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Long Term Project Work: Synthesis and Analysis of Nanocrystals
for Thermoelectric and Photovoltaic Applications
Suzanne Christé, Julien Fernandez, Tianhao Zhang and Laura Garcia Gonzalez
April 11, 2016

1

Special Thanks
We would like to thank first Mme Eirini SARIGIANNIDOU and Mme Annie ANTONI-ZDZIOBEK,
for permitting to us working on such an important project during our studies.
Our special thanks go to Mr. Fabio AGNESE, our tutor during this project, for having guided
us all along it, and for having given some precious advices. He let us enter in the laboratory and
discover the environment in which he works, but also manipulate the machines of the laboratory.
We also want to thank Mr. Louis VAURE, for letting us study his work, for having given to us
good recommendations and for having shown us how to synthesize the nanocrystals. In addition,
we would like to thank Mathilde BOUCHARD, who synthesized the nanocrystals of CsPbBr3 that
allowed us to work in very nice conditions.

Abstract
During our project, we have studied two different types of nanocrystals, from their synthesis to
their analysis at the nanometric scale : nanocrystals of CsP bBr3 , and CuF eS2 . The latter were
synthesized at the CEA in Grenoble, and were part of a thesis made by PhD students, whereas the
CsP bBr3 were completely new to study.
The purpose of the project was to get a bit more familiar with nanocrystals, and learn how to
use latest characterization techniques such as TEM, SEM, or STEM. We also did image analysis,
and some identification with crystallographic structure models thanks to particular softwares.

Key words: Nanocrystal, thermoelectric, photovoltaic, semi-conductor, image analysis, characterization

2

Contents
1 Introduction
2 Generalities about semiconductor
2.1 Size effect . . . . . . . . . . . . .
2.2 Elaboration . . . . . . . . . . . .
2.3 Elements involved . . . . . . . . .

4
nanocrystals
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 Transmission Electron Microscopy
3.1 Basics of TEM . . . . . . . . . . . . . . . .
3.2 Resolution . . . . . . . . . . . . . . . . . . .
3.3 Contrast . . . . . . . . . . . . . . . . . . . .
3.4 Operation Details of TEM . . . . . . . . . .
3.4.1 Magnification and Focusing . . . . .
3.4.2 Astigmatism and Aberrations . . . .
3.4.3 Tilting . . . . . . . . . . . . . . . . .
3.4.4 Improvement of Signal-to-noise Ratio
3.5 STEM . . . . . . . . . . . . . . . . . . . . .

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4 CuF eS2 nanocrystals for thermoelectric applications
4.1 Background . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Crystallographic structure of CuF eS2 nanocrystals . .
4.3 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 TEM analysis . . . . . . . . . . . . . . . . . . . . . . .
4.4.1 A1 sample: at 200 o C . . . . . . . . . . . . . .
4.4.2 A5 sample: at 210 o C . . . . . . . . . . . . . .
4.4.3 B1 sample: at 280 o C . . . . . . . . . . . . . .
4.4.4 Comparison and conclusion . . . . . . . . . . .

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5 CsP bBr3 nanocrystals for photovoltaic applications
5.1 Background . . . . . . . . . . . . . . . . . . . . . . .
5.2 TEM analysis . . . . . . . . . . . . . . . . . . . . . .
5.2.1 Size analysis . . . . . . . . . . . . . . . . . . .
5.2.2 Discussion about the shape . . . . . . . . . .
5.2.3 Diffraction pattern analysis . . . . . . . . . .
5.3 STEM analysis . . . . . . . . . . . . . . . . . . . . .
5.4 SEM Analysis . . . . . . . . . . . . . . . . . . . . . .
5.5 Energy Dispersive X-ray Spectroscopy . . . . . . . .

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1

Introduction

Nanocrystals are very special and, as their name suggests, very small crystalline particles with at
least one dimension of the crystal being in the nanometer scale (<100 nm). Colloidal nanocrystals,
which are made with chemical colloidal techniques, have become an important class of materials
with great potential for applications ranging from medicine to electronic and optoelectronic devices,
like for example : bio-tags for gene identification, self-organized smart materials, medical imaging,
or flat-panel displays.
In our project we did not have a look at their physical properties, but we analysed the nanocrystals,
measured their size, and tried to understand their arrangement. For that we used powerful characterization machines such as Transmission Electronic Microscope (TEM) or Scanning Transmission
Electronic Microscope (STEM). These tools allowed us to take many images and try to understand
better how the nanocrystals are disposed, their structure and their size. What was important also,
is to see if the process of synthesizing has an impact on the size and the shape of the crystals. But
the real purpose of our project was to discover a laboratory operating, how researchers work and in
which environment.
In this report, we will detail what we did all along the project, and we will present our work
on the images. We first want to talk about microscopy, especially TEM, and explain how it works,
because it is an essential part of our project. Then we will talk about the nanocrystals we studied,
their properties, and our observations on it. This report is our final work, that we realised in order
to present what we did to a general scientific audience . The main tasks and experiments will be
detailed. However it is also a work we did for ourselves, in order to remind of what we did.

2
2.1

Generalities about semiconductor nanocrystals
Size effect

Nanocrystals have been studied lately for their huge potential of application in optical physics and
electronics. When the nanocrystals reach a size of about 10 nm, they are called "Quantum Dots" :
because of their small size, electrons are confined with discrete levels of energy. The key to understand the power of such nanocrystals is "Quantum confinement". In a bulk crystal, the properties of
the material are independent of the size and are only chemical composition-dependent. As the size of
a crystal decreases to the nanometer regime, the size of the particle begins to modify the properties
of the crystal. The electronic structure is altered from the continuous electronic bands to discrete
or quantized electronic levels. As a result, the continuous optical transitions between the electronic
bands become discrete and the properties of the nanomaterial become size-dependent. When the
size of the nanocrystal is smaller than the Bohr radius of the exciton (elementary excitation state
that occurs in semiconductors) of the corresponding bulk material, the band energy evolves into
discrete energy levels.
As a result of their small size, surface of nanoparticles plays an important role in their fundamental
properties. The surface atoms are chemically more active compared to the bulk atoms because they
usually have fewer adjacent coordinate atoms and unsaturated sites or more dangling bonds. At
4

the same time, the imperfection of the particle surface induces additional electronic states in the
band gap, which act as electron or hole trap centers. At high densities of surface defects, a decrease
in the observed transition energy can be observed due to defect band formation. As the size of
the materials decreases, the surface-to-volume ratio increases and the surface effects become more
apparent and thereby easier to explore. The smaller the nanocrystal, the larger the contribution
made by the surface energy to the overall energy of the system and, thus, the larger the melting
temperature.
This "quantum confinement" will give it particular physical behaviors compared to larger crystals, and are mainly used in semi-conductors, but also in our case, for thermoelectric applications.
The power of such materials is characterized by the thermal conductivity and the electrical conductivity. Thermal conductivity has to be minimized, and electrical conductivity has to be maximized
in order to have a good device. In a bulk material, those factors are 7000 W/[m.K] for the thermal
conductivity and 2500 S/m for the electrical conductivity. Using nanocrystals of CuF eS2 can reduce
the thermal conductivity to 6 W/[m.K]and improve the electrical one up to 20000 S/m.

