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Previous analysis focused only on diffraction from a perfectly flat surface of a crystal surface. However, non-flat surfaces add additional diffraction conditions to RHEED analysis.
Streaked or elongated spots are common to RHEED patterns. As Fig 3 shows, the reciprocal lattice rods with the lowest orders intersect the Ewald sphere at very small angles, so the intersection between the rods and sphere is not a singular point if the sphere and rods have thickness. The incident electron beam diverges and electrons in the beam have a range of energies, so in practice, the Ewald sphere is not infinitely thin as it is theoretically modeled. The reciprocal lattice rods have a finite thickness as well, with their diameters dependent on the quality of the sample surface. Streaks appear in the place of perfect points when broadened rods intersect the Ewald sphere. Diffraction conditions are fulfilled over the entire intersection of the rods with the sphere, yielding elongated points or ‘streaks’ along the vertical axis of the RHEED pattern. In real cases, streaky RHEED patterns indicate a flat sample surface while the broadening of the streaks indicate small area of coherence on the surface.
Surface features and polycrystalline surfaces add complexity or change RHEED patterns from those from perfectly flat surfaces. Growing films, nucleating particles, crystal twinning, grains of varying size and adsorbed species add complicated diffraction conditions to those of a perfect surface. Superimposed patterns of the substrate and heterogeneous materials, complex interference patterns and degradation of the resolution are characteristic of complex surfaces or those partially covered with heterogeneous materials. | 1 | Crystallography |
Time resolved crystallography utilizes X-ray crystallography imaging to visualize reactions in four dimensions (x, y, z and time). This enables the studies of dynamical changes that occur in for example enzymes during their catalysis. The time dimension is incorporated by triggering the reaction of interest in the crystal prior to X-ray exposure, and then collecting the diffraction patterns at different time delays. In order to study these dynamical properties of macromolecules three criteria must be met;
* The macromolecule must be biologically active in the crystalline state
* It must be possible to trigger the reaction in the crystal
* The intermediate of interest must be detectable, i.e. it must have a reasonable amount of concentration in the crystal (preferably over 25%).
This has led to the development of several techniques that can be divided into two groups, the pump-probe method and diffusion-trapping methods. | 1 | Crystallography |
A thermometric titration is one of a number of instrumental titration techniques where endpoints can be located accurately and precisely without a subjective interpretation on the part of the analyst as to their location. Enthalpy change is arguably the most fundamental and universal property of chemical reactions, so the observation of temperature change is a natural choice in monitoring their progress. It is not a new technique, with possibly the first recognizable thermometric titration method reported early in the 20th century (Bell and Cowell, 1913). In spite of its attractive features, and in spite of the considerable research that has been conducted in the field and a large body of applications that have been developed; it has been until now an under-utilized technique in the critical area of industrial process and quality control. Automated potentiometric titration systems have pre-dominated in this area since the 1970s. With the advent of cheap computers able to handle the powerful thermometric titration software, development has now reached the stage where easy to use automated thermometric titration systems can in many cases offer a superior alternative to potentiometric titrimetry. | 0 | Chromatography + Titration + pH indicators |
Not only volume crystals can be imaged by topography, but also crystalline layers on a foreign substrate. For very thin layers, the scattering volume and thus the diffracted intensities are very low. In these cases, topographic imaging is therefore a rather demanding task, unless incident beams with very high intensities are available. | 1 | Crystallography |
Environmental UCMs result from highly degraded petroleum hydrocarbons and once formed they can stay largely unchanged in sediments for many years. For example, in 1969 a diesel oil spill contaminated saltmarsh sediment within Wild Harbor River, US; by 1973 only a baseline hump was observed, which remained largely unchanged within the anaerobic sediment for the next 30 years. In a study of the potential for UCM-dominated oil to be further degraded, it was concluded that even using bacteria specifically adapted for complex UCM hydrocarbons in conjunction with nutrient enrichment, biodegradation rates would still be relatively slow. Bacterial degradation of hydrocarbons is complex and will depend on environmental conditions (e.g. aerobic or anaerobic, temperature, nutrient availability, available species of bacteria etc.). | 0 | Chromatography + Titration + pH indicators |
Polytypes are a special case of polymorphs, where multiple close-packed crystal structures differ in one dimension only. Polytypes have identical close-packed planes, but differ in the stacking sequence in the third dimension perpendicular to these planes. Silicon carbide (SiC) has more than 170 known polytypes, although most are rare. All the polytypes of SiC have virtually the same density and Gibbs free energy. The most common SiC polytypes are shown in Table 1.
Table 1: Some polytypes of SiC.
A second group of materials with different polytypes are the transition metal dichalcogenides, layered materials such as molybdenum disulfide (MoS). For these materials the polytypes have more distinct effects on material properties, e.g. for MoS, the 1T polytype is metallic in character, while the 2H form is more semiconducting.
Another example is tantalum disulfide, where the common 1T as well as 2H polytypes occur, but also more complex mixed coordination types such as 4Hb and 6R, where the trigonal prismatic and the octahedral geometry layers are mixed. Here, the 1T polytype exhibits a charge density wave, with distinct influence on the conductivity as a function of temperature, while the 2H polytype exhibits superconductivity.
ZnS and CdI are also polytypical. It has been suggested that this type of polymorphism is due to kinetics where screw dislocations rapidly reproduce partly disordered sequences in a periodic fashion. | 1 | Crystallography |
Transformation and annealing twinning takes place when a cooling crystal experiences a displacive polymorphic transition. For example, leucite has an isometric crystal structure above about , but becomes tetragonal below this temperature. Any one of the three original axes of a crystal can become the long axis when this phase change takes place. Twinning results when different parts of the crystal break their isometric symmetry along a different choice of axis. This is typically polysynthetic twinning, which enables the crystal to maintain its isometric shape by averaging out the displacement in each direction. This produces a pseudomorphic crystal that appears to have isometric symmetry. Potassium feldspar likewise experiences polysynthetic twinning as it transforms from a monoclinic structure (orthoclase) to a triclinic structure (microcline) on slow cooling. | 1 | Crystallography |
The micelle velocity is defined by:
where is the electrophoretic velocity of a micelle.
The retention time of a given sample should depend on the capacity factor, :
where is the total number of moles of solute in the micelle and is the total moles in the aqueous phase. The retention time of a solute should then be within the range:
Charged analytes have a more complex interaction in the capillary because they exhibit electrophoretic mobility, engage in electrostatic interactions with the micelle, and participate in hydrophobic partitioning.
The fraction of the sample in the aqueous phase, , is given by:
where is the migration velocity of the solute. The value can also be expressed in terms of the capacity factor:
Using the relationship between velocity, tube length from the injection end to the detector cell (), and retention time, , and , a relationship between the capacity factor and retention times can be formulated:
The extra term enclosed in parentheses accounts for the partial mobility of the hydrophobic phase in MEKC. This equation resembles an expression derived for in conventional packed bed chromatography:
A rearrangement of the previous equation can be used to write an expression for the retention factor:
From this equation it can be seen that all analytes that partition strongly into the micellar phase (where is essentially ∞) migrate at the same time, . In conventional chromatography, separation of similar compounds can be improved by gradient elution. In MEKC, however, techniques must be used to extend the elution range to separate strongly retained analytes.
Elution ranges can be extended by several techniques including the use of organic modifiers, cyclodextrins, and mixed micelle systems. Short-chain alcohols or acetonitrile can be used as organic modifiers that decrease and to improve the resolution of analytes that co-elute with the micellar phase. These agents, however, may alter the level of the EOF. Cyclodextrins are cyclic polysaccharides that form inclusion complexes that can cause competitive hydrophobic partitioning of the analyte. Since analyte-cyclodextrin complexes are neutral, they will migrate toward the cathode at a higher velocity than that of the negatively charged micelles. Mixed micelle systems, such as the one formed by combining SDS with the non-ionic surfactant Brij-35, can also be used to alter the selectivity of MEKC. | 0 | Chromatography + Titration + pH indicators |
In a highly basic solution, phenolphthalein's slow change from pink to colorless as it is converted to its Ph(OH) form is used in chemistry classes for the study of reaction kinetics. | 0 | Chromatography + Titration + pH indicators |
Another approach to evaluation of ion suppression is to make a comparison between:
* Detector response of calibration standard (either aqueous or in another suitable solvent) - This gives the best case scenario for detector response, i.e. under conditions of zero ion suppression
* Pre-prepared sample matrix spiked with an identical concentration of analyte - This demonstrates the effect of ion suppression
* Detector response of sample matrix spiked with an identical concentration of analyte and subjected to the usual sample preparation procedure - This can demonstrate the difference between any signal loss due to under-recovery during the sample preparation process and true ion suppression | 0 | Chromatography + Titration + pH indicators |
* [http://www.piercenet.com/method/desalting-gel-filtration#gelfiltration Animation of desalting using gel filtration chromatography] | 0 | Chromatography + Titration + pH indicators |
In the sintering of ceramic materials, abnormal grain growth is often viewed as an undesirable phenomenon because rapidly growing grains may lower the hardness of the bulk material through Hall-Petch-type effects. However, the controlled introduction of dopants to bring about controlled AGG may be used to impart fibre-toughening in ceramic materials. Additionally, AGG is undesirable in piezoelectric ceramics, as it may degrade the piezoelectric effect. | 1 | Crystallography |
HPLC detectors fall into two main categories: universal or selective. Universal detectors typically measure a bulk property (e.g., refractive index) by measuring a difference of a physical property between the mobile phase and mobile phase with solute while selective detectors measure a solute property (e.g., UV-Vis absorbance) by simply responding to the physical or chemical property of the solute. HPLC most commonly uses a UV-Vis absorbance detector; however, a wide range of other chromatography detectors can be used. A universal detector that complements UV-Vis absorbance detection is the charged aerosol detector (CAD). A kind of commonly utilized detector includes refractive index detectors, which provide readings by measuring the changes in the refractive index of the eluant as it moves through the flow cell. In certain cases, it is possible to use multiple detectors, for example LCMS normally combines UV-Vis with a mass spectrometer.
