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By the turn of the 20th century, the science of forensics had become largely established in the sphere of criminal investigation. Scientific and surgical investigation was widely employed by the Metropolitan Police during their pursuit of the mysterious Jack the Ripper, who had killed a number of women in the 1880s. This case is a watershed in the application of forensic science. Large teams of policemen conducted house-to-house inquiries throughout Whitechapel. Forensic material was collected and examined. Suspects were identified, traced and either examined more closely or eliminated from the inquiry. Police work follows the same pattern today. Over 2000 people were interviewed, "upwards of 300" people were investigated, and 80 people were detained.
The investigation was initially conducted by the Criminal Investigation Department (CID), headed by Detective Inspector Edmund Reid. Later, Detective Inspectors Frederick Abberline, Henry Moore, and Walter Andrews were sent from Central Office at Scotland Yard to assist. Initially, butchers, surgeons and physicians were suspected because of the manner of the mutilations. The alibis of local butchers and slaughterers were investigated, with the result that they were eliminated from the inquiry. Some contemporary figures thought the pattern of the murders indicated that the culprit was a butcher or cattle drover on one of the cattle boats that plied between London and mainland Europe. Whitechapel was close to the London Docks, and usually such boats docked on Thursday or Friday and departed on Saturday or Sunday. The cattle boats were examined, but the dates of the murders did not coincide with a single boat's movements, and the transfer of a crewman between boats was also ruled out.
At the end of October, Robert Anderson asked police surgeon Thomas Bond to give his opinion on the extent of the murderers surgical skill and knowledge. The opinion offered by Bond on the character of the "Whitechapel murderer" is the earliest surviving offender profile. Bonds assessment was based on his own examination of the most extensively mutilated victim and the post mortem notes from the four previous canonical murders. In his opinion the killer must have been a man of solitary habits, subject to "periodical attacks of homicidal and erotic mania", with the character of the mutilations possibly indicating "satyriasis". Bond also stated that "the homicidal impulse may have developed from a revengeful or brooding condition of the mind, or that religious mania may have been the original disease but I do not think either hypothesis is likely".
Handbook for Coroners, police officials, military policemen was written by the Austrian criminal jurist Hans Gross in 1893, and is generally acknowledged as the birth of the field of criminalistics. The work combined in one system fields of knowledge that had not been previously integrated, such as psychology and physical science, and which could be successfully used against crime. Gross adapted some fields to the needs of criminal investigation, such as crime scene photography. He went on to found the Institute of Criminalistics in 1912, as part of the University of Graz' Law School. This Institute was followed by many similar institutes all over the world.
In 1909, Archibald Reiss founded the Institut de police scientifique of the University of Lausanne (UNIL), the first school of forensic science in the world. Dr. Edmond Locard, became known as the "Sherlock Holmes of France". He formulated the basic principle of forensic science: "Every contact leaves a trace", which became known as Locard's exchange principle. In 1910, he founded what may have been the first criminal laboratory in the world, after persuading the Police Department of Lyon (France) to give him two attic rooms and two assistants.
Symbolic of the newfound prestige of forensics and the use of reasoning in detective work was the popularity of the fictional character Sherlock Holmes, written by Arthur Conan Doyle in the late 19th century. He remains a great inspiration for forensic science, especially for the way his acute study of a crime scene yielded small clues as to the precise sequence of events. He made great use of trace evidence such as shoe and tire impressions, as well as fingerprints, ballistics and handwriting analysis, now known as questioned document examination. Such evidence is used to test theories conceived by the police, for example, or by the investigator himself. All of the techniques advocated by Holmes later became reality, but were generally in their infancy at the time Conan Doyle was writing. In many of his reported cases, Holmes frequently complains of the way the crime scene has been contaminated by others, especially by the police, emphasising the critical importance of maintaining its integrity, a now well-known feature of crime scene examination. He used analytical chemistry for blood residue analysis as well as toxicology examination and determination for poisons. He used ballistics by measuring bullet calibres and matching them with a suspected murder weapon. | 0 | Chromatography + Titration + pH indicators |
For the analysis of volatile compounds, a purge and trap (P&T) concentrator system may be used to introduce samples. The target analytes are extracted by mixing the sample with water and purge with inert gas (e.g. Nitrogen gas) into an airtight chamber, this is known as purging or sparging. The volatile compounds move into the headspace above the water and are drawn along a pressure gradient (caused by the introduction of the purge gas) out of the chamber. The volatile compounds are drawn along a heated line onto a trap. The trap is a column of adsorbent material at ambient temperature that holds the compounds by returning them to the liquid phase. The trap is then heated and the sample compounds are introduced to the GC–MS column via a volatiles interface, which is a split inlet system. P&T GC–MS is particularly suited to volatile organic compounds (VOCs) and BTEX compounds (aromatic compounds associated with petroleum).
A faster alternative is the "purge-closed loop" system. In this system the inert gas is bubbled through the water until the concentrations of organic compounds in the vapor phase are at equilibrium with concentrations in the aqueous phase. The gas phase is then analysed directly. | 0 | Chromatography + Titration + pH indicators |
Friedel's law, named after Georges Friedel, is a property of Fourier transforms of real functions.
Given a real function , its Fourier transform
has the following properties.
where is the complex conjugate of .
Centrosymmetric points are called Friedel's pairs.
The squared amplitude () is centrosymmetric:
The phase of is antisymmetric:
Friedels law is used in X-ray diffraction, crystallography and scattering from real potential within the Born approximation. Note that a [http://reference.iucr.org/dictionary/Twin_operation twin operation] ( Opération de maclage) is equivalent to an inversion centre and the intensities from the individuals are equivalent under Friedels law. | 1 | Crystallography |
In geometry, close-packing of equal spheres is a dense arrangement of congruent spheres in an infinite, regular arrangement (or lattice). Carl Friedrich Gauss proved that the highest average density – that is, the greatest fraction of space occupied by spheres – that can be achieved by a lattice packing is
The same packing density can also be achieved by alternate stackings of the same close-packed planes of spheres, including structures that are aperiodic in the stacking direction. The Kepler conjecture states that this is the highest density that can be achieved by any arrangement of spheres, either regular or irregular. This conjecture was proven by T. C. Hales. Highest density is known only for 1, 2, 3, 8, and 24 dimensions.
Many crystal structures are based on a close-packing of a single kind of atom, or a close-packing of large ions with smaller ions filling the spaces between them. The cubic and hexagonal arrangements are very close to one another in energy, and it may be difficult to predict which form will be preferred from first principles.
__TOC__ | 1 | Crystallography |
A crystal is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. Crystal growth is a major stage of a crystallization process, and consists of the addition of new atoms, ions, or polymer strings into the characteristic arrangement of the crystalline lattice. The growth typically follows an initial stage of either homogeneous or heterogeneous (surface catalyzed) nucleation, unless a "seed" crystal, purposely added to start the growth, was already present.
The action of crystal growth yields a crystalline solid whose atoms or molecules are close packed, with fixed positions in space relative to each other.
The crystalline state of matter is characterized by a distinct structural rigidity and very high resistance to deformation (i.e. changes of shape and/or volume). Most crystalline solids have high values both of Young's modulus and of the shear modulus of elasticity. This contrasts with most liquids or fluids, which have a low shear modulus, and typically exhibit the capacity for macroscopic viscous flow. | 1 | Crystallography |
The unit sphere in three-dimensional space is the set of points such that . Let be the "north pole", and let be the rest of the sphere. The plane runs through the center of the sphere; the "equator" is the intersection of the sphere with this plane.
For any point on , there is a unique line through and , and this line intersects the plane in exactly one point , known as the stereographic projection of onto the plane.
In Cartesian coordinates on the sphere and on the plane, the projection and its inverse are given by the formulas
In spherical coordinates on the sphere (with the zenith angle, , and the azimuth, ) and polar coordinates on the plane, the projection and its inverse are
Here, is understood to have value when = 0. Also, there are many ways to rewrite these formulas using trigonometric identities. In cylindrical coordinates on the sphere and polar coordinates on the plane, the projection and its inverse are | 1 | Crystallography |
Electron crystallographic studies on inorganic crystals using high-resolution electron microscopy (HREM) images were first performed by Aaron Klug in 1978 and by Sven Hovmöller and coworkers in 1984. HREM images were used because they allow to select (by computer software) only the very thin regions close to the edge of the crystal for structure analysis (see also crystallographic image processing). This is of crucial importance since in the thicker parts of the crystal the exit-wave function (which carries the information about the intensity and position of the projected atom columns) is no longer linearly related to the projected crystal structure. Moreover, not only do the HREM images change their appearance with increasing crystal thickness, they are also very sensitive to the chosen setting of the defocus Δf of the objective lens (see the HREM images of for example). To cope with this complexity methods based upon the Cowley-Moodie multislice algorithm and non-linear imaging theory have been developed to simulate images; this only became possible once the FFT method was developed.
There was a serious disagreement in the field of electron microscopy of inorganic compounds; while some have claimed that "the phase information is present in EM images" others have the opposite view that "the phase information is lost in EM images". The reason for these opposite views is that the word "phase" has been used with different meanings in the two communities of physicists and crystallographers. The physicists are more concerned about the "electron wave phase" - the phase of a wave moving through the sample during exposure by the electrons. This wave has a wavelength of about 0.02-0.03 Ångström (depending on the accelerating voltage of the electron microscope). Its phase is relative to the phase of the undiffracted direct electron beam. The crystallographers, on the other hand, mean the "crystallographic structure factor phase" when they simply say "phase". This phase is the phase of standing waves of potential in the crystal (very similar to the electron density measured in X-ray crystallography). Each of these waves have their specific wavelength, called d-value for distance between so-called Bragg planes of low/high potential. These d-values range from the unit cell dimensions to the resolution limit of the electron microscope, i.e. typically from 10 or 20 Ångströms down to 1 or 2 Ångströms. Their phases are related to a fixed point in the crystal, defined in relation to the symmetry elements of that crystal. The crystallographic phases are a property of the crystal, so they exist also outside the electron microscope. The electron waves vanish if the microscope is switched off. In order to determine a crystal structure, it is necessary to know the crystallographic structure factors, but not to know the electron wave phases. A more detailed discussion how (crystallographic structure factor) phases link with the phases of the electron wave can be found in.
Just as with proteins, it has been possible to determine the atomic structures of inorganic crystals by electron crystallography. For simpler structure it is sufficient to use three perpendicular views, but for more complicated structures, also projections down ten or more different diagonals may be needed.
In addition to electron microscopy images, it is also possible to use electron diffraction (ED) patterns for crystal structure determination. The utmost care must be taken to record such ED patterns from the thinnest areas in order to keep most of the structure related intensity differences between the reflections (quasi-kinematical diffraction conditions). Just as with X-ray diffraction patterns, the important crystallographic structure factor phases are lost in electron diffraction patterns and must be uncovered by special crystallographic methods such as direct methods, maximum likelihood or (more recently) by the charge-flipping method. On the other hand, ED patterns of inorganic crystals have often a high resolution (= interplanar spacings with high Miller indices) much below 1 Ångström. This is comparable to the point resolution of the best electron microscopes. Under favourable conditions it is possible to use ED patterns from a single orientation to determine the complete crystal structure. Alternatively a hybrid approach can be used which uses HRTEM images for solving and intensities from ED for refining the crystal structure.
Recent progress for structure analysis by ED was made by introducing the Vincent-Midgley precession technique for recording electron diffraction patterns. The thereby obtained intensities are usually much closer to the kinematical intensities, so that even structures can be determined that are out of range when processing conventional (selected area) electron diffraction data.
Crystal structures determined via electron crystallography can be checked for their quality by using first-principles calculations within density functional theory (DFT). This approach has been used to assist in solving surface structures and for the validation of several metal-rich structures which were only accessible by HRTEM and ED, respectively.
Recently, two very complicated zeolite structures have been determined by electron crystallography combined with X-ray powder diffraction. These are more complex than the most complex zeolite structures determined by X-ray crystallography. | 1 | Crystallography |
The use of micelles in high performance liquid chromatography was first introduced by Armstrong and Henry in 1980. The technique is used mainly to enhance retention and selectivity of various solutes that would otherwise be inseparable or poorly resolved. Micellar liquid chromatography (MLC) has been used in a variety of applications including separation of mixtures of charged and neutral solutes, direct injection of serum and other physiological fluids, analysis of pharmaceutical compounds, separation of enantiomers, analysis of inorganic organometallics, and a host of others.
One of the main drawbacks of the technique is the reduced efficiency that is caused by the micelles. Despite the sometimes poor efficiency, MLC is a better choice than ion-exchange LC or ion-pairing LC for separation of charged molecules and mixtures of charged and neutral species. Some of the aspects which will be discussed are the theoretical aspects of MLC, the use of models in predicting retentive characteristics of MLC, the effect of micelles on efficiency and selectivity, and general applications of MLC.
