Southeast university
School Of Science
Bsc In Textile Engineering
Course Title: Textile Physics-01
Course Code: tex-2037
Assignment On:
01.
a)X ray diffraction method for fiber investigation
b) Electron microscope
02.Details description of all factors related to luster
03. Details description of Birefringence
Submitted To
Lecturer
Morshed Rahman
Dept. of Textile Engineering
Submitted By
Md.Nazmul Hossain Khan
ID:2012000400022
Batch:19th ,Section:A
Dept. of Textile Engineerin
Date of Submission:
X-ray diffraction method for fiber investigation
Definition
X-ray fiber diffraction is a technique that enables structure determination of
fibrous or polymeric molecules based on the ordered arrangement of molecular
structure along a fiber axis. Diffraction patterns are generated by the X-ray
scattering from the molecular organization of the fibrous molecule. The fibrous
structures are generally cylindrically symmetric around an uniaxial direction,
which results in diffraction data with a characteristic four quadrant symmetry,
with diffraction signals arranged symmetrically across the "meridian" (usually
vertical) and "equator" (horizontal) (Fig. 1). Unlike single crystal diffraction,
diffraction signals are often overlapping and, depending on the quality of the
diffracting sample, may show diffraction peaks arranged along "layer lines."
X-radiation (composed of X-rays) is a form of electromagnetic radiation.
X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding
to frequencies in the range 30 petahertz to 30 exahertz (3×1016 Hz to 3×1019
Hz) and energies in the range 100 eV to 100 keV. The wavelengths are shorter
than those of UV rays and longer than those of gamma rays.
Fig1: Fiber diffraction geometry
changes as the fiber is tilted
fig2: 3D representation of
the reciprocal space filled with
scattering data
1) In Bragg’s law, when x-rays are scattered from a crystal lattice, peaks of
scattered intensity are observed which correspond to the following conditions:
a.The angle of incidence = angle of scattering.
b.The path length difference is equal to an integer number of wavelengths.
2) The condition for maximum intensity contained in Bragg's law above allow
us to calculate details about the crystal structure, or if the crystal structure is
known, to determine the wavelength of the x-rays incident upon the crystal.
n λ = 2d sin θ
A crystal can be regarded as made up of layers of atoms, themselves regular in
their two-dimensional plan, stacked regularly on top of one another. Although
analysis of the diffraction from such a three-dimensional lattice is more
complicated than for a simple grating, it does result in a very similar equation;
for it can be shown that, if a beam of X-rays is directed at a crystal, it is strongly
reflected whenever it strikes layers of atoms at an angle θ, shown in Fig. above,
such that:
nλ = 2d sinθ
where n= integer
λ =is the wavelrngth of x- ray
d is the distance between atomic layes
3) The condition that a particular reflection should occur is that the layer of
atoms should make the required angle with the X-ray beam. This will happen
for a series of orientations of the crystals distributed around a cone. The X-rays
will be reflected around a cone of twice this angle, as show in the fig
Layers of atoms giving rise to a particular reflection will make a constant angle,
φ, with this crystal axis, but, if there is no preferred orientation perpendicular to
the fiber axis, the layers can occur at a series of positions distributed around the
fiber axis on a cone, as shown in Fig. 1.11. If an X-ray beam is directed at right
angles to the fiber axis, the reflections will now occur, not round a whole cone,
but only at those four angles at which the cone of Fig. 1.10 (defining the
characteristic angles of reflection) intersects with the cone of Fig. 1.11 (defining
the angles at which the particular layers of atoms occur). This is illustrated in
Fig.
X-ray diffraction is a most important tool for the study of fiber structure:
Firstly, because it gives information at the most important level of fine
structure; &
Secondly, because focusing of X-rays is not possible, so that diffraction
methods have to be used.
Three advances have made the technique more powerful than was available
to the pioneers of X-ray diffraction:
Arrays of detectors give enhanced quantitative information on the diffraction
pattern;
Computer software then enables the data to be analyzed and interpreted; &
The increased power of synchrotron radiation reduces exposure times and
allows small spot sizes to be used.
Electron Microscopy
The electron microscope is a type of microscope that uses a beam of electrons to
create an image of the specimen. It is capable of much higher magnifications
and has a greater resolving power than a light microscope, allowing it to see
much smaller objects in finer detail. They are large, expensive pieces of
equipment, generally standing alone in a small, specially designed room and
requiring trained personnel to operate them.
