In physics, the terms order and disorder designate the presence or absence of some symmetry or correlation in a many-particle system.
In condensed matter physics, systems typically are ordered at low temperatures; upon heating, they undergo one or several phase transitions into less ordered states.
Examples for such an order-disorder transition are:
The degree of freedom that is ordered or disordered can be translational (crystalline ordering), rotational (ferroelectric ordering), or a spin state (magnetic ordering).
The order can consist either in a full crystalline space group symmetry, or in a correlation. Depending on how the correlations decay with distance, one speaks of long range order or short range order.
If a disordered state is not in thermodynamic equilibrium, one speaks of quenched disorder. For instance, a glass is obtained by quenching (supercooling) a liquid. By extension, other quenched states are called spin glass, orientational glass. In some contexts, the opposite of quenched disorder is annealed disorder.
Characterizing order
Lattice periodicity and X-ray crystallinity
The strictest form of order in a solid is lattice periodicity: a certain pattern (the arrangement of atoms in a unit cell) is repeated again and again to form a translationally invariant tiling of space. This is the defining property of a crystal. Possible symmetries have been classified in 14 Bravais lattices and 230 space groups.
Lattice periodicity implies long-range order:
if only one unit cell is known, then by virtue of the translational
symmetry it is possible to accurately predict all atomic positions at
arbitrary distances. During much of the 20th century, the converse was
also taken for granted – until the discovery of quasicrystals in 1982 showed that there are perfectly deterministic tilings that do not possess lattice periodicity.
It is a thermodynamicentropy concept often displayed by a second-order phase transition.
Generally speaking, high thermal energy is associated with disorder and
low thermal energy with ordering, although there have been violations
of this. Ordering peaks become apparent in diffraction experiments at
low energy.
Long-range order
Long-range order characterizes physical systems in which remote portions of the same sample exhibit correlated behavior.
where s is the spin quantum number and x is the distance function within the particular system.
This function is equal to unity when and decreases as the distance increases. Typically, it decays exponentially
to zero at large distances, and the system is considered to be
disordered. But if the correlation function decays to a constant value
at large
then the system is said to possess long-range order. If it decays to
zero as a power of the distance then it is called quasi-long-range order
(for details see Chapter 11 in the textbook cited below. See also Berezinskii–Kosterlitz–Thouless transition). Note that what constitutes a large value of is understood in the sense of asymptotics.
Quenched disorder
In statistical physics, a system is said to present quenched disorder when some parameters defining its behavior are random variables which do not evolve with time. These parameters are said to be quenched or frozen. Spin glasses are a typical example. Quenched disorder is contrasted with annealed disorder in which the parameters are allowed to evolve themselves.
Mathematically, quenched disorder is more difficult to analyze
than its annealed counterpart as averages over thermal noise and
quenched disorder play distinct roles. Few techniques to approach each
are known, most of which rely on approximations. Common techniques used
to analyzed systems with quenched disorder include the replica trick, based on analytic continuation, and the cavity method,
where a system's response to the perturbation due to an added
constituent is analyzed. While these methods yield results agreeing with
experiments in many systems, the procedures have not been formally
mathematically justified. Recently, rigorous methods have shown that in
the Sherrington-Kirkpatrick model, an archetypal spin glass model, the replica-based solution is exact. The generating functional formalism, which relies on the computation of path integrals, is a fully exact method but is more difficult to apply than the replica or cavity procedures in practice.
Transition from disordered (left) to ordered (right) states
Annealed disorder
A system is said to present annealed disorder when some parameters entering its definition are random variables, but whose evolution is related to that of the degrees of freedom defining the system. It is defined in opposition to quenched disorder, where the random variables may not change their values.
Systems with annealed disorder are usually considered to be
easier to deal with mathematically, since the average on the disorder
and the thermal average may be treated on the same footing.
A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macroscopic single crystals are usually identifiable by their geometrical shape, consisting of flat faces with specific, characteristic orientations. The scientific study of crystals and crystal formation is known as crystallography. The process of crystal formation via mechanisms of crystal growth is called crystallization or solidification.
The word crystal derives from the Ancient Greek word κρύσταλλος (krustallos), meaning both "ice" and "rock crystal", from κρύος (kruos), "icy cold, frost".
