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Size-exclusion chromatography

Size-exclusion chromatography, also known as molecular sieve chromatography, is a chromatographic method in which molecules in solution are separated by their size, and in some cases molecular weight. It is usually applied to large molecules or macromolecular complexes such as proteins and industrial polymers. Typically, when an aqueous solution is used to transport the sample through the column, the technique is known as gel-filtration chromatography, versus the name gel permeation chromatography, which is used when an organic solvent is used as a mobile phase. The chromatography column is packed with fine, porous beads which are commonly composed of dextran, agarose, or polyacrylamide polymers. The pore sizes of these beads are used to estimate the dimensions of macromolecules. SEC is a widely used polymer characterization method because of its ability to provide good molar mass distribution (Mw) results for polymers.

Size exclusion chromatography (SEC) is fundamentally different from all other chromatographic techniques in that separation is based on a simple procedure of classifying molecule sizes rather than any type of interaction.

Applications
The main application of size-exclusion chromatography is the fractionation of proteins and other water-soluble polymers, while gel permeation chromatography is used to analyze the molecular weight distribution of organic-soluble polymers. Either technique should not be confused with gel electrophoresis, where an electric field is used to "pull" molecules through the gel depending on their electrical charges. The amount of time a solute remains within a pore is dependent on the size of the pore. Larger solutes will have access to a smaller volume and vice versa. Therefore, a smaller solute will remain within the pore for a longer period of time compared to a larger solute.

Even though size exclusion chromatography is widely utilized to study natural organic material, there are limitations. One of these limitations include that there is no standard molecular weight marker; thus, there is nothing to compare the results back to. If precise molecular weight is required, other methods should be used.

Advantages
The advantages of this method include good separation of large molecules from the small molecules with a minimal volume of eluate, and that various solutions can be applied without interfering with the filtration process, all while preserving the biological activity of the particles to separate. The technique is generally combined with others that further separate molecules by other characteristics, such as acidity, basicity, charge, and affinity for certain compounds. With size exclusion chromatography, there are short and well-defined separation times and narrow bands, which lead to good sensitivity. There is also no sample loss because solutes do not interact with the stationary phase.

The other advantage to this experimental method is that in certain cases, it is feasible to determine the approximate molecular weight of a compound. The shape and size of the compound (eluent) determine how the compound interacts with the gel (stationary phase). To determine approximate molecular weight, the elution volumes of compounds with their corresponding molecular weights are obtained and then a plot of “Kav” vs “log(Mw)” is made, where $$K_{av} = (V_e-V_o)/(V_t-V_o)$$ and Mw is the molecular mass. This plot acts as a calibration curve, which is used to approximate the desired compound's molecular weight. The Ve component represents the volume at which the intermediate molecules elute such as molecules that have partial access to the beads of the column. In addition, Vt is the sum of the total volume between the beads and the volume within the beads. The Vo component represents the volume at which the larger molecules elute, which elute in the beginning. Disadvantages are, for example, that only a limited number of bands can be accommodated because the time scale of the chromatogram is short, and, in general, there must be a 10% difference in molecular mass to have a good resolution.

Discovery
The technique was invented in 1955 by Grant Henry Lathe and Colin R Ruthven, working at Queen Charlotte's Hospital, London. They later received the John Scott Award for this invention. While Lathe and Ruthven used starch gels as the matrix, Jerker Porath and Per Flodin later introduced dextran gels; other gels with size fractionation properties include agarose and polyacrylamide. A short review of these developments has appeared.

There were also attempts to fractionate synthetic high polymers; however, it was not until 1964, when J. C. Moore of the Dow Chemical Company published his work on the preparation of gel permeation chromatography (GPC) columns based on cross-linked polystyrene with controlled pore size, that a rapid increase of research activity in this field began. It was recognized almost immediately that with proper calibration, GPC was capable to provide molar mass and molar mass distribution information for synthetic polymers. Because the latter information was difficult to obtain by other methods, GPC came rapidly into extensive use.

Theory and method

SEC is used primarily for the analysis of large molecules such as proteins or polymers. SEC works by trapping smaller molecules in the pores of the adsorbent ("stationary phase"). This process is usually performed within a column, which typically consists of a hollow tube tightly packed with micron-scale polymer beads containing pores of different sizes. These pores may be depressions on the surface or channels through the bead. As the solution travels down the column some particles enter into the pores. Larger particles cannot enter into as many pores. The larger the particles, the faster the elution. The larger molecules simply pass by the pores because those molecules are too large to enter the pores. Larger molecules therefore flow through the column more quickly than smaller molecules, that is, the smaller the molecule, the longer the retention time.

One requirement for SEC is that the analyte does not interact with the surface of the stationary phases, with differences in elution time between analytes ideally being based solely on the solute volume the analytes can enter, rather than chemical or electrostatic interactions with the stationary phases. Thus, a small molecule that can penetrate every region of the stationary phase pore system can enter a total volume equal to the sum of the entire pore volume and the interparticle volume. This small molecule elutes late (after the molecule has penetrated all of the pore- and interparticle volume—approximately 80% of the column volume). At the other extreme, a very large molecule that cannot penetrate any the smaller pores can enter only the interparticle volume (~35% of the column volume) and elutes earlier when this volume of mobile phase has passed through the column. The underlying principle of SEC is that particles of different sizes elute (filter) through a stationary phase at different rates. This results in the separation of a solution of particles based on size. Provided that all the particles are loaded simultaneously or near-simultaneously, particles of the same size should elute together.

However, as there are various measures of the size of a macromolecule (for instance, the radius of gyration and the hydrodynamic radius), a fundamental problem in the theory of SEC has been the choice of a proper molecular size parameter by which molecules of different kinds are separated. Experimentally, Benoit and co-workers found an excellent correlation between elution volume and a dynamically based molecular size, the hydrodynamic volume, for several different chain architecture and chemical compositions. The observed correlation based on the hydrodynamic volume became accepted as the basis of universal SEC calibration.

Still, the use of the hydrodynamic volume, a size based on dynamical properties, in the interpretation of SEC data is not fully understood. This is because SEC is typically run under low flow rate conditions where hydrodynamic factor should have little effect on the separation. In fact, both theory and computer simulations assume a thermodynamic separation principle: the separation process is determined by the equilibrium distribution (partitioning) of solute macromolecules between two phases: a dilute bulk solution phase located at the interstitial space and confined solution phases within the pores of column packing material. Based on this theory, it has been shown that the relevant size parameter to the partitioning of polymers in pores is the mean span dimension (mean maximal projection onto a line). Although this issue has not been fully resolved, it is likely that the mean span dimension and the hydrodynamic volume are strongly correlated.

Each size exclusion column has a range of molecular weights that can be separated. The exclusion limit defines the molecular weight at the upper end of the column 'working' range and is where molecules are too large to get trapped in the stationary phase. The lower end of the range is defined by the permeation limit, which defines the molecular weight of a molecule that is small enough to penetrate all pores of the stationary phase. All molecules below this molecular mass are so small that they elute as a single band.

The filtered solution that is collected at the end is known as the eluate. The void volume includes any particles too large to enter the medium, and the solvent volume is known as the column volume.

Following are the materials which are commonly used for porous gel beads in size exclusion chromatography

Factors affecting filtration
In real-life situations, particles in solution do not have a fixed size, resulting in the probability that a particle that would otherwise be hampered by a pore passing right by it. Also, the stationary-phase particles are not ideally defined; both particles and pores may vary in size. Elution curves, therefore, resemble Gaussian distributions. The stationary phase may also interact in undesirable ways with a particle and influence retention times, though great care is taken by column manufacturers to use stationary phases that are inert and minimize this issue.

Like other forms of chromatography, increasing the column length enhances resolution, and increasing the column diameter increases column capacity. Proper column packing is important for maximum resolution: An over-packed column can collapse the pores in the beads, resulting in a loss of resolution. An under-packed column can reduce the relative surface area of the stationary phase accessible to smaller species, resulting in those species spending less time trapped in pores. Unlike affinity chromatography techniques, a solvent head at the top of the column can drastically diminish resolution as the sample diffuses prior to loading, broadening the downstream elution.

Analysis
In simple manual columns, the eluent is collected in constant volumes, known as fractions. The more similar the particles are in size the more likely they are in the same fraction and not detected separately. More advanced columns overcome this problem by constantly monitoring the eluent. The collected fractions are often examined by spectroscopic techniques to determine the concentration of the particles eluted. Common spectroscopy detection techniques are refractive index (RI) and ultraviolet (UV). When eluting spectroscopically similar species (such as during biological purification), other techniques may be necessary to identify the contents of each fraction. It is also possible to analyze the eluent flow continuously with RI, LALLS, Multi-Angle Laser Light Scattering MALS, UV, and/or viscosity measurements.

The elution volume (Ve) decreases roughly linear with the logarithm of the molecular hydrodynamic volume. Columns are often calibrated using 4-5 standard samples (e.g., folded proteins of known molecular weight), and a sample containing a very large molecule such as thyroglobulin to determine the void volume. (Blue dextran is not recommended for Vo determination because it is heterogeneous and may give variable results) The elution volumes of the standards are divided by the elution volume of the thyroglobulin (Ve/Vo) and plotted against the log of the standards' molecular weights.

Biochemical applications
In general, SEC is considered a low-resolution chromatography as it does not discern similar species very well, and is therefore often reserved for the final step of a purification. The technique can determine the quaternary structure of purified proteins that have slow exchange times, since it can be carried out under native solution conditions, preserving macromolecular interactions. SEC can also assay protein tertiary structure, as it measures the hydrodynamic volume (not molecular weight), allowing folded and unfolded versions of the same protein to be distinguished. For example, the apparent hydrodynamic radius of a typical protein domain might be 14 Å and 36 Å for the folded and unfolded forms, respectively. SEC allows the separation of these two forms, as the folded form elutes much later due to its smaller size.