The History of EM
The first electromagnetic lens was developed in 1926 by Hans Busch.
According to Dennis Gabor, the physicist Leó Szilárd tried in 1928 to convince
Busch to build an electron microscope, for which he had filed a patent.
The German physicist Ernst Ruska and the electrical engineer Max Knoll
constructed the prototype electron microscope in 1931, capable of fourhundred-power magnification; the apparatus was the first demonstration of the
principles of electron microscopy.[4] Two years later, in 1933, Ruska built an
electron microscope that exceeded the resolution attainable with an optical
(light) microscope.[4] Moreover, Reinhold Rudenberg, the scientific director of
Siemens-Schuckertwerke, obtained the patent for the electron microscope in
May 1931.
In 1932, Ernst Lubcke of Siemens & Halske built and obtained images from a
prototype electron microscope, applying concepts described in the Rudenberg
patent applications.[5] Five years later (1937), the firm financed the work of
Ernst Ruska and Bodo von Borries, and employed Helmut Ruska (Ernst’s
brother) to develop applications for the microscope, especially with biological
specimens.[4][6] Also in 1937, Manfred von Ardenne pioneered the scanning
electron microscope.[7] The first practical electron microscope was constructed
in 1938, at the University of Toronto, by Eli Franklin Burton and students Cecil
Hall, James Hillier, and Albert Prebus; and Siemens produced the first
commercial transmission electron microscope (TEM) in 1939.[8] Although
contemporary electron microscopes are capable of two million-power
magnification, as scientific instruments, they remain based upon Ruska’s
prototype.
Types of Electron Microscopes
Transmission Electron Microscope (TEM)
The original form of electron microscopy, Transmission electron microscopy
(TEM) involves a high voltage electron beam emitted by a cathode and formed
by magnetic lenses. The electron beam that has been partially transmitted
through the very thin (and so semitransparent for electrons) specimen carries
information about the structure of the specimen. The spatial variation in this
information (the "image") is then magnified by a series of magnetic lenses until
it is recorded by hitting a fluorescent screen, photographic plate, or light
sensitive sensor such as a CCD (charge-coupled device) camera. The image
detected by the CCD may be displayed in real time on a monitor or computer.
Transmission electron microscopes produce two-dimensional, black and white
images.Resolution of the TEM is also limited by spherical and chromatic
aberration, but a new generation of aberration correctors has been able to
overcome or limit these aberrations. Software correction of spherical aberration
has allowed the production of images with sufficient resolution to show carbon
atoms in diamond separated by only 0.089 nm and atoms in silicon at 0.078 nm
at magnifications of 50 million times. The ability to determine the positions of
atoms within materials has made the TEM an indispensable tool for nanotechnologies research and development in many fields, including heterogeneous
catalysis and the development of semiconductor devices for electronics and
photonics. In the life sciences, it is still mainly the specimen preparation which
limits the resolution of what we can see in the electron microscope, rather than
the microscope itself.
At JIC we have a high voltage (200kV) TEM, which was installed in 2008. We
have two digital cameras on it, one is higher resolution than the other, so that
the need for developing and printing film has been negated. Our TEM is
designed for use with biological samples and is capable of resolving to better
than 1nm. It is also capable of 3-D tomography which involves taking a
succession of images whilst tilting the specimens through increasing angles,
which can then be combined to form a three-dimensional image of the
specimen.
Scanning Electron Microscope (SEM)
Unlike the TEM, where the electrons in the primary beam are transmitted
through the sample, the Scanning Electron Microscope (SEM) produces images
by detecting secondary electrons which are emitted from the surface due to
excitation by the primary electron beam. In the SEM, the electron beam is
scanned across the surface of the sample in a raster pattern, with detectors
building up an image by mapping the detected signals with beam position.SEM
image of a fly's foot plate showing the drawing of a fly's foot SEM image of a
fly's foot taken at JIC in 2006 From "Micrographia", by Robert Hooke, 1665:
plate showing the drawing of a fly's foot
TEM resolution is about an order of magnitude better than the SEM resolution.