2.2

Elaboration

Nanoparticles are small and are not thermodynamically stable for crystal growth kinetically. To
finally produce stable nanoparticles, these nanoparticles must be arrested during the reaction either
by adding surface protecting reagents, such as organic ligands, or an inorganic outer layer shell. This
leads to the formation of a "core-shell" nanocrystal. Core-shell nanocrystals are mainly composed,
as their name suggests, of 2 or 3 different material : one inner material (core) and an outer layer
material (shell). These can consist of a wide range of different combinations in close interaction,
including inorganic/inorganic, inorganic/organic, organic/inorganic, and organic/organic materials.
In our case we use a ligand to surround the nanocrystal core. This ligand is here to protect the
nanocrystal from interactions with other particles. It sticks to the nanocrystal core, to form a shell
around it.

Figure 1: Schematic representing the nanocrystal core surrounded by the organic ligand shell
The nanocrystal dispersion is stable if the interaction between the ligand and the solvent is
favorable, providing an energetic barrier to counteract the Van der Waals and magnetic (in case of
magnetic particles) attractions between nanoparticles. And to help this process, different solvents
5

are also used to change the solubility or the reaction rate, thus will be discussed in synthesizing part
of nanocrystals.

2.3

Elements involved

If we interest ourselves to the particular case of semiconductor nanoparticles, we can draw a table of
elements that are often used or involved in the elaboration of such nanocrystals. The recommended
band gap for semiconductor particles is normally greater than that for conductor materials but
less than 4 eV, which are those normally found in insulating materials. In the early years of this
research, pure group XIV (Si, Ge) elements were used as the semiconductor material, whereas later,
compounds of different element groups, such as XIII-XV (GaAs, InP, InAs), XII-XVI (CdSe, CdS,
CdTe), and XI-XVII (CuBr, AgBr), also became popular as semiconductor materials.

Figure 2: Periodic Table of the Elements, where the main semiconductors elements are highlighted
in colors and by pairs

3
3.1

Transmission Electron Microscopy
Basics of TEM

TEM is a powerful electron microscopy technique to study the internal structure of materials. The
microscope is operated at a high voltage, which accelerates the electrons to strike the sample ma6

terial. Generally, the possible interactions of electrons with the sample materials can be scattering,
diffraction, direct transmission, absorption, etc. Among these interactions, the signal of directly
transmitted and diffracted beams are collected for imaging and patterning, which requires the sample
to be thin enough for the electron beams to penetrate. For this technical reason, in our experiment,
we deposited our nanocrystals onto a metallic grid substrate coated by ultra-thin amorphous carbon
(<3nm) [1] (See the illustration below).

Figure 3: Schematic of the metallic grid substrate
Below is a TEM image of our sample deposited on the grid substrate. The white spots are the
nanocrystals deposited onto the grid. The black region represents the coating of amorphous carbon
on the metallic grid in order to eliminate the contribution of grid to the diffraction pattern for our
sample material.

7

Figure 4: TEM Image of the metallic grid
In common practices, the sample is polished by chemical, electrochemical, or ion milling means.
Our tutor showed us the instrument for focused ion beam (FIB) milling. FIB utilizes a highly focused beam with high current density. When the ion beam strikes a specimen, it causes physical
sputtering and material removal. It allows for selective thinning at desired locations by cutting
trenches in the sample.[2]
The electron microscope is, in many aspects, analogous to an optical microscope. The source is
an electron gun instead of a light filament. The lens are magnetic, being composed of a current
carrying coil. Below is a schematic representation of the instrument.

8

Figure 5: TEM Instrument
In addition to imaging, a diffraction pattern can also be obtained by TEM for crystallographic
analysis. The diffraction pattern is formed by the diffraction of electrons from the crystallographic
planes of the sample being investigated. Consider Fig. below,

9

Figure 6: Schematic Drawing of Part of the Transmission Electron Microscope
Here it is assumed that some of the electrons, in passing through the sample, are diffracted by
one of the sets of planes in the sample. In general, only part of the electrons will be diffracted, and
the remainder will pass directly through the sample without being diffracted. These latter electrons
will form a spot at position a and an image of the sample at the plane I2. On the other hand, the
diffracted electrons will enter the objective lens at a slightly different angle and will converge to form
a spot at point b. These beams that pass through point b will also form an image of the specimen
at I2 that is superimposed over that from the direct beam. In the above, it has been assumed that
the crystal is oriented that the electrons are reflected primarily from a single crystallographic plane.
This should cause the formation of a single pronounced spot at point b. It is also possible to have
simultaneous reflections from a number of planes. In this case, instead of a single spot appearing in
I1 at point b, a typical array of spots or a diffraction pattern will form.

A high speed electron beam has an extremely low wavelength, leading to a extremely small
diffraction angle, according to the Bragg’s Equation. Then, we can take θ to approximate sinθ
to simply the Bragg’s Equation: 2θ/λ = 1/d = d∗, where d* is the magnitude of a reciprocal
lattice vector. Then we can use a sphere with a radius 1/λ to geometrically represent the diffraction
condition (see the illustration below). The arc OG corresponding to the diffraction angle θ is 2θx1/λ,
which is exactly equal to 1/d or d∗. As 2θ is very small, the arc OG is approximately equal to the
length of the line OG, or d*.Therefore, we would expect each diffraction plane to correspond to
a reciprocal lattice point located at the surface of the sphere, or what we called Ewald Sphere.
Compared to the X-ray Diffraction, the Ewald Sphere for elctron diffraction is very much bigger[3].