Reverse phase high-performance liquid chromatography (RP-HPLC) involves a non-polar stationary phase, often a hydrocarbon chain, and a polar mobile or liquid phase. The mobile phase generally consists of an aqueous portion with an organic addition, such as methanol or acetonitrile. When a solution of analytes is injected into the system, the components begin to partition out of the mobile phase and interact with the stationary phase. Each component interacts with the stationary phase in a different manner depending upon its polarity and hydrophobicity. In reverse phase HPLC, the solute with the greatest polarity will interact less with the stationary phase and spend more time in the mobile phase. As the polarity of the components decreases, the time spent in the column increases. Thus, a separation of components is achieved based on polarity. The addition of micelles to the mobile phase introduces a third phase into which the solutes may partition. | 0 | Chromatography + Titration + pH indicators |
Prior to these studies, HPLC analyses were tuned by modifying the mobile and stationary phases only. Gradient elution for HPLC merely meant changing the ratio of solvents to improve column efficiency, and this requires the use of sophisticated solvent pumping mechanisms along with extra steps and precautions in the chromatographic analysis. Enlightened by the prospect of using temperature gradient elutions for HPLC analyses, Hosoya et al. sought to make surface modification of HPLC stationary phases more accessible. Their study utilizes graft-type copolymerization of PNIPAAm onto macroporous polymeric materials. The in-situ preparation compared the use of cyclohexanol and toluene as porogens in the preparation of the modified polystyrene seeds. Reverse-phased size-exclusion chromatography (SEC) revealed pore size and pore size distribution of the particles and its dependence on temperature. Cyclohexanol acted as a successful porogen showing a dependent relationship of pore size to temperature. The use of toluene as a porogen gave results that were similar to unmodified macroporous particles. This indicates that PNIPAAm can be successfully grafted onto the surface and within the pores of macroporous materials. The application of this preparatory technique gives rise to tunable pore sizes. Temperature gradient elutions can be used to improve column efficiency through the changing of pore size in SEC. The mechanism of the change in pore size is simple, the pores are smaller under LCST due to the elongated chains of PNIPAAm within the pores, as temperature increases to and above LCST, the chains retract into a globular formation increasing the pore size. | 0 | Chromatography + Titration + pH indicators |
Packings where all spheres are constrained by their neighbours to stay in one location are called rigid or jammed. The strictly jammed (mechanically stable even as a finite system) sphere packing with the lowest known density is a diluted ("tunneled") fcc crystal with a density of only . The loosest known jammed packing has a density of approximately 0.0555. | 1 | Crystallography |
In 1975, John H. Beynon was appointed the Royal Society Research Professor and established the Mass Spectrometry Research Unit at Swansea University (at that time known as the University College of Swansea). In 1986, Dai Games moved from Cardiff University to become the Units new Director.
In 1984, the first observation of He was made at the unit, its the same as molecular hydrogen (isolectronic molecules) except it has lots more energy 3310 kJ per mole. | 0 | Chromatography + Titration + pH indicators |
Neutral red (toluylene red, Basic Red 5, or C.I. 50040) is a eurhodin dye used for staining in histology. It stains lysosomes red. It is used as a general stain in histology, as a counterstain in combination with other dyes, and for many staining methods. Together with Janus Green B, it is used to stain embryonal tissues and supravital staining of blood. Can be used for staining Golgi apparatus in cells and Nissl granules in neurons.
In microbiology, it is used in the MacConkey agar to differentiate bacteria for lactose fermentation.
[https://medium.com/@GSPChem/neutral-red-8d9c51584fa Neutral red] can be used as a vital stain. The Neutral Red Cytotoxicity Assay was first developed by Ellen Borenfreund in 1984. In the Neutral Red Assay live cells incorporate neutral red into their lysosomes. As cells begin to die, their ability to incorporate neutral red diminishes. Thus, loss of neutral red uptake corresponds to loss of cell viability. The neutral red is also used to stain cell cultures for plate titration of viruses.
Neutral red is added to some growth media for bacterial and cell cultures. It usually is available as a chloride salt.
Neutral red acts as a pH indicator, changing from red to yellow between pH 6.8 and 8.0. | 0 | Chromatography + Titration + pH indicators |
Cesium chloride is a simple cubic crystal lattice with a basis of Cs at (0,0,0) and Cl at (1/2, 1/2, 1/2) (or the other way around, it makes no difference). Equation () becomes
We then arrive at the following result for the structure factor for scattering from a plane :
and for scattered intensity, | 1 | Crystallography |
Gels are used as stationary phase for GPC. The pore size of a gel must be carefully controlled in order to be able to apply the gel to a given separation. Other desirable properties of the gel forming agent are the absence of ionizing groups and, in a given solvent, low affinity for the substances to be separated. Commercial gels like PLgel & Styragel (cross-linked polystyrene-divinylbenzene), LH-20 (hydroxypropylated Sephadex), Bio-Gel (cross-linked polyacrylamide), HW-20 & HW-40 (hydroxylated methacrylic polymer), and agarose gel are often used based on different separation requirements. | 0 | Chromatography + Titration + pH indicators |
For each uniform structure, there also exists a related but different structure, called a line-slip arrangement.
The differences between uniform and line-slip structures are marginal and difficult to spot from images of the sphere packings. However, by comparing their rolled-out contact networks, one can spot that certain lines (which represent contacts) are missing.
All spheres in a uniform structure have the same number of contacts, but the number of contacts for spheres in a line slip may differ from sphere to sphere. For the example line slip in the image on the right side, some spheres count five and others six contacts. Thus a line slip structure is characterised by these gaps or loss of contacts.
Such a structure is termed line slip because the losses of contacts occur along a line in the rolled-out contact network. It was first identified by Picket et al., but not termed line slip.
The direction, in which the loss of contacts occur can be denoted in the phyllotactic notation , since each number represents one of the lattice vectors in the hexagonal lattice. This is usually indicated by a bold number.
By shearing the row of spheres below the loss of contact against a row above the loss of contact, one can regenerate two uniform structures related to this line slip. Thus, each line slip is related to two adjacent uniform structures, one at a higher and one at a lower diameter ratio .
Winkelmann et al. were the first to experimentally realise such a structure using soap bubbles in a system of deformable spheres. | 1 | Crystallography |
Alkalimetry and acidimetry are types of volumetric analyses in which the fundamental reaction is a neutralization reaction. They involve the controlled addition of either an acid or a base (titrant) of known concentration to the solution of the unknown concentration (titrate) until the reaction reaches its stoichiometric equivalence point. At this point, the moles of acid and base are equal, resulting in a neutral solution:
:acid + base → salt + water
For example:
:HCl + NaOH → NaCl + HO
Acidimetry is the specialized analytical use of acid-base titration to determine the concentration of a basic (alkaline) substance using standard acid. This can be used for weak bases and strong bases. An example of an acidimetric titration involving a strong base is as follows:
:Ba(OH) + 2 H → Ba + 2 HO
In this case, the strong base (Ba(OH)) is neutralized by the acid until all of the base has reacted. This allows the viewer to calculate the concentration of the base from the volume of the standard acid that is used.
Alkalimetry follows uses same concept of specialized analytic acid-base titration, but to determine the concentration of an acidic substance using standard base. An example of an alkalimetric titration involving a strong acid is as follows:
:HSO + 2 OH → SO + 2 HO
In this case, the strong acid (HSO) is neutralized by the base until all of the acid has reacted. This allows the viewer to calculate the concentration of the acid from the volume of the standard base that is used.
The standard solution (titrant) is stored in the burette, while the solution of unknown concentration (analyte/titrate) is placed in the Erlenmeyer flask below it with an indicator. | 0 | Chromatography + Titration + pH indicators |
QR is synthesized by a condensation reaction between the methyl group of 1-ethyl-2-methylquinolinium iodide and the carbonyl of para-dimethylaminobenzaldehyde. | 0 | Chromatography + Titration + pH indicators |
We can recognize which of these isometries we have according to whether it preserves hands or swaps them, and whether it has at least one fixed point or not, as shown in the following table (omitting the identity). | 1 | Crystallography |
This technique brings together protein and precipitation solutions without premixing them, but instead, injecting them through either sides of a channel, allowing equilibrium through diffusion. The two solutions come into contact in a reagent chamber, both at their maximum concentrations, initiating spontaneous nucleation. As the system comes into equilibrium, the level of supersaturation decreases, favouring crystal growth. | 1 | Crystallography |
Here the solvent travels up the chromatographic paper. Both descending and ascending paper chromatography are used for the separation of organic and inorganic substances.
The sample and solvent move upward. | 0 | Chromatography + Titration + pH indicators |
Countercurrent chromatography and related liquid-liquid separation techniques have been used on both industrial and laboratory scale to purify a wide variety of chemical substances. Separation realizations include proteins, DNA, Cannabidiol (CBD) from Cannabis Sativa antibiotics, vitamins, natural products, pharmaceuticals, metal ions, pesticides, enantiomers, polyaromatic hydrocarbons from environmental samples, active enzymes, and carbon nanotubes. Countercurrent chromatography is known for its high dynamic range of scalability: milligram to kilogram quantities purified chemical components may be obtained with this technique. It also has the advantage of accommodating chemically complex samples with undissolved particulates. | 0 | Chromatography + Titration + pH indicators |
It is used to determine the ability of an organism to produce mixed acids by fermentation of glucose and to overcome the buffering capacity of the medium. | 0 | Chromatography + Titration + pH indicators |
The trihexagonal tiling has Schläfli symbol of r{6,3}, or Coxeter diagram, , symbolizing the fact that it is a rectified hexagonal tiling, {6,3}. Its symmetries can be described by the wallpaper group p6mm, (*632), and the tiling can be derived as a Wythoff construction within the reflectional fundamental domains of this group. The trihexagonal tiling is a quasiregular tiling, alternating two types of polygons, with vertex configuration (3.6). It is also a uniform tiling, one of eight derived from the regular hexagonal tiling. | 1 | Crystallography |
Crystal formation requires two steps: nucleation and growth. Nucleation is the initiation step for crystallization. At the nucleation phase, protein molecules in solution come together as aggregates to form a stable solid nucleus. As the nucleus forms, the crystal grows bigger and bigger by molecules attaching to this stable nucleus. The nucleation step is critical for crystal formation since it is the first-order phase transition of samples moving from having a high degree of freedom to obtaining an ordered state (aqueous to solid). For the nucleation step to succeed, the manipulation of crystallization parameters is essential. The approach behind getting a protein to crystallize is to yield a lower solubility of the targeted protein in solution. Once the solubility limit is exceeded and crystals are present, crystallization is accomplished. | 1 | Crystallography |
If the superspots are located at simple fractions of the vectors of the reciprocal lattice of the substructure, e.g., at q=(½,0,0), the resulting broken symmetry is a multiple of the unit cell along that axis. Such a modulation is called a commensurate superstructure. | 1 | Crystallography |
DCCC has been employed to separate a wide variety of phytochemicals from their crude extracts. The long list of natural product separations includes: saponins, alkaloids, senna glycosides, monosaccarides, triterpene glycosides, flavone glycosides, xanthones, iridoid glycosides, vitamin B, lignans, imbricatolic acid, gallic acid, carotenoids, and triterpenoids.
DCCC instruments have been commercially manufactured and distributed by Büchi and Tokyo Rikakikai (Eyela). | 0 | Chromatography + Titration + pH indicators |
The Avrami equation describes how solids transform from one phase to another at constant temperature. It can specifically describe the kinetics of crystallisation, can be applied generally to other changes of phase in materials, like chemical reaction rates, and can even be meaningful in analyses of ecological systems.
The equation is also known as the Johnson–Mehl–Avrami–Kolmogorov (JMAK) equation. The equation was first derived by Johnson, Mehl, Avrami and Kolmogorov (in Russian) in a series of articles published in the Journal of Chemical Physics between 1939 and 1941. Moreover, Kolmogorov treated statistically the crystallization of a solid in 1937 (in Russian, Kolmogorov, A. N., Izv. Akad. Nauk. SSSR., 1937, 3, 355). | 1 | Crystallography |
Crystal violet is used as a textile and paper dye, and is a component of navy blue and black inks for printing, ball-point pens, and inkjet printers. It is sometimes used to colourize diverse products such as fertilizer, antifreeze, detergent, and leather.
The dye is used as a histological stain, particularly in Gram staining for classifying bacteria.
When conducting DNA gel electrophoresis, crystal violet can be used as a nontoxic DNA stain as an alternative to fluorescent, intercalating dyes such as ethidium bromide. Used in this manner, it may be either incorporated into the agarose gel or applied after the electrophoresis process is finished. Used at a 0.001% concentration and allowed to stain a gel after electrophoresis for 30 minutes, it can detect as little as 16 ng of DNA. Through use of a methyl orange counterstain and a more complex staining method, sensitivity can be improved further to 8 ng of DNA. When crystal violet is used as an alternative to fluorescent stains, it is not necessary to use ultraviolet illumination; this has made crystal violet popular as a means of avoiding UV-induced DNA destruction when performing DNA cloning in vitro.
In biomedical research, crystal violet can be used to stain the nuclei of adherent cells. In this application, crystal violet works as an intercalating dye and allows the quantification of DNA which is proportional to the number of cells.
In forensics, crystal violet was used to develop fingerprints. Crystal violet is also used as a tissue stain in the preparation of light microscopy sections. In laboratory, solutions containing crystal violet and formalin are often used to simultaneously fix and stain cells grown in tissue culture to preserve them and make them easily visible, since most cells are colourless. It is also sometimes used as a cheap way to put identification markings on laboratory mice; since many strains of lab mice are albino, the purple colour stays on their fur for several weeks.