Our TEM can easily resolve details of 0.2nm. Our two SEMs at JIC are both
relatively recent acquisitions and are high-resolution instruments capable of
about 2 nm resolution on biological samples. Because the SEM image relies on
electron interactions at the surface rather than transmission it is able to image
bulk samples and has a much greater depth of view, and so can produce images
that are a good representation of the 3D structure of the sample. SEM images
are therefore considered to provide us with 3D, topographical information about
the sample surface but will still always be only in black and white.
In the SEM, we use much lower accelerating voltages to prevent beam
penetration into the sample since what we require is generation of the secondary
electrons from the true surface structure of a sample. Therefore, it is common
to use low KV, in the range 1-5kV for biological samples, even though our
SEMs are capable of up to 30 kV.At JIC we currently have two SEMs, both
with high-resolution capabilities, digital imaging facilities and cryo-systems
which enable them to be used for looking at frozen-hydrated specimens.
Reflection electron microscope (REM)
In the reflection electron microscope (REM) as in the TEM, an electron beam
is incident on a surface but instead of using the transmission (TEM) or
secondary electrons (SEM), the reflected beam of elastically scattered electrons
is detected. This technique is typically coupled with reflection high energy
electron diffraction (RHEED) and reflection high-energy loss spectroscopy
(RHELS). Another variation is spin-polarized low-energy electron microscopy
(SPLEEM), which is used for looking at the microstructure of magnetic
domains.
Sample Preparation
Materials to be viewed in an electron microscope generally require processing
to produce a suitable sample. This is mainly because the whole of the inside of
an electron microscope is under high vacuum in order to enable the electron
beam to travel in straight lines. The technique required varies depending on the
specimen, the analysis required and the type of microscope:
Cryofixation - freezing a specimen rapidly, typically to liquid nitrogen
temperatures or below, that the water forms ice. This preserves the specimen in
a snapshot of its solution state with the minimal of artefacts. An entire field
called cryo-electron microscopy has branched from this technique. With the
development of cryo-electron microscopy, it is now possible to observe
virtually any biological specimen close to its native state.
Fixation - a general term used to describe the process of preserving a sample at
a moment in time and to prevent further deterioration so that it appears as close
as possible to what it would be like in the living state, although it is now dead.
In chemical fixation for electron microscopy, glutaraldehyde is often used to
crosslink protein molecules and osmium tetroxide to preserve lipids.
Dehydration - removing water from the samples. The water is generally
replaced with organic solvents such as ethanol or acetone as a stepping stone
towards total drying for SEM specimens or infiltration with resin and
subsequent embedding for TEM specimens.
Embedding - infiltration of the tissue with wax (for light microscopy) or a resin
(for electron microscopy) such as araldite or LR White, which can then be
polymerised into a hardened block for subsequent sectioning.
Sectioning - the production of thin slices of the specimen. For light
microscopy, the sections can be a few micrometres thick but for electron
microscopy they must be very thin so that they are semitransparent to electrons,
typically around 90nm. These ultra-thin sections for electron microscopy are cut
on an ultramicrotome with a glass or diamond knife. Glass knives can easily be
made in the laboratory and are much cheaper than diamond, but they blunt very
quickly and therefore need replacing frequently.
Staining - uses heavy metals such as lead and uranium to scatter imaging
electrons and thus give contrast between different structures, since many
(especially biological) materials are nearly "transparent" to the electron beam.
By staining the samples with heavy metals, we add electron density to it which
results in there being more interactions between the electrons in the primary
beam and those of the sample, which in turn provides us with contrast in the
resultant image. In biology, specimens can be stained "en bloc" before
embedding and/or later, directly after sectioning, by brief exposure of the
sections to solutions of the heavy metal stains.
Freeze-fracture and freeze-etch - a preparation method particularly useful for
examining lipid membranes and their incorporated proteins in "face on" view.
The fresh tissue or cell suspension is frozen rapidly (cryofixed), then fractured
by simply breaking or by using a microtome while maintained at liquid nitrogen
temperature. The cold, fractured surface is generally "etched" by increasing the
temperature to about -95°C for a few minutes to let some surface ice sublime to
reveal microscopic details. For the SEM, the sample is now ready for imaging.