10

Figure 7: Bragg’s Condition: Ewald Sphere
By measuring d*, we can calculate the d values corresponding to each spot present in the diffraction pattern, and then identify the crystal structure of the sample material by comparing the calculated values with the diffraction database.
In real operation, to switch from the imaging mode to the diffraction mode, we focus our beam
to the back focal plane, and insert the diaphragm to acquire the pattern, instead of focusing the
beam to the first image plane, as is shown below [4]:

Figure 8: Image plane and back focal plane

3.2

Resolution

Resolution is one of the most important factors to technically define the quality of the imaging
technique. In electron microscopy, it is roughly defined as the distance of two closest points in
the image that the microscope is able to distinguish [4]. In a diffraction pattern, resolution can
11

be seen as the farthest observable diffraction spot away from the center spot, which represents the
crystallographic plane with the smallest inter-planar spacing that is detectable by electron diffraction.
For simplicity, here we do not consider the effect of astigmatism and aberration, but only consider
the influence of electron wavelength. In this regard, the resolution of a perfect microscope can be
described mathematically by Abbe’s equation [5]:
d=

0.612λ
n × sin α

(1)

Where:
d is the resolution
λ is the wavelength of imaging radiation, here it is the wavelength of electron beams
n is the refractive index of the media between point source and lens, relative to free space
α is half the angle of the cone of light from specimen plane accepted by the objective, n ∗ Sinα
is often expressed as NA (numerical aperture).
By combining some principles of classical physics with the quantum theory, De Broglie proposed
that moving particles have wave-like properties and that their wavelength can be calculated, based
on their mass and energy levels. The general form of the De Broglie equation is as follows:
λ=

h
mv

where:
λ is the wavelength of the particle
h is Plank’s constant
m is the mass of the particle
v is the velocity of the particle
When an electron passes through a potential difference, its energy can be stated as follows:
eV = (1/2)mv 2
where:
eV is energy in electron volts

12

(2)

m is the mass of the particle
v is the velocity of the particle
By using some assumptions about the velocity of the particle and its mass, it is possible to express either wavelength (λ) or velocity (v) in terms of the accelerating voltage (V). By further
substituting the values of h and m above, the equation for λ reduces to the following:
λ=

1.23nm

V

(3)

Equation of Resolution in TEM: This value for λ can then be substituted into Abbe’s
equation. Since angle a is usually very small, for example 0.01 radians (a likely figure for TEM, 1
radian is roughly equal to 57.3 degrees), the value of a approaches that of sinα , so we replace it.
Since n (refractive index) is essentially 1, we eliminate it, and we multiply 0.612 by 12.3 to obtain
0.753. Therefore, the equation reduces to the following:
d=

0.753

α× V

(4)

According to this formula, a higher accelerating voltage produces more energetic electron beam,
and thus provides a better resolution. This is an fundamentally approximated expression that
indicates the voltage-dependence of resolution in TEM technique.

3.3

Contrast

Contrast is another technical criterion to evaluate the performance of a TEM instrument. In a
TEM image, the contrast arises from the fact that the incident electrons interact differently with
the specimen in different regions. More importantly, the real, visible contrast in an image is also
dependant on how the information, from the electron-specimen interaction, is transferred to a final
image. This is defined as Phase Contrast Transfer Function, or CTF, given below [4]:

Figure 9: Contrast Transfer Function
where:
A(u) is the Aperture Function
E(u) is the Envelope Function
X(u) is a function of the aberration of the electron microscope
If one takes into account only spherical aberration to third order and defocus, X(u) can be simply given by:
13

Figure 10: The approximated formula of X(u)
where:
Cs is the quality of objective lens defined by spherical aberration coefficient
λ is the wavelength of incident electrons
δf is the defocus value
u is the spatial frequency
Depending on the defocus, the CTF may oscillate strongly. A typical CTF curve varying with
the spatial frequency u, is given below [6],

Figure 11: A typical CTF curve
At larger spatial frequencies, it is strongly damped mainly due to the effect of chromatic aberration, focus spread and energy instabilities. Since the defocus is variable and can be adjusted at
the microscope, an adequate value can be chosen to optimize the imaging conditions. Other four
important points about the CTF curve are given below [7]:
1. CTF is oscillatory: there are "passbands" where it is not equal to zero (good "transmittance")
and there are "gaps" where it is equal (or very close to) zero (no "transmittance").
2. When CTF is negative, positive phase contrast occurs, meaning that atoms will appear dark
against a bright background.
3. When CTF is positive, negative phase contrast occurs, meaning that atoms will appear bright
against a dark background.

14

4. When CTF is equal to zero, there is no contrast (information transfer) for this spatial frequency.

3.4

Operation Details of TEM

In TEM, an optimal image is never immediately acquired. We need to adjust the working conditions
in order to improve the quality of the images, which can be a long-lasting, trial-and-error procedure.
An introduction to several typical and important operations (mainly for alignment) is made below:
3.4.1

Magnification and Focusing

It’s always interesting to "zoom" the image to observe as more details as possible. Therefore,
magnification is one of the most important operations in TEM technique. To do that, the current of
the magnetic lens is adjusted to control the strength of the lens, thus controlling the magnification.
Consider the following illustration:

Figure 12: Strengthening the lens shortens the focal length f. So a weaker lens (f1) produces a higher
magnification of the object than a stronger lens (f2) since the image distance d1 increases, but the
object distance, d0, is unchanged. [4]
In principle, the larger the strength of the lens is, the less the image is magnified, and vice versa,
assuming the object-to-lens distance d0 is fixed. Alternatively, we can reduce the d0 value to make
the lens closer to the object plane, to magnify the image. In TEM, The specimen height adjustment
is an important operation concept, called "Encentric Height Adjustment" or "Z-adjustment".