In body piercing, gentian violet is commonly used to mark the location for placing piercings, including surface piercings.
Marking blue, used to mark out pieces in metalworking, is composed of methylated spirits, shellac, and gentian violet. | 0 | Chromatography + Titration + pH indicators |
Since 1975 ion chromatography has been widely used in many branches of industry. The main beneficial advantages are reliability, very good accuracy and precision, high selectivity, high speed, high separation efficiency, and low cost of consumables. The most significant development related to ion chromatography are new sample preparation methods; improving the speed and selectivity of analytes separation; lowering of limits of detection and limits of quantification; extending the scope of applications; development of new standard methods; miniaturization and extending the scope of the analysis of a new group of substances. Allows for quantitative testing of electrolyte and proprietary additives of electroplating baths. It is an advancement of qualitative hull cell testing or less accurate UV testing. Ions, catalysts, brighteners and accelerators can be measured. Ion exchange chromatography has gradually become a widely known, universal technique for the detection of both anionic and cationic species. Applications for such purposes have been developed, or are under development, for a variety of fields of interest, and in particular, the pharmaceutical industry. The usage of ion exchange chromatography in pharmaceuticals has increased in recent years, and in 2006, a chapter on ion exchange chromatography was officially added to the United States Pharmacopia-National Formulary (USP-NF). Furthermore, in 2009 release of the USP-NF, the United States Pharmacopia made several analyses of ion chromatography available using two techniques: conductivity detection, as well as pulse amperometric detection. Majority of these applications are primarily used for measuring and analyzing residual limits in pharmaceuticals, including detecting the limits of oxalate, iodide, sulfate, sulfamate, phosphate, as well as various electrolytes including potassium, and sodium. In total, the 2009 edition of the USP-NF officially released twenty eight methods of detection for the analysis of active compounds, or components of active compounds, using either conductivity detection or pulse amperometric detection. | 0 | Chromatography + Titration + pH indicators |
A crystallization adjutant is a material used to promote crystallization, normally in a context where a material does not crystallize naturally from a pure solution. | 1 | Crystallography |
In three-dimensional Euclidean space, the densest packing of equal spheres is achieved by a family of structures called close-packed structures. One method for generating such a structure is as follows. Consider a plane with a compact arrangement of spheres on it. Call it A. For any three neighbouring spheres, a fourth sphere can be placed on top in the hollow between the three bottom spheres. If we do this for half of the holes in a second plane above the first, we create a new compact layer. There are two possible choices for doing this, call them B and C. Suppose that we chose B. Then one half of the hollows of B lies above the centers of the balls in A and one half lies above the hollows of A which were not used for B. Thus the balls of a third layer can be placed either directly above the balls of the first one, yielding a layer of type A, or above the holes of the first layer which were not occupied by the second layer, yielding a layer of type C. Combining layers of types A, B, and C produces various close-packed structures.
Two simple arrangements within the close-packed family correspond to regular lattices. One is called cubic close packing (or face-centred cubic, "FCC")—where the layers are alternated in the ABCABC... sequence. The other is called hexagonal close packing ("HCP"), where the layers are alternated in the ABAB... sequence. But many layer stacking sequences are possible (ABAC, ABCBA, ABCBAC, etc.), and still generate a close-packed structure. In all of these arrangements each sphere touches 12 neighboring spheres, and the average density is
In 1611, Johannes Kepler conjectured that this is the maximum possible density amongst both regular and irregular arrangements—this became known as the Kepler conjecture. Carl Friedrich Gauss proved in 1831 that these packings have the highest density amongst all possible lattice packings. In 1998, Thomas Callister Hales, following the approach suggested by László Fejes Tóth in 1953, announced a proof of the Kepler conjecture. Hales proof is a proof by exhaustion involving checking of many individual cases using complex computer calculations. Referees said that they were "99% certain" of the correctness of Hales proof. On 10 August 2014, Hales announced the completion of a formal proof using automated proof checking, removing any doubt. | 1 | Crystallography |
Volume Bragg gratings (VBG) or volume holographic gratings (VHG) consist of a volume where there is a periodic change in the refractive index. Depending on the orientation of the refractive index modulation, VBG can be used either to transmit or reflect a small bandwidth of wavelengths. Bragg's law (adapted for volume hologram) dictates which wavelength will be diffracted:
where is the Bragg order (a positive integer), the diffracted wavelength, Λ the fringe spacing of the grating, the angle between the incident beam and the normal () of the entrance surface and the angle between the normal and the grating vector (). Radiation that does not match Bragg's law will pass through the VBG undiffracted. The output wavelength can be tuned over a few hundred nanometers by changing the incident angle (). VBG are being used to produce widely tunable laser source or perform global hyperspectral imagery (see Photon etc.). | 1 | Crystallography |
Cleavage, in mineralogy and materials science, is the tendency of crystalline materials to split along definite crystallographic structural planes. These planes of relative weakness are a result of the regular locations of atoms and ions in the crystal, which create smooth repeating surfaces that are visible both in the microscope and to the naked eye. If bonds in certain directions are weaker than others, the crystal will tend to split along the weakly bonded planes. These flat breaks are termed "cleavage". The classic example of cleavage is mica, which cleaves in a single direction along the basal pinacoid, making the layers seem like pages in a book. In fact, mineralogists often refer to "books of mica".
Diamond and graphite provide examples of cleavage. Each is composed solely of a single element, carbon. In diamond, each carbon atom is bonded to four others in a tetrahedral pattern with short covalent bonds. The planes of weakness (cleavage planes) in a diamond are in four directions, following the faces of the octahedron. In graphite, carbon atoms are contained in layers in a hexagonal pattern where the covalent bonds are shorter (and thus even stronger) than those of diamond. However, each layer is connected to the other with a longer and much weaker van der Waals bond. This gives graphite a single direction of cleavage, parallel to the basal pinacoid. So weak is this bond that it is broken with little force, giving graphite a slippery feel as layers shear apart. As a result, graphite makes an excellent dry lubricant.
While all single crystals will show some tendency to split along atomic planes in their crystal structure, if the differences between one direction or another are not large enough, the mineral will not display cleavage. Corundum, for example, displays no cleavage. | 1 | Crystallography |
Epitaxy is used in nanotechnology and in semiconductor fabrication. Indeed, epitaxy is the only affordable method of high quality crystal growth for many semiconductor materials. In surface science, epitaxy is used to create and study monolayer and multilayer films of adsorbed organic molecules on single crystalline surfaces via scanning tunnelling microscopy. | 1 | Crystallography |
The instrumentation needed to perform capillary electrophoresis is relatively simple. A basic schematic of a capillary electrophoresis system is shown in figure 1. The systems main components are a sample vial, source and destination vials, a capillary, electrodes, a high voltage power supply, a detector, and a data output and handling device. The source vial, destination vial and capillary are filled with an electrolyte such as an aqueous buffer solution. To introduce the sample, the capillary inlet is placed into a vial containing the sample. Sample is introduced into the capillary via capillary action, pressure, siphoning, or electrokinetically, and the capillary is then returned to the source vial. The migration of the analytes is initiated by an electric field that is applied between the source and destination vials and is supplied to the electrodes by the high-voltage power supply. In the most common mode of CE, all ions, positive or negative, are pulled through the capillary in the same direction by electroosmotic flow. The analytes separate as they migrate due to their electrophoretic mobility, and are detected near the outlet end of the capillary. The output of the detector is sent to a data output and handling device such as an integrator or computer. The data is then displayed as an electropherogram, which reports detector response as a function of time. Separated chemical compounds appear as peaks with different migration times in an electropherogram. The technique is often attributed to James W. Jorgensen and Krynn DeArman Lukacs, who first demonstrated the capabilities of this technique. Capillary electrophoresis was first combined with mass spectrometry by Richard D. Smith and coworkers, and provides extremely high sensitivity for the analysis of very small sample sizes. Despite the very small sample sizes (typically only a few nanoliters of liquid are introduced into the capillary), high sensitivity and sharp peaks are achieved in part due to injection strategies that result in a concentration of analytes into a narrow zone near the inlet of the capillary. This is achieved in either pressure or electrokinetic injections simply by suspending the sample in a buffer of lower conductivity (e.g.' lower salt concentration) than the running buffer. A process called field-amplified sample stacking (a form of isotachophoresis) results in concentration of analyte in a narrow zone at the boundary between the low-conductivity sample and the higher-conductivity running buffer.
To achieve greater sample throughput, instruments with arrays of capillaries are used to analyze many samples simultaneously. Such capillary array electrophoresis (CAE) instruments with 16 or 96 capillaries are used for medium- to high-throughput capillary DNA sequencing, and the inlet ends of the capillaries are arrayed spatially to accept samples directly from SBS-standard footprint 96-well plates. Certain aspects of the instrumentation (such as detection) are necessarily more complex than for a single-capillary system, but the fundamental principles of design and operation are similar to those shown in Figure 1. | 0 | Chromatography + Titration + pH indicators |
A powerful solution is the multi-wavelength anomalous dispersion (MAD) method. In this technique, atoms inner electrons absorb X-rays of particular wavelengths, and reemit the X-rays after a delay, inducing a phase shift in all of the reflections, known as the anomalous dispersion effect'. Analysis of this phase shift (which may be different for individual reflections) results in a solution for the phases. Since X-ray fluorescence techniques (like this one) require excitation at very specific wavelengths, it is necessary to use synchrotron radiation when using the MAD method. | 1 | Crystallography |
In some materials, superspots will occur at positions that do not represent a simple fraction, say q=(0.5234,0,0). In this case the structure strictly speaking has lost all translational symmetry in a particular direction. This is called an incommensurate structure. | 1 | Crystallography |
While the above techniques use a spatially extended, wide incident beam, section topography is based on a narrow beam on the order of some 10 micrometers (in one or, in the case of pinhole topography with a pencil beam, in both lateral dimensions). Section topographs therefore investigate only a restricted volume of the sample.
On its path through the crystal, the beam is diffracted at different depths, each one contributing to image formation on a different location on the detector (film). Section topography can therefore be used for depth-resolved defect analysis.
In section topography, even perfect crystals display fringes. The technique is very sensitive to crystalline defects and strain, as these distort the fringe pattern in the topograph. Quantitative analysis can be performed with the help of image simulation by computer algorithms, usually based on the Takagi-Taupin equations.
An enlarged synchrotron X-ray transmission section topograph on the right shows a diffraction image of the section of a sample having a gallium nitride (GaN) layer grown by metal-organic vapour phase epitaxy on sapphire wafer. Both the epitaxial GaN layer and the sapphire substrate show numerous defects. The GaN layer actually consists of about 20 micrometers wide small-angle grains connected to each other. Strain in the epitaxial layer and substrate is visible as elongated streaks parallel to the diffraction vector direction. The defects on the underside of the sapphire wafer section image are surface defects on the unpolished backside of the sapphire wafer. Between the sapphire and GaN the defects are interfacial defects. | 1 | Crystallography |
The idea of rigid unit modes was developed for crystalline materials to enable an understanding of the origin of displacive phase transitions in materials such as silicates, which can be described as infinite three-dimensional networks of corner-lined SiO and AlO tetrahedra. The idea was that rigid unit modes could act as the soft modes for displacive phase transitions.
The original work in silicates showed that many of the phase transitions in silicates could be understood in terms of soft modes that are RUMs.
After the original work on displacive phase transitions, the RUM model was also applied to understanding the nature of the disordered high-temperature phases of materials such as cristobalite, the dynamics and localised structural distortions in zeolites, and negative thermal expansion. | 1 | Crystallography |
Silica gel particles are commonly used as a stationary phase in high-performance liquid chromatography (HPLC) for several reasons, including:
# High surface area: Silica gel particles have a high surface area, allowing direct interactions with solutes or after bonding of variety of ligands for versatile interactions with the sample molecules, leading to better separations.
# Chemical and thermal stability and inertness: Silica gel is chemically stable, as it usually does not react with either the solvents of the mobile phase nor the compounds being separated, resulting in accurate, repeatable and reliable analyses.
# Wide applicability: Silica gel is versatile and can be modified with various functional groups, making it suitable for a wide range of analytes and applications.
# Efficient separation: The unique properties of silica gel particles, combined with their high surface area and controlled average particle diameter pore size, facilitate efficient and precise separation of compounds in HPLC.
# Reproducibility: Silica gel particles can offer high batch-to-batch reproducibility, which is crucial for consistent and reliable HPLC analyses throughout decades.
# Particle diameter and pore size control: Silica gel can be engineered to have specific pore sizes, enabling precise control over separation based on molecular size.
# Cost-effectiveness: Silica is the most abundant element on earth, hence its gel is a cost-effective choice for HPLC applications, making it widely adopted in laboratories.
