text
stringlengths 107
11k
| label
int64 0
1
| label_text
stringclasses 2
values |
|---|---|---|
Almost two decades later, René Just Haüy introduced wooden crystal models to illustrate the two-dimensional drawings in the atlas volume of his "Traité de Minéralogie" (1801). For the production of crystal models, wood appeared to be much more convenient than clay. Especially pear wood permitted getting smooth faces, sharp edges and accurate dihedral angles required for the production of these three-dimensional objects. In general, the angular accuracy was very high and some models, especially those illustrating crystal twins and Haüy's figures of decrement, still appear as masterpieces of fine woodwork and carving. Skilful craftsmen such as Pleuvin, Beloeuf and Lambotin (to name only a few) became specialists in this field and the models they offered were highly esteemed.
Between 1802 and 1804, Martin van Marum bought 597 of these pear wood models, 550 of these are still present in the collection of Teylers Museum. Each model is labeled, mentioning a number and the name of the crystal form. This set is the most complete collection of Haüy crystal models that still survives. That Van Marum was able to acquire such a unique collection was due to his networking. Van Marum allowed Haüy as a member of the Hollandsche Maatschappij, a nomination to which Haüy attached great value. Haüy mentioned this membership in all of his publications.
After their introduction by Romé de l'Isle and Haüy, crystal models were increasingly demanded both by scholars for teaching purposes as well as by mineral collectors. The quality of the models improved due to the technical progress in their production. Several mineralogists and crystallographers started designing their own series of models. Although pear wood kept a prominent place, models were also manufactured using materials like plaster, cast iron, lead, brass, glass, porcelain, cardboard, etc. | 1 | Crystallography |
Facets () are flat faces on geometric shapes. The organization of naturally occurring facets was key to early developments in crystallography, since they reflect the underlying symmetry of the crystal structure. Gemstones commonly have facets cut into them in order to improve their appearance by allowing them to reflect light. | 1 | Crystallography |
In statistical physics, a system is said to present quenched disorder when some parameters defining its behavior are random variables which do not evolve with time. These parameters are said to be quenched or frozen. Spin glasses are a typical example. Quenched disorder is contrasted with annealed disorder in which the parameters are allowed to evolve themselves.
Mathematically, quenched disorder is more difficult to analyze than its annealed counterpart as averages over thermal noise and quenched disorder play distinct roles. Few techniques to approach each are known, most of which rely on approximations. Common techniques used to analyzed systems with quenched disorder include the replica trick, based on analytic continuation, and the cavity method, where a system's response to the perturbation due to an added constituent is analyzed. While these methods yield results agreeing with experiments in many systems, the procedures have not been formally mathematically justified. Recently, rigorous methods have shown that in the Sherrington-Kirkpatrick model, an archetypal spin glass model, the replica-based solution is exact. The generating functional formalism, which relies on the computation of path integrals, is a fully exact method but is more difficult to apply than the replica or cavity procedures in practice. | 1 | Crystallography |
The phenomenon was discovered in 1832 by Friedrich Wöhler and Justus von Liebig. They observed that the silky needles of freshly crystallized benzamide slowly converted to rhombic crystals. Present-day analysis identifies three polymorphs for benzamide: the least stable one, formed by flash cooling is the orthorhombic form II. This type is followed by the monoclinic form III (observed by Wöhler/Liebig). The most stable form is monoclinic form I. The hydrogen bonding mechanisms are the same for all three phases; however, they differ strongly in their pi-pi interactions. | 1 | Crystallography |
Droplet countercurrent chromatography (DCCC) was introduced in 1970 by Tanimura, Pisano, Ito, and Bowman. DCCC uses only gravity to move the mobile phase through the stationary phase which is held in long vertical tubes connected in series. In the descending mode, droplets of the denser mobile phase and sample are allowed to fall through the columns of the lighter stationary phase using only gravity. If a less-dense mobile phase is used it will rise through the stationary phase; this is called ascending mode. The eluent from one column is transferred to another; the more columns that are used, the more theoretical plates can be achieved. DCCC enjoyed some success with natural product separations but was largely eclipsed by the rapid development of high-speed countercurrent chromatography. The main limitation of DCCC is that flow rates are low, and poor mixing is achieved for most binary solvent systems. | 0 | Chromatography + Titration + pH indicators |
Inoculate a tube of glucose phosphate broth with a pure inoculum of test organism and incubate at 35 °C for 24 hours.
To 1 mL of this broth add 0.6 mL of 5% α-Naphthol followed by 0.2 mL of 40% KOH. Shake the tube gently to expose the medium to atmospheric oxygen and allow the tube to remain undisturbed for 10–15 minutes. | 0 | Chromatography + Titration + pH indicators |
* Orbifold signature:
* Coxeter notation: [(∞,2),∞] or [∞,(2,∞)]
* Lattice: rectangular
* Point group: D
* The group pg contains glide reflections only, and their axes are all parallel. There are no rotations or reflections.
;Examples of group pg
Without the details inside the zigzag bands the mat is pmg; with the details but without the distinction between brown and black it is pgg.
Ignoring the wavy borders of the tiles, the pavement is pgg. | 1 | Crystallography |
GC–MS is becoming the tool of choice for tracking organic pollutants in the environment. The cost of GC–MS equipment has decreased significantly, and the reliability has increased at the same time, which has contributed to its increased adoption in environmental studies. | 0 | Chromatography + Titration + pH indicators |
For a simple cubic packing, the number of atoms per unit cell is one. The side of the unit cell is of length 2r, where r is the radius of the atom. | 1 | Crystallography |
Back titration is a titration done in reverse; instead of titrating the original sample, a known excess of standard reagent is added to the solution, and the excess is titrated. A back titration is useful if the endpoint of the reverse titration is easier to identify than the endpoint of the normal titration, as with precipitation reactions. Back titrations are also useful if the reaction between the analyte and the titrant is very slow, or when the analyte is in a non-soluble solid. | 0 | Chromatography + Titration + pH indicators |
Phenol red is a weak estrogen mimic, and in cell cultures can enhance the growth of cells that express the estrogen receptor. It has been used to induce ovarian epithelial cells from post-menopausal women to differentiate into cells with properties of oocytes (eggs), with potential implications for both fertility treatment and stem cell research. | 0 | Chromatography + Titration + pH indicators |
In dual-mode, the mobile and stationary phases are reversed part way through the separation experiment. This requires changing the phase being pumped through the column as well as the direction of flow. Dual-mode operation is likely to elute the entire sample from the column but the order of elution is disrupted by switching the phase and direction of flow. | 0 | Chromatography + Titration + pH indicators |
Desalting and buffer exchange are methods to separate soluble macromolecules from smaller molecules (desalting) or replace the buffer system used for another one suitable for a downstream application (buffer exchange). These methods are based on gel filtration chromatography, also called molecular sieve chromatography, which is a form of size-exclusion chromatography. Desalting and buffer exchange are two of the most common gel filtration chromatography applications, and they can be performed using the same resin.
Desalting and buffer exchange both entail recovering the components of a sample in whatever buffer is used to pre-equilibrate the small, porous polymer beads (resin). Desalting occurs when buffer salts and other small molecules are removed from a sample in exchange for water (with the resin being pre-equilibrated in water). Buffer exchange occurs when the buffer salts in a sample are exchanged for those in another buffer. | 0 | Chromatography + Titration + pH indicators |
The tool called gpaGUI provides an interactive interface for geometric phase analysis. It allows to generate 2D maps of various crystallographic quantities using high-resolution images.
Since the geometric phase analysis is performed in frequency domain, the high-resolution image needs to be transformed into frequential representation using Fourier transform. Mathematically, the frequential image is a complex matrix with the size equal to the original image. Crystallographically, it can be seen as an artificial diffraction pattern of the original image depicting intensity peaks corresponding to the crystallographic planes present in the original image. After performing desired calculations, the frequential representation can be transformed back to the original spatial domain using inverse Fourier transform.
Various crystallographic analyses can be performed using the frequential image. If it is filtered so that only the information from a region close to a particular diffraction spot is used (the rest is set to zero), a filtered direct image obtained by inverse Fourier transform then depicts only the planes corresponding to the selected diffraction spot. Moreover, due to its complex nature, the frequential image can be used to calculate amplitude and phase. Together with a vector of one crystallographic plane depicted in the image, they can be used to generate a 2D map interplanar distance of given plane. If two vectors of non-parallel planes are known, the method can be used to generate maps of strain and displacement.
Graphical user interface of gpaGUI is vertically divided into two halves, each of which contains:
* Diffractogram preview allowing to select one diffraction spot corresponding to a crystallographic plane.
* Visualization of a selected quantity (input image, filtered image or one of the maps mentioned above) allowing to select point of interest or region of interest for further analysis.
* Results of detailed analysis of point or region of interest. The point analysis allows the user to select any pixel of the visualized map to see exact values of the particular pixel and its closest neighbourhood. If analysis of broader area is needed, a polygonal region can be outlined in the map allowing to enumerate its statistical details: mean, standard deviation, median, minimum, maximum and total area of the polygon.
Since each half of the interface allows to specify one crystallographic plane, gpaGUI allows to calculate all the aforementioned crystallographic quantities including those which require two vectors. Precision and repeatability of the whole analysis relies on accuracy of the diffraction peak localization. To overcome inaccuracy of manual peak localization (with a mouse click), gpaGUI provides a possibility to process the input image with in order to accurately localize and index the peaks. | 1 | Crystallography |
Thermometric titrations employing sodium salts of ethylenediaminetetra-acetic acid (EDTA) have been demonstrated for the determination of a range of metal ions. Reaction enthalpies are modest, so titrations are normally carried out with titrant concentrations of 1 mol/L. This necessitates the use of the tetra-sodium salt of EDTA rather than the more common di-sodium salt which is saturated at a concentration of only approximately 0.25 mol/L.
An excellent application is the sequential determination of calcium and magnesium. Although calcium reacts exothermically with EDTA (heat of chelation ~-23.4 kJ/mol), magnesium reacts endothermically with a heat of chelation of ~+20.1 kJ/mol. This is illustrated in the titration plot of EDTA with calcium and magnesium in sea water (Figure 14). Following the solution temperature curve, the breakpoint for the calcium content (red-tagged endpoint) is followed by a region of modest temperature rise due to competition between the heats of dilution of the titrant with the solution, and the endothermic reaction of Mg and EDTA. The breakpoint for the consumption of Mg (blue-tagged endpoint) by EDTA is revealed by upswing in temperature caused purely by the heat of dilution.
Direct EDTA titrations with metal ions are possible when reaction kinetics are fast, for example zinc, copper, calcium and magnesium. However, with slower reaction kinetics such as those exhibited by cobalt and nickel, back-titrations are used. Titrations for cobalt and nickel are carried out in an ammoniacal environment; buffered with ammonia:ammonium chloride solution. An excess of EDTA is added, and is back-titrated with Cu(II) solution. It is postulated that the breakpoint is revealed by the difference in reaction enthalpies between the formation of the Cu-EDTA complex, and that for the formation of the Cu-amine complex.
A catalyzed endpoint procedure to determine trace amounts of metal ions in solution (down to approximately 10 mg/L) employs 0.01 mol/L EDTA. This has been applied to the determination of low level Cu(II) in specialized plating baths, and to the determination of total hardness in water. The reaction enthalpies of EDTA with most metal ions are often quite low, and typically titrant concentrations around 1 mol/L are employed with commensurately high amounts of titrand in order to obtain sharp, reproducible endpoints. Using a catalytically indicated endpoint, very low EDTA titrant concentrations can be used. A back-titration is used. An excess of EDTA solution is added. The excess of EDTA is back-titrated with a suitable metal ion such as Mn or Cu. At the endpoint, the first excess of metal ion catalyzes a strongly exothermic reaction between a polyhydric phenol (such as resorcinol) and hydrogen peroxide. | 0 | Chromatography + Titration + pH indicators |
The separation of compounds by capillary electrophoresis is dependent on the differential migration of analytes in an applied electric field. The electrophoretic migration velocity () of an analyte toward the electrode of opposite charge is:
The electrophoretic mobility can be determined experimentally from the migration time and the field strength:
where is the distance from the inlet to the detection point, is the time required for the analyte to reach the detection point (migration time), is the applied voltage (field strength), and is the total length of the capillary. Since only charged ions are affected by the electric field, neutral analytes are poorly separated by capillary electrophoresis.