15

Everytime we change the magnification, the lens will be out of focus. If the lens strength is increased such that the image is formed above the image plane, the lens will be overfocused, reversely,
if the lens strength is decreased such that the image is formed below the image plane, the lens will
be under focused, as is shown below:

Figure 13: The concept of overfocus in which a strong lens focuses the rays from a point in the
object above the normal image plane where a focused image (B) of the object is usually formed. At
underfocus (C) the lens is weakened and focuses the rays below the image plane. It is clear from (C)
that a given underfocus the convergent rays are more parallel than the equivalent divergent rays at
overfocus (α1 < α2).
The so-called "focusing" operation is simply adjusting the screen to image plane to obtain the
clearest image. Once we are at zero defocus, we are at a reference eucentric height. After that, we
will never move the sample and correct the objective lens to further improve the image quality.
Usually, before we get a final image, we first adjust the Z-height, then set the focus to be zero
to minimize the contrast. After that, we correct the astigmatism of the lens to further improve the
image quality.
3.4.2

Astigmatism and Aberrations

Spherical Aberration
In all microscopy techniques, Spherical Aberration is a common issue arising from the quality of
the lens used. It occurs when the lens field behaves differently for the off-axis beams. Consider the
following figure:

16

Figure 14: Spherical Aberration
The more off-axis beams passing through a spherically aberrated lens are brought to a focus
closer to the lens than the less off-axis beams are. All the electron beams will therefore not reach
the same focal point. These incorrectly focused, more off-axis beams produce a stigma in the image
formed, represented in the above image by a blue disk. To reduce the spherical aberration, an
aperture is introduced to block some periphery electron beams [8], as is illustrated below.

Figure 15: An aperture is used to minimize the spherically aberrated beams
Chromatic Aberration
Another common issue in microscopy is Chromatic Aberration, resulting from the fact that electrons
of different wavelengths passing through the lens are focused at different planes. The low-wavelength,
high-energy electron are less strongly bended by the lens, focused at a plane farther away from the
lens, than those high-wavelength, low energy ones. Below is a schematic illustration:

17

Figure 16: Schematic Illustration of Chromatic Aberration
The difference in electron wavelength or energy is mainly due to the energy loss of a certain
portion of electrons passing through the lens. Generally, the thinner the specimen is prepared, the
more chromatic electrons passing out of the specimen tend to be, and hence the less chromatically
aberrated the lens will be. Another possible reason for the chromatic aberration is because the
electron before striking the specimen is not perfectly monochromatic, depending on how the electrons are produced or the electron source materials. To correct the chromatic aberration, common
methods are increasing accelerating voltage, improving the vacuum condition, preparing a thinner
specimen [8] and using a monochromator.
Astigmatism
As is mentioned before, the electron beams are deflected by the magnetic field generated by the
lens. Astigmatism occurs when electrons feel a non-uniform magnetic field as they spiral around
the zone-axis, which may distort the image formed. This problem arises due to many unavoidable
factors. For example, The soft iron may also have microstructural inhomogeneities which cause
local variations in the magnetic field strength. astigmatism can be easily corrected using stigmators, which are small octupoles that introduce a compensating field to balance the inhomogeneities
causing the astigmatism.
A possible consequence of astigmatism is the distorsion of the diffraction pattern. For example,
astigmatism may cause the ring-like diffraction pattern to be ellipsoidal.

18

3.4.3

Tilting

As is mentioned before, the diffraction angle in TEM is constrained to be extremely small, which
means a set of crystallographic planes need to be nearly parallel to the incident electron beam to
satisfy the Bragg condition. Therefore, in order to improve the diffraction contrast, we can tilt the
sample in two orthogonal directions to make more crystallographic planes well-oriented (parallel)
with respect to the incident beams.
In our case, we have nanocrystals with different orientations in our sample. Therefore, we only
need to search for the well-oriented crystallite to obtain the best diffraction pattern.
3.4.4

Improvement of Signal-to-noise Ratio

In the imaging mode of STEM(See the introduction in the next section), generally the image becomes
more noisy when the contrast is improved. Usually, we can lower the scanning rate to reduce the
signal-to-noise ratio, which refines the image obtained. Presently, many newly developed methods
to improve signal-to-noise ratio, including some image-processing softwares, are widely used.

3.5

STEM

STEM, for Scanning Transmission Electron Microscopy, is a characterization technique which working principle is close to SEM and TEM. An electron gun, a field effect gun more precisely, will emit
an electron beam with an energy between 80 and 300 keV. This electron beam will go through the
sample, as in TEM, but in the STEM, the focused beam will analyse each point step by step, and
we’ll get an image pixel by pixel. The intensity of the image is a function of the square of the atomic
number or the elements composing the sample. If the electron beam in the transmission microscope
is focused to form a probe, and then scanned across the surface of the sample, it is possible to make
a local, small-area analysis of the material, including imaging, diffraction and chemical composition
analysis (EDX). That’s basic working principle for Scanning Transmission Electron Microscopy, or
STEM.
What happens if we don’t pay much attention to the focus and magnification is, knowing that
the electron beam as a very high energy, we can burn the sample if we get too close to the surface.
That is what happened to our sample, and we can see it in this picture :

19

Figure 17: STEM image showing the burning region of the sample
In this picture, we can clearly see a white rectangle on the surface of the sample. This is due to
the beam burning the surface of the sample.

20

CuF eS2 nanocrystals for thermoelectric applications

4
4.1

Background

Recently, nanotechnology has been used in thermoelectric materials, which have the potential to
greatly enhance our current energy production efficiency. Thermoelectric materials rely on the Seebeck and Peltier effects to convert an electric current to a heat gradient, or vice versa. By utilizing
these phenomena, thermoelectric materials can be used to generate electricity from nearly any heat
source, for example an automobile engine, in steam turbine electricity generation, or even direct
geothermal energy.
The very best thermoelectric materials available today (i.e., Bi2 T e3 , BiSbT e3 , P dT e, etc.)
contain either rare or toxic elements that limit their practical application. New sustainable thermoelectric materials must be investigated to elucidate and identify new techniques for optimizing
thermoelectric properties through the material characteristics such as particle size, shape, composition and structure.
Chalcopyrite nanoparticles are composed of copper, iron and sulfur, which is attractive because
of the abundant nature of the constituent elements. Cu-Fe-S system is chosen for its structural
properties, which is proven to be beneficial for good thermoelectric characteristics. This class of
compound shows relatively large carrier mobility, which is beneficial for thermoelectric performance.
[12,13,14,15]

4.2

Crystallographic structure of CuF eS2 nanocrystals

We can create the crystal structure using the TEM-UCA Server created by University of Cadiz,
Spain. [17]. To do so, we need to know the crystal parameters of chalcopyrite CuF eS2 . We can
find such information in the literature. [16] Chalcopyrite has a tetragonal structure with lattice
constants a=b=5.277 Å and c=10.441 Å, and all angles α, β and γ equal to 90 degrees. The space
group is I ¯42d and the atomic coordinates of Cu, Fe and S are respectively (0, 0, 0), (0, 0, 12 ) and
( 41 , 41 , 18 ).
To access the crystal structures, either one can find the structures already saved on a specific
database (the structure we use here has been saved in the CEA database) by entering the “Personal
Servers” or create a new one from the menu in “Global Server”. To find an existing crystal, it requires
a username and password of the server you want to reach (CEA for example) and then to select
“Data” to find the structure in the list. Otherwise, the creation of a new crystal structure is done
by entering the “Global Server” and select “Edit”.
In all cases, there are two different ways to create crystal structures:
• Eje-Z to obtain crystalline structures
• Rhodius to build complex models (cubes, spheres, plans, etc.)