When used with an electrochemical detector (ECD) the HPLC-ECD selectively detects neurotransmitters such as: norepinephrine, dopamine, serotonin, glutamate, GABA, acetylcholine and others in neurochemical analysis research applications. The HPLC-ECD detects neurotransmitters to the femtomolar range. Other methods to detect neurotransmitters include liquid chromatography-mass spectrometry, ELISA, or radioimmunoassays. | 0 | Chromatography + Titration + pH indicators |
The basis vectors of unit cell U can be transformed to basis vectors of supercell S by linear transformation
where is a transformation matrix. All elements should be integers with (with the transformation preserves volume). For example, the matrix
transforms a primitive cell to body-centered. Another particular case of the transformation is a diagonal matrix (i.e., ). This called diagonal supercell expansion and can be represented as repeating of the initial cell over crystallographic axes of the initial cell. | 1 | Crystallography |
At the beginning of the run, a mixture of solutes to be separated is applied to the column, under conditions selected to promote high retention. The higher-affinity solutes are preferentially retained near the head of the column, with the lower-affinity solutes moving farther downstream. The fastest moving component begins to form a pure zone downstream. The other components also begin to form zones, but the continued supply of the mixed feed at head of the column prevents full resolution. | 0 | Chromatography + Titration + pH indicators |
A system is said to present annealed disorder when some parameters entering its definition are random variables, but whose evolution is related to that of the degrees of freedom defining the system. It is defined in opposition to quenched disorder, where the random variables may not change their values.
Systems with annealed disorder are usually considered to be easier to deal with mathematically, since the average on the disorder and the thermal average may be treated on the same footing. | 1 | Crystallography |
If the chromatographic separation can be modified to prevent coelution of suppressing species then other approaches need not be considered. The effect of chromatographic modification may be evaluated using the detector response monitoring under constant infusion approach described previously. | 0 | Chromatography + Titration + pH indicators |
A solution containing the analyte, A, in the presence of some conductive buffer. If an electrolytic potential is applied to the solution through a working electrode, then the measured current depends (in part) on the concentration of the analyte. Measurement of this current can be used to determine the concentration of the analyte directly; this is a form of amperometry. However, the difficulty is that the measured current depends on several other variables, and it is not always possible to control all of them adequately. This limits the precision of direct amperometry.
If the potential applied to the working electrode is sufficient to reduce the analyte, then the concentration of analyte close to the working electrode will decrease. More of the analyte will slowly diffuse into the volume of solution close to the working electrode, restoring the concentration. If the potential applied to the working electrode is great enough (an overpotential), then the concentration of analyte next to the working electrode will depend entirely on the rate of diffusion. In such a case, the current is said to be diffusion limited. As the analyte is reduced at the working electrode, the concentration of the analyte in the whole solution will very slowly decrease; this depends on the size of the working electrode compared to the volume of the solution.
What happens if some other species which reacts with the analyte (the titrant) is added? (For instance, chromate ions can be added to oxidize lead ions.) After a small quantity of the titrant (chromate) is added, the concentration of the analyte (lead) has decreased due to the reaction with chromate. The current from the reduction of lead ion at the working electrode will decrease. The addition is repeated, and the current decreases again. A plot of the current against volume of added titrant will be a straight line.
After enough titrant has been added to react completely with the analyte, the excess titrant may itself be reduced at the working electrode. Since this is a different species with different diffusion characteristics (and different half-reaction), the slope of current versus added titrant will have a different slope after the equivalence point. This change in slope marks the equivalence point, in the same way that, for instance, the sudden change in pH marks the equivalence point in an acid–base titration.
The electrode potential may also be chosen such that the titrant is reduced, but the analyte is not. In this case, the presence of excess titrant is easily detected by the increase in current above background (charging) current. | 0 | Chromatography + Titration + pH indicators |
The (oral, mouse) is 80 mg/kg. Rats fed malachite green experience "a dose-related increase in liver DNA adducts" along with lung adenomas. Leucomalachite green causes an "increase in the number and severity of changes". As leucomalachite green is the primary metabolite of malachite green and is retained in fish muscle much longer, most human dietary intake of malachite green from eating fish would be in the leuco form. During the experiment, rats were fed up to 543 ppm of leucomalachite green, an extreme amount compared to the average 5 ppb discovered in fish. After a period of two years, an increase in lung adenomas in male rats was discovered but no incidences of liver tumors. Therefore, it could be concluded that malachite green caused carcinogenic symptoms, but a direct link between malachite green and liver tumor was not established. | 0 | Chromatography + Titration + pH indicators |
In four dimensions, there are 64 Bravais lattices. Of these, 23 are primitive and 41 are centered. Ten Bravais lattices split into enantiomorphic pairs. | 1 | Crystallography |
An emulator for the APEXC series has been developed by MESS. They describe its functioning as follows:
<blockquote>The APEXC is an incredibly simple machine.
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Instruction and data words are always 32 bits long. The processor uses integer arithmetic with 2's complement representation. Addresses are 10 bits long. The APEXC has no RAM, except for a 32-bit accumulator and a 32-bit data register (used along with the 32-bit accumulator to implement 64-bit shift instructions and hold the 64-bit result of a multiplication). Instructions and data are stored in two magnetic drums, for a total of 32 circular magnetic tracks of 32 words. Since the rotation rate is 3750rpm (62.5 rotations per second), the program execution speed can go from as high as the theoretical maximum of 1 kIPS to lower than 100IPS if program instructions and data are not contiguous. Nowadays, many say a pocket calculator is faster.
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One oddity is that there is no program counter: each machine instruction includes the address of the next instruction. This design may sound weird, but it is the only way to achieve optimal performance with this cylinder-based memory.
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The machine code is made of 15 instructions only, namely addition, subtraction, multiplication, load (3 variants), store (2 variants), conditional branch, right arithmetic bit shift, right bit rotation, punched-card input, punched-card output, machine stop, and bank-switching (which is never used on the APEXC, since it only has 1024 words of storage, and addresses are 10-bit-long). A so-called vector mode enables to repeat the same operation 32 times with 32 successive memory locations. Note the lack of bitwise and/or/xor and division. Also, note the lack of indirect addressing modes: dynamic modification of opcodes is the only way one may simulate it.
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Another oddity is that the memory bus and the ALU are 1-bit-wide. There is a 64 kHz bit-clock and a 2 kHz word-clock, and each word memory and arithmetic operation is decomposed into 32 1-bit memory and arithmetic operations: this takes 32 bit cycles, for a total of 1 word cycle.
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The processor is fairly efficient: most instructions take only 2 word cycles (1 for fetch, 1 for read operand and execute), with the exception of stores, shifts and multiplications. The APEXC CPU qualifies as RISC; there is no other adequate word.
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Note there is no read-only memory (ROM), and therefore no bootstrap loader or default start-up program whatsoever. It is believed that no executive or operating system was ever written for the APEXC, although there were subroutine libraries of sorts for common arithmetic, I/O and debug tasks.
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Operation of the machine is normally done through a control panel which allows the user to start, stop and resume the central processing unit, and to alter registers and memory when the CPU is stopped. When starting the machine, the address of the first instruction of the program to be executed must be entered in the control panel, then the run switch must be pressed. Most programs end with a stop instruction, which enables the operator to check the state of the machine, possibly run some post-mortem debugging procedures (a core dump routine is described in an APEXC programming book), then enter the address of another program and run it.
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Two I/O devices were supported: a paper tape reader, and a paper tape puncher. The puncher output could be fed to a printer (teletyper) unit when desirable. Printer output is emulated and is displayed on screen. Tape input was either computer-generated by the APEXC, or hand-typed with a special 32-key keyboard (each tape row had 5 data holes ( | 1 | Crystallography |
The crystallographic restriction theorem can be formulated in terms of isometries of Euclidean space. A set of isometries can form a group. By a discrete isometry group we will mean an isometry group that maps each point to a discrete subset of R, i.e. the orbit of any point is a set of isolated points. With this terminology, the crystallographic restriction theorem in two and three dimensions can be formulated as follows.
:For every discrete isometry group in two- and three-dimensional space which includes translations spanning the whole space, all isometries of finite order are of order 1, 2, 3, 4 or 6.
Isometries of order n include, but are not restricted to, n-fold rotations. The theorem also excludes S, S, D, and D (see point groups in three dimensions), even though they have 4- and 6-fold rotational symmetry only.
Rotational symmetry of any order about an axis is compatible with translational symmetry along that axis.
The result in the table above implies that for every discrete isometry group in four- and five-dimensional space which includes translations spanning the whole space, all isometries of finite order are of order 1, 2, 3, 4, 5, 6, 8, 10, or 12.
All isometries of finite order in six- and seven-dimensional space are of order 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 24 or 30 . | 1 | Crystallography |
Grain boundaries are interfaces where crystals of different orientations meet. A grain boundary is a single-phase interface, with crystals on each side of the boundary being identical except in orientation. The term "crystallite boundary" is sometimes, though rarely, used. Grain boundary areas contain those atoms that have been perturbed from their original lattice sites, dislocations, and impurities that have migrated to the lower energy grain boundary.
Treating a grain boundary geometrically as an interface of a single crystal cut into two parts, one of which is rotated, we see that there are five variables required to define a grain boundary. The first two numbers come from the unit vector that specifies a rotation axis. The third number designates the angle of rotation of the grain. The final two numbers specify the plane of the grain boundary (or a unit vector that is normal to this plane).
Grain boundaries disrupt the motion of dislocations through a material, so reducing crystallite size is a common way to improve strength, as described by the Hall–Petch relationship. Since grain boundaries are defects in the crystal structure they tend to decrease the electrical and thermal conductivity of the material. The high interfacial energy and relatively weak bonding in most grain boundaries often makes them preferred sites for the onset of corrosion and for the precipitation of new phases from the solid. They are also important to many of the mechanisms of creep.
Grain boundaries are in general only a few nanometers wide. In common materials, crystallites are large enough that grain boundaries account for a small fraction of the material. However, very small grain sizes are achievable. In nanocrystalline solids, grain boundaries become a significant volume fraction of the material, with profound effects on such properties as diffusion and plasticity. In the limit of small crystallites, as the volume fraction of grain boundaries approaches 100%, the material ceases to have any crystalline character, and thus becomes an amorphous solid. | 1 | Crystallography |
CBED was first introduced in 1939 by Kossel and Möllenstedt. The development of the Field Emission Gun (FEG) in the 1970s, the Scanning Transmission Electron Microscopy (STEM), energy filtering devices and so on, made possible smaller probe diameters and larger convergence angles, and all this made CBED more popular. In the seventies, CBED was being used for the determination of the point group and space group symmetries by Goodman and Lehmpfuh, and Buxton, and starting in 1985, CBED was used by Tanaka et al. for studying crystals structure. | 1 | Crystallography |
Before exploring Rietveld refinement, it is necessary to establish a greater understanding of powder diffraction data and what information is encoded therein in order to establish a notion of how to create a model of a diffraction pattern, which is of course necessary in Rietveld refinement. A typical diffraction pattern can be described by the positions, shapes, and intensities of multiple Bragg reflections. Each of the three mentioned properties encodes some information relating to the crystal structure, the properties of the sample, and the properties of the instrumentation. Some of these contributions are shown in Table 1, below.