Examples of large crystals include snowflakes, diamonds, and table salt. Most inorganic solids are not crystals but polycrystals, i.e. many microscopic crystals fused together into a single solid. Polycrystals include most metals, rocks, ceramics, and ice. A third category of solids is amorphous solids, where the atoms have no periodic structure whatsoever. Examples of amorphous solids include glass, wax, and many plastics.
Despite the name, lead crystal, crystal glass, and related products are not crystals, but rather types of glass, i.e. amorphous solids.
Crystals, or crystalline solids, are often used in pseudoscientific practices such as crystal therapy, and, along with gemstones, are sometimes associated with spellwork in Wiccan beliefs and related religious movements.
Crystal structure (microscopic)
Halite (table salt, NaCl): Microscopic and macroscopic
Microscopic structure of a halite crystal. (Purple is sodium ion, green is chlorine ion). There is cubic symmetry in the atoms' arrangement
Macroscopic
(~16 cm) halite crystal. The right-angles between crystal faces are due
to the cubic symmetry of the atoms' arrangement
The scientific definition of a "crystal" is based on the microscopic arrangement of atoms inside it, called the crystal structure. A crystal is a solid where the atoms form a periodic arrangement. (Quasicrystals are an exception, see below).
Not all solids are crystals. For example, when liquid water
starts freezing, the phase change begins with small ice crystals that
grow until they fuse, forming a polycrystalline structure. In the final block of ice, each of the small crystals (called "crystallites" or "grains") is a true crystal with a periodic arrangement of atoms, but the whole polycrystal does not have a periodic arrangement of atoms, because the periodic pattern is broken at the grain boundaries. Most macroscopic inorganic solids are polycrystalline, including almost all metals, ceramics, ice, rocks, etc. Solids that are neither crystalline nor polycrystalline, such as glass, are called amorphous solids, also called glassy,
vitreous, or noncrystalline. These have no periodic order, even
microscopically. There are distinct differences between crystalline
solids and amorphous solids: most notably, the process of forming a
glass does not release the latent heat of fusion, but forming a crystal does.
A crystal structure (an arrangement of atoms in a crystal) is characterized by its unit cell, a small imaginary box containing one or more atoms in a specific spatial arrangement. The unit cells are stacked in three-dimensional space to form the crystal.
As a halite crystal is growing, new atoms can very easily attach to the parts of the surface with rough atomic-scale structure and many dangling bonds.
Therefore, these parts of the crystal grow out very quickly (yellow
arrows). Eventually, the whole surface consists of smooth, stable faces, where new atoms cannot as easily attach themselves.
Crystals are commonly recognized, macroscopically, by their shape,
consisting of flat faces with sharp angles. These shape characteristics
are not necessary for a crystal—a crystal is scientifically
defined by its microscopic atomic arrangement, not its macroscopic
shape—but the characteristic macroscopic shape is often present and easy
to see.
Euhedral crystals are those that have obvious, well-formed flat faces. Anhedral crystals do not, usually because the crystal is one grain in a polycrystalline solid.
The flat faces (also called facets) of a euhedral crystal are oriented in a specific way relative to the underlying atomic arrangement of the crystal: they are planes of relatively low Miller index. This occurs because some surface orientations are more stable than others (lower surface energy).
As a crystal grows, new atoms attach easily to the rougher and less
stable parts of the surface, but less easily to the flat, stable
surfaces. Therefore, the flat surfaces tend to grow larger and smoother,
until the whole crystal surface consists of these plane surfaces. (See
diagram on right.)
One of the oldest techniques in the science of crystallography consists of measuring the three-dimensional orientations of the faces of a crystal, and using them to infer the underlying crystal symmetry.
A crystal's crystallographic forms are sets of possible faces of the crystal that are related by one of the symmetries of the crystal. For example, crystals of galena
often take the shape of cubes, and the six faces of the cube belong to a
crystallographic form that displays one of the symmetries of the isometric crystal system.
Galena also sometimes crystallizes as octahedrons, and the eight faces
of the octahedron belong to another crystallographic form reflecting a
different symmetry of the isometric system. A crystallographic form is
described by placing the Miller indices of one of its faces within
brackets. For example, the octahedral form is written as {111}, and the
other faces in the form are implied by the symmetry of the crystal.
Forms may be closed, meaning that the form can completely enclose
a volume of space, or open, meaning that it cannot. The cubic and
octahedral forms are examples of closed forms. All the forms of the
isometric system are closed, while all the forms of the monoclinic and
triclinic crystal systems are open. A crystal's faces may all belong to
the same closed form, or they may be a combination of multiple open or
closed forms.