Polymer synthesis
SEC can be used as a measure of both the size and the polydispersity of a synthesized polymer, that is, the ability to find the distribution of the sizes of polymer molecules. If standards of a known size are run previously, then a calibration curve can be created to determine the sizes of polymer molecules of interest in the solvent chosen for analysis (often THF). In alternative fashion, techniques such as light scattering and/or viscometry can be used online with SEC to yield absolute molecular weights that do not rely on calibration with standards of known molecular weight. Due to the difference in size of two polymers with identical molecular weights, the absolute determination methods are, in general, more desirable. A typical SEC system can quickly (in about half an hour) give polymer chemists information on the size and polydispersity of the sample. The preparative SEC can be used for polymer fractionation on an analytical scale.

Drawbacks
In SEC, mass is not measured so much as the hydrodynamic volume of the polymer molecules, that is, how much space a particular polymer molecule takes up when it is in solution. However, the approximate molecular weight can be calculated from SEC data because the exact relationship between molecular weight and hydrodynamic volume for polystyrene can be found. For this, polystyrene is used as a standard. But the relationship between hydrodynamic volume and molecular weight is not the same for all polymers, so only an approximate measurement can be obtained. Another drawback is the possibility of interaction between the stationary phase and the analyte. Any interaction leads to a later elution time and thus mimics a smaller analyte size.

When performing this method, the bands of the eluting molecules may be broadened. This can occur by turbulence caused by the flow of the mobile phase molecules passing through the molecules of the stationary phase. In addition, molecular thermal diffusion and friction between the molecules of the glass walls and the molecules of the eluent contribute to the broadening of the bands. Besides broadening, the bands also overlap with each other. As a result, the eluent usually gets considerably diluted. A few precautions can be taken to prevent the likelihood of the bands broadening. For instance, one can apply the sample in a narrow, highly concentrated band on the top of the column. The more concentrated the eluent is, the more efficient the procedure would be. However, it is not always possible to concentrate the eluent, which can be considered as one more disadvantage.

Absolute size-exclusion chromatography
Absolute size-exclusion chromatography (ASEC) is a technique that couples a light scattering instrument, most commonly multi-angle light scattering (MALS) or another form of static light scattering (SLS), but possibly a dynamic light scattering (DLS) instrument, to a size-exclusion chromatography system for absolute molar mass and/or size measurements of proteins and macromolecules as they elute from the chromatography system.

The definition of “absolute” in this case is that calibration of retention time on the column with a set of reference standards is not required to obtain molar mass or the hydrodynamic size, often referred to as hydrodynamic diameter (DH in units of nm). Non-ideal column interactions, such as electrostatic or hydrophobic surface interactions that modulate retention time relative to standards, do not impact the final result. Likewise, differences between conformation of the analyte and the standard have no effect on an absolute measurement; for example, with MALS analysis, the molar mass of inherently disordered proteins are characterized accurately even though they elute at much earlier times than globular proteins with the same molar mass, and the same is true of branched polymers which elute late compared to linear reference standards with the same molar mass. Another benefit of ASEC is that the molar mass and/or size is determined at each point in an eluting peak, and therefore indicates homogeneity or polydispersity within the peak. For example, SEC-MALS analysis of a monodisperse protein will show that the entire peak consists of molecules with the same molar mass, something that is not possible with standard SEC analysis.

Determination of molar mass with SLS requires combining the light scattering measurements with concentration measurements. Therefore SEC-MALS typically includes the light scattering detector and either a differential refractometer or UV/Vis absorbance detector. In addition, MALS determines the rms radius Rg of molecules above a certain size limit, typically 10 nm. SEC-MALS can therefore analyze the conformation of polymers via the relationship of molar mass to Rg. For smaller molecules, either DLS or, more commonly, a differential viscometer is added to determine hydrodynamic radius and evaluate molecular conformation in the same manner.

In SEC-DLS, the sizes of the macromolecules are measured as they elute into the flow cell of the DLS instrument from the size exclusion column set. The hydrodynamic size of the molecules or particles are measured and not their molecular weights. For proteins a Mark-Houwink type of calculation can be used to estimate the molecular weight from the hydrodynamic size.

A major advantage of DLS coupled with SEC is the ability to obtain enhanced DLS resolution. Batch DLS is quick and simple and provides a direct measure of the average size, but the baseline resolution of DLS is a ratio of 3:1 in diameter. Using SEC, the proteins and protein oligomers are separated, allowing oligomeric resolution. Aggregation studies can also be done using ASEC. Though the aggregate concentration may not be calculated with light scattering (an online concentration detector such as that used in SEC-MALS for molar mass measurement also determines aggregate concentration), the size of the aggregate can be measured, only limited by the maximum size eluting from the SEC columns.

Limitations of ASEC with DLS detection include flow-rate, concentration, and precision. Because a correlation function requires anywhere from 3–7 seconds to properly build, a limited number of data points can be collected across the peak. ASEC with SLS detection is not limited by flow rate and measurement time is essentially instantaneous, and the range of concentration is several orders of magnitude larger than for DLS. However, molar mass analysis with SEC-MALS does require accurate concentration measurements. MALS and DLS detectors are often combined in a single instrument for more comprehensive absolute analysis following separation by SEC.

title: Size-exclusion chromatography


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Vostok

Vostok (Восток) refers to east in Russian but may also refer to:

Spaceflight

 * Vostok programme, Soviet human spaceflight project
 * Vostok (spacecraft), a type of spacecraft built by the Soviet Union
 * Vostok (rocket family), family of rockets derived from the Soviet R-7 Semyorka ICBM designed for the human spaceflight programme
 * Vostok (crater), a crater explored by the Mars rover Opportunity
 * Vostok 1, the first human spaceflight

Places

 * Vostok Island, located in the south of Kiribati's Line Islands
 * Uschod (Minsk Metro) (Russian name Vostok), a station of Minsk Metro, Minsk, Belarus
 * Vostok Rupes, a mountain chain on planet Mercury

Antarctica

 * Cape Vostok, the west extremity of the Havre Mountains and the northwest extremity of Alexander Island
 * Vostok Station, Russian (originally Soviet) Antarctic research station
 * Lake Vostok, a subglacial lake located beneath Vostok Station
 * Vostok Subglacial Highlands, an east extension of Gamburtsev Subglacial Mountains

Russia

 * Vostok (inhabited locality), several inhabited localities
 * Vostok Bay, bay in south Primorsky Krai

Organizations

 * Vostok watches, a brand of watch made in Chistopol, Tatarstan, Russia
 * Vostok motorcycles, a motorcycle company, participant in 1965 Grand Prix motorcycle racing season
 * Vostok Gas, a Bermuda-based oil and gas investment company
 * Vostok Games, a Ukrainian game developer
 * Special Battalion Vostok, a Chechen military unit

Sport

 * Vostok Arsenyev, a Russian bandy club
 * FC Vostok, a Kazakhstani football club

Fictional entities

 * Valentina Vostok, a fictional comic book character appearing in books published by DC Comics
 * Vostok, a member of the fictional superhero team Soviet Super-Soldiers, which appears in Marvel Comics
 * Vostok-X, a member of the fictional superhero team Aquaman and the Others, which appears in DC Comics

Other uses

 * Vostok (novel), a 2015 The Loch/Meg crossover novel by Steve Alten
 * Vostok (sloop-of-war), an 1818 ship of Faddey Bellingshausen during the First Russian Antarctic Expedition
 * Vostok traverse, a 1962 Australian expedition across Antarctica
 * Exercise Vostok, Russian military exercises, similar to Exercise Zapad

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Vostok


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Differential scanning calorimetry

Differential scanning calorimetry (DSC) is a thermoanalytical technique in which the difference in the amount of heat required to increase the temperature of a sample and reference is measured as a function of temperature. Both the sample and reference are maintained at nearly the same temperature throughout the experiment. Generally, the temperature program for a DSC analysis is designed such that the sample holder temperature increases linearly as a function of time. The reference sample should have a well-defined heat capacity over the range of temperatures to be scanned. Additionally, the reference sample must be stable, of high purity, and must not experience much change across the temperature scan. Typically, reference standards have been metals such as indium, tin, bismuth, and lead, but other standards such as polyethylene and fatty acids have been proposed to study polymers and organic compounds, respectively.

The technique was developed by E. S. Watson and M. J. O'Neill in 1962, and introduced commercially at the 1963 Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy. The first adiabatic differential scanning calorimeter that could be used in biochemistry was developed by P. L. Privalov and D. R. Monaselidze in 1964 at Institute of Physics in Tbilisi, Georgia. The term DSC was coined to describe this instrument, which measures energy directly and allows precise measurements of heat capacity.

Types
There are two main types of DSC: Heat-flux DSC which measures the difference in heat flux between the sample and a reference (which gives it the alternative name Multi-Cell DSC) and Power differential DSC which measures the difference in power supplied to the sample and a reference.

Heat-flux DSC
With Heat-flux DSC, the changes in heat flow are calculated by integrating the ΔTref- curve. For this kind of experiment, a sample and a reference crucible are placed on a sample holder with integrated temperature sensors for temperature measurement of the crucibles. This arrangement is located in a temperature-controlled oven. Unlike the traditional design, the special feature of heat-flux DSC is that it uses flat temperature sensors placed vertically around a flat heater. This setup makes it possible to have a small, light, and low-heat capacity structure while still working like a regular DSC oven.

Power differential DSC
For this kind of setup, also known as Power compensating DSC, the sample and reference crucible are placed in thermally insulated furnaces and not next to each other in the same furnace as in heat-flux-DSC experiments. Then the temperature of both chambers is controlled so that the same temperature is always present on both sides. The electrical power that is required to obtain and maintain this state is then recorded rather than the temperature difference between the two crucibles.

Fast-scan DSC
The 2000s have witnessed the rapid development of Fast-scan DSC (FSC), a novel calorimetric technique that employs micromachined sensors. The key advances of this technique are the ultrahigh scanning rate, which can be as high as 106 K/s, and the ultrahigh sensitivity, with a heat capacity resolution typically better than 1 nJ/K. Nanocalorimetry has attracted much attention in materials science, where it is applied to perform quantitative analysis of rapid phase transitions, particularly on fast cooling. Another emerging area of application of FSC is physical chemistry, with a focus on the thermophysical properties of thermally labile compounds. Quantities like fusion temperature, fusion enthalpy, sublimation, and vaporization pressures, and enthalpies of such molecules became available.