21

Here we create the crystalline structure of chalcopyrite CuF eS2 by using Eje-Z. In the main menu,
we click on “Edit”, then we chose “New phase” on the list and click on “Edit” again to start entering
the structure parameters. First, as displayed in Figure 18, we need to choose a space name: we call
it "CuFeS2", then the space group corresponding to the structure: "122 I-42d" and the number of
atoms present in the space unit: 3. Then we click on “Submit” to go to the next step.

Figure 18: First step for crystal structure creation using Eje-Z on TEM-UCA Server.
Second, we must enter all the crystallographic constants, Wycoff parameters and atoms coordinates found in the literature [16] and click on “Submit”. (Figure 19)

Figure 19: Second step for crystal structure creation using Eje-Z on TEM-UCA Server.
A serie of results is then displayed for the crystallographic structure created in which we can find
the unit cell dimensions, the asymmetric unit, the number of atoms, the metric tensor, the reciprocal
unit cell dimensions, etc. We can also visualize the created structure by clicking on "DATA_mol”.
22

It allows us to visualize the 3D structure of CuF eS2 . In Figure 20, we can observe the 3D view of
the unit cell (left) and the 1x1x1 standard view (right image).

Figure 20: Unit cell structure (left) and Standard view (right) of Chalcopyrite CuF eS2 created on
TEM-UCA server.
The structure created using TEM-UCA server enables to generate a .CIF file that can be opened
by any crystallographic software in order to analyze and model the structure with more details, here
we use the software VESTA. (Figure 21)

Figure 21: Structure of Chalcopyrite CuF eS2 opened with the Software VESTA.

23

4.3

Synthesis

We first observed the synthesis of CuF eS2 nanocrystals. Several routes to synthesized chalcopyrite nanocrystals exist, such as modified polyol method [13] or other general techniques to enhance
thermoelectric properties [14]. Here we describe a general technique for nanocrystals synthesis
called colloidal synthesis, in which we obtain a suspension of spherical nanocrystals in a continuous
medium. For the synthesis of CuF eS2 nanocrystals, the needed reactants are:
• F eCl3 : Iron (Fe) precursor,
• CuCl2 : Copper (Cu) precursor,
• DEDTC Na: Sulfur (S) precursor,
• Dodecaine thiol (DDT): solvent,
• Oleic Acid (OA): solvent.
First, we add the DEDTC Na to the DDT and we mix the solution with a magnetic stir bar.
This way we obtain a suspension containing sulfur.
Second, the two precursors for metals Cu and Fe are weighted and put together in a 3 necks
Berlin flask.
Third we add the OA to the metallic precursors and heat the mixture up to 120 o C. During the
growth of the nanocrystals, the OA will induce the formation of a ligand "membrane" around them
to avoid their agglomeration and allow controlled growth. At this temperature, the sulfur suspension
is added to the mixture in the 3 necks flask and the resulting solution is heated to a temperature
between 200-280 o C typically. The lowest temperature for crystallization of CuF eS2 nanocrystals
is 200 o C. Heating is done by a resistance which surrounds the 3 necks flask, as in the picture we
took during the laboratory session figure (see Figure 22).

Figure 22: Picture of the experimental device during the synthesis of CuF eS2 nanocrystals
24

Heating is performed under vacuum to degas the solvent.At the end of the heating step, argon
is injected to avoid oxidation of the chemical substances of the solution. The mixture rests at
room-temperature and the flask is then put in water to cool down.
Fourth, purification steps are done to remove the impurities, the unreacted substances and side
products. This purification consists in the repetition of the cycle:
• Addition of an anti-solvent which leads to precipitation of the nanocrystals
• Centrifugation: 5 minutes at 12k rps (revolutions per second)
• Remaining liquid, called "supernatant", is discarded
• Addition of a solvent which leads to dispersion
In our case, the solvent and anti-solvent are respectively chloroform and a solution of methanol
and acetone 1-1.
After the purification, a last precipitation and centrifugation can finally be done to collect the
nanocrystals and cold press them. Before that, the ligands can be removed or not, depending on
their nature and the final application. They can indeed have a specific property such as conductivity.
The removal is done by heat treatment or chemically by using acetic acid.
In the case of CuF eS2 nanocrystals, the thermoelectric properties can then be tested. The tested
properties can vary depending on the wanted application. To play on the size, shape, and phase of
the nanocrystals, one can modify the temperature during the synthesis. For CuF eS2 nanocrystals,
the shape at high temperature is more hexagonal and at low temperature, more spherical. Moreover,
the stoichiometry can also be tuned by varying the proportions of the 3 precursors. Three samples
were synthesized at different temperature, namely:
• A1 at 200 o C
• A5 at 210 o C
• B1 at 280 o C
Where A1, A5 and B1 corresponds to the position in the grid storage box.

4.4

TEM analysis

Chalcopyrite nanocrystals can be characterized using TEM. For that, we use the solution obtained at the end of the purification step and perform the last purification cycle using toluene instead
of chloroform. Some of the solution is dropped on a TEM grid and the analysis can be performed
after evaporation of the solvent. The use of toluene is indeed better than chloroform to obtain a
more homogeneous dispersion of the nanocrystals on the grid. This is also good for conservation
purpose because toluene evaporates slowly.

25

4.4.1

A1 sample: at 200 o C

We can observe in Figure 23 that the sample present itself as sticks (left image), in which we can
clearly see the crystal orientation by magnifying on the dark areas (right image).