For the TEM, it can then be rotary-shadowed with evaporated platinum at low
angle (typically about 6°) in a high vacuum evaporator. A second coat of
carbon, evaporated perpendicular to the average surface plane is generally
performed to improve stability of the replica coating. The specimen is returned
to room temperature and pressure, and then the extremely fragile "shadowed"
metal replica of the fracture surface is released from the underlying biological
material by careful chemical digestion with acids, hypochlorite solution or SDS
detergent. The floating replica is thoroughly washed from residual chemicals,
carefully picked up on an EM grid, dried then viewed in the TEM.
Sputter Coating - an ultra-thin coating of electrically-conducting material,
deposited by low vacuum coating of the sample. This is done to prevent
charging of the specimen which would occur because of the accumulation of
static electric fields due to the electron irradiation required during imaging. It
also increases the amount of secondary electrons that can be detected from the
surface of the sample in the SEM and therefore increases the signal to noise
ratio. Such coatings include gold, gold/palladium, platinum, chromium etc.
Disadvantages of Electron Microscopy
Electron microscopes are very expensive to buy and maintain. They are
dynamic rather than static in their operation: requiring extremely stable high
voltage supplies, extremely stable currents to each electromagnetic coil/lens,
continuously-pumped high/ultra-high vacuum systems and a cooling water
supply circulation through the lenses and pumps. As they are very sensitive to
vibration and external magnetic fields, microscopes aimed at achieving high
resolutions must be housed in buildings with special services.
A significant amount of training is required in order to operate an electron
microscope successfully and electron microscopy is considered a specialised
skill.
The samples have to be viewed in a vacuum, as the molecules that make up air
would scatter the electrons. This means that the samples need to be specially
prepared by sometimes lengthy and difficult techniques to withstand the
environment inside an electron microscope. Recent advances have allowed
some hydrated samples to be imaged using an environmental scanning electron
microscope, but the applications for this type of imaging are still limited.
Artefacts
It must be emphasised from the outset that every electron micrograph is, in a
sense, an artefact. Changes in the ultra-structure are inevitable during all the
steps of processing that samples must undergo: material is extracted,
dimensions are changed and molecular rearrangement occurs. The best thing
we can do is to keep these changes to a minimum by understanding the
processes involved so that we make informed choices of the best preparative
procedures to use for each sample.
Artefacts present themselves in many
ways: there could be loss of continuity in the membranes, distortion or
disorganisation of organelles, empty spaces in the cytoplasm of cells or sharp
bends or curves in filamentous structures that are usually straight, such as
microtubules and so on. With experience, microscopists learn to recognise the
difference between an artefact of preparation and true structure, mainly by
looking at the same or similar specimens prepared in the same or a different
way.
Scanning electron microscopes usually image conductive or semi-conductive
materials best. Non-conductive materials can be imaged, either by an
environmental scanning electron microscope or more usually by coating the
sample with a conductive layer of metal. A common preparation technique is to
coat the sample with a layer of conductive material, a few nanometers thick,
such as 10nm of gold, from a sputtering machine. This process does, however,
have the potential to disturb delicate samples and cover some detail. When
using chemical fixation and dehydration as part of the sample preparation, there
is often much shrinkage and collapse of delicate structures and so, especially for
our interests at JIC in botanical specimens which are highly hydrated, we tend
to use the cryo-fixation technique which is far less prone to artefacts.For the
TEM, samples are generally prepared by exposure to many nasty chemicals, in
order to give good ultra-structural detail which may result in artefacts purely as
a result of preparation. This gives the problem of distinguishing artefacts from
genuine structures within the specimen, particularly in biological samples.
Scientists maintain that the results from various preparation techniques have
been compared, and as there is no reason that they should all produce similar
artefacts, it is therefore reasonable to believe that electron microscopy features
correlate with living cells. In addition, higher resolution work has been directly
compared to results from X-ray crystallography, providing independent
confirmation of the validity of this technique. Recent work performed on
unfixed, vitrified (rapidly frozen, without the use of any chemicals, to form ice
without any crystallisation) specimens has also been performed, further
confirming the validity of this technique. However, even cryo-fixation
techniques are not without their own artefacts of preparation and ice crystal
damage, due to the fact that as water freezes it expands, is a common problem
when trying to image a large specimen (greater than 200 µm) which cannot be
frozen rapidly enough to vitrify the water
Birefringence
.
Birefringence is the optical property of a material having a refractive index that
depends on the polarization and propagation direction of light.[1] These optically
anisotropic materials are said to be birefringent (or birefractive). The
birefringence is often quantified as the maximum difference between refractive
indices exhibited by the material. Crystals with asymmetric crystal structures
are often birefringent, as well as plastics under mechanical stress.
