Characterization Techniques

Why XRD

• Measure the average spacings between layers or rows of atoms

• Determine the orientation of a single crystal or grain

• Find the crystal structure of an unknown material

• Measure the size, and internal stress of small crystalline regions

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 Characterization Techniques

1. XRD

English physicists Sir W.H. Bragg and his son Sir W.L. Bragg developed a relationship in 1913 to explain why the
cleavage faces of crystals appear to reflect X-ray beams at certain angles of incidence (theta, q). The variable d is the
distance between atomic layers in a crystal, and the variable lambda λ is the wavelength of the incident X-ray beam;
n is an integer. This observation is an example of X-ray wave interference commonly known as X-ray diffraction
(XRD), and was direct evidence for the periodic atomic structure of crystals postulated for several centuries.

A.W. Hull 1919 “every crystalline substance gives a pattern; the same substance always gives the same
pattern; and in a mixture of substances, each produces its pattern independently of the others. “

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Production of X-rays
Cross section of sealed-off filament X-ray tube

X-rays are produced whenever high-speed electrons collide with a

metaltarget. A source of electrons – hot W filament, a high accelerating
voltage between the cathode (W) and the anode and a metal target, Cu,
Al, Mo,Mg. The anode is a water-cooled block of Cu containing desired
target metal.
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Automated X-ray Diffractometer

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Basic Features of Typical XRD Experiment

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Detection of Diffracted X-rays by a Diffractometer

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Schematic diagram of XRD

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Bragg’s Law and Diffraction:

How waves reveal the atomic structure of crystals

Diffraction occurs only when Bragg’s Law is satisfied Condition

for constructive interference (X-rays 1 & 2) from planes with
spacing d

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Introduction to X-ray diffraction

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Introduction to X-ray diffraction

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Planes in Crystals-2 dimension

To satisfy Bragg’s Law, θ must change as d

changes e.g., θ decreases as d
increases.

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Scherrer formula
Scherrer (1918) first observed that small crystallite size could give rise to
peak broadening. He derived a well-known equation for relating the
crystallite size to the peak width, which is called the Scherrer formula:

t = Kλ/(β cosθ)
where K is the shape factor, λ is the x-ray wavelength, β is the line
broadening at half the maximum intensity (FWHM) radians, and θ is the
bragg angle. τ is the mean size of the ordered (crystalline) domains,
which may be smaller or equal to the grain size
XRD Crystallite Size Calculator using Scherer Formula

λ =1.542 A0

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FWHM (Full width half maximum)

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JCDPS Card Characterization Techniques

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Seven Crystal Systems

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Miller indices= hkl

(i) c
6- 8
2- 4

4 12

-
-
1
Reciprocals Reciprocals =0

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Several Atomic Planes and Their d-spacings in

a Simple Cubic

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Several Atomic Planes and Their d-spacings in

a Simple Cubic

Planes with different Miller indices in cubic crystals

Crystallographic features of cubic systems, such as vectors and

atomic plane families can be described using a three-value
Miller index notation
The l, m and n directional indices are separated by 90 degrees, and are thus orthogonal. In
fact, the l component is mutually perpendicular to the m and n indices.

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 Characterization Techniques

Several Atomic Planes and Their d-spacings in

a Simple Cubic
c
.b a

Planes with different Miller indices in cubic crystals

Crystallographic features of cubic systems, such as vectors and

atomic plane families can be described using a three-value
Miller index notation
The l, m and n directional indices are separated by 90 degrees, and are thus orthogonal. In
fact, the l component is mutually perpendicular to the m and n indices.

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Several Atomic Planes and Their d-spacings in

a Simple Cubic

(ii) (iii)

. .

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Indexing of Planes and Directions

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XRD pattern of ZnO

Miller indices: The peak is due to Xray

diffraction from the {101} planes.

Nanoparticles
Materials letters 61 2007, 4094-4096
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Fig. 2 XRD results of (a) bare GaN and (b) single-crystalline rutileTiO2 nanorods array on GaN.