A crystal's habit is its visible external shape. This is determined by the crystal structure
(which restricts the possible facet orientations), the specific crystal
chemistry and bonding (which may favor some facet types over others),
and the conditions under which the crystal formed.
By volume and weight, the largest concentrations of crystals in the Earth are part of its solid bedrock.
Crystals found in rocks typically range in size from a fraction of a
millimetre to several centimetres across, although exceptionally large
crystals are occasionally found. As of 1999, the world's largest known naturally occurring crystal is a crystal of beryl from Malakialina, Madagascar, 18 m (59 ft) long and 3.5 m (11 ft) in diameter, and weighing 380,000 kg (840,000 lb).
Some crystals have formed by magmatic and metamorphic processes, giving origin to large masses of crystalline rock. The vast majority of igneous rocks
are formed from molten magma and the degree of crystallization depends
primarily on the conditions under which they solidified. Such rocks as granite, which have cooled very slowly and under great pressures, have completely crystallized; but many kinds of lava were poured out at the surface and cooled very rapidly, and in this latter group a small amount of amorphous or glassy matter is common. Other crystalline rocks, the metamorphic rocks such as marbles, mica-schists and quartzites, are recrystallized. This means that they were at first fragmental rocks like limestone, shale and sandstone and have never been in a molten condition nor entirely in solution, but the high temperature and pressure conditions of metamorphism have acted on them by erasing their original structures and inducing recrystallization in the solid state.
Other rock crystals have formed out of precipitation from fluids, commonly water, to form druses or quartz veins. Evaporites such as halite, gypsum and some limestones have been deposited from aqueous solution, mostly owing to evaporation in arid climates.
Ice
Water-based ice in the form of snow, sea ice, and glaciers are common crystalline/polycrystalline structures on Earth and other planets. A single snowflake is a single crystal or a collection of crystals, while an ice cube is a polycrystal. Ice crystals may form from cooling liquid water below its freezing point, such as ice cubes or a frozen lake. Frost, snowflakes, or small ice crystals suspended in the air (ice fog) more often grow from a supersaturated gaseous-solution of water vapor and air, when the temperature of the air drops below its dew point,
without passing through a liquid state. Another unusual property of
water is that it expands rather than contracts when it crystallizes.
The same group of atoms can often solidify in many different ways. Polymorphism is the ability of a solid to exist in more than one crystal form. For example, water ice is ordinarily found in the hexagonal form Ice Ih, but can also exist as the cubic Ice Ic, the rhombohedralice II, and many other forms. The different polymorphs are usually called different phases.
In addition, the same atoms may be able to form noncrystalline phases. For example, water can also form amorphous ice, while SiO2 can form both fused silica (an amorphous glass) and quartz (a crystal). Likewise, if a substance can form crystals, it can also form polycrystals.
For pure chemical elements, polymorphism is known as allotropy. For example, diamond and graphite are two crystalline forms of carbon, while amorphous carbon
is a noncrystalline form. Polymorphs, despite having the same atoms,
may have very different properties. For example, diamond is the hardest
substance known, while graphite is so soft that it is used as a
lubricant. Chocolate
can form six different types of crystals, but only one has the suitable
hardness and melting point for candy bars and confections. Polymorphism
in steel is responsible for its ability to be heat treated, giving it a wide range of properties.
Crystallization is the process of forming a crystalline structure
from a fluid or from materials dissolved in a fluid. (More rarely,
crystals may be deposited directly from gas; see: epitaxy and frost.)
Crystallization is a complex and extensively-studied field,
because depending on the conditions, a single fluid can solidify into
many different possible forms. It can form a single crystal, perhaps with various possible phases, stoichiometries, impurities, defects, and habits. Or, it can form a polycrystal,
with various possibilities for the size, arrangement, orientation, and
phase of its grains. The final form of the solid is determined by the
conditions under which the fluid is being solidified, such as the
chemistry of the fluid, the ambient pressure, the temperature, and the speed with which all these parameters are changing.
Large single crystals can be created by geological processes. For example, selenite crystals in excess of 10 m are found in the Cave of the Crystals in Naica, Mexico. For more details on geological crystal formation, see above.
Crystals can also be formed by biological processes, see above. Conversely, some organisms have special techniques to prevent crystallization from occurring, such as antifreeze proteins.
