Jackson S.D., Hargreaves J.S.J. Metal Oxide Catalysis

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Figure 10.3 Three examples of electron microscopic images

showing different formation mechanisms of image contrast,

(a) mass – thickness contrast; (b) diffraction contrast and

the principles of the contrast formation.

10.2 HRTEM and Related Techniques 447

448 10 Transmission Electron Microscopy

is no intensity ( I = A

) variation in the exit wave, and a minimum contrast image

is observed when the exit wave is properly imaged at the in - focus condition. The

image contrast due to the phase change is called phase contrast, which can be

increased by defocusing.

Unlike optical microscopy or electron microscopy at low magniﬁ cation, where

mass – thickness contrast (absorption/amplitude contrast) plays an important role,

HRTEM image interpretation uses phase contrast and needs a full understanding

of the beam – specimen interaction and the effects of lens errors. Figure 10.3 c is a

HRTEM image of YSrCo

[9] . The black spots correspond to atomic columns.

This can be altered by changing the phase of the electron wave using a change in

the lens focus value. Therefore, the black spots can be changed into white spots

or vice versa. The phase - contrast image has three important differences from the

amplitude - contrast image. (1) An amplitude - contrast image is focused on the ideal

image plane, the so - called Gaussian image plane. For a phase - object image at the

Gaussian image plane, if there is no lens error, the image wave function is a copy

of the exit wave, so that the image intensity is uniformly unity. In order to obtain

phase contrast, HRTEM images must be taken at a plane away from the Gaussian

image plane. (2) The nature of phase contrast is the interfering effect of waves

scattered by individual atoms. Therefore, the incident electron wave must be

coherent. (3) The least distinguishable distance criterion is no longer valid in

phase - contrast images.

10.2.5

Resolution of TEM

The overall resolution in HRTEM is governed partly by the electron wavelength

and partly by the optical characteristics of the objective lens. The most important

effect of the latter arises from spherical aberration. This aberration introduces a

phase difference into the individual diffracted beams and when the real image is

synthesized by the lens from these diffracted beams this can give rise to consider-

able confusion in the image contrast.

Figure 10.4 shows two rays emanating from the point Q, one along the

optic axis and another at a scattering angle α (generally of the order of 10 millira-

dians). If the lens is perfect, these two rays should intersect at a point P. If spherical

aberration is present, the non - axial ray would reach the Gaussian image plane at

the point P ′ with an amount ∆ r from the optic axis, where ∆ r is the radius of

the disk of least confusion. The total phase shift introduced from the spherical

aberration is:

()

(

)

where C

is coefﬁ cient of spherical aberration.

Increasing the focal length by an amount ∆ F causes a non - axial ray to be brought

to the optic axis further from the specimen. The phase difference between axial

and non - axial rays is:

()

∆

The phase shifts from spherical aberration and defocus have opposite signs.

Consequently, owing to the imperfection of the lens and an introduced defocus

value, electrons scattered through a scattering angle α have their phase altered by

a factor exp(i χ ), where χ is deﬁ ned by:

χα

αα

()

=−

(

)

∆FC

which is Scherzer ’ s equation, derived in 1949 [4] .

By differentiating the Scherzer equation, an interpretable resolution limit

can be derived,

rAC=

at the Scherzer focus

∆FBC=− λ

, where A and B are

positive constants [10] . Therefore, reducing either C

or λ may lead to an increase

of the resolution of TEM. For example, for a microscope operating at 200 kV ( λ =

0.002 51 nm) with C

= 0.41 mm and Scherzer focus ∆ F = − 380 nm, the resolution

limit, r , is 0.18 nm. When the accelerating voltage is increased to 800 kV and

1300 kV, the resolution limit may be improved to 0.14 nm and 0.104 nm respec-

tively [11] .

The most exciting recent development of HRTEM is the so - called C

- corrected

HRTEM. This type of HRTEM, based on the design of Rose [12] , functions through

two electromagnetic hexapoles and some additional lenses. It allows the value of

to be tuned from positive to zero and even to negative numbers. In 2003, Urban

and coworkers demonstrated that, using C

- corrected TEM, the resolution was

improved from 0.24 nm to 0.13 nm [13] . Oxygen atoms in SrTiO

were directly

imaged. The most recent achievement of high resolution in HRTEM is the unique

microscope at the Department of Energy ’ s National Center for Electron Micros-

copy at the Lawrence Berkeley National Laboratory in collaboration with several

National Laboratories and FEI, which is one of the largest companies producing

electron microscopes. This microscope has a further improved resolution of 0.5 Å

Figure 10.4 Schematic diagram showing the effect of

spherical aberration on a ray with a scattering angle.