Temperature Modulated DSC
When performing Temperature Modulated DSC (TMDSC, MDSC), the underlying linear heating rate is superimposed by a sinusoidal temperature variation. The benefit of this procedure is the ability to separate overlapping DSC effects by calculating the reversing and the non-reversing signals. The reversing heat flow is related to the changes in specific heat capacity (→ glass transition) while the non-reversing heat flow corresponds to time-dependent phenomena such as curing, dehydration and relaxation.

Detection of phase transitions
The basic principle underlying this technique is that when the sample undergoes a physical transformation such as phase transitions, more or less heat will need to flow to it than the reference to maintain both at the same temperature. Whether less or more heat must flow to the sample depends on whether the process is exothermic or endothermic. For example, as a solid sample melts to a liquid, it will require more heat flowing to the sample to increase its temperature at the same rate as the reference. This is due to the absorption of heat by the sample as it undergoes the endothermic phase transition from solid to liquid. Likewise, as the sample undergoes exothermic processes (such as crystallization) less heat is required to raise the sample temperature. By observing the difference in heat flow between the sample and reference, differential scanning calorimeters are able to measure the amount of heat absorbed or released during such transitions. DSC may also be used to observe more subtle physical changes, such as glass transitions. It is widely used in industrial settings as a quality control instrument due to its applicability in evaluating sample purity and for studying polymer curing.

DTA
An alternative technique, which shares much in common with DSC, is differential thermal analysis (DTA). In this technique it is the heat flow to the sample and reference that remains the same rather than the temperature. When the sample and reference are heated identically, phase changes and other thermal processes cause a difference in temperature between the sample and reference. Both DSC and DTA provide similar information. DSC measures the energy required to keep both the reference and the sample at the same temperature whereas DTA measures the difference in temperature between the sample and the reference when the same amount of energy has been introduced into both.

DSC curves

The result of a DSC experiment is a curve of heat flux versus temperature or versus time. There are two different conventions: exothermic reactions in the sample shown with a positive or negative peak, depending on the kind of technology used in the experiment. This curve can be used to calculate enthalpies of transitions. This is done by integrating the peak corresponding to a given transition. It can be shown that the enthalpy of transition can be expressed using the following equation:

$$\Delta H = K A$$

where $$\Delta H$$ is the enthalpy of transition, $$K$$ is the calorimetric constant, and $$A$$ is the area under the curve. The calorimetric constant will vary from instrument to instrument, and can be determined by analyzing a well-characterized sample with known enthalpies of transition.

Applications
Differential scanning calorimetry can be used to measure a number of characteristic properties of a sample. Using this technique it is possible to observe fusion and crystallization events as well as glass transition temperatures Tg. DSC can also be used to study oxidation, as well as other chemical reactions.

Glass transitions may occur as the temperature of an amorphous solid is increased. These transitions appear as a step in the baseline of the recorded DSC signal. This is due to the sample undergoing a change in heat capacity; no formal phase change occurs.

As the temperature increases, an amorphous solid will become less viscous. At some point the molecules may obtain enough freedom of motion to spontaneously arrange themselves into a crystalline form. This is known as the crystallization temperature (Tc). This transition from amorphous solid to crystalline solid is an exothermic process, and results in a peak in the DSC signal. As the temperature increases the sample eventually reaches its melting temperature (Tm). The melting process results in an endothermic peak in the DSC curve. The ability to determine transition temperatures and enthalpies makes DSC a valuable tool in producing phase diagrams for various chemical systems.

Differential scanning calorimetry can also be used to obtain valuable thermodynamics information about proteins. The thermodynamics analysis of proteins can reveal important information about the global structure of proteins, and protein/ligand interaction. For example, many mutations lower the stability of proteins, while ligand binding usually increases protein stability. Using DSC, this stability can be measured by obtaining Gibbs Free Energy values at any given temperature. This allows researchers to compare the free energy of unfolding between ligand-free protein and protein-ligand complex, or wild type and mutant proteins. DSC can also be used in studying protein/lipid interactions, nucleotides, drug-lipid interactions. In studying protein denaturation using DSC, the thermal melt should be at least to some degree reversible, as the thermodynamics calculations rely on chemical equilibrium.

Experimental considerations
There are various experimental and environmental parameters to consider during DSC measurements. Exemplary potential issues are briefly discussed in the following sections. All statements in these paragraphs are based on the books of Gabbott and Brown.

Crucibles
DSC measurements without crucibles promote the thermal transfer towards the sample and are possible if the DSC is designed for this purpose. Measurements without crucible should only be conducted with chemically stable materials at low temperatures, as otherwise there may be contamination or damage of the calorimeter. The safer way is to use a crucible, which is specified for the desired temperatures and does not react with the sample material (e.g. alumina, gold or platinum crucibles). If the sample is likely to evolve volatiles or is in the liquid state, the crucible should be sealed to prevent contamination. However, if the crucible is sealed, increasing pressure and possible measurement artefacts due to deformation of the crucible must be considered. In this case, crucibles with very small holes (∅~50 μm) or crucibles that can withstand very high pressures should be used.

Sample condition
The sample should be in good contact with the crucible surface. Therefore, the contact surface of a solid bulk sample should be plane parallel. For DSC measurements with powders, stronger signal might be observed for finer powders due to the enlarged contact surface. The minimum sample mass depends on the transformation to be analyzed. A small sample mass (~10 mg) is sufficient if the released or consumed heat during the transformation is high enough. Heavier samples could be used to obtain transformation associated with low heat release or consumption, as larger samples also enlarge the obtained peaks. However, the increasing sample size might worsen the resolution due to thermal gradients which may evolve during heating.

Temperature and scan rates
If the peaks are very small, it is possible to enlarge them by increasing the scan rate. Due to the faster scan rate, more energy is released or consumed in a shorter time which leads to higher and therefore more distinct peaks. However, faster scan rates lead to poor temperature resolution because of thermal lag. Due to this thermal lag, two phase transformations (or chemical reactions) occurring in a narrow temperature range might overlap. Generally, heating or cooling rates are too high to detect equilibrium transitions, so there is always a shift to higher or lower temperatures compared to phase diagrams representing equilibrium conditions.

Purge gas
Purge gas is used to control the sample environment, in order to reduce signal noise and to prevent contamination. Mostly nitrogen is used and for temperatures above 600 °C, argon can be utilized to minimize heat loss due to the low thermal conductivity of argon. Air or pure oxygen can be used for oxidative tests like oxidative induction time and He is used for very low temperatures due to the low boiling temperature (~4.2K at 101.325 kPa ).

Examples
The technique is widely used across a range of applications, both as a routine quality test and as a research tool. The equipment is easy to calibrate, using low melting indium at 156.5985 °C for example, and is a rapid and reliable method of thermal analysis.

Polymers
DSC is used widely for examining polymeric materials to determine their thermal transitions. Important thermal transitions include the glass transition temperature (Tg), crystallization temperature (Tc), and melting temperature (Tm). The observed thermal transitions can be utilized to compare materials, although the transitions alone do not uniquely identify composition. The composition of unknown materials may be completed using complementary techniques such as IR spectroscopy. Melting points and glass transition temperatures for most polymers are available from standard compilations, and the method can show polymer degradation by the lowering of the expected melting temperature. Tm depends on the molecular weight of the polymer and thermal history.

The percent crystalline content of a polymer can be estimated from the crystallization/melting peaks of the DSC graph using reference heats of fusion found in the literature. DSC can also be used to study thermal degradation of polymers using an approach such as Oxidative Onset Temperature/Time (OOT); however, the user risks contamination of the DSC cell, which can be problematic. Thermogravimetric Analysis (TGA) may be more useful for decomposition behavior determination. Impurities in polymers can be determined by examining thermograms for anomalous peaks, and plasticisers can be detected at their characteristic boiling points. In addition, examination of minor events in first heat thermal analysis data can be useful as these apparently "anomalous peaks" can in fact also be representative of process or storage thermal history of the material or polymer physical aging. Comparison of first and second heat data collected at consistent heating rates can allow the analyst to learn about both polymer processing history and material properties. (see J.H.Flynn.(1993) Analysis of DSC results by integration. Thermochimica     Acta, 217, 129-149.)

Liquid crystals
DSC is used in the study of liquid crystals. As some forms of matter go from solid to liquid they go through a third state, which displays properties of both phases. This anisotropic liquid is known as a liquid crystalline or mesomorphous state. Using DSC, it is possible to observe the small energy changes that occur as matter transitions from a solid to a liquid crystal and from a liquid crystal to an isotropic liquid.

Oxidative stability
Using differential scanning calorimetry to study the stability to oxidation of samples generally requires an airtight sample chamber. It can be used to determine the oxidative-induction time (OIT) of a sample. Such tests are usually done isothermally (at constant temperature) by changing the atmosphere of the sample. First, the sample is brought to the desired test temperature under an inert atmosphere, usually nitrogen. Oxygen is then added to the system. Any oxidation that occurs is observed as a deviation in the baseline. Such analysis can be used to determine the stability and optimum storage conditions for a material or compound. DSC equipment can also be used to determine the Oxidative-Onset Temperature (OOT) of a material. In this test a sample (and a reference) are exposed to an oxygen atmosphere and subjected to a constant rate of heating (typically from 50 to 300 °C). The DSC heat flow curve will deviate when the reaction with oxygen begins (the reaction being either exothermic or endothermic). Both OIT and OOT tests are used as a tools for determining the activity of antioxidants.

Safety screening
DSC makes a reasonable initial safety screening tool. In this mode the sample will be housed in a non-reactive crucible (often gold or gold-plated steel), and which will be able to withstand pressure (typically up to 100 bar). The presence of an exothermic event can then be used to assess the stability of a substance to heat. However, due to a combination of relatively poor sensitivity, slower than normal scan rates (typically 2–3 °C/min, due to much heavier crucible) and unknown activation energy, it is necessary to deduct about 75–100 °C from the initial start of the observed exotherm to suggest a maximal temperature for the material. A much more accurate data set can be obtained from an adiabatic calorimeter, but such a test may take 2–3 days from ambient at a rate of a 3 °C increment per half-hour.