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The structure of a powder pattern is essentially defined by instrumental parameters and two crystallographic parameters: unit cell dimensions, and atomic content and coordination. So, a powder pattern model can be constructed as follows:
# Establish peak positions: Bragg peak positions are established from Bragg's law using the wavelength and d-spacing for a given unit cell.
# Determine peak intensity: Intensity depends on the structure factor, and can be calculated from the structural model for individual peaks. This requires knowledge of the specific atomic coordination in the unit cell and geometrical parameters.
# Peak shape for individual Bragg peaks: Represented by functions of the FWHM (which vary with Bragg angle) called the peak shape functions. Realistically ab initio modelling is difficult, and so empirically selected peak shape functions and parameters are used for modelling.
# Sum: The individual peak shape functions are summed and added to a background function, leaving behind the resultant powder pattern.
It is easy to model a powder pattern given the crystal structure of a material. The opposite, determining the crystal structure from a powder pattern, is much more complicated. A brief explanation of the process follows, though it is not the focus of this article.
To determine structure from a powder diffraction pattern the following steps should be taken. First, Bragg peak positions and intensities should be found by fitting to a peak shape function including background. Next, peak positions should be indexed and used to determine unit cell parameters, symmetry, and content. Third, peak intensities determine space group symmetry and atomic coordination. Finally, the model is used to refine all crystallographic and peak shape function parameters. To do this successfully, there is a requirement for excellent data which means good resolution, low background, and a large angular range. | 1 | Crystallography |
Long-range order characterizes physical systems in which remote portions of the same sample exhibit correlated behavior.
This can be expressed as a correlation function, namely the spin-spin correlation function:
where s is the spin quantum number and x is the distance function within the particular system.
This function is equal to unity when and decreases as the distance increases. Typically, it decays exponentially to zero at large distances, and the system is considered to be disordered. But if the correlation function decays to a constant value at large then the system is said to possess long-range order. If it decays to zero as a power of the distance then it is called quasi-long-range order (for details see Chapter 11 in the textbook cited below. See also Berezinskii–Kosterlitz–Thouless transition). Note that what constitutes a large value of is understood in the sense of asymptotics. | 1 | Crystallography |
Chloridometers are used to determine the concentration of chloride ions in biological fluids. For example, fish plasma chloride ion concentration is measured to gauge the effects of stress on osmoregulation in aquacultures. A small quantity of plasma (10 μL) combined with an acid reagent results in a chemical reaction that ultimately provides a concentration measure of chloride ions in meq/L.
Because they require alternating current, chloridometers are not portable and are better suited to a "bench-top location". This may necessitate freezing biological fluid specimens collected in the field for later analysis.
Chloridometers represent the most common use of coulometry in clinical biochemistry. | 0 | Chromatography + Titration + pH indicators |
A primitive cell is a unit cell that contains exactly one lattice point. For unit cells generally, lattice points that are shared by cells are counted as of the lattice points contained in each of those cells; so for example a primitive unit cell in three dimensions which has lattice points only at its eight vertices is considered to contain of each of them. An alternative conceptualization is to consistently pick only one of the lattice points to belong to the given unit cell (so the other lattice points belong to adjacent unit cells).
The primitive translation vectors , , span a lattice cell of smallest volume for a particular three-dimensional lattice, and are used to define a crystal translation vector
where , , are integers, translation by which leaves the lattice invariant. That is, for a point in the lattice , the arrangement of points appears the same from as from .
Since the primitive cell is defined by the primitive axes (vectors) , , , the volume of the primitive cell is given by the parallelepiped from the above axes as
Usually, primitive cells in two and three dimensions are chosen to take the shape parallelograms and parallelepipeds, with an atom at each corner of the cell. This choice of primitive cell is not unique, but volume of primitive cells will always be given by the expression above. | 1 | Crystallography |
The Le Bail method extracts intensities (I) from powder diffraction data. This is done in order to find intensities that are suitable to determine the atomic structure of a crystalline material and to refine the unit cell and has the added advantage of checking phase-purity. Generally, the intensities of powder diffraction data are complicated by overlapping diffraction peaks with similar d-spacings. For the Le Bail method, the unit cell and the approximate space group of the sample must be predetermined because they are included as a part of the fitting technique. The algorithm involves refining the unit cell, the profile parameters, and the peak intensities to match the measured powder diffraction pattern. It is not necessary to know the structural factor and associated structural parameters, since they are not considered in this type of analysis. Le Bail can be used to find phase transitions in high pressure and temperature experiments. It generally provides a quick method to refine the unit cell, which allows better experimental planning. Le Bail analysis provides a more reliable estimate for the intensities of allowed reflections for different crystal symmetries.
Crystallographic structural determination can be accomplished in multiple ways. Le Bail technique is relevant for diffraction studies that involve using a radiation source, which may be neutron or synchrotron, to collect a high resolution, high quality powder diffraction profile. Initially, peak positions are found in the data. Next, the pattern is indexed in order to determine the unit cell or lattice parameters. Then, space group determination follows based on symmetry and the presence or absence of certain reflections. Then, either Le Bail or Pawley technique may be used to extract intensities and refine the unit cell. | 1 | Crystallography |
Due to their high photoluminescence quantum efficiencies, perovskites may find use in light-emitting diodes (LEDs). Although the stability of perovskite LEDs is not yet as good as III-V or organic LEDs, there is ongoing research to solve this problem, such as incorporating organic molecules or potassium dopants in perovskite LEDs. Perovskite-based printing ink can be used to produce OLED display and quantum dot display panels. | 1 | Crystallography |
Aurin may cause eye, skin, and respiratory tract irritation. Ingestion and inhalation should be avoided.
Aurin was reported to have endocrine disruptor chemical (EDC) properties. | 0 | Chromatography + Titration + pH indicators |
Only the CHO+ ions formed from the ionization of carbon compounds are detected. Thus, the non-methane byproducts of the reactions are not detected by the FID.
Since every compound goes through the catalyst bed in the reactor, it can alter certain substances that might be harmful or negatively affect the efficiency and durability of the FID into safer forms. For instance, cyanide is catalytically changed into methane, water, and nitrogen. | 0 | Chromatography + Titration + pH indicators |
The principle of the Rietveld method is to minimize a function which analyzes the difference between a calculated profile and the observed data . Rietveld defined such an equation as:
where is the statistical weight and is an overall scale factor such that . | 1 | Crystallography |
Certain nonlinear optical phenomena such as the electro-optic effect cause a variation of a medium's permittivity tensor when an external electric field is applied, proportional (to lowest order) to the strength of the field. This causes a rotation of the principal axes of the medium and alters the behaviour of light travelling through it; the effect can be used to produce light modulators.
In response to a magnetic field, some materials can have a dielectric tensor that is complex-Hermitian; this is called a gyro-magnetic or magneto-optic effect. In this case, the principal axes are complex-valued vectors, corresponding to elliptically polarized light, and time-reversal symmetry can be broken. This can be used to design optical isolators, for example.
A dielectric tensor that is not Hermitian gives rise to complex eigenvalues, which corresponds to a material with gain or absorption at a particular frequency. | 1 | Crystallography |
Tairus (, a portmanteau of Тайско (Thai) and Русский (Russian)) is a synthetic gemstone manufacturer. It was formed in 1989 as part of Mikhail Gorbachev's perestroika initiative to establish a joint venture between the Russian Academy of Sciences and Tairus Created Gems Co Ltd. of Bangkok, Thailand. Today Tairus is a major supplier of hydrothermally grown gemstones to the jewellery industry. Later, Tairus became a privately held enterprise, operating out of its Bangkok distribution hub under the trade name Tairus, owned by Tairus Created Gems Co Ltd. of Bangkok, Thailand.
In the beginning, the team was led by the scientist and developer of the hydrothermal process, the late Alexander Lebedev, whose name was kept secret by the Soviet regime for many years, and Walter Barshai, who was appointed to be the Chairman of the Board of the Joint Venture Tairus. Their objective was to grow and to supply emeralds, rubies, sapphires, alexandrite and other gems to the jewelry industry. The driving force was late Academician Nikolai Dobretsov, former President of the Siberian Branch of the Russian Academy of Sciences. Tairus has achieved many scientific breakthroughs. For example, the development of the hydrothermally grown corundum, aquamarine and the development of a revolutionary process of horizontal crystallization for growing corundum (ruby), chrysoberyl and alexandrite.
After many years of development, scientists at Tairus had succeeded to commercially grow emeralds in a laboratory environment that resemble in color and have gemological properties that “overlap natural emeralds from various localities, especially those of low alkali-bearing stones from Colombia” ([https://docs.wixstatic.com/ugd/31202c_ba81f0c232274bd6b1183aff1242b3ff.pdf The Journal of Gemmology, 2006, Vol. 30, Nos 1/2, 59-74]). | 1 | Crystallography |
Faster GC methods have shorter times but Kovats indexes of the compounds may be conserved if proper method translation is applied.
Temperatures of the temperature program stay the same, but ramps and times change when using a smaller column or faster carrier gas.
If column dimensions Length×diameter×film are divided by 2 and gas velocity is doubled by using H2 in place of Helium, the hold times must be divided by 4 and the ramps must be multiplied by 4 to keep the same index and the same retention temperature for the same compound analyzed. Method translation rules are incorporated in some chromatography data systems. | 0 | Chromatography + Titration + pH indicators |
Aqueous normal-phase chromatography (ANP) is a chromatographic technique that involves the mobile phase compositions and polarities between reversed-phase chromatography (RP) and normal-phase chromatography (NP), while the stationary phases are polar. | 0 | Chromatography + Titration + pH indicators |
The discovery of paper chromatography in 1943 by Martin and Synge provided, for the first time, the means of surveying constituents of plants and for their separation and identification. Erwin Chargaff credits in Weintraub's history of the man the 1944 article by Consden, Gordon and Martin. There was an explosion of activity in this field after 1945. | 0 | Chromatography + Titration + pH indicators |
There are disadvantages to GPC, however. First, there is a limited number of peaks that can be resolved within the short time scale of the GPC run. Also, as a technique GPC requires around at least a 10% difference in molecular weight for a reasonable resolution of peaks to occur. In regards to polymers, the molecular masses of most of the chains will be too close for the GPC separation to show anything more than broad peaks. Another disadvantage of GPC for polymers is that filtrations must be performed before using the instrument to prevent dust and other particulates from ruining the columns and interfering with the detectors. Although useful for protecting the instrument, there is the possibility of the pre-filtration of the sample removing higher molecular weight sample before it can be loaded on the column. Another possibility to overcome these issues is the separation by field-flow fractionation (FFF). | 0 | Chromatography + Titration + pH indicators |
The reds, purples, and their blended combinations responsible for autumn foliage are derived from anthocyanins. Unlike carotenoids, anthocyanins are not present in the leaf throughout the growing season, but are produced actively, toward the end of summer. They develop in late summer in the sap of leaf cells, resulting from complex interactions of factors inside and outside the plant. Their formation depends on the breakdown of sugars in the presence of light as the level of phosphate in the leaf is reduced. Orange leaves in autumn result from a combination of anthocyanins and carotenoids.