10.2 HRTEM and Related Techniques 449

450 10 Transmission Electron Microscopy

and therefore was named TEAM0.5 ( TEAM stands for Transmission Electron

Aberration - corrected Microscope ).

In addition to its power of directly imaging atomic structures of crystals, HRTEM

is often equipped with several other powerful devices for characterization of solids,

such as electron diffraction ( ED ), EDX, electron energy loss spectroscopy ( EELS ),

scanning transmission electron microscopy ( STEM ) and so on. In this chapter,

only the most commonly used supporting techniques for HRTEM, ED and EDX,

are discussed in detail.

10.2.6

Electron Diffraction

Like other diffraction techniques, ED obeys Bragg ’ s law, that is, 2 d sin θ = n λ , where

d is the d - spacing of the crystal planes deﬁ ned by (h k l), n the order of reﬂ ection,

θ the angle of incidence (Bragg angle) and λ the wavelength of the electron beam.

If d (h k l) = 0.5 nm, n = 1, λ = 0.0251 nm, the Bragg angle, θ , is then 0.14 ° , which

is signiﬁ cantly smaller than that in conventional X - ray diffraction.

One of the advantages of electron microscopy is that a very small specimen area

can be examined. An aperture, inserted into the intermediate image plane (Figure

10.1 ), enables us to collect beams scattered from only a small area in a specimen.

This operation is called selected area electron diffraction ( SAED ). Therefore, SAED

patterns can be obtained from very small particles and even from a single nanoscale

domain in a particle.

Powder XRD shows one - dimensional patterns created from three - dimensional

structures, while SAED patterns are two - dimensional pictures reﬂ ecting two -

dimensional structural information. The disadvantage of SAED is that the struc-

tural information along the projected direction is lost, unless a special technique

is used, for example high - order Laue zone ( HOLZ ) diffraction [14, 15] . The advan-

tage of SAED is that the relation between any two diffraction spots in a pattern,

i.e. an interplane angle, can be easily revealed. This helps greatly in determination

of a unit cell.

Since the Ewald sphere (diffraction sphere) is large, with a radius of 1/ λ , the set

of diffraction spots obtained along a principal zone axis is an almost undistorted

picture of the zero level of the reciprocal lattice. Calculation of d - spacings from

SAED patterns is relatively simple. Derived from Bragg ’ s law, a reciprocal d -

spacing ( d * ) can be calculated according to the following equation (Figure 10.5 ):

2sinθ

λλ

where λ is the wavelength of the electron beam, L the camera length and D * the

distance directly measured from the recorded SAED pattern corresponding

to 2 θ .

Reciprocal interplane angles can be directly measured from SAED patterns. If

several SAED patterns are recorded from a crystal through tilting, a 3D reciprocal

unit cell can be determined with the parameters of a * , b * , c * , α * , β * , γ * . Real space

unit cell parameters can then be calculated according to the group of equations

below:

−

⎡

⎣

⎢

⎤

⎦

⎥

−

** *

sin

cos

cos cos cos

sin sin

βγ α

βγ

−

⎡

⎣

⎢

⎤

⎦

⎥

−

** *

sin

cos

cos cos cos

sin sin

αγ β

αγ

−

⎡

⎣

⎢

⎤

⎦

⎥

−

** *

sin

cos

cos cos cos

sin sin

βα γ

βα

where V and V * are unit cell volumes in real space and reciprocal space,

respectively.

The positions of the diffraction spots give us the unit cell information. The

intensities of these spots are dependent on the positions of atoms, i.e. the crystal

structure. Electrons are scattered by the electrical potential in a specimen, φ ( r ) and

the scattering factor, f

, may be written as:

−

[]

πλ

θsin

where f

is the X - ray scattering factor, m and e are the electron mass and charge,

Z is the atomic number, λ is the wavelength of electron beam, h is Planck ’ s con-

stant, and

is the scattering angle. If f

is evaluated, it is found that its value varies

from atom to atom in a manner which is very roughly proportional to Z

1/3

. This

means that scattering is less sensitive to the atomic numbers. Consequently, elec-

tron diffraction is a far better method of detecting light atoms than X - ray diffrac-

tion, for example being more sensitive to oxygen in metal oxides.