An ideal crystal has every atom in a perfect, exactly repeating pattern. However, in reality, most crystalline materials have a variety of crystallographic defects,
places where the crystal's pattern is interrupted. The types and
structures of these defects may have a profound effect on the properties
of the materials.
Another common type of crystallographic defect is an impurity, meaning that the "wrong" type of atom is present in a crystal. For example, a perfect crystal of diamond would only contain carbon atoms, but a real crystal might perhaps contain a few boron atoms as well. These boron impurities change the diamond's color to slightly blue. Likewise, the only difference between ruby and sapphire is the type of impurities present in a corundum crystal.
In semiconductors, a special type of impurity, called a dopant, drastically changes the crystal's electrical properties. Semiconductor devices, such as transistors, are made possible largely by putting different semiconductor dopants into different places, in specific patterns.
Twinning is a phenomenon somewhere between a crystallographic defect and a grain boundary.
Like a grain boundary, a twin boundary has different crystal
orientations on its two sides. But unlike a grain boundary, the
orientations are not random, but related in a specific, mirror-image
way.
Mosaicity is a spread of crystal plane orientations. A mosaic crystal consists of smaller crystalline units that are somewhat misaligned with respect to each other.
Metals crystallize rapidly and are almost always polycrystalline, though there are exceptions like amorphous metal
and single-crystal metals. The latter are grown synthetically, for
example, fighter-jet turbines are typically made by first growing a
single crystal of titanium alloy, increasing its strength and melting
point over polycrystalline titanium. A small piece of metal may
naturally form into a single crystal, such as Type 2 telluric iron, but larger pieces generally do not unless extremely slow cooling occurs. For example, iron meteorites
are often composed of single crystal, or many large crystals that may
be several meters in size, due to very slow cooling in the vacuum of
space. The slow cooling may allow the precipitation of a separate phase
within the crystal lattice, which form at specific angles determined by
the lattice, called Widmanstatten patterns.
Ionic compounds
typically form when a metal reacts with a non-metal, such as sodium
with chlorine. These often form substances called salts, such as sodium
chloride (table salt) or potassium nitrate (saltpeter),
with crystals that are often brittle and cleave relatively easily.
Ionic materials are usually crystalline or polycrystalline. In practice,
large salt crystals can be created by solidification of a molten fluid, or by crystallization out of a solution. Some ionic compounds can be very hard, such as oxides like aluminium oxide found in many gemstones such as ruby and synthetic sapphire.
Covalently bonded solids (sometimes called covalent network solids)
are typically formed from one or more non-metals, such as carbon or
silicon and oxygen, and are often very hard, rigid, and brittle. These
are also very common, notable examples being diamond and quartz respectively.
Weak van der Waals forces also help hold together certain crystals, such as crystalline molecular solids, as well as the interlayer bonding in graphite. Substances such as fats, lipids and wax
form molecular bonds because the large molecules do not pack as tightly
as atomic bonds. This leads to crystals that are much softer and more
easily pulled apart or broken. Common examples include chocolates,
candles, or viruses. Water ice and dry ice are examples of other materials with molecular bonding.Polymer
materials generally will form crystalline regions, but the lengths of
the molecules usually prevent complete crystallization—and sometimes
polymers are completely amorphous.
A quasicrystal
consists of arrays of atoms that are ordered but not strictly periodic.
They have many attributes in common with ordinary crystals, such as
displaying a discrete pattern in x-ray diffraction, and the ability to form shapes with smooth, flat faces.
Quasicrystals are most famous for their ability to show five-fold
symmetry, which is impossible for an ordinary periodic crystal (see crystallographic restriction theorem).
The International Union of Crystallography
has redefined the term "crystal" to include both ordinary periodic
crystals and quasicrystals ("any solid having an essentially discrete diffraction diagram").
Quasicrystals, first discovered in 1982, are quite rare in
practice. Only about 100 solids are known to form quasicrystals,
compared to about 400,000 periodic crystals known in 2004. The 2011 Nobel Prize in Chemistry was awarded to Dan Shechtman for the discovery of quasicrystals.