Anthocyanins are present in approximately 10% of tree species in temperate regions, although in certain areas such as New England, up to 70% of tree species may produce anthocyanins. | 0 | Chromatography + Titration + pH indicators |
By using CBED, the following information can be obtained:
*parameters of the crystal lattice, sample thickness
*strain distribution
*defects such as stacking faults, dislocations, grain boundaries, three-dimensional deformations, lattice displacements
*crystal symmetry information - by looking at the symmetries that appear in the CBED disks, point group and space group determination are performed.
*Diagnosis of aberrations in the electron probe that limit resolution, through analysis of CBED patterns (i.e. Ronchigrams) acquired on amorphous specimens. | 1 | Crystallography |
In chemical ionization (CI) a reagent gas, typically methane or ammonia is introduced into the mass spectrometer. Depending on the technique (positive CI or negative CI) chosen, this reagent gas will interact with the electrons and analyte and cause a soft ionization of the molecule of interest. A softer ionization fragments the molecule to a lower degree than the hard ionization of EI. One of the main benefits of using chemical ionization is that a mass fragment closely corresponding to the molecular weight of the analyte of interest is produced.
In positive chemical ionization (PCI) the reagent gas interacts with the target molecule, most often with a proton exchange. This produces the species in relatively high amounts.
In negative chemical ionization (NCI) the reagent gas decreases the impact of the free electrons on the target analyte. This decreased energy typically leaves the fragment in great supply. | 0 | Chromatography + Titration + pH indicators |
Coward was born on 2 July 1885 in Blackburn, Lancashire. She studied Botany and graduated M.Sc. from University of Manchester. After a few years, she joined University College London to study biochemistry and perform research under J. C. Drummond on Vitamin A, paving the way for her to be nominated to the Fellow of the Chemical Society in 1923. | 0 | Chromatography + Titration + pH indicators |
Ordinarily, Miller indices are always integers by definition, and this constraint is physically significant. To understand this, suppose that we allow a plane (abc) where the Miller "indices" a, b and c (defined as above) are not necessarily integers.
If a, b and c have rational ratios, then the same family of planes can be written in terms of integer indices (hkℓ) by scaling a, b and c appropriately: divide by the largest of the three numbers, and then multiply by the least common denominator. Thus, integer Miller indices implicitly include indices with all rational ratios. The reason why planes where the components (in the reciprocal-lattice basis) have rational ratios are of special interest is that these are the lattice planes: they are the only planes whose intersections with the crystal are 2d-periodic.
For a plane (abc) where a, b and c have irrational ratios, on the other hand, the intersection of the plane with the crystal is not periodic. It forms an aperiodic pattern known as a quasicrystal. This construction corresponds precisely to the standard "cut-and-project" method of defining a quasicrystal, using a plane with irrational-ratio Miller indices. (Although many quasicrystals, such as the Penrose tiling, are formed by "cuts" of periodic lattices in more than three dimensions, involving the intersection of more than one such hyperplane.) | 1 | Crystallography |
The CRFs in thin layer chromatography characterize the equal-spreading of the spots. The ideal case, when the RF of the spots are uniformly distributed in <0,1> range (for example 0.25,0.5 and 0.75 for three solutes) should be characterized as the best situation possible.
The simplest criteria are and product (Wang et al., 1996). They are the smallest difference between sorted RF values, or product of such differences.
Another function is the multispot response function (MRF) as developed by De Spiegeleer et al.{Analytical Chemistry (1987):59(1),62-64} It is based also of differences product. This function always lies between 0 and 1. When two RF values are equal, it is equal to 0, when all RF values are equal-spread, it is equal to 1. The L and U values – upper and lower limit of RF – give possibility to avoid the band region.
The last example of coefficient sensitive to minimal distance between spots is Retention distance (Komsta et al., 2007)
The second group are criteria insensitive for minimal difference between RF values (if two compounds are not separated, such CRF functions will not indicate it). They are equal to zero in equal-spread state increase when situation is getting worse.
There are:
Separation response (Bayne et al., 1987)
Performance index (Gocan et al., 1991)
Informational entropy (Gocan et al., 1991, second reference)
Retention uniformity (Komsta et al., 2007)
In all above formulas, n is the number of compounds separated, R are the Retention factor of the compounds sorted in non-descending order, R = 0 and R = 1. | 0 | Chromatography + Titration + pH indicators |
Let be an orientation-preserving rigid motion of R. The set of these transformations is a subgroup of Euclidean motions known as the special Euclidean group SE(3). These rigid motions are defined by transformations of x in R given by
consisting of a three-dimensional rotation A followed by a translation by the vector d.
A three-dimensional rotation A has a unique axis that defines a line L. Let the unit vector along this line be S so that the translation vector d can be resolved into a sum of two vectors, one parallel and one perpendicular to the axis L, that is,
In this case, the rigid motion takes the form
Now, the orientation preserving rigid motion D* = A(x) + d transforms all the points of R so that they remain in planes perpendicular to L. For a rigid motion of this type there is a unique point c in the plane P perpendicular to L through 0, such that
The point C can be calculated as
because d does not have a component in the direction of the axis of A.
A rigid motion D* with a fixed point must be a rotation of around the axis L through the point c. Therefore, the rigid motion
consists of a rotation about the line L followed by a translation by the vector d in the direction of the line L.
Conclusion: every rigid motion of R is the result of a rotation of R about a line L followed by a translation in the direction of the line. The combination of a rotation about a line and translation along the line is called a screw motion. | 1 | Crystallography |
The predecessor of modern countercurrent chromatography theory and practice was countercurrent distribution (CCD). The theory of CCD was described in the 1930s by Randall and Longtin. Archer Martin and Richard Laurence Millington Synge developed the methodology further during the 1940s. Finally, Lyman C. Craig introduced the Craig countercurrent distribution apparatus in 1944 which made CCD practical for laboratory work. CCD was used to separate a wide variety of useful compounds for several decades. | 0 | Chromatography + Titration + pH indicators |
The sublimation sandwich method (also called the sublimation sandwich process and the sublimation sandwich technique) is a kind of physical vapor deposition used for creating man-made crystals. Silicon carbide is the most common crystal grown this way, though others crystals may also be created with it (notably gallium nitride).
In this method, the environment around a single crystal or a polycrystalline plate is filled with vapor heated to between 1600°C and 2100°C-- changes to this environment can affect the gas phase stoichiometry. The source-to-crystal distance is kept between 0.02-0.03mm (very low). Parameters that can affect crystal growth include source-to-substrate distance, temperature gradient, and the presence of tantalum for gathering excess carbon. High growth rates are the result of small source-to-seed distances combined with a large heat flux onto a small amount of source material with no more than a moderate temperature difference between the substrate and the source (0.5-10°C). The growth of large boules, however, remains quite difficult using this method, and it is better suited to the creation of epitaxial films with uniform polytype structures. Ultimately, samples with a thickness of up to 500µm can be produced using this method. | 1 | Crystallography |
The primitive unit cell for the body-centered cubic crystal structure contains several fractions taken from nine atoms (if the particles in the crystal are atoms): one on each corner of the cube and one atom in the center. Because the volume of each of the eight corner atoms is shared between eight adjacent cells, each BCC cell contains the equivalent volume of two atoms (one central and one on the corner).
Each corner atom touches the center atom. A line that is drawn from one corner of the cube through the center and to the other corner passes through 4r, where r is the radius of an atom. By geometry, the length of the diagonal is a. Therefore, the length of each side of the BCC structure can be related to the radius of the atom by
Knowing this and the formula for the volume of a sphere, it becomes possible to calculate the APF as follows: | 1 | Crystallography |
It is used as a pH indicator and as a tracking dye for DNA agarose gel electrophoresis. It can be used in its free acid form (light brown solid), or as a sodium salt (dark green solid). It is also an inhibitor of the prostaglandin E transport protein. Additional applications include use in sol-gel matrices, the detection of ammonia, and the measurement of albumin in human plasma and serum. | 0 | Chromatography + Titration + pH indicators |
The primary goal of crystallography is to determine the three dimensional arrangement of atoms in a crystalline material. While historically, x-ray crystallography has been the predominant experimental method used to solve crystal structures ab initio, the advantages of precession electron diffraction make it one of the preferred methods of electron crystallography. | 1 | Crystallography |
Red HE-3B or Reactive Red 120 has a formula of CHClNOS and a molecular weight of 1338.1 g/mol, containing two monochlorotriazine rings. It is highly soluble in water. The dehydrogenases binding ability of Red HE-3B is greater to NADP+ dependent dehydrogenases than NAD+ dependent dehydrogenases, vice versa for Cibacron Blue F3G-A. It can be used to purify enterotoxins A, B, and C from Staphylococcus aureus using Procion Red HE-3B on sepharose, eluting out with 60 mM and 150 mM phosphate. | 0 | Chromatography + Titration + pH indicators |
In chromatography, resolution is a measure of the separation of two peaks of different retention time t in a chromatogram. | 0 | Chromatography + Titration + pH indicators |
In the low- limit, as the system is probed over large length scales, the structure factor contains thermodynamic information, being related to the isothermal compressibility of the liquid by the compressibility equation: | 1 | Crystallography |
Ion-exchange chromatography (IEC) or ion chromatography (IC) is an analytical technique for the separation and determination of ionic solutes in aqueous samples from environmental and industrial origins such as metal industry, industrial waste water, in biological systems, pharmaceutical samples, food, etc. Retention is based on the attraction between solute ions and charged sites bound to the stationary phase. Solute ions charged the same as the ions on the column are repulsed and elute without retention, while solute ions charged oppositely to the charged sites of the column are retained on it. Solute ions that are retained on the column can be eluted from it by changing the mobile phase composition, such as increasing its salt concentration and pH or increasing the column temperature, etc.
Types of ion exchangers include polystyrene resins, cellulose and dextran ion exchangers (gels), and controlled-pore glass or porous silica gel. Polystyrene resins allow cross linkage, which increases the stability of the chain. Higher cross linkage reduces swerving, which increases the equilibration time and ultimately improves selectivity. Cellulose and dextran ion exchangers possess larger pore sizes and low charge densities making them suitable for protein separation.