Drug analysis
DSC is widely used in the pharmaceutical and polymer industries. For the polymer chemist, DSC is a handy tool for studying curing processes, which allows the fine tuning of polymer properties. The cross-linking of polymer molecules that occurs in the curing process is exothermic, resulting in a negative peak in the DSC curve that usually appears soon after the glass transition.

In the pharmaceutical industry it is necessary to have well-characterized drug compounds in order to define processing parameters. For instance, if it is necessary to deliver a drug in the amorphous form, it is desirable to process the drug at temperatures below those at which crystallization can occur.

General chemical analysis
Freezing-point depression can be used as a purity analysis tool when analysed by differential scanning calorimetry. This is possible because the temperature range over which a mixture of compounds melts is dependent on their relative amounts. Consequently, less pure compounds will exhibit a broadened melting peak that begins at lower temperature than a pure compound.

title: Differential scanning calorimetry


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Small-angle neutron scattering

Small-angle neutron scattering (SANS) is an experimental technique that uses elastic neutron scattering at small scattering angles to investigate the structure of various substances at a mesoscopic scale of about 1–100 nm.

Small angle neutron scattering is in many respects very similar to small-angle X-ray scattering (SAXS); both techniques are jointly referred to as small-angle scattering (SAS). The most important feature of the SAS method is its potential for analyzing the inner structure of disordered systems, and frequently the application of this method is a unique way to obtain direct structural information on systems with random arrangement of density inhomogeneities in such large-scales. Advantages of SANS over SAXS are its sensitivity to light elements, the possibility of isotope labelling, and the strong scattering by magnetic moments.

Technique
During a SANS experiment a beam of neutrons is directed at a sample, which can be an aqueous solution, a solid, a powder, or a crystal. The neutrons are elastically scattered by nuclear interaction with the nuclei or interaction with magnetic momentum of unpaired electrons. In X-ray scattering, photons interact with the electronic cloud so the bigger the element, the bigger the effect is. In neutron scattering, neutrons interact with nuclei and the interaction depends on the isotope; some light elements like deuterium show similar scattering cross section as heavy elements like Pb.

In zero order dynamical theory of diffraction the refractive index is directly related to the scattering length density and is a measure of the strength of the interaction of a neutron wave with a given nucleus. The following table shows the neutron scattering length for a few chemical elements (in 10−12 cm). Note that the relative scale of the scattering lengths is the same. Another important point is that the scattering from hydrogen is distinct from that of deuterium. Also, hydrogen is one of the few elements that has a negative scattering length, which means that neutrons deflected from hydrogen are 180° out of phase relative to those deflected by the other elements. These features are important for the technique of contrast variation (see below).

Related techniques
SANS usually uses collimation of the neutron beam to determine the scattering angle of a neutron, which results in an ever lower signal-to-noise ratio for data that contains information on the properties of a sample at relatively long length scales, beyond ~1 μm. The traditional solution is to increase the brightness of the source, as in Ultra Small Angle Neutron Scattering (USANS). As an alternative Spin-echo Small-angle Neutron Scattering (SESANS) was introduced, using neutron spin echo to track the scattering angle, and expanding the range of length scales which can be studied by neutron scattering to well beyond 10 μm.

Grazing-incidence small-angle scattering (GISANS) combines ideas of SANS and of neutron reflectometry.

In biology

A crucial feature of SANS that makes it particularly useful for the biological sciences is the special behavior of hydrogen, especially compared to deuterium. In biological systems hydrogen can be exchanged with deuterium which usually has minimal effect on the sample but has dramatic effects on the scattering.

The technique of contrast variation (or contrast matching) relies on the differential scatter of hydrogen vs. deuterium. Figure 1 shows the scattering length density for water and various biological macromolecules as a function of the deuterium concentration. (Adapted from. ) Biological samples are usually dissolved in water, so their hydrogens are able to exchange with any deuteriums in the solvent. Since the overall scatter of a molecule depends on the scatter of all its components, this will depend on the ratio of hydrogen to deuterium in the molecule. At certain ratios of H2O to D2O, called match points, the scatter from the molecule will equal that of the solvent, and thus be eliminated when the scatter from the buffer is subtracted from the data. For instance the match point for proteins is typically around 40–45% D2O, and at that concentration the scatter from the protein will be indistinguishable from that of the buffer.

To use contrast variation, different components of a system must scatter differently. This can be based on inherent scattering differences, e.g. DNA vs. protein, or arise from differentially labeled components, e.g. having one protein in a complex deuterated while the rest are protonated. In terms of modelling, small-angle X-ray and neutron scattering data can be combined with the program MONSA. An example in which SAXS, SANS and EM data has been used to build an atomic model of a large multi-subunit enzyme has recently been published. For some examples of this method see.

For the study of large scales of matter (e.g. Soft matter) and slow dynamics, very cold neutrons (VCN) should be used. However, because of the weak neutron flux and lack of optical components in this range, most scientists use neutrons of shorter wavelengths. Efforts are being made to remedy this lack.

Instruments
There are numerous SANS instruments available worldwide at neutron facilities such as research reactors or spallation sources.

Textbooks

 * Fejgin, Lev A.: Structure analysis by small-angle X-ray and neutron scattering. New York: Plenum (1987).
 * Higgins, Julia S.; Benoît, Henri: Polymers and neutron scattering. Oxford: Clarendon Press (1994?).
 * Hamley, Ian,: Small-Angle Scattering: Theory, Instrumentation, Data, and Applications Chichester: Wiley (2022).

title: Small-angle neutron scattering


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St Davids Cathedral

St Davids Cathedral (Eglwys Gadeiriol Tyddewi) is an Anglican cathedral situated in St Davids, Britain's smallest city, in the county of Pembrokeshire, near the most westerly point of Wales.

Early history
The monastic community was founded by Saint David, Abbot of Menevia, who died in 589. Between 645 and 1097, the community was attacked many times by raiders, including the Vikings; however it was of such note as both a religious and an intellectual centre that King Alfred summoned help from the monastic community at St Davids in rebuilding the intellectual life of the Kingdom of Wessex. Many of the bishops were murdered by raiders and marauders, including Bishop Moregenau in 999 and Bishop Abraham in 1080. The stone that marked his grave, known as the "Abraham Stone", is intricately carved with early Celtic symbols and is now on permanent display within the Cathedral Exhibition at Porth-y-Tŵr.

In 1081, William the Conqueror visited St Davids to pray, and thus recognised it as a holy and respected place. In 1089, the shrine of David was vandalised and stripped of its precious metals. In 1090, the Welsh scholar Rhigyfarch wrote his Latin Life of David, highlighting David's sanctity, thus beginning the almost cult-like status he achieved.

In 1115, with the area under Norman control, King Henry I of England appointed Bishop Bernard as Bishop of St Davids. He began to improve life within the community, and commenced construction of a new cathedral. In 1123, Pope Calixtus II granted Bishop Bernard's request to bestow a papal privilege upon St Davids, making it a centre of pilgrimage for the Western world; the Pope decreed that "Two pilgrimages to St Davids is equal to one to Rome, and three pilgrimages to one to Jerusalem". The new cathedral was quickly constructed and Bishop Bernard consecrated it in 1131. Henry II of England's visit in 1171 saw the following of David increase and the need for a larger cathedral.

The present cathedral was begun in 1181 and completed not long after. Problems beset the new building and the community in its infancy: the collapse of the new tower in 1220 and earthquake damage in 1247/48.

Under Bishop Gower (1328–1347) the cathedral was modified further, with the rood screen and the Bishops Palace intended as permanent reminders of his episcopacy; the palace is now a picturesque ruin.

In 1365, Bishop Adam Houghton and John of Gaunt began to build St Mary's College and a chantry. He later added the cloister, which connects it to the cathedral.

The episcopacy of Edward Vaughan (1509–1522) saw the building of the Holy Trinity chapel, with its fan vaulting which some say inspired the roof of King's College, Cambridge. This period also saw great developments for the nave, whose roof and Irish oak ceiling were constructed between 1530 and 1540. Bishop Barlow, unlike his predecessor as bishop, wished to suppress the following of David, and stripped St David's shrine of its jewels and confiscated the relics of St David and St Justinian in order to counteract "superstition" in 1538. In 1540, the body of Edmund Tudor, Earl of Richmond and father of Henry VII, was brought to be entombed in front of the high altar from the dissolved Greyfriars' Priory in Carmarthen.

The establishment of the Commonwealth of England under Oliver Cromwell greatly affected many cathedrals and churches, and was particularly felt in St Davids. The cathedral was all but destroyed by Cromwell's forces and the lead was stripped from the Bishops Palace roof.

Present cathedral
There is a pronounced slope to the floor of the cathedral, amounting to a height difference of nearly four metres between the east and west ends, and the building is still shifting minutely.

The Welsh architect John Nash was commissioned to restore the west front in 1793 to repair the damage done two hundred years previously. Eclectic in style (with Gothic and Perpendicular characteristics – the latter attributed partly to his destruction of the windows of the chapel of St Mary's College in order to reuse that tracery for his west front), his work soon proved to be substandard (as had his previous work on the chapter house). Within a century the Nash west front had become unstable and the whole building was restored by George Gilbert Scott between 1862 and 1870. The lady chapel was restored by public subscription in 1901 and the eastern chapels were restored through a legacy of the Countess of Maidstone, granddaughter of Bishop John Jenkinson, between 1901 and 1910.

The cathedral suffered the pains of disestablishment in 1923, as did the whole Church in Wales. The diocese was made smaller by the removal of the Archdeaconry of Brecon to form the new Diocese of Swansea and Brecon. However, this left a large area as a diocese to govern and St Davids began to deteriorate as the centre of the diocese, being nowhere near the centre – the bishop's residence had been at Carmarthen since the 16th century, but administration and the focus moved from the cathedral to the diocese's now largest town.

The 1950s saw the appointment of the Reverend Carl Witton-Davies as dean; appointed in his thirties, his driving vision and energy was short-lived as he was offered what some was believed as a preferment as Archdeacon of Oxford, but did not leave that position for the rest of his service in the church. The cathedral began to have life again and the famous Welsh Youth Pilgrimages to St Davids (Cymry'r Groes) led many to a life of service in the church and provided the Church in Wales with inspired clergy for a decade following. It was Grade I-listed by Cadw in 1951.