The velocity of migration of an analyte in capillary electrophoresis will also depend upon the rate of electroosmotic flow (EOF) of the buffer solution. In a typical system, the electroosmotic flow is directed toward the negatively charged cathode so that the buffer flows through the capillary from the source vial to the destination vial. Separated by differing electrophoretic mobilities, analytes migrate toward the electrode of opposite charge. As a result, negatively charged analytes are attracted to the positively charged anode, counter to the EOF, while positively charged analytes are attracted to the cathode, in agreement with the EOF as depicted in figure 3.
The velocity of the electroosmotic flow, can be written as:
where is the electroosmotic mobility, which is defined as:
where is the zeta potential of the capillary wall, and is the relative permittivity of the buffer solution. Experimentally, the electroosmotic mobility can be determined by measuring the retention time of a neutral analyte. The velocity () of an analyte in an electric field can then be defined as:
Since the electroosmotic flow of the buffer solution is generally greater than that of the electrophoretic mobility of the analytes, all analytes are carried along with the buffer solution toward the cathode. Even small, triply charged anions can be redirected to the cathode by the relatively powerful EOF of the buffer solution. Negatively charged analytes are retained longer in the capillary due to their conflicting electrophoretic mobilities. The order of migration seen by the detector is shown in figure 3: small multiply charged cations migrate quickly and small multiply charged anions are retained strongly.
Electroosmotic flow is observed when an electric field is applied to a solution in a capillary that has fixed charges on its interior wall. Charge is accumulated on the inner surface of a capillary when a buffer solution is placed inside the capillary. In a fused-silica capillary, silanol (Si-OH) groups attached to the interior wall of the capillary are ionized to negatively charged silanoate (Si-O) groups at pH values greater than three. The ionization of the capillary wall can be enhanced by first running a basic solution, such as NaOH or KOH through the capillary prior to introducing the buffer solution. Attracted to the negatively charged silanoate groups, the positively charged cations of the buffer solution will form two inner layers of cations (called the diffuse double layer or the electrical double layer) on the capillary wall as shown in figure 4. The first layer is referred to as the fixed layer because it is held tightly to the silanoate groups. The outer layer, called the mobile layer, is farther from the silanoate groups. The mobile cation layer is pulled in the direction of the negatively charged cathode when an electric field is applied. Since these cations are solvated, the bulk buffer solution migrates with the mobile layer, causing the electroosmotic flow of the buffer solution. Other capillaries including Teflon capillaries also exhibit electroosmotic flow. The EOF of these capillaries is probably the result of adsorption of the electrically charged ions of the buffer onto the capillary walls. The rate of EOF is dependent on the field strength and the charge density of the capillary wall. The wall's charge density is proportional to the pH of the buffer solution. The electroosmotic flow will increase with pH until all of the available silanols lining the wall of the capillary are fully ionized.
In certain situations where strong electroosmotic flow toward the cathode is undesirable, the inner surface of the capillary can be coated with polymers, surfactants, or small molecules to reduce electroosmosis to very low levels, restoring the normal direction of migration (anions toward the anode, cations toward the cathode). CE instrumentation typically includes power supplies with reversible polarity, allowing the same instrument to be used in "normal" mode (with EOF and detection near the cathodic end of the capillary) and "reverse" mode (with EOF suppressed or reversed, and detection near the anodic end of the capillary). One of the most common approaches to suppressing EOF, reported by Stellan Hjertén in 1985, is to create a covalently attached layer of linear polyacrylamide. The silica surface of the capillary is first modified with a silane reagent bearing a polymerizable vinyl group (e.g. 3-methacryloxypropyltrimethoxysilane), followed by introduction of acrylamide monomer and a free radical initiator. The acrylamide is polymerized in situ, forming long linear chains, some of which are covalently attached to the wall-bound silane reagent. Numerous other strategies for covalent modification of capillary surfaces exist. Dynamic or adsorbed coatings (which can include polymers or small molecules) are also common. For example, in capillary sequencing of DNA, the sieving polymer (typically polydimethylacrylamide) suppresses electroosmotic flow to very low levels. Besides modulating electroosmotic flow, capillary wall coatings can also serve the purpose of reducing interactions between "sticky" analytes (such as proteins) and the capillary wall. Such wall-analyte interactions, if severe, manifest as reduced peak efficiency, asymmetric (tailing) peaks, or even complete loss of analyte to the capillary wall. | 0 | Chromatography + Titration + pH indicators |
Pyrazinamide has at least 4 polymorphs. All of them transforms to stable α form at room temperature upon storage or mechanical treatment. Recent studies prove that α form is thermodynamically stable at room temperature. | 1 | Crystallography |
The Kapustinskii equation calculates the lattice energy U for an ionic crystal, which is experimentally difficult to determine. It is named after Anatoli Fedorovich Kapustinskii who published the formula in 1956.
The calculated lattice energy gives a good estimation for the Born–Landé equation; the real value differs in most cases by less than 5%.
Furthermore, one is able to determine the ionic radii (or more properly, the thermochemical radius) using the Kapustinskii equation when the lattice energy is known. This is useful for rather complex ions like sulfate (SO) or phosphate (PO). | 1 | Crystallography |
The serendipity discovery of dye-ligand ability is from a blue dye called blue dextran. The blue dye is used as a void volume (V) marker for a gel filtration column. It has shown that the dye has a property to bind to some certain proteins like pyruvate kinase and elute out with the void volume. Later on, it was found that "cibacron blue FG3-A", reactive dye link to dextran, is responsible for the interaction with the proteins. | 0 | Chromatography + Titration + pH indicators |
The x-ray beam used for topography is generated by an x-ray source, typically either a laboratory x-ray tube (fixed or rotating) or a synchrotron source. The latter offers advantages due to its higher beam intensity, lower divergence, and its continuous wavelength spectrum. X-ray tubes are still useful, however, due to easier access and continuous availability, and are often used for initial screening of samples and/or training of new staff.
For white beam topography, not much more is required: most often, a set of slits to precisely define the beam shape and a (well polished) vacuum exit window will suffice. For those topography techniques requiring a monochromatic x-ray beam, an additional crystal monochromator is mandatory. A typical configuration at synchrotron sources is a combination of two Silicon crystals, both with surfaces oriented parallel to [111]-lattice planes, in geometrically opposite orientation. This guarantees relatively high intensity, good wavelength selectivity (about 1 part in 10000) and the possibility to change the target wavelength without having to change the beam position ("fixed exit"). | 1 | Crystallography |
Friedel's salt discovery is relatively difficult to trace back from the recent literature, simply because it is an ancient finding of a poorly known and non-natural product. It has been synthesised and identified in 1897 by Georges Friedel, mineralogist and crystallographer, son of the famous French chemist Charles Friedel. Georges Friedel also synthesised calcium aluminate (1903) in the framework of his work on the macles theory (twin crystals). This point requires further verification. | 1 | Crystallography |
The reactor operates by converting organic analytes after GC separation into methane before detection by FID. The oxidation and reduction reactions occur sequentially, wherein the organic compound is first combusted into molecules of carbon dioxide, which are subsequently reduced to methane molecules. The following reactions demonstrate the combustion/reduction process for formic acid.
HCOH + 0.5O ↔ CO + HO
CO + 4H ↔ CH + 2HO
The reactions are faster compared to the time scales of typical chromatography, resulting in manageable peak broadening and tailing. Elements other than carbon are not ionized in the hydrogen and oxygen flames of the FID and thus do not contribute to the FID signal. | 0 | Chromatography + Titration + pH indicators |
The manifold topographic techniques can be categorized according to several criteria.
One of them is the distinction between restricted-beam techniques on the one hand (such as section topography or pinhole topography) and extended-beam techniques on the other hand, which use the full width and intensity of the incoming beam. Another, independent distinction is between integrated-wave topography, making use of the full spectrum of incoming X-ray wavelengths and divergences, and plane-wave (monochromatic) topopgraphy, more selective in both wavelengths and divergence. Integrated-wave topography can be realized as either single-crystal or double-crystal topography. Further distinctions include the one between topography in reflection geometry (Bragg-case) and in transmission geometry (Laue case).
For a full discussion and a graphical hierarchy of topographic techniques, see
[https://web.archive.org/web/20041107130433/http://www.esrf.fr/exp_facilities/ID19/homepage/DiffTopo/X-raytopography.htm]. | 1 | Crystallography |
Ordered columnar structures without internal spheres are categorised into two separate classes: uniform and line-slip structures. For each structure that can be identified with the triplet , there exist a uniform structure and at least one line slip. | 1 | Crystallography |
A suitable pH indicator must be chosen in order to detect the end point of the titration. The colour change or other effect should occur close to the equivalence point of the reaction so that the experimenter can accurately determine when that point is reached. The pH of the equivalence point can be estimated using the following rules:
* A strong acid will react with a strong base to form a neutral (pH = 7) solution.
* A strong acid will react with a weak base to form an acidic (pH < 7) solution.
* A weak acid will react with a strong base to form a basic (pH > 7) solution.
These indicators are essential tools in chemistry and biology, aiding in the determination of a solution's acidity or alkalinity through the observation of colour transitions. The table below serves as a reference guide for these indicator choices, offering insights into the pH ranges and colour transformations associated with specific indicators:
Phenolphthalein is widely recognized as one of the most commonly used acid-base indicators in chemistry. Its popularity is because of its effectiveness in a broad pH range and its distinct colour transitions. Its sharp and easily detectable colour changes makes phenolphthalein a valuable tool for determining the endpoint of acid-base titrations, as a precise pH change signifies the completion of the reaction.
When a weak acid reacts with a weak base, the equivalence point solution will be basic if the base is stronger and acidic if the acid is stronger. If both are of equal strength, then the equivalence pH will be neutral. However, weak acids are not often titrated against weak bases because the colour change shown with the indicator is often quick, and therefore very difficult for the observer to see the change of colour.
The point at which the indicator changes colour is called the endpoint. A suitable indicator should be chosen, preferably one that will experience a change in colour (an endpoint) close to the equivalence point of the reaction.
In addition to the wide variety of indicator solutions, pH papers, crafted from paper or plastic infused with combinations of these indicators, serve as a practical alternative. The pH of a solution can be estimated by immersing a strip of pH paper into it and matching the observed colour to the reference standards provided on the container. | 0 | Chromatography + Titration + pH indicators |
Consider two lattice points A and B separated by a translation vector r. Consider an angle α such that a rotation of angle α about any lattice point is a symmetry of the lattice. Rotating about point B by α maps point A to a new point A. Similarly, rotating about point A by α maps B to a point B. Since both rotations mentioned are symmetry operations, A and B must both be lattice points. Due to periodicity of the crystal, the new vector r which connects them must be equal to an integer multiple of r':
with integer. The four translation vectors, three of length and one, connecting A and B, of length , form a trapezium. Therefore, the length of r' is also given by:
Combining the two equations gives:
where is also an integer. Bearing in mind that we have allowed integers . Solving for possible values of reveals that the only values in the 0° to 180° range are 0°, 60°, 90°, 120°, and 180°. In radians, the only allowed rotations consistent with lattice periodicity are given by 2π/n, where n = 1, 2, 3, 4, 6. This corresponds to 1-, 2-, 3-, 4-, and 6-fold symmetry, respectively, and therefore excludes the possibility of 5-fold or greater than 6-fold symmetry. | 1 | Crystallography |
The Rodrigues equation, named for Alírio Rodrigues, is an extension of the Van Deemter equation used to describe the efficiency of a bed of permeable (large-pore) particles.
The equation is:
where
and is the intraparticular Péclet number. | 0 | Chromatography + Titration + pH indicators |
* Art forensics concerns the art authentication cases to help research the work's authenticity. Art authentication methods are used to detect and identify forgery, faking and copying of art works, e.g. paintings.