Figure 23: TEM images of CuF eS2 nanocrystals, A1 sample
At higher magnification and by moving through the sample, we obtain a better area that shows
the crystal orientation (on Figure 24 left image), it allows us to perform the FFT on this area and
obtain the diffraction pattern (right image).
Diffraction
The diffraction pattern obtained seems to corresponds to chalcopyrite. The distance between
dots is approximately 40 (nm) which corresponds to the interplanar distance. The angle between
the center and two of the closer dots is 60 o . This operation using FFT calculation in ImageJ has
been performed on two other images at different positions and gave the same pattern.

Figure 24: TEM image of CuF eS2 nanocrystals, A1 sample (left) with diffraction pattern (top right)
and measurement of angle (bottom right)

26

Size distribution
Using the software ImageJ, one can perform a size distribution analysis on a specific area of the
TEM image (Figure 25, yellow square). A detailed explanation on how to obtain results for particles
size is given in the next section on perovskite nanocrystals. For our chalcopyrite nanocrystals at 200
o C we obtain a final average size of 74.663 nm2 .

Figure 25: TEM image of CuF eS2 nanocrystals, A1 sample with size distribution analysis (top left)
and result for average size (top)
Feret’s Diameter
For many applications not only the particle size but also the shape is of importance. A characteristic distance used to define particle size and shape is the Feret’s diameter. Feret’s diameter is
"the distance between two parallel tangents of the particle at an arbitrary angle". [19]
This distance is deducted from the projected area of the particles using a slide gauge (See figure
26). In practice the minimum xF,min and maximum Feret diameter xF,max , the mean Feret diameter
and the Feret diameters obtained at 90o to direction of the minimum and maximum Feret diameters
xF,max90 are used.

27

Figure 26: Definition of the Feret’s diameter
According to ImageJ user’s guide [9Suzanne], the Feret’s diameter is defined as the longest
distance between any two points along the selection boundary. The angle (0–180 degrees) of the
Feret’s diameter is displayed as FeretAngle, as well as the minimum caliper diameter (MinFeret).
The starting coordinates of the Feret diameter (FeretX and FeretY) are also displayed. On Figure
25, ImageJ results of size distribution can give Feret parameters, among them we can find Feret =
12.063 nm, FeretX = 66.904 nm, FeretY = 60.936 nm, FeretAngle = 101.978 degrees and MinFeret
= 8.229 nm. The one we will use here to compare with the other samples is Feret = 12.063 nm.

28

4.4.2

A5 sample: at 210 o C

In figure 27 (left), we can observe the frame obtained for sample A5 at 210 o C. It is important
to note also that if we do not take enough care while analyzing the sample using TEM, we can burn
the organics from the sample with the beams, that is what gives the dark rings present in Figure 27
(right image).

Figure 27: TEM image of CuF eS2 nanocrystals, A5 sample (left) with dark rings (right)
Diffraction
Unfortunately, no image was good enough to allow us to see the ordered crystal lattice to obtain the FFT diffraction pattern for this sample A5. But we can analyze the size distribution of
nanocrystals thanks to the following images in Figure 28.
Size distribution
Some of the TEM images obtained for this sample are used to perform a size analysis. It is the
case on the following Figures x and x, where the particles sizes were analyzed at 2 different positions
in the image. The resulting average size obtained for the first area is 32.480 nm2 . The particles in
this area (left yellow square on Figure 28) are well dispersed i.e. they seem to have approximately
the same size.

29

Figure 28: Size distribution analysis with ImageJ: initial image(left), counting of particles (right)
and results (up)
The second area (bottom right yellow square on Figure 29) gave an average size of 62.683 nm2 , in
which some particles are clearly significantly bigger than in the rest of the sample, the size dispersion
in this area is not as good as previously due to the presence of the big crystals.

Figure 29: Size distribution analysis with ImageJ: initial image(left), counting of particles (right)
and results (up)

30

4.4.3

B1 sample: at 280 o C

The TEM images for sample B1 at 280 o C show unexpected results because we can notice the
presence of perovskite nanocrystals (small squares) in between the chalcopyrite crystals (See images
on figure 30). This could be due to some contamination during the preparation step, possibly because
a micropipette tip was not changed while we prepared the different samples.

Figure 30: TEM images of CuF eS2 nanocrystals contaminated by perovskites, B1 sample.
Size distribution
We can measure the size of these hexagons using ImageJ, but this time another method than
the automatic one is used to obtain the area and diameter of the 5 particles displayed in Figure 31.

Figure 31: Hexagonal chalcopyrite crystals being measured (from 1 to 5).

31

In Figure 31 we can notice that some hexagons are quite regular (hexagons number 1, 3, 4 and
5) but one has an irregular shape (number 2). Moreover, particles seem to be dispersed in size.
Because some of the hexagons are irregular, we use a triangulation method to obtain the area
of an hexagon. [18] We measure each particular distance (a, b, c, d, e, f, g, h, i, j) of the hexagon
and by measuring the surface of each triangle and adding them together we obtain the total surface
of the hexagon. (See hexagon and distances on Figure 32). We know from the scale on Figure 31
that 180 pixels corresponds to 0.5 µm (or 500 nm), therefore each distance measured with ImageJ
in pixels is converted to nanometers to have the final area in nm2 .

Figure 32: Values of distances and corresponding area for each hexagonal crystal calculated with
triangulation method.
Hexagons number 2 and 5 are big compared to 1, 3 and 4 (more or less twice the size). Also,
we can calculate the approximate value of each hexagon diameter in order to compare it with other
particle sizes like square perovskite nanocrystals for example.

Figure 33: Values of diameters from point to point (A, B, C) and side to side (D, E, F) and mean
diameter obtained for each hexagonal crystal.
The final size of hexagonal crystals of CuF eS2 goes from 171.8 nm to 324.5 nm (twice the size)
with an average size of 249.2 nm. It seems to corresponds to the measured size of perovskite (in
next section). To verify we can look at what is visualized in Figure 30 (left image), on which the
chalcopyrite nanocrystal is approximately 30 times bigger (300 nm) than a randomly chosen perovskite nanocrystal (10 nm).
Diffraction

32

On Figure 34 (left image), despite the contamination by perovskite in the chalcopyrite sample,
we can find areas in which it seems that only the CuF eS2 crystals are present, when the orientation
of atoms is well visible, we obtain a similar diffraction pattern to the one obtained for sample A1.