The 1960s saw the restoration of St Mary's College as the cathedral hall, for the use of the cathedral parish and for use as an area for art exhibitions and poetry readings. It was dedicated by Archbishop Edwin Morris in 1966 and the inaugural event was a poetry reading by the poet R. S. Thomas, who served as a vicar in the Bangor diocese.

During the 1980s a number of official events in cathedral life took place: in 1981, Charles, Prince of Wales, visited to celebrate the 800th anniversary of the consecration of the cathedral; and on Maundy Thursday 1982, Queen Elizabeth II distributed the Royal Maundy at the cathedral. This was the first occasion that the ceremony had taken place outside England. In 1989–90, the 1,400th anniversary of the death of St David was presided over by the Archbishop of Wales, George Noakes, who was also diocesan Bishop of St Davids.

The decades leading to and immediately following the year 2000 have been the most notable in the cathedral's history since its construction. First, the British Government decided to reinstate the title of "city" to St Davids and this was formally conferred by Queen Elizabeth II on 1 June 1995. The task that lay before the dean, the Very Reverend Wyn Evans, on his appointment in 1994 was huge: a new organ was badly needed and the west front needed extensive restoration. It was also thought to be time for the cathedral to invest in its future by creating a visitor centre within the bell tower, enlarging the peal of bells from eight to ten and by the "reconstruction", or completion, of the cathedral cloisters to house the cathedral choir, vestries, an education suite, rooms for parish use and a refectory as a reminder of the monastic beginnings. The first project was the restoration of the west front, with the original quarry that was used for stone at Caerbwdi Bay being reopened. This phase was completed in 1998, in time for the organ to be dismantled and rebuilt by the organ builders Harrison and Harrison of Durham. The organ was completed in the middle months of 2000 and dedicated on 15 October that year.

The ring of bells was cast by Whitechapel Bell Foundry of London and presented as a gift by the American Friends of St Davids Cathedral. The substantial task of rebuilding the cloisters as an education centre and refectory began in 2003 and was completed in May 2007. The translation of Wyn Evans from dean to bishop led to the appointment of Jonathan Lean as dean in 2009.

The bells are not hung in the central tower of the cathedral but in the old gatehouse, Porth y Twr. There are 10 bells, with the heaviest weighing in D. The back eight bells were cast in 1928 by Mears & Stainbank, London and two trebles added in 2000 cast by Whitechapel Bell Foundry, London. Details of the bells:

The restored Shrine of St David was unveiled and re-dedicated by the Right Reverend Wyn Evans, Bishop of St Davids, at a Choral Eucharist on St Davids Day 2012.

Cathedral life
There are at least three services said or sung per day, each week, with sung services on five out of seven days.

The cathedral choir at St Davids was the first cathedral choir in the United Kingdom to use girls and men as the main choir, rather than boys and men. (Salisbury Cathedral introduced boys and girls earlier on an equal basis, whereas St Davids uses girls as their "main" cathedral choristers.) There is also a boys' choir whose weekly Evensong is a major event within the cathedral week. They sing with the vicars choral regularly.

The St Davids Cathedral Festival runs through the Whitsun school holiday each year and showcases some of the world's best performers. The week sees performers, both professional and young, play in front of thousands. The cathedral choir serve as a highlight each year, being a very popular concert, as well as the Festival Chorus and Orchestra who perform a major work on the final night of the festival.

List of deans
Before 1840 the senior residentiary cleric was the precentor and not a dean due to a complication during the dissolution of the monasteries. Since 1840 the title "Dean" has been appended to that of Precentor, hence the deans of St Davids are formally the "Dean and Precentor" and their seat being on what is normally regarded in most places the cantoris side, with a stall "in quire" reserved for the bishop.

 * 1839–1878 Llewelyn Lewellin (title of Dean granted in 1840)
 * 1878–1895 James Allen
 * 1895–1897 Owen Phillips
 * 1897–1903 David Howell
 * 1904–1918 James Allan Smith
 * 1919–1930 William Williams
 * 1931–1940 David Watcyn Morgan
 * 1940–1949 Albert Parry
 * 1950–1957 Carlyle Witton-Davies (afterwards Archdeacon of Oxford, 1957)
 * 1957–1972 Edward Jenkins
 * 1972–1984 Lawrence Bowen
 * 1984–1990 Gordon MacWilliam
 * 1990–1994 Bertie Lewis
 * 1994–2008 Wyn Evans (afterwards Bishop of St Davids)
 * 2009–2017 Jonathan Lean
 * 2018–present Sarah Rowland Jones

Sarah Caroline Rowland Jones (born 8 September 1959, Stoke-on-Trent) was instituted as Dean of St Davids on 5 May 2018. Having served in the Diplomatic Service, she trained for the ministry at St John's College, Nottingham; she was then made deacon at Petertide 1999 (26 June) and ordained priest the following Petertide (24 June 2000) — both times by Alwyn Rice Jones, Bishop of St Asaph and Archbishop of Wales, at St Asaph Cathedral. She served in South Africa, 2003–2013 (where she also married Justus Marcus, late Regional Bishop of Saldanha Bay, Diocese of Cape Town), then returned to Wales as Priest-in-Charge of St John the Baptist Church, Cardiff until her appointment to the Deanery.

Local legends
Gerald of Wales (Giraldus Cambrensis) in the 13th century relates the strange story of a marble footbridge leading from the church over the Alun rivulet in St Davids. The marble stone was called "Llechllafar" ("the talking stone") because it once spoke when a corpse was carried over it to the cemetery for interment. The effort of speech had caused it to break, despite its size of ten feet in length, six in breadth and one in thickness. This bridge was worn smooth due to its age and the thousands of people who had walked over it, however the superstition was so great that corpses were no longer carried over it. This ancient bridge was replaced in the 16th century and its present whereabouts are not known.

Another legend is that Merlin had prophesied the death on Llechllafar of an English king, conqueror of Ireland, who had been injured by a man with a red hand. King Henry II, whilst on a pilgrimage to Saint Davids, having come over from Ireland, heard of the prophecy and crossed Llechllafar without ill effect. He boasted that Merlin was a liar, to which a bystander replied that the King would not conquer Ireland and was therefore not the king of the prophecy. This turned out to be true, for Henry never did conquer the whole of Ireland.

Burials

 * Rhys ap Gruffydd
 * Gerald of Wales
 * Thomas Fastolf
 * Adam Houghton
 * Edward Vaughan (bishop)
 * Benedict Nichols
 * Edmund Tudor, 1st Earl of Richmond (father of Henry VII)

Organ
A specification of the organ can be found on the National Pipe Organ Register.

List of organists
• 1509 John Norman

• 1563 Thomas Elliot

• c. 1570–c. 1586 Thomas Tomkins (father of the composer Thomas Tomkins)

• 1713 R. Mordant

• 1714 Henry Mordant

• 1719 Richard Tomkins

• 1719 Williarn Bishop

• 1720 Henry Williams

• 1725 Matthew Maddox

• 1734 Matthew Philpott

• 1793 Arthur Richardson

• 1827 John Barrett

• 1851 William Peregrine Propert

• 1883 Frederick Garton

• 1894 D. John Codner

• 1896 Herbert C. Morris

• 1922 Joseph Soar

• 1953 Peter Boorman

• 1977 Nicholas Jackson

• 1984 Malcolm Watts

• 1990 Kerry Beaumont

• 1995 Geraint Bowen

• 2001 Timothy Noon

• 2007 Alexander Mason

• 2011 Daniel Cook

• 2013 Oliver Waterer

• 2021 Simon Pearce

In popular culture
The cathedral's exterior and overall design were used as the basis of the fictional Nemeton monastery in the video game Koudelka and its sequels Shadow Hearts and Shadow Hearts: Covenant.

title: St Davids Cathedral


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Digital image processing

Digital image processing is the use of a digital computer to process digital images through an algorithm. As a subcategory or field of digital signal processing, digital image processing has many advantages over analog image processing. It allows a much wider range of algorithms to be applied to the input data and can avoid problems such as the build-up of noise and distortion during processing. Since images are defined over two dimensions (perhaps more) digital image processing may be modeled in the form of multidimensional systems. The generation and development of digital image processing are mainly affected by three factors: first, the development of computers; second, the development of mathematics (especially the creation and improvement of discrete mathematics theory); third, the demand for a wide range of applications in environment, agriculture, military, industry and medical science has increased.

History
Many of the techniques of digital image processing, or digital picture processing as it often was called, were developed in the 1960s, at Bell Laboratories, the Jet Propulsion Laboratory, Massachusetts Institute of Technology, University of Maryland, and a few other research facilities, with application to satellite imagery, wire-photo standards conversion, medical imaging, videophone, character recognition, and photograph enhancement. The purpose of early image processing was to improve the quality of the image. It was aimed for human beings to improve the visual effect of people. In image processing, the input is a low-quality image, and the output is an image with improved quality. Common image processing include image enhancement, restoration, encoding, and compression. The first successful application was the American Jet Propulsion Laboratory (JPL). They used image processing techniques such as geometric correction, gradation transformation, noise removal, etc. on the thousands of lunar photos sent back by the Space Detector Ranger 7 in 1964, taking into account the position of the Sun and the environment of the Moon. The impact of the successful mapping of the Moon's surface map by the computer has been a success. Later, more complex image processing was performed on the nearly 100,000 photos sent back by the spacecraft, so that the topographic map, color map and panoramic mosaic of the Moon were obtained, which achieved extraordinary results and laid a solid foundation for human landing on the Moon.

The cost of processing was fairly high, however, with the computing equipment of that era. That changed in the 1970s, when digital image processing proliferated as cheaper computers and dedicated hardware became available. This led to images being processed in real-time, for some dedicated problems such as television standards conversion. As general-purpose computers became faster, they started to take over the role of dedicated hardware for all but the most specialized and computer-intensive operations. With the fast computers and signal processors available in the 2000s, digital image processing has become the most common form of image processing, and is generally used because it is not only the most versatile method, but also the cheapest.

Image sensors
The basis for modern image sensors is metal–oxide–semiconductor (MOS) technology, which originates from the invention of the MOSFET (MOS field-effect transistor) by Mohamed M. Atalla and Dawon Kahng at Bell Labs in 1959. This led to the development of digital semiconductor image sensors, including the charge-coupled device (CCD) and later the CMOS sensor.