Birefringence is responsible for the phenomenon of double refraction whereby
a ray of light, when incident upon a birefringent material, is split by polarization
into two rays taking slightly different paths. This effect was first described by
the Danish scientist Rasmus Bartholin in 1669, who observed it[2] in calcite, a
crystal having one of the strongest birefringences. However it was not until the
19th century that Augustin-Jean Fresnel correctly described the phenomenon in
terms of polarization, understanding light as a wave with field components in
transverse polarizations (perpendicular to the direction of the wave vector).
Fig1:Displacement of light rays with perpendicular
fig2: A calcite crystal laid upon a graph paper
polarization through a birefringent material.
with blue lines showing the double refraction
Explanation
The simplest (and most common) type of birefringence is that of materials with
uniaxial anisotropy. That is, the structure of the material is such that it has an
axis of symmetry with all perpendicular directions optically equivalent. This
axis is known as the optic axis of the material, and components of light with
linear polarizations parallel and perpendicular to it have unequal indices of
refraction, denoted ne and no, respectively, where the subscripts stand for
extraordinary and ordinary. The names reflect the fact that, if unpolarized light
enters the material at some angle of incidence, the component of the incident
radiation whose polarization is perpendicular to the optic axis will be refracted
according to the standard law of refraction for a material of refractive index no,
while the other polarization component, the so-called extraordinary ray will
refract at a different angle determined by the angle of incidence, the orientation
of the optic axis, and the birefringence
What's more, the extraordinary ray is an inhomogeneous wave whose power
flow (given by the Poynting vector) is not exactly parallel to the wave vector.
This causes a shift in that beam, even when launched at normal incidence, that
is popularly observed using a crystal of calcite as photographed above. Rotating
the calcite crystal will cause one of the two images, that of the extraordinary
ray, to rotate slightly around that of the ordinary ray which remains fixed.
When the light propagates either along or orthogonal to the optic axis, such a
lateral shift does not occur. In the first case, both polarizations see the same
effective refractive index, so there is no extraordinary ray. In the second case
the extraordinary ray propagates at a different phase velocity (corresponding to
ne) but is not an inhomogeneous wave. A crystal with its optic axis in this
orientation, parallel to the optical surface, may be used to create a waveplate, in
which there is no distortion of the image but an intentional modification of the
state of polarization of the incident wave. For instance, a quarter-wave plate is
commonly used to create circular polarization from a linearly polarized source.
The more general case of biaxially anisotropic materials, also known as
trirefringent[citation needed materials, is substantially more complex. Then there are
three refractive indices corresponding to three principal axes of the crystal.
Generally both polarizations are extraordinary rays with different effective
refractive indices which can be determined using the index ellipsoid for a given
polarization vector.
Sources of optical birefringence
While birefringence is usually obtained using an anisotropic crystal, it can result
from an optically isotropic material in a few ways:



Stress birefringence results when isotropic materials are stressed or
deformed such that the isotropy is lost in one direction (i.e., stretched or
bent). Example
By the Kerr effect, whereby an applied electric field induces
birefringence at optical frequencies through the effect of nonlinear optics;
By the Faraday effect, where a magnetic field causes some materials to
become circularly birefringent (having slightly different indices of
refraction for left and right handed circular polarizations), making the
material optically active until the field is removed;

By self or forced alignment of highly polar molecules such as lipids,
some surfactants or liquid crystals, that generate highly birefringent thin
films.
Examples of uniaxial birefringent materials
The best-studied birefringent materials are crystalline; the refractive indices (at
wavelength ~ 590 nm) of several such uniaxial crystals are tabulated to the right
.[4]
Many plastics are birefringent, because their molecules are 'frozen' in a
stretched conformation when the plastic is molded or extruded. [5] For example,
ordinary cellophane is birefringent. Polarizers are routinely used to detect stress
in plastics such as polystyrene and polycarbonate.
Cotton (gossypium hirsutum) fiber is birefringent because of high levels of
cellulosic material in the fiber's secondary cell wall.