Crystals can have certain special electrical, optical, and mechanical properties that glass and polycrystals normally cannot. These properties are related to the anisotropy of the crystal, i.e. the lack of rotational symmetry in its atomic arrangement. One such property is the piezoelectric effect, where a voltage across the crystal can shrink or stretch it. Another is birefringence, where a double image appears when looking through a crystal. Moreover, various properties of a crystal, including electrical conductivity, electrical permittivity, and Young's modulus, may be different in different directions in a crystal. For example, graphite
crystals consist of a stack of sheets, and although each individual
sheet is mechanically very strong, the sheets are rather loosely bound
to each other. Therefore, the mechanical strength of the material is
quite different depending on the direction of stress.
An electron microprobe (EMP), also known as an electron probe microanalyzer (EPMA) or electron micro probe analyzer
(EMPA), is an analytical tool used to non-destructively determine the
chemical composition of small volumes of solid materials. It works
similarly to a scanning electron microscope: the sample is bombarded with an electron beam,
emitting x-rays at wavelengths characteristic to the elements being
analyzed. This enables the abundances of elements present within small
sample volumes (typically 10-30 cubic micrometers or less) to be determined, when a conventional accelerating voltage of 15-20 kV is used. The concentrations of elements from lithium to plutonium may be measured at levels as low as 100 parts per million (ppm), material dependent, although with care, levels below 10 ppm are possible. The ability to quantify lithium by EPMA became a reality in 2008.
History
The electron microprobe (electron probe microanalyzer) developed from two technologies: electron microscopy — using a focused high energy electron beam to impact a target material, and X-ray spectroscopy
— identification of the photons scattered from the electron beam
impact, with the energy/wavelength of the photons characteristic of the
atoms excited by the incident electrons. Ernst Ruska and Max Knoll are associated with the prototype electron microscope in 1931. Henry Moseley
was involved in the discovery of the direct relationship between the
wavelength of X-rays and the identity of the atom from which it
originated.
There have been at several historical threads to electron beam microanalysis. One was developed by James Hillier and Richard Baker at RCA. In the early 1940s, they built an electron microprobe, combining an electron microscope and an energy loss spectrometer. A patent application was filed in 1944. Electron energy loss spectroscopy
is very good for light element analysis and they obtained spectra of
C-Kα, N-Kα and O-Kα radiation. In 1947, Hiller patented the concept of
using an electron beam to produce analytical X-rays, but never
constructed a working model. His design proposed using Bragg diffraction from a flat crystal to select specific X-ray wavelengths and a photographic plate as a detector. However, RCA had no interest in commercializing this invention.
A second thread developed in France in the late 1940s. In 1948–1950, Raimond Castaing, supervised by André Guinier, built the first electron “microsonde électronique” (electron microprobe) at ONERA.
This microprobe produced an electron beam diameter of 1-3 μm with a
beam current of ~10 nanoamperes (nA) and used a Geiger counter to detect
the X-rays produced from the sample. However, the Geiger counter could
not distinguish X-rays produced from specific elements and in 1950,
Castaing added a quartz
crystal between the sample and the detector to permit wavelength
discrimination. He also added an optical microscope to view the point of
beam impact. The resulting microprobe was described in Castaing's 1951
PhD Thesis, translated into English by Pol Duwez and David Wittry,
in which he laid the foundations of the theory and application of
quantitative analysis by electron microprobe, establishing the
theoretical framework for the matrix corrections of absorption and
fluorescence effects. Castaing (1921-1999) is considered the father of
electron microprobe analysis.
The 1950s was a decade of great interest in electron beam X-ray
microanalysis, following Castaing's presentations at the First European
Microscopy Conference in Delft in 1949 and then at the National Bureau of Standards conference on Electron Physics
in Washington, DC, in 1951, as well as at other conferences in the
early to mid-1950s. Many researchers, mainly material scientists,
developed their own experimental electron microprobes, sometimes
starting from scratch, but many times using surplus electron
microscopes.
One of the organizers of the Delft 1949 Electron Microscopy conference was Vernon Ellis Cosslett at the Cavendish Laboratory at Cambridge University, a center of research on electron microscopy, as well as scanning electron microscopy with Charles Oatley as well as X-ray microscopy with Bill Nixon. Peter Duncumb
combined all three technologies and developed a scanning electron X-ray
microanalyzer for his PhD thesis (1957), which was commercialized as
the Cambridge MicroScan.
Pol Duwez,
a Belgian material scientist who fled the Nazis and settled at the
California Institute of Technology and collaborated with Jesse DuMond,
encountered André Guinier
on a train in Europe in 1952, where he learned of Castaing's new
instrument and the suggestion that Caltech build a similar instrument.