* Bloodstain pattern analysis is the scientific examination of blood spatter patterns found at a crime scene to reconstruct the events of the crime.
* Comparative forensics is the application of visual comparison techniques to verify similarity of physical evidence. This includes fingerprint analysis, toolmark analysis, and ballistic analysis.
* Computational forensics concerns the development of algorithms and software to assist forensic examination.
* Criminalistics is the application of various sciences to answer questions relating to examination and comparison of biological evidence, trace evidence, impression evidence (such as fingerprints, footwear impressions, and tire tracks), controlled substances, ballistics, firearm and toolmark examination, and other evidence in criminal investigations. In typical circumstances, evidence is processed in a crime lab.
* Digital forensics is the application of proven scientific methods and techniques in order to recover data from electronic / digital media. Digital Forensic specialists work in the field as well as in the lab.
* Ear print analysis is used as a means of forensic identification intended as an identification tool similar to fingerprinting. An earprint is a two-dimensional reproduction of the parts of the outer ear that have touched a specific surface (most commonly the helix, antihelix, tragus and antitragus).
* Election forensics is the use of statistics to determine if election results are normal or abnormal. It is also used to look into and detect the cases concerning gerrymandering.
* Forensic accounting is the study and interpretation of accounting evidence, financial statement namely: Balance sheet, Income statement, Cash flow statement.
* Forensic aerial photography is the study and interpretation of aerial photographic evidence.
* Forensic anthropology is the application of physical anthropology in a legal setting, usually for the recovery and identification of skeletonized human remains.
* Forensic archaeology is the application of a combination of archaeological techniques and forensic science, typically in law enforcement.
* Forensic astronomy uses methods from astronomy to determine past celestial constellations for forensic purposes.
* Forensic botany is the study of plant life in order to gain information regarding possible crimes.
* Forensic chemistry is the study of detection and identification of illicit drugs, accelerants used in arson cases, explosive and gunshot residue.
* Forensic dactyloscopy is the study of fingerprints.
* Forensic document examination or questioned document examination answers questions about a disputed document using a variety of scientific processes and methods. Many examinations involve a comparison of the questioned document, or components of the document, with a set of known standards. The most common type of examination involves handwriting, whereby the examiner tries to address concerns about potential authorship.
* Forensic DNA analysis takes advantage of the uniqueness of an individual's DNA to answer forensic questions such as paternity/maternity testing and placing a suspect at a crime scene, e.g. in a rape investigation.
* Forensic engineering is the scientific examination and analysis of structures and products relating to their failure or cause of damage.
* Forensic entomology deals with the examination of insects in, on and around human remains to assist in determination of time or location of death. It is also possible to determine if the body was moved after death using entomology.
* Forensic geology deals with trace evidence in the form of soils, minerals and petroleum.
* Forensic geomorphology is the study of the ground surface to look for potential location(s) of buried object(s).
* Forensic geophysics is the application of geophysical techniques such as radar for detecting objects hidden underground or underwater.
* Forensic intelligence process starts with the collection of data and ends with the integration of results within into the analysis of crimes under investigation.
* Forensic interviews are conducted using the science of professionally using expertise to conduct a variety of investigative interviews with victims, witnesses, suspects or other sources to determine the facts regarding suspicions, allegations or specific incidents in either public or private sector settings.
* Forensic histopathology is the application of histological techniques and examination to forensic pathology practice.
* Forensic limnology is the analysis of evidence collected from crime scenes in or around fresh-water sources. Examination of biological organisms, in particular diatoms, can be useful in connecting suspects with victims.
* Forensic linguistics deals with issues in the legal system that requires linguistic expertise.
* Forensic meteorology is a site-specific analysis of past weather conditions for a point of loss.
* Forensic metrology is the application of metrology to assess the reliability of scientific evidence obtained through measurements
* Forensic microbiology is the study of the necrobiome.
* Forensic nursing is the application of Nursing sciences to abusive crimes, like child abuse, or sexual abuse. Categorization of wounds and traumas, collection of bodily fluids and emotional support are some of the duties of forensic nurses.
* Forensic odontology is the study of the uniqueness of dentition, better known as the study of teeth.
* Forensic optometry is the study of glasses and other eyewear relating to crime scenes and criminal investigations.
* Forensic pathology is a field in which the principles of medicine and pathology are applied to determine a cause of death or injury in the context of a legal inquiry.
* Forensic podiatry is an application of the study of feet footprint or footwear and their traces to analyze scene of crime and to establish personal identity in forensic examinations.
* Forensic psychiatry is a specialized branch of psychiatry as applied to and based on scientific criminology.
* Forensic psychology is the study of the mind of an individual, using forensic methods. Usually it determines the circumstances behind a criminal's behavior.
* Forensic seismology is the study of techniques to distinguish the seismic signals generated by underground nuclear explosions from those generated by earthquakes.
* Forensic serology is the study of the body fluids.
* Forensic social work is the specialist study of social work theories and their applications to a clinical, criminal justice or psychiatric setting. Practitioners of forensic social work connected with the criminal justice system are often termed Social Supervisors, whilst the remaining use the interchangeable titles forensic social worker, approved mental health professional or forensic practitioner and they conduct specialist assessments of risk, care planning and act as an officer of the court.
* Forensic toxicology is the study of the effect of drugs and poisons on/in the human body.
* Forensic video analysis is the scientific examination, comparison and evaluation of video in legal matters.
* Mobile device forensics is the scientific examination and evaluation of evidence found in mobile phones, e.g. Call History and Deleted SMS, and includes SIM Card Forensics.
* Trace evidence analysis is the analysis and comparison of trace evidence including glass, paint, fibres and hair (e.g., using micro-spectrophotometry).
* Wildlife forensic science applies a range of scientific disciplines to legal cases involving non-human biological evidence, to solve crimes such as poaching, animal abuse, and trade in endangered species. | 0 | Chromatography + Titration + pH indicators |
Methyl violet is a mutagen and mitotic poison, therefore concerns exist regarding the ecological impact of the release of methyl violet into the environment. Methyl violet has been used in vast quantities for textile and paper dyeing, and 15% of such dyes produced worldwide are released to environment in wastewater. Numerous methods have been developed to treat methyl violet pollution. The three most prominent are chemical bleaching, biodegradation, and photodegradation. | 0 | Chromatography + Titration + pH indicators |
In mathematics, especially in geometry, a double lattice in is a discrete subgroup of the group of Euclidean motions that consists only of translations and point reflections and such that the subgroup of translations is a lattice. The orbit of any point under the action of a double lattice is a union of two Bravais lattices, related to each other by a point reflection. A double lattice in two dimensions is a p2 wallpaper group. In three dimensions, a double lattice is a space group of the type , as denoted by international notation. | 1 | Crystallography |
Glide planes are noted in the Hermann–Mauguin notation by a, b or c, depending on which axis the glide is along. (The orientation of the plane is determined by the position of the symbol in the Hermann–Mauguin designation.) If the axis is not defined, then the glide plane may be noted by g. When the glide plane is parallel to the screen, these planes may be indicated by a bent arrow in which the arrowhead indicates the direction of the glide. When the glide plane is perpendicular to the screen, these planes can be represented either by dashed lines when the glide is parallel to the plane of the screen or dotted lines when the glide is perpendicular to the plane of the screen. Additionally, a centered lattice can cause a glide plane to exist in two directions at the same time. This type of glide plane may be indicated by a bent arrow with an arrowhead on both sides when the glide plan is parallel to the plane of the screen or a dashed and double-dotted line when the glide plane is perpendicular to the plane of the screen. There is also the n glide, which is a glide along the half of a diagonal of a face, and the d glide, which is along a fourth of either a face or space diagonal of the unit cell . The latter is often called the diamond glide plane as it features in the diamond structure. The n glide plane may be indicated by diagonal arrow when it is parallel to the plane of the screen or a dashed-dotted line when the glide plane is perpendicular to the plane of the screen. A d glide plane may be indicated by a diagonal half-arrow if the glide plane is parallel to the plane of the screen or a dashed-dotted line with arrows if the glide plane is perpendicular to the plane of the screen. If a d glide plane is present in a crystal system, then that crystal must have a centered lattice.
In todays version of Hermann–Mauguin notation, the symbol e is used in cases where there are two possible ways of designating the glide direction because both are true. For example if a crystal has a base-centered Bravais lattice centered on the C face, then a glide of half a cell unit in the a direction gives the same result as a glide of half a cell unit in the b' direction.
The isometry group generated by just a glide reflection is an infinite cyclic group. Combining two equal glide plane operations gives a pure translation with a translation vector that is twice that of the glide reflection, so the even powers of the glide reflection form a translation group.
In the case of glide-reflection symmetry, the symmetry group of an object contains a glide reflection and the group generated by it. For any symmetry group containing a glide reflection, the glide vector is one half of an element of the translation group. If the translation vector of a glide plane operation is itself an element of the translation group, then the corresponding glide plane symmetry reduces to a combination of reflection symmetry and translational symmetry. | 1 | Crystallography |
Dislocations in a crystal lattice are line defects that are associated with local stress fields. Dislocations allow shear at lower stress than that needed for a perfect crystal structure. The local stress fields result in interactions between the dislocations which then result in strain hardening or cold working. | 1 | Crystallography |
Supercritical fluid chromatography (SFC) is a form of normal phase chromatography that uses a supercritical fluid such as carbon dioxide as the mobile phase. It is used for the analysis and purification of low to moderate molecular weight, thermally labile molecules and can also be used for the separation of chiral compounds. Principles are similar to those of high performance liquid chromatography (HPLC); however, SFC typically utilizes carbon dioxide as the mobile phase. Therefore, the entire chromatographic flow path must be pressurized. Because the supercritical phase represents a state whereby bulk liquid and gas properties converge, supercritical fluid chromatography is sometimes called convergence chromatography. The idea of liquid and gas properties convergence was first envisioned by Giddings. | 0 | Chromatography + Titration + pH indicators |
Another type of topographic contrast, extinction contrast, is slightly more complex. While the two above variants are explicable in simple terms based on geometrical theory (basically, the Bragg law) or kinematical theory of X-ray diffraction, extinction contrast can be understood based on dynamical theory.
Qualitatively, extinction contrast arises e.g. when the thickness of a sample, compared to the respective extinction length (Bragg case) or Pendelloesung length (Laue case), changes across the image. In this case, diffracted beams from areas of different thickness, having suffered different degrees of extinction, are recorded within the same image, giving rise to contrast. Topographists have systematically investigated this effect by studying wedge-shaped samples, of linearly varying thickness, allowing to directly record in one image the dependence of diffracted intensity on sample thickness as predicted by dynamical theory.
In addition to mere thickness changes, extinction contrast also arises when parts of a crystal are diffracting with different strengths, or when the crystal contains deformed (strained) regions.
The governing quantity for an overall theory of extinction contrast in deformed crystals is called the effective misorientation
where is the displacement vector field, and and are the directions of the incident and diffracted beam, respectively.
In this way, different kinds of disturbances are "translated" into equivalent misorientation values, and contrast formation can be understood analogously to orientation contrast.
For instance, a compressively strained material requires larger Bragg angles for diffraction at unchanged wavelength. To compensate for this and to reach diffraction conditions, the sample needs to be rotated, similarly as in the case of lattice tilts.
A simplified and more "transparent" formula taking into account the combined effect of tilts and strains onto contrast is the following: | 1 | Crystallography |
Droplet countercurrent chromatography (DCCC or DCC) was introduced in 1970 by Tanimura, Pisano, Ito, and Bowman. DCCC is considered to be a form of liquid-liquid separation, which includes countercurrent distribution and countercurrent chromatography, that employs a liquid stationary phase held in a collection of vertical glass columns connected in series. The mobile phase passes through the columns in the form of droplets. The DCCC apparatus may be run with the lower phase stationary and the upper phase being introduced to the bottom of each column. Or it may be run with the upper phase stationary and the lower phase being introduced from the top of the column. In both cases, the work of gravity is allowed influence the two immiscible liquids of different densities to form the signature droplets that rise or descend through the column. The mobile phase is pumped at a rate that will allow droplets to form that maximize the mass transfer of a compound between the upper and lower phases. Compounds that are more soluble in the upper phase will travel quickly through the column, while compounds that are more soluble in the stationary phase will linger. Separation occurs because different compounds distribute differently, in a ratio called the partition coefficient, between the two phases.