In general, ion exchangers favor the binding of ions of higher charge and smaller radius.
An increase in counter ion (with respect to the functional groups in resins) concentration reduces the retention time, as it creates a strong competition with the solute ions. A decrease in pH reduces the retention time in cation exchange while an increase in pH reduces the retention time in anion exchange. By lowering the pH of the solvent in a cation exchange column, for instance, more hydrogen ions are available to compete for positions on the anionic stationary phase, thereby eluting weakly bound cations.
This form of chromatography is widely used in the following applications: water purification, preconcentration of trace components, ligand-exchange chromatography, ion-exchange chromatography of proteins, high-pH anion-exchange chromatography of carbohydrates and oligosaccharides, and others. | 0 | Chromatography + Titration + pH indicators |
Bilbao Crystallographic Server is an open access website offering online crystallographic database and programs aimed at analyzing, calculating and visualizing problems of structural and mathematical crystallography, solid state physics and structural chemistry. Initiated in 1997 by the Materials Laboratory of the Department of Condensed Matter Physics at the University of the Basque Country, Bilbao, Spain, the Bilbao Crystallographic Server is developed and maintained by academics. | 1 | Crystallography |
In X-ray crystallography, a difference density map or Fo–Fc map shows the spatial distribution of the difference between the measured electron density of the crystal and the electron density explained by the current model.
A way to compute this map has been formulated for cyro-EM. | 1 | Crystallography |
Density functional theory seeks to solve for an approximate form of the electronic density of a system. In general, atoms are split into ionic cores and valence electrons. The ionic cores (nuclei plus non-bonding electrons) are assumed to be stable and are treated as a single object. Each valence electron is treated separately. Thus, for example, a Lithium atom is treated as two bodies – Li+ and e- – while oxygen is treated as three bodies, namely O and 2e.
The “true” ground state of a crystal system is generally unsolvable. However, the variational theorem assures us that any guess as to the electronic state function of a system will overestimate the ground state energy. Thus, by beginning with a suitably parametrized guess and minimizing the energy with respect to each of those parameters, an extremely accurate prediction may be made. The question as to what one's initial guess should be is a topic of active research.
In the large majority of crystal systems, electronic relaxation times are orders of magnitude shorter than ionic relaxation times. Thus, an iterative scheme is adopted. First, the ions are considered fixed and the electronic state is relaxed by considering the ionic and electron-electron pair potentials. Next, the electronic states are considered fixed and the ions are allowed to move under the influence of the electronic and ion-ion pair potentials. When the decrease in energy between two iterative steps is sufficiently small, the structure of the crystal is considered solved. | 1 | Crystallography |
Centrifugal partition chromatography does not uses any solid stationary phase, so it guarantees a cost-effective separation for the highest industrial levels. As opposed to countercurrent chromatography, it is possible to get very high flow rates (for example 10 liters / min) with active stationary phase ratio of >80%, which guarantees good separation and high productivity. As in centrifugal partition chromatography, material is dissolved, and loaded the column in mass / volume units, loading capability can be much higher than standard solid-liquid chromatographic techniques, where material is loaded to the active surface area of the stationary phase, which takes up less than 10% of the column.
Industrial instrument like Gilson (Armen Instrument), Kromaton (Rousselet Robatel) and RotaChrom Technologies (RotaChrom) differ from laboratory scale instruments by the applicable flow rate with satisfactory stationary phase retention (70–90%). Industrial instruments have flow rates of multiple liter / minutes, while able to purify materials from 10 kg to tonnes per month.
Operating the production scale equipment requires industrial volume solvent preparation (mixer/settler) and solvent recovery equipment. | 0 | Chromatography + Titration + pH indicators |
Ion-exchange chromatography separates molecules based on their respective charged groups. Ion-exchange chromatography retains analyte molecules on the column based on coulombic (ionic) interactions. The ion exchange chromatography matrix consists of positively and negatively charged ions. Essentially, molecules undergo electrostatic interactions with opposite charges on the stationary phase matrix. The stationary phase consists of an immobile matrix that contains charged ionizable functional groups or ligands. The stationary phase surface displays ionic functional groups (R-X) that interact with analyte ions of opposite charge. To achieve electroneutrality, these immobilized charges couple with exchangeable counterions in the solution. Ionizable molecules that are to be purified, compete with these exchangeable counterions, for binding to the immobilized charges on the stationary phase. These ionizable molecules are retained or eluted based on their charge. Initially, molecules that do not bind or bind weakly to the stationary phase are first to be washed away. Altered conditions are needed for the elution of the molecules that bind to the stationary phase. The concentration of the exchangeable counterions, which competes with the molecules for binding, can be increased, or the pH can be changed to affect the ionic charge of the eluent or the solute. A change in pH affects the charge on the particular molecules and, therefore, alter their binding. When reducing the net charge of the solute's molecules, they start eluting out. This way, such adjustments can be used to release the proteins of interest. Additionally, concentration of counterions can be gradually varied to affect the retention of the ionized molecules, thus separate them. This type of elution is called gradient elution. On the other hand, step elution can be used, in which the concentration of counterions are varied in steps. This type of chromatography is further subdivided into cation exchange chromatography and anion-exchange chromatography. Positively charged molecules bind to cation exchange resins, while negatively charged molecules bind to anion exchange resins. The ionic compound consisting of the cationic species M+ and the anionic species B− can be retained by the stationary phase.
Cation exchange chromatography retains positively charged cations because the stationary phase displays a negatively charged functional group:
Anion exchange chromatography retains anions using positively charged functional group:
Note that the ion strength of either C+ or A− in the mobile phase can be adjusted to shift the equilibrium position, thus retention time.
The ion chromatogram shows a typical chromatogram obtained with an anion exchange column. | 0 | Chromatography + Titration + pH indicators |
The relationship between fractional and Cartesian coordinates can be described by the matrix transformation :
Similarly, the Cartesian coordinates can be converted back to fractional coordinates using the matrix transformation : | 1 | Crystallography |
Transition metal sulfates form a variety of hydrates, each of which crystallizes in only one form. The sulfate group often binds to the metal, especially for those salts with fewer than six aquo ligands. The heptahydrates, which are often the most common salts, crystallize as monoclinic and the less common orthorhombic forms. In the heptahydrates, one water is in the lattice and the other six are coordinated to the ferrous center. Many of the metal sulfates occur in nature, being the result of weathering of mineral sulfides. Many monohydrates are known. | 1 | Crystallography |
After the last solute has been eluted, it is necessary to strip the displacer from the column. Since the displacer was chosen for high affinity, this can pose a challenge. On reverse-phase materials, a wash with a high percentage of organic solvent may suffice. Large pH shifts are also often employed. One effective strategy is to remove the displacer by chemical reaction; for instance if hydrogen ion was used as displacer it can be removed by reaction with hydroxide, or a polyvalent metal ion can be removed by reaction with a chelating agent. For some matrices, reactive groups on the stationary phase can be titrated to temporarily eliminate the binding sites, for instance weak-acid ion exchangers or chelating resins can be converted to the protonated form. For gel-type ion exchangers, selectivity reversal at very high ionic strength can also provide a solution. Sometimes the displacer is specifically designed with a titratable functional group to shift its affinity. After the displacer is washed out, the column is washed as needed to restore it to its initial state for the next run. | 0 | Chromatography + Titration + pH indicators |
Columnar structures were first studied in botany due to their diverse appearances in plants. D'Arcy Thompson analysed such arrangement of plant parts around the stem in his book "On Growth and Form" (1917). But they are also of interest in other biological areas, including bacteria, viruses, microtubules, and the notochord of the zebra fish.
One of the largest flowers where the berries arrange in a regular cylindrical form is the titan arum. This flower can be up to 3m in height and is natively solely found in western Sumatra and western Java.
On smaller length scales, the berries of the Arum maculatum form a columnar structure in autumn. Its berries are similar to that of the corpse flower, since the titan arum is its larger relative. However, the cuckoo-pint is much smaller in height (height ≈ 20 cm). The berry arrangement varies with the stem to berry size.
Another plant that can be found in many gardens of residential areas is the Australian bottlebrush. It assembles its seed capsules around a branch of the plant. The structure depends on the seed capsule size to branch size. | 1 | Crystallography |
By 1982 the technology was sufficiently advanced for the technique to be called "high-speed" countercurrent chromatography (HSCCC). Peter Carmeci initially commercialized the PC Inc. Ito Multilayer Coil Separator/Extractor which utilized a single bobbin (onto which the coil is wound) and a counterbalance, plus a set of "flying leads" which are tubing that connect the bobbins. Dr. Walter Conway & others later evolved the bobbin design such that multiple coils, even coils of different tubing sizes, could be placed on the single bobbin. Edward Chou later evolved and commercialized a triple bobbin design as the Pharmatech CCC which had a de-twist mechanism for leads between the three bobbins. The Quattro CCC released in 1993 further evolved the commercially available instruments by utilizing a novel mirror image, twin bobbin design that did not need the de-twist mechanism of the Pharmatech between the multiple bobbins, so could still accommodate multiple bobbins on the same instrument. Hydrodynamic CCC are now available with up to 4 coils per instrument. These coils can be in PTFE, PEEK, PVDF, or stainless steel tubing. The 2, 3 or 4 coils can all be of the same bore to facilitate "2D" CCC (see below). The coils may be connected in series to lengthen the coil and increase the capacity, or the coils may be linked in parallel so that 2, 3, or 4 separations may be done simultaneously. The coils can also be of different sizes, on one instrument, ranging from 1 to 6 mm on one instrument, thus allowing a single instrument to optimize from mg to kilos per day. More recently instrument derivatives have been offered with rotating seals for various hydrodynamic CCC designs, instead of flying leads, either as custom or standard options. | 0 | Chromatography + Titration + pH indicators |
Originally, n was held to have an integer value between 1 and 4, which reflected the nature of the transformation in question. In the derivation above, for example, the value of 4 can be said to have contributions from three dimensions of growth and one representing a constant nucleation rate. Alternative derivations exist, where n has a different value.
If the nuclei are preformed, and so all present from the beginning, the transformation is only due to the 3-dimensional growth of the nuclei, and n has a value of 3.
An interesting condition occurs when nucleation occurs on specific sites (such as grain boundaries or impurities) that rapidly saturate soon after the transformation begins. Initially, nucleation may be random, and growth unhindered, leading to high values for n (3 or 4). Once the nucleation sites are consumed, the formation of new particles will cease.