Another characteristic of electron diffraction in comparison with other diffrac-

tion methods is multiple scattering. The interaction between the electron beam

10.2 HRTEM and Related Techniques 451

Figure 10.5 Schematic illustration showing the relation

between camera length and recorded reciprocal space

corresponding to a scattering angle.

452 10 Transmission Electron Microscopy

and matter is so strong that the electrons may be scattered several times by differ-

ent atomic planes before leaving a specimen. This makes the intensities of the

scattered electron beams hard to predict, because they depend not only on the

specimen structure but also on the specimen thickness. Unlike single scattering,

after multiple scattering the intensities of some beams increase and some decrease.

Some diffraction peaks, which should be systematically absent, may appear in

SAED patterns, so that extracting space group information from SAED patterns

is normally difﬁ cult. Fortunately, determination of unit cell dimensions is not

complicated by multiple scattering. In fact, the appearance due to multiple scat-

tering of systematically absent diffraction spots may help to reveal unit cell dimen-

sions, because SAED patterns may show a correct unit cell with a lower

symmetry.

To identify an extra diffraction spot caused by multiple scattering of the electron

beam, we may try to record several SAED patterns from one crystallite with a

change of specimen thickness to observe the relative intensity of the spot. Alter-

natively, we may tilt the specimen around the axis including the spot to see a

change of its relative intensity. The relative intensity of a diffraction peak due to

multiple scattering may reduce signiﬁ cantly or the peak may even disappear com-

pletely with a reduction of specimen thickness or with a small angle tilt. A more

reliable method for detecting the space group of a crystal structure is convergent

beam electron diffraction ( CBED ) [16, 17] .

10.2.7

Energy Dispersive X - ray Spectroscopy

The electrons in atoms are located in different shells, each of them having a deﬁ -

nite energy within a particular type of atom. Starting with the shell closest to the

nucleus, the shells are termed K, L, M, N and so on with a certain number of

electrons in each shell, that is, the K shell holds a maximum of two electrons, the

L shell eight, the M shell eighteen, and the N shell thirty - two electrons.

If one electron in the K shell is ejected from an atom by an incident electron,

one electron in the L shell may drop down to the vacancy in the K shell. According

to energy conservation laws a quantum of radiation will be emitted with a discrete

energy corresponding to the difference in energy between the K level and the L

level, h ν = E

− E

. The vacancy in the K shell may also be ﬁ lled by an electron

directly from the M shell, resulting in a quantum of radiation with another energy,

h ν = E

− E

. The vacancy in the L shell will also be re - occupied by an electron

from a shell with a higher energy level, such as the M shell, and so on. A series

of characteristic X - rays are emitted from the solid with the energies being com-

pletely dependent upon the atomic numbers of the elements present. The radia-

tion corresponding to the transition between the L and K levels is designated K

radiation. The radiation corresponding to the M to K transition is designated K

, L

, and so on denote the radiations corresponding to the electron transitions

from the M shell to the L shell, and so on.

An X - ray photon carrying a certain energy is collected by the EDX detector. The

Si detector is a semiconductor with a band gap of 3.8 eV. Therefore, to excite an

electron to form a charge pair, 3.8 eV is required. For example, a Ca K

X - ray

photon has an energy value of 3.7 KeV and it can generate about 1000 charge pairs

in the detector. The charge deposited in the detector is collected in 30 to 40 micro-

seconds and appears at the output as a voltage step (pulse).

There are two different situations concerning pulses: (1) The pulses are sepa-

rated from each other. The detector collects these pulses and transfers the signals

to an EDX spectrum. (2) Two pulses overlap and the corresponding current gener-

ated gives incorrect information. In this case, the detection system will reject them

(by identifying the shapes of the pulses). While such rejection is taking place, the

system is unable to respond to other incoming pulses, and this produces a counter

“ dead time. ” It is for this reason that using the highest intensity electron beam on

a sample, and consequently generating very large amounts of X - rays, does not

always produce better EDX spectra, as most pulses are rejected. Therefore, the

dead time is normally kept to below 30%.