Inevitable manufacturing imperfections in optical fiber leads to birefringence
which is one cause of pulse broadening in fiber-optic communications. Such
imperfections can be geometrical (lack of circular symmetry), due to stress
applied to the optical fiber, and/or due to bending of the fiber. Birefringence is
intentionally introduced (for instance, by making the cross-section elliptical) in
order to produce polarization-maintaining optical fibers.In addition to
anisotropy in the electric polarizability (electric susceptibility), anisotropy in the
magnetic polarizability magnetic permeability]) will also cause birefringence.
However at optical frequencies, values of magnetic permeability for natural
materials are not measurably different from µ0 so this is not a source of optical
birefringence in practice.
Uniaxial materials, at 590 nm[4]
Material
Crystal system
no
ne
Δn
barium borate BaB2O4
Trigonal
1.6776 1.5534 -0.1242
beryl Be3Al2(SiO3)6
Hexagonal
1.602 1.557 -0.045
calcite CaCO3
Trigonal
1.658 1.486 -0.172
ice H2O
Hexagonal
1.309 1.313 +0.004
lithium niobate LiNbO3
Trigonal
2.272 2.187 -0.085
magnesium fluoride MgF2
Tetragonal
1.380 1.385 +0.006
quartz SiO2
Trigonal
1.544 1.553 +0.009
Uniaxial materials, at 590 nm[4]
Material
Crystal system
no
ne
Δn
ruby Al2O3
Trigonal
1.770 1.762 -0.008
rutile TiO2
Tetragonal
2.616 2.903 +0.287
sapphire Al2O3
Trigonal
1.768 1.760 -0.008
silicon carbide SiC
Hexagonal
2.647 2.693 +0.046
tourmaline (complex silicate ) Trigonal
1.669 1.638 -0.031
zircon, high ZrSiO4
Tetragonal
1.960 2.015 +0.055
zircon, low ZrSiO4
Tetragonal
1.920 1.967 +0.047
Fast and slow rays
For a given propagation direction, in general there are two perpendicular
polarizations for which the medium behaves as if it had a single effective
refractive index. In a uniaxial material, these polarizations are called the
extraordinary and the ordinary ray (e and o rays), with the ordinary ray having
the effective refractive index
. A biaxial crystal is characterized by three
refractive indices α, β, and γ applying to its principal axes. A wave in a
specified direction will consist of two polarization components with generally
different effective refractive indices. The so-called slow ray is the component
for which the material has the higher effective refractive index (slower phase
velocity), while the fast ray has a lower effective refractive index. For a uniaxial
material with the z axis defined to be the optical axis, the effective refractive
indices are as in the table on the right. For rays propagating in directions other
than z, the effective refractive index of the extraordinary ray is in between
and
, depending on the angle between the polarization vector and the z axis.
The effective refractive index can be determined using the index ellipsoid.
Effective refractive indices in negative uniaxial materials
Propagation
direction
Ordinary ray
Extraordinary ray
Polarization neff Polarization
Z
xy-plane
n/a
xy-plane
xy-plane
z
xz-plane
Y
xz-plane
Other
analogous to xz-plane
neff
n/a
Fig: Rays passing through a positively birefringent material. The incident light has parallel
and perpendicular polarisation components (linear polarization at 45º the optic axis). The
optic axis is perpendicular to the direction of the perpendicular component of incident ray, so
the ray polarized parallel to the optic axis has a greater refractive index than the ray polarized
perpendicular to it.
Positive or negative
Uniaxial birefringence is classified as positive when the extraordinary index of
refraction ne is greater than the ordinary index no. Negative birefringence means
that Δn = ne - no is less than zero.[6] In other words, the polarization of the fast
(or slow) wave is perpendicular to the optical axis when the birefringence of the
crystal is positive (or negative, respectively). The terms "positive" and
"negative" are not applied in the case of biaxial crystals, since all three of the
principal axes have different refractive indices, rather than two being the same
but different from the one that's designated as the optic axis in a uniaxial crystal.
Biaxial birefringence
Biaxial birefringence, also known as trirefringence[citation
needed]
, describes an
anisotropic material in which the optical properties are not invariant under
rotation about a particular axis (the optic axis, in uniaxial crystals). For such a
material, the refractive index tensor n, will in general have three distinct
eigenvalues that can be labeled nα, nβ and nγ.
