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Processing and structure of nanoparticlesDutka, Mikhail Vasilievich

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Chapter 3

3Characterization of nanoparticles

Chapter 3 summarizes the various experimental methods that have been

employed during this thesis work so as to characterize nanostructured materials.

The principal technique used is high resolution transmission electron microscopy. It

will be shown that the concepts of resolution in high-resolution transmission

electron microscopy (HRTEM) are still not without pitfalls, and a thorough

understanding of image formation is essential for a sound interpretation. High-

resolution TEM imaging is based on the same principles as introduced by Frits

Zernike for optical microscopy and phase contrast imaging in HRTEM derives

contrast from the phase differences among the different beams scattered by the

specimen, causing addition and subtraction of amplitude from the forward-scattered

beam. However, in reality a HRTEM is not a perfect phase contrast microscope and

electron beams at different angles with the optical axis obtain different phase shifts.

Besides HRTEM this chapter presents a concise introduction to scanning electron

microscopy and to the important issues of image processing and analysis of

nanostructured materials.

3.1 Introduction to electron microscopy

Electron Microscopy in the field of nanostructured materials is devoted to

linking structural observations to functional performance. In turn, the

microstructural features are determined by chemical composition and processing.

Unfortunately a straightforward correlation between structural information obtained

by electron microscopy and properties of nanostructured systems is still hampered

by fundamental and practical reasons. First, defects affecting the properties of

nanostructured systems are in fact not in thermodynamic equilibrium and their

behavior may be very much non-linear. Second, a quantitative evaluation of the

structure-property relationship can be rather difficult because of statistics.

Chapter 3

30

The wave-like characteristics of electrons that are essential for electron

microscopy were first postulated in 1924 by Louis de Broglie (in fact in his PhD

thesis [1] sic!, Nobel Prize in Physics in 1929), with a wavelength far less than

visible light. In the same period Busch revealed that an electromagnetic field might

act as a focusing lens on electrons [2]. Subsequently, the first electron microscope

was constructed in 1932 by Ernst Ruska. For his research, he was awarded, much

too late of course, in 1986 the Nobel Prize in Physics together with Gerd Binnig and

Heinrich Rohrer who invented the scanning tunneling microscope. The electron

microscope opened new horizons to visualize materials structures far below the

resolution reached in light microscopy. The most attractive point is that the

wavelength of electrons is much smaller than atoms and it is at least theoretically

possible to see details well below the atomic level.

However, currently it is impossible to build transmission electron microscopes

with a resolution limited by the electron wavelength, mainly because of

imperfections of the magnetic lenses. In the middle of the 70’s the last century

commercial TEMs became available that were capable of resolving individual

columns of atoms in crystalline materials. High voltage electron microscopes, i.e.

with accelerating voltages between 1 MV and 3 MV have the advantage of shorter

wavelength of the electrons, but a drawback is that also radiation damage increases.

After that period HRTEMs operating with intermediate voltages between 200 kV –

400 kV were designed offering very high resolution close to that achieved

previously in the ranging between 1 and 3 MV.

More recently, developments were seen to reconstruct the exit wave (from a

defocus series) and to improve the directly interpretable resolution to the

information limit. In fact during the last two decades, electron microscopy has

witnessed a number of innovations that enhanced existing approaches of exit wave

reconstruction and introduced qualitatively new techniques. One of the most

important novel technologies is aberration correction. Correction of spherical

aberration sC has been demonstrated by Haider et al. [3]. In the years that followed,

this hexapole corrector was applied to various materials science problems [4-6]. A

quadrupole/octopole corrector was developed and applied by Dellby et al. [7] for

scanning transmission electron microscopy (STEM) mode. Since then, aberration

correction has been used to help solve various material science problems [8-10].

Recently, correction of chromatic aberration has been demonstrated [11] and

successfully applied to improve resolution in energy-filtered TEM (EFTEM) by a

factor of five or so. Furthermore, there has been significant progress in EELS,

resulting in improved energy resolution (monochromator) and a larger field of view

Characterization of nanoparticles

31

for electron-spectroscopic [12] and energy-filtered imaging [13]. For a review

reference is made to [14].

Elastically scattered electrons provide the basics of the image formation in

HRTEM and they are the predominant fraction of the transmitted electrons for small

sample thickness (< 15 nm). In contrast, the thicker the sample the more electrons

become inelastically scattered and this must be prevented as much as possible,

because they contribute mostly to the background intensity of the image. Therefore,

the thinner the specimen (< 15 nm) the better the quality of the HRTEM images. The

inelastic scattered electrons can be removed by inserting an energy filter in the

microscope between specimen and recording device. In the following section on

image formation, only the elastic scattered electrons are considered. The main

technique for detailed examination of the structure of nanoparticles in our work

concerns transmission electron microscopy but also scanning electron microscopy

(SEM) has been employed.

Here we present a concise review of electron microscopy and other

nanoparticle characterization techniques for non-experts, without going into every

detail. This part is based on summaries that were also presented in several reviews

[15,16] and by former PhDs of our MK group, in particular by Bas Groen, Patricia

Carvalho, Wouter Soer, Zhenguo Chen, Sriram Venkatesan, Stefan Mogck and

Sergey Punzhin [17-23].

3.2 Transmission electron microscopy

A schematic picture of a TEM is shown in Figs. 3.1 and 3.2. A transmission

electron microscope consists of an illumination system, specimen stage and imaging

system, analogous to a conventional light microscope. Several textbooks and

reviews have been written on the subject of (high resolution) microscopy, sadly with

different notation conventions. This chapter adopts the notation used in [24,25].