The United States Pharmacopoeia (USP) has classified HPLC columns by L# types. The most popular column in this classification is an octadecyl carbon chain (C18)-bonded silica (USP classification L1). This is followed by C8-bonded silica (L7), pure silica (L3), cyano-bonded silica (CN) (L10) and phenyl-bonded silica (L11). Note that C18, C8 and phenyl are dedicated reversed-phase stationary phases, while CN columns can be used in a reversed-phase mode depending on analyte and mobile phase conditions. Not all C18 columns have identical retention properties. Surface functionalization of silica can be performed in a monomeric or a polymeric reaction with different short-chain organosilanes used in a second step to cover remaining silanol groups (end-capping). While the overall retention mechanism remains the same, subtle differences in the surface chemistries of different stationary phases will lead to changes in selectivity.
Modern columns have different polarity depending on the ligand bonded to the stationary phase. PFP is pentafluorphenyl. CN is cyano. NH2 is amino. ODS is octadecyl or C18. ODCN is a mixed mode column consisting of C18 and nitrile.
Recent developments in chromatographic supports and instrumentation for liquid chromatography (LC) facilitate rapid and highly efficient separations, using various stationary phases geometries. Various analytical strategies have been proposed, such as the use of silica-based monolithic supports, elevated mobile phase temperatures, and columns packed with sub-3 μm superficially porous particles (fused or solid core) or with sub-2 μm fully porous particles for use in ultra-high-pressure LC systems (UHPLC). | 0 | Chromatography + Titration + pH indicators |
A subset X of a metric space is relatively dense if there exists a number r such that all points of X are within distance r of X, and it is uniformly discrete if there exists a number ε such that no two points of X are within distance ε of each other. A set that is both relatively dense and uniformly discrete is called a Delone set. When X is a subset of a vector space, its Minkowski difference X − X is the set {x − y | x, y in X} of differences of pairs of elements of X.
With these definitions, a Meyer set may be defined as a relatively dense set X for which X − X is uniformly discrete. Equivalently, it is a Delone set for which X − X is Delone, or a Delone set X for which there exists a finite set F with X − X ⊂ X + F
Some additional equivalent characterizations involve the set
defined for a given X and ε, and approximating (as ε approaches zero) the definition of the reciprocal lattice of a lattice. A relatively dense set X is a Meyer set if and only if
* For all ε > 0, X is relatively dense, or equivalently
* There exists an ε with 0 is relatively dense.
A character of an additively closed subset of a vector space is a function that maps the set to the unit circle in the plane of complex numbers, such that the sum of any two elements is mapped to the product of their images. A set X is a harmonious set if, for every character χ on the additive closure of X and every ε > 0, there exists a continuous character on the whole space that ε-approximates χ. Then a relatively dense set X is a Meyer set if and only if it is harmonious. | 1 | Crystallography |
Redox reactions are normally strongly exothermic, and can make excellent candidates for thermometric titrations. In the classical determination of ferrous ion with permanganate, the reaction enthalpy is more than double that of a strong acid/strong base titration:ΔH =
−123.9 kJ/mol of Fe. The determination of hydrogen peroxide by permanganate titration is even more strongly exothermic at ΔH =
−149.6 kJ/mol HO | 0 | Chromatography + Titration + pH indicators |
For the special case of simple cubic crystals, the lattice vectors are orthogonal and of equal length (usually denoted a); similarly for the reciprocal lattice. So, in this common case, the Miller indices (ℓmn) and [ℓmn] both simply denote normals/directions in Cartesian coordinates. For cubic crystals with lattice constant a, the spacing d between adjacent (ℓmn) lattice planes is (from above):
Because of the symmetry of cubic crystals, it is possible to change the place and sign of the integers and have equivalent directions and planes:
*Coordinates in angle brackets such as denote a family of directions that are equivalent due to symmetry operations, such as [100], [010], [001] or the negative of any of those directions.
*Coordinates in curly brackets or braces such as {100} denote a family of plane normals that are equivalent due to symmetry operations, much the way angle brackets denote a family of directions.
For face-centered cubic (fcc) and body-centered cubic (bcc) lattices, the primitive lattice vectors are not orthogonal. However, in these cases the Miller indices are conventionally defined relative to the lattice vectors of the cubic supercell and hence are again simply the Cartesian directions. | 1 | Crystallography |
CellViewer allows to visualize the sample material in four modes widely used in material research:
* 3D model of atomic structure (direct space),
* simulated diffraction pattern (reciprocal space),
* stereographic projection (projection of 3D space of crystallographic planes and directions to 2D),
* inverse pole figure (defined part of stereographic projection).
Graphical user interface provides user with two interactive views side by side. These views can display arbitrary combination of the four aforementioned visualization modes allowing to perceive their mutual relations. For instance, rotation of the atomic structure in direct space leads (if set so) to an instant update of the simulated diffraction pattern. If any diffraction spot is selected, corresponding crystallographic planes are shown in the unit cell etc. Such interconnections are implemented for each pair of the four available visualization modes. The electronic visualization allows to simplify understanding of widely used, yet less intuitive representations such as the inverse pole figure. For instance by drawing the coloured triangle of the inverse pole figure into the stereographic projection or to the more intuitive 3D atomic structure. | 1 | Crystallography |
The drawbacks of the SMB are higher investment cost compared to single column operations, a higher complexity, as well as higher maintenance costs. But these drawbacks are effectively compensated by the better yield and a much lower solvent consumption as well as a much higher productivity compared to simple batch separations.
For purifications, in particular the isolation of an intermediate single component or a fraction out of a multicomponent mixture, the SMB is not as ideally suited. Normally, a single SMB will separate only two fractions from each other, but a series or "train" of SMBs can perform multiple cuts and purify one or more products from a multi-component mixture. SMB is not readily suited for solvent gradients. Solvent gradient purification may be preferred for the purification of some biomolecules. A continuous chromatography technique to overcome the two fraction limit and to apply gradients is multicolumn countercurrent solvent gradient purification (MCSGP). | 0 | Chromatography + Titration + pH indicators |
Bromocresol green (BCG) is a dye of the triphenylmethane family (triarylmethane dyes). It belongs to a class of dyes called sulfonephthaleins. It is used as a pH indicator in applications such as growth mediums for microorganisms and titrations. In clinical practise, it is commonly used as a diagnostic technique. The most common use of bromocresol green is to measure serum albumin concentration within mammalian blood samples in possible cases of kidney failure and liver disease. In chemistry, bromocresol green is used in Thin-layer chromatography staining solutions to visualize acidic compounds. | 0 | Chromatography + Titration + pH indicators |
For any 3-dimensional lattice, the conventional unit cells are parallelepipeds, which in special cases may have orthogonal angles, or equal lengths, or both. Seven of the fourteen three-dimensional Bravais lattices are represented using conventional primitive cells, as shown below.
The other seven Bravais lattices (known as the centered lattices) also have primitive cells in the shape of a parallelepiped, but in order to allow easy discrimination on the basis of symmetry, they are represented by conventional cells which contain more than one lattice point. | 1 | Crystallography |
GC–MS can analyze the particles from a human body in order to help link a criminal to a crime. The analysis of fire debris using GC–MS is well established, and there is even an established American Society for Testing and Materials (ASTM) standard for fire debris analysis. GCMS/MS is especially useful here as samples often contain very complex matrices and results, used in court, need to be highly accurate. | 0 | Chromatography + Titration + pH indicators |
Micellar electrokinetic chromatography (MEKC) is a chromatography technique used in analytical chemistry. It is a modification of capillary electrophoresis (CE), extending its functionality to neutral analytes, where the samples are separated by differential partitioning between micelles (pseudo-stationary phase) and a surrounding aqueous buffer solution (mobile phase).
The basic set-up and detection methods used for MEKC are the same as those used in CE. The difference is that the solution contains a surfactant at a concentration that is greater than the critical micelle concentration (CMC). Above this concentration, surfactant monomers are in equilibrium with micelles.
In most applications, MEKC is performed in open capillaries under alkaline conditions to generate a strong electroosmotic flow. Sodium dodecyl sulfate (SDS) is the most commonly used surfactant in MEKC applications. The anionic character of the sulfate groups of SDS causes the surfactant and micelles to have electrophoretic mobility that is counter to the direction of the strong electroosmotic flow. As a result, the surfactant monomers and micelles migrate quite slowly, though their net movement is still toward the cathode. During a MEKC separation, analytes distribute themselves between the hydrophobic interior of the micelle and hydrophilic buffer solution as shown in figure 1.
Analytes that are insoluble in the interior of micelles should migrate at the electroosmotic flow velocity, , and be detected at the retention time of the buffer, . Analytes that solubilize completely within the micelles (analytes that are highly hydrophobic) should migrate at the micelle velocity, , and elute at the final elution time, . | 0 | Chromatography + Titration + pH indicators |
Anthocyanins have been used in organic solar cells because of their ability to convert light energy into electrical energy. The many benefits to using dye-sensitized solar cells instead of traditional p-n junction silicon cells, include lower purity requirements and abundance of component materials, as well as the fact that they may be produced on flexible substrates, making them amenable to roll-to-roll printing processes. | 0 | Chromatography + Titration + pH indicators |
A Biomolecular Analysis Mass Spectrometry (BAMS) facility was officially opened in 2003, headed by Professor Newton and Dr Dudley. It was a collaborative entity between the Department of Biological Sciences and the Medical School. It focused on the study of nucleosides, nucleotides and cyclic nucleotides. | 0 | Chromatography + Titration + pH indicators |
A relatively recent analytical tool that has been used for the separation of UCMs is comprehensive two-dimensional GC (GCxGC). This powerful technique, introduced by Liu and Phillips combines two GC columns with different separation mechanisms: typically a primary column that separates compounds based on volatility coupled to a second short column that separates by polarity. The two columns are connected by a modulator, a device that traps, focuses and re-injects the peaks that elute from the first column into the second column. Each peak eluting from the first column (which may be a number of co-eluting peaks) is further separated on the second column. The second separation is rapid, allowing the introduction of subsequent fractions from the first column without mutual interference. Dallüge et al. reviewed the principles, advantages and main characteristics of this technique. One of the main advantages is the very high separation power, making the technique ideal for unravelling the composition of complex mixtures. Another important feature of GC×GC is that chemically related compounds show up as ordered structures within the chromatograms, i.e. isomers appear as distinct groups in the chromatogram as a result of their similar interaction with the second dimension column phase. The use of GC×GC for the characterization of complex petrochemical mixtures has been extensively reviewed. Most research into petrochemical hydrocarbons using GC×GC has utilised flame ionisation detection (FID) but mass spectrometry (MS) is necessary to obtain the structural information necessary to identify unknown compounds. Currently, only time-of-flight MS (ToF-MS) can deliver the high acquisition rates required to analyse GC×GC. | 0 | Chromatography + Titration + pH indicators |
Binding to the solid phase may be achieved by column chromatography whereby the solid medium is packed onto a column, the initial mixture run through the column to allow settling, a wash buffer run through the column and the elution buffer subsequently applied to the column and collected. These steps are usually done at ambient pressure. Alternatively, binding may be achieved using a batch treatment, for example, by adding the initial mixture to the solid phase in a vessel, mixing, separating the solid phase, removing the liquid phase, washing, re-centrifuging, adding the elution buffer, re-centrifuging and removing the elute.
Sometimes a hybrid method is employed such that the binding is done by the batch method, but the solid phase with the target molecule bound is packed onto a column and washing and elution are done on the column.
The ligands used in affinity chromatography are obtained from both organic and inorganic sources. Examples of biological sources are serum proteins, lectins and antibodies. Inorganic sources are moronic acid, metal chelates and triazine dyes.
A third method, expanded bed absorption, which combines the advantages of the two methods mentioned above, has also been developed. The solid phase particles are placed in a column where liquid phase is pumped in from the bottom and exits at the top. The gravity of the particles ensure that the solid phase does not exit the column with the liquid phase.
Affinity columns can be eluted by changing salt concentrations, pH, pI, charge and ionic strength directly or through a gradient to resolve the particles of interest.
More recently, setups employing more than one column in series have been developed. The advantage compared to single column setups is that the resin material can be fully loaded since non-binding product is directly passed on to a consecutive column with fresh column material. These chromatographic processes are known as periodic counter-current chromatography (PCC). The resin costs per amount of produced product can thus be drastically reduced. Since one column can always be eluted and regenerated while the other column is loaded, already two columns are sufficient to make full use of the advantages. Additional columns can give additional flexibility for elution and regeneration times, at the cost of additional equipment and resin costs. | 0 | Chromatography + Titration + pH indicators |
While relatively unstable and requiring frequent standardization, sodium hypochlorite has been used in a very rapid thermometric titration method for the determination of ammonium ion. This is an alternative to the classical approach of ammonia distillation from basic solution and consequent acid–base titration. The thermometric titration is carried out in bicarbonate solution containing bromide ion (Brown et al., 1969). | 0 | Chromatography + Titration + pH indicators |
A rotation symmetry in dimension 2 or 3 must move a lattice point to a succession of other lattice points in the same plane, generating a regular polygon of coplanar lattice points. We now confine our attention to the plane in which the symmetry acts , illustrated with lattice vectors in the figure.