The biphasic solvent system must be carefully formulated so that it will perform appropriately in the DCCC column. The solvent system must form two phases without excess emulsification in order to form droplets. The densities of the two phases must also be sufficiently different so that the phases will move past each other in the column. Many DCCC solvent systems contain both chloroform and water. The solvent system used in the seminal publication was made from chloroform, acetic acid, and aqueous 0.1 M hydrochloric acid. Many subsequent solvents systems were made with chloroform, methanol, and water which is sometimes represented as a ChMWat solvent system. Solvent systems formulated with n-butanol, water and a modifier such as acetic acid, pyridine or n-propanol have also enjoyed some success in DCCC. In some cases, non-aqueous biphasic solvent systems such as acetonitrile and methanol have been utilized.
The main difference between DCCC and other types of countercurrent chromatography techniques is that there is no vigorous mixing of phases to enhance the mass transfer of compounds that allows them to distribute between the two phases. In 1951 Kies and Davis described an apparatus similar to the DCCC. They created a series of open tubes that were arranged in a cascade to either drip a more dense phase through a less dense stationary phase or, conversely, a less dense phase could be introduced into the bottom of the tube to dribble through the more dense phase. In 1954, a fractionation column was introduced by Kepes the resembled a CCC column divided into chambers with perforated plastic disks. Similar DCCC-type instruments have been created by A. E. Kostanyan and collaborators which employ vertical columns that are divided into partitions with porous disks. Once the columns are filled with stationary phase, the mobile phase is pumped through, not continuously but, in pulses. The solvent motion created by a pulsed pumping action creates the mixing and settling that is common to most all forms of countercurrent chromatography. | 0 | Chromatography + Titration + pH indicators |
Boronate affinity chromatography consists of using boronic acid or boronates to elute and quantify amounts of glycoproteins. Clinical adaptations have applied this type of chromatography for use in determining long term assessment of diabetic patients through analysis of their glycated hemoglobin. | 0 | Chromatography + Titration + pH indicators |
In condensed matter physics, a time crystal is a quantum system of particles whose lowest-energy state is one in which the particles are in repetitive motion. The system cannot lose energy to the environment and come to rest because it is already in its quantum ground state. Time crystals were first proposed theoretically by Frank Wilczek in 2012 as a time-based analogue to common crystals – whereas the atoms in crystals are arranged periodically in space, the atoms in a time crystal are arranged periodically in both space and time. Several different groups have demonstrated matter with stable periodic evolution in systems that are periodically driven. In terms of practical use, time crystals may one day be used as quantum computer memory.
The existence of crystals in nature is a manifestation of spontaneous symmetry breaking, which occurs when the lowest-energy state of a system is less symmetrical than the equations governing the system. In the crystal ground state, the continuous translational symmetry in space is broken and replaced by the lower discrete symmetry of the periodic crystal. As the laws of physics are symmetrical under continuous translations in time as well as space, the question arose in 2012 as to whether it is possible to break symmetry temporally, and thus create a "time crystal" that is resistant to entropy.
If a discrete time-translation symmetry is broken (which may be realized in periodically driven systems), then the system is referred to as a discrete time crystal. A discrete time crystal never reaches thermal equilibrium, as it is a type (or phase) of non-equilibrium matter. Breaking of time symmetry can only occur in non-equilibrium systems. Discrete time crystals have in fact been observed in physics laboratories as early as 2016 (published in 2017). One example of a time crystal, which demonstrates non-equilibrium, broken time symmetry is a constantly rotating ring of charged ions in an otherwise lowest-energy state. | 1 | Crystallography |
Now, given the considerations of background, peak shape functions, integrated intensity, and non-linear least squares minimization, the parameters used in the Rietveld refinement which put these things together can be introduced. Below are the groups of independent least squares parameters generally refined in a Rietveld refinement.
* Background parameters: usually 1 to 12 parameters.
* Sample displacement: sample transparency, and zero shift corrections. (move peak position)
* Multiple peak shape parameters.
** FWHM parameters: i.e. Caglioti parameters (see section 3.1.2)
** Asymmetry parameters (FCJ parameters)
* Unit cell dimensions
** one to six parameters (a, b, c, α, β, γ), depending on the crystal family/system, for each present phase.
* Preferred orientation, and sometimes absorption, porosity, and extinction coefficients, which can be independent for each phase.
* Scale factors (for each phase)
* Positional parameters of all independent atoms in the crystal model (generally 0 to 3 per atom).
* Population parameters
** Occupation of site positions by atoms.
* Atomic displacement parameters
** Isotropic and anisotropic (temperature) parameters.
Each Rietveld refinement is unique and there is no prescribed sequence of parameters to include in a refinement. It is up to the user to determine and find the best sequence of parameters for refinement. It is worth noting that it is rarely possible to refine all relevant variables simultaneously from the beginning of a refinement, nor near the end since the least squares fitting will be destabilized or lead to a false minimum. It is important for the user to determine a stopping point for a given refinement. Given the complexity of Rietveld refinement it is important to have a clear grasp of the system being studied (sample, and instrumentation) to ensure that results are accurate, realistic, and meaningful. High data quality, a large enough range, and a good model – to serve as the initial approximation in the least squares fitting – are necessary for a successful, reliable, and meaningful Rietveld refinement. | 1 | Crystallography |
Sulfate may be rapidly and easily titrated thermometrically using standard solutions of Ba as titrant. Industrially, the procedure has been applied to the determination of sulfate in brine (including electrolysis brines), in nickel refining solutions and particularly for sulfate in wet process phosphoric acid, where it has proven to be quite popular. The procedure can also be used to assist in the analysis of complex acid mixtures containing sulfuric acid where resorting to titration in non-aqueous media is not feasible.
The reaction enthalpy for the formation of barium sulfate is a modest −18.8 kJ/mol. This can place a restriction on the lower limit of sulfate in a sample which can be analyzed. | 0 | Chromatography + Titration + pH indicators |
Reciprocal space (also called -space) provides a way to visualize the results of the Fourier transform of a spatial function. It is similar in role to the frequency domain arising from the Fourier transform of a time dependent function; reciprocal space is a space over which the Fourier transform of a spatial function is represented at spatial frequencies or wavevectors of plane waves of the Fourier transform. The domain of the spatial function itself is often referred to as real space. In physical applications, such as crystallography, both real and reciprocal space will often each be two or three dimensional. Whereas the number of spatial dimensions of these two associated spaces will be the same, the spaces will differ in their quantity dimension, so that when the real space has the dimension length (L), its reciprocal space will of inverse length, so L (the reciprocal of length).
Reciprocal space comes into play regarding waves, both classical and quantum mechanical. Because a sinusoidal plane wave with unit amplitude can be written as an oscillatory term , with initial phase , angular wavenumber and angular frequency , it can be regarded as a function of both and (and the time-varying part as a function of both and ). This complementary role of and leads to their visualization within complementary spaces (the real space and the reciprocal space). The spatial periodicity of this wave is defined by its wavelength , where ; hence the corresponding wavenumber in reciprocal space will be .
In three dimensions, the corresponding plane wave term becomes , which simplifies to at a fixed time , where is the position vector of a point in real space and now is the wavevector in the three dimensional reciprocal space. (The magnitude of a wavevector is called wavenumber.) The constant is the phase of the wavefront (a plane of a constant phase) through the origin at time , and is a unit vector perpendicular to this wavefront. The wavefronts with phases , where represents any integer, comprise a set of parallel planes, equally spaced by the wavelength . | 1 | Crystallography |
Methyl violet 2B (IUPAC name: N-(4-(bis(4-(dimethylamino)phenyl)methylene)cyclohexa-2,5-dien-1-ylidene)methanaminium chloride) is a green powder which is soluble in water and ethanol but not in xylene. It appears yellow in solution of low pH (~0.15) and changes to violet with pH increasing toward 3.2. | 0 | Chromatography + Titration + pH indicators |
In order to perform geometric phase analysis, a computer tool is needed. Firstly, because manual evaluation of transforms between spatial and frequential domain would be highly impractical. Secondly, a vector of crystallographic plane is an important input parameter and the analysis is sensitive to the accuracy of its localization. Therefore, the accuracy and repeatability of the analysis can be increased by an automated localization of diffraction spots.
The required functionalities are available in crystallographic suite CrysTBox. It offers an interactive implementation geometric phase analysis called gpaGUI. Within gpaGUI, it is possible to index the diffraction spots and localize them with sub-pixel precision using an automated tool diffractGUI. | 1 | Crystallography |
Friedel's salt is an anion exchanger mineral belonging to the family of the layered double hydroxides (LDHs). It has affinity for anions as chloride and iodide and is capable of retaining them to a certain extent in its crystallographical structure. | 1 | Crystallography |
Cryo bio-crystallography is the application of crystallography to biological macromolecules at cryogenic temperatures. | 1 | Crystallography |
The coefficient lies always in range values equal to 0 or 1), value 1 indicates ideal equal-spreading of the spots, for example (0.25,0.5,0.75) for three solutes, or (0.2,0.4,0.6,0.8) for four solutes.
This coefficient was proposed as an alternative to earlier approaches, such as D (separation response), I (performance index) or S (informational entropy). Besides its stable range, the advantage is a stable distribution as a random variable, regardless of compounds investigated.
In contrast to the similar concept called Retention distance, R is insensitive to R values close to 0 or 1, or close to themselves. If two values are not separated, it still indicates some uniformity of chromatographic system. For example, the R values (0,0.2,0.2,0.3) (two compounds not separated at 0.2 and one at the start ) result in R equal to 0.3609. | 0 | Chromatography + Titration + pH indicators |
The process for TLC is similar to paper chromatography but provides faster runs, better separations, and the choice between different stationary phases. Plates can be labelled before or after the chromatography process with a pencil or other implement that will not interfere with the process.
There are four main stages to running a thin-layer chromatography plate:
Plate preparation: Using a capillary tube, a small amount of a concentrated solution of the sample is deposited near the bottom edge of a TLC plate. The solvent is allowed to completely evaporate before the next step. A vacuum chamber may be necessary for non-volatile solvents. To make sure there is sufficient compound to obtain a visible result, the spotting procedure can be repeated. Depending on the application, multiple different samples may be placed in a row the same distance from the bottom edge; each sample will move up the plate in its own "lane."
Development chamber preparation: The development solvent or solvent mixture is placed into a transparent container (separation/development chamber) to a depth of less than 1 centimetre. A strip of filter paper (aka "wick") is also placed along the container wall. This filter paper should touch the solvent and almost reach the top of the container. The container is covered with a lid and the solvent vapors are allowed to saturate the atmosphere of the container. Failure to do so results in poor separation and non-reproducible results.
Development: The TLC plate is placed in the container such that the sample spot(s) are not submerged into the mobile phase. The container is covered to prevent solvent evaporation. The solvent migrates up the plate by capillary action, meets the sample mixture, and carries it up the plate (elutes the sample). The plate is removed from the container before the solvent reaches the top of the plate; otherwise, the results will be misleading. The solvent front, the highest mark the solvent has travelled along the plate, is marked.
Visualization: The solvent evaporates from the plate. Visualization methods include UV light, staining, and many more. | 0 | Chromatography + Titration + pH indicators |
The difficulty of predicting stable crystal structures based on the knowledge of only the chemical composition has long been a stumbling block on the way to fully computational materials design. Now, with more powerful algorithms and high-performance computing, structures of medium complexity can be predicted using such approaches as evolutionary algorithms, random sampling, or metadynamics.
The crystal structures of simple ionic solids (e.g., NaCl or table salt) have long been rationalized in terms of Pauling's rules, first set out in 1929 by Linus Pauling, referred to by many since as the "father of the chemical bond". Pauling also considered the nature of the interatomic forces in metals, and concluded that about half of the five d-orbitals in the transition metals are involved in bonding, with the remaining nonbonding d-orbitals being responsible for the magnetic properties. Pauling was therefore able to correlate the number of d-orbitals in bond formation with the bond length, as well as with many of the physical properties of the substance. He subsequently introduced the metallic orbital, an extra orbital necessary to permit uninhibited resonance of valence bonds among various electronic structures.