The charge-coupled device was invented by Willard S. Boyle and George E. Smith at Bell Labs in 1969. While researching MOS technology, they realized that an electric charge was the analogy of the magnetic bubble and that it could be stored on a tiny MOS capacitor. As it was fairly straightforward to fabricate a series of MOS capacitors in a row, they connected a suitable voltage to them so that the charge could be stepped along from one to the next. The CCD is a semiconductor circuit that was later used in the first digital video cameras for television broadcasting.

The NMOS active-pixel sensor (APS) was invented by Olympus in Japan during the mid-1980s. This was enabled by advances in MOS semiconductor device fabrication, with MOSFET scaling reaching smaller micron and then sub-micron levels. The NMOS APS was fabricated by Tsutomu Nakamura's team at Olympus in 1985. The CMOS active-pixel sensor (CMOS sensor) was later developed by Eric Fossum's team at the NASA Jet Propulsion Laboratory in 1993. By 2007, sales of CMOS sensors had surpassed CCD sensors.

MOS image sensors are widely used in optical mouse technology. The first optical mouse, invented by Richard F. Lyon at Xerox in 1980, used a 5μm NMOS integrated circuit sensor chip. Since the first commercial optical mouse, the IntelliMouse introduced in 1999, most optical mouse devices use CMOS sensors.

Image compression
An important development in digital image compression technology was the discrete cosine transform (DCT), a lossy compression technique first proposed by Nasir Ahmed in 1972. DCT compression became the basis for JPEG, which was introduced by the Joint Photographic Experts Group in 1992. JPEG compresses images down to much smaller file sizes, and has become the most widely used image file format on the Internet. Its highly efficient DCT compression algorithm was largely responsible for the wide proliferation of digital images and digital photos, with several billion JPEG images produced every day.

Medical imaging techniques produce very large amounts of data, especially from CT, MRI and PET modalities. As a result, storage and communications of electronic image data are prohibitive without the use of compression. JPEG 2000 image compression is used by the DICOM standard for storage and transmission of medical images. The cost and feasibility of accessing large image data sets over low or various bandwidths are further addressed by use of another DICOM standard, called JPIP, to enable efficient streaming of the JPEG 2000 compressed image data.

Digital signal processor (DSP)
Electronic signal processing was revolutionized by the wide adoption of MOS technology in the 1970s. MOS integrated circuit technology was the basis for the first single-chip microprocessors and microcontrollers in the early 1970s, and then the first single-chip digital signal processor (DSP) chips in the late 1970s. DSP chips have since been widely used in digital image processing.

The discrete cosine transform (DCT) image compression algorithm has been widely implemented in DSP chips, with many companies developing DSP chips based on DCT technology. DCTs are widely used for encoding, decoding, video coding, audio coding, multiplexing, control signals, signaling, analog-to-digital conversion, formatting luminance and color differences, and color formats such as YUV444 and YUV411. DCTs are also used for encoding operations such as motion estimation, motion compensation, inter-frame prediction, quantization, perceptual weighting, entropy encoding, variable encoding, and motion vectors, and decoding operations such as the inverse operation between different color formats (YIQ, YUV and RGB) for display purposes. DCTs are also commonly used for high-definition television (HDTV) encoder/decoder chips.

Medical imaging
In 1972, the engineer from British company EMI Housfield invented the X-ray computed tomography device for head diagnosis, which is what is usually called CT (computer tomography). The CT nucleus method is based on the projection of the human head section and is processed by computer to reconstruct the cross-sectional image, which is called image reconstruction. In 1975, EMI successfully developed a CT device for the whole body, which obtained a clear tomographic image of various parts of the human body. In 1979, this diagnostic technique won the Nobel Prize. Digital image processing technology for medical applications was inducted into the Space Foundation Space Technology Hall of Fame in 1994.

As of 2010, 5 billion medical imaging studies had been conducted worldwide. Radiation exposure from medical imaging in 2006 made up about 50% of total ionizing radiation exposure in the United States. Medical imaging equipment is manufactured using technology from the semiconductor industry, including CMOS integrated circuit chips, power semiconductor devices, sensors such as image sensors (particularly CMOS sensors) and biosensors, and processors such as microcontrollers, microprocessors, digital signal processors, media processors and system-on-chip devices. , annual shipments of medical imaging chips amount to 46million units and US$1.1 billion.

Tasks
Digital image processing allows the use of much more complex algorithms, and hence, can offer both more sophisticated performance at simple tasks, and the implementation of methods which would be impossible by analogue means.

In particular, digital image processing is a concrete application of, and a practical technology based on:
 * Classification
 * Feature extraction
 * Multi-scale signal analysis
 * Pattern recognition
 * Projection

Some techniques which are used in digital image processing include:
 * Anisotropic diffusion
 * Hidden Markov models
 * Image editing
 * Image restoration
 * Independent component analysis
 * Linear filtering
 * Neural networks
 * Partial differential equations
 * Pixelation
 * Point feature matching
 * Principal components analysis
 * Self-organizing maps
 * Wavelets

Filtering
Digital filters are used to blur and sharpen digital images. Filtering can be performed by:
 * convolution with specifically designed kernels (filter array) in the spatial domain
 * masking specific frequency regions in the frequency (Fourier) domain

The following examples show both methods:

Image padding in Fourier domain filtering
Images are typically padded before being transformed to the Fourier space, the highpass filtered images below illustrate the consequences of different padding techniques:

Notice that the highpass filter shows extra edges when zero padded compared to the repeated edge padding.

Filtering code examples
MATLAB example for spatial domain highpass filtering.

Affine transformations
Affine transformations enable basic image transformations including scale, rotate, translate, mirror and shear as is shown in the following examples:

To apply the affine matrix to an image, the image is converted to matrix in which each entry corresponds to the pixel intensity at that location. Then each pixel's location can be represented as a vector indicating the coordinates of that pixel in the image, [x, y], where x and y are the row and column of a pixel in the image matrix. This allows the coordinate to be multiplied by an affine-transformation matrix, which gives the position that the pixel value will be copied to in the output image.

However, to allow transformations that require translation transformations, 3 dimensional homogeneous coordinates are needed. The third dimension is usually set to a non-zero constant, usually 1, so that the new coordinate is [x, y, 1]. This allows the coordinate vector to be multiplied by a 3 by 3 matrix, enabling translation shifts. So the third dimension, which is the constant 1, allows translation.

Because matrix multiplication is associative, multiple affine transformations can be combined into a single affine transformation by multiplying the matrix of each individual transformation in the order that the transformations are done. This results in a single matrix that, when applied to a point vector, gives the same result as all the individual transformations performed on the vector [x, y, 1] in sequence. Thus a sequence of affine transformation matrices can be reduced to a single affine transformation matrix.

For example, 2 dimensional coordinates only allow rotation about the origin (0, 0). But 3 dimensional homogeneous coordinates can be used to first translate any point to (0, 0), then perform the rotation, and lastly translate the origin (0, 0) back to the original point (the opposite of the first translation). These 3 affine transformations can be combined into a single matrix, thus allowing rotation around any point in the image.

Image denoising with Morphology
Mathematical morphology is suitable for denoising images. Structuring element are important in Mathematical morphology.

The following examples are about Structuring elements. The denoise function, image as I, and structuring element as B are shown as below and table.

e.g. $$(I') = \begin{bmatrix} 45 & 50 & 65 \\ 40 & 60 & 55 \\ 25 & 15 & 5 \end{bmatrix} B = \begin{bmatrix} 1 & 2 & 1 \\ 2 & 1 & 1 \\ 1 & 0 & 3 \end{bmatrix}$$

Define Dilation(I, B)(i,j) = $$max\{I(i+m, j+n) + B(m,n)\}$$. Let Dilation(I,B) = D(I,B)

D(I', B)(1,1) = $$max(45+1,50+2,65+1,40+2,60+1,55+1,25+1,15+0,5+3) = 66$$

Define Erosion(I, B)(i,j) = $$min\{I(i+m, j+n) - B(m,n)\}$$. Let Erosion(I,B) = E(I,B)

E(I', B)(1,1) = $$min(45-1,50-2,65-1,40-2,60-1,55-1,25-1,15-0,5-3) = 2$$

After dilation $$(I') = \begin{bmatrix} 45 & 50 & 65 \\ 40 & 66 & 55 \\ 25 & 15 & 5 \end{bmatrix} $$ After erosion $$(I') = \begin{bmatrix} 45 & 50 & 65 \\ 40 & 2 & 55 \\ 25 & 15 & 5 \end{bmatrix} $$

An opening method is just simply erosion first, and then dilation while the closing method is vice versa. In reality, the D(I,B) and E(I,B) can implemented by Convolution

Digital camera images
Digital cameras generally include specialized digital image processing hardware – either dedicated chips or added circuitry on other chips – to convert the raw data from their image sensor into a color-corrected image in a standard image file format. Additional post processing techniques increase edge sharpness or color saturation to create more naturally looking images.

Film
Westworld (1973) was the first feature film to use the digital image processing to pixellate photography to simulate an android's point of view. Image processing is also vastly used to produce the chroma key effect that replaces the background of actors with natural or artistic scenery.

Face detection
Face detection can be implemented with Mathematical morphology, Discrete cosine transform which is usually called DCT, and horizontal Projection (mathematics).

General method with feature-based method

The feature-based method of face detection is using skin tone, edge detection, face shape, and feature of a face (like eyes, mouth, etc.) to achieve face detection. The skin tone, face shape, and all the unique elements that only the human face have can be described as features.

Process explanation

 * 1) Given a batch of face images, first, extract the skin tone range by sampling face images. The skin tone range is just a skin filter.
 * 2) Structural similarity index measure (SSIM) can be applied to compare images in terms of extracting the skin tone.
 * 3) Normally, HSV or RGB color spaces are suitable for the skin filter. E.g. HSV mode, the skin tone range is [0,48,50] ~ [20,255,255]
 * 4) After filtering images with skin tone, to get the face edge, morphology and DCT are used to remove noise and fill up missing skin areas.
 * 5) Opening method or closing method can be used to achieve filling up missing skin.
 * 6) DCT is to avoid the object with tone-like skin. Since human faces always have higher texture.
 * 7) Sobel operator or other operators can be applied to detect face edge.
 * 8) To position human features like eyes, using the projection and find the peak of the histogram of projection help to get the detail feature like mouth, hair, and lip.
 * 9) Projection is just projecting the image to see the high frequency which is usually the feature position.