Spence [26] has presented a more in-depth description of imaging in HRTEM

theory. Williams and Carter [27] have written a very inspirational and practical

textbook on general aspects of electron microscopy. In our work two different

transmission electron microscopes were used, a JEOL 4000 EX/II (LaB6, 400 kV)

for atomic structure observations (Fig. 3.3) and a JEOL 2010F (FEG, 200kV) for

EDS analysis (Fig. 3.4). For a textbook on theory behind elastic and inelastic

scattering processes in TEM reference is also made to [28].

Chapter 3

32

Figure 3.1. Cross section of a basic TEM. Figure adapted from Ref. [29].

Characterization of nanoparticles

33

(a) (b)

Figure 3.2. Simplified ray diagram showing the two basic operations modes of the

TEM. (a) Diffraction pattern mode and (b) Imaging mode. Figure adapted from

Ref. [27].

Chapter 3

34

Figure 3.3. Transmission electron microscope JEOL 4000 EX/II (LaB6, 400 kV).

Figure 3.4. Transmission electron microscope JEOL 2010F (FEG, 200kV).

Characterization of nanoparticles

35

3.2.1 Illumination system

Electrons are generated in an electron gun, accelerated towards the anode and

focused at the specimen with condenser lenses. High resolution TEM requires planar

coherent electron waves, since high-resolution micrographs are formed by phase

contrast. For elemental analysis, it is also important to have the possibility to focus

the electron beam within a diameter (FWHM) of the order of 1 nm to determine

chemical compositions in the nanometer range. Several demands must be fulfilled:

high brightness, small source size and little energy spread of the electrons. The

brightness of the beam is an important parameter and is defined as follows

I

BA

=Ω

(3.1)

i.e. the brightness value B is related to the electron current I emitted from the area

A (which also determines the spatial coherency) into the spatial angle Ω . The

conventional way to generate electrons is to use thermionic emission. Any material

that is heated to a high enough temperature will emit electrons when they have

enough energy to overcome the work function. In practice this can only be done with

high melting materials (such as tungsten) or low work function materials like LaB6.

Richardson’s law describes thermionic emission as a function of the work function

W and temperature T

2 expW

J CTkT

= − (3.2)

with the current density J at the tip and C the so-called Richardson-Dushman's

constant depending on the material used for the tip. In electron microscopes tungsten

filaments were most commonly used until the introduction of LaB6. LaB6 sources

have the advantages of a lower operating temperature that reduces the energy spread

of the electrons and increases the brightness.

Another way of extracting electrons from a material is to apply a high electric

field to the emitter that enables the electrons to tunnel through the barrier.

Sharpening the tip may enhance the electric field since the electric field at the apex

of the tip is inversely proportional to the radius of the apex

V

EkR

= , (3.3)

with k a correction factor for the tip geometry (usually around 2). The advantage of

this cold field emitter gun (cold FEG) is that the emission process can be to done at

room temperature, reducing the energy spread of the electrons. The small size of the

emitting area and the shape of the electric field results in a very small (virtual)

Chapter 3

36

source size in the order of nanometers with a brightness that is three orders of

magnitude higher than for thermionic sources. It is thus possible to focus the beam

to a very small probe for chemical analysis at an atomistic level or to fan the beam to

produce a beam with high spatial coherence over a large area of the specimen. The

disadvantages of this type of emitter are the need for (expensive) UHV equipment to

keep the surface clean, the need for extra magnetic shielding around the emitter and

the limited lifetime. For electric fields E > 107 V/cm the electron current density J

can be described according the modified Fowler-Nordheim relation

6 7 3 2

22

1 54 10 6 8 10 /. . ( )exp

( )

v y WJ E

EWt y

− − × × = − ’ (3.4)

where J is the field-emitted current density in A/m2, E is the applied electric field at

the tip, and W is the work function in eV. The functions v and t of the variable

1 243 79 10.y E ϕ−= × depend weakly on the applied electric field and have been

tabulated in literature [30]. In our FEG-TEM it is therefore possible to focus the

beam to a very small probe for chemical analysis at a sub-nanometer range and

produce a beam with high spatial coherence over a large area of the specimen. The

small (virtual) source size reaches values for the brightness in the order of B = 1011

to 1014 Am-2sr-1 with an energy spread of 0.2 – 0.5 eV compared with ~109 Am-2sr-1

and an energy spread of 0.8 – 1 eV for thermionic emission.

Table 3.1. Properties of different electron sources [31].

Parameter Tungsten LaB6 Cold FEG Schottky Heated

FEG

Brightness, A/m2sr (0.3-2)⋅109 (3-20)⋅109 1011-1014 1011-1014 1011-1014

Temperature, K 2500-3000 1400-2000 300 1800 1800

Work function, eV 4.6 2.7 4.6 2.8 4.6

Source size, µm 20-50 10-20 <0.01 <0.01 <0.01

Energy spread, eV 3.0 1.5 0.3 0.8 0.5

Some of these disadvantages of cold FEG emitters can be circumvented by

heating the emitter to moderate temperatures (1500 °C) in the case of a thermally

assisted FEG or by coating the tip with ZrO2 which reduces the work function at

elevated temperatures and keeps the emission stable (Schottky emitter). For thermal

assisted FEGs the work function is often reduced by coating the tip with ZrO2 which

keeps the emission stable (Schottky emitter). This increases the energy spread of the

emitted electrons by about a factor of 2 and some reduction of the temporal

Characterization of nanoparticles

37

coherency compared with cold FEGs. The Schottky emitter is widely used in

commercial FEG-TEMs, because of the stability, lifetime and high intensity.