J. Mater. Chem., 2012, 22, 3916-3921

Characterization Techniques

Fig. 5 XRD patterns of the SnO2 samples prepared using precursor solutions with
different pH values (fixed at T = 190 °C, t = 48 h): (a) standard data file of a
SnO2 crystal, (b) pH = 5, (c) pH = 7–8 and (d) pH = 12.

CrystEngComm, 2015, 17, 2030-2040

 Characterization Techniques

• Non-destructive, fast, easy sample prep

• High accuracy for d-spacing calculations

• Can be done in-situ

• Single crystal, poly, and amorphous materials

• Standards are available for thousands of material systems

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 Characterization Techniques

The powder diffractometers typically use the

Bragg-Brentano geometry

Detector
X-ray
tube

ω θ 2
θ

• The incident angle, ω , is defined between the X-ray source and the sample.
• The diffracted angle, 2θ , is defined between the incident beam and the detector angle.
• The incident angle ω is always ½ of the detector angle 2θ .
• In a θ :2θ instrument (e.g. Rigaku RU300), the tube is fixed, the sample rotates at θ °/min and the detector
rotates at 2θ °/min.
• In a θ :θ instrument (e.g. PANalytical X’Pert Pro), the sample is fixed and the tube rotates at a rate -θ °/min and
the detector rotates at a rate of θ °/min. 12
 Characterization Techniques
A single crystal specimen in a Bragg-Brentano diffractometer
would produce only one family of peaks in the diffraction
pattern.

2
θ

The (110) planes would diffract at 29.3

At 20.6 °2θ , Bragg’s law °2θ ; however, they are not properly The (200) planes are parallel to the (100)
fulfilled for the (100) planes, aligned to produce a diffraction peak planes. Therefore, they also diffract for this
producing a diffraction peak. (the perpendicular to those planes does crystal. Since d200 is ½ d100, they appear at
not bisect the incident and diffracted 42 °2θ . 13
beams). Only background is observed.
 Characterization Techniques
A polycrystalline sample should contain thousands of crystallites.
Therefore, all possible diffraction peaks should be observed.

2θ 2θ 2θ

• For every set of planes, there will be a small percentage of crystallites that are properly
oriented to diffract (the plane perpendicular bisects the incident and diffracted beams).
• Basic assumptions of powder diffraction are that for every set of planes there is an equal
number of crystallites that will diffract and that there is a statistically relevant number of
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crystallites, not just one or two.
 https://www.mdpi.com/2076-3417/11/2/526

X-ray diffraction (XRD) spectra of the platinum-based powder (A), sintered material (B) and mixture (1:1 by weight) of
the platinum-based powder with ZnO powder, used as a crystalline internal standard (C). The spectra were acquired by
using Cu Kα radiation. The lines corresponding to Al2O3 observed in the spectrum of the sintered material are due to
the contribution of alumina substrate, used for the deposition of the formulated ink.
https://www.sciencedirect.com/science/article/pii/S223878542031454X?via%3Dihub

Fig. 1 shows the XRD pattern of flower-like CeO2/TiO2 heterostructure.

First, all the observed black labeled diffraction peaks in the XRD pattern
can well correspond to the anatase TiO2 structure (JCPDS Card #21-
1272). The XRD pattern shows diffraction peaks on the (1 0 1), (0 0 4),
(2 0 0), (1 0 5), (2 2 0), and (2 1 5) crystal surfaces of TiO2 in the
heterostructure, and the crystallinity of (1 0 1) crystal surface is high.
Second, the red mark in the XRD shows obvious diffraction peaks on
the (1 1 1), (2 0 0), (2 2 0), (2 2 2), (3 3 1), and (4 2 0) crystal surfaces of
CeO2 in the heterostructure. Among them, all the red mark diffraction
peaks observed in the XRD can well correspond to the pure cubic
structure of CeO2 (JCPDS Card #34-0394). At the same time, the
diffraction peaks of other species were not detected in the pattern,
indicating the successful preparation of the CeO2/TiO2 heterostructure.
Fan et al. [16] reported that the crystallinity of
CeO2/TiO2 heterostructure is lower than that of single-phase TiO2,
which may be attributed to the lattice distortion caused by the
difference of lattice parameters between CeO2 and TiO2 crystal.
Moreover, the peak of CeO2 in Fig. 1 is not as sharp and high as that of
TiO2, indicating that the crystallinity of CeO2 is not as good as that of
TiO2, thus supporting the research results of Meng et al. [16].
https://pubs.rsc.org/en/content/articlelanding/2018/RA/C8RA03015D