Furthermore, if the distribution of nucleation sites is non-random, then the growth may be restricted to 1 or 2 dimensions. Site saturation may lead to n values of 1, 2 or 3 for surface, edge and point sites respectively. | 1 | Crystallography |
Experimentally it was determined that extent of gas adsorption varies directly with pressure, and then it directly varies with pressure raised to the power until saturation pressure is reached. Beyond that point, the rate of adsorption saturates even after applying higher pressure. Thus, the Freundlich adsorption isotherm fails at higher pressure. | 0 | Chromatography + Titration + pH indicators |
With hexagonal and rhombohedral lattice systems, it is possible to use the Bravais–Miller system, which uses four indices (h k i ℓ) that obey the constraint
: h + k + i = 0.
Here h, k and ℓ are identical to the corresponding Miller indices, and i is a redundant index.
This four-index scheme for labeling planes in a hexagonal lattice makes permutation symmetries apparent. For example, the similarity between (110) ≡ (110) and (10) ≡ (110) is more obvious when the redundant index is shown.
In the figure at right, the (001) plane has a 3-fold symmetry: it remains unchanged by a rotation of 1/3 (2/3 rad, 120°). The [100], [010] and the [0] directions are really similar. If S is the intercept of the plane with the [0] axis, then
: i = 1/S.
There are also ad hoc schemes (e.g. in the transmission electron microscopy literature) for indexing hexagonal lattice vectors (rather than reciprocal lattice vectors or planes) with four indices. However they don't operate by similarly adding a redundant index to the regular three-index set.
For example, the reciprocal lattice vector (hkℓ) as suggested above can be written in terms of reciprocal lattice vectors as . For hexagonal crystals this may be expressed in terms of direct-lattice basis-vectors a, a and a as
Hence zone indices of the direction perpendicular to plane (hkℓ) are, in suitably normalized triplet form, simply . When four indices are used for the zone normal to plane (hkℓ), however, the literature often uses instead. Thus as you can see, four-index zone indices in square or angle brackets sometimes mix a single direct-lattice index on the right with reciprocal-lattice indices (normally in round or curly brackets) on the left.
And, note that for hexagonal interplanar distances, they take the form | 1 | Crystallography |
From 1943 on, Booth started working on the determination of crystal structures using X-ray diffraction data. The computations involved were extremely tedious and there was ample incentive for automating the process and he developed an analogue computer to compute the reciprocal spacings of the diffraction pattern.
In 1947, along with his collaborator and future spouse Kathleen Britten, he spent a few months with von Neumann's team, which was the leading edge in computer research at the time. | 1 | Crystallography |
Anthocyanins may be used as pH indicators because their color changes with pH; they are red or pink in acidic solutions (pH < 7), purple in neutral solutions (pH ≈ 7), greenish-yellow in alkaline solutions (pH > 7), and colorless in very alkaline solutions, where the pigment is completely reduced. | 0 | Chromatography + Titration + pH indicators |
There are several ways to retrieve the lost phases. The phase problem must be solved in x-ray crystallography, neutron crystallography, and electron crystallography.
Not all of the methods of phase retrieval work with every wavelength (x-ray, neutron, and electron) used in crystallography. | 1 | Crystallography |
The use of a solvent gradient is very well developed in column chromatography but is less common in CCC. A solvent gradient is produced by increasing (or decreasing) the polarity of the mobile phase during the separation to achieve optimal resolution across a wider range of polarities. For example, a methanol-water mobile phase gradient may be employed using heptane as the stationary phase. This is not possible with all biphasic solvent systems, due to excessive loss of stationary phase created by disruption the equilibrium conditions within the column. Gradients may either be produced in steps, or continuously. | 0 | Chromatography + Titration + pH indicators |
The absorbance pattern responsible for the red color of anthocyanins may be complementary to that of green chlorophyll in photosynthetically active tissues such as young Quercus coccifera leaves. It may protect the leaves from attacks by herbivores that may be attracted by green color. | 0 | Chromatography + Titration + pH indicators |
The art of cutting a gem is an exacting procedure performed on a faceting machine. The ideal product of facet cutting is a gemstone that displays a pleasing balance of internal reflections of light known as brilliance, strong and colorful dispersion which is commonly referred to as "fire", and brightly colored flashes of reflected light known as scintillation. Typically transparent to translucent stones are faceted, although opaque materials may occasionally be faceted as the luster of the gem will produce appealing reflections. Pleonaste (black spinel) and black diamond are examples of opaque faceted gemstones. | 1 | Crystallography |
The word "titration" descends from the French word titrer (1543), meaning the proportion of gold or silver in coins or in works of gold or silver; i.e., a measure of fineness or purity. Tiltre became titre, which thus came to mean the "fineness of alloyed gold", and then the "concentration of a substance in a given sample". In 1828, the French chemist Joseph Louis Gay-Lussac first used titre as a verb (titrer), meaning "to determine the concentration of a substance in a given sample".
Volumetric analysis originated in late 18th-century France. François-Antoine-Henri Descroizilles (fr) developed the first burette (which was similar to a graduated cylinder) in 1791. Gay-Lussac developed an improved version of the burette that included a side arm, and invented the terms "pipette" and "burette" in an 1824 paper on the standardization of indigo solutions. The first true burette was invented in 1845 by the French chemist Étienne Ossian Henry (1798–1873). A major improvement of the method and popularization of volumetric analysis was due to Karl Friedrich Mohr, who redesigned the burette into a simple and convenient form, and who wrote the first textbook on the topic, Lehrbuch der chemisch-analytischen Titrirmethode (Textbook of analytical chemistry titration methods), published in 1855. | 0 | Chromatography + Titration + pH indicators |
The spatial resolution achievable in topographic images can be limited by one or several of three factors:
the resolution (grain or pixel size) of the detector, the experimental geometry, and intrinsic diffraction effects.
First, the spatial resolution of an image can obviously not be better than the grain size (in the case of film) or the pixel size (in the case of digital detectors) with which it was recorded. This is the reason why topography requires high-resolution X-ray films or CCD cameras with the smallest pixel sizes available today. Secondly, resolution can be additionally blurred by a geometric projection effect. If one point of the sample is a "hole" in an otherwise opaque mask, then the X-ray source, of finite lateral size S, is imaged through the hole onto a finite image domain given by the formula
where I is the spread of the image of one sample point in the image plane, D is the source-to-sample distance, and d is the sample-to-image distance. The ratio S/D corresponds to the angle (in radians) under which the source appears from the position of the sample (the angular source size, equivalent to the incident divergence at one sample point). The achievable resolution is thus best for small sources, large sample distances, and small detector distances. This is why the detector (film) needed to be placed very close to the sample in the early days of topography; only at synchrotrons, with their small S and (very) large D, could larger values of d finally be afforded, introducing much more flexibility into topography experiments.
Thirdly, even with perfect detectors and ideal geometric conditions, the visibility of special contrast features, such as the images of single dislocations, can be additionally limited by diffraction effects.
A dislocation in a perfect crystal matrix gives rise to contrast only in those regions where the local orientation of the crystal lattice differs from average orientation by more than about the Darwin width of the Bragg reflection used. A quantitative description is provided by the dynamical theory of X-ray diffraction. As a result, and somehow counter-intuitively, the widths of dislocation images become narrower when the associated rocking curves are large. Thus, strong reflections of low diffraction order are particularly appropriate for topographic imaging. They permit topographists to obtain narrow, well-resolved images of dislocations, and to separate single dislocations even when the dislocation density in a material is rather high. In more unfavourable cases (weak, high-order reflections, higher photon energies), dislocation images become broad, diffuse, and overlap for high and medium dislocation densities. Highly ordered, strongly diffracting materials – like minerals or semiconductors – are generally unproblematic, whereas e.g. protein crystals are particularly challenging for topographic imaging.
Apart from the Darwin width of the reflection, the width of single dislocation images may additionally depend on the Burgers vector of the dislocation, i.e. both its length and its orientation (relative to the scattering vector), and, in plane wave topography, on the angular departure from the exact Bragg angle. The latter dependence follows a reciprocity law, meaning that dislocations images become narrower inversely as the angular distance grows. So-called weak beam conditions are thus favourable in order to obtain narrow dislocation images. | 1 | Crystallography |
In general, a geometric lattice is an infinite, regular array of vertices (points) in space, which can be modelled vectorially as a Bravais lattice. Some lattices may be skew, which means that their primary lines may not necessarily be at right angles. In reciprocal space, a reciprocal lattice is defined as the set of wavevectors of plane waves in the Fourier series of any function whose periodicity is compatible with that of an initial direct lattice in real space. Equivalently, a wavevector is a vertex of the reciprocal lattice if it corresponds to a plane wave in real space whose phase at any given time is the same (actually differs by with an integer ) at every direct lattice vertex.
One heuristic approach to constructing the reciprocal lattice in three dimensions is to write the position vector of a vertex of the direct lattice as , where the are integers defining the vertex and the are linearly independent primitive translation vectors (or shortly called primitive vectors) that are characteristic of the lattice. There is then a unique plane wave (up to a factor of negative one), whose wavefront through the origin contains the direct lattice points at and , and with its adjacent wavefront (whose phase differs by or from the former wavefront passing the origin) passing through . Its angular wavevector takes the form , where is the unit vector perpendicular to these two adjacent wavefronts and the wavelength must satisfy , means that is equal to the distance between the two wavefronts. Hence by construction and .
Cycling through the indices in turn, the same method yields three wavevectors with , where the Kronecker delta equals one when and is zero otherwise. The comprise a set of three primitive wavevectors or three primitive translation vectors for the reciprocal lattice, each of whose vertices takes the form , where the are integers. The reciprocal lattice is also a Bravais lattice as it is formed by integer combinations of the primitive vectors, that are , , and in this case. Simple algebra then shows that, for any plane wave with a wavevector on the reciprocal lattice, the total phase shift between the origin and any point on the direct lattice is a multiple of (that can be possibly zero if the multiplier is zero), so the phase of the plane wave with will essentially be equal for every direct lattice vertex, in conformity with the reciprocal lattice definition above. (Although any wavevector on the reciprocal lattice does always take this form, this derivation is motivational, rather than rigorous, because it has omitted the proof that no other possibilities exist.)
The Brillouin zone is a primitive cell (more specifically a Wigner–Seitz cell) of the reciprocal lattice, which plays an important role in solid state physics due to Bloch's theorem. In pure mathematics, the dual space of linear forms and the dual lattice provide more abstract generalizations of reciprocal space and the reciprocal lattice. | 1 | Crystallography |
There was only one proven polymorph Form I of aspirin, though the existence of another polymorph was debated since the 1960s, and one report from 1981 reported that when crystallized in the presence of aspirin anhydride, the diffractogram of aspirin has weak additional peaks. Though at the time it was dismissed as mere impurity, it was, in retrospect, Form II aspirin.