Table 3.1 gives an overview of the technical data of different electron sources.

Transmission electron microscopes operate generally between 80 kV and

1000 kV meaning that the velocity of the electron includes relativistic effects (with

rest mass and energy, 0m and 0E , respectively. This must be taken into account

applying the De Broglie relationship to calculate the wavelength

1 2

00 0 2

0

2 12

/eE

h m eEm c

λ

− = + . (3.5)

For 400 kV electrons λ = 1.64 pm which is much smaller than the resolution

of any electron microscope because the resolution is limited by aberrations of the

objective lens and not by the wavelength of the electrons. The electron beam is now

focused on the specimen with the condenser lenses and aligned using several

alignment coils. The function of the condenser lens system is to provide a parallel

beam of electrons at the specimen surface. In practice this is not possible and the

beam always possesses a certain kind of convergence when imaging at high

resolution, usually in the range of 1 mrad for LaB6 emitters and 0.1 mrad for FEGs.

3.2.2 Interaction with specimen

After entering the specimen most of the electrons are scattered elastically by

the nuclei of the atoms in the specimen. Some electrons are inelastically scattered by

the electrons in the specimen. Compared to X-ray or neutron diffraction the

interaction of electrons with the specimen is huge and multiple scattering events are

common. For thick specimens at lower resolutions an incoherent particle model can

describe the interaction of the electrons with the specimen. However, with thin

specimens at high resolution this description fails because the wave character of the

electrons is then predominant. The electrons passing the specimen near the nuclei

are somewhat accelerated towards the nuclei causing small, local, reductions in

wavelength, resulting in a small phase change of the electrons. Information about the

specimen structure is therefore transferred to the phase of the electrons [14]. In the

following we take the convention for the wave description in solids which is

commonly used in crystallography. Spence [26] presents an interesting table listing

the differences, mainly in sign, between the Dirac notations and crystallography and

indeed one should be careful and aware of this when comparing different textbooks.

After the (plane) electron wave strikes the specimen a part of the electrons

experience a phase shift. The essential part of image formation in TEM is the

Chapter 3

38

transformation of the phase shift stored in the exit wave into amplitude modulation,

and therefore into visible contrast. With the assumption that the specimen is a pure

phase object the phase shift can be described with the exit plane function:

( )( ) exp ( )ep objectiϕ = − Φr r (3.6)

For sufficiently thin objects the phase of the object wave function can be considered

as weak 1( )objectΦ r ≪ and ( )epϕ r can be approximated to first order:

1( ) ( )ep objectiϕ = − Φr r . ( )objectΦ r is the projected potential distribution in the

materials slice, averaged over the electron beam direction. The technique of

HRTEM has a base in the technique of phase contrast microscopy, introduced by

Zernike [32] for optical microscopy in the physics department of our own university,

the University of Groningen. In 1953 he received the Nobel Prize in Physics for this

invention which made an undisputed immense impact, in particular into bio- and

medical sciences. The principle and very basic problem in any microscopy, both in

optical and electron microscopy, is to derive information about the object we are

interested in. The object is defined by amplitude and phase and to retrieve

information about ( )Φ r from the intensity of the image is a very complex because of

the so-called transfer function that takes ( )epϕ r into ( )imageϕ r . Even in an ideal but

non-existing (because of aberrations in any optical system in practice) microscope

the intensity of the image is exactly equal to the intensity of the object function but

unfortunately phase information is already lost in the intensity.

Zernike had a brilliant and at the same time an utmost simple idea – i.e. most

probably a prerequisite of any Nobel Prize. He realized that if the phase of the

diffracted beam can be shifted over 2/π it is as if the image function has the form

1( )

( )objecti

image objecte iϕ− Φ∝ ≅ − Φr

r and in fact neglecting any transfer function of

the microscope, the weak phase object acts as an amplitude object, i.e. the intensity

observed, i.e. 2

1 2( ) ( )image objectI ϕ= = + Φr r , can be connected to ( )objectΦ r .

High-resolution TEM imaging is based on the same principles. Phase-contrast

imaging derives contrast from the phase differences among the different beams

scattered by the specimen, causing addition and subtraction of amplitude from the

forward-scattered beam. Components of the phase difference come from both the

scattering processes itself and the electron optics of the microscope. Just because of

a fortunate balance between spherical aberration and defocus we can perform high-

resolution TEM with atomic resolution as will be shown in the following.

Characterization of nanoparticles

39

A possibility to visualize the phase contrast in TEM was introduced by

Scherzer. Perfect lenses do not show an amplitude modulation, but imaging

introduces an extra phase shift between the central beam and the beam further away

from the optical axis of the objective lens (deviation from the ideal Gaussian wave

front). Deviations from the ideal Gaussian wave front in lenses are known as

spherical aberration. For particular frequencies the phase contrast of the exit wave

will be nearly at optimum transferred into amplitude contrast. Therefore the

observed contrast in TEM micrographs is mainly controlled by the extra phase shift

of the spherical aberration and the defocus. The influence of the extra phase shift on

the image contrast can be taken into account by multiplying the wave function at the

back focal plane with the function describing the extra phase shift as a function of

the distance from the optical axis. The lenses can be conceived cylindrical

symmetric, and will be represented as a function of the distance of the reciprocal

lattice point to the optical axis ( )1 22 2U u v= + , where u and v are the angular

variables in reciprocal space. The extra phase factor ( )Uχ depends on the spherical

aberration and defocus [26]