Crystal structures of the synthesized CSF-160 were investigated by XRD,

and the phase and purity of the product were determined from the
results, as shown in Fig. 1. From the XRD pattern, the main peaks of
Fe3O4 were observed at 2θ values of 29.85°, 35.59°, 43.10°, 52.83°,
57.02° and 63.04° corresponding to (220), (311), (400), (422), (511) and
(440) Bragg reflections, respectively. Furthermore, these diffraction peaks
matched well with those of the standard XRD pattern of Fe3O4 with cubic
spinel structure (PDF#89-4319). This result indicated that the crystallinity
of Fe3O4 remained unchanged after the introduction of CuS. In addition, the
remaining diffraction peaks located at 29.01°, 30.69°, 32.75°, 48.03°,
53.15° and 59.41° were due to (102), (103), (006), (110), (108) and (116)
planes, which could be well indexed to the pure hexagonal phase of CuS
(PDF#06-0464). The (220) plane of Fe3O4 was very close to the (103) plane
of CuS; thus, the two peaks overlapped and could not be easily
distinguished. Since no other clear impurity peaks appeared, it was
concluded that CSF-160 has good crystallinity.
 mdpi.com/2073-4344/9/4/379

The X-ray diffraction (XRD) patterns of as-prepared samples are

displayed in Figure 1. The black curve is the XRD pattern of the
pure MoS2. The diffraction peaks located at around 14.4°, 32.7°,
33.5°, 35.7°, 39.6°, 44.2°, 49.8°, 58.4°, and 60.4°, which can be
assigned to (002), (100), (101), (102), (103), (006), (105), (110),
and (112) planes, respectively, of the hexagonal structure of
MoS2 crystalline (JCPDS file no. 87-2416). For the MoS2/CdS
nanocomposites, some new peaks were observed at 24.8°, 26.5°,
28.2°, 43.7°, 47.9°, and 51.9°, which can be assigned to (100),
(002), (101), (110), (103), and (112) planes, respectively, of CdS
(JCPDS file no. 70-2553). Further, these peaks were also shown
in the pure CdS sample. No diffraction peaks of other
impurities were detected, which indicates the high purity of
the samples.
 https://pubs.rsc.org/en/content/articlelanding/2016/RA/C6RA05968F

To obtain the structural information and phase identification, the X-

ray diffraction (XRD) measurements were conducted. A series of peaks
appeared the XRD pattern of α-Fe2O3/Fe3O4 heterostructured
nanoparticles (Fig. 2) could be ascribed to crystal planes of α-
Fe2O3 (PDF card no. 33-0664, including (012), (024), (104), (110),
(113), (116), (119), (214) and (300)) and Fe3O4 (PDF card no. 19-
0629, including (012), (220), (222), (311), (400), (422), (440) and
(511)), respectively. The phase ratio of α-Fe2O3 : Fe3O4 in
heterostructure nanoparticles was 57 : 43, which was calculated base
on XRD results. In addition, compared with the pure Fe3O4 and α-
Fe2O3, the diffraction peaks were sharp and intense, the results
indicated that the nanocomposites were high purity and good
crystallinity with a mixture of two phases, i.e., Fe3O4 and α-Fe2O3.
https://link.springer.com/article/10.1007/s10853-019-03466-z
 *
NiFe-LDH/BiVO4
* * * * * * * * *
* CoFe-LDH/BiVO4
Intensity (a.u)

* * * * * * * * *
*
NiCo-LDH/BiVO4
* * * * * * * * *
* BiVO4
* * * * * * * * *
Bi2O3
+ + + +

10 20 30 40 50 60 70
2θ / degree