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Surface crytallography and diffraction
Surface symmetry
Any crytslalline solid materials composed of repeated units in 3 dimension structure
called “crystals”. These crystals can possess restricted number of types which
repeated in a so-called “translational symmetry”. The science which study this is
called “crytallography”.
** Many properties of solids are intimately related to the special symmetry properties of
these materials.
** The surface has two dimension structure, i.e. a thin layer from the crystals on the
surface make like sheet in two dimensional structure. This layer strongly affects the
properties of the surface because it has influences on the electronic properties of the
surface. Also, this layer plays dominant role in allowing the electron, X-ray and atom
diffraction techniques to provide information on the structure of the surface.
** Therefore, “surface structure” phrase means the structure of the solid in the vicinity of
the surface “selvedge” .
** We have to understand the crytallography of the surface because it is very important in
the analytical techniques. The signal which emerges in the solid is likely to contain
large contribution from the top atom layer “surface”, a weaker contribution from the
next layer, and so on. Therefore, if there is a layer from adsorbate atoms it will affect
the characterization.
Surface crystallography
• There is a scientific way to characterize the surface crystallography, it is called space groups. The number
of the units in the space group depends on the dimensions, for example in two dimension space there are
17 patterns, while 219 patterns in three dimensional space
• Space groups in two dimensional space
• These are the basic shapes
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Generally in 2 or 3 dimension the space group consists of 4 letters
1. The first one is p or c p primitive
C non - primitive
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In two dimensions crytallography, only the centered rectangular cells are the non-primitive.
2. The second is a digit denotes the number of the highest order of rotational symmetry: 1fold (none), 2-fold, 3-fold, 4-fold, or 6-fold.
• 1- fold means can not rotate
• 2-fold means can rotate with angle 180o
3-fold means can rotate with angle 120o
• 4-fold means can rotate with angle 90o
6-fold means can rotate with angle 60o
• Rotation can be done at one or several centers in the cells
• The next two symbols indicate symmetries relative to one translation
axis of the pattern, referred to as the "main" one; if there is a mirror
perpendicular to a translation axis we choose that axis as the main one
(or if there are two, one of them). The symbols are either
• m for mirror
• g glide reflection
• 1 none.
P211 (p2)
Primitive cell, 2-fold rotation symmetry, no mirrors or glide
reflections.
• p4g (p4gm): Primitive cell, 4-fold rotation,
• glide reflection perpendicular
• to main axis, mirror axis at 90°.
• cmm (c2mm): Centered cell, 2-fold rotation, mirror axes both
perpendicular and parallel to main axis.
• p31m (p31m): Primitive cell, 3-fold rotation, mirror axis at 60°.
• The two dimension space group is not enough to characterize the bulk
structure, so the more accurate is the three dimensional space groups.
• For example, if we have a material with FCC (faced centered cube), the
{100} surface (i.e. the plane par
Miller indices
Definition
Miller indices are a notation system in
crystallography for planes and directions in crystal
(Bravais) lattices.
Presentation
In particular, a family of lattice planes is determined by
three integers ℓ, m, and n, the Miller indices. They are
written (hkl), and each index denotes a plane
orthogonal to a direction (x, y, z) in the basis of the
reciprocal lattice vectors. Miller index (100) represents
a plane orthogonal to direction x; index 010 represents
a plane orthogonal to direction y, and index 001
represents a plane orthogonal to z.
General Notes
1. Sometimes we specify the origin and the axes locations in the reciprocal lattice
so we may have negative integers, they are written with a bar, as in 3 for −3. The
integers are usually written in lowest terms, i.e. their greatest common divisor
should be 1.
2. The notation {ℓmn} denotes the set of all planes that are equivalent to (ℓmn) by
the symmetry of the lattice.