Now consider an 8-fold rotation, and the displacement vectors between adjacent points of the polygon. If a displacement exists between any two lattice points, then that same displacement is repeated everywhere in the lattice. So collect all the edge displacements to begin at a single lattice point. The edge vectors become radial vectors, and their 8-fold symmetry implies a regular octagon of lattice points around the collection point. But this is impossible, because the new octagon is about 80% as large as the original. The significance of the shrinking is that it is unlimited. The same construction can be repeated with the new octagon, and again and again until the distance between lattice points is as small as we like; thus no discrete lattice can have 8-fold symmetry. The same argument applies to any k-fold rotation, for k greater than 6.
A shrinking argument also eliminates 5-fold symmetry. Consider a regular pentagon of lattice points. If it exists, then we can take every other edge displacement and (head-to-tail) assemble a 5-point star, with the last edge returning to the starting point. The vertices of such a star are again vertices of a regular pentagon with 5-fold symmetry, but about 60% smaller than the original.
Thus the theorem is proved.
The existence of quasicrystals and Penrose tilings shows that the assumption of a linear translation is necessary. Penrose tilings may have 5-fold rotational symmetry and a discrete lattice, and any local neighborhood of the tiling is repeated infinitely many times, but there is no linear translation for the tiling as a whole. And without the discrete lattice assumption, the above construction not only fails to reach a contradiction, but produces a (non-discrete) counterexample. Thus 5-fold rotational symmetry cannot be eliminated by an argument missing either of those assumptions. A Penrose tiling of the whole (infinite) plane can only have exact 5-fold rotational symmetry (of the whole tiling) about a single point, however, whereas the 4-fold and 6-fold lattices have infinitely many centres of rotational symmetry. | 1 | Crystallography |
Large numbers of samples can be automatically injected onto an HPLC system, by the use of HPLC autosamplers. In addition, HPLC autosamplers have an injection volume and technique which is exactly the same for each injection, consequently they provide a high degree of injection volume precision.
It is possible to enable sample stirring within the sampling-chamber, thus promoting homogeneity. | 0 | Chromatography + Titration + pH indicators |
A chromatography detector is a device that detects and quantifies separated compounds as they elute from the chromatographic column. These detectors are integral to various chromatographic techniques, such as gas chromatography, liquid chromatography, and high-performance liquid chromatography, and supercritical fluid chromatography among others. The main function of a chromatography detector is to translate the physical or chemical properties of the analyte molecules into measurable signal, typically electrical signal, that can be displayed as a function of time in a graphical presentation, called a chromatograms. Chromatograms can provide valuable information about the composition and concentration of the components in the sample.
Detectors operate based on specific principles, including optical, electrochemical, thermal conductivity, fluorescence, mass spectrometry, and more. Each type of detector has its unique capabilities and is suitable for specific applications, depending on the nature of the analytes and the sensitivity and selectivity required for the analysis.
There are two general types of detectors: destructive and non-destructive. The destructive detectors perform continuous transformation of the column effluent (burning, evaporation or mixing with reagents) with subsequent measurement of some physical property of the resulting material (plasma, aerosol or reaction mixture). The non-destructive detectors are directly measuring some property of the column eluent (for example, ultraviolet absorption) and thus affords greater analyte recovery. | 0 | Chromatography + Titration + pH indicators |
The "elution time" of a solute is the time between the start of the separation (the time at which the solute enters the column) and the time at which the solute elutes. In the same way, the elution volume is the volume of eluent required to cause elution. Under standard conditions for a known mix of solutes in a certain technique, the elution volume may be enough information to identify solutes. For instance, a mixture of amino acids may be separated by ion-exchange chromatography. Under a particular set of conditions, the amino acids will elute in the same order and at the same elution volume. | 0 | Chromatography + Titration + pH indicators |
The sphere packing problem is the three-dimensional version of a class of ball-packing problems in arbitrary dimensions. In two dimensions, the equivalent problem is packing circles on a plane. In one dimension it is packing line segments into a linear universe.
In dimensions higher than three, the densest lattice packings of hyperspheres are known up to 8 dimensions. Very little is known about irregular hypersphere packings; it is possible that in some dimensions the densest packing may be irregular. Some support for this conjecture comes from the fact that in certain dimensions (e.g. 10) the densest known irregular packing is denser than the densest known regular packing.
In 2016, Maryna Viazovska announced a proof that the E lattice provides the optimal packing (regardless of regularity) in eight-dimensional space, and soon afterwards she and a group of collaborators announced a similar proof that the Leech lattice is optimal in 24 dimensions. This result built on and improved previous methods which showed that these two lattices are very close to optimal.
The new proofs involve using the Laplace transform of a carefully chosen modular function to construct a radially symmetric function such that and its Fourier transform both equal 1 at the origin, and both vanish at all other points of the optimal lattice, with negative outside the central sphere of the packing and positive. Then, the Poisson summation formula for is used to compare the density of the optimal lattice with that of any other packing. Before the proof had been formally refereed and published, mathematician Peter Sarnak called the proof "stunningly simple" and wrote that "You just start reading the paper and you know this is correct."
Another line of research in high dimensions is trying to find asymptotic bounds for the density of the densest packings. It is known that for large , the densest lattice in dimension has density between (for some constant ) and . to | 1 | Crystallography |
An orbifold can be viewed as a polygon with face, edges, and vertices which can be unfolded to form a possibly infinite set of polygons which tile either the sphere, the plane or the hyperbolic plane. When it tiles the plane it will give a wallpaper group and when it tiles the sphere or hyperbolic plane it gives either a spherical symmetry group or Hyperbolic symmetry group. The type of space the polygons tile can be found by calculating the Euler characteristic, χ = V − E + F, where V is the number of corners (vertices), E is the number of edges and F is the number of faces. If the Euler characteristic is positive then the orbifold has an elliptic (spherical) structure; if it is zero then it has a parabolic structure, i.e. a wallpaper group; and if it is negative it will have a hyperbolic structure. When the full set of possible orbifolds is enumerated it is found that only 17 have Euler characteristic 0.
When an orbifold replicates by symmetry to fill the plane, its features create a structure of vertices, edges, and polygon faces, which must be consistent with the Euler characteristic. Reversing the process, one can assign numbers to the features of the orbifold, but fractions, rather than whole numbers. Because the orbifold itself is a quotient of the full surface by the symmetry group, the orbifold Euler characteristic is a quotient of the surface Euler characteristic by the order of the symmetry group.
The orbifold Euler characteristic is 2 minus the sum of the feature values, assigned as follows:
*A digit n without or before a * counts as .
*A digit n after a * counts as .
*Both * and × count as 1.
*The "no symmetry" o counts as 2.
For a wallpaper group, the sum for the characteristic must be zero; thus the feature sum must be 2.
;Examples
Now enumeration of all wallpaper groups becomes a matter of arithmetic, of listing all feature strings with values summing to 2.
Feature strings with other sums are not nonsense; they imply non-planar tilings, not discussed here. (When the orbifold Euler characteristic is negative, the tiling is hyperbolic; when positive, spherical or bad). | 1 | Crystallography |
Rietveld refinement is a technique described by Hugo Rietveld for use in the characterisation of crystalline materials. The neutron and X-ray diffraction of powder samples results in a pattern characterised by reflections (peaks in intensity) at certain positions. The height, width and position of these reflections can be used to determine many aspects of the material's structure.
The Rietveld method uses a least squares approach to refine a theoretical line profile until it
matches the measured profile. The introduction of this technique was a significant step forward in the
diffraction analysis of powder samples as, unlike other techniques at that time, it was able to deal reliably with strongly overlapping reflections.
The method was first implemented in 1967, and reported in 1969 for the diffraction of monochromatic neutrons where the reflection-position is reported in terms of the Bragg angle, 2θ. This terminology will be used here although the technique is
equally applicable to alternative scales such as x-ray energy or neutron time-of-flight. The only wavelength and technique independent scale is in reciprocal space units or momentum transfer Q, which is historically rarely used in powder diffraction but very common in all other diffraction and optics techniques. The relation is | 1 | Crystallography |
A packing that can be described as the orbit of a body under the action of a double lattice is called a double lattice packing. In many cases the highest known packing density for a body is achieved by a double lattice. Examples include the regular pentagon, heptagon, and nonagon and the equilateral triangular bipyramid.
Włodzimierz Kuperberg and Greg Kuperberg showed that all convex planar bodies can pack at a density of at least by using a double lattice.
In a preprint released in 2016, Thomas Hales and Wöden Kusner announced a proof that the double lattice packing of the regular pentagon has the optimal density among all packings of regular pentagons in the plane. This packing has been used as a decorative pattern in China since at least 1900, and in this context has been called the "pentagonal ice-ray". , the proof of its optimality has not yet been refereed and published.
It has been conjectured that, among all convex shapes, the regular heptagon has the lowest packing density for its optimal double lattice packing, but this remains unproven. | 1 | Crystallography |
Conductive measurements began as early as the 18th century, when Andreas Baumgartner noticed that salt and mineral waters from Bad Gastein in Austria conducted electricity. As such, using conductometry to determine water purity, which is often used today to test the effectiveness of water purification systems, began in 1776. Friedrich Kohlrausch further developed conductometry in the 1860s when he applied alternating current to water, acids, and other solutions. It was also around this time when Willis Whitney, who was studying the interactions of sulfuric acid and chromium sulfate complexes, found the first conductometric endpoint. These finding culminated into potentiometric titrations and the first instrument for volumetric analysis by Robert Behrend in 1883 while titrating chloride and bromide with HgNO. This development allowed for testing the solubility of salts and hydrogen ion concentration, as well as acid/base and redox titrations. Conductometry was further improved with the development of the glass electrode, which began in 1909. | 0 | Chromatography + Titration + pH indicators |
o-Cresolphthalein is not produced industrially, rather, it is commercially available. To be produced, the method generally used to synthesize phthalein dyes is effective. This method is used to synthesize phenolphthalein and thymolphthalein. To begin, a 2M equivalent of a phenol or a substituted phenol should be combined with a 1M equivalent of a phthalic anhydride. | 0 | Chromatography + Titration + pH indicators |
In Cartesian coordinates the basis vectors are represented by a cell tensor :
The hypervolume of the unit cell, , is given by the determinant of the cell tensor: | 1 | Crystallography |
Size exclusion chromatography applications for separating macromolecules based on subtle differences in size typically use resins with large and varied pore sizes in long chromatography columns. However, for buffer exchange and desalting applications, it is mainly the maximum effective pore size (exclusion limit or molecular weight cut off (MWCO) of the resin) that determines the size of molecules that can be separated. Molecules that are significantly smaller than the MWCO penetrate into the pores of the resin, while molecules larger than the MWCO are unable to enter the pores and remain together in the void volume of the column. By passing samples through a column resin bed with sufficient length and volume, macromolecules can be fully separated from small molecules that travel a greater distance though the pores of the resin bed. No significant separation of molecules larger than the exclusion limit occurs.
In order for the desired macromolecules to remain in the void volume, resins with very small pores sizes must be utilized. For typical desalting and buffer exchange applications choosing a resin with a molecular weight cut off between 5 and 10KDa is usually best. For other applications, such as separating peptides from full-sized proteins, resins with larger exclusion limits may be necessary. The macromolecular components are recovered in the buffer used to pre-equilibrate the gel-filtration matrix, while the small molecules can be collected in a later fraction volume or be left trapped in the resin. One important feature to note when choosing a resin is that the small molecules targeted for removal must be several times smaller than the MWCO for proper separation. | 0 | Chromatography + Titration + pH indicators |
In mineralogy, epitaxy is the overgrowth of one mineral on another in an orderly way, such that certain crystal directions of the two minerals are aligned. This occurs when some planes in the lattices of the overgrowth and the substrate have similar spacings between atoms.
If the crystals of both minerals are well formed so that the directions of the crystallographic axes are clear then the epitaxic relationship can be deduced just by a visual inspection.
Sometimes many separate crystals form the overgrowth on a single substrate, and then if there is epitaxy all the overgrowth crystals will have a similar orientation. The reverse, however, is not necessarily true. If the overgrowth crystals have a similar orientation there is probably an epitaxic relationship, but it is not certain.
Some authors consider that overgrowths of a second generation of the same mineral species should also be considered as epitaxy, and this is common terminology for semiconductor scientists who induce epitaxic growth of a film with a different doping level on a semiconductor substrate of the same material. For naturally produced minerals, however, the International Mineralogical Association (IMA) definition requires that the two minerals be of different species.
Another man-made application of epitaxy is the making of artificial snow using silver iodide, which is possible because hexagonal silver iodide and ice have similar cell dimensions. | 1 | Crystallography |
It is not always possible to eliminate ion suppression by sample preparation and/or chromatographic resolution. In such cases it may be possible to compensate for the effects of ion suppression on accuracy and precision (although not for analytical sensitivity) by adopting complex calibration strategies. | 0 | Chromatography + Titration + pH indicators |
A typical titration begins with a beaker or Erlenmeyer flask containing a very precise amount of the analyte and a small amount of indicator (such as phenolphthalein) placed underneath a calibrated burette or chemistry pipetting syringe containing the titrant. Small volumes of the titrant are then added to the analyte and indicator until the indicator changes color in reaction to the titrant saturation threshold, representing arrival at the endpoint of the titration, meaning the amount of titrant balances the amount of analyte present, according to the reaction between the two. Depending on the endpoint desired, single drops or less than a single drop of the titrant can make the difference between a permanent and temporary change in the indicator. | 0 | Chromatography + Titration + pH indicators |
The screw axis is noted by a number, n, where the angle of rotation is . The degree of translation is then added as a subscript showing how far along the axis the translation is, as a portion of the parallel lattice vector. For example, 2 is a 180° (twofold) rotation followed by a translation of of the lattice vector. 3 is a 120° (threefold) rotation followed by a translation of of the lattice vector.