2 3 40 5( ) . sU fU C Uχ πλ π λ= ∆ + (3.7)

with f∆ the defocus value and sC the spherical aberration coefficient. The function

that multiplies the exit wave is the so-called transfer function ( )Uξ

( ) ( )exp ( )U E U i Uξ χ = (3.8)

For the final image wave and intensity after the objective lens, assuming a weak

phase object with

21 2

( ) ( ) ( )

( ) ( ) ( ( ) ( )

image ep

image objectI

ϕ ϕ ξ

ϕ ξ

= ⊗

= = + Φ ⊗ ℑ

r r r

r r r r

(3.9)

where ℑ represents the Fourier transform. In fact the Fourier transform of the object

wave function is the electron diffractogram in the back focal plane of the objective

lens. As said before because of a fortunate balance between spherical aberration and

defocus, i.e. with the transfer function ( )ξ r in Eq. 2.9 going close to unity,

information about the object can be obtained from the image. After the

multiplication of Eq. (3.9) with its complex conjugate and neglecting the terms of

second order and higher the image formation results in

11 2( ) ( ) [ ( )sin( ( ))]imageI E U Uχ−= + Φ ⊗ ℑr r (3.10)

Chapter 3

40

Under ideal imaging conditions the wave aberration must be 2/π or 1sin ( )Uχ = for all spatial frequencies U . Therefore sin ( )Uχ is called the contrast transfer

function (CTF). Only the real part is considered since the phase information from

the specimen is converted in intensity information by the phase shift of the objective

lens. In the microscope an aperture is inserted in the back focal plane of the

objective lens, only transmitting beams to a certain angle. This can be represented by

an aperture function ( )AU which is unity for 0U U< and zero outside this radius.

When ( )Uξ is negative the atoms in the specimen would appear as dark spots

against a bright background and vice-versa. For 0( )Uξ = no contrast results. An

ideal behavior of ( )Uξ would be zero at 0U = (very long distances in the

specimen) and 0U U> (frequencies beyond the aperture size) and large and

negative for 00 U U< < .

The contrast of a high-resolution image depends strongly on the microscope

settings and parameters. In practice not all the information in ( )Uξ is visible in the

image. This is caused by electrical instabilities in the microscope causing a spread of

focus because of the chromatic aberration of the objective lens, resulting in damped

higher frequencies. Mechanical instabilities and energy loss due to inelastic

scattering of the electrons by the specimen also contribute to the spread in defocus.

The inelastic scattered electrons contributing to the image can be removed by

inserting an energy filter in the microscope between the objective lens and the image

recording media. Another factor that damps the higher frequencies is the beam

convergence. Since the electron beam has to be focused on a small spot on the

specimen there is some convergence of the beam present. This also affects the

resolution since the specimen is now illuminated from different angles at the same

time.

These effects which affect the resolution can be represented by multiplying

sin ( )Uχ by the damping envelopes Eα and E∆ which represent the damping by

the convergence and spread in defocus respectively

( )

2 2 2 412

22 2 2 2 2

( ) exp

( ) exp ,s

E U U

E U U f C Uα

π λ

π α λ

∆ = − ∆

= − ∆ +

(3.11)

where ∆ is the half-width of a Gaussian spread of focus and α is the semi-angle of

the convergence cone at the specimen surface. The resulting contrast transfer

Characterization of nanoparticles

41

function (CTF) for the microscopes we used are plotted in Fig. 3.5 with the damping

envelopes Eα and E∆ . For higher frequencies the CTF is now damped and

approaching zero. It becomes clear that defining a resolution for the HRTEM is not

obvious.

0 2 4 6 8 10 12

-1.0

-0.5

0.0

0.5

1.0

Eα

E∆

sin(χ(U))

Contr

ast,

a.u

.

Scattering vector, U, nm-1

EαE∆sin(χ(U))

0 2 4 6 8 10 12

-1.0

-0.5

0.0

0.5

1.0

Contr

ast,

a.u

.

Scattering vector, U, nm-1

Eα

E∆

EαE∆sin(χ(U))

Figure 3.5. Contrast transfer functions and damping envelopes of the JEOL 4000

EX/II (top) and JEOL 2010F (bottom) at optimum defocus of 47 and 58 nm,

respectively. The highly coherent electron source used in the 2010F, a FEG, is

apparent from the many oscillations in the CTF of the 2010F.

Chapter 3

42

Several different resolutions can be defined as stated by O’Keefe [33]:

(1) Fringe or lattice resolution. This is related to the highest spatial frequency

present in the image. In thicker crystals second-order or non-linear interference

may cause this. Since the sign of sin ( )Uχ is not known there is in general no

correspondence between the structure and the image. This resolution is limited

by the beam convergence and the spread in defocus.

(2) Information limit resolution. This is related to the highest spatial frequency

that is transferred linearly to the intensity spectrum. These frequencies may fall

in a passband, with blocked lower frequencies. Usually this resolution is almost

equal to the lattice resolution. A definition used is that the information limit is

defined as the frequency where the overall value of the damping envelopes

corresponds to 2e− (e.g. the damping is 5% of the CTF intensity).

(3) Point resolution. This is the definition of the first zero point in the contrast

transfer function, right hand side of the Scherzer band. For higher spatial

frequencies, the image contrast and thus the structure cannot be unambiguously

interpreted. The optimal transmitted phase contrast is defined as a Scherzer

defocus: ( )1 24 3

/

sC λ and the highest transferred frequency is equal to

1 4 3 41 5 /. sC λ− − .

In Fig. 3.5 the CTFs of the JEOL 4000EX and JEOL 2010F at optimum

defocus are plotted with the damping envelopes. The corresponding electrical-

optical properties are listed in Table 3.2.