Miller indices for directions
• In the context of crystal directions (not planes), the corresponding
notations are:
• [ℓmn], with square instead of round brackets, denotes a direction in the
basis of the direct lattice vectors instead of the reciprocal lattice; and
• similarly, the notation 〈hkl〉 denotes the set of all directions that are
equivalent to [hkl] by symmetry.
Spectroscopy
Definition
Spectroscopy is the study of the interaction between matter and radiated energy.
Historically, spectroscopy originated through the study of visible light dispersed
according to its wavelength, e.g., by a prism. Later the concept was expanded greatly
to comprise any interaction with radiative energy as a function of its wavelength or
frequency. Spectroscopic data is often represented by a spectrum, a plot of the
response of interest as a function of wavelength or frequency.
• Fields
• We can find application fields of spectroscopy in our life in many fields.
1. Neon lamps: Neon lighting is a direct application of atomic spectroscopy.
Neon and other noble gases have characteristic emission colors, and
neon lamps use electricity to excite these emissions.
2. Ink, dyes and paints which reflects the complementary colors when a
light falls on it.
3. Astronomy: Most research telescopes have spectrographs. The measured
spectra are used to determine the chemical composition and physical
properties of astronomical objects (such as their temperature and
velocity).
4. Remote sensing.
• Type of radiative energy
• Types of spectroscopy are distinguished by
the type of radiative energy involved in the
interaction. In many applications, the
spectrum is determined by measuring
changes in the intensity or frequency of this
energy. The types of radiative energy studied
include:
1. Electromagnetic radiation was the
first source of energy used for
spectroscopic studies. Techniques
that employ electromagnetic
radiation are typically classified by
the wavelength region of the
spectrum and include microwave,
terahertz, infrared, near infrared,
visible and ultraviolet, x-ray and
gamma spectroscopy.
• 2. Particles, due to their de Broglie wavelength, can also be a
source of radiative energy and both electrons and neutrons
are commonly used. For a particle, its kinetic energy
determines its wavelength.
• 3. Acoustic spectroscopy involves radiated pressure waves
• 4. Mechanical methods can be employed to impart radiating
energy, similar to acoustic waves, to solid materials. An
acoustic wave is an oscillation of pressure that travels
through a solid, liquid, or gas in a wave pattern. It transmits
sound by vibrating organs in the ear that produce the
sensation of hearing. Acoustic waves, or sound waves, are
defined by three characteristics: wavelength, frequency, and
amplitude.
• Nature of the interaction
Types of spectroscopy can also be distinguished by the nature of the
interaction between the energy and the material. These interactions
include:
1.
2.
3.
Absorption occurs when energy from the radiative source is absorbed by
the material. Absorption is often determined by measuring the fraction of
energy transmitted through the material; absorption will decrease the
transmitted portion.
Emission indicates that radiative energy is released by the material. A
material's blackbody spectrum is a spontaneous emission spectrum
determined by its temperature. Emission can also be induced by other
sources of energy such as a flames or sparks or electromagnetic radiation in
the case of fluorescence.
Elastic scattering and reflection spectroscopy determine how incident
radiation is reflected or scattered by a material. Crystallography employs
the scattering of high energy radiation, such as x-rays and electrons, to
examine the arrangement of atoms in proteins and solid crystals.
5. Impedance spectroscopy studies the ability of a medium to impede or slow
the transmittance of energy. For optical applications, this is characterized
by the index of refraction.
6. Inelastic scattering phenomena involve an exchange of energy between the
radiation and the matter that shifts the wavelength of the scattered
radiation. These include Raman and Compton scattering.
7. Coherent or resonance spectroscopy are techniques where the radiative
energy couples two quantum states of the material in a coherent
interaction that is sustained by the radiating field. The coherence can be
disrupted by other interactions, such as particle collisions and energy
transfer, and so often require high intensity radiation to be sustained.
Nuclear magnetic resonance (NMR) spectroscopy is a widely used
resonance method and ultrafast laser methods are also now possible in
the infrared and visible spectral regions.