In the resonating valence bond theory, the factors that determine the choice of one from among alternative crystal structures of a metal or intermetallic compound revolve around the energy of resonance of bonds among interatomic positions. It is clear that some modes of resonance would make larger contributions (be more mechanically stable than others), and that in particular a simple ratio of number of bonds to number of positions would be exceptional. The resulting principle is that a special stability is associated with the simplest ratios or "bond numbers": , , , , , etc. The choice of structure and the value of the axial ratio (which determines the relative bond lengths) are thus a result of the effort of an atom to use its valency in the formation of stable bonds with simple fractional bond numbers.
After postulating a direct correlation between electron concentration and crystal structure in beta-phase alloys, Hume-Rothery analyzed the trends in melting points, compressibilities and bond lengths as a function of group number in the periodic table in order to establish a system of valencies of the transition elements in the metallic state. This treatment thus emphasized the increasing bond strength as a function of group number. The operation of directional forces were emphasized in one article on the relation between bond hybrids and the metallic structures. The resulting correlation between electronic and crystalline structures is summarized by a single parameter, the weight of the d-electrons per hybridized metallic orbital. The "d-weight" calculates out to 0.5, 0.7 and 0.9 for the fcc, hcp and bcc structures respectively. The relationship between d-electrons and crystal structure thus becomes apparent.
In crystal structure predictions/simulations, the periodicity is usually applied, since the system is imagined as being unlimited in all directions. Starting from a triclinic structure with no further symmetry property assumed, the system may be driven to show some additional symmetry properties by applying Newton's Second Law on particles in the unit cell and a recently developed dynamical equation for the system period vectors
(lattice parameters including angles), even if the system is subject to external stress. | 1 | Crystallography |
Topography is "classically" applied to inorganic crystals, such a metals and semiconductors. However, it is nowadays applied more and more often also to organic crystals, most notably proteins. Topographic investigations can help to understand and optimize crystal growth processes also for proteins. Numerous studies have been initiated in the last 5–10 years, using both white-beam and plane-wave topography.
Although considerable progress has been achieved, topography on protein crystals remains a difficult discipline: Due to large unit cells, small structure factors and high disorder, diffracted intensities are weak. Topographic imaging therefore requires long exposure times, which may lead to radiation damage of the crystals, generating in the first place the defects which are then imaged. In addition, the low structure factors lead to small Darwin widths and thus to broad dislocation images, i.e. rather low spatial resolution.
Nevertheless, in some cases, protein crystals were reported to be perfect enough to achieve images of single dislocations.
Literature: | 1 | Crystallography |
One important characteristic of a crystalline structure is its atomic packing factor (APF). This is calculated by assuming that all the atoms are identical spheres, with a radius large enough that each sphere abuts on the next. The atomic packing factor is the proportion of space filled by these spheres which can be worked out by calculating the total volume of the spheres and dividing by the volume of the cell as follows:
Another important characteristic of a crystalline structure is its coordination number (CN). This is the number of nearest neighbours of a central atom in the structure.
The APFs and CNs of the most common crystal structures are shown below:
The 74% packing efficiency of the FCC and HCP is the maximum density possible in unit cells constructed of spheres of only one size. | 1 | Crystallography |
The Wigner–Seitz cell around a lattice point is defined as the locus of points in space that are closer to that lattice point than to any of the other lattice points.
It can be shown mathematically that a Wigner–Seitz cell is a primitive cell. This implies that the cell spans the entire direct space without leaving any gaps or holes, a property known as tessellation. | 1 | Crystallography |
High-performance thin-layer chromatography (HPTLC) serves as an extension of thin-layer chromatography (TLC), offering robustness, simplicity, speed, and efficiency in the quantitative analysis of compounds. This TLC-based analytical technique enhances compound resolution for quantitative analysis. Some of these improvements involve employing higher-quality TLC plates with finer particle sizes in the stationary phase, leading to improved resolution. Additionally, the separation can be further refined through repeated plate development using a multiple development device. As a result, HPTLC provides superior resolution and lower Limit of Detection (LODs). | 0 | Chromatography + Titration + pH indicators |
The antiviral drug ritonavir exists as two polymorphs, which differ greatly in efficacy. Such issues were solved by reformulating the medicine into gelcaps and tablets, rather than the original capsules. | 1 | Crystallography |
As describes, the vertices of the Laves graph can be defined by selecting one out of every eight points in the three-dimensional integer lattice, and forming their nearest neighbor graph. Specifically, one chooses the points
and all the other points formed by adding multiples of four to these coordinates. The edges of the Laves graph connect pairs of points whose Euclidean distance from each other is the square root of two, , as the points of each pair differ by one unit in two coordinates, and are the same in the third coordinate. The edges meet at 120° angles at each vertex, in a flat plane. All pairs of vertices that are non-adjacent are farther apart, at a distance of at least from each other. The edges of the resulting geometric graph are diagonals of a subset of the faces of the regular skew polyhedron with six square faces per vertex, so the Laves graph is embedded in this skew polyhedron.
It is possible to choose a larger set of one out of every four points of the integer lattice, so that the graph of distance- pairs of this larger set forms two mirror-image copies of the Laves graph, disconnected from each other, with all other pairs of points farther than apart. | 1 | Crystallography |
To discuss the visibility of defects in topographic images according to theory, consider the exemplary case of a single dislocation: It will give rise to contrast in topography only if the lattice planes involved in diffraction are distorted in some way by the existence of the dislocation. This is true in the case of an edge dislocation if the scattering vector of the Bragg reflection used is parallel to the Burgers vector of the dislocation, or at least has a component in the plane perpendicular to the dislocation line, but not if it is parallel to the dislocation line. In the case of a screw dislocation, the scattering vector has to have a component along the Burgers vector, which is now parallel to dislocation line. As a rule of thumb, a dislocation will be invisible in a topograph if the vector product
is zero.
(A more precise rule will have to distinguish between screw and edge dislocations and to also take the direction of the dislocation line into account – see e.g. [http://www.msel.nist.gov/practiceguides/SP960_10.pdf].)
If a defect is visible, often there occurs not only one, but several distinct images of it on the topograph. Theory predicts three images of single defects: The so-called direct image, the kinematical image, and the intermediary image.
For details see e.g. (Authier 2003). | 1 | Crystallography |
Affinity chromatography is a method of separating a biomolecule from a mixture, based on a highly specific macromolecular binding interaction between the biomolecule and another substance. The specific type of binding interaction depends on the biomolecule of interest; antigen and antibody, enzyme and substrate, receptor and ligand, or protein and nucleic acid binding interactions are frequently exploited for isolation of various biomolecules. Affinity chromatography is useful for its high selectivity and resolution of separation, compared to other chromatographic methods. | 0 | Chromatography + Titration + pH indicators |
There are actually two versions in mathematics of the abstract dual lattice concept, for a given lattice L in a real vector space V, of finite dimension.
The first, which generalises directly the reciprocal lattice construction, uses Fourier analysis. It may be stated simply in terms of Pontryagin duality. The dual group V^ to V is again a real vector space, and its closed subgroup L^ dual to L turns out to be a lattice in V^. Therefore, L^ is the natural candidate for dual lattice, in a different vector space (of the same dimension).
The other aspect is seen in the presence of a quadratic form Q on V; if it is non-degenerate it allows an identification of the dual space V of V with V. The relation of V to V is not intrinsic; it depends on a choice of Haar measure (volume element) on V. But given an identification of the two, which is in any case well-defined up to a scalar, the presence of Q allows one to speak to the dual lattice to L while staying within V.
In mathematics, the dual lattice of a given lattice L in an abelian locally compact topological group G is the subgroup L of the dual group of G consisting of all continuous characters that are equal to one at each point of L.
In discrete mathematics, a lattice is a locally discrete set of points described by all integral linear combinations of linearly independent vectors in R. The dual lattice is then defined by all points in the linear span of the original lattice (typically all of R) with the property that an integer results from the inner product with all elements of the original lattice. It follows that the dual of the dual lattice is the original lattice.
Furthermore, if we allow the matrix B to have columns as the linearly independent vectors that describe the lattice, then the matrix has columns of vectors that describe the dual lattice. | 1 | Crystallography |
In an conventional CCC experiment the biphasic solvent system is pre-equilibrated before the instrument is filled with the stationary phase and equilibrated with the mobile phase. An ion-exchange mode has been created by modifying both of the phases after pre-equilibration. Generally, an ionic displacer (or eluter) is added to mobile phase and an ionic retainer is added to the stationary phase. For example, the aqueous mobile phase may contain NaI as a displacer and the organic stationary phase may be modified with the quaternary ammonium salt called Aliquat 336 as a retainer. The mode known a pH-zone-refining is a type of ion-exchange mode that utilizes acids and/or bases as solvent modifiers. Typically, the analytes are eluted in an order determined by their pKa values. For example, 6 oxindole alkaloids were isolated from a 4.5g sample of Gelsemium elegans stem extract with a biphasic solvent system composed of hexane–ethyl acetate–methanol–water (3:7:1:9, v/v) where 10 mM triethylamine (TEA) was added to the upper organic stationary phase as a retainer and 10 mM hydrochloric acid (HCl) to the aqueous mobile phase as an eluter. Ion-exchange modes such as pH-zone-refining have tremendous potential because high sample loads can be achieved without sacrificing separation power. It works best with ionizable compounds such as nitrogen containing alkaloids or carboxylic acid containing fatty acids. | 0 | Chromatography + Titration + pH indicators |
Dilution of sample or reducing the volume of sample injected may give a reduction of ion suppression by reducing the quantity of interfering species present, although the quantity of analyte of interest will also be reduced, making this an undesirable approach for trace analysis.
Similar is the effect of reducing the mobile phase flow rate to the nanolitre-per-minute range since, in addition to resulting in improved desolvation, the smaller droplets formed are more tolerant to the presence of non-volatile species in the sample matrix. | 0 | Chromatography + Titration + pH indicators |
In theory, any complexation reaction can be used as a volumetric technique provided that:
# The reaction reaches equilibrium rapidly after each portion of titrant is added.
# Interfering situations do not arise. For instance, the stepwise formation of several different complexes of the metal ion with the titrant, resulting in the presence of more than one complex in solution during the titration process.
# A complexometric indicator capable of locating equivalence point with fair accuracy is available.
In practice, the use of EDTA as a titrant is well established. | 0 | Chromatography + Titration + pH indicators |
The Lely method produces bulk silicon carbide crystals through the process of sublimation. Silicon carbide powder is loaded into a graphite crucible, which is purged with argon gas and heated to approximately . The silicon carbide near the outer walls of the crucible sublimes and is deposited on a graphite rod near the center of the crucible, which is at a lower temperature.