David Wittry was hired to build such an instrument as his PhD thesis,
which he completed in 1957. It became the prototype for the ARL EMX electron microprobe.
During the late 1950s and early 1960s there were over a dozen
other laboratories in North America, the United Kingdom, Europe, Japan
and the USSR developing electron beam X-ray microanalyzers.
The first commercial electron microprobe, the "MS85" was produced by CAMECA (France) in 1956. It was soon followed in the early-mid 1960s by microprobes from other companies; however, all companies except CAMECA, JEOL and Shimadzu Corporation
went out of business. In addition, many researchers build electron
microprobes in their labs. Significant subsequent improvements and
modifications to microprobes included scanning the electron beam to make
X-ray maps (1960), the addition of solid state EDS detectors (1968) and
the development of synthetic multilayer diffracting crystals for
analysis of light elements (1984). Later, CAMECA pioneered manufacturing a shielded electron microprobe for nuclear applications. Several advances in CAMECA instruments in recent decades expanded the range of applications on metallurgy, electronics, geology, mineralogy, nuclear plants, trace elements, and dentistry.
Operation
A beam of electrons is fired at a sample. The beam causes each element in the sample to emit X-rays at a characteristic frequency; the X-rays can then be detected by the electron microprobe.
The size and current density of the electron beam determines the
trade-off between resolution and scan time and/or analysis time.
Detailed description
Low-energy electrons are produced from a tungsten filament, a lanthanum hexaboride crystal cathode or a field emission electron source and accelerated by a positively biased anode plate to 3 to 30 thousand electron volts
(keV). The anode plate has central aperture and electrons that pass
through it are collimated and focused by a series of magnetic lenses and
apertures. The resulting electron beam (approximately 5 nm to 10 μm
diameter) may be rastered across the sample or used in spot mode to
produce excitation of various effects in the sample. Among these effects
are: phonon excitation (heat), cathodoluminescence (visible light fluorescence), continuum X-ray radiation (bremsstrahlung), characteristic X-ray radiation, secondary electrons (plasmon production), backscattered electron production, and Auger electron production.
When the beam electrons (and scattered electrons from the sample)
interact with bound electrons in the innermost electron shells of the
atoms of the various elements in the sample, they can scatter the bound
electrons from the electron shell producing a vacancy in that shell
(ionization of the atom). This vacancy is unstable and must be filled by
an electron from either a higher energy bound shell in the atom
(producing another vacancy which is in turn filled by electrons from yet
higher energy bound shells) or by unbound electrons of low energy. The
difference in binding energy between the electron shell in which the
vacancy was produced and the shell from which the electron comes to fill
the vacancy is emitted as a photon. The energy of the photon is in the
X-ray region of the electromagnetic spectrum.
As the electron structure of each element is unique, the series X-ray
line energies produced by vacancies in the innermost shells is
characteristic of that element, although lines from different elements
may overlap. As the innermost shells are involved, the X-ray line
energies are generally not affected by chemical effects produced by
bonding between elements in compounds except in low atomic number (Z)
elements ( B, C, N, O and F for Kalpha and Al to Cl for Kbeta)
where line energies may be shifted as a result of the involvement of
the electron shell from which vacancies are filled in chemical bonding.
The characteristic X-rays are used for chemical analysis.
Specific X-ray wavelengths or energies are selected and counted, either
by wavelength dispersive X-ray spectroscopy (WDS) or energy dispersive X-ray spectroscopy (EDS). WDS utilizes Bragg diffraction
from crystals to select X-ray wavelengths of interest and direct them
to gas-flow or sealed proportional detectors. In contrast, EDS uses a
solid state semiconductor detector
to accumulate X-rays of all wavelengths produced from the sample. While
EDS yields more information and typically requires a much shorter
counting time, WDS is generally more precise with lower limits of
detection due to its superior X-ray peak resolution and greater peak to
background ratio.
Chemical composition is determined by comparing the intensities
of characteristic X-rays from the sample with intensities from standards
of known composition. Counts from the sample must be corrected for matrix effects (depth of production of the X-rays, absorption and secondary fluorescence)
to yield quantitative chemical compositions. The resulting chemical
data is gathered in textural context. Variations in chemical composition
within a material (zoning), such as a mineral grain or metal, can be
readily determined.