Table 3.2. Technical data of the used microscopes.

Parameter JEOL 4000EX/II JEOL 2010F

Emission LaB6 (filament)

FEG (Schottky emitter)

Operating voltage, 0E , kV 400 200

Spherical aberration coefficient, sC , mm 0.97 1.0

Spread of defocus, ∆ , nm 7.8 4.0

Beam convergence angle, α , mrad 0.8 0.1

Optimum defocus, f∆ , nm –47 –58

Information limit, nm 0.14 0.11

Point resolution, nm 0.165 0.23

Characterization of nanoparticles

43

For the two microscopes in the MK group with a different illumination system, it is

clearly visible that with the JEOL 2010F a rapid oscillation of the CTF occurs.

These oscillations arise because the spatial coherence is higher for the 2010F (spread

of defocus and in particular beam convergence is smaller) than for the 4000 EX/II.

Correspondingly, the information limit of the JEOL 2010F is better than of the

4000EX/II. For the JEOL 2010F the information limit is a factor 2 higher compared

with the point resolution. For microscopes with higher operating voltages, a FEG

will not significantly increase the information limit, because the higher the voltage

the larger the energy spread of the electrons and the damping envelope is limited by

the spread of defocus, instead of beam convergence. For lower (≤ 200 kV) voltage

TEMs the situation is clearly more favorable and a FEG thus significantly improves

the information limit. With higher voltage instruments the higher acceleration

voltage increases the brightness of the source and the damping envelope is limited

by the spread of defocus. The spherical aberration of the objective lens can be

lowered but generally at the expense of a decrease in tilt capabilities of the

specimen. It is possible to compensate sC by a set of hexapole lenses as suggested

by Scherzer [34] in 1947 but it was only feasible recently due to the complex

technology involved. Haider demonstrated a sC corrected 200 kV FEG microscope

[35] in which sC was set at 0.05 mm to reach an optimum between contrast and

resolution. The point resolution of this microscope was now equal to the information

limit of 0.14 nm. Successful application of this technology would put the limiting

factors of the microscope at the chromatic aberration and mechanical vibrations that

currently limit the resolution around 0.1 nm.

For a correct interpretation of the structure the specimen has to be carefully

aligned along a zone axis, which is done with the help of Kikuchi patterns and an

even distribution of the spot intensities in diffraction. The misalignment of the

crystal is in this way reduced to a fraction of a mrad. Beam tilt has a more severe

influence on the image because the tilted beam enters the objective lens at an angle

causing phase changes in the electron wave front. To correct the beam tilt the

voltage center alignment is used by which the acceleration voltage is varied to find

the center of magnification that is then placed on-axis. This alignment might not be

correct due to misalignments in the imaging system after the objective lens. For a

better correction of the beam-tilt the coma-free alignment procedure is necessary.

This is done by varying the beam tilt between two values in both directions and

optimizing the values until images with opposite beam tilts are similar. This

procedure is only practically feasible with a computer-controlled microscope

Chapter 3

44

equipped with a CCD camera and is not used here; instead, the voltage center

alignment is used which could result in some residual beam tilt.

3.2.3 Quantitative X-ray microanalysis

Quantitative X-ray microanalysis was performed using a JEOL 2010F

analytical transmission electron microscope. Additionally to the operation in the

TEM-mode (parallel incidence of the electron beam) there exists also the possibility

to operate in X-ray energy-dispersive spectrometry (EDS) and nano-beam-

diffraction (NBD) mode. In the NBD-mode the convergences angle α of the beam

incidence is smaller, whereas in the EDS-mode these angles are larger. In the latter

case, the diameter of the electron probe can be reduced to approximately 0.5 nm

(FWHM) and thus enables very localized chemical analysis. The NBD-mode will be

not considered in the present work.

In EDS the inelastic scattered electrons are essential. In general, the highly

accelerated primary electrons are able to remove one of the tightly bound inner-shell

electrons of the atoms in the irradiated sample. This “hole” in the inner-shell will be

filled by an electron from one of the outer-shells of the atom to lower the energy

state of the configuration. After recombination each element emits its specific

characteristic X-rays or an Auger electron. The electron of the incident beam also

interacts with the Coulomb field of the nuclei.

These Coulomb interactions of the electrons with the nuclei lower their

velocity and produce a continuum of Bremsstrahlung in the spectrum. The results is

that the characteristic X-rays of a detected element in the specimen appear as

Gaussian shaped peaks on top of the background of Bremsstrahlung. This

background of the EDS spectrum must be taken into account in quantitative

analysis. In practice we have used a Bruker QUANTAX EDS microanalysis system

for TEM.

A Si(Li)-detector is mounted between the objective pole pieces with a ultra-

thin window in front of it. This has the advantage that X-rays from light elements

down to boron can be detected. The EDS unit in an analytical TEM has three main

parts: the Si(Li)-detector, the processing electronics and the multi-channel analyzer

(MCA) display. After the X-rays penetrate the Si(Li)-detector a charge pulse

proportional to the X-ray energy will be generated that is converted into a voltage.