Figure 34: TEM image of CuF eS2 nanocrystals, B1 sample (left) with diffraction pattern (top right)
and measurement of angle (bottom right).
However, it is hard to be sure that only chalcopyrite crystals are present, in some cases the
superimposition of both nanocrystals can give strange results after FFT calculations, this pattern
do not give any structural information about the sample. (see Figure 35).

33

Figure 35: TEM image of CuF eS2 nanocrystals, B1 sample (left) with diffraction pattern (top right)
and measurement of angle (bottom right).
4.4.4

Comparison and conclusion

The diffraction pattern was analyzed for samples A1 and B1, and they gave similar results (distances
and angles).
The size distribution gave the following the different samples:
• A1: Feret’s diameter = 12.063 nm
• A5: Feret’s diameters = 7.855 nm (first area); 10.179 nm (second area)
• B1: Approximate diameter = 249.2 nm A lot bigger for B1, is it due to temperature ? Did I
make a mistake in the measurement ? Or maybe can’t just compare these values.

34

5
5.1

CsP bBr3 nanocrystals for photovoltaic applications
Background

As explained in the previous sections, colloidal semiconductor nanocrystals are investigated for their
size- and shape-dependent properties. Another major advantage is the possibility to deposit them
as ink to substitute the high cost vacuum-based deposition processes. One of the applications is
the fabrication of thin films for solar cells. In this section, we present and characterize CsP bBr3
nanocrystals which are totally inorganic halide perovskite nanocrystals.
Halide perovskites of the type AM X3 grow in interest in the field of photovoltaics due to their
remarkable power conversion efficiency and their ability to be processed into thin films. The research
explode in 2009 and halide perovskite photovoltaics were implemented in solid state devices by 2012,
reaching a conversion efficiency of about 20%.
The perovskite structure is composed of [M X6 ]4− octahedron sharing corners as illustrated in
figure 36. The elements involved in halide perovskites materials are coloured in the periodic table
of figure 37.

Figure 36: Illustration of the perovskite structure

35

Figure 37: Periodic table with the elements that are involved in halide perovskites put in colour.
The size, shape and charge distribution of the A+ cations are key factors for the stabilization of
the perovskite structure. Moreover, the radii of all the elements are linked in the namesake tolerance
factor introduced by Goldshmidt to characterize the perovskite formation:
rA + rX
t= p
2(rM + rX )

(5)

where rA , rM and rX are the radii of the respective ions in the AM X3 formula.
Several perovskite phases can be observed depending on external factors such as the temperature
or the pressure. Indeed, the structure can vary from the ideal cubic structure Pm-3m with a M-X-M
angle of 180 o C to other phases characterized by the tilting of the octahedra leading to a variation
of the M-X-M angle (cf figure 38).

36

Figure 38: Examples of crystal structures of halide perovskites of undistorted α-phase and distorted
β-phases for the Cs, methylammonium, and formamidinium.
Halide perovskites present a high absorption coefficient and a sharp light absorption edge due
to a direct band gap (cf figure 40). The gap is directly linked to the orbital overlap between the
metals and the halide ions whereas it is only indirectly influenced by the A+ cation through its
structure directing role. A resulting tilt will induce a change of the electronic structure around the
band edges and a modification of the gap. In figure 39 we can see the variation of the gap with the
average distorsion angle depending on the nature of the A+ cation. This experiment has been made
for AP bI3 series.

37

Figure 39: Evolution of the band gap with the average distorsion angle.
Finally, the band gap can be tuned by making solid solutions on the M and X sites but only
if these two are immediate neighbours in the periodic table. The gap will be modified and seems
0
to follow Vegard’s law in the case of a true AM X3−x
Xx solid solution as illustrated in the case of
CH3 N H3 SnI3−x Brx in figure 40. This behaviour is not observed for other compositions.
For a binary solid solution A-B, Vegard’s law is:
a = aA ∗ (1 − x) + aB ∗ x

(6)

where a is the lattice parameter of the solid solution, x is the mole fraction of component B and
aA and aB are the lattice parameters of pure components A and B respectively. For semiconductors,
the band gap is more or less a linear function of the lattice parameter. This is why if the lattice
parameter is evolving following Vegard’s law, the band gap is also following it.

38

Figure 40: Evolution of the energy gap with the fraction of solute in the case of different
CH3 N H3 SnI3−x Brx compounds.
In the case of our sample, we were expecting the Pm-3m cubic structure from previous powder
analysis. Nevertheless, the Pnma orthorhombic structure was also observed by Constantinos C.
Stoumpos and Mercouri G. Kanatzidis from the department of Chemistry of Northwestern University, Evanston in the United States in there article The Renaissance of Halide Perovskites and Their
Evolution as Emerging Semiconductors, published in September 9 2015 as part of the Accounts of
Chemical Research special issue “Lead Halide Perovskites for Solar Energy Conversion”. An illustration of both structures are shown in figures 41 and 42. The unit cells were made using the UCA
Cadiz server and the 3D nanocrystals were made using the software Vesta. Both projections in the


b direction are presented. The tilt in the case of the orthorhombic structure is clearly visible.

Figure 41: Left: illustration of a 3D perovskite nanocrystal in the cubic case made with the software


Vesta. Right: its projection in the b direction.
39

Figure 42: Left: illustration of a 3D perovskite nanocrystal in the orthorhombic case made with the


software Vesta. Right: its projection in the b direction.

5.2
5.2.1

TEM analysis
Size analysis

Figure 43 illustrates a TEM image of the CsP bBr3 nanocrystals. We could observe a tendency of
nanocrystals of the same size to gather. To have an objective idea of the size distribution, we used
ImageJ software. There are different ways of analysing the size of the particles with ImageJ. We
used two different ones that are described below.

40

Figure 43: TEM image of perovskite CsPbBr3 used for size distribution analysis
First method
The first method uses the colour of the pixels composing the image. If we take few particles
of same size and we draw the spectra of pixel’s colour, we can make the difference between the
background and particles and measure their size. The graph below show the repartition of pixel’s
colour in the area selected. The software can analyse the image and give the repartition of the colour
of pixels, black ones having a code of 255 and white ones having a code of 0. The peaks correspond
to darker pixel, and between the peaks is the background with whiter pixels.