Volume from which chemical information is gathered (volume of X-rays generated) is 0.3 – 3 cubic micrometers.
Limitations
WDS
cannot determine elements below number 3 (lithium). This restricts WDS
when analyzing geologically important elements such as H, Li, and Be.
Despite the improved spectral resolution of elemental peaks, some
peaks exhibit significant overlap that causes analytical challenges
(e.g., VKα and TiKβ). WDS analyses are unable to distinguish the valence
states of elements (e.g. Fe2+ vs. Fe3+) which must be obtained by other techniques such as Mössbauer spectroscopy or electron energy loss spectroscopy.
Element isotopes cannot be determined by WDS, but are most commonly obtained with a mass spectrometer.
The technique is commonly used for analyzing the chemical composition of metals, alloys, ceramics, and glasses.
It is particularly useful for assessing the composition of individual
particles or grains and chemical changes on the scale of a few
micrometres to millimeters. The electron microprobe is widely used for
research, quality control, and failure analysis.
Mineralogy and petrology
This technique is most commonly used by mineralogists and petrologists.
Most rocks are aggregates of small mineral grains. These grains may
preserve chemical information acquired during their formation and
subsequent alteration. This information may illuminate geologic
processes such as crystallization, lithification, volcanism, metamorphism, orogenic events (mountain building), and plate tectonics. This technique is also used for the study of extraterrestrial rocks (meteorites), and provides chemical data which is vital to understanding the evolution of the planets, asteroids, and comets.
The change in elemental composition from the center (also known
as core) to the edge (or rim) of a mineral can yield information about
the history of the crystal's formation, including the temperature,
pressure, and chemistry of the surrounding medium. Quartz crystals, for
example, incorporate a small, but measurable amount of titanium into
their structure as a function of temperature, pressure, and the amount
of titanium available in their environment. Changes in these parameters
are recorded by titanium as the crystal grows.
In exceptionally preserved fossils, such as those of the Burgess shale,
soft parts of organisms may be preserved. Since these fossils are often
compressed into a planar film, it can be difficult to distinguish the
features: a famous example is the triangular extensions in Opabinia,
which were interpreted as either legs or extensions of the gut.
Elemental mapping showed that their composition was similar to the gut,
favoring that interpretation. Because of the thinness of carbon films, only low voltages (5-15 kV) can be used on them.
Meteorite analysis
The
chemical composition of meteorites can be analyzed quite accurately
using EPMA. This can reveal much about the conditions that existed in
the early Solar System.
EDS spectrum of the mineral crust of the vent shrimp Rimicaris exoculata Most of these peaks are X-rays emitted when electrons return to the K electron shell (K-alpha and K-beta lines). One peak is from the L shell of iron.
Energy-dispersive X-ray spectroscopy (EDS, EDX, EDXS or XEDS), sometimes called energy dispersive X-ray analysis (EDXA or EDAX) or energy dispersive X-ray microanalysis (EDXMA), is an analytical technique used for the elemental analysis or chemical characterization of a sample. It relies on an interaction of some source of X-ray
excitation and a sample. Its characterization capabilities are due in
large part to the fundamental principle that each element has a unique atomic structure allowing a unique set of peaks on its electromagnetic emission spectrum (which is the main principle of spectroscopy). The peak positions are predicted by the Moseley's law with accuracy much better than experimental resolution of a typical EDX instrument.
To stimulate the emission of characteristic X-rays from a
specimen a beam of electrons or X-ray is focused into the sample being
studied. At rest, an atom within the sample contains ground state (or unexcited) electrons in discrete energy levels or electron shells bound to the nucleus. The incident beam may excite an electron in an inner shell, ejecting it from the shell while creating an electron hole
where the electron was. An electron from an outer, higher-energy shell
then fills the hole, and the difference in energy between the
higher-energy shell and the lower energy shell may be released in the
form of an X-ray. The number and energy of the X-rays emitted from a
specimen can be measured by an energy-dispersive spectrometer. As the
energies of the X-rays are characteristic of the difference in energy
between the two shells and of the atomic structure of the emitting
element, EDS allows the elemental composition of the specimen to be
measured.
Equipment
Four primary components of the EDS setup are
the excitation source (electron beam or x-ray beam)
The excess energy of the electron that migrates to an inner shell to fill the newly created hole can do more than emit an X-ray.[3]
Often, instead of X-ray emission, the excess energy is transferred to a
third electron from a further outer shell, prompting its ejection. This
ejected species is called an Auger electron, and the method for its analysis is known as Auger electron spectroscopy (AES).