This signal is subsequently amplified through the field-effect transistor. Finally, a

digitized signal is stored as a function of energy in the MCA. After manual

subtraction of the background from the X-ray dispersive spectra the quantification of

the concentration iC ( ,i A B= ) of elements A and B can be related to the

Characterization of nanoparticles

45

intensities iI in the X-ray spectrum by using the Cliff-Lorimer [29] ratio technique

in the thin-film approximation

A AAB

B B

C Ik

C I= . (3.12)

For the quantification, the Cliff-Lorimer factor ABk is not a unique factor and can

only be compared under identical conditions (same: accelerating voltage, detector

configuration, peak-integration, background-subtraction routine). The ABk factor

can be user-defined or theoretical ABk values are stored in the library of the

quantification software package [36]. With modern quantification software, it is

possible nowadays to obtain an almost fully automated quantification of X-ray

spectra using the MCA system. The intensities AI and BI are measured, their

background is subtracted and they are integrated. For the quantification the Kα -

lines are most suitable, since the L- or M-lines are more difficult due to the

overlapping lines in each family. However, highly energetic Kα -lines (for energies

> 20 keV non-linear effects in the Si(Li)-detector) should be excluded for

quantification in heavy elements and L- or M-lines must be taken into account

instead. The possible overlapping peaks in X-ray spectra must be carefully analyzed.

Poor counting statistics, because of the thin foil can be a further source of error in

particular for detection of low concentrations. A longer acquisition time increases

the count rates (better statistics), but this may have the drawback of higher

contamination and sample drift during the recording of the spectra. Sample drift is

extremely disadvantageous in experiments where spatial resolution is essential.

The correction procedure in bulk microanalysis is often performed with the

ZAF correction; Z for the atomic number, A for absorption of X-rays and F for

fluorescence of X-rays within the specimen. For thin electron-transparent specimen

the correction procedure can be simplified, because the A- and F factors are very

small and only generally the Z-correction is necessary. All acquisitions of the

present work were performed using a double-tilt beryllium specimen holder. The

beryllium holder prevents generation of detectable X-rays from parts of the

specimen holder. A cold finger near the specimen (cooled with liquid nitrogen)

reduces hydrocarbon contamination at the surface of the specimen.

Chapter 3

46

3.2.4 Image recording

At present digital cameras are widely used to acquire high-quality electron-

microscope images. A typical sensor for these cameras is a charge-coupled device

(CCD), which can be manufactured with a broad range of sensing properties and can

be packaged in rugged arrays of 4000x4000 elements or more [37]. The response of

each sensor is proportional to the integral of the photon energy projected onto the

surface of the sensor. A scintillator is positioned directly on the top of CCD chip to

convert the electron image into a light image. It is made either of YAG (yttrium

aluminum garnet) or powdered-phosphor. These materials exhibit some properties

that make it particularly attractive for electron microscopy applications (e.g. high

electron conversion efficiency, good resolution, mechanical ruggedness and long

lifetime).

Important parameters of digital cameras for TEM are: sensitivity, dynamic

range, thermal noise (or dark current), resolution and readout rate [38]. Sensitivity is

the minimum number of detectable electrons. Dynamic range of a camera is usually

defined as the ratio of the brightest point of an image to the darkest point of the same

image. Dark current is due to thermal energy within CCD. Electrons can be freed

from the CCD material itself through thermal excitation and then, trapped in the

CCD well, be indistinguishable from “true” photoelectrons. By cooling the CCD

chip it is possible to reduce significantly the number of “thermal electrons” that give

rise to thermal noise. Resolution is a function of the number of pixels and their size

relative to the projected image. Readout rate is the rate at which data is read from

the sensor chip. Table 3.3 summarizes these parameters for several cameras used

during this project.

Table 3.3. Characteristics of the camera systems used in this thesis.

Microscope JEOL 4000EX/II JEOL 2010F

Camera TVIPS FastScan-F114T Gatan MSC794 Gatan DV300

Sensor type CCD

Format, pixel 1024x1024 1300x1030

Pixel size, µm 14 24 6.7

Frame rate, fps 12 5 3

Scintillator type Polycrystalline Phosphor YAG

Sensor cooling Peltier

Post-magnification 1.4x 25x 0.2x

Characterization of nanoparticles

47

Signal-to-noise ratio is another important parameter of any TEM digital

camera. It can be improved by letting the sensor integrate the input signal over

longer time or by taking multiple images with short exposure time. The latter

approach is more advantageous when sample drift is present. The software can apply

a drift correction by using image cross-correlation and consequent averaging of

obtained multiple images giving much better results compared to ones acquired by

single long exposure method.

As shown in Table 3.3, JEOL 2010F of our MK group has two cameras

installed. Gatan DV300 is mounted in the 35mm port of a TEM column just above

the fluorescent screen. It is mainly used to obtain conventional bright and dark field

images. Special anti-blooming design enables this camera to record diffraction

patterns. The other camera, MSC794, is a part of post-column energy filter called

Gatan Imaging Filter (GIF). It has a post-magnification of 25x and therefore suitable

for obtaining high-resolution TEM images.

A dedicated high-resolution microscope JEOL 4000EX/II at Applied Physics-

Materials Science group has been originally installed only with an option to record

images on a photographic film. Later during the course of this PhD project, a new

camera was installed expanding possibilities of the microscope. TVIPS FastScan-

F114T has fast readout rate, high dynamic range and single-electron sensitivity. In

combination with sophisticated software it brings the microscope performance to a

higher level.

3.3 Scanning electron microscopy

The Scanning Electron Microscopy (SEM) is a type of electron microscope that

study microstructural and morphological features of the sample surface by scanning

it with a high-energy electron beam in a raster scanning pattern. The electrons

interact with the sample matter producing a variety of signals that contain

information about the sample surface topography, composition and other properties.