Several modified versions of the Lely process exist, most commonly the silicon carbide is heated from the bottom end rather than the walls of the crucible, and deposited on the lid. Other modifications include varying the temperature, temperature gradient, argon pressure, and geometry of the system. Typically, an induction furnace is used to achieve the required temperatures of . | 1 | Crystallography |
Laserspray Ionization (LSI) is a newer mass spectrometric technique commonly used with biomolecules, such as proteins. This method is similar to matrix-assisted laser desorption/ionization (MALDI) at atmospheric pressure in that it involves an analyte and matrix mixture. It also contains features from electrospray ionization, in which it produces a similar mass spectra. The mechanism was initially thought to involve laser induced production of highly charge matrix/analyte clusters that upon evaporation of the matrix produces ions by the same mechanism as ESI. LSI's ability to ablate proteins at atmospheric pressure in order to form a multiple of charged ions with a mass resolution of 100,000 when coupled with a quadrupole orbitrap mass spectrometer. The advantages of using LSI includes a solvent-free ionization technique, fast data acquisition, simply to use, and the improved fragmentation through multiple charging. | 0 | Chromatography + Titration + pH indicators |
In mathematics, a Meyer set or almost lattice is a relatively dense set X of points in the Euclidean plane or a higher-dimensional Euclidean space such that its Minkowski difference with itself is uniformly discrete. Meyer sets have several equivalent characterizations; they are named after Yves Meyer, who introduced and studied them in the context of diophantine approximation. Nowadays Meyer sets are best known as mathematical model for quasicrystals. However, Meyer's work precedes the discovery of quasicrystals by more than a decade and was entirely motivated by number theoretic questions. | 1 | Crystallography |
#Anthocyanin pigments are assembled like all other flavonoids from two different streams of chemical raw materials in the cell:
#* One stream involves the shikimate pathway to produce the amino acid phenylalanine, (see phenylpropanoids)
#* The other stream produces three molecules of malonyl-CoA, a C unit from a C unit (acetyl-CoA),
#These streams meet and are coupled together by the enzyme chalcone synthase, which forms an intermediate chalcone-like compound via a polyketide folding mechanism that is commonly found in plants,
#The chalcone is subsequently isomerized by the enzyme chalcone isomerase to the prototype pigment naringenin,
#Naringenin is subsequently oxidized by enzymes such as flavanone hydroxylase, flavonoid 3-hydroxylase, and flavonoid 3,5'-hydroxylase,
#These oxidation products are further reduced by the enzyme dihydroflavonol 4-reductase to the corresponding colorless leucoanthocyanidins,
#Leucoanthocyanidins once were believed to be the immediate precursors of the next enzyme, a dioxygenase referred to as anthocyanidin synthase, or, leucoanthocyanidin dioxygenase. Flavan-3-ols, the products of leucoanthocyanidin reductase (LAR), recently have been shown to be their true substrates,
#The resulting unstable anthocyanidins are further coupled to sugar molecules by enzymes such as UDP-3-O-glucosyltransferase, to yield the final relatively-stable anthocyanins.
Thus, more than five enzymes are required to synthesize these pigments, each working in concert. Even a minor disruption in any of the mechanisms of these enzymes by either genetic or environmental factors, would halt anthocyanin production. While the biological burden of producing anthocyanins is relatively high, plants benefit significantly from the environmental adaptation, disease tolerance, and pest tolerance provided by anthocyanins.
In anthocyanin biosynthetic pathway, -phenylalanine is converted to naringenin by phenylalanine ammonialyase, cinnamate 4-hydroxylase, 4-coumarate CoA ligase, chalcone synthase, and chalcone isomerase. Then, the next pathway is catalyzed, resulting in the formation of complex aglycone and anthocyanin through composition by flavanone 3-hydroxylase, flavonoid 3'-hydroxylase, dihydroflavonol 4-reductase, anthocyanidin synthase, UDP-glucoside: flavonoid glucosyltransferase, and methyl transferase. | 0 | Chromatography + Titration + pH indicators |
The setup for projection topography (also called "traverse" topography") is essentially identical to section topography, the difference being that both sample and film are now scanned laterally (synchronously) with respect to the narrow incident beam. A projection topograph therefore corresponds to the superposition of many adjacent section topographs, able to investigate not just a restricted portion, but the entire volume of a crystal.
The technique is rather simple and has been in routine use at "Lang cameras" in many research laboratories. | 1 | Crystallography |
The idea of a quantized time crystal was theorized in 2012 by Frank Wilczek, a Nobel laureate and professor at MIT. In 2013, Xiang Zhang, a nanoengineer at University of California, Berkeley, and his team proposed creating a time crystal in the form of a constantly rotating ring of charged ions.
In response to Wilczek and Zhang, Patrick Bruno (European Synchrotron Radiation Facility) and Masaki Oshikawa (University of Tokyo) published several articles stating that space–time crystals were impossible.
Subsequent work developed more precise definitions of time-translation symmetry-breaking, which ultimately led to the Watanabe–Oshikawa "no-go" statement that quantum space–time crystals in equilibrium are not possible. Later work restricted the scope of Watanabe and Oshikawa: strictly speaking, they showed that long-range order in both space and time is not possible in equilibrium, but breaking of time-translation symmetry alone is still possible.
Several realizations of time crystals, which avoid the equilibrium no-go arguments, were later proposed. In 2014 at Jagiellonian University in Kraków predicted the behaviour of discrete time crystals in a periodically driven system with "an ultracold atomic cloud bouncing on an oscillating mirror".
In 2016, research groups at Princeton and at Santa Barbara independently suggested that periodically driven quantum spin systems could show similar behaviour. Also in 2016, Norman Yao at Berkeley and colleagues proposed a different way to create discrete time crystals in spin systems. These ideas were successful and independently realized by two experimental teams: a group led by Harvards Mikhail Lukin and a group led by Christopher Monroe at University of Maryland. Both experiments were published in the same issue of Nature' in March 2017.
Later, time crystals in open systems, so called dissipative time crystals, were proposed in several platforms breaking a discrete and a continuous time-translation symmetry. A dissipative time crystal was experimentally realized for the first time in 2021 by the group of Andreas Hemmerich at the Institute of Laser Physics at the University of Hamburg. The researchers used a Bose–Einstein condensate strongly coupled to a dissipative optical cavity and the time crystal was demonstrated to spontaneously break discrete time-translation symmetry by periodically switching between two atomic density patterns. In an earlier experiment in the group of Tilman Esslinger at ETH Zurich, limit cycle dynamics was observed in 2019, but evidence of robustness against perturbations and the spontaneous character of the time-translation symmetry breaking were not addressed.
In 2019, physicists Valerii Kozin and Oleksandr Kyriienko proved that, in theory, a permanent quantum time crystal can exist as an isolated system if the system contains unusual long-range multiparticle interactions. The original "no-go" argument only holds in the presence of typical short-range fields that decay as quickly as for some . Kozin and Kyriienko instead analyzed a spin-1/2 many-body Hamiltonian with long-range multispin interactions, and showed it broke continuous time-translational symmetry. Certain spin correlations in the system oscillate in time, despite the system being closed and in a ground energy state. However, demonstrating such a system in practice might be prohibitively difficult, and concerns about the physicality of the long-range nature of the model have been raised.
In 2022, the Hamburg research team, supervised by Hans Keßler and Andreas Hemmerich, demonstrated, for the first time, a continuous dissipative time crystal exhibiting spontaneous breaking of continuous time-translation symmetry.
In February 2024, a team from Dortmund University in Germany built a time crystal from indium gallium arsenide that lasted for 40 minutes, nearly 10 million times longer than the previous record of around 5 milliseconds. In addition, the lack of any decay suggest the crystal have lasted even longer, stating that it could last
"at least a few hours, perhaps even longer".https://phys.org/news/2024-02-physicists-highly-robust-crystal.html | 1 | Crystallography |
The Ewald sphere is a geometric construction used in electron, neutron, and x-ray diffraction which shows the relationship between:
* the wavevector of the incident and diffracted beams,
* the diffraction angle for a given reflection,
* the reciprocal lattice of the crystal.
It was conceived by Paul Peter Ewald, a German physicist and crystallographer. Ewald himself spoke of the sphere of reflection. It is often simplified to the two-dimensional "Ewald's circle" model or may be referred to as the Ewald sphere. | 1 | Crystallography |
The crystallographic restriction theorem in its basic form was based on the observation that the rotational symmetries of a crystal are usually limited to 2-fold, 3-fold, 4-fold, and 6-fold. However, quasicrystals can occur with other diffraction pattern symmetries, such as 5-fold; these were not discovered until 1982 by Dan Shechtman.
Crystals are modeled as discrete lattices, generated by a list of independent finite translations . Because discreteness requires that the spacings between lattice points have a lower bound, the group of rotational symmetries of the lattice at any point must be a finite group (alternatively, the point is the only system allowing for infinite rotational symmetry). The strength of the theorem is that not all finite groups are compatible with a discrete lattice; in any dimension, we will have only a finite number of compatible groups. | 1 | Crystallography |
If with , , as integers represents the reciprocal lattice for a crystal lattice (defined by ) in real space, we know that with an integer due to the known orthogonality between primitive vectors for the reciprocal lattice and those for the crystal lattice. (We use the physical, not crystallographers, definition for reciprocal lattice vectors which gives the factor of .) But notice that this is nothing but the Laue equations. Hence we identify , means that allowed scattering vectors are those equal to reciprocal lattice vectors for a crystal in diffraction, and this is the meaning of the Laue equations. This fact is sometimes called the Laue condition. In this sense, diffraction patterns are a way to experimentally measure the reciprocal lattice for a crystal lattice.'
The Laue condition can be rewritten as the following.
Applying the elastic scattering condition (In other words, the incoming and diffracted waves are at the same (temporal) frequency. We can also say that the energy per photon does not change.)
To the above equation, we obtain
The second equation is obtained from the first equation by using .
The result (also ) is an equation for a plane (as the set of all points indicated by satisfying this equation) as its equivalent equation is a plane equation in geometry. Another equivalent equation, that may be easier to understand, is (also ). This indicates the plane that is perpendicular to the straight line between the reciprocal lattice origin and and located at the middle of the line. Such a plane is called Bragg plane. This plane can be understood since for scattering to occur. (It is the Laue condition, equivalent to the Laue equations.) And, the elastic scattering has been assumed so , , and form a rhombus. Each is by definition the wavevector of a plane wave in the Fourier series of a spatial function which periodicity follows the crystal lattice (e.g., the function representing the electronic density of the crystal), wavefronts of each plane wave in the Fourier series is perpendicular to the plane waves wavevector , and these wavefronts are coincident with parallel crystal lattice planes. This means that X-rays are seemingly "reflected" off parallel crystal lattice planes perpendicular at the same angle as their angle of approach to the crystal with respect to the lattice planes; in the elastic light (typically X-ray)-crystal scattering, parallel crystal lattice planes perpendicular to a reciprocal lattice vector for the crystal lattice play as parallel mirrors for light which, together with , incoming (to the crystal) and outgoing (from the crystal by scattering) wavevectors forms a rhombus.'
Since the angle between and is , (Due to the mirror-like scattering, the angle between and is also .) . Recall, with as the light (typically X-ray) wavelength, and with as the distance between adjacent parallel crystal lattice planes and as an integer. With these, we now derive Bragg's law that is equivalent to the Laue equations (also called the Laue condition): | 1 | Crystallography |
Minerals that have the same structure (isomorphic minerals) may have epitaxic relations. An example is albite on microcline . Both these minerals are triclinic, with space group , and with similar unit cell parameters, a = 8.16 Å, b = 12.87 Å, c = 7.11 Å, α = 93.45°, β = 116.4°, γ = 90.28° for albite and a = 8.5784 Å, b = 12.96 Å, c = 7.2112 Å, α = 90.3°, β = 116.05°, γ = 89° for microcline. | 1 | Crystallography |
The perovskite structure is adopted at high pressure by bridgmanite, a silicate with the chemical formula , which is the most common mineral in the Earth's mantle. As pressure increases, the SiO tetrahedral units in the dominant silica-bearing minerals become unstable compared with SiO octahedral units. At the pressure and temperature conditions of the lower mantle, the second most abundant material is likely the rocksalt-structured oxide, periclase.
At the high pressure conditions of the Earths lower mantle, the pyroxene enstatite, MgSiO, transforms into a denser perovskite-structured polymorph; this phase may be the most common mineral in the Earth. This phase has the orthorhombically distorted perovskite structure (GdFeO-type structure) that is stable at pressures from ~24 GPa to ~110 GPa. However, it cannot be transported from depths of several hundred km to the Earths surface without transforming back into less dense materials. At higher pressures, MgSiO perovskite, commonly known as silicate perovskite, transforms to post-perovskite. | 1 | Crystallography |
However, fluctuations that cause the correlations between pairs of atoms to decrease as their separation increases, causes the Bragg peaks in the structure factor of a crystal to broaden. To see how this works, we consider a one-dimensional toy model: a stack of plates with mean spacing . The derivation follows that in chapter 9 of Guinier's textbook. This model has been pioneered by and applied to a number of materials by Hosemann and collaborators over a number of years. Guinier and they termed this disorder of the second kind, and Hosemann in particular referred to this imperfect crystalline ordering as paracrystalline ordering. Disorder of the first kind is the source of the Debye–Waller factor.