Form II was reported in 2005, found after attempted co-crystallization of aspirin and levetiracetam from hot acetonitrile.
In form I, pairs of aspirin molecules form centrosymmetric dimers through the acetyl groups with the (acidic) methyl proton to carbonyl hydrogen bonds. In form II, each aspirin molecule forms the same hydrogen bonds, but with two neighbouring molecules instead of one. With respect to the hydrogen bonds formed by the carboxylic acid groups, both polymorphs form identical dimer structures. The aspirin polymorphs contain identical 2-dimensional sections and are therefore more precisely described as polytypes.
Pure Form II aspirin could be prepared by seeding the batch with aspirin anhydrate in 15% weight. | 1 | Crystallography |
The fundamental resolution equation is used in chromatography to help relate adjustable chromatographic parameters to resolution, and is as follows:
R = [N/4][(α-1)/α][k/(1+k)], where
N = Number of theoretical plates
α = Selectivity Term = k/k
The [N/4] term is the column factor, the [(α-1)/α] term is the thermodynamic factor, and the [k/(1+k)] term is the retention factor. The 3 factors are not completely independent, but they are very close, and can be treated as such.
So what does this mean? It means that to increase resolution of two peaks on a chromatogram, one of the three terms of the equation need to be modified.
1) N can be increased by lengthening the column (least effective, as doubling the column will get a 2 or 1.44x increase in resolution).
2) Increasing k' also helps. This can be done by lowering the column temperature in G.C., or by choosing a weaker mobile phase in L.C. (moderately effective)
3) Changing α is the most effective way of increasing resolution. This can be done by choosing a stationary phase that has a greater difference between k and k. It can also be done in L.C. by using pH to invoke secondary equilibria (if applicable).
The fundamental resolution equation is derived as follows:
For two closely spaced peaks, ω = ω, and σ = σ
so R = (t - t)/ω = (t - t)/4σ
Where t and t are the retention times of two separate peaks.
Since N = [(t)/σ], then σ = t/ N
Using substitution, R = N[(t - t)/4t] = (N/4)(1 - t/t)
Now using the following equations and solving for t and t
k = (t - t)/t ; t = t(k + 1)
k = (t - t)/t ; t = t(k + 1)
Substituting again and you get:
R = [N/4][1 - (k + 1)/(k + 1] = [N/4][(k - k)/(1 + k')]
And finally substituting once more α = k/k and you get the Fundamental Resolution Equation:
R = [N/4][(α-1)/α][k/(1+k)] | 0 | Chromatography + Titration + pH indicators |
By recording the ionic positions at each time step, one can observe how far, on average, each ion has moved from its original position. The mean squared displacement of each ion type is related to the diffusion coefficient for a particle undergoing Brownian motion. | 1 | Crystallography |
Geometric phase analysis is a method of digital signal processing used to determine crystallographic quantities such as d-spacing or strain from high-resolution transmission electron microscope images. The analysis needs to be performed using specialized computer program. | 1 | Crystallography |
In crystallography, atomic packing factor (APF), packing efficiency, or packing fraction is the fraction of volume in a crystal structure that is occupied by constituent particles. It is a dimensionless quantity and always less than unity. In atomic systems, by convention, the APF is determined by assuming that atoms are rigid spheres. The radius of the spheres is taken to be the maximum value such that the atoms do not overlap. For one-component crystals (those that contain only one type of particle), the packing fraction is represented mathematically by
where N is the number of particles in the unit cell, V is the volume of each particle, and V is the volume occupied by the unit cell. It can be proven mathematically that for one-component structures, the most dense arrangement of atoms has an APF of about 0.74 (see Kepler conjecture), obtained by the close-packed structures. For multiple-component structures (such as with interstitial alloys), the APF can exceed 0.74.
The atomic packing factor of a unit cell is relevant to the study of materials science, where it explains many properties of materials. For example, metals with a high atomic packing factor will have a higher "workability" (malleability or ductility), similar to how a road is smoother when the stones are closer together, allowing metal atoms to slide past one another more easily. | 1 | Crystallography |
Aqueous normal-phase chromatography (ANP) is also called hydrophilic interaction liquid chromatography (HILIC). This is a chromatographic technique which encompasses the mobile phase region between reversed-phase chromatography (RP) and organic normal phase chromatography (ONP). HILIC is used to achieve unique selectivity for hydrophilic compounds, showing normal phase elution order, using "reversed-phase solvents", i.e., relatively polar mostly non-aqueous solvents in the mobile phase. Many biological molecules, especially those found in biological fluids, are small polar compounds that do not retain well by reversed phase-HPLC. This has made hydrophilic interaction LC (HILIC) an attractive alternative and useful approach for analysis of polar molecules. Additionally, because HILIC is routinely used with traditional aqueous mixtures with polar organic solvents such as ACN and methanol, it can be easily coupled to MS. | 0 | Chromatography + Titration + pH indicators |
Since the diameter of the probing convergent beam is smaller than in the case of a parallel beam, most of the information in the CBED pattern is obtained from very small regions, which other methods cannot reach. For example, in Selected Area Electron Diffraction (SAED), where a parallel beam illumination is used, the smallest area that can be selected is 0.5 µm at 100 kV, whereas in CBED, it is possible to go to areas smaller than 100 nm. Also, the amount of information that is obtained from a CBED pattern is larger than that from a SAED pattern.
Nonetheless, CBED also has its disadvantages. The focused probe may generate contamination, which can cause localized stresses. But this was more of a problem in the past, and now, with the high vacuum conditions, one should be able to probe a clean region of the specimen in minutes to hours. Another disadvantage is that the convergent beam may heat or damage the chosen region of the specimen.
Since 1939, CBED has been mainly used to study thicker materials. | 1 | Crystallography |
Euhedral crystals have flat faces with sharp angles. The flat faces (also called facets) are oriented in a specific way relative to the underlying atomic arrangement of the crystal: They are planes of relatively low Miller index. This occurs because some surface orientations are more stable than others (lower surface energy). As a crystal grows, new atoms attach easily to the rougher and less stable parts of the surface, but less easily to the flat, stable surfaces. Therefore, the flat surfaces tend to grow larger and smoother, until the whole crystal surface consists of these plane surfaces. (See diagram on right.) | 1 | Crystallography |
As a separation technique, GPC has many advantages. First of all, it has a well-defined separation time due to the fact that there is a final elution volume for all unretained analytes. Additionally, GPC can provide narrow bands, although this aspect of GPC is more difficult for polymer samples that have broad ranges of molecular weights present. Finally, since the analytes do not interact chemically or physically with the column, there is a lower chance for analyte loss to occur. For investigating the properties of polymer samples in particular, GPC can be very advantageous. GPC provides a more convenient method of determining the molecular weights of polymers. In fact most samples can be thoroughly analyzed in an hour or less. Other methods used in the past were fractional extraction and fractional precipitation. As these processes were quite labor-intensive molecular weights and mass distributions typically were not analyzed. Therefore, GPC has allowed for the quick and relatively easy estimation of molecular weights and distribution for polymer samples | 0 | Chromatography + Titration + pH indicators |
In linear elasticity, the stress and strain are related by Hooke's law, i.e.,
or, using Voigt notation,
The condition for material symmetry in linear elastic materials is.
where | 1 | Crystallography |
Informally, a Euclidean plane isometry is any way of transforming the plane without "deforming" it. For example, suppose that the Euclidean plane is represented by a sheet of transparent plastic sitting on a desk. Examples of isometries include:
* Shifting the sheet one inch to the right.
* Rotating the sheet by ten degrees around some marked point (which remains motionless).
* Turning the sheet over to look at it from behind. Notice that if a picture is drawn on one side of the sheet, then after turning the sheet over, we see the mirror image of the picture.
These are examples of translations, rotations, and reflections respectively. There is one further type of isometry, called a glide reflection (see below under classification of Euclidean plane isometries).
However, folding, cutting, or melting the sheet are not considered isometries. Neither are less drastic alterations like bending, stretching, or twisting. | 1 | Crystallography |
A Euclidean graph in three-dimensional space is a pair (V, E), where V is a set of vertices (sometimes called points or nodes) and E is a set of edges (sometimes called bonds or spacers) where each edge joins two vertices. There is a tendency in the polyhedral and chemical literature to refer to geometric graphs as nets (contrast with polyhedral nets), and the nomenclature in the chemical literature differs from that of graph theory. | 1 | Crystallography |
A post–September 11 development, explosive detection systems have become a part of all US airports. These systems run on a host of technologies, many of them based on GC–MS. There are only three manufacturers certified by the FAA to provide these systems, one of which is Thermo Detection (formerly Thermedics), which produces the EGIS, a GC–MS-based line of explosives detectors. The other two manufacturers are Barringer Technologies, now owned by Smith's Detection Systems, and Ion Track Instruments, part of General Electric Infrastructure Security Systems. | 0 | Chromatography + Titration + pH indicators |
An example of back titration, the Volhard method, named after Jacob Volhard, involves the addition of excess silver nitrate to the analyte; the silver chloride is filtered, and the remaining silver nitrate is titrated against ammonium thiocyanate, with ferric ammonium sulfate as an indicator which forms blood-red [[Thiocyanate#Test for iron.28III.29|[Fe(OH)(SCN)]]] at the end point:
: Ag (aq) + SCN (aq) → AgSCN (s) (K = 1.16 × 10)
: Fe(OH)(OH) (aq) + SCN (aq)→ [Fe(OH)(SCN)] + OH | 0 | Chromatography + Titration + pH indicators |
The translational invariance of a crystal lattice is described by a set of unit cell, direct lattice basis vectors (contravariant or polar) called a, b, and c, or equivalently by the lattice parameters, i.e. the magnitudes of the vectors, called a, b and c, and the angles between them, called α (between b and c), β (between c and a), and γ (between a and b). Direct lattice vectors have components measured in distance units, like meters (m) or angstroms (Å).
A lattice vector is indexed by its coordinates in the direct lattice basis system and is generally placed between square brackets []. Thus a direct lattice vector , or , is defined as . Angle brackets ⟨⟩ are used to refer to a symmetrically equivalent class of lattice vectors (i.e. the set of vectors generated by an action of the lattice's symmetry group). In the case of a cubic lattice, for instance, ⟨100⟩ represents [100], [010], [001], [00], [00] and [00] because each of these vectors is symmetrically equivalent under a 90 degree rotation along an axis. A bar over a coordinate is equivalent to a negative sign (e.g., ).