The first SEM image was obtained by Max Knoll, who in 1935 obtained an

image of silicon steel showing electron channeling contrast [39]. The first true

scanning electron microscope, i.e. with a high magnification by scanning a very

small raster with a demagnified and finely focused electron beam, was produced by

von Ardenne a couple of years later [40]. The instrument was further developed by

Sir Charles Oatley and his postgraduate student Gary Stewart and was first marketed

in 1965 by the Cambridge Instrument Company as the “Stereoscan”.

The signals produced by an SEM include secondary and back-scattered

electrons (SE & BSE), characteristic X-rays, cathodoluminescence (light), specimen

Chapter 3

48

current and transmitted electrons. SE detector is the most common one in SEM. As

shown by the schematic Fig. 3.6, in a FEI /Philips XL-30 FEG-SEM (Field Emission

Gun) of the Applied Physics–Materials Science group electrons are generated by the

field emission gun using a high electrostatic field. They are accelerated with

energies between 1 keV and 30 keV down through the column towards the

specimen. While the magnetic lenses (condenser and objective lenses) focus the

electron beam to a spot with a diameter of approximately 10 nm, the scanning coils

sweep the focused electron beam over the specimen surface. If the microscope is

operated in the backscattered mode, the result is a lateral resolution on the order of

micrometers. The number of back-scattered electrons produced is proportional to the

atomic number of the element bombarded. The result is that material with a high(er)

atomic number produces a brighter image. To capture this information a detector is

required which can either be metal, which is the least effective, but is versatile and

used in environmental scanning electron microscopy (ESEM); semi-conductor,

which is most common or a scintillator/light pipe/photomultiplier, which are the

most efficient.

Figure 3.6. Schematic view of a Scanning Electron Microscopy.

The primary electron current is approximately 10-8 to 10-7A. The large

penetration depth of the high energy electrons will cause the electrons to be trapped

in the material. When studying conducting materials, the electrons will be

transported away from the point of incidence. If the specimen is a non-conducting

Characterization of nanoparticles

49

material, the excess electrons will cause charging of the surface. The electrostatic

charge on the surface deflects the incoming electrons, giving rise to distortion of the

image. To reduce surface charging effects, a conducting layer of metal, with typical

thicknesses 5-10 nm, can be sputtered onto the surface. This layer will transport the

excess electrons, reducing the negative charging effects. An adverse effect of the

sputtered layer is that it may diminish the resolving power of the microscope, since

topographical information is no longer gained from the surface of the material, but

from the sputtered layer. Charging of the surface is not the only factor determining

the resolution of a scanning electron microscope. The width of the electron beam is

also an important factor for the lateral resolution. A narrow electron beam results in

a high resolution. The spot size however, is a function of the accelerating voltage

2 22 2 2 6

20

1 1

2p c s

i Ed C C

B Eλ α α

α

∆ = + + + . (3.13)

The broadening of the spot size is the sum of broadening effects due to several

processes. The first contributor is the beam itself, B is the brightness of the source,

i is the beam current and α its divergence angle. The second part is the

contribution due to diffraction of the electrons of wavelength λ by the size of the

final aperture. The last two parts are the broadening caused by chromatic and

spherical aberrations. Where 0E is the electron energy and E∆ is the energy

spread, sC represents the spherical aberration and cC is the chromatic aberration

coefficient. To achieve the smallest spot size, all contributions should be as small as

possible. Decreasing the accelerating voltage will not only cause the wavelength of

the electrons to increase, but also the chromatic aberration increases as well,

resulting in increasing of the spot size and, as a consequence, a decrease in resolving

power of the microscope.

A field emission gun has a very high brightness B , reducing the contribution

in broadening due to the beam itself. The energy spread E∆ in the electron energies

is also small. Together with the fact that the coefficients sC and cC can be reduced

by optimizing the lenses for low-energy electrons, provides the FEG low voltage

scanning electron microscope with very high resolving power. In this thesis part of

the work is concentrated on silica particles. Since these particles are not electrical

conductive, the XL30-ESEM-FEG SEM in high vacuum and wet modes and FEI

Philips XL30s-FEG with TLD detector were used. All MK scanning electron

microscopes are equipped with field emission guns (FEG).

Chapter 3

50

3.4 Image processing and analysis

Digital image processing and analysis is the computer-aided manipulation with

an image aimed at improving the image quality and extracting useful information

about the objects depicted in the image [41]. Image processing is concerned with

transforming image, i.e. the input of the processing is an image; the output is an

image again. Image enhancement, restoration and segmentation are among the most

common image processing tasks. In image analysis we want to obtain quantitative

data from the images, such as dimensions of nanoparticles, their concentration and

fractal dimension; in this case, input consists of one or more images, whereas the

output contains numeric or symbolic data.

Images acquired by digital camera always contain noise and other artefacts

caused by imperfections in the measurement equipment: gain and offset of

individual elements of any multi-element detector will never be precisely the same.

These variations result from the physical nature of the scintillator and optical

coupling. Noise reduction is usually the first step in image processing methods. In

this thesis, all image processing and analysis methods are applied to TEM

micrographs. Advantage of TEM digital cameras is its ability to correct for gain

variations; they can be measured and cancelled automatically. Therefore this

processing was done during the image acquisition stage by digital camera software.

Figure 3.7 shows an example of a typical TEM image used in this study.

Figure 3.7. TEM image of agglomerates composed of multiple primary particles.

Characterization of nanoparticles

51

For image analysis to produce meaningful results, the spatial calibration must

be known. In our case, the magnification and other acquisition parameters can be

read from the microscope then the spatial calibration of the image can be

determined.

Further processing and analysis was performed with a Matlab software package

and the associated image processing toolbox. It is particularly well-suited for our

aim and enables one to concentrate on the image processing concepts and techniques

while keeping concerns about programming syntax and data management to a

minimum.