To derive the model we start with the definition (in one dimension) of the
To start with we will consider, for simplicity an infinite crystal, i.e., . We will consider a finite crystal with disorder of the second-type below.
For our infinite crystal, we want to consider pairs of lattice sites. For large each plane of an infinite crystal, there are two neighbours planes away, so the above double sum becomes a single sum over pairs of neighbours either side of an atom, at positions and lattice spacings away, times . So, then
where is the probability density function for the separation of a pair of planes, lattice spacings apart. For the separation of neighbouring planes we assume for simplicity that the fluctuations around the mean neighbour spacing of a are Gaussian, i.e., that
and we also assume that the fluctuations between a plane and its neighbour, and between this neighbour and the next plane, are independent. Then is just the convolution of two s, etc. As the convolution of two Gaussians is just another Gaussian, we have that
The sum in is then just a sum of Fourier transforms of Gaussians, and so
for . The sum is just the real part of the sum and so the structure factor of the infinite but disordered crystal is
This has peaks at maxima , where . These peaks have heights
i.e., the height of successive peaks drop off as the order of the peak (and so ) squared. Unlike finite-size effects that broaden peaks but do not decrease their height, disorder lowers peak heights. Note that here we assuming that the disorder is relatively weak, so that we still have relatively well defined peaks. This is the limit , where . In this limit, near a peak we can approximate , with and obtain
which is a Lorentzian or Cauchy function, of FWHM , i.e., the FWHM increases as the square of the order of peak, and so as the square of the wave vector at the peak.
Finally, the product of the peak height and the FWHM is constant and equals , in the limit. For the first few peaks where is not large, this is just the limit. | 1 | Crystallography |
Knowledge of hydration is essential for calculating the masses for many compounds. The reactivity of many salt-like solids is sensitive to the presence of water.
The hydration and dehydration of salts is central to the use of phase-change materials for energy storage. | 1 | Crystallography |
The Avrami equation was applied in cancer biophysics in two aspects. First aspect is connected with tumor growth and cancer cells kinetics, which can be described by the sigmoidal curve. In this context the Avrami function was discussed as an alternative to the widely used Gompertz curve. In the second aspect the Avrami nucleation and growth theory was used together with multi-hit theory of carcinogenesis to show how the cancer cell is created. The number of oncogenic mutations in cellular DNA can be treated as nucleation particles which can transform whole DNA molecule into cancerous one (neoplastic transformation). This model was applied to clinical data of gastric cancer, and shows that Avramis constant n is between 4 and 5 which suggest the fractal geometry of carcinogenic dynamics. Similar findings were published for breast and ovarian cancers, where n'=5.3. | 1 | Crystallography |
The Freundlich equation or Freundlich adsorption isotherm, an adsorption isotherm, is an empirical relationship between the quantity of a gas adsorbed into a solid surface and the gas pressure. The same relationship is also applicable for the concentration of a solute adsorbed onto the surface of a solid and the concentration of the solute in the liquid phase. In 1909, Herbert Freundlich gave an expression representing the isothermal variation of adsorption of a quantity of gas adsorbed by unit mass of solid adsorbent with gas pressure. This equation is known as Freundlich adsorption isotherm or Freundlich adsorption equation. As this relationship is entirely empirical, in the case where adsorption behavior can be properly fit by isotherms with a theoretical basis, it is usually appropriate to use such isotherms instead (see for example the Langmuir and BET adsorption theories). The Freundlich equation is also derived (non-empirically) by attributing the change in the equilibrium constant of the binding process to the heterogeneity of the surface and the variation in the heat of adsorption. | 0 | Chromatography + Titration + pH indicators |
Phenol red (also known as phenolsulfonphthalein or PSP) is a pH indicator frequently used in cell biology laboratories. | 0 | Chromatography + Titration + pH indicators |
When collecting data in the full scan mode, a target range of mass fragments is determined and put into the instruments method. An example of a typical broad range of mass fragments to monitor would be m/z 50 to m/z 400. The determination of what range to use is largely dictated by what one anticipates being in the sample while being cognizant of the solvent and other possible interferences. A MS should not be set to look for mass fragments too low or else one may detect air (found as m/z 28 due to nitrogen), carbon dioxide (m/z' 44) or other possible interference. Additionally if one is to use a large scan range then sensitivity of the instrument is decreased due to performing fewer scans per second since each scan will have to detect a wide range of mass fragments.
Full scan is useful in determining unknown compounds in a sample. It provides more information than SIM when it comes to confirming or resolving compounds in a sample. During instrument method development it may be common to first analyze test solutions in full scan mode to determine the retention time and the mass fragment fingerprint before moving to a SIM instrument method. | 0 | Chromatography + Titration + pH indicators |
The Pearson symbol does not uniquely identify the space group of a crystal structure. For example, both the NaCl structure (space group Fmm) and diamond (space group Fdm) have the same Pearson symbol cF8.
Confusion also arises in the rhombohedral lattice, which is alternatively described in a centred hexagonal (a = b, c, α = β = 90°, γ = 120°) or primitive rhombohedral (a = b = c, α = β = γ) setting. The more commonly used hexagonal setting has 3 translationally equivalent points per unit cell. The Pearson symbol refers to the hexagonal setting in its letter code (hR), but the following figure gives the number of translationally equivalent points in the primitive rhombohedral setting. Examples: hR1 and hR2 are used to designate the Hg and Bi structures respectively.
Because there are many possible structures that can correspond to one Pearson symbol, a prototypical compound may be useful to specify. Examples of how to write this would be hP12-MgZn or cF8-C. Prototypical compounds for particular structures can be found on the Inorganic Crystal Structure Database (ICSD) or on the AFLOW Library of Crystallographic Prototypes. | 1 | Crystallography |
Forensic DNA analysis was first used in 1984. It was developed by Sir Alec Jeffreys, who realized that variation in the genetic sequence could be used to identify individuals and to tell individuals apart from one another. The first application of DNA profiles was used by Jeffreys in a double murder mystery in the small English town of Narborough, Leicestershire, in 1985. A 15-year-old school girl by the name of Lynda Mann was raped and murdered in Carlton Hayes psychiatric hospital. The police did not find a suspect but were able to obtain a semen sample.
In 1986, Dawn Ashworth, 15 years old, was also raped and strangled in the nearby village of Enderby. Forensic evidence showed that both killers had the same blood type. Richard Buckland became the suspect because he worked at Carlton Hayes psychiatric hospital, had been spotted near Dawn Ashworths murder scene and knew unreleased details about the body. He later confessed to Dawns murder but not Lynda's. Jefferys was brought into the case to analyze the semen samples. He concluded that there was no match between the samples and Buckland, who became the first person to be exonerated using DNA. Jefferys confirmed that the DNA profiles were identical for the two murder semen samples. To find the perpetrator, DNA samples from the entire male population, more than 4,000 aged from 17 to 34, of the town were collected. They all were compared to semen samples from the crime. A friend of Colin Pitchfork was heard saying that he had given his sample to the police claiming to be Colin. Colin Pitchfork was arrested in 1987 and it was found that his DNA profile matched the semen samples from the murder.
Because of this case, DNA databases were developed. There is the national (FBI) and international databases as well as the European countries (ENFSI: European Network of Forensic Science Institutes). These searchable databases are used to match crime scene DNA profiles to those already in a database. | 0 | Chromatography + Titration + pH indicators |
A crystal model is a teaching aid used for understanding concepts in crystallography and the morphology of crystals. Models are ideal to learn recognizing symmetry elements in crystals. | 1 | Crystallography |
A feature of the LHPG technique is its high convection speed in the liquid phase due to Marangoni convection. It is possible to see that it spins very fast. Even when it appears to be standing still, it is in fact spinning fast on its axis. | 1 | Crystallography |
A titration curve is a curve in graph the x-coordinate of which represents the volume of titrant added since the beginning of the titration, and the y-coordinate of which represents the concentration of the analyte at the corresponding stage of the titration (in an acid–base titration, the y-coordinate usually represents the pH of the solution).
In an acid–base titration, the titration curve represents the strength of the corresponding acid and base. For a strong acid and a strong base, the curve will be relatively smooth and very steep near the equivalence point. Because of this, a small change in titrant volume near the equivalence point results in a large pH change and many indicators would be appropriate (for instance litmus, phenolphthalein or bromothymol blue).
If one reagent is a weak acid or base and the other is a strong acid or base, the titration curve is irregular and the pH shifts less with small additions of titrant near the equivalence point. For example, the titration curve for the titration between oxalic acid (a weak acid) and sodium hydroxide (a strong base) is pictured. The equivalence point occurs between pH 8-10, indicating the solution is basic at the equivalence point and an indicator such as phenolphthalein would be appropriate. Titration curves corresponding to weak bases and strong acids are similarly behaved, with the solution being acidic at the equivalence point and indicators such as methyl orange and bromothymol blue being most appropriate.
Titrations between a weak acid and a weak base have titration curves which are very irregular. Because of this, no definite indicator may be appropriate and a pH meter is often used to monitor the reaction.
The type of function that can be used to describe the curve is termed a sigmoid function. | 0 | Chromatography + Titration + pH indicators |
Let be primitive translation vectors (shortly called primitive vectors) of a crystal lattice , where atoms are located at lattice points described by with , , and as any integers. (So indicating each lattice point is an integer linear combination of the primitive vectors.)
Let be the wave vector of an incoming (incident) beam or wave toward the crystal lattice , and let be the wave vector of an outgoing (diffracted) beam or wave from . Then the vector , called the scattering vector or transferred wave vector, measures the difference between the incoming and outgoing wave vectors.
The three conditions that the scattering vector must satisfy, called the Laue equations, are the following:
where numbers are integer numbers. Each choice of integers , called Miller indices, determines a scattering vector . Hence there are infinitely many scattering vectors that satisfy the Laue equations as there are infinitely many choices of Miller indices . Allowed scattering vectors form a lattice , called the reciprocal lattice of the crystal lattice , as each indicates a point of . (This is the meaning of the Laue equations as shown below.) This condition allows a single incident beam to be diffracted in infinitely many directions. However, the beams corresponding to high Miller indices are very weak and can't be observed. These equations are enough to find a basis of the reciprocal lattice (since each observed indicates a point of the reciprocal lattice of the crystal under the measurement), from which the crystal lattice can be determined. This is the principle of x-ray crystallography. | 1 | Crystallography |
The reciprocal lattice is easily constructed in one dimension: for particles on a line with a period , the reciprocal lattice is an infinite array of points with spacing . In two dimensions, there are only five Bravais lattices. The corresponding reciprocal lattices have the same symmetry as the direct lattice. 2-D lattices are excellent for demonstrating simple diffraction geometry on a flat screen, as below.
Equations (1)–(7) for structure factor apply with a scattering vector of limited dimensionality and a crystallographic structure factor can be defined in 2-D as .
However, recall that real 2-D crystals such as graphene exist in 3-D. The reciprocal lattice of a 2-D hexagonal sheet that exists in 3-D space in the plane is a hexagonal array of lines parallel to the or axis that extend to and intersect any plane of constant in a hexagonal array of points.
The Figure shows the construction of one vector of a 2-D reciprocal lattice and its relation to a scattering experiment.
A parallel beam, with wave vector is incident on a square lattice of parameter . The scattered wave is detected at a certain angle, which defines the wave vector of the outgoing beam, (under the assumption of elastic scattering, ). One can equally define the scattering vector and construct the harmonic pattern . In the depicted example, the spacing of this pattern coincides to the distance between particle rows: , so that contributions to the scattering from all particles are in phase (constructive interference). Thus, the total signal in direction is strong, and belongs to the reciprocal lattice. It is easily shown that this configuration fulfills Bragg's law. | 1 | Crystallography |
A perovskite is any material with a crystal structure following the formula ABX, which was first discovered as the mineral called perovskite, which consists of calcium titanium oxide (CaTiO). The mineral was first discovered in the Ural mountains of Russia by Gustav Rose in 1839 and named after Russian mineralogist L. A. Perovski (1792–1856). A and B are two positively charged ions (i.e. cations), often of very different sizes, and X is a negatively charged ion (an anion, frequently oxide) that bonds to both cations. The A atoms are generally larger than the B atoms. The ideal cubic structure has the B cation in 6-fold coordination, surrounded by an octahedron of anions, and the A cation in 12-fold cuboctahedral coordination. Additional perovskite forms may exist where either/both the A and B sites have a configuration of A1A2 and/or B1B2 and the X may deviate from the ideal coordination configuration as ions within the A and B sites undergo changes in their oxidation states.