Figure 44: Screen capture of the size distribution calculation methode with ImageJ
We can see here that in a row of 5-6 particles, the peaks are well represented and allow us to
41

measure the size of the particles. For that, we measure the width of the peaks and we calculate the
ratio of that width over the total length of the area. In this case the area was 128 pixels long, and
the peaks were approximately 10 percent of that distance. Knowing that 50 nm is 74 pixels, we can
estimate the size of the particles. In this area the particles are from 9 to 10 nanometers long.
In another area of the image, where the particles seemed bigger, we do the same method to
estimate their size.

Figure 45:
In this case the area was 138 pixels long, and the peaks were 15 percent of that distance. We
can estimate here the size of the particles from 15 to 16 nanometers long.
Technique description step-by-step : First, choose the image you want to analyse and open it
with ImageJ. Then, you need to turn the image in a way you can select properly few particles in
a same row. Once you have done it, apply Ctrl+1, Ctrl+2, Ctrl+3. This will read your selection,
and open a new window in which you will be able to find the distribution of the pixel’s color along
the area selected (Fig. 29 and 30). The total horizontal length is always 520 pixel, but corresponds
to the size of your selected area. What you need to do next is to measure the width of each peak
calculate the ratio of this width over the total length (for example in if the width of the first peak
is 67 pixel, we calculate :
67/520 = 0.1288
(7)
This same ratio needs to be multiply by the real length of the selected area you have chosen (use
the scale in the image to find it). Finally you repeat the operation for each peak, and you will be
able to find the size distribution of the nanocrystals in your area. In the Fig.29 for example, the
width of the first peak was 67 pixels, so the ratio is the same that before and gives 0.1288. And
then we multiply by the real length of the selection which is 86 nm. At the end we obtain :
0.1288 × 86 = 11.075 nm

42

(8)

Second method
There is another technique to measure the size of the particles, which is more useful for us
because it allows to determine the average size of the particles in a particular area, and it can clearly
show if the particles arrange themselves by size and shape.
We first open the".dm3" file with imagej. Then, in order to be able to adjust the contrast and
luminosity of the image, we change its type to 16bits for example. This step is shown on figure 46
and 47.

Figure 46: Change of the image type in the software imagej

Figure 47: Adjustments of the brightness and contrast in the software imagej
43

On figure 48 is shown the kind of image we can obtain after playing on contrast and luminosity.
But one should be careful not to play on these too much and then obtain something close to a binary
picture. Indeed this could be a problem for the next step consisting in making a binary with the
tool called "Binary" on figure 49.

Figure 48: Example of an image after adjustments of the brightness and contrast in the software
imagej

44

Figure 49: Binary tool in the software imagej
When making the binary, the particles to analyse can often become white and the environment,
black. In that case, the colors must be invert as shown in figure 50.

Figure 50: Inversion tool in the software imagej
When the binary is made and the particles are black, there is two last adjustments before the
particles analysis. In the case particles seem to be glued together in the binary, they should be
45

separated with the tool "watershed" by going in the folder Process>Binary>Watershed. This is
not working so well sometimes and it is better to select an area to do it instead of doing it for the
entire image. This tool was essential for the size analysis of the chalcoprite nanocrystals in section
4.3 TEM analysis, but did not work in this case with the perovskite nanocrystals. In the case of a
blurred background with small dots, it is possible to make it uniform. This is done with the tool in
found in Process>Filters>mean by playing on a certain radius.
Finally, the geometry of the particles can be analysed and an important parameter to set is the
range size of the particles to be analysed (cf. figure 51). It avoids image j to take into account
some unwanted particles. If "count Masks" is selected in the same window, an analysis as in figure
52 is obtained. Several tables are given including one with a dialing of the particles and there
characteristics. This table allow us to do some modifications. An example is presented where we
deleted a particle that shouldn’t be taken into account. Particles that are too different is size from
the real image should as well be deleted. Another table gives a summary of the calculations including
the average size of the particles analysed. With this average size which is a surface given in nm2
we can deduce the average length of the square size by taking the square root. A last table give the
values obtained for each particle.

Figure 51: Particles analysis tool in the software imagej

46

Figure 52: Example of the results obtained with the particles analysis in the software imagej
In the image below (figure 53), we chose to analyse a particular area where particles seamed
to arrange in a certain size, and we measured the average size of these particles. In this case the
average size is an area of 165.901 nm2 . So if we consider the square root of this value we should get
an approximate value of the size of the nanocrystals. Here, the size would be 12.88 nm.

47

Figure 53: Particles analysis of one self-organised domain
If we take another region of the image (figure 54), where particles look smaller, and we measure
the average size, we get 74.485 nm2 . Here again, by taking the square root of the average area we
get 8.63 nm. In this region particles are much smaller.

Figure 54: Particles analysis of another self-organised domain

48

What is interesting is that we can clearly see that the nanocrystals tend to arrange themselves
in packs of same size. In one region the nanocrystals can be 8 to 9 nanometers long, and in another
region they can be 12 nanometers long, or even bigger. We could say that they do so in order to
gain some surface energy. Indeed, the size dispersion in one domain seems to be very low and the
passage from one domain to another seem to be smooth. This is typical of a system that tends to
diminish its surface energy.
We also found interesting that some crystals were isolated from the others. We decided to have
a look at them, and noticed that they had a particular shape or/and size. They seem to be isolated
because they are uncommon. For irregular shaped nanocrystals, this could be understood by the
short-range property of surface energy. With irregular shape comes a too small surface interaction
and then a force too weak to keep particles in contact. Cubes maximize the contact with other cubes
and the rounder the surface, the less contacts can be made with other cubes. For nanocrystals with
irregular size, we could understand that they can be isolated because they can create holes inside
the structure and thereby increase its energy.
5.2.2

Discussion about the shape

The shape of these nanocrystals should be more like cubes than pallets. Indeed, if these were
platelets, we suppose we should be able to see some arrangements of vertical platelets. It should
appear as rectangles of different sizes in the images we obtain and we only see squares (exception
for the few irregular ones) as is figure 55. A powder diffraction of the nanocrystals and an analyse
of the peaks width in the different directions of space could be done to determine the kind of shape
that is present.

Figure 55: The first drawing on the left is what the shape of the perovskite nanocrystals should
look like in the TEM images if they were platelets. The drawing on the right illustrates the vertical
packing of platelets corresponding to a rectangle from the drawing on the left. The drawing on the
bottom illustrates a packing of horizontal platelets that correspond to a square from the drawing on
the left.
49



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