often deposited on high surface area substrates to
i Grinding: Excessive grinding induces changes amor-
minimize the mass of costly metals. To demonstrate the effect
phism, strain, decomposition via local heating, and loss
of the substrate on the LOQ, we prepared five samples of Ru on
of volatile components. Some clays, zeolites, and engi-
TiO2 , activated carbon, and zeolite (ZSM-5). Ruthenium(III)
neered materials are sensitive to low-temperature dam-
chloride (45 % to 55 %) and activated charcoal (DARCO R —
age. Shatter boxes or ball-mills produce a tail’ of very
100 mesh particle size, powder) were purchased from Sigma-
fine particles that broaden the diffraction peaks. Tung-
Aldrich. ZSM-5, ammonium (powder, S.A 400 m2 g−1 , 30:1
sten carbide and other brittle grinding media contam-
mole ratio SiO2 :Al2 O3 ) were obtained from Alfa Aesar. Vena-
inate the sample and introduce additional peaks. Non-
tor forwarded the titanium oxide (TP Hombikat, 100 µm).
percussive techniques, like a mortar and pestle, reduce
We followed a wetness impregnation method in which we
these errors.
first added water to determine the total pore volume. We dis-
ii Irradiation: Incident x-rays can interact with samples solved the ruthenium(III) chloride in the calculated volume.
and change the composition, particularly for organic For a more intimate contact between the active phase and the
compounds. X-rays change the colour or cloud inorganic catalyst, we mixed the liquid and the solid in a rotary evap-
compounds without changing the diffractogram. orator for 3 h at 70 rpm. After increasing the temperature by
5 ◦C every 30 min until 85 ◦C, we decreased the pressure to
iii Environment: Elevated temperatures expand solids,
300 mbar for 2 h to dry the catalyst. A furnace calcined the
inducing stress and strain. Water and other liquids

This article is protected by copyright. All rights reserved.

10 Khan ET AL

(a) Detector (b) Detector

Tube Tube 00 00 00 00 00 00 00
Receiving slits Receiving slits 00 00 00 00 00 00 00
00 00 00 00 00 00 00
00 00 00 00 00 00 00
0000000

00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
(c) 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
Detector Sample
Sample
Tube
Receiving slits
00 00 00 00 00 00
000 000 000 000 000 000
00 00 00 00 00 00
000 000 000 000 000 000
00 00 00 00 00 00
00 00 00 00 00 00
000 000 000 000 000 000
000000

Sample

FIGURE 12 XRD instrument error: A, sample displacement error; B, sample transparency error; and, C, flat sample error

TABLE 3 Ru mass fraction on supports: The second column to see more RuO2 on the surface. The Ru shoulder on the TiO2
summarizes concentration based on the recipe and the third is is more evident for the sample with a mass fraction of 5 %
based on nuclear activation analysis. The last column is the (Figure 14). The surface area of ZSM-5 is 240 m2 g−1 so per-
uncertainty in the nuclear activation. The Ru/AC concentration haps more of the Ru enters the structure. [52] AC is composed
is high since the carbon is undetected. of carbon (graphite) layers of fused hexagons held by weak
van de Waals forces and surface area can exceed 1000 m2 g−1 .
Catalyst Wet deposition Nuclear Δ Interestingly, XRD readily detects the 1.5 % Ru and the peaks
g g−1 , % g g−1 , % g g−1 , % grow for the sample with a mass fraction of 3 % (Figure 15).
At 2𝜃 between 65◦ to 70◦ the two peaks are better resovled at a
Ru/ZSM-5 1.5 1.38 0.06
mass fraction of 3 % compared to 1.5 %. SEM-EDX analysis of
Ru/AC 1.5 32.2 1.3
these samples showed that the RuO2 interacted little with the
Ru /AC 3 46.2 1.8
AC and rather formed large independent crystals. XRD anal-
Ru/TiO2 5 4.76 0.19
ysis alone was incapable of differentiating between a species
Ru/TiO2 1.5 2.01 0.08
deposited on a support and the same species present as a seg-
regated phase in the same sample. SEM-EDX analysis locates
the different phase compositions in a small specimen and is
solid: first it maintained the temperature constant at 120 ◦C for
complementary to XRD.
4 h to remove traces of water followed by a 2.5 ◦C min−1 ramp
to 600 ◦C, then a 4 h hold in air.
To ensure that the Ru remained on the supports after syn- 4.5 Crystallinity
thesis, we measured the concentration with a SLOWPOKE
nuclear reactor (Table 3). Nuclear bombardment detects all ele- Sample crystallinity is the ratio of the total intensities in the
ments from F to higher molar mass (except Pb because of its diffraction pattern, 𝑁net , and the sum of all the measured inten-
very short half life). For this reason, the analysis reports high sities, 𝑁tot , including the amorphous part and air scatter, 𝑁scat .
mass fractions of Ru for the AC samples. Otherwise, agree- The latter must be determined separately (measuring a zero
ment between the expected value based on the recipe agrees background holder) and then subtracted:
with that measured value by nuclear bombardment. 𝛴𝑁net
𝐶 = 100 (11)
The minimum concentration that XRD detects depends on 𝛴𝑁tot − 𝛴𝑁scat
the nature of the support and distribution (Figure 13): a mass The ratio between the pure crystalline phase and the amor-
fraction of 1.5 % RuO2 on ZSM-5 is undetectable, while a phous phase of the sample, 𝐶, depends on the peak position of
slight shoulder is evident at 38◦ on the TiO2 sample. TiO2 has
a very compact tetragonal crystalline structure and we expect