Examples for the spectroscopy techniques
• As aforementioned, there are many techniques of the spectroscopy based
on the natures of the radiant energy and the interaction.
• Usually, the particles radiant energy (electrons , neutrons or ions) is used in
the surface science due to the good results obtained, however these
particles can not be used to investigate the bulk of the material due to the
size so the electromagnetic radiation is more preferable. Below is two main
techniques for both categories:
1. Low Energy Electron Diffraction (LEED)
• Low-energy electron diffraction (LEED) is a technique for the determination of
the surface structure of crystalline materials by bombardment with a
collimated beam of low energy electrons (20-200eV) and observation of
diffracted electrons as spots on a fluorescent screen.
• LEED may be used in one of two ways:
1. Qualitatively, where the diffraction pattern is recorded and analysis of the spot positions
gives information on the symmetry of the surface structure. In the presence of an adsorbate
the qualitative analysis may reveal information about the size and rotational alignment of the
adsorbate unit cell with respect to the substrate unit cell.
2. Quantitatively, where the intensities of diffracted beams are recorded as a function of
incident electron beam energy to generate the so-called I-V curves. By comparison with
theoretical curves, these may provide accurate information on atomic positions on the
surface at hand.
Experimental Setup
In order to keep the sample clean and free from unwanted adsorbates,
LEED experiments are performed in an ultra-high-vacuum environment
(10−9mbar).
The most important elements in an LEED experiment are
1. A sample holder with the prepared sample
2. An electron gun
3. A display system, usually a hemispherical fluorescent screen
on which the diffraction pattern can be observed directly
4. A sputtering gun for cleaning the surface
5. An Auger-Electron Spectroscopy system in order to determine
the purity of the surface.
LEED pattern of a Si(100)
reconstructed surface.
X-Ray analysis
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•
Because it is relatively easy to use electrons or neutrons having wavelengths
smaller than a nanometre, electrons and neutrons may be used to study crystal
structure in a manner very similar to X-ray diffraction. Electrons do not penetrate
as deeply into matter as X-rays, hence electron diffraction reveals structure near
the surface; neutrons do penetrate easily and have an advantage that they possess
an intrinsic magnetic moment that causes them to interact differently with atoms
having different alignments of their magnetic moments.
X-ray scattering techniques are a family of non-destructive analytical techniques
which reveal information about the crystallographic structure, chemical
composition, and physical properties of materials and thin films. These techniques
are based on observing the scattered intensity of an X-ray beam hitting a sample as
a function of incident and scattered angle, polarization, and wavelength or energy.
• X-ray diffraction techniques
1. X-ray diffraction yields the atomic structure of materials and is based on the elastic
scattering of X-rays from the electron clouds of the individual atoms in the system.
2. Single-crystal X-ray diffraction is a technique used to solve the complete structure
of crystalline materials, ranging from simple inorganic solids to complex
macromolecules, such as proteins.
3. Powder diffraction (XRD) is a technique used to characterize the
crystallographic structure, crystallite size (grain size), and
preferred orientation in polycrystalline or powdered solid samples.
Powder diffraction is commonly used to identify unknown
substances, by comparing diffraction data against a database
maintained by the International Centre for Diffraction Data. It may
also be used to characterize heterogeneous solid mixtures to
determine relative abundance of crystalline compounds and,
when coupled with lattice refinement techniques.
4. Thin film diffraction and grazing incidence X-ray diffraction may be used to
characterize the crystallographic structure and preferred orientation of substrateanchored thin films.
5. High-resolution X-ray diffraction is used to characterize thickness, crystallographic
structure, and strain in thin epitaxial films. It employs parallel-beam optics.
6. X-ray pole figure analysis enables one to analyze and determine the distribution of
crystalline orientations within a crystalline thin-film sample.
7. X-ray rocking curve analysis is used to quantify grain size and mosaic spread in
crystalline materials.