X-ray photoelectron spectroscopy
(XPS) is another close relative of EDS, utilizing ejected electrons in a
manner similar to that of AES. Information on the quantity and kinetic energy of ejected electrons is used to determine the binding energy of these now-liberated electrons, which is element-specific and allows chemical characterization of a sample.
EDS is often contrasted with its spectroscopic counterpart, wavelength dispersive X-ray spectroscopy (WDS). WDS differs from EDS in that it uses the diffraction
of X-rays on special crystals to separate its raw data into spectral
components (wavelengths). WDS has a much finer spectral resolution than
EDS. WDS also avoids the problems associated with artifacts in EDS
(false peaks, noise from the amplifiers, and microphonics).
EDS
can be used to determine which chemical elements are present in a
sample, and can be used to estimate their relative abundance. EDS also
helps to measure multi-layer coating thickness of metallic coatings and
analysis of various alloys. The accuracy of this quantitative analysis
of sample composition is affected by various factors. Many elements will
have overlapping X-ray emission peaks (e.g., Ti Kβ and V Kα, Mn Kβ and Fe Kα).
The accuracy of the measured composition is also affected by the nature
of the sample. X-rays are generated by any atom in the sample that is
sufficiently excited by the incoming beam. These X-rays are emitted in
all directions (isotropically), and so they may not all escape the
sample. The likelihood of an X-ray escaping the specimen, and thus being
available to detect and measure, depends on the energy of the X-ray and
the composition, amount, and density of material it has to pass through
to reach the detector. Because of this X-ray absorption effect and
similar effects, accurate estimation of the sample composition from the
measured X-ray emission spectrum requires the application of
quantitative correction procedures, which are sometimes referred to as
matrix corrections.
Emerging technology
There is a trend towards a newer EDS detector, called the silicon drift detector
(SDD). The SDD consists of a high-resistivity silicon chip where
electrons are driven to a small collecting anode. The advantage lies in
the extremely low capacitance of this anode, thereby utilizing shorter
processing times and allowing very high throughput. Benefits of the SDD
include:
High count rates and processing,
Better resolution than traditional Si(Li) detectors at high count rates,
Lower dead time (time spent on processing X-ray event),
Faster analytical capabilities and more precise X-ray maps or particle data collected in seconds,
Ability to be stored and operated at relatively high temperatures, eliminating the need for liquid nitrogen cooling.
Because the capacitance of the SDD chip is independent of the active
area of the detector, much larger SDD chips can be utilized (40 mm2 or more). This allows for even higher count rate collection. Further benefits of large area chips include:
Minimizing SEM beam current allowing for optimization of imaging under analytical conditions,
Reduced sample damage and
Smaller beam interaction and improved spatial resolution for high speed maps.
Where the X-ray energies of interest are in excess of ~ 30 keV,
traditional silicon-based technologies suffer from poor quantum
efficiency due to a reduction in the detector stopping power. Detectors produced from high density semiconductors such as cadmium telluride (CdTe) and cadmium zinc telluride
(CdZnTe) have improved efficiency at higher X-ray energies and are
capable of room temperature operation. Single element systems, and more
recently pixelated imaging detectors such as the high energy X-ray imaging technology (HEXITEC) system, are capable of achieving energy resolutions of the order of 1% at 100 keV.
In recent years, a different type of EDS detector, based upon a superconducting microcalorimeter,
has also become commercially available. This new technology combines
the simultaneous detection capabilities of EDS with the high spectral
resolution of WDS. The EDS microcalorimeter consists of two components:
an absorber, and a superconducting transition-edge sensor (TES) thermometer.
The former absorbs X-rays emitted from the sample and converts this
energy into heat; the latter measures the subsequent change in
temperature due to the influx of heat. The EDS microcalorimeter has
historically suffered from a number of drawbacks, including low count
rates and small detector areas. The count rate is hampered by its
reliance on the time constant of the calorimeter's electrical circuit. The detector area must be small in order to keep the heat capacity small and maximize thermal sensitivity (resolution).
However, the count rate and detector area have been improved by the
implementation of arrays of hundreds of superconducting EDS
microcalorimeters, and the importance of this technology is growing.