Improvement of image quality method
Image quality can be influenced by camera vibration, over-exposure, gray level distribution too centralized, and noise, etc. For example, noise problem can be solved by Smoothing method while gray level distribution problem can be improved by histogram equalization.

Smoothing method

In drawing, if there is some dissatisfied color, taking some color around dissatisfied color and averaging them. This is an easy way to think of Smoothing method.

Smoothing method can be implemented with mask and Convolution. Take the small image and mask for instance as below.

image is $$ \begin{bmatrix} 2 & 5 & 6 & 5\\ 3 & 1 & 4 & 6 \\ 1 & 28 & 30 & 2 \\ 7 & 3 & 2 & 2 \end{bmatrix} $$

mask is $$ \begin{bmatrix} 1/9 & 1/9 & 1/9 \\ 1/9 & 1/9 & 1/9 \\ 1/9 & 1/9 & 1/9 \end{bmatrix} $$

After Convolution and smoothing, image is $$ \begin{bmatrix} 2 & 5 & 6 & 5\\ 3 & 9 & 10 & 6 \\ 1 & 9 & 9 & 2 \\ 7 & 3 & 2 & 2 \end{bmatrix} $$

Oberseving image[1, 1], image[1, 2], image[2, 1], and image[2, 2].

The original image pixel is 1, 4, 28, 30. After smoothing mask, the pixel becomes 9, 10, 9, 9 respectively.

new image[1, 1] = $$\tfrac{1}{9}$$ * (image[0,0]+image[0,1]+image[0,2]+image[1,0]+image[1,1]+image[1,2]+image[2,0]+image[2,1]+image[2,2])

new image[1, 1] = floor($$\tfrac{1}{9}$$ * (2+5+6+3+1+4+1+28+30)) = 9

new image[1, 2] = floor({$$\tfrac{1}{9}$$ * (5+6+5+1+4+6+28+30+2)) = 10

new image[2, 1] = floor($$\tfrac{1}{9}$$ * (3+1+4+1+28+30+7+3+2)) = 9

new image[2, 2] = floor($$\tfrac{1}{9}$$ * (1+4+6+28+30+2+3+2+2)) = 9

Gray Level Histogram method

Generally, given a gray level histogram from an image as below. Changing the histogram to uniform distribution from an image is usually what we called Histogram equalization.

In discrete time, the area of gray level histogram is $$\sum_{i=0}^{k}H(p_i)$$(see figure 1) while the area of uniform distribution is $$\sum_{i=0}^{k}G(q_i)$$(see figure 2). It is clear that the area will not change, so $$\sum_{i=0}^{k}H(p_i) = \sum_{i=0}^{k}G(q_i)$$.

From the uniform distribution, the probability of $$q_i$$ is $$\tfrac{N^2}{q_k - q_0}$$ while the $$ 0 < i < k $$

In continuous time, the equation is $$\displaystyle \int_{q_0}^{q} \tfrac{N^2}{q_k - q_0}ds = \displaystyle \int_{p_0}^{p}H(s)ds$$.

Moreover, based on the definition of a function, the Gray level histogram method is like finding a function $$f$$ that satisfies f(p)=q.

Challenges

 * 1) Noise and Distortions: Imperfections in images due to poor lighting, limited sensors, and file compression can result in unclear images that impact accurate image conversion.
 * 2) Variability in Image Quality: Variations in image quality and resolution, including blurry images and incomplete details, can hinder uniform processing across a database.
 * 3) Object Detection and Recognition: Identifying and recognising objects within images, especially in complex scenarios with multiple objects and occlusions, poses a significant challenge.
 * 4) Data Annotation and Labelling: Labelling diverse and multiple images for machine recognition is crucial for further processing accuracy, as incorrect identification can lead to unrealistic results.
 * 5) Computational Resource Intensity: Accessing adequate computational resources for image processing can be challenging and costly, hindering progress without sufficient resources.

title: Digital image processing


text:
Binary image

A binary image is one that consists of pixels that can have one of exactly two colors, usually black and white. Binary images are also called bi-level or two-level, Pixelart made of two colours is often referred to as 1-Bit or 1bit. This means that each pixel is stored as a single bit—i.e., a 0 or 1. The names black-and-white, B&W, monochrome or monochromatic are often used for this concept, but may also designate any images that have only one sample per pixel, such as grayscale images. In Photoshop parlance, a binary image is the same as an image in "Bitmap" mode.

Binary images often arise in digital image processing as masks or thresholding, and dithering. Some input/output devices, such as laser printers, fax machines, and bilevel computer displays, can only handle bilevel images.

A binary image can be stored in memory as a bitmap, a packed array of bits. A 640×480 image requires 37.5 KiB of storage. Because of the small size of the image files, fax machine and document management solutions usually use this format. Most binary images also compress well with simple run-length compression schemes.

Binary images can be interpreted as subsets of the two-dimensional integer lattice Z2; the field of morphological image processing was largely inspired by this view.

Operations on binary images
An entire class of operations on binary images operates on a 3×3 window of the image. This contains nine pixels, so 29 or 512 possible values. Considering only the central pixel, it is possible to define whether it remains set or unset, based on the surrounding pixels. Examples of such operations are thinning, dilating, finding branch points and endpoints, removing isolated pixels, shifting the image a pixel in any direction, and breaking H-connections. Conway's Game of Life is also an example of a 3×3 window operation.

Another class of operations is based on the notion of filtering with a structuring element. The structuring element is binary image, usually small, which is passed over the target image, in a similar manner to a filter in gray scale image processing. Since the pixels can only have two values, the morphological operations are erosion (any unset pixels within the structuring element cause the pixel to be unset) and dilation (any set pixels within the structuring element cause the pixel to be set). Important operations are morphological opening and morphological closing which consist of erosion followed by dilation and dilation followed by erosion, respectively, using the same structuring element. Opening tends to enlarge small holes, remove small objects, and separate objects. Closing retains small objects, removes holes, and joins objects.

A very important characteristic of a binary image is the distance transform. This gives the distance of every set pixel from the nearest unset pixel. The distance transform can be efficiently calculated. It allows efficient computation of Voronoi diagrams, where each pixel in an image is assigned to the nearest of a set of points. It also allows skeletonization, which differs from thinning in that skeletons allow recovery of the original image. The distance transform is also useful for determining the center of the object, and for matching in image recognition.

Another class of operations is gathering orientation-free metrics. This is often important in image recognition where the orientation of the camera needs to be removed. Orientation-free metrics of a group of connected or surrounded pixels include the Euler number, the perimeter, the area, the compactness, the area of holes, the minimum radius, the maximum radius.

Image segmentation
Binary images are produced from color images by segmentation. Segmentation is the process of assigning each pixel in the source image to two or more classes. If there are more than two classes then the usual result is several binary images. The simplest form of segmentation is probably Otsu's method which assigns pixels to foreground or background based on grayscale intensity. Another method is the watershed algorithm. Edge detection also often creates a binary image with some pixels assigned to edge pixels, and is also a first step in further segmentation.

Skeletons
Thinning or  skeletonization  produces binary images which consist of pixel-wide lines. The branchpoints and endpoints can then be extracted, and the image converted to a graph. This is important in image recognition, for example in optical character recognition.

Interpretation
The interpretation of the pixel's binary value is also device-dependent. Some systems interprets the bit value of 0 as black and 1 as white, while others reversed the meaning of the values. In the TWAIN standard PC interface for scanners and digital cameras, the first flavor is called vanilla and the reversed one chocolate.

Dithering is often used for displaying halftone images.

1-bit in digital art
Binary pixelart, better known as 1-Bit or 1bit art, has been a method of displaying graphics since early computers. While early computers such as the ZX81 used the restriction as a necessity of the hardware, hand-held LCD games such as Game & Watch and Tamagotchi, alongside early computers with a focus on graphic user interfaces like the Macintosh made large steps in promoting the culture, technique and aesthetic of the restrictions of 1-bit art.

Modern examples of 1bit art are visible in indie videogames and other digital art. Best-seller games like Gato Roboto, Return of the Obra Dinn, Minit and World of Horror use 1bit as a style to give their games a retro feel or to simply save the graphic designers time in development. There is even new 1-Bit hardware in development, such as the experimental handheld console Playdate.

For pixel artists, 1-Bit has become a common challenge for creating art. The pixelart contest Pixtogether required its participants to use only two colours for its 10th monthly contest. Not a lot of artists mainly do 1bit art, but many of them stay in contact with each other to exchange knowledge about working with the restriction, and hosting own collaborations.

Brandon James Greer, who makes popular YouTube tutorials on 1bit and other pixel artwork, says that "the restriction leads to some unique approaches" and that working in 1-Bit is "a very fun and unique challenge".

While 1bit can be called an art style itself, each piece falls under a second style too. Obvious differences in 1bit art styles are for example whether, how much and what kind of dithering is being used, the image resolution, the use of outlines and how detailed the artwork is.

Use in visual cryptography

In 1994, Moni Naor and Adi Shamir demonstrated a visual secret sharing scheme, where a binary image was broken up into n shares so that only someone with all n shares could decrypt the image, while any n − 1 shares revealed no information about the original image. Each share was printed on a separate transparency, and decryption was performed by overlaying the shares. When all n shares were overlaid, the original image would appear. There are several generalizations of the basic scheme including k-out-of-n visual cryptography, and using opaque sheets but illuminating them by multiple sets of identical illumination patterns under the recording of only one single-pixel detector.

Image sensor capture binary images
Oversampled binary image sensor is an image sensor reminiscent of traditional photographic film. Each pixel in the sensor has a binary response, giving only a one-bit quantized measurement of the local light intensity.

title: Binary image


text:
User:WojPob/donated images

Considering my complete lack of photographic talent, I'd still like to donate some images to the project. Hence, I hereby release the images below into the public domain.