This article is protected by copyright. All rights reserved.

Khan ET AL 11

FIGURE 15 XRD diffractograms of RuO2 on activated car-

bon. The intensity scale is identical to that of Figures 13 and
14

FIGURE 13 XRD diffractograms of 1.5 % RuO2 on activated

carbon, TiO2 , and ZSM-5 supports 5 SAFETY CONSIDERATIONS

XRD instruments are user friendly, however, x-rays are

extremely hazardous so both trained personnel and occasional
users must take the necessary precautions to avoid exposure
to direct and secondary radiation. The effects of exposure to
x-ray radiation are cumulative and cause serious and perma-
nent injury—burns, for example. Frequent users should wear
a dosimetry badge and check it and their blood to confirm that
radiation exposure is negligible. [48]

6 CONCLUSIONS

Availability and accuracy of XRD instrumentation and soft-

ware has improved rapid analysis and characterization of com-
FIGURE 14 XRD diffractograms of RuO2 on TiO2 . The posite materials. However, there remains room to advance
intensity scale is identical to that of Figures 13 and 15 the technology to overcome limitations with respect to time
(analysis under 20 min), low sensitivity for hybrid materials,
each reflection in the mixture. hybrid peaks at high angles, and a common control library
[ ] of simulated diffraction patterns of various nanomaterials.
𝑁(2𝜃) = 𝑚 𝐶 ⋅ 𝑁𝑐 ⋅ (2𝜃) + (1 − 𝐶) ⋅ 𝐼𝑎 ⋅ 2𝜃 (12) Advances in software address some of these limitations to
where 𝑁(2𝜃) is the intensity at (2𝜃) of the actual sample and of derive more from the wealth of information in XRD spec-
both the pure crystalline (𝑐) sample, pure amorphous (𝑎) sam- tra. For example, big data tools could analyze collimated
ple, and the sample mass, 𝑚. The three diffractograms have to nanobeams that resolve crystals at the nanoscale with mil-
be corrected for air scattering by measuring a reference sample. lisecond temporal resolution. Integrating XRD with SEM-
The formula is valid for an amorphous material with the same EDX/TGA/DSC/FTIR/Raman instruments and microreactors
elemental composition and the same density as the crystalline expands its capability providing crystallographic data in situ
materials. that will also address issues in pharmaceuticals and other
industries.

This article is protected by copyright. All rights reserved.

12 Khan ET AL

ACKNOWLEDGEMENTS [18] A. Bunaciu, E. Udristioiu, H. Aboul-Enein, Critical Rev.

Anal. Chem. 2015, 45, 289.
The authors gratefully acknowledge the assistance of Marco
[19] G. S. Patience, Experimental Methods and Instrumenta-
Rigamonti for the XRD diffractorgrams of the VPP and Bren-
tion for Chemical Engineers, 2nd edition, Elsevier B.V.,
dan Patience for collecting the bibliometric data.
Amsterdam, Netherlands 2017.

[20] K. Hasegawa, Rigaku 2012, 28, 14.

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