Biaxial materials, at 590 nm[4]
Material
Crystal system nα
nβ
nγ
borax Na2(B4O5)(OH)4·8(H2O)
Monoclinic
1.447 1.469 1.472
epsom salt MgSO4·7(H2O)
Monoclinic
1.433 1.455 1.461
mica, biotite K(Mg,Fe)
3AlSi
3O
Monoclinic
10(F,OH)
2
mica, muscovite KAl2(AlSi3O10)(F,OH)2 Monoclinic
olivine (Mg, Fe)2SiO4
Orthorhombic
perovskite CaTiO3
Orthorhombic
topaz Al2SiO4(F,OH)2
Orthorhombic
ulexite NaCaB5O6(OH)6•5(H2O)
Triclinic
1.595 1.640 1.640
1.563 1.596 1.601
1.640 1.660 1.680
2.300 2.340 2.380
1.618 1.620 1.627
1.490 1.510 1.520
Measurement
Birefringence and other polarization based optical effects (such as optical
rotation and linear or circular dichroism) can be measured by measuring the
changes in the polarization of light passing through the material. These
measurements are known as polarimetry.
Birefringence of lipid bilayers can be measured using dual polarisation
interferometry. This provides a measure of the degree of order within these fluid
layers and how this order is disrupted when the layer interacts with other
biomolecules.
Applications
Birefringence is used in many optical devices. Liquid crystal displays, the most
common sort of flat panel display, cause their pixels to become lighter or darker
through rotation of the polarization (circular birefringence) of linearly polarized
light as viewed through a sheet polarizer at the screen's surface. Similarly, light
modulators modulate the intensity of light through electrically induced
birefringence of polarized light followed by a polarizer. The Lyot filter is a
specialized narrowband spectral filter employing the wavelength dependence of
birefringence. Wave plates are thin birefringent sheets widely used in certain
optical equipment for modifying the polarization state of light passing through
it.
Birefringence also plays an important role in second harmonic generation and
other nonlinear optical components, as the crystals used for this purpose are
almost always birefringent. By adjusting the angle of incidence, the effective
refractive index of the extraordinary ray can be tuned in order to achieve phase
matching which is required for efficient operation of these devices.
Fig: Reflective twisted nematic liquid crystal display. Light reflected by surface (6) (or
coming from a backlight) is horizontally polarized (5) and passes through the liquid crystal
modulator (3) sandwiched in between transparent layers (2,4) containing electrodes.
Horizontally polarized light is blocked by the vertically oriented polarizer (1) except where
its polarization has been rotated by the liquid crystal (3), appearing bright to the viewer
Stress induced birefringence
Isotropic solids do not exhibit birefringence. However, when they are under
mechanical stress, birefringence results. The stress can be applied externally or
is ‘frozen’ in after a birefringent plastic ware is cooled after it is manufactured
using injection molding. When such a sample is placed between two crossed
polarizers, colour patterns can be observed, because polarization of a light ray is
rotated after passing through a birefingent material and the amount of rotation is
dependent on wavelength. The experimental method called photoelasticity used
for analyzing stress distribution in solids is based on the same principle.
Other cases of birefringence
Birefringence is observed in anisotropic elastic materials. In these materials, the
two polarizations split according to their effective refractive indices which are
also sensitive to stress. The study of birefringence in shear waves traveling
through the solid earth (the earth's liquid core does not support shear waves) is
widely used in seismology. Birefringence is widely used in mineralogy to
identify rocks, minerals, and gemstones
Theory
Birefringence results when a material's permittivity is not describable using a
scalar value, but requires a tensor to relate the electric displacement (D) with the
electric field (E). Consider a plane wave propagating in an anisotropic medium,
with a permittivity tensor ε and assuming no magnetic permeability in the
medium:
. We shall assume that the electric field of a wave of angular
frequency ω can be written in the form:
(2)
where r is the position vector, t is time, and E0 is a vector describing the electric
field at r=0, t=0. Then we shall find the possible wave vectors k using
Maxwell's equations from which we obtain:
(3a)
(3b)
where the so-called electric displacement vector
field through the permittivity tensor ε:
Substituting the definition of
conditions:
is now related to the electric
and eqn. 2 into eqns. 3a-b leads to the
(4a)
(4b)
Eqn. 4b indicates that is orthogonal to the direction of the wavevector k, even
though that is no longer generally true for as would be the case in an isotropic
medium.