In EDX experiments on thick samples, for example in SEM, almost all the

energy of the incident electron beam is consumed to produce X - rays and

the number of atoms in a sample can be calculated from the X - ray intensities in

the EDX spectra, by carrying out the ZAF calibration (Z = the atomic number

effect; A = the absorption effect and F = the ﬂ uorescence effect) [18] . However,

HRTEM specimens are usually thin, 200 nm or less. In this case, most electrons

in the incident beam will pass through the specimen and the ZAF calibration

cannot be done. In practice, we use some standard specimens (whose composi-

tions are known) as references to obtain a relative composition of a target sample.

A good approximation is that, for a very thin sample ( < 100 nm) the concentration

ratio of two types of atoms, x and y, can be written:

where I

and I

are the intensities of the selected X - ray emission lines from ele-

ments x and y and K

is a constant related to these X - ray emission lines, which

can be obtained by using standard specimens containing the elements x and y.

Quantitative analysis of the chemical composition of the specimen by EDX relies

on obtaining good EDX spectra with the intensities of all the emission lines being

almost purely proportional to the concentration of the atoms in the sample.

However, there are several technical problems that could affect the quality of an

EDX spectrum. The most important one is the absorption problem. Absorption of

X - rays can occur in various situations. For example, the X - rays may be absorbed

by the specimen itself, by the sample near the examined area, by the specimen

grid bars and so on. Therefore isolated particles and thin areas of the particles are

always selected to collect the EDX spectra so that the absorption can be reduced

to its lowest level. Even when the experimental conditions are well controlled, the

10.2 HRTEM and Related Techniques 453

454 10 Transmission Electron Microscopy

accuracy of the EDX results may still be low, normally > ± 5% on an elemental

ratio. Therefore, it is necessary to analyze many particles (e.g. 20 to 30) and take

an average value of the results. The absorption rate is a function of the energy of

the X - rays. At the low energy range, the absorption increases very quickly. This is

why it is always difﬁ cult to obtain a quantitative composition of oxygen in

oxides.

In the following sections, some typical cases of TEM investigations of metal

oxides are reviewed, with most examples being taken from the author ’ s own

research since the mid - 1980s.

10.3

Basic Structures of Oxide Crystals

As mentioned above, the unit cell of a crystalline specimen can be determined by

SAED. However, the accuracy of the unit cell dimensions obtained is largely

dependent upon the calibration of camera length, which is a function of specimen

position and the conditions of the microscope. The procedure is complicated, and

in most cases the unit cell parameters determined by SAED are less accurate than

those obtained from XRD or neutron diffraction. Owing to the multiple scattering

problem, determination of space group by SAED is less reliable. Consequently,

HRTEM is not an ideal technique for ﬁ nal determination of crystal structure.

On the other hand, since HRTEM gives direct atomic images, atomic arrange-

ment in a complicated structure can be revealed. Figure 10.6 shows a HRTEM

Figure 10.6 HRTEM image and the corresponding SAED

pattern (inset) of a crystal of Tl

viewed down

the [110] zone axis of a tetragonal unit cell with a = 0.545 and

c = 3.661 nm.

image of superconducting oxide Tl

[19] . The atomic layers can be

recognized from the image contrast and their relative spaces in the unit cell. This

information helps to elucidate the structure. However, accurate atomic positions

in the structure can only be determined by XRD and neutron diffraction methods.

A combination of powder diffraction and HRTEM thus becomes a very powerful

tool in the determination of crystal structures.

HRTEM examines individual crystallites or small areas of a crystallite. It is very

useful in identifying different structures, especially the minor phases in multipha-

sic specimens. In the ﬁ rst decade of high Tc superconductivity research, many

new phases were discovered from HRTEM evidence together with compositional

information from EDX, including YBa

[20] , Y

[21] , Bi

[22] , TlBa

n − 1

2 n +3

[23] , Pb

SrLaCu

[24] and so on.

Although HRTEM has atomic resolution, most images of oxides show only

metal atoms, as oxygen ’ s contribution to the image contrast is not signiﬁ cant. As

a result of the development of Cs - corrected TEM, it has become possible to “ see ”

directly oxygen atoms [13] . Even then, determination of the positions and occupa-

tion factors of oxygen in oxides still has to be rely on diffraction methods.

The most important role of HRTEM in the structural investigation of oxides is

the detection of microstructures derived from their basic structures, such as super-

structures, various defects and also nano - scale materials, where XRD and neutron

diffraction are less powerful since their intensities are very low.

10.4

Superstructures

Superstructures refer to secondary ordering derived from the basic unit cells of

oxide crystals. The formation of superstructures in oxides can be due to cation

ordering, oxygen ordering or both.