The first image processing step done in Matlab is thresholding. It is a basic

point transform which produces a binary image from a grey-scale image by setting

pixel values to 1 or 0 depending on whether they are above or below the threshold

value [42]. This is commonly used to separate or segment a region or object within

the image based upon its pixel values. In its basic operation, thresholding operates

on an image as follows

1

0

, ( , )( , )

,

if I x y thresholdI x y

otherwise

>= (3.14)

Thresholding is a primary operator for the separation of image foreground from

background. An important question is how to select an appropriate and efficient

threshold. Many image processing tasks require full automation, and there is often a

need for a criterion for selecting a threshold automatically. Selection of these criteria

is often based on actual consideration of image histogram. For a review and further

details references are made to [43-47]. However in our case, required precision of

threshold, low object contrast to the background and total number of images to

process, makes it more beneficial to inspect images by human eye and to set an

appropriate threshold manually.

In this work we used a common variation of threshold – double threshold

method. The double threshold method consists in thresholding the input image for

two ranges of grey scale values, one being included in the other [48]. The threshold

for the narrow range is then used as a seed for the reconstruction of the threshold for

the wide range. The resulting binary image is much cleaner than that obtained with a

unique threshold. Moreover, the result is more stable to slight modifications of

threshold values. The double threshold technique is illustrated in Fig 3.8 for

extracting a shape of agglomerate that could not be obtained with a unique

threshold. Sometimes in the literature the double threshold technique is also called

hysteresis threshold [49].

Chapter 3

52

Another image processing method used in this project is area opening. In most

images, intensities of some background pixels might be comparable to or higher

than the intensity of agglomerate. It is also possible that some of agglomerates have

lower contrast to the background. After applying the narrow threshold operation,

those pixels represent some kind of noise in resulting binary image. In this case, the

area opening operation removes all connected components whose area in number of

pixels is smaller than a given threshold value [48]. It is important to eliminate all

incorrectly identified pixels by choosing a proper threshold value; otherwise they

could be erroneously used as seeds during image reconstruction.

Figure. 3.8. Double threshold technique (also called hysteresis threshold). The input

image is thresholded twice: for a narrow and a wide range of intensity values

( )n wT T∈ . The wide threshold is then reconstructed using the narrow threshold as

marker set.

Agglomerates analyzed in this work mostly consist of multiple primary

particles; that makes a projected image contrast rather complex, particularly at

overlap and interface of adjacent primary particles. Apart from this, additional

difficulty concerns the noise which was not removed during previous processing

Characterization of nanoparticles

53

steps. These are the reasons for appearance of holes in a binary image after applying

the double threshold operation. The holes are defined as a set of background

components which are not connected to the image border [48]. For proper projected

area calculation it is required to remove all the holes. This is done by a function

from Matlab image processing toolbox. It uses a morphological reconstruction by

erosion where mask image equals the input image and marker is an image of

constant value having the same border values as the input image.

On majority of examined images some agglomerates extended beyond the edge

of the image. Certainly, they may introduce some bias when performing statistics on

particle measurements. Therefore it is necessary to remove all such objects from

further analysis. Particles where the contrast was too low to accurately separate

particle from background were also removed from evaluation.

The complete image processing procedure is demonstrated in Fig. 3.9. The

original grey-scale image (Fig. 3.9a) was modified using the operations mentioned

earlier and following closely the techniques described in literature [48,50,51]. So, to

summarize, the image processing consists of:

- Narrow thresholding of the original image (Fig. 3.9b).

- Noise removal by area opening of the binary image (Fig. 3.9d).

- Wide thresholding of the original image (Fig. 3.9c).

- The wide threshold reconstruction using the narrow threshold as marker set

(Fig. 3.9e).

- Filling holes in the binary image (Fig. 3.9g).

- Removal of agglomerates connected to the image border and low contrast

particles.

Examination of obtained binary image (Fig. 3.9g) needs to be performed to

verify the correct identification of particle boundaries with manual adjustments

where necessary. Final image after processing is presented in Fig. 3.9f. Identified

border of agglomerate is shown in green. Blue circles with center marks are primary

particles. Their diameter and position with respect to the geometric center of the

agglomerate was manually measured for each object. Agglomerates with

unidentified primary particles were rejected from the analysis.

Further image analysis was done automatically by in-house made Matlab code.

It allows us to determine the projected area of agglomerate, its maximum projected

length L and width W in the direction perpendicular to L . These parameters were

calculated by measuring a set of properties for each connected component (object) in

the binary image. The projected area is simply the actual number of pixels in the

object. But maximum projected length can be measured in different ways. In

principle, it is possible to calculate the distance between each pair of pixels in the

Chapter 3

54

object and find the maximum. This will give the most precise result, although

requires very long computational time, especially for large agglomerates. Another

approach is to use convex hull. By definition a convex hull is the smallest convex

polygon that can contain the object. It is obvious the pair of points that gives

maximum length belong to the convex hull. Practically, this method gives the same

result as calculating the distance between each pair of pixels, but significantly

reduces the number of distances to compute.

a

b c

d e

f g

Narrow threshold Wide threshold

Area opening

Reconstruction(double threshold)

Filling holes

Figure. 3.9. Complete image processing procedure of typical agglomerate including

manual identification of primary particles.

During this thesis work a significant number of images were analyzed for each

experimental condition. As will be shown in the following chapters the electron

microscopy results contribute to the understanding of the kinetics of particle

formation and provides us with the possibility to compare experimental data with

theoretical model developed within this project.

Characterization of nanoparticles

55

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