As one of the most abundant structural families, perovskites are found in an enormous number of compounds which have wide-ranging properties, applications and importance. Natural compounds with this structure are perovskite, loparite, and the silicate perovskite bridgmanite. Since the 2009 discovery of perovskite solar cells, which contain methylammonium lead halide perovskites, there has been considerable research interest into perovskite materials. | 1 | Crystallography |
The impact of an ethanol-based universal indicator may seem negligible at first glance. However, in the case of dilute solutions prepared with bidistilled water, this influence becomes readily discernible and measurable. [https://github.com/ddiesing/universal_indicator_conductivity/blob/main/indicator_conc_conduct.csv] | 0 | Chromatography + Titration + pH indicators |
Since the separation of biological molecules such as proteins would be better served by isocratic elution with an aqueous solvent, resolution of HPLC analysis should be tweaked in the area of stationary phases to elute such analytes that may be sensitive to organic solvents. Kanazawa et al. recognized the possibility of changing the LCST parameter through the addition of different moieties. Kanazawa’s group investigated the reversible changes of PNIPAAm once modifying it with a carboxyl end. It was suggested that the modification leads to faster changes in conformation due to the restrictions introduced by the carboxyl group. They attached the carboxyl-terminated PNIPAAm chains to (aminopropyl)silica and used it as packing material for HPLC analysis of steroids. The separation took place under isocratic conditions using pure water as the mobile phase, and controlled the temperature using a water bath. They were able to shift the LCST from 32 °C to 20 °C by making the solution 1M in NaCl concentration. Of the 5 steroids and benzene, only testosterone could be resolved from the other peaks below the LCST (5 °C, LCST=20 °C in 1M NaCl). Above the LCST (25 °C, LCST=20 °C in 1M NaCl), all of the peaks are well resolved, and there is an increasing trend of retention time versus temperature up to 50 °C. | 0 | Chromatography + Titration + pH indicators |
Aromatic polyamides and polyamides are practical compounds due to their temperature resistance, electrical or insulating characteristics, and their mechanical strength. Some of the polyamides and polyimides that can be synthesized by o-Cresophthalein are polycarbonate, polyacrylate, and epoxy-resin.
The diether-diamine 3,3-bis[4-(4-amino-phenoxy)-3-methylphenyl]phthalide, or BNMP, is synthesized by 12 g o-cresophthalein, 11.5 g p-chloronitrobenzene, 5.1 g anhydrous potassium carbonate, and 55 mL of DMF. The compounds should be refluxed together at 160 °C for eight hours. Once it is done and has cooled, it should be mixed with 0.3 L methanol. A precipitate should form and be vacuum filtered to obtain a solid. It should then be washed with water and dried, yielding a yellow product. It should then be recrystallized from glacial acetic acid to yield yellow needles. The product is BNMP. The reaction can go further by combining 15.5 g of BNMP with 0.18 g 10% Pd/C and 50 mL ethanol. They should be stirred at 80 °C. 7 mL of hydrazine monohydrate should be added drop by drop for one hour. The solution should then be mixed for eight hours. It should then be filtered to separated from the Pd/C and concentrated. The concentrated solution should be added to water, and a precipitate should be formed. It should then be vacuum filtered to isolate the solid, yelding 3,3-Bis[4-(4-aminophenoxy)-3-methylphenyl]pthalide, or BAMP, as a white solid. It should then be purified by water and ethanol. | 0 | Chromatography + Titration + pH indicators |
A crystal family is determined by lattices and point groups. It is formed by combining crystal systems that have space groups assigned to a common lattice system. In three dimensions, the hexagonal and trigonal crystal systems are combined into one hexagonal crystal family. | 1 | Crystallography |
Methyl Orange is an azobenzene derivative that can be formed from dimethylaniline and sulfanilic acid through first, a diazonium salt formation with the sulfanilic acid, followed by a nucleophilic attack from the dimethylaniline and rearomatization. | 0 | Chromatography + Titration + pH indicators |
In the geometry of crystal nets, one can treat edges as line segments. For example, in a crystal net, it is presumed that edges do not “collide” in the sense that when treating them as line segments, they do not intersect. Several polyhedral constructions can be derived from crystal nets. For example, a vertex figure can be obtained by subdividing each edge (treated as a line segment) by the insertion of subdividing points, and then the vertex figure of a given vertex is the convex hull of the adjacent subdividing points (i.e., the convex polyhedron whose vertices are the adjacent subdividing points).
Another polyhedral construction is to determine the neighborhood of a vertex in the crystal net. One application is to define an energy function as a (possibly weighted) sum of squares of distances from vertices to their neighbors, and with respect to this energy function, the net is in equilibrium (with respect to this energy function) if each vertex is positioned at the centroid of its neighborhood, this is the basis of the crystal net identification program SYSTRE. (mathematicians
use the term ``harmonic realiaztions" instead of ``crystal nets in equilibrium positions" because the positions are characterized by the discrete Laplace equation; they also introduced the notion of standard realizations which are special harmonic realizations characterized by a certain minimal principle as well;see ). Some crystal nets are isomorphic to crystal nets in equilibrium positions, and since an equilibrium position is a normal form, the crystal net isomorphism problem (i.e., the query whether two given crystal nets are isomorphic as graphs; not to be confused with crystal isomorphism) is readily computed even though, as a subsumption of the graph isomorphism problem, it is apparently computationally difficult in general. | 1 | Crystallography |
Several points of high symmetry are of special interest – these are called critical points.
Other lattices have different types of high-symmetry points. They can be found in the illustrations below. | 1 | Crystallography |
Although anthocyanins have been shown to have antioxidant properties in vitro, there is no evidence for antioxidant effects in humans after consuming foods rich in anthocyanins. Unlike controlled test-tube conditions, the fate of anthocyanins in vivo shows they are poorly conserved (less than 5%), with most of what is absorbed existing as chemically modified metabolites that are excreted rapidly. The increase in antioxidant capacity of blood seen after the consumption of anthocyanin-rich foods may not be caused directly by the anthocyanins in the food, but instead by increased uric acid levels derived from metabolizing flavonoids (anthocyanin parent compounds) in the food. It is possible that metabolites of ingested anthocyanins are reabsorbed in the gastrointestinal tract from where they may enter the blood for systemic distribution and have effects as smaller molecules.
In a 2010 review of scientific evidence concerning the possible health benefits of eating foods claimed to have "antioxidant properties" due to anthocyanins, the European Food Safety Authority concluded that 1) there was no basis for a beneficial antioxidant effect from dietary anthocyanins in humans, 2) there was no evidence of a cause-and-effect relationship between the consumption of anthocyanin-rich foods and protection of DNA, proteins, and lipids from oxidative damage, and 3) there was no evidence generally for consumption of anthocyanin-rich foods having any "antioxidant", "anti-cancer", "anti-aging", or "healthy aging" effects. | 0 | Chromatography + Titration + pH indicators |
By considering the arrangement of atoms relative to each other, their coordination numbers, interatomic distances, types of bonding, etc., it is possible to form a general view of the structures and alternative ways of visualizing them. | 1 | Crystallography |
Congo red is an organic compound, the sodium salt of 3,3′-([1,1′-biphenyl]-4,4′-diyl)bis(4-aminonaphthalene-1-sulfonic acid). It is an azo dye. Congo red is water-soluble, yielding a red colloidal solution; its solubility is greater in organic solvents. The use of Congo red in the textile industry has long been abandoned, primarily because of its carcinogenic properties, but it is still used for histological staining. | 0 | Chromatography + Titration + pH indicators |
Mant et al. reported that HILIC/CEX offered unique selectivity, stronger separation power and wider range of applications compared to RPLC for peptide separations. | 0 | Chromatography + Titration + pH indicators |
A number of possible routes can be used to prepare crystal violet. The original procedure developed by the German chemists Kern and Caro involved the reaction of dimethylaniline with phosgene to give 4,4′-bis(dimethylamino)benzophenone (Michler's ketone) as an intermediate. This was then reacted with additional dimethylaniline in the presence of phosphorus oxychloride and hydrochloric acid.
The dye can also be prepared by the condensation of formaldehyde and dimethylaniline to give a leuco dye:
:CHO + 3 CHN(CH) → CH(CHN(CH)) + HO
Second, this colourless compound is oxidized to the coloured cationic form (hereafter with oxygen, but a typical oxidizing agent is manganese dioxide, MnO):
:CH(CHN(CH)) + HCl + O → [C(CHN(CH))]Cl + HO | 0 | Chromatography + Titration + pH indicators |
Acridine has been obtained as eight polymorphs and aripiprazole has nine. The record for the largest number of well-characterised polymorphs is held by a compound known as ROY. Glycine crystallizes as both monoclinic and hexagonal crystals. Polymorphism in organic compounds is often the result of conformational polymorphism. | 1 | Crystallography |
DiffractGUI allows for an automated analysis of diffraction patterns and high-resolution images of single crystal or limited number of crystallites. It is able to determine crystal orientation, index individual diffraction spots and measure interplanar angles and distances in picometric precision. The input image may depict:
* selected area diffraction pattern,
* high-resolution image,
* nanodiffraction pattern or
* convergent beam electron diffraction.
The input image is processed in the following steps:
# Preprocessing with accordance to the settings and image nature (resolution and noise reduction, Fourier transform for direct space images etc.).
# Detection of diffraction reflections at various scales (difference of Gaussians typically used for spot detection, Hough transform for CBED disk detection).
# The strongest detections are selected across the scale space.
# A regular lattice is fit to the set of the strongest detections using RANSAC algorithm.
# Lengths and angles of the lattice basis vectors are measured.
# Crystal lattice orientation is determined and diffraction reflections are identified using theoretical parameters of the sample material.
Compared to human evaluation, considers tens or even hundreds of diffraction spots at once and, therefore, can localize the pattern with sub-pixel precision. | 1 | Crystallography |
The internal diameter (ID) of an HPLC column is an important parameter. It can influence the detection response when reduced due to the reduced lateral diffusion of the solute band. It can also affect the separation selectivity, when flow rate and injection volumes are not scaled down or up proportionally to the smaller or larger diameter used, both in the isocratic and in gradient modes. It determines the quantity of analyte that can be loaded onto the column. Larger diameter columns are usually seen in preparative applications, such as the purification of a drug product for later use. Low-ID columns have improved sensitivity and lower solvent consumption in the recent ultra-high performance liquid chromatography (UHPLC).
Larger ID columns (over 10 mm) are used to purify usable amounts of material because of their large loading capacity.
Analytical scale columns (4.6 mm) have been the most common type of columns, though narrower columns are rapidly gaining in popularity. They are used in traditional quantitative analysis of samples and often use a UV-Vis absorbance detector.
Narrow-bore columns (1–2 mm) are used for applications when more sensitivity is desired either with special UV-vis detectors, fluorescence detection or with other detection methods like liquid chromatography-mass spectrometry
Capillary columns (under 0.3 mm) are used almost exclusively with alternative detection means such as mass spectrometry. They are usually made from fused silica capillaries, rather than the stainless steel tubing that larger columns employ. | 0 | Chromatography + Titration + pH indicators |
The units of the structure-factor amplitude depend on the incident radiation. For X-ray crystallography they are multiples of the unit of scattering by a single electron (2.82 m); for neutron scattering by atomic nuclei the unit of scattering length of m is commonly used.
The above discussion uses the wave vectors and . However, crystallography often uses wave vectors and . Therefore, when comparing equations from different sources, the factor may appear and disappear, and care to maintain consistent quantities is required to get correct numerical results. | 1 | Crystallography |