To find the allowed values of k, E0 can be eliminated from eq 4a. If eqn 4a is
written in Cartesian coordinates with the x, y and z axes chosen in the principal
directions of the permitivity tensor ε, then
(4c)
where the diagonal values are squares of the refractive indices for polarizations
along the three principal axes x, y and z. With ε in this form, and noting that the
speed of light
, eqn. 4a becomes
(5a)
(5b)
(5c)
where Ex, Ey, Ez, kx, ky and kz are the components of E0 and k. This is a set of
linear equations in Ex, Ey, Ez, and they have a non-trivial solution if the
following determinant is zero:
(6)
Evaluating the determinant of eqn (6), and rearranging the terms, we obtain
In the case of a uniaxial material, choosing the optic axis to be in the z direction
so that nx=ny=no and nz=ne, this expression can be factored into
(8)
Setting either of the factors in eqn 8 to zero will define an ellipsoidal surface in
space of allowed wave vectors k. The first factor being zero defines a sphere
corresponding to ordinary rays, in which the effective refractive index is exactly
no. The second defines a spheroid symmetric about the z axis. This solution
corresponds to extraordinary rays in which the effective refractive index is in
between no and ne. Therefore for any arbitrary direction of propagation, two
distinct wavevectors k are allowed corresponding to the polarizations of the
ordinary and extraordinary rays. A general state of polarization launched into
the medium can be decomposed into two such waves which will then propagate
with different k vectors (except in the case of propagation in the direction of the
optic axis). For a biaxial material a similar but somewhat more complicated
condition on the two waves can be described.[11]
Factor Related to Luster
1.Angle of incident:
The light falls across the fiber or along the fiber .If a fiber behaves as a perfect
reflecting circular cylinder it could reflect light as like figure (a) and (b)
It is clear that if the light falls across the fiber,it is reflecter at various angle
whwre as if the light falls along the fibers ,here it is reflected at constant angle.
2.Fineness of the fibers:
Fibers exhibit a varity of cross sectional shaps and they also vary in section
along their length and vary from fiber to fiber .fineness denoteds the size of the
cross sectional diamentions of the fiber.As the cross sectional feasure are
irregular ,direct determination of the area of cross section is difficult an
laborious.some dimensional feature such as sowellen diameter,ribbon width
etc,can be determined directly and sone times used to specify the fineness of
cotton fiber. The finer the fibers incorporated in a fabric the greater is the
number of the individual reflecting surface per unit area of the fabric.The fiber
fineness affects the lustre for the same types of smoothness and regularity the
coarser fiber will have more luster than the finer fibers
Fineness increase------- luster decease
Short staple fiber increase------ luster decease
Long staple fiber increase--------luster increase
Coarser fiber incease------------ luster increase
3.Irregularity of the fiber surface:
Irregularity on the surface of the fibers and in its cross-sectional shape will
cause the light to be reflected in various direction and will reduce lustre.It is
essential that the fibers should be uniform along its length for this reason luster
is greater in regular filaments such those of silk and man made fiber.
4.Fiber shape :
The particular types of lustre associated with nylon.rayon and silk must be very
due to pattern of light reflected from their respective circulas,serrated and
triangular shap.
Nylon—circular---more luster
Viscose---serrated—dull luster
Silk---triangular---less luster
5.Maturity of fibers:
Maturity of fiber is a characteristic which express the relative degree of
thickening of the fiber wall.In other words it is the measure of primary and
secondary wall thickness.
mature fibers:
Mature fibers with well developed cell wall and after swelling it apear rod like
from raw stste and it also show no continuous lumen in the longitudinal section
of matured fiber.
Dead fibers:
Dead fibers are those fiber that after sweeling it has a continuous lumen and the
wall thickness is less than the ribbon width.
Thin wall fibers: Thin wall fibers are those fiber that are not classed as normal
or dead,being of intermediate appearance and thickening.
Maturity increase---luster increase---reflection increas
6.Presentation:
Presentation of a small particle on fibers like TIO2 that minimize the luster of
the manmade fibers. when a beam of light falls on the fibers ,it is not only
reflected but also transmitted .some of the transmitter light will reflect from
the internal surface as fig (a)
If the fiber contain small particles e.g TIO2 or cavities as fig (b),these will
scatter the transmitted light at varying angles and causes it to emerge as
particularly diffuse reflection..TIO2 is used as delustrants in manmade to reduce
its luster.