The possible screw axes are: 2, 3, 3, 4, 4, 4, 6, 6, 6, 6, and 6.
There are 4 enantiomorphic pairs of axes: (3 – 3), (4 – 4), (6 – 6), and (6 – 6). This enantiomorphism results in 11 pairs of enantiomorphic space groups, namely | 1 | Crystallography |
With the development of native chemical ligation in 1994, total chemical synthesis of pairs of D-protein and L-protein enantiomers became feasible. In the first practical application to solving an unknown structure, racemic and quasi-racemic X-ray crystallography were used to determine the structure of snow flea anti-freeze protein. In the course of that work it was observed that racemic and even quasi-racemic protein mixtures dramatically facilitated the formation of diffraction quality, centrosymmetric crystals. Quasi-racemates are formed by mirror image protein molecules that are not true enantiomers but which are sufficiently similar mirror image objects to form ordered pseudo-centrosymmetric arrays.
Subsequently, pairs of racemic and quasi-racemic protein molecules prepared by total chemical synthesis have been shown to dramatically increase the rate of success in forming diffraction-quality crystals from a wide range of globular protein molecules.
Rv1738, a protein of Mycobacterium tuberculosis is the most up-regulated gene product when M. tb enters persistent dormancy. Preparations of recombinantly expressed Rv1738 L-protein resisted extensive attempts to form crystals. A racemic mixture of the chemically synthesized D-protein and L-protein forms of Rv1738 gave crystals in the centrosymmetric space group C2/c. The structure, containing L-protein and D-protein dimers in a centrosymmetric space group, revealed structural similarity to hibernation-promoting factors that can bind to ribosomes and suppress translation.
Crystallization of ubiquitin protein was successfully done using racemic crystallography. Crystallization of either D-ubiquitin or L-ubiquitin alone is difficult, whereas a racemic mixture of D-ubiquitin and L-ubiquitin was readily crystallized and diffraction quality crystals were obtained overnight in almost half the conditions tested in a standard commercial crystallization screen.
Crystallization of racemates of disulfide-containing microprotein molecules was used to determine the structure of trypsin inhibitor SFTI-1 (14 amino acids,1 disulfide), conotoxin cVc1.1 (22 amino acids, 2 disul-fides) and cyclotide kB1 (29 amino acids, 3 disulfides). Using X-ray diffraction, it was found that the racemates crystallized in the centrosymmetric spacegroups P3(bar), Pbca and P1(bar).
Interestingly, achiral "peptoid" chains were found to fold as racemic pairs and crystallize in highly preferred centrosymmetric space groups.
A high-resolution crystal structure of the racemate of a heterochiral D-protein complex with vascular endothelial growth factor A (VEGF-A). The mirror image D-protein form of VEGF-A was used in phage display to identify a 56 residue L-protein binder with nanomolar affinity; the chemically synthesized D-protein binder had the same affinity for the L-protein form of VEGF-A. A mixture of chemically synthesized proteins consisting of D-VEGF-A, L-VEGF-A, and two equivalents each of the D-protein binder and L-protein binder, gave racemic crystals in the centrosymmetric space group P21/n. The structure of this 71kDa heterochiral protein complex was solved at a resolution of 1.6 Å | 1 | Crystallography |
Miller indices form a notation system in crystallography for lattice planes in crystal (Bravais) lattices.
In particular, a family of lattice planes of a given (direct) Bravais lattice is determined by three integers h, k, and ℓ, the Miller indices. They are written (hkℓ), and denote the family of (parallel) lattice planes (of the given Bravais lattice) orthogonal to , where are the basis or primitive translation vectors of the reciprocal lattice for the given Bravais lattice. (Note that the plane is not always orthogonal to the linear combination of direct or original lattice vectors because the direct lattice vectors need not be mutually orthogonal.) This is based on the fact that a reciprocal lattice vector (the vector indicating a reciprocal lattice point from the reciprocal lattice origin) is the wavevector of a plane wave in the Fourier series of a spatial function (e.g., electronic density function) which periodicity follows the original Bravais lattice, so wavefronts of the plane wave are coincident with parallel lattice planes of the original lattice. Since a measured scattering vector in X-ray crystallography, with as the outgoing (scattered from a crystal lattice) X-ray wavevector and as the incoming (toward the crystal lattice) X-ray wavevector, is equal to a reciprocal lattice vector as stated by the Laue equations, the measured scattered X-ray peak at each measured scattering vector is marked by Miller indices. By convention, negative integers are written with a bar, as in for −3. The integers are usually written in lowest terms, i.e. their greatest common divisor should be 1. Miller indices are also used to designate reflections in X-ray crystallography. In this case the integers are not necessarily in lowest terms, and can be thought of as corresponding to planes spaced such that the reflections from adjacent planes would have a phase difference of exactly one wavelength (2), regardless of whether there are atoms on all these planes or not.
There are also several related notations:
*the notation denotes the set of all planes that are equivalent to by the symmetry of the lattice.
In the context of crystal directions (not planes), the corresponding notations are:
* with square instead of round brackets, denotes a direction in the basis of the direct lattice vectors instead of the reciprocal lattice; and
*similarly, the notation denotes the set of all directions that are equivalent to by symmetry.
Note, for Laue–Bragg interferences
* lacks any bracketing when designating a reflection
Miller indices were introduced in 1839 by the British mineralogist William Hallowes Miller, although an almost identical system (Weiss parameters) had already been used by German mineralogist Christian Samuel Weiss since 1817. The method was also historically known as the Millerian system, and the indices as Millerian, although this is now rare.
The Miller indices are defined with respect to any choice of unit cell and not only with respect to primitive basis vectors, as is sometimes stated. | 1 | Crystallography |
A further dynamic method to assemble such structures was introduced by Lee et al. Here, polymeric beads are placed together with a fluid of higher density inside a rotating lathe.
When the lathe is static, the beads float on top of the liquid. With increasing rotational speed, the centripetal force then pushes the fluid outwards and the beads toward the central axis. Hence, the beads are essentially confined by a potential given by the rotational energywhere is the mass of the beads, the distance from the central axis, and the rotational speed. Due to the proportionality, the confining potential resembles that of a cylindrical harmonic oscillator.
Depending on number of spheres and rotational speed, a variety of ordered structures that are comparable to the dense sphere packings were discovered.
A comprehensive theory to this experiment was developed by Winkelmann et al. It is based on analytic energy calculations using a generic sphere model and predicts peritectoid structure transitions. | 1 | Crystallography |
Complexometric titrations rely on the formation of a complex between the analyte and the titrant. In general, they require specialized complexometric indicators that form weak complexes with the analyte. The most common example is the use of starch indicator to increase the sensitivity of iodometric titration, the dark blue complex of starch with iodine and iodide being more visible than iodine alone. Other complexometric indicators are Eriochrome Black T for the titration of calcium and magnesium ions, and the chelating agent EDTA used to titrate metal ions in solution. | 0 | Chromatography + Titration + pH indicators |
Crystallographic features of HCP systems, such as vectors and atomic plane families, can be described using a four-value Miller index notation ( hkil ) in which the third index i denotes a convenient but degenerate component which is equal to −h − k. The h, i and k index directions are separated by 120°, and are thus not orthogonal; the l component is mutually perpendicular to the h, i and k index directions. | 1 | Crystallography |
Compounds elute in the carrier gas phase only. Compounds solved in the stationary phase stay put. The ratio of gas time and residence time in the stationary liquid polymer phase is called the capacity factor :
where the variables used are:
* gas constant (8.314J/mole/k)
* temperature [k]
* solubility of compound i in polymer stationary phase [mole/m]
* vapor pressure of pure liquid i [Pa]
Capillary tubes with uniform coatings have this phase ratio β:
Capillary inner diameter is well defined but film thickness reduces by bleed and thermal breakdown that occur after column heating over time, depending on chemical bonding to the silica glass wall and polymer cross-linking of the stationary phase.
Above capacity factor can be expressed explicit for retention time:
Retention time is shorter by reduced over column life time. Column length is introduced with average gas velocity :
and temperature have a direct relation with . However, warmer columns ↑ do not have longer but shorter, following temperature programming experience. Pure liquid vapor pressure rises exponentially with so that we do get shorter warming the column ↑. Solubility of compounds in the stationary phase may rise or fall with , but not exponentially. is referred to as selectivity or polarity by gas chromatographers today.
Isothermal Kovats index in terms of the physical properties becomes:
Isothermal Kovats index is independent of , any GC dimension or ß or carrier gas velocity , which compares favorable to retention time . Isothermal Kovats index is based on solubility and vapor pressure of compound i and n-Alkanes (). dependence depends on the compound compared to the n-alkanes. Kovats index of n-alkanes is independent of .
Isothermal Kovats indices of hydrocarbon were measured by Axel Lubeck and Donald Sutton. | 0 | Chromatography + Titration + pH indicators |
Silica monoliths have only been commercially available since 2001, when Merck began their Chromolith campaign. The Chromolith technology was licensed from Soga and Nakanishi's group at Kyoto University. The new product won the PittCon Editors’ Gold Award for Best New Product, as well as an R&D 100 Award, both in 2001.
Individual monolith columns have a life cycle that generally exceeds that of its particulate competitors. When selecting an HPLC column supplier, column lifetime was second only to column-to-column reproducibility in importance to the purchaser. Chromolith columns, for example, have demonstrated reproducibility of 3,300 sample injections and 50,000 column volumes of mobile phase. Also important to the life cycle of the monolith is its increased mechanical robustness; polymeric monoliths are able to withstand pH ranges from 1 to 14, can endure elevated temperatures, and do not need to be handled delicately. “Monoliths are still teenagers,” affirms Frantisec Svec, a leader in the field of novel stationary phases for LC. | 0 | Chromatography + Titration + pH indicators |
An eluotropic series is listing of various compounds in order of eluting power for a given adsorbent. The "eluting power" of a solvent is largely a measure of how well the solvent can "pull" an analyte off the adsorbent to which it is attached. This often happens when the eluent adsorbs onto the stationary phase, displacing the analyte. Such series are useful for determining necessary solvents needed for chromatography of chemical compounds. Normally such a series progresses from non-polar solvents, such as n-hexane, to polar solvents such as methanol or water. The order of solvents in an eluotropic series depends both on the stationary phase as well as on the compound used to determine the order. | 0 | Chromatography + Titration + pH indicators |
Rotation axes are denoted by a number n – 1, 2, 3, 4, 5, 6, 7, 8, ... (angle of rotation ). For improper rotations, Hermann–Mauguin symbols show rotoinversion axes, unlike Schoenflies and Shubnikov notations, that shows rotation-reflection axes. The rotoinversion axes are represented by the corresponding number with a macron, – , , , , , , , , ... . is equivalent to a mirror plane and usually notated as m. The direction of the mirror plane is defined as the direction perpendicular to it (the direction of the axis).
Hermann–Mauguin symbols show non-equivalent axes and planes in a symmetrical fashion. The direction of a symmetry element corresponds to its position in the Hermann–Mauguin symbol. If a rotation axis n and a mirror plane m have the same direction (i.e. the plane is perpendicular to axis n), then they are denoted as a fraction or n/m.
If two or more axes have the same direction, the axis with higher symmetry is shown. Higher symmetry means that the axis generates a pattern with more points. For example, rotation axes 3, 4, 5, 6, 7, 8 generate 3-, 4-, 5-, 6-, 7-, 8-point patterns, respectively. Improper rotation axes , , , , , generate 6-, 4-, 10-, 6-, 14-, 8-point patterns, respectively. If a rotation and a rotoinversion axis generate the same number of points, the rotation axis should be chosen. For example, the combination is equivalent to . Since generates 6 points, and 3 generates only 3, should be written instead of (not , because already contains the mirror plane m). Analogously, in the case when both 3 and axes are present, should be written. However we write , not , because both 4 and generate four points. In the case of the combination, where 2, 3, 6, , and axes are present, axes , , and 6 all generate 6-point patterns, as we can see on the figure in the right, but the latter should be used because it is a rotation axis – the symbol will be
Finally, the Hermann–Mauguin symbol depends on the type of the group. | 1 | Crystallography |
Light detectors, such as photographic plates or CCDs, measure only the intensity of the light that hits them. This measurement is incomplete (even when neglecting other degrees of freedom such as polarization and angle of incidence) because a light wave has not only an amplitude (related to the intensity), but also a phase (related to the direction), and polarization which are systematically lost in a measurement. In diffraction or microscopy experiments, the phase part of the wave often contains valuable information on the studied specimen. The phase problem constitutes a fundamental limitation ultimately related to the nature of measurement in quantum mechanics.