The term "zone axis" more specifically refers to the direction of a direct-space lattice vector. For example, since the [120] and [240] lattice vectors are parallel, their orientations both correspond the ⟨120⟩ zone of the crystal. Just as a set of lattice planes in direct space corresponds to a reciprocal lattice vector in the complementary space of spatial frequencies and momenta, a "zone" is defined as a set of reciprocal lattice planes in frequency space that corresponds to a lattice vector in direct space.
The reciprocal space analog to a zone axis is a "lattice plane normal" or "g-vector direction". Reciprocal lattice vectors (one-form or axial) are Miller-indexed using coordinates in the reciprocal lattice basis instead, generally between round brackets () (similar to square brackets [] for direct lattice vectors). Curly brackets {} (not to be confused with a mathematical set) are used to refer to a symmetrically equivalent class of reciprocal lattice vectors, similar to angle brackets ⟨⟩ for classes of direct lattice vectors.
Here, , , and , where the unit cell volume is ( denotes a dot product and a cross product). Thus a reciprocal lattice vector or has a direction perpendicular to a crystallographic plane and a magnitude equal to the reciprocal of the spacing between those planes, measured in spatial frequency units, e.g. of cycles per angstrom (cycles/Å).
A useful and quite general rule of crystallographic "dual vector spaces in 3D", e.g. reciprocal lattices, is that the condition for a direct lattice vector [uvw] (or zone axis) to be perpendicular to a reciprocal lattice vector (hkl) can be written with a dot product as . This is true even if, as is often the case, the basis vector set used to describe the lattice is not Cartesian. | 1 | Crystallography |
RingGUI allows for an automated processing of ring diffraction images of polycrystalline or powder samples. It can be used to identify the diffraction rings, quantify the interplanar distances and thus characterize or identify the sample material. With known material, it can assist in microscope calibration. The input image is processed as follows:
# beam-stopper detection,
# localization of the ring center,
# quantification of the diffraction profile and estimation of its background intensity,
# identification of the rings in the image (peaks in the profile).
The results can be further processed and visualized in two interactive, functionally interconnected graphical elements:
* Interactive diffraction image – allows the user to improve readability of the diffraction image by removing the beam-stopper, subtracting the background, revealing faint or spotty rings or by crystallographic identification of the depicted rings.
* Diffraction profile – circular average of the image intensities depicts the peaks corresponding to the rings and their match with theoretical values known for given sample material.
Both, the diffraction image as well as diffraction profile can be used to select diffraction rings with a mouse click. The corresponding ring is then highlighted in both graphical representations and details are listed. | 1 | Crystallography |
An amperostat delivers a constant current of about 6—8 mA to the generator electrodes for the titration of the solution, and a digital timer is started. A second pair of silver electrodes are used as a detector to measure the conductance of the solution. The same constant current is known to titrate a given number of moles of a chloride standard solution in time . Titration of the assay solution will result in the generation of insoluble silver chloride until the chloride ions are consumed, after which time an increase in silver ions will be detected at the detector electrodes. This time, , is the titration time of the solution being measured. The concentration of chloride ions in this solution is then calculated as:
Although the absolute quantity of silver ions () required to react with the chloride ions can be determined using Faraday's laws of electrolysis, in practice calibration is required.
Silver ions are generated by oxidation at the anode when an electric potential is applied across the silver electrodes. This is the anodic reaction.
The silver ions enter the solution at a rate proportional to the electrical current. Because the current is constant, the rate of silver ion production is hence proportional to the time of current flow, and silver ions enter the solution at a constant rate from the silver wire anode. These ions react with the chloride ions in the titration reaction, resulting in insoluble silver chloride.
The end point, which occurs when there are no more chloride ions with which silver ions may react, is detected by a pair of silver microelectrodes in the solution, which is connected in series with a microammeter. The increasing concentration of silver ions creates a current between the microelectrodes, activating a switch that shuts off power to the main electrodes and the timer, terminating the measurement. The duration of the titration is the titration time , which is proportional to the amount of silver ions released, and hence to the amount of chloride in the assay solution. | 0 | Chromatography + Titration + pH indicators |
Each of the groups in this section has two cell structure diagrams, which are to be interpreted as follows (it is the shape that is significant, not the colour):
On the right-hand side diagrams, different equivalence classes of symmetry elements are colored (and rotated) differently.
The brown or yellow area indicates a fundamental domain, i.e. the smallest part of the pattern that is repeated.
The diagrams on the right show the cell of the lattice corresponding to the smallest translations; those on the left sometimes show a larger area. | 1 | Crystallography |
In crystallography, the transition temperature is the temperature at which a material changes from one crystal state (allotrope) to another. More formally, it is the temperature at which two crystalline forms of a substance can co-exist in equilibrium. For example, when rhombic sulfur is heated above 95.6 °C, it changes form into monoclinic sulfur; when cooled
below 95.6 °C, it reverts to rhombic sulfur. At 95.6 °C the two forms can co-exist. Another example is tin, which transitions from a cubic crystal below 13.2 °C to a tetragonal crystal above that temperature.
In the case of ferroelectric or ferromagnetic crystals, a transition temperature may be known as the Curie temperature. | 1 | Crystallography |
In its earliest form, liquid chromatography was used to separate the pigments of chlorophyll by a Russian botanist. Decades later, other chemists used the procedure for the study of carotins. Liquid chromatography was then used for the isolation of small molecules and organic compounds like amino acids, and most recently has been used in peptide and DNA research. Monolith columns have been instrumental in advancing the field of biomolecular research.
In recent trade shows and international meetings for HPLC, interest in column monoliths and biomolecular applications has grown steadily, and this correlation is no coincidence. Monoliths have been shown to possess great potential in the “omics” fields- genomics, proteomics, metabolomics, and pharmacogenomics, among others. The reductionist approach to understanding the chemical pathways of the body and reactions to different stimuli, like drugs, are essential to new waves of healthcare like personalized medicine.
Pharmacogenomics studies how responses to pharmaceutical products differ in efficacy and toxicity based on variations in the patients genome; it is a correlation of drug response to gene expression in a patient. Jeremy K. Nicholson of the Imperial College, London, used a postgenomic viewpoint to understand adverse drug reactions and the molecular basis of human disesase. His group studied gut microbial metabolic profiles and were able to see distinct differences in reactions to drug toxicity and metabolism even among various geographical distributions of the same race. Affinity monolith chromatography provides another approach to drug response measurements. David Hage at the University of Nebraska binds ligands to monolithic supports and measures the equilibrium phenomena of binding interactions between drugs and serum proteins. A monolith-based approach at the University of Bologna, Italy, is currently in use for high-speed screening of drug candidates in the treatment of Alzheimers. In 2003, Regnier and Liu of Purdue University described a multi-dimensional LC procedure for identifying single nucleotide polymorphisms (SNPs) in proteins. SNPs are alterations in the genetic code that can sometimes cause changes in protein conformation, as is the case with sickle cell anemia. Monoliths are particularly useful in these kinds of separations because of their superior mass transport capabilities, low backpressures coupled with faster flow rates, and relative ease of modification of the support surface.
Bioseparations on a production scale are enhanced by monolith column technologies as well. The fast separations and high resolving power of monoliths for large molecules means that real-time analysis on production fermentors is possible. Fermentation is well known for its use in making alcoholic beverages, but is also an essential step in the production of vaccines for rabies and other viruses. Real-time, on-line analysis is critical for monitoring of production conditions, and adjustments can be made if necessary. Boehringer Ingelheim Austria has validated a method with cGMP (commercial good manufacturing practices) for production of pharmaceutical-grade DNA plasmids. They are able to process 200L of fermentation broth on an 800mL monolith. At BIA Separations, processing time of the tomato mosaic virus decreased considerably from the standard five days of manually intensive work to equivalent purity and better recovery in only two hours with a monolith column. Other viruses have been purified on monoliths as well.
Another area of interest for HPLC is forensics. GC-MS (Gas Chromatography-Mass Spectroscopy) is generally considered the gold standard for forensic analysis. It is used in conjunction with online databases for rapid analysis of compounds in tests for blood alcohol, cause of death, street drugs, and food analysis, especially in poisoning cases. Analysis of buprenorphine, a heroin substitute, demonstrated the potential utility of multidimensional LC as a low-level detection method. HPLC methods can measure this compound at 40 ng/mL, compared to GC-MS at 0.5 ng/mL, but LC-MS-MS can detect buprenorphine at levels as low as 0.02 ng/mL. The sensitivity of multidimensional LC is therefore 2000 times greater than that of conventional HPLC. | 0 | Chromatography + Titration + pH indicators |
The following is an example of the algorithm for determining the axis/angle representation of misorientation between two texture components given as Euler angles:
:Copper [90,35,45]
:S3 [59,37,63]
The first step is converting the Euler angle representation, to an orientation matrix by:
where and represent and of the respective Euler component. This yields the following orientation matrices:
The misorientation is then:
The axis/angle description (with the axis as a unit vector) is related to the misorientation matrix by:
(There are errors in the similar formulae for the components of r given in the book by Randle and Engler (see refs.), which will be corrected in the next edition of their book. The above are the correct versions, note a different form for these equations has to be used if Θ = 180 degrees.)
For the copper—S misorientation given by , the axis/angle description is 19.5° about [0.689,0.623,0.369], which is only 2.3° from <221>. This result is only one of the 1152 symmetrically related possibilities but does specify the misorientation. This can be verified by considering all possible combinations of orientation symmetry (including switching symmetry). | 1 | Crystallography |
The centrifugal partition chromatograph instrument is constituted with a unique rotor which contains the column. This rotor rotates on its central axis (while HSCCC column rotates on its planetary axis and simultaneously rotates eccentrically about another solar axis). With less vibrations and noise, the CPC offers a typical rotation speed range from 500 to 2000 rpm. Contrary to hydrodynamic CCC, the rotation speed is not directly proportional to the retention volume ratio of the stationary phase. Like DCCC, CPC can be operated in either descending or ascending mode, where the direction is relative to the force generated by the rotor rather than gravity. A redesigned CPC column with larger chambers and channels has been named centrifugal partition extraction (CPE). In the CPE design, faster flow rates and increased column loading can be achieved. | 0 | Chromatography + Titration + pH indicators |
Because gas molecules diffract electrons and affect the quality of the electron gun, RHEED experiments are performed under vacuum. The RHEED system must operate at a pressure low enough to prevent significant scattering of the electron beams by gas molecules in the chamber. At electron energies of 10keV, a chamber pressure of 10 mbar or lower is necessary to prevent significant scattering of electrons by the background gas. In practice, RHEED systems are operated under ultra high vacuums. The chamber pressure is minimized as much as possible in order to optimize the process. The vacuum conditions limit the types of materials and processes that can be monitored in situ with RHEED. | 1 | Crystallography |