10.4.1

Superstructures Based on Cation Ordering

Secondary cation ordering often occurs when one type of cation in a metal oxide

is partially substituted by another. Mixed oxides are good examples. Many oxide

catalysts fall within this category.

General speaking, when a solid solution of mixed oxides is identiﬁ ed, its XRD

pattern does not change signiﬁ cantly when the composition varies in the solid -

solution range. It is generally assumed that the location of the guest cation in the

host oxide crystal is random. However, this is not always the case. In many mixed

oxides, cation ordering often leads to the occurrence of superstructures, for

example superstructures in Bi

- based solid solutions [25 – 32] . The high tempera-

ture δ - phase of Bi

, has a defect ﬂ uorite structure, which is face centered cubic

with a = 0.56 nm. The unit cell contains four Bi

cations occupying the corner and

face - centered positions. When a small proportion of Bi is replaced by Nb, a 2 × 2

10.4 Superstructures 455

456 10 Transmission Electron Microscopy

× 2 superstructure (type I) forms. The guest cations selectively replace Bi at the

body - centered positions of this superunit cell. The ideal unit cell formula is there-

fore Bi

[25] , which was conﬁ rmed by experimental data. The superstruc-

ture was clearly revealed by the SAED patterns and also seen from the HRTEM

image contrast patterns, although both the diffraction intensities in SAED and the

image contrast corresponding to the superstructure were very weak. Similar super-

structures were also found in other Bi

- based solid solutions, such as the Bi

–

[27] and Bi

– WO

[31] systems. The type I superunit cell dimensions in

the latter systems were 3 × 3 × 3 instead of 2 × 2 × 2 in the Bi

– Nb

system.

Other types of superstructure, such as type II or type III, in these systems also

occur owing to cation ordering.

TlBa

(Tl - 1223) is a high Tc superconductor with low thermal stability.

Partial substitution of Tl by Bi can stabilize the structure. The Tl - 1223 phase has

a perovskite - related tetragonal unit cell with a = 0.382 and c = 1.53 nm. When the

substitution was performed, it was found that the amount of Tl replaced by Bi was

limited to 25%, as indicated by the change of unit cell dimensions (Figure 10.7 a).

SAED patterns from the compound with 25% substitution seem to be very com-

plicated (Figure 10.7 b). The smallest possible superunit cell is 4 × 4 × 4 based on

the basic cell. The positions of Bi in the Tl layers were proposed by consideration

of the appearance of the diffraction spots, and were conﬁ rmed by computer simu-

lation of the SAED patterns. In the ﬁ nal model, it was found that Bi replaces Tl

in the Tl layers only at the corners and the center of 2 a × 4 b or 4 a × 2 b 2D super-

lattices (Figure 10.7 c) [33] . When all these sites are occupied by Bi, the ratio of

Bi : Tl is exactly 1 : 3, i.e. there is 25% substitution. The local distortion resulting

from this substitution prevented any further substitution beyond the 25% limit.

The computer simulation indicated that the two types of 2D supercells with

dimensions of 2 a × 4 b and 4 a × 2 b can give identical SAED patterns along the

[001] projection by a 90 ° rotation around the [001] axis, as shown at the bottom of

Figure 10.7 . The combination of these two patterns resulted in a SAED pattern

similar to the experimental one in Figure 10.7 b. In this case, for an approximate

measure, a complicated SAED pattern can be divided into two or more simpler

patterns, which may aid structure solution.

Because the cations in the host and guest oxides in the above solid solutions

have different oxygen coordination, cation ordering is usually accompanied by

anion ordering. Bearing in mind that, in most metal oxides, metal atoms are much

heavier than oxygen atoms and therefore can scatter electrons more strongly,

cation ordering dominates in the contribution to the diffraction intensities of

SAED and the image contrast patterns in HRTEM corresponding to the

superstructures.

In some layered compounds, electric charge separation between the layers may

destabilize the structures: Aurivillius phases [Bi

]

n − 1

3 n +1

]

2 −

are examples.

If oxygen vacancies are introduced into an Aurivillius phase, a stepped superstruc-

ture may form to release the charge separation and, probably, reduce the number

of oxygen vacancies. For example, Bi

is a well known n = 1 member of the

family of Aurivillius phases. The unit cell consists of ﬂ uorite - like [Bi

] and