(A 19th century Prussian bayonet)

David Murray live in Warsaw

title: User:WojPob/donated images


text:
Metal matrix composite

In materials science, a metal matrix composite (MMC) is a composite material with fibers or particles dispersed in a metallic matrix, such as copper, aluminum, or steel. The secondary phase is typically a ceramic (such as alumina or silicon carbide) or another metal (such as steel ). They are typically classified according to the type of reinforcement: short discontinuous fibers (whiskers), continuous fibers, or particulates. There is some overlap between MMCs and cermets, with the latter typically consisting of less than 20% metal by volume. When at least three materials are present, it is called a hybrid composite. MMCs can have much higher strength-to-weight ratios, stiffness, and ductility than traditional materials, so they are often used in demanding applications. MMCs typically have lower thermal and electrical conductivity and poor resistance to radiation, limiting their use in the very harshest environments.

Composition
MMCs are made by dispersing a reinforcing material into a metal matrix. The reinforcement surface can be coated to prevent a chemical reaction with the matrix. For example, carbon fibers are commonly used in aluminium matrix to synthesize composites showing low density and high strength. However, carbon reacts with aluminium to generate a brittle and water-soluble compound Al4C3 on the surface of the fiber. To prevent this reaction, the carbon fibers are coated with nickel or titanium boride.

Matrix
The matrix is the monolithic material into which the reinforcement is embedded, and is completely continuous. This means that there is a path through the matrix to any point in the material, unlike two materials sandwiched together. In structural applications, the matrix is usually a lighter metal such as aluminum, magnesium, or titanium, and provides a complete support for the reinforcement. In high-temperature applications, cobalt and cobalt–nickel alloy matrices are common.

Reinforcement
The reinforcement material is embedded into a matrix. The reinforcement does not always serve a purely structural task (reinforcing the compound), but is also used to change physical properties such as wear resistance, friction coefficient, or thermal conductivity. The reinforcement can be either continuous or discontinuous. Discontinuous MMCs can be isotropic and can be worked with standard metalworking techniques, such as extrusion, forging, or rolling. In addition, they may be machined using conventional techniques, but commonly would need the use of polycrystalline diamond tooling (PCD).

Continuous reinforcement uses monofilament wires or fibers such as carbon fiber or silicon carbide. Because the fibers are embedded into the matrix in a certain direction, the result is an anisotropic structure in which the alignment of the material affects its strength. One of the first MMCs used boron filament as reinforcement. Discontinuous reinforcement uses "whiskers", short fibers, or particles. The most common reinforcing materials in this category are alumina and silicon carbide.

Manufacturing and forming methods
MMC manufacturing can be broken into three types—solid, liquid, and vapor.

Solid state methods

 * Powder blending and consolidation (powder metallurgy): Powdered metal and discontinuous reinforcement are mixed and then bonded through a process of compaction, degassing, and thermo-mechanical treatment (possibly via hot isostatic pressing (HIP) or extrusion)
 * Foil diffusion bonding: Layers of metal foil are sandwiched with long fibers, and then pressed through to form a matrix

Liquid state methods

 * Electroplating and electroforming: A solution containing metal ions loaded with reinforcing particles is co-deposited forming a composite material
 * Stir casting: Discontinuous reinforcement is stirred into molten metal, which is allowed to solidify
 * Pressure infiltration: Molten metal is infiltrated into the reinforcement through use a kind of pressure such as gas pressure
 * Squeeze casting: Molten metal is injected into a form with fibers pre-placed inside it
 * Spray deposition: Molten metal is sprayed onto a continuous fiber substrate
 * Reactive processing: A chemical reaction occurs, with one of the reactants forming the matrix and the other the reinforcement

Semi-solid state methods

 * Semi-solid powder processing: Powder mixture is heated up to semi-solid state and pressure is applied to form the composites.

Vapor deposition

 * Physical vapor deposition: The fiber is passed through a thick cloud of vaporized metal, coating it.

In-situ fabrication technique

 * Controlled unidirectional solidification of a eutectic alloy can result in a two-phase microstructure with one of the phases, present in lamellar or fiber form, distributed in the matrix.

Residual stress
MMCs are fabricated at elevated temperatures, which is an essential condition for diffusion bonding of the fiber/matrix interface. Later on, when they are cooled down to the ambient temperature, residual stresses (RS) are generated in the composite due to the mismatch between the coefficients of the metal matrix and fiber. The manufacturing RS significantly influence the mechanical behavior of the MMCs in all loading conditions. In some cases, thermal RS are high enough to initiate plastic deformation within the matrix during the manufacturing process.

Effect on Mechanical Properties
The addition of ceramic particles in general increases the strength of the material while having a tradeoff on material ductility. For example, a Al-Al2O3 composite can increase the yield strength of cast Al 6061 alloys from 105 to 120 MPa and increase the young’s modulus from 70 to 95 GPa. However, the composite had negative effects on the ductility decreasing it from 10% to 2%. Ultimately, the increase in elastic modulus is significant because the metals get the benefit of the higher specific stiffness of ceramics while retaining some ductility. Metal-matrix composites can also significantly increase the wear resistance and hardness of aluminum alloys. Al2O3 particles were found to significantly increase the wear resistance of an Al-Si alloy, and SiO2 particles increased the hardness of a Al-Mg alloy significantly. The application of this is in light, wear-resistant alloys for wear components such as piston liners in automobile engines. Current aluminum alloys are soft and often require hard, heavy cast iron liners which reduces the benefits of the lightweight aluminum engines.

Fracture toughness of the composites is typically dominated by the metal phases; however, it can also be dominated by the ceramic phase or delamination depending on the material system. For example the Cu/Al2O3 system has a high thermal expansion mismatch causing localized stresses encouraging crack propagation in the form of delamination. This significantly inhibits its fracture toughness compared to other compositions. In an Al/Al2O3 co-continuous system the crack propagated through the ceramic phase and was deflected upon reaching interfaces with the metallic phases. As a result, more energy was needed to deflect the crack around the phases and the composite was significantly toughened. Overall, fracture toughness is largely dependent on MMC composition due to thermal mismatch and crack modes but can toughen composites with low thermal mismatch.

MMCs strengthen materials against plasticity for a variety of reasons. The first is direct load transfer to the stronger ceramic particles. The second is due to the difference in plastic deformation of the two components. This causes a dislocation to become pinned on the stronger particles and bow around them to continue moving. Dislocations typically drive plastic deformation due to the lower energy to move them rather than moving an entire plane of atoms. Therefore, pinning them causes a large increase in the energy and stress required for plastic deformation (see Precipitation hardening). The final mechanism is caused by the stress from thermal and coherency mismatch. This creates a stress field which traps dislocations creating a pileup further inhibiting plastic deformation.

Applications

 * High performance tungsten carbide cutting tools are made from a tough cobalt matrix cementing the hard tungsten carbide particles; lower performance tools can use other metals such as bronze as the matrix.
 * Some tank armors may be made from metal matrix composites, probably steel reinforced with boron nitride, which is a good reinforcement for steel because it is very stiff and it does not dissolve in molten steel.
 * Some automotive disc brakes use MMCs. Early Lotus Elise models used aluminum MMC rotors, but they have less than optimal heat properties, and Lotus has since switched back to cast iron. Modern high-performance sport cars, such as those built by Porsche, use rotors made of carbon fiber within a silicon carbide matrix because of its high specific heat and thermal conductivity. 3M developed a preformed aluminum matrix insert for strengthening cast aluminum disc brake calipers, reducing weight by half compared to cast iron while retaining similar stiffness. 3M has also used alumina preforms for AMC pushrods.
 * Ford offers a Metal Matrix Composite (MMC) driveshaft upgrade. The MMC driveshaft is made of an aluminum matrix reinforced with boron carbide, allowing the critical speed of the driveshaft to be raised by reducing inertia. The MMC driveshaft has become a common modification for racers, allowing the top speed to be increased far beyond the safe operating speeds of a standard aluminum driveshaft.
 * Honda has used aluminum matrix composite cylinder liners in some of their engines, including the B21A1, H22A and H23A, F20C and F22C, and the C32B used in the NSX.
 * Toyota has since used metal matrix composites in the Yamaha-designed 2ZZ-GE engine which is used in the later Lotus Lotus Elise S2 versions as well as Toyota car models, including the eponymous Toyota Matrix. Porsche also uses MMCs to reinforce the engine's cylinder sleeves in the Boxster and 911.
 * The F-16 Fighting Falcon uses monofilament silicon carbide fibers in a titanium matrix for a structural component of the jet's landing gear.
 * Specialized Bicycles has used aluminum MMC compounds for its top of the range bicycle frames for several years. Griffen Bicycles also made boron carbide-aluminum MMC bike frames, and Univega briefly did so as well.
 * Some equipment in particle accelerators such as Radio Frequency Quadrupoles (RFQs) or electron targets use copper MMC compounds such as Glidcop to retain the material properties of copper at high temperatures and radiation levels.
 * Copper-silver alloy matrix containing 55% by volume diamond particles, known as Dymalloy, is used as a substrate for high-power, high-density multi-chip modules in electronics for its very high thermal conductivity. AlSiC is an aluminium-silicon carbide composite for similar applications.
 * Aluminium-Graphite composites are used in power electronic modules because of their high thermal conductivity, the adjustable coefficient of thermal expansion and the low density.

MMCs are nearly always more expensive than the more conventional materials they are replacing. As a result, they are found where improved properties and performance can justify the added cost. Today these applications are found most often in aircraft components, space systems and high-end or "boutique" sports equipment. The scope of applications will certainly increase as manufacturing costs are reduced.

In comparison with conventional polymer matrix composites, MMCs are resistant to fire, can operate in wider range of temperatures, do not absorb moisture, have better electrical and thermal conductivity, are resistant to radiation damage, and do not display outgassing. On the other hand, MMCs tend to be more expensive, the fiber-reinforced materials may be difficult to fabricate, and the available experience in use is limited.

title: Metal matrix composite


text:
User talk:Yaroslavvb

yaroslavvb, aka Yaroslav V. Bulatov

title: User talk:Yaroslavvb


text: User:Yaroslavvb

title: User:Yaroslavvb


title: User:Kchishol1970