In X-ray crystallography, the diffraction data when properly assembled gives the amplitude of the 3D Fourier transform of the molecule's electron density in the unit cell. If the phases are known, the electron density can be simply obtained by Fourier synthesis. This Fourier transform relation also holds for two-dimensional far-field diffraction patterns (also called Fraunhofer diffraction) giving rise to a similar type of phase problem. | 1 | Crystallography |
In terms of complex numbers, the isometries of the plane are either of the form
or of the form
for some complex numbers and with |ω| = 1. This is easy to prove: if and and if one defines
then is an isometry, , and . It is then easy to see that g is either the identity or the conjugation, and the statement being proved follows from this and from the fact that .
This is obviously related to the previous classification of plane isometries, since:
* functions of the type are translations;
* functions of the type are rotations (when |ω| = 1);
* the conjugation is a reflection.
Note that a rotation about complex point p is obtained by complex arithmetic with
where the last expression shows the mapping equivalent to rotation at 0 and a translation.
Therefore, given direct isometry one can solve to obtain as the center for an equivalent rotation, provided that , that is, provided the direct isometry is not a pure translation. As stated by Cederberg, "A direct isometry is either a rotation or a translation." | 1 | Crystallography |
Enterics that subsequently metabolize pyruvic acid to other acids lower the pH of the medium to 4.2. At this pH, methyl red turns red, a positive test. Enterics that subsequently metabolize pyruvic acid to neutral end products lower the pH of the medium to only 6.0. At this pH, methyl red is yellow, a negative test. | 0 | Chromatography + Titration + pH indicators |
A crystal net is an infinite molecular model of a crystal. Similar models existed in Antiquity, notably the atomic theory associated with Democritus, which was criticized by Aristotle because such a theory entails a vacuum, which Aristotle believed nature abhors. Modern atomic theory traces back to Johannes Kepler and his work on geometric packing problems. Until the twentieth century, graph-like models of crystals focused on the positions of the (atomic) components, and these pre-20th century models were the focus of two controversies in chemistry and materials science.
The two controversies were (1) the controversy over Robert Boyle’s corpuscular theory of matter, which held that all material substances were composed of particles, and (2) the controversy over whether crystals were minerals or some kind of vegetative phenomenon. During the eighteenth century, Kepler, Nicolas Steno, René Just Haüy, and others gradually associated the packing of Boyle-type corpuscular units into arrays with the apparent emergence of polyhedral structures resembling crystals as a result. During the nineteenth century, there was considerably more work done on polyhedra and also of crystal structure, notably in the derivation of the Crystallographic groups based on the assumption that a crystal could be regarded as a regular array of unit cells. During the early twentieth century, the physics and chemistry community largely accepted Boyle's corpuscular theory of matter—by now called the atomic theory—and X-ray crystallography was used to determine the position of the atomic or molecular components within the unit cells (by the early twentieth century, unit cells were regarded as physically meaningful).
However, despite the growing use of stick-and-ball molecular models, the use of graphical edges or line segments to represent chemical bonds in specific crystals have become popular more recently, and the publication of encouraged efforts to determine graphical structures of known crystals, to generate crystal nets of as yet unknown crystals, and to synthesize crystals of these novel crystal nets. The coincident expansion of interest in tilings and tessellations, especially those modeling quasicrystals, and the development of modern Nanotechnology, all facilitated by the dramatic increase in computational power, enabled the development of algorithms from computational geometry for the construction and analysis of crystal nets. Meanwhile, the ancient association between models of crystals and tessellations has expanded with Algebraic topology. There is also a thread of interest in the very-large-scale integration (VLSI) community for using these crystal nets as circuit designs. | 1 | Crystallography |
A: α-naphthol – 5 g
*Absolute ethyl alcohol – 100 mL – 0.6 mL – 3 parts
*B: KOH – 40 g
*Distilled water – 100 mL – 0.2 mL – 1 part | 0 | Chromatography + Titration + pH indicators |
An abbreviated form of the Hermann–Mauguin notation commonly used for space groups also serves to describe crystallographic point groups. Group names are | 1 | Crystallography |
To work out which wallpaper group corresponds to a given design, one may use the following table.
See also this overview with diagrams. | 1 | Crystallography |
Mikhail Tsvet was born on 14 May 1872 in Asti, Italy. His mother was Italian, and his father was a Russian official. His mother died soon after his birth, and he was raised in Geneva, Switzerland. He received his BS degree from the Department of Physics and Mathematics at the University of Geneva in 1893. However, he decided to dedicate himself to botany and received his PhD degree in 1896 for his work on cell physiology. He moved to Saint Petersburg, Russia, in 1896 because his father was recalled from the foreign service. There he started to work at the Biological Laboratory of the Russian Academy of Sciences. His Geneva degrees were not recognized in Russia, and he had to earn Russian degrees. In 1897 he became a teacher of botany courses for women. In 1902 he became a laboratory assistant at the Institute of Plant Physiology of the Warsaw University (now in Poland). In 1903 he became an assistant professor and taught also at other Warsaw universities. After the beginning of World War I, the Warsaw University of Technology was evacuated to Moscow, Russia, and in 1916 again to Gorki near Moscow. In 1917 he became a Professor of Botany and the director of the botanical gardens at the University of Tartu (Yuryev) (now in Estonia). In 1918 when German troops occupied the city, the university was evacuated to Voronezh, a large city in the south of Central Russia. Tsvet died of a chronic inflammation of the throat on 26 June 1919 at the age of 47. | 0 | Chromatography + Titration + pH indicators |
Questions about certain areas of forensic science, such as fingerprint evidence and the assumptions behind these disciplines have been brought to light in some publications including the New York Post. The article stated that "No one has proved even the basic assumption: That everyone's fingerprint is unique." The article also stated that "Now such assumptions are being questioned—and with it may come a radical change in how forensic science is used by police departments and prosecutors." Law professor Jessica Gabel said on NOVA that forensic science "lacks the rigors, the standards, the quality controls and procedures that we find, usually, in science".
The National Institute of Standards and Technology has reviewed the scientific foundations of bite-mark analysis used in forensic science. Bite mark analysis is a forensic science technique that analyzes the marks on the victim's skin compared to the suspects teeth. NIST reviewed the findings of the National Academies of Sciences, Engineering, and Medicine 2009 study. The National Academics of Sciences, Engineering, and Medicine conducted research to address the issues of reliability, accuracy, and reliability of bitemark analysis, where they concluded that there is a lack of sufficient scientific foundation to support the data. Yet the technique is still legal to use in court as evidence. NIST funded a 2019 meeting that consisted of dentists, lawyers, researchers and others to address the gaps in this field.
In the US, on 25 June 2009, the Supreme Court issued a 5-to-4 decision in Melendez-Diaz v. Massachusetts stating that crime laboratory reports may not be used against criminal defendants at trial unless the analysts responsible for creating them give testimony and subject themselves to cross-examination. The Supreme Court cited the National Academies of Sciences report Strengthening Forensic Science in the United States in their decision. Writing for the majority, Justice Antonin Scalia referred to the National Research Council report in his assertion that "Forensic evidence is not uniquely immune from the risk of manipulation."
In the US, another area of forensic science that has come under question in recent years is the lack of laws requiring the accreditation of forensic labs. Some states require accreditation, but some states do not. Because of this, many labs have been caught performing very poor work resulting in false convictions or acquittals. For example, it was discovered after an audit of the Houston Police Department in 2002 that the lab had fabricated evidence which led George Rodriguez being convicted of raping a fourteen-year-old girl. The former director of the lab, when asked, said that the total number of cases that could have been contaminated by improper work could be in the range of 5,000 to 10,000.
The Innocence Project database of DNA exonerations shows that many wrongful convictions contained forensic science errors. According to the Innocence project and the US Department of Justice, forensic science has contributed to about 39 percent to 46 percent of wrongful convictions. As indicated by the National Academy of Sciences report Strengthening Forensic Sciences in the United States, part of the problem is that many traditional forensic sciences have never been empirically validated; and part of the problem is that all examiners are subject to forensic confirmation biases and should be shielded from contextual information not relevant to the judgment they make.
Many studies have discovered a difference in rape-related injuries reporting based on race, with white victims reporting a higher frequency of injuries than black victims. However, since current forensic examination techniques may not be sensitive to all injuries across a range of skin colors, more research needs to be conducted to understand if this trend is due to skin confounding healthcare providers when examining injuries or if darker skin extends a protective element. In clinical practice, for patients with darker skin, one study recommends that attention must be paid to the thighs, labia majora, posterior fourchette and fossa navicularis, so that no rape-related injuries are missed upon close examination. | 0 | Chromatography + Titration + pH indicators |
The known cases up to 2015 are discussed in a review article by Bučar, Lancaster, and Bernstein.
Dibenzoxazepines
Multidisciplinary studies involving experimental and computational approaches were applied to pharmaceutical molecules to facilitate the comparison of their solid-state structures. Specifically, this study has focused on exploring how changes in molecular structure affect the molecular conformation, packing motifs, interactions in the resultant crystal lattices and the extent of solid-state diversity of these compounds. The results highlight the value of crystal structure prediction studies and PIXEL calculations in the interpretation of the observed solid-state behaviour and quantifying the intermolecular interactions in the packed structures and identifying the key stabilising interactions. An experimental screen yielded 4 physical forms for clozapine as compared to 60 distinct physical forms for olanzapine. The experimental screening results of clozapine are consistent with its crystal energy landscape which confirms that no alternate packing arrangement is thermodynamically competitive to the experimentally obtained structure. Whilst in case of olanzapine, crystal energy landscape highlights that the extensive experimental screening has probably not found all possible polymorphs of olanzapine, and further solid form diversity could be targeted with a better understanding of the role of kinetics in its crystallisation. CSP studies were able to offer an explanation for the absence of the centrosymmetric dimer in anhydrous clozapine. PIXEL calculations on all the crystal structures of clozapine revealed that similar to olanzapine, the intermolecular interaction energy in each structure is also dominated by the Ed. Despite the molecular structure similarity between amoxapine and loxapine (molecules in group 2), the crystal packing observed in polymorphs of loxa differs significantly from the amoxapine. A combined experimental and computational study demonstrated that the methyl group in loxapine has a significant influence in increasing the range of accessible solid forms and favouring various alternate packing arrangements. CSP studies have again helped in explaining the observed solid-state diversity of loxapine and amoxapine. PIXEL calculations showed that in absence of strong H-bonds, weak H-bonds such as C–H...O, C–H...N and dispersion interactions play a key role in stabilising the crystal lattice of both the molecules. Efficient crystal packing of amoxapine seems to be contributing towards its monomorphic behaviour as compared to the comparatively less efficient packing of loxapine molecules in both polymorphs. The combination of experimental and computational approaches has provided a deeper understanding of the factors influencing the solid-state structure and diversity in these compounds. Hirshfeld surfaces using Crystal Explorer represent another way of exploring packing modes and intermolecular interactions in molecular crystals. The influence of changes in the small substituents on shape and electron distribution can also be investigated by mapping the total electron density on the electrostatic potential for molecules in the gas phase. This allows straightforward visualisation and comparison of overall shape, electron-rich and electron-deficient regions within molecules. The shape of these molecules can be further investigated to study its influence on diverse solid-state diversity.
Posaconazole
The original formulations of posaconazole on the market licensed as Noxafil were formulated utilising form I of posaconazole. The discovery of polymorphs of posaconazole increased rapidly and resulted in much research in crystallography of posaconazole. A methanol solvate and a 1,4-dioxane co-crystal were added to the Cambridge Structural Database (CSD). | 1 | Crystallography |
In the pump-probe method the reaction is first triggered (pump) by photolysis (most often laser light) and then a diffraction pattern is collected by an X-ray pulse (probe) at a specific time delay. This makes it possible to obtain many images at different time delays after reaction triggering, and thereby building up a chronological series of images describing the events during reaction.
To obtain a reasonable signal to noise ratio this pump-probe cycle has to be performed many times for each spatial rotation of the crystal, and many times for the same time delay. Therefore, the reaction that one wishes to study with pump-probe must be able to relax back to its original conformation after triggering, enabling many measurements on the same sample.
The time resolution of the observed phenomena is dictated by the time width of the probing pulse (full width at half maximum). All processes that happen on a faster time scale than that are going to be averaged out by the convolution of the probe pulse intensity in time with the intensity of the actual x-ray reflectivity of the sample. | 1 | Crystallography |
A colloidal crystal is a highly ordered array of particles that forms over a long range (from a few millimeters to one centimeter in length); colloidal crystals have appearance and properties roughly analogous to their atomic or molecular counterparts. It has been known for many years that, due to repulsive Coulombic interactions, electrically charged macromolecules in an aqueous environment can exhibit long-range crystal-like correlations, with interparticle separation distances often being considerably greater than the individual particle diameter. Periodic arrays of spherical particles give rise to interstitial voids (the spaces between the particles), which act as a natural diffraction grating for visible light waves, when the interstitial spacing is of the same order of magnitude as the incident lightwave. In these cases brilliant iridescence (or play of colours) is attributed to the diffraction and constructive interference of visible lightwaves according to Bragg's law, in a matter analogous to the scattering of X-rays in crystalline solid. The effects occur at visible wavelengths because the interplanar spacing is much larger than for true crystals. Precious opal is one example of a colloidal crystal with optical effects. | 1 | Crystallography |
In crystallography, a periodic graph or crystal net is a three-dimensional periodic graph, i.e., a three-dimensional Euclidean graph whose vertices or nodes are points in three-dimensional Euclidean space, and whose edges (or bonds or spacers) are line segments connecting pairs of vertices, periodic in three linearly independent axial directions. There is usually an implicit assumption that the set of vertices are uniformly discrete, i.e., that there is a fixed minimum distance between any two vertices. The vertices may represent positions of atoms or complexes or clusters of atoms such as single-metal ions, molecular building blocks, or secondary building units, while each edge represents a chemical bond or a polymeric ligand.
Although the notion of a periodic graph or crystal net is ultimately mathematical (actually a crystal net is nothing but a periodic realization of an abelian covering graph over a finite graph
), and is closely related to that of a Tessellation of space (or honeycomb) in the theory of polytopes and similar areas, much of the contemporary effort in the area is motivated by crystal engineering and prediction (design), including metal-organic frameworks (MOFs) and zeolites. | 1 | Crystallography |
Ella Jones (born 1955) is an American chromatographer, pastor, and politician who serves as the 12th mayor of Ferguson, Missouri. A former member of the Ferguson City Council, Jones is the first African-American and woman elected mayor of the city. | 0 | Chromatography + Titration + pH indicators |
Transitions between scales are always fluent. There is no sharp cut that defines the end of small- and the beginning of medium/pilot scale. However, chromatography columns with an inner diameter (ID) of up to 5 cm are generally considered small scale or laboratory scale columns.
Small scale chromatography columns are mostly intended for design of experiments (DoE); proof of concept; validation (drug manufacture) or research and development experiments. Columns of this scale category are distinguished by their small dimensions in comparison to chromatography columns intended for larger scales as well as relatively high pressure tolerance and selection of materials in contact with the liquid phase. This is especially important for applications in the biopharmaceutical industry which underlie close scrutiny by regulatory agencies (U.S. Food and Drug Administration; European Medicines Agency). | 0 | Chromatography + Titration + pH indicators |
The first precession electron diffraction system was developed by Vincent and Midgley in Bristol, UK and published in 1994. Preliminary investigation into the ErGeO crystal structure demonstrated the feasibility of the technique at reducing dynamical effects and providing quasi-kinematical patterns that could be solved through direct methods to determine crystal structure. Over the next ten years, a number of university groups developed their own precession systems and verified the technique by solving complex crystal structures, including the groups of J. Gjønnes (Oslo), Migliori (Bologna), and L. Marks (Northwestern).
In 2004, [http://nanomegas.com/ NanoMEGAS] developed the first commercial precession system capable of being retrofit to any modern TEM. This hardware solution enabled more widespread implementation of the technique and spurred its more mainstream adoption into the crystallography community. Software methods have also been developed to achieve the necessary scanning and descanning using the built-in electronics of the TEM. HREM Research Inc has developed the [http://www.hremresearch.com/index.html QED plug-in] for the DigitalMicrograph software. This plug-in enables the widely used software package to collect precession electron diffraction patterns without additional modifications to the microscope.
According to NanoMEGAS, as of June, 2015, more than 200 publications have relied on the technique to solve or corroborate crystal structures; many on materials that could not be solved by other conventional crystallography techniques like x-ray diffraction. Their retrofit hardware system is used in more than 75 laboratories across the world. | 1 | Crystallography |
* [http://www.anilaggrawal.com/ij/indexpapers.html Anil Aggrawal's Internet Journal of Forensic Medicine and Toxicology] .
* Forensic Magazine – [http://www.forensicmag.com Forensicmag.com].
* [https://web.archive.org/web/20110222013558/http://www2.fbi.gov/hq/lab/fsc/current/index.htm Forensic Science Communications], an open access journal of the FBI.
* [http://www.elsevier.com/wps/find/journaldescription.cws_home/505512/description#description Forensic sciences international] – An international journal dedicated to the applications of medicine and science in the administration of justice – – Elsevier
* [https://www.pbs.org/wgbh/pages/frontline/real-csi/ "The Real CSI"], PBS Frontline documentary, 17 April 2012.
* Baden, Michael; Roach, Marion. Dead Reckoning: The New Science of Catching Killers, Simon & Schuster, 2001. .
* Bartos, Leah, [https://www.propublica.org/article/no-forensic-background-no-problem "No Forensic Background? No Problem"], ProPublica, 17 April 2012.
* Guatelli-Steinberg, Debbie; Mitchell, John C. [http://www.struers.com/default.asp?doc_id=404 Structure Magazine no. 40, "RepliSet: High Resolution Impressions of the Teeth of Human Ancestors"].
* Holt, Cynthia. [https://web.archive.org/web/20061031175558/https://lu.com/showbook.cfm?isbn=9781591582212 Guide to Information Sources in the Forensic Sciences] Libraries Unlimited, 2006. .
* Jamieson, Allan; Moenssens, Andre (eds). [http://ca.wiley.com/WileyCDA/WileyTitle/productCd-0470018267,descCd-description.html Wiley Encyclopedia of Forensic Science] John Wiley & Sons Ltd, 2009. . [https://archive.today/20121211065812/http://mrw.interscience.wiley.com/emrw/9780470061589/home/ Online version].
* Kind, Stuart; Overman, Michael. Science Against Crime Doubleday, 1972. .
* Lewis, Peter Rhys; Gagg Colin; Reynolds, Ken. Forensic Materials Engineering: Case Studies CRC Press, 2004.
* Nickell, Joe; Fischer, John F. Crime Science: Methods of Forensic Detection, University Press of Kentucky, 1999. .
* Owen, D. (2000). Hidden Evidence: The Story of Forensic Science and how it Helped to Solve 40 of the Worlds Toughest Crimes' Quintet Publishing, London. .
* Quinche, Nicolas, and Margot, Pierre, "Coulier, Paul-Jean (1824–1890): A precursor in the history of fingermark detection and their potential use for identifying their source (1863)", Journal of forensic identification (Californie), 60 (2), March–April 2010, pp. 129–134.
* Silverman, Mike; Thompson, Tony. Written in Blood: A History of Forensic Science. 2014. | 0 | Chromatography + Titration + pH indicators |
Minerals that have the same composition but different structures (polymorphic minerals) may also have epitaxic relations. Examples are pyrite and marcasite, both FeS, and sphalerite and wurtzite, both ZnS. | 1 | Crystallography |
The principal steps for solving a structure of an inorganic crystal from HREM images by CIP are as follows (for a detailed discussion see ).
# Selecting the area of interest and calculation of the Fourier transform (= power spectrum consisting of a 2D periodic array of complex numbers)
# Determining the defocus value and compensating for the contrast changes imposed by the objective lens (done in Fourier space)
# Indexing and refining the lattice (done in Fourier space)
# Extracting amplitudes and phase values at the refined lattice positions (done in Fourier space)
# Determining the origin of the projected unit cell and determining the projected (plane group) symmetry
# Imposing constrains of the most likely plane group symmetry on the amplitudes an phases. At this step the image phases are converted into the phases of the structure factors.
# Calculating the pseudo-potential map by Fourier synthesis with corrected (structure factor) amplitudes and phases (done in real space)
# Determining 2D (projected) atomic co-ordinates (done in real space)
A few computer programs are available which assist to perform the necessary steps of processing. The most popular programs used by materials scientists (electron crystallographers) are CRISP, VEC, and the EDM package. There is also the recently developed crystallographic image processing program EMIA, but so far there do not seem to be reports by users of this program.
Structural biologists achieve resolutions of a few ångströms (up from a to few nanometers in the past when samples used to be negatively stained) for membrane forming proteins in regular two-dimensional arrays, but prefer the usage of the programs 2dx, EMAN2, and IPLT. These programs are based on the Medical Research Council (MRC) image processing programs and possess additional functionality such as the "unbending" of the image. As the name suggests, unbending of the image is conceptually equivalent to "flattening out and relaxing to equilibrium positions" one building block thick samples so that all 2D periodic motifs are as similar as possible and all building blocks of the array possess the same crystallographic orientation with respect to a cartesian coordinate system that is fixed to the microscope. (The microscope's optical axis typically serves as the z-axis.) Unbending is often necessary when the 2D array of membrane proteins is paracrystalline rather than genuinely crystalline. It was estimated that unbending approximately doubles the spatial resolution with which the shape of molecules can be determined
Inorganic crystals are much stiffer than 2D periodic protein membrane arrays so that there is no need for the unbending of images that were taken from suitably thinned parts of these crystals. Consequently, the CRISP program does not possess the unbending image processing feature but offers superior performance in the so-called phase origin refinement.
The latter feature is particularly important for electron crystallographers as their samples may possess any space group out of the 230 possible groups types that exist in three dimensions. The regular arrays of membrane forming proteins that structural biologists deal with are, on the other hand, restricted to possess one out of only 17 (two-sided/black-white) layer group types (of which there are 46 in total and which are periodic only in 2D) due to the chiral nature of all (naturally occurring) proteins. Different crystallographic settings of four of these layer group types increase the number of possible layer group symmetries of regular arrays of membrane forming proteins to just 21.
All 3D space groups and their subperiodic 2D periodic layer groups (including the above-mentioned 46 two-sided groups) project to just 17 plane space group types, which are genuinely 2D periodic and are sometimes referred to as the wallpaper groups. (Although quite popular, this is a misnomer because wallpapers are not restricted to possess these symmetries by nature.)
All individual transmission electron microscopy images are projections from the three-dimensional space of the samples into two dimensions (so that spatial distribution information along the projection direction is unavoidably lost). Projections along prominent (i.e. certain low-index) zone axes of 3D crystals or along the layer normal of a membrane forming protein sample ensure the projection of 3D symmetry into 2D. (Along arbitrary high-index zone axes and inclined to the layer normal of membrane forming proteins, there will be no useful projected symmetry in transmission images.) The recovery of 3D structures and their symmetries relies on electron tomography techniques, which use sets of transmission electron microscopy images.
The origin refinement part of CIP relies on the definition of the plane symmetry group types as provided by the International Tables of Crystallography, where all symmetry equivalent positions in the unit cell and their respective site symmetries are listed along with systematic absences in reciprocal space. Besides plane symmetry groups p1, p3, p3m1 and p31m, all other plane group symmetries are centrosymmetric so that the origin refinement simplifies to the determination of the correct signs of the amplitudes of the Fourier coefficients.
When crystallographic image processing is utilized in scanning probe microscopy, the symmetry groups to be considered are just the 17 plane space group types in their possible 21 settings. | 1 | Crystallography |
*For biodiesel fuel: waste vegetable oil (WVO) must be neutralized before a batch may be processed. A portion of WVO is titrated with a base to determine acidity, so the rest of the batch may be neutralized properly. This removes free fatty acids from the WVO that would normally react to make soap instead of biodiesel fuel.
*Kjeldahl method: a measure of nitrogen content in a sample. Organic nitrogen is digested into ammonia with sulfuric acid and potassium sulfate. Finally, ammonia is back titrated with boric acid and then sodium carbonate.
*Acid value: the mass in milligrams of potassium hydroxide (KOH) required to titrate fully an acid in one gram of sample. An example is the determination of free fatty acid content.
*Saponification value: the mass in milligrams of KOH required to saponify a fatty acid in one gram of sample. Saponification is used to determine average chain length of fatty acids in fat.
*Ester value (or ester index): a calculated index. Ester value = Saponification value – Acid value.
*Amine value: the mass in milligrams of KOH equal to the amine content in one gram of sample.
*Hydroxyl value: the mass in milligrams of KOH corresponding to hydroxyl groups in one gram of sample. The analyte is acetylated using acetic anhydride then titrated with KOH. | 0 | Chromatography + Titration + pH indicators |
In mathematics, a stereographic projection is a perspective projection of the sphere, through a specific point on the sphere (the pole or center of projection), onto a plane (the projection plane) perpendicular to the diameter through the point. It is a smooth, bijective function from the entire sphere except the center of projection to the entire plane. It maps circles on the sphere to circles or lines on the plane, and is conformal, meaning that it preserves angles at which curves meet and thus locally approximately preserves shapes. It is neither isometric (distance preserving) nor equiareal (area preserving).
The stereographic projection gives a way to represent a sphere by a plane. The metric induced by the inverse stereographic projection from the plane to the sphere defines a geodesic distance between points in the plane equal to the spherical distance between the spherical points they represent. A two-dimensional coordinate system on the stereographic plane is an alternative setting for spherical analytic geometry instead of spherical polar coordinates or three-dimensional cartesian coordinates. This is the spherical analog of the Poincaré disk model of the hyperbolic plane.
Intuitively, the stereographic projection is a way of picturing the sphere as the plane, with some inevitable compromises. Because the sphere and the plane appear in many areas of mathematics and its applications, so does the stereographic projection; it finds use in diverse fields including complex analysis, cartography (see stereographic map projection), geology, and photography. Sometimes stereographic computations are done graphically using a special kind of graph paper called a stereographic net, shortened to stereonet, or Wulff net. | 1